They conceptualized them along a spectrum from most tractable — that is to say, workable and manageable — to least tractable.
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The third criterion was that it has to be tractable.
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All are tractable, potentially significantly ameliorated by our collective impact.
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So, you make a table: like tractable, neglected, and important. Important?
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It's that it's not tractable — we still don't know what works.
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This is perhaps a more tractable problem, but still must be considered.
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That's why the researchers call it tractable; it doesn't require international coordination.
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Tractable problems are ones where we can actually make progress right now.
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For technical reasons, this problem is more tractable than the original Set problem.
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With more money and more research, the remaining technical challenges might prove tractable.
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For example, big data is rapidly getting more tractable, and therefore more valuable.
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Meanwhile, Ann Coulter tweeted: Hispanic workers are so much more tractable than Americans!
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That makes things more computationally tractable, but it's a bit of a fudge.
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That will get us most of the way there, and it's a tractable task.
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Google started with the premise that computer science, at scale, makes the intractable tractable.
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This approach may have performance trade-offs, but would make model management more tractable.
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The magazine love the KTM's lightweight, compact dimensions, tractable power delivery, and solid performance.
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There's no tractable way for the government to take all these considerations into account.
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Some charitable causes are a lot more tractable, and a lot more impactful, than others.
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" When the intermediary proved less tractable than he desired, Mr Stone called him "a rat.
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And so in that sense, this is way more tractable than preparing for alien risk.
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In philanthropy, like in business, there are some opportunities that are particularly important, tractable, and neglected.
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But I think I would argue much less tractable than the AI risk is at this stage.
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Part of the reason for the excitement is that epigenes may be vastly more tractable than genes.
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" Ramirez is confident that "to the extent that we can do this in animals, it's actually tractable.
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Maybe increasing clearance rates for serial killers is more tractable, an easier lift than bringing those numbers down.
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" When the intermediary proved less tractable than Mr Stone would have liked, Mr Stone called him "a rat.
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It's tractable in a way that visual systems are not for studying general computational challenges, some scientists argue.
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In this case, the savings of American lives and the bandwidth our leaders can devote to tractable issues.
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He further claims that his company is the only one with a tractable roadmap capable of achieving this.
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Also, the Sound's relatively calm waters make the project more tractable here than, let's say, on the outer coast.
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For Shelby, ghettos are something more troubling and less tractable: symptoms of the "systemic injustice" of the United States.
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"Sorry, we've gone from production hell to delivery logistics hell, but this problem is far more tractable," Musk said.
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The non-neglectedness of K-12 education in America itself makes the issue less tractable, for the reasons described above.
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The pine is nice because it has a tractable shape—it's basically just a long skinny cylinder (ignoring the branches).
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But a third concern—that AI will be used principally to the benefit of China's government—is a less tractable problem.
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But if that thing could be identified, and proved tractable to treatment, then dialysis might become a thing of the past.
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A quantum machine could therefore make the classically intractable problem of simulating large quantum-mechanical systems tractable, or so it appeared.
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Cycle World praised the Yamaha for its powerful and tractable 450 CC engine, its suspension tuning, and its go-anywhere ability.
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" Commenting on the funding in a statement, Lonne Jaffe, MD at Insight Partners and also Tractable board director, said: "Tractable has achieved tremendous scale in the past year with a customer base across nine countries, a differentiated data asset, and the expansion of their team to over 100 employees across London, New York and now Tokyo.
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That will bring environmental problems, for aviation is the least tractable of industries to decarbonisation in order to reduce greenhouse-gas emissions.
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When we think of the American moment for its beginning-middle-end, it starts to feel like something digestible, perhaps even tractable.
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Mr Obama has sometimes entertained the hope that the deal might strengthen moderates in Tehran and make Iran a more tractable partner.
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Soften any of these restraints even a little and the cost target that storage must meet rises to something far more tractable.
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But after Tuesday's elections, for policymakers interested in crafting a climate plan, this guide at least makes it seem a little more tractable.
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Road safety: Traffic deaths are a major global problem with scientifically-tractable solutions, and Bloomberg Philanthropies has donated $259 million over 12 years.
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Climate change increases the need for resilience, for communities of tractable size that are at least partially self-sufficient in food, water, and energy.
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If you keep chaining systems together, sooner or later you end up with a model that is "too large to be tractable," she says.
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In recent years, firms have learned that the ITC can be far more tractable in issuing these orders than courts in issuing injunctive relief.
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If that doesn't happen, he believes it won't just be Tractable that will suffer, but the continued belief and investment in AI as a whole.
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That makes the influence of past rain on future legislation a tractable subject for quantitative social science research, which is how we got this paper.
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A different kind of economist, committed to the algorithms more than the schools, might have dropped education for problems tractable to similar approaches in other fields.
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But critically, Ryan's main ideas never got enacted largely because they did not make sense; there turned out to be no tractable way of accomplishing them.
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You can't really apprehend and remove 11 million people in a manner consistent with due process in any kind of logistically tractable or financially feasible way.
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The portfolio includes deep tech firms (Magic Pony Technology, Adbrain, and Tractable), marketplaces (Hubble, ClickMechanic), consumer products (Prizeo, Code Kingdoms), and hardware (Blaze, Pi-Top, Speakset).
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The PS103 show, curated with abundant wall texts by Peter Eleey and Ruba Katrib, sputters with attempts to seize on tractable aspects of a daunting complexity.
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Visionary thought leaders like Gevers, who took Silicon Valley's monopoly on startup financing to be a more tractable menace than African sheriffs, seemed by comparison exceptionally reasonable.
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In making the case for these non-gun control ideas, Doleac argues that the fixation on gun control might be distracting advocates from presumably more tractable alternatives.
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The Tesla chief said that the delivery problem was "far more tractable" than the production issues, but that the company was "making rapid progress" on solving it.
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Hair pigmentation is such an accessible and tractable system to start with — and besides, we were genuinely curious to see if stress indeed leads to hair graying.
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"Currently operating in nine countries, Tractable is expanding into new markets using its data driven approach to ensure that claims can be settled faster and livelihoods restored."
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For a cause to be tractable, funders don't just have to know of cost-effective interventions that can help; they have to know ways to get those interventions adopted.
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If an approach turns out to have some insurmountable barriers, then the sooner we know about that, the sooner we can transition our focus to other, more tractable approaches.
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Having acknowledged that politics will dominate this year, allow me to turn to the somewhat more tractable field of the state of the economy and its short-term prospects.
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How they break your life down into such tidy realms, making each seem tractable, because discrete, in a way they never are beyond the white noise of the waiting room.
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Dutton has to have four kids, for example, otherwise, you'd never understand their four different ways of seeing the Western world and how they contrast with his older, less tractable one.
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Decamping her husband (a delightfully tractable Nicholas Rowe) and daughter from north London, she moves to her crumbling ancestral pile, dreaming of renovating its once-envied English garden to its former splendour.
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Perhaps we are drawn to this futile quest because economic problems seem more tractable — more easily dealt with through the levers of government policy — while cultural issues seem more resistant to change.
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"We're incredibly excited to partner with the Tractable team to help them move even faster on bringing the next wave of technological innovation to accident and disaster recovery across the world," she added.
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"Sorry, we've gone from production hell to delivery logistics hell, but this problem is far more tractable," Musk said in a tweet here on Sunday, in response to a customer complaint on delivery delay.
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Alex Dalyac, chief executive and co-founder of a computer vision start-up called Tractable, acknowledged that machine learning will soon produce fake audio and video that humans cannot distinguish from the real thing.
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This has been a slowly and painfully learned lesson in global development, where cheap, tractable, and impactful interventions — like giving everyone bednets — are getting more attention as givers sour on flashy interventions that don't work.
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The first 3 of 5 UK's EPSRC Principles of Robotics are meant to update those laws in a way that is not only computationally tractable, but would allow the most stability in our justice system.
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At the tractable end of the spectrum, they placed a politics of pure economic materialism: They include conflicts over allocation of resources — disputes between producers and buyers, workers and employers, tenants and owners, and so on.
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Open Philanthropy, which is the largest philanthropic organization that supports existential risk reduction, have this system where they say that the cause has to be important, it has to be tractable, and it has to be neglected.
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Wolf articulated the feeling that roiled in my belly alongside an unfulfilling banquet of fat-free foods: "Dieting is the most potent political sedative in women's history; a quietly mad population is a tractable one," she wrote.
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"There is an ancient analogy between integers and polynomials, which allows you to transform problems about integers, which are potentially very difficult, into problems about polynomials, which are also potentially difficult, but possibly more tractable," Shusterman said.
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And the film gets plenty of pathos out of Andy's relationship with Rosie, a generally sweet and tractable kid who's too young to understand any of what's going on, but not too young to respond warmly to displays of affection.
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In particular, it reveals the critical part played by a British agent, Norman Darbyshire, who was in charge of handing out the money that precipitated the violent ouster of the country's democratically elected leader in favor of the more tractable Shah.
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Why it's hot in 2020: "AI is the biggest revolution affecting the insurance industry and London-based Tractable uses AI technology to assess accident and disaster recovery in real-time, leading to much faster claims settlements for customers," Maar said.
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Whereas in the Grand Central model, the TSO will have to single-handedly keep track of all the blooming and buzzing DERs beneath it — which, let's be serious, will eventually overwhelm it — in the LDO model, each layer is its own, tractable domain.
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The fact that they rely on extremely rare materials and are so complex and expensive to build makes it far more tractable to keep them from being used than it would be if the materials for them had happened to be abundant.
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He also exhorted black and white Southerners to "cast down your buckets where you are" in the region—an appeal that offered white employers tractable, low-wage black labor and consigned blacks to the most humble opportunities that racial subordination relegated to them.
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The reference to acqui-hire or IP exit takes on more meaning when you consider that Tractable was in the same cohort at Entrepreneur First as Magic Pony Technology, the AI startup acquired by Twitter for up to $150 million for its image enhancing technology.
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To ensure that Tractable can continue its mission of applying AI to accident and disaster recovery — and presumably not sell too early — the startup has closed $20 million in Series B investment in a round led by U.S. venture capital firm Insight Venture Partners.
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Using cheater squares to the left of 25 and above 58, I was able to include nine uniclue pairs, which seemed like a respectable number and which was more tractable than an earlier grid that had 11 pairs, eight of which overlapped with other pairs.
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" But at the same time, she keeps emphasizing uncomfortable details, like the intimidating size of the men fighting over her, or the feeling that her "fat face with a chunky body" made her tractable, even though she knew drinking was "the most idiotic choice I could make.
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London-based insurtech AI startup Tractable, which is applying artificial intelligence to speed up accident and disaster recovery by using computer vision to perform visual damage appraisal instead of getting humans to do the job, has closed a $25 million Series C, led by Canadian investment fund Georgian Partners.
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Effective altruists tend to think the best charities will focus on an issue that meets three criteria: It's important (it affects many lives in a massive way), it's tractable (extra resources will do a lot to fix it), and it's neglected (not that many people are devoted to this issue yet).
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Congressional leaders hoped that Mr. Trump's need for political cover might make him tractable, and that unified government would enable them to finally set America on the path to broad-based prosperity through tax cuts, entitlement reform and the replacement of Obamacare with something no one had bothered to work out.
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"Happy to spend 10 minutes on our vision and the journey we're on, but then, really, 15 minutes on what we've got today, what it is we've achieved, what it is our AI does," says Tractable co-founder and CEO Alexandre Dalyac when I video called him a couple of weeks ago.
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But concentrated control over roadways could make the politics of road fees more tractable: as the winning firms' bargaining power rose, as fewer middle-income households owned their own cars, and especially if, as Daniel Rauch and David Schleicher of Yale University suggest, AV firms join with governments to provide public transport and mobility services.
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Tractable is applying AI to accident and disaster appraisal Two years on the startup isn't breaking out any hard metrics — but says its product is used by a number of multinational insurance firms, including Ageas in the UK, France's Covéa, Japan's Tokio Marine and Polish insurer Talanx-Warta — to analyse vehicle damage "effectively and efficiently".
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The computer scientist Alan Turing noted that the question of whether a machine can think is incredibly difficult to determine, not least because of the lack of a clear definition of "thinking"; he proposed investigating instead the more tractable question of whether a machine can convince a human interlocutor that it's human — the so-called Turing test.
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Although the problems of listing maximal cliques or finding maximum cliques are unlikely to be fixed-parameter tractable with the parameter , they may be fixed-parameter tractable for other parameters of instance complexity. For instance, both problems are known to be fixed-parameter tractable when parametrized by the degeneracy of the input graph..
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Boundaries between tractable and intractable cases have been an active area of research.
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To make the method tractable, we approximate this distribution by six equiprobable rate categories.
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Model-counting is tractable (solvable in polynomial time) for (ordered) BDDs and for d-DNNFs.
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The latter was obtained by introducing an equivalent but tractable form of the Heston characteristic function.
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An officer was appointed to locate suitable outside boarding for those that were more tractable cases.
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German equipment destroyed near Mont Ormel Due to the successive offensives of early August, exact Canadian casualties for Operation Tractable are not known. Losses during Totalise and Tractable are put at 5,500 men. Jarymowycz, p. 203 German casualties during Operation Tractable are also uncertain; approximate figures can be found for casualties within the Falaise Pocket but not for the Canadian operations during Tractable. After the Falaise Pocket, the German 7th Army was severely depleted, having lost from 50,000–200,000 men, over 200 tanks, 1,000 guns and 5,000 other vehicles. In the fighting around the Germans lost 2,000 men killed, 5,000 taken prisoner, 55 tanks, 152 other armoured vehicles and 44 guns.
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He is also known for his computationally tractable solutions of problems associated with the predictions of radiation fields.
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Eulerian path strategies are computationally more tractable because they try to find a Eulerian path through a deBruijn graph.
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Allied gains during the Canadian offensives of Operations Totalize and Tractable Operation Tractable incorporated lessons learned from Operation Totalize, notably the effectiveness of mechanized infantry units and tactical bombing raids by heavy bombers.Bercuson, p. 231 Unlike the previous operation, Tractable was launched in daylight. An initial bombing raid was to weaken German defences and was to be followed by an advance by the Canadian 4th Armoured Division on the western flank of Hill 195, while the Canadian 3rd Infantry Division attacked on the eastern flank with the Canadian 2nd Armoured Brigade in support.
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In contrast, the Whiley language was designed from scratch in an effort to avoid common pitfalls and make verification more tractable.
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Unique design considerations for motorcycles include tractable power delivery; and packaging for heat removal, space conservation, and desired center of gravity.
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This has led to the development of approximation algorithms and fixed-parameter tractable algorithms to improve the theoretical calculation of such problems.
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When this is possible, it results in a fixed- parameter tractable algorithm whose running time is the sum of the (polynomial time) kernelization step and the (non-polynomial but bounded by the parameter) time to solve the kernel. Indeed, every problem that can be solved by a fixed- parameter tractable algorithm can be solved by a kernelization algorithm of this type.
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The first general tractable 3D solutions were presented in 2002 by Nirenstein et al. and Bittner.Jiri Bittner. Hierarchical Techniques for Visibility Computations, PhD Dissertation.
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Wright and Ricardo Lagos (2005) attempt to overcome this shortcoming by proposing a more general, yet still tractable, framework for the analysis of monetary policy.
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Tractable subcases of the general constraint satisfaction problems can be obtained by placing suitable restrictions on the problems. Various kinds of restrictions have been considered.
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Using color-coding, the dependence on path length can be reduced to singly exponential.... A similar dynamic programming technique shows that the longest path problem is also fixed-parameter tractable when parameterized by the treewidth of the graph. For graphs of bounded clique-width, the longest path can also be solved by a polynomial time dynamic programming algorithm. However, the exponent of the polynomial depends on the clique-width of the graph, so this algorithms is not fixed-parameter tractable. The longest path problem, parameterized by clique-width, is hard for the parameterized complexity class W[1], showing that a fixed-parameter tractable algorithm is unlikely to exist..
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However, male cattle used for hard labor are often castrated in order to make them more tractable, as well as providing better quality meat when finally consumed.
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Trainer Bill Winfrey said the colt was "a regular Jekyll and Hyde" – ordinarily quiet and tractable but with a playful streak that could make him a handful.
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Thus, according to their conjecture, clique has no fixed-parameter tractable algorithm. Moreover, this result provides the basis for proofs of W[1]-hardness of many other problems, and thus serves as an analogue of the Cook–Levin theorem for parameterized complexity. showed that finding -vertex cliques cannot be done in time unless the exponential time hypothesis fails. Again, this provides evidence that no fixed-parameter tractable algorithm is possible.
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A sufficient condition of tractability is that a non-uniform problem is tractable if the set of its unsatisfiable instances can be expressed by a Boolean Datalog query. In other words, if the set of sets of literals that represent unsatisfiable instances of the non-uniform problem is also the set of sets of literals that satisfy a Boolean Datalog query, then the non-uniform problem is tractable.
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The engine was very tractable and had excellent mid-range. 250/400 use a new larger magneto rotor/flywheel. Superb quick-change rear wheel system. 6 clutch plates vs.
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The result is also stronger, since it holds for an unknown number of applicants and since the model based on an arrival time distribution F is more tractable for applications.
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Ty5 is a relative of the Retroviridae family of retroviruses, which includes the human pathogen HIV. Ty5 is a tractable system in which to study the biology of retrovirus integration.
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Some tractable members of the Five Hundred, rounded up afterwards, served to give these measures the confirmation of their House. Thus the Directory and the Councils came to an end.
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Counting solutions is intractable (#P-complete) in many special cases for which satisfiability is tractable (in P), as well as when satisfiability is intractable (NP-complete). This includes the following.
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The graphs with any finite bound on the Hadwiger number are sparse, and have small chromatic number. Determining the Hadwiger number of a graph is NP-hard but fixed-parameter tractable.
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Determining if a general graph is k edge deletions away from a trivially perfect graph is NP- complete, fixed-parameter tractable and can be solved in O(2.45k(m + n)) time.
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The main occupation of the people is agriculture. Father Juan de Medina noted in 1630 that the natives are ‘the humblest and most tractable known and lived in nest and large settlements'.
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It is notable that Gregory Cromwell was under the age of majority of twenty-one. His election is to be seen as one move in Thomas Cromwell's campaign to ensure a "tractable" Parliament.
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Tusell 2002, p. 103, Blinkhorn 2008, p. 281 Franco himself kept meeting with right-wing politicians, usually ignoring the intransigent ones and speaking only to these deemed tractable. No political plans were discussed.
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In 1990, while working at Stanford University on large bioinformatic applications, Cooper proved that exact inference in Bayesian networks is NP-hard. This result prompted research on approximation algorithms with the aim of developing a tractable approximation to probabilistic inference. In 1993, Dagum and Luby proved two surprising results on the complexity of approximation of probabilistic inference in Bayesian networks. First, they proved that no tractable deterministic algorithm can approximate probabilistic inference to within an absolute error ɛ < 1/2.
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For analytically tractable functions, the indices above may be calculated analytically by evaluating the integrals in the decomposition. However, in the vast majority of cases they are estimated – this is usually done by the Monte Carlo method.
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Wilberforce is a man "of many excellent and admirable qualifications": he is eloquent, "amiable, charitable, conscientious, pious, loyal, [and] humane". But he is also "tractable to power" and "accessible to popularity".Hazlitt 1930, vol. 11, p. 147.
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The white vertex sets are maximal nonblockers In graph theory, a nonblocker is a subset of vertices in an undirected graph, all of which are adjacent to vertices outside of the subset. Equivalently, a nonblocker is the complement of a dominating set. The computational problem of finding the largest nonblocker in a graph was formulated by , who observed that it belongs to MaxSNP. Although computing a dominating set is not fixed-parameter tractable under standard assumptions, the complementary problem of finding a nonblocker of a given size is fixed-parameter tractable.
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Because edge coloring is NP-complete even for three colors, it is unlikely to be fixed parameter tractable when parametrized by the number of colors. However, it is tractable for other parameters. In particular, showed that for graphs of treewidth , an optimal edge coloring can be computed in time , a bound that depends superexponentially on but only linearly on the number of vertices in the graph. formulate the edge coloring problem as an integer program and describe their experience using an integer programming solver to edge color graphs.
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Bounding the width of a decomposition method by a constant creates a structural restriction, that is, it limits the possible scopes of constraints, but not their relations. The complementary way for obtaining tractable subclasses of constraint satisfaction is by placing restriction over the relations of constraints; these are called relational restriction, and the set of allowed relations is called constraint language. If solving problems having a decomposition width bounded by a constant is in P, the decomposition leads to a tractable structural restriction. As explained above, tractability requires that two conditions are met.
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120 Just as the class P can be thought of as the tractable problems (Cobham's thesis), so NC can be thought of as the problems that can be efficiently solved on a parallel computer.Arora & Barak (2009) p.118 NC is a subset of P because polylogarithmic parallel computations can be simulated by polynomial-time sequential ones. It is unknown whether NC = P, but most researchers suspect this to be false, meaning that there are probably some tractable problems that are "inherently sequential" and cannot significantly be sped up by using parallelism.
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As with any type of reduction, a holographic reduction does not, by itself, yield a polynomial time algorithm. In order to get a polynomial time algorithm, the problem being reduced to must also have a polynomial time algorithm. Valiant's original application of holographic algorithms used a holographic reduction to a problem where every constraint is realizable by matchgates, which he had just proved is tractable by a further reduction to counting the number of perfect matchings in a planar graph. The latter problem is tractable by the FKT algorithm, which dates to the 1960s.
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As an example, if the domain is binary and all constraints are binary, establishing satisfiability is a polynomial-time problem because this problem is equivalent to 2-SAT, which is tractable. Research has shown a number of tractable subcases. Some of these classes are based on restricting the allowed domains or relations, some on restricting the way constraints are placed over variables, and some on both kinds of restrictions. One line of research used a correspondence between constraint satisfaction problem and the problem of establishing the existence of a homomorphism between two relational structures.
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This structure theory has led to new advances in polyhedral combinatorics and new bounds on the chromatic number of claw-free graphs, as well as to new fixed- parameter-tractable algorithms for dominating sets in claw-free graphs.
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Even though the hinge-loss is not differentiable, it can also give rise to a tractable variant of the 0/1- loss based learning problem, since the hinge-loss allows it to recast to the equivalent constrained optimization problem.
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Antwerp: ICALP, 1984 Boundedness, deadlocks, and unspecified reception state are all decidable in polynomial time (which means that a particular problem can be solved in tractable, not infinite, amount of time) since the decision problems regarding them are nondeterministic logspace complete.
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As the laws of physics can be written in any coordinate system, it is convenient to choose one that simplifies the geodesic equations. Mathematically, this means a coordinate chart is chosen in which the geodesic equations have a particularly tractable form.
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The bacterial genus Legionella includes the species that causes legionnaire's disease in humans. D. discoideum is also a host for Legionella and is a suitable model for studying the infection process.Bruhn H. 2008. Dictyostelium, a tractable model host organism for Legionella.
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The coefficient of variation is the square root of the variance of the incomes divided by the mean income. It has the advantages of being mathematically tractable and its square is subgroup decomposable, but it is not bounded from above.
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1995: "The Dynamic Database". In: Machine Tractable Dictionaries, (ed.) Cheng- ming Guo, Ablex Publishing Corporation, Norwood, NJ. 131-143. 1995: (with Charles J. Fillmore and Ulrich Heid) "Lexicographical Relevance in Corpus Evidence", Deliverable D-IX-2 of DELIS Project (LRE 61.034).
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A chapter of Pineau's Masters thesis, Point-based value iteration: An anytime algorithm for POMDPs, has been published and cited almost 1,000 times. Her doctoral thesis, Tractable Planning Under Uncertainty: Exploiting Structure, was supervised by Sebastian Thrun and Geoff Gordon.
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Because the exponent of depends on , this algorithm is not fixed-parameter tractable. Although it can be improved by fast matrix multiplication the running time still has an exponent that is linear in Thus, although the running time of known algorithms for the clique problem is polynomial for any fixed , these algorithms do not suffice for fixed-parameter tractability. defined a hierarchy of parametrized problems, the W hierarchy, that they conjectured did not have fixed-parameter tractable algorithms. They proved that independent set (or, equivalently, clique) is hard for the first level of this hierarchy, W[1].
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Adding scalar quarks (squarks) and fermionic gluons (gluinos) to the theory makes it more tractable, but the thermodynamics of quark matter depends crucially on the fact that only fermions can carry quark number, and on the number of degrees of freedom in general.
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Allied and German positions around the Falaise–Argentan area in the aftermath of Operation Tractable, 17 August 1944. The German 7th Army and elements of 5th Panzer Army face encirclement. On 25 July 1944, Lieutenant General Omar Bradley launched Operation Cobra.Wilmot, pp.
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He argued that: > His [Keynes's] followers understandably decided to skip the problematical > dynamic analysis of Chapter 19 and focus on the relatively tractable static > IS-LM model.Peter Howitt, English draft of entry on Leijonhufvud's book for > the Darroz Dictionnaire des grandes oeuvres économiques.
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The concept of a boundary layer is important in many problems in aerodynamics. The viscosity and fluid friction in the air is approximated as being significant only in this thin layer. This assumption makes the description of such aerodynamics much more tractable mathematically.
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Although the finite difference approach is mathematically sophisticated, it is particularly useful where changes are assumed over time in model inputs – for example dividend yield, risk-free rate, or volatility, or some combination of these – that are not tractable in closed form.
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In the area of the theory of Horn functions, proved that all "prime implicates" of a Horn CNF can be generated efficiently, extended Horn logic to q-Horn and showed that this extension forms in some sense the boundary between tractable and intractable logic.
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Closest string is a special case of the more general closest substring problem, which is strictly more difficult. While closest string turns out to be fixed- parameter tractable in a number of ways, closest substring is W[1]-hard with regard to these parameters.
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A similar restriction can be placed on the first structure; for any fixed first structure, the homomorphism problem is tractable. A uniform constraint satisfaction problem is an arbitrary restriction to the sets of structures for the first and second structure of the homomorphism problem.
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It may also be solved in polynomial time for graphs of bounded cyclomatic number , but this algorithm is again not fixed-parameter tractable (for the parameter "cyclomatic number") because the exponent in the polynomial depends on the cyclomatic number. There exist fixed-parameter tractable algorithms to solve the metric dimension problem for the parameters "vertex cover" , "max leaf number" and "modular width" . Graphs with bounded cyclomatic number, vertex cover number or max leaf number all have bounded treewidth, however it is an open problem to determine the complexity of the metric dimension problem even on graphs of treewidth 2, that is, series-parallel graphs .
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The class P, typically taken to consist of all the "tractable" problems for a sequential computer, contains the class NC, which consists of those problems which can be efficiently solved on a parallel computer. This is because parallel computers can be simulated on a sequential machine. It is not known whether NC = P. In other words, it is not known whether there are any tractable problems that are inherently sequential. Just as it is widely suspected that P does not equal NP, so it is widely suspected that NC does not equal P. Similarly, the class L contains all problems that can be solved by a sequential computer in logarithmic space.
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Klebanov and Maldacena 2009 Much of the usefulness of the duality results from the fact that it is a strong-weak duality: when the fields of the quantum field theory are strongly interacting, the ones in the gravitational theory are weakly interacting and thus more mathematically tractable. This fact has been used to study many aspects of nuclear and condensed matter physics by translating problems in those subjects into more mathematically tractable problems in string theory. The AdS/CFT correspondence was first proposed by Juan Maldacena in late 1997. Important aspects of the correspondence were elaborated in articles by Steven Gubser, Igor Klebanov, and Alexander Polyakov, and by Edward Witten.
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Klebanov and Maldacena 2009 Much of the usefulness of the duality results from the fact that it is a strong-weak duality: when the fields of the quantum field theory are strongly interacting, the ones in the gravitational theory are weakly interacting and thus more mathematically tractable. This fact has been used to study many aspects of nuclear and condensed matter physics by translating problems in those subjects into more mathematically tractable problems in string theory. The AdS/CFT correspondence was first proposed by Juan Maldacena in late 1997. Important aspects of the correspondence were elaborated in articles by Steven Gubser, Igor Klebanov, and Alexander Markovich Polyakov, and by Edward Witten.
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As part of the 4th Armoured Division, the 10th Brigade did not arrive in Normandy until the end of July 1944. It was present for Operation Totalize, Operation Tractable, and the Battle of Falaise. After reaching the River Seine, they advanced along the French coast to Belgium.
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Fixing a maximal allowed width is a way for identifying a subclass of constraint satisfaction problems. Solving problems in this class is polynomial for most decompositions; if this holds for a decomposition, the class of fixed-width problems form a tractable subclass of constraint satisfaction problems.
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McGilvray, p. 54 Polish casualties for Operation Tractable (until 22 August) are 1,441 men, of whom 325 were killed (including 21 officers), 1,002 were wounded (35 officers) and 114 missing, which includes 263 men lost before the Chambois and Ormel actions from 14 to 18 August.
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All problems in FPTAS are fixed-parameter tractable with respect to the standard parameterization. Both the knapsack problem and bin packing problem admit an FPTAS. Any strongly NP-hard optimization problem with a polynomially bounded objective function cannot have an FPTAS unless P=NP. However, the converse fails: e.g.
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More subtly, dimension 5 is the cut-off because the middle dimension has codimension more than 2: when the codimension is 2, one encounters knot theory, but when the codimension is more than 2, embedding theory is tractable, via the calculus of functors. This is discussed further below.
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Cawthorne, p. 126 On 14 August, Canadian forces launched Operation Tractable, in conjunction with American movements northwards to Chambois. On 19 August, a brigade of the Polish 1st Armoured Division linked up with forces of the 90th U.S. Infantry Division, sealing off some 50,000 German troops in the pocket.
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Allied and German positions around the Falaise–Argentan area in the aftermath of Operation Tractable, 17 August 1944. The German 7th Army and elements of 5th Panzer Army face encirclement. Following the success of Operation Totalize south of Caen on August 8 and 9, General Harry Crerar, commander of the First Canadian Army, pushed south. Operation Tractable was launched to break through the German lines and capture the tactically important towns of Falaise and then the smaller towns of Trun and Chambois and to encircle large German formations. On August 18, 1944, Canadian forces captured Trun, while General Stanisław Maczek's Polish 1st Armoured Division headed towards Chambois to encircle 110,000 Germans in the Falaise pocket.
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Azotobacter vinelandii is Gram-negative diazotroph that can fix nitrogen while grown aerobically. It is a genetically tractable system that is used to study nitrogen fixation. These bacteria are easily cultured and grown. A. vinelandii is a free-living N2 fixer known to produce many phytohormones and vitamins in soils.
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The model is built on three main concepts. Features: Represents physical objects in AR scene; Virtual Assets: Represents virtual objects in Augmented Reality scene; and Anchor: Define the spatial relationship between a physical and virtual object in AR scene. The Anchors are four different types—Geometries, Tractable, Relative To, and Screen Anchor.
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The biclique partition problem takes as input an arbitrary undirected graph, and asks for a partition of its edges into a minimum number of complete bipartite graphs. It is NP-hard, but fixed-parameter tractable. The best approximation algorithm known for the problem has an approximation ratio of O(n/\log n).
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Junyent remained tractable and conciliatory; in June 1923, when the ayuntamiento was locked in internal crisis, he offered to resign his tenencia de alcaldía.La Correspondencia de España 11.06.23, available here He also intervened in favor of Traditionalist trade-unionists from Sindicatos Libres, at times in trouble with the forces of order.El Sol 14.04.
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Furthermore, the vertex cover problem is fixed-parameter tractable and a central problem in parameterized complexity theory. The minimum vertex cover problem can be formulated as a half-integral linear program whose dual linear program is the maximum matching problem. Vertex cover problems have been generalized to hypergraphs, see Vertex cover in hypergraphs.
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Totalise at 51st HD website.Totalise accounts at 51st HD website. The Canadians renewed the advance to Falaise on 14 August in Operation Tractable, with 51st (H) Division attacking towards the Laison Valley on the left flank. By 21 August the Falaise Pocket had been closed and the division was advancing eastwards towards Lisieux.
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It remains open whether the exact clique-width, or a tighter approximation to it, can be calculated in fixed-parameter tractable time, whether it can be calculated in polynomial time for every fixed bound on the clique-width, or even whether the graphs of clique-width four can be recognized in polynomial time.
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A Swedish Warmblood on a cross country course. The Swedish Warmblood is used as a riding horse, a job it is suitable for because of its easy, straight paces. It is also handsome, sound, tractable, and definitely versatile. Swedish Warmbloods are commonly used as dressage horses, jumpers, and in three-day event.
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The modulus 7 is just the third Mersenne number and Cai and Lu showed that these types of problems with parameter k can be solved in polynomial time exactly when the modulus is the kth Mersenne number by using holographic reductions to matchgates and the Chinese remainder theorem. Around the same time, Jin-Yi Cai, Pinyan Lu and Mingji Xia gave the first holographic algorithm that did not reduce to a problem that is tractable by matchgates. Instead, they reduced to a problem that is tractable by Fibonacci gates, which are symmetric constraints whose truth tables satisfy a recurrence relation similar to one that defines the Fibonacci numbers. They also used holographic reductions to prove that certain counting problems are #P-hard.
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Parameterized complexity is the complexity-theoretic study of problems that are naturally equipped with a small integer parameter and for which the problem becomes more difficult as increases, such as finding -cliques in graphs. A problem is said to be fixed- parameter tractable if there is an algorithm for solving it on inputs of size , and a function , such that the algorithm runs in time . That is, it is fixed-parameter tractable if it can be solved in polynomial time for any fixed value of and moreover if the exponent of the polynomial does not depend on .. Technically, there is usually an additional requirement that be a computable function. For finding -vertex cliques, the brute force search algorithm has running time .
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Pre-pub PDF. In contrast to other standard modeling methods, ACE events are driven solely by initial conditions, whether or not equilibria exist or are computationally tractable. ACE modeling, however, includes agent adaptation, autonomy, and learning.Tesfatsion, Leigh (2006), "Agent-Based Computational Economics: A Constructive Approach to Economic Theory", ch. 16, Handbook of Computational Economics, v.
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Vázquez de Prada 2011, p. 188, Vázquez de Prada 2016, p. 38, Javier Lavardín, Historia del ultimo pretendiente a la corona de España, Paris 1976, pp. 27-28 Despite these threats Don Javier and the new Carlist political leader Valiente still deemed Iturmendi tractable and their best liaison with Franco;Vázquez de Prada 2011, p.
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It provides a compact theory that makes empirical predictions with a relatively sparse model - just a description of the agent's objectives and constraints. Furthermore, optimization theory is a well-developed field of mathematics. These two factors make rational choice models tractable compared to other approaches to choice. Most importantly, this approach is strikingly general.
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To cope with the heat, they like to burrow and make dens. They are a good companion dog. Females are generally more tractable and better companion dogs than males. Like most livestock guardian dogs, they bond with the flock; they are independent thinkers; and they must be trained to respond to their master's voice.
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This operator is extremely well formed, and thus very numerically tractable. The Gauss–Kuzmin constant is easily computed to high precision by numerically diagonalizing the upper-left n by n portion. There is no known closed-form expression that diagonalizes this operator; that is, there are no closed-form expressions known for the eigenvectors.
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This gave a total population of around 550 at work there. The ‘Malays’ had proved ‘tractable...quick to learn...pleasant,’ excellent on the land, though not the equal of the Aborigines in the water. Despite that they were doing well, except for Broadhurst's men who were again a dismal failure producing results far worse than those around.
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Synthesis of a specific zeolite de novo from a novel crystal net design remains one of the major goals of contemporary research. There are similar efforts in sulfides and phosphates. Control is more tractable if the constituents are molecular building blocks, i.e., stable molecules that can be readily induced to assemble in accordance with geometric restrictions.
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The division, now under Major General Rennie, transferring from I Corps to Lieutenant General Guy Simonds' II Canadian Corps, then took part in Operation Totalize, which succeeded, with Cassels' brigade taking Tilly-la-Campagne, its objective, with light casualties. The division then participated in Operation Tractable, in an attempt to prevent the German Army from escaping the Falaise Pocket.
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The regular Platonic solids are the only full-sphere layouts for which closed-form solutions for decoding matrices exist. Before the development and adoption of modern mathematical tools for the optimisation of irregular layouts and the generation of T-designs and Lebedev grids with higher numbers of speakers, the regular polyhedra were the only tractable options.
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The necessary condition for tractability based on the universal gadget holds for reduced languages. Such a language is tractable if the universal gadget has a solution that, when viewed as a function in the way specified above, is either a constant function, a majority function, an idempotent binary function, an affine function, or a semi-projection.
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In fact, some systems in nature are observed to exhibit emergence based upon the interactions of autonomous parts, and some others exhibit emergence that at least at present cannot be reduced in this way. In particular renormalization methods in theoretical physics enable scientists to study systems that are not tractable as the combination of their parts.
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Boris and Andrey then sought support in Pskov, but to no avail. In order to settle the conflict, Ivan III offered Andrei Bolshoy the cities of Kaluga and Aleksin, but he refused. The invasion of Khan Akhmat in 1480 reconciled the grand prince with his brothers. Ivan III became more tractable and promised to fulfill all their demands.
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A subcoloring of a graph is a partition of its vertices into induced cluster graphs. Thus, the cluster graphs are exactly the graphs of subchromatic number 1.. The computational problem of finding a small set of edges to add or remove from a graph to transform it into a cluster graph is called cluster editing. It is NP-complete. but fixed-parameter tractable..
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The random velocity field U(x,t) is statistically stationary if all statistics are invariant under a shift in time. This roughly means that all statistical properties are constant in time. Often, the mean field is the object of interest, and this is constant too in a statistically stationary flow. Steady flows are often more tractable than otherwise similar unsteady flows.
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"Existence of an Equilibrium for a Competitive Economy", Econometrica 22(3), pp. 265-290. More concretely, many problems are amenable to analytical (formulaic) solution. Many others may be sufficiently complex to require numerical methods of solution, aided by software. Still others are complex but tractable enough to allow computable methods of solution, in particular computable general equilibrium models for the entire economy.
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Most classes of CSPs that are known to be tractable are those where the hypergraph of constraints has bounded treewidth (and there are no restrictions on the set of constraint relations), or where the constraints have arbitrary form but there exist essentially non-unary polymorphisms of the set of constraint relations. Every CSP can also be considered as a conjunctive query containment problem.
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The case of a connected compact Lie group K (including the just-mentioned case of SO(3)) is particularly tractable. Part III In that case, every finite-dimensional representation of K decomposes as a direct sum of irreducible representations. The irreducible representations, in turn, were classified by Hermann Weyl. The classification is in terms of the "highest weight" of the representation.
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The coverage probability of the typical user is then interpreted as the proportion of network users who can connect to the cellular network. Building off previous work done on an Aloha model, the coverage probability for the typical user was derived for a Poisson network.J. G. Andrews, F. Baccelli, and R. K. Ganti. A tractable approach to coverage and rate in cellular networks.
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A partition of the edges of the complete graph K5 into two triangle-free subsets In graph theory and theoretical computer science, the monochromatic triangle problem is an algorithmic problem on graphs, in which the goal is to partition the edges of a given graph into two triangle-free subgraphs. It is NP-complete but fixed-parameter tractable on graphs of bounded treewidth.
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Entrepreneur First invests £80,000 in each startup in Europe, and SG$75,000 in Asia. In return, it claims a 10 percent equity share. Among its successful startups are Adbrain, Echobox, Blaze bike lights, Pi-Top, Permutive, Tractable, Bloomsbury.ai, Transcelestial, and Magic Pony Technology - who sold to Twitter for a reported $150m only 18 months after the founders met on the programme.
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This was later followed by a simpler and more tractable method which was patented by Harvard and subsequently licensed to PharmaMar. The current supply is based on a semisynthetic process developed by PharmaMar starting from safracin B, an antibiotic obtained by fermentation of the bacterium Pseudomonas fluorescens. PharmaMar entered into an agreement with Johnson & Johnson to market the compound outside Europe.
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Most inference tools include some heuristic step to make inference computationally tractable. Examples of tools that infer phylogenies from noisy VAF data include AncesTree, Canopy, CITUP, EXACT, and PhyloWGS. In particular, EXACT performs exact inference by using GPUs to compute a posterior probability on all possible trees for small size problems. Extensions to the PPM have been made with accompanying tools.
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Researchers at Standard Oil Development Company and the U. S. Rubber Company discovered that addition of a mercaptan modifier to the recipe not only produced a lower molecular weight and more tractable rubber, but it also increased the polymerization rate.Synthetic Rubber, Whitby, G. S., ed., John Wiley, NY 1954, p. 243. Use of a mercaptan modifier became standard in the Mutual recipe.
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Their corresponding X-ray diffraction & scattering patterns are characteristic of molecular paracrystals with a significant degree of disorder (over 20%), and the structure is not tractable using only the standard analysis. In contrast, the standard analysis, involving only Fourier transforms of Bessel functions and DNA molecular models, is still routinely used to analyze A-DNA and Z-DNA X-ray diffraction patterns.
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In other words, the problem is fixed-parameter tractable. It remains difficult for larger , such as . There are also efficient approximation algorithms for approximating on graphs of bounded degree. In practice heuristic algorithms are used, such as the simple algorithm which starts with no edges and continually adds each new edge in a way that produces the fewest additional crossings possible.
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The medium to large size long-muzzled head has a straight or slightly convex profile with wide-set eyes. The croup is sloping, the haunches well-muscled, and the back, short with a strong loin. The criollo is tractable, intelligent, willing and sensible. Criollo horses average 14.3 hands high, being the maximum height for stallions and geldings of 14 to 15 hands high.
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The advantage of these recursive techniques is that they are computationally tractable. The coding algorithm for Tanner graphs is extremely efficient in practice, although it is not guaranteed to converge except for cycle-free graphs, which are known not to admit asymptotically good codes.T. Etzion, A. Trachtenberg, and A. Vardy, Which Codes have Cycle-Free Tanner Graphs?, IEEE Trans. Inf.
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The Hosoya index is #P-complete to compute, even for planar graphs.. However, it may be calculated by evaluating the matching polynomial mG at the argument 1.. Based on this evaluation, the calculation of the Hosoya index is fixed-parameter tractable for graphs of bounded treewidth. and polynomial (with an exponent that depends linearly on the width) for graphs of bounded clique-width..
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In 1797, the Directory appointed him minister plenipotentiary to the king of Sardinia. After seven months, Ginguené retired to his country house of St Prix, in the valley of Montmorency. He was appointed a member of the tribunate, but Napoleon, finding that he was not sufficiently tractable, had him expelled at the first "purge", and Ginguené returned to his literary pursuits.
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The size of the automaton constructed in this way is not an elementary function of the size of the input MSO formula. This non- elementary complexity is necessary, in the sense that (unless P = NP) it is not possible to test MSO properties on trees in a time that is fixed-parameter tractable with an elementary dependence on the parameter..
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This assumption is so fundamental that it is rarely mentioned, but like most linearity assumptions, it is rarely exact and often simply made to obtain a tractable model. Additionally, data should always be categorical. Continuous data can first be converted to categorical data, with some loss of information. With both continuous and categorical data, it would be best to use logistic regression.
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Proceedings of the National Conference on Artificial Intelligence, Washington DC. During the 1990s researchers including Peter Dayan, Geoffrey Hinton and Richard Zemel proposed that the brain represents knowledge of the world in terms of probabilities and made specific proposals for tractable neural processes that could manifest such a Helmholtz Machine.Dayan, P., Hinton, G. E., & Neal, R. M. (1995). The Helmholtz machine. Neural Computation, 7, 889–904.
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A handful of comparative psychologists have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of rats and pigeons. These studies draw on the tenets of comparative psychology, where the main goal is to discover analogs to human behavior in experimentally-tractable non-human animals. They are also methodologically similar to the work of Ferster and Skinner.
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The same is true for detecting whether the pattern graph is an induced subgraph of the larger graph, or whether it has a graph homomorphism to the larger graph., Corollary 18.1, p. 401.. For the same reason, the problem of testing whether a graph of bounded book thickness obeys a given formula of first order logic is fixed-parameter tractable., Theorem 18.7, p. 405.
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The self-consistent mean field (SCMF) method is an adaptation of mean field theory used in protein structure prediction to determine the optimal amino acid side chain packing given a fixed protein backbone. It is faster but less accurate than dead-end elimination and is generally used in situations where the protein of interest is too large for the problem to be tractable by DEE.
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Rodezno was also surprised and concerned by detention of Manuel Hedilla. However, he still held trust in earlier Franco’s assurance that Traditionalist doctrine will be embodied in outlook of the new party "en su dia", Peñalba Sotorrio 2013, p. 54 In few days he and his men visited Franco to voice their unease, yet they remained tractable and did not mount explicit protest or opposition.
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Councillors drive it along with the other beasts to make it tractable, through the narrow doorway of the inhlambelo, and all the other animals come out after a few seconds. The 'pure' stand tense, ready to pounce as the umdvutshulwa emerges and pummel it with their strong young hands. To throw the bull with naked hands is a trial of strength and a test of purity.
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The inlet tracts have been reduced and only one injector per cylinder is fitted. This reduces peak power to 115 hp @ 11,000 rpm but gives a more tractable engine. Usable torque is available from 2,000 rpm. The machine is fitted with a hydraulic clutch, which reduces the width of the engine by 40 mm. A quickshifter and a ‘blipper’ downshifter are fitted to the 6 speed gearbox.
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Alternative parametric approaches have been proposed, notably the highly tractable mixture dynamical local volatility models by Damiano Brigo and Fabio Mercurio. Since in local volatility models the volatility is a deterministic function of the random stock price, local volatility models are not very well used to price cliquet options or forward start options, whose values depend specifically on the random nature of volatility itself.
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Even more generally, first-order model checking can be performed in near- linear time for nowhere-dense graphs, classes of graphs for which, at each possible depth, there is at least one forbidden shallow minor. Conversely, if model checking is fixed-parameter tractable for any hereditary family of graphs, that family must be nowhere-dense., 18.3 The Subgraph Isomorphism Problem and Boolean Queries, pp. 400–401; ; .
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Before computers, statisticians used methods that were computationally tractable, at the cost of known limitations. Since the 1980s these approximate statistical methods have been discarded: Modern twin methods based on structural equation modeling are not subject to the limitations and heritability estimates such as those noted above are mathematically impossible.M. C. Neale, S. M. Boker, G. Xie and H. H. Maes. (2002). Mx: Statistical Modelling. Journal.
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We are working to solve this problem for a large number of known protein folds (a representative subset: about 1500 folds). The most expensive step is to build a database of energy functions that describe all these structures. For each structure, we consider all possible sequences of amino acids. Surprisingly, this is computationally tractable, because our energy functions are sums over pairs of interactions.
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A number of decomposition methods exist. Most of them generate a tractable class by bounding the width of instances. The following are the decomposition methods defined for binary constraint satisfaction problems. Since a problem can be made binary by translating it into its dual problem or using hidden variables, these methods can be indirectly used to provide a tree decomposition for arbitrary constraint satisfaction problems.
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Morton wrote a 1637 book New English Canaan about his experiences, partly in verse, and may have thereby become America's first poet to write in English.New English Canaan or New Canaan. Containing an abstract of New England, composed in three bookes. The first booke setting forth the originall of the natives, their manners and customes, together with their tractable nature and love towards the English.
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Ground covering trot with a slight flick of feather at the point of extension." The Gypsy horse should be a "strong, kind, (very) intelligent partner that works willingly and harmoniously with its handler. They are also described as mannerly and manageable, eager to please, confident, courageous, alert, and loyal with a genuine sociable outlook. The Gypsy Horse is renowned for its gentle, tractable nature and sensible disposition.
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This method provides an approximation algorithm for the problem with an approximation ratio of two. A similar approach of partitioning into subproblems along shared diagonals leads to a fixed-parameter tractable algorithm for computing the rotation distance exactly. Determining the complexity of computing the rotation distance exactly without parameterization remains unsolved, and the best algorithms currently known for the problem run in exponential time.
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These horses have good endurance and are easy keepers, thriving on relatively little fodder. They have a reputation for being independent of temperament, but tractable. On adult horses, the lay of the hair can create the appearance of stars and flags on the neck and chest. Also due to the lay of the hair, newborn foals can appear to have stripes all over, reminiscent of zebra stripes.
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Modern technologies in genetic engineering and metabolic engineering enabled the production of these natural products in microorganisms. Complete biosynthesis of opiate compounds has been achieved in genetically tractable organisms Saccharomyces cerevisiae and Escherichia coli. Morphinone reductase was also successfully expressed in these two organisms. The enzyme represents a promising candidate for downstream modifications of opiate compounds, allowing the biosynthesis of valuable semi-synthetic opiate drugs in microorganisms.
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The Spanish municipality of Cartagena has 24 districts, known as diputaciónes (councils). The original 17 districts established at the beginning of the 18th century were maintained throughout that century, and were the equivalent of the pedanías (municipal districts) in other areas. This administrative structure was put in place in response to population increase in that era, and because the municipality was becoming less tractable.
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It is impossible to calculate outcomes with any certainty in a decision situation that involves qualitative variables. This is based on the theory of computability which states that a problem is computable if an algorithm exists, the algorithm is efficient/tractable and if there is a well defined solution state. Because of their very nature, qualitative problems lack well-defined state and hence the law.
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The breed has a firmness on point, is an excellent retriever, and has the determination to remain on the scent even when swimming. The overall appearance embodies the qualities of a multi- purpose pointing dog, endurance, working ability and an easily satisfied nature. This is a dog of power and drive in the field, yet is a tractable and affectionate companion in the home.
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Deciding whether the metric dimension of a graph is at most a given integer is NP- complete . It remains NP-complete for bounded-degree planar graphs , split graphs, bipartite graphs and their complements, line graphs of bipartite graphs , unit disk graphs , interval graphs of diameter 2 and permutation graphs of diameter 2 . For any fixed constant k, the graphs of metric dimension at most k can be recognized in polynomial time, by testing all possible k-tuples of vertices, but this algorithm is not fixed-parameter tractable (for the natural parameter k, the solution size). Answering a question posed by , show that the metric dimension decision problem is complete for the parameterized complexity class W[2], implying that a time bound of the form nO(k) as achieved by this naive algorithm is likely optimal and that a fixed-parameter tractable algorithm (for the parameterization by k) is unlikely to exist.
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They participated in the later battles of the Invasion of Normandy, taking part in Operation Totalize and finally closing the Falaise pocket in Operation Tractable. The South Albertas went on to participate in the liberation of the Netherlands and the Battle of the Scheldt. In January 1945, they took part in the Battle for the Kapelsche Veer. They spent the last weeks of the war fighting in northern Germany.
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Under mild regularity conditions this process converges on maximum likelihood (or maximum posterior) values for parameters. A more fully Bayesian approach to parameters is to treat them as additional unobserved variables and to compute a full posterior distribution over all nodes conditional upon observed data, then to integrate out the parameters. This approach can be expensive and lead to large dimension models, making classical parameter-setting approaches more tractable.
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FP (complexity) (standing for "Function Polynomial") is the class of function problems that can be solved in deterministic polynomial time. FP \subseteq CLS, and it is conjectured that this inclusion is strict. This class represents the class of function problems that are believed to be computationally tractable (without randomization). If TFNP = FP, then P = NP ∩ coNP, which should be intuitive given the fact that TFNP = F(NP \cap coNP).
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Similarly, biochemists use NMR to identify proteins and other complex molecules. Besides identification, NMR spectroscopy provides detailed information about the structure, dynamics, reaction state, and chemical environment of molecules. The most common types of NMR are proton and carbon-13 NMR spectroscopy, but it is applicable to any kind of sample that contains nuclei possessing spin. NMR spectra are unique, well-resolved, analytically tractable and often highly predictable for small molecules.
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When the region was first settled, the land south of the Zeelberg was very rugged and impassable. Since the region was not tractable to extensive exploration, the early settlers probably never realized that the Tongelreep was a continuation of the Warmbeek. This theory is reinforced by early maps of the region, which show varying sources for the Tongelreep but do not suggest any link to the Belgian river.Aalst.
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Some empirical relationships are merely approximations, often equivalent to the first few terms of the Taylor series of the analytical solution describing the phenomenon. Other relationships only hold under certain specific conditions, reducing them to special cases of more general relationship. Some approximations, in particular phenomenological models, may even contradict theory; they are employed because they are more mathematically tractable than some theories, and are able to yield results.
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A Hamiltonian cycle can be found from a proper interval representation of the graph in time O(n\log n), but when the graph itself is given as input, the same problem admits linear-time solution that can be generalized to interval graphs... List coloring remains NP-complete even when restricted to indifference graphs.. However, it is fixed-parameter tractable when parameterized by the total number of colors in the input.
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Although it is commonly (and mistakenly) thought that this was the first horse of the breed, by the 1760s, all other male lines of the breed had died out, resulting in a genetic bottleneck. Another bottleneck occurred in the late 18th century. In 1784, the breed was described as " high, short and compact with bony legs, often light sorrel in color, gentle, tractable, strong" and with "shoulders loaded with flesh".
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Labradors are known as intelligent and suitable for a variety of working roles, such as this dog trained to detect signs of arson. game The AKC describes the Labrador's temperament as a kind, pleasant, outgoing and tractable nature. Labradors' sense of smell allows them to home in on almost any scent and follow the path of its origin. They generally stay on the scent until they find it.
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The philosophical background of revision theory is developed by Gupta and Belnap.Gupta and Belnap (1993) Other philosophers, such as Aladdin Yaqūb, have developed philosophical interpretations of revision theory in the context of theories of truth, but not in the general context of circular definitions.Yaqūb (1993) Gupta and Belnap maintain that circular concepts are meaningful and logically acceptable. Circular definitions are formally tractable, as demonstrated by the formal semantics of revision theory.
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Williams, p. 194 With von Kluge's few remaining battleworthy formations destroyed by the First Army, the Allied commanders realized that the entire German position in Normandy was collapsing.Williams, p. 197 Bradley declared: On 14 August, in conjunction with U.S. movements northward to Chambois, Canadian forces launched Operation Tractable; the Allied intention was to trap and destroy the German 7th Army and 5th Panzer Army near the town of Falaise.
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See also pp. 756 and 766 of the Handbook His fuzzy ontology also includes a fuzzy mereology and mereotopology by means of which vague part-whole relationships, for example in anatomy, surgery and other medical fields, become logically tractable. In addition, he has developed a technique to bring to light the ontological commitments of any piece of medical knowledge so as to ascertain the ontological prerequisites of its satisfiability.
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Bulls should be slightly thicker and heavier than cows showing masculinity. Texas Longhorns have a mild, tractable disposition, not showing aggressiveness or nervousness. According to the TLBAA, mature Miniature Texas Longhorns must have horns (measured tip-to- tip) of at least 50% their hip height with > 100% their hip height considered to be desirable. Miniature Texas Longhorns are not considered to be mature until they are 5 years of age.
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The attack began before dawn and by first light the break-in was going well, with a number of villages taken. After a second artillery preparation the 4th Canadian and 1st Polish Armoured Divisions passed through to continue the advance.Ellis, Normandy, pp. 419–424. The Canadians renewed the advance to Falaise on 14 August in Operation Tractable, with 51st (H) Division attacking towards the Laison Valley on the left flank.
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According to Courcelle's theorem, every fixed MSO2 property can be tested in linear time on graphs of bounded treewidth, and every fixed MSO1 property can be tested in linear time on graphs of bounded clique-width. The version of this result for graphs of bounded treewidth can also be implemented in logarithmic space. Applications of this result include a fixed-parameter tractable algorithm for computing the crossing number of a graph.; .
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Gammaherpesviruses are of primary interest due to the two human viruses, EBV and KSHV and the diseases they cause. The gammaherpesviruses replicate and persist in lymphoid cells but some are capable of undergoing lytic replication in epithelial or fibroblast cells. Gammaherpesviruses may be a cause of chronic fibrotic lung diseases in humans and in animals. Murid herpesvirus 68 is an important model system for the study of gammaherpesviruses with tractable genetics.
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In constraint satisfaction, a decomposition method translates a constraint satisfaction problem into another constraint satisfaction problem that is binary and acyclic. Decomposition methods work by grouping variables into sets, and solving a subproblem for each set. These translations are done because solving binary acyclic problems is a tractable problem. Each structural restriction defined a measure of complexity of solving the problem after conversion; this measure is called width.
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The Jalpa was a development of the earlier Silhouette intended to fill a role as a more "affordable" Lamborghini, being much less expensive than the flagship Countach and being also designed by Bertone. Compared to the Countach, the Jalpa was much easier to drive, having better visibility and being more tractable in heavy traffic and at slow speeds, although reviewers have noted that it had a heavy steering and accelerator.
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Myrmecophilous interactions provide an important model system for exploring ecological and evolutionary questions regarding coevolution, plant defense theory, food web structure, species coexistence, and evolutionarily stable strategies. Because many myrmecophilous relationships are easily manipulable and tractable, they allow for testing and experimentation that may not be possible in other interactions. Therefore, they provide ideal model systems in which to explore the magnitude, dynamics, and frequency of mutualism in nature.
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It has also been demonstrated that parallel algorithms may yield significant speedups for MCMC-based inference in phylogenetics, which may be a tractable approach also for ABC-based methods. Yet an adequate model for a complex system is very likely to require intensive computation irrespectively of the chosen method of inference, and it is up to the user to select a method that is suitable for the particular application in question.
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Attempts to model the effects of fading started almost immediately after the effect was first characterized. Earlier models included simplifications in order to make the math tractable. Rayleigh fading is named for its use of the Rayleigh distribution of the signal. This is, in effect, the 2D distribution that results from the product of X and Y components that are separately and randomly distributed according to a normal distribution.
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This problem is called the "specification problem". The second problem concerns computation. It asks questions about whether a combinatorially complex model, once specified, is computationally tractable, given the large number of states and the even larger number of possible transitions between states, whether it can be stored electronically, and whether it can be evaluated in a reasonable amount of computing time. This problem is called the "computation problem".
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For graph invariants with the property that, for each k, the graphs with invariant at most k are minor-closed, the same method applies. For instance, by this result, treewidth, branchwidth, and pathwidth, vertex cover, and the minimum genus of an embedding are all amenable to this approach, and for any fixed k there is a polynomial time algorithm for testing whether these invariants are at most k, in which the exponent in the running time of the algorithm does not depend on k. A problem with this property, that it can be solved in polynomial time for any fixed k with an exponent that does not depend on k, is known as fixed-parameter tractable. However, this method does not directly provide a single fixed-parameter-tractable algorithm for computing the parameter value for a given graph with unknown k, because of the difficulty of determining the set of forbidden minors.
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It was believed that one way to obtain the protein structure of a potassium channel was to identify a gene encoding the channel protein in a genetically tractable organism, and then combine newly developed tools in biophysics, molecular genetics, DNA sequencing in eukaryotes, and molecular cloning, to clone and sequence the gene and functionally express the encoded channel in a heterologous expression system. To this end, as a postdoctoral researcher, Salkoff adapted the voltage clamp technique to the fruit fly Drosophila which had been used by Alan Lloyd Hodgkin and Andrew Huxley to reveal the ionic basis of the nerve action potential. This enabled the direct observation of ion currents in a genetically tractable organism. This technique was then used to show that the Drosophila Shaker gene was the structural gene for a potassium channel, a claim which was based on several genetic criteria and confirmed by biophysical analysis of the expected ion channel current phenotype.
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Solving a constraint satisfaction problem on a finite domain is an NP complete problem with respect to the domain size. Research has shown a number of tractable subcases, some limiting the allowed constraint relations, some requiring the scopes of constraints to form a tree, possibly in a reformulated version of the problem. Research has also established relationship of the constraint satisfaction problem with problems in other areas such as finite model theory.
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In principle, ab initio methods eventually converge to the exact solution of the underlying equations as the number of approximations is reduced. In practice, however, it is impossible to eliminate all approximations, and residual error inevitably remains. The goal of computational chemistry is to minimize this residual error while keeping the calculations tractable. In some cases, the details of electronic structure are less important than the long-time phase space behavior of molecules.
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More generally, formal power series can include series with any finite (or countable) number of variables, and with coefficients in an arbitrary ring. In algebraic geometry and commutative algebra, rings of formal power series are especially tractable topologically complete local rings, allowing calculus-like arguments within a purely algebraic framework. They are analogous in many ways to p-adic numbers. Formal power series can be created from Taylor polynomials using formal moduli.
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In wireless networks, the factors that contribute to the SINR are often random (or appear random) including the signal propagation and the positioning of network transmitters and receivers. Consequently, in recent years this has motivated research in developing tractable stochastic geometry models in order to estimate the SINR in wireless networks. The related field of continuum percolation theory has also been used to derive bounds on the SINR in wireless networks.M. Franceschetti and R. Meester.
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Paul Cockshott, Allin Cottrell, and Andy Pollack have proposed new forms of coordination based on modern information technology for non-market socialism. They argue that economic planning in terms of physical units without any reference to money or prices is computationally tractable given the high-performance computers available for particle physics and weather forecasting. Cybernetic planning would involve an a priori simulation of the equilibration process that idealized markets are intended to achieve.
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In infinite dimensions, the spectrum need not consist solely of isolated eigenvalues. However, the case of a compact operator on a Hilbert space (or Banach space) is still tractable, since the eigenvalues are at most countable with at most a single limit point λ = 0\. The most studied isospectral problem in infinite dimensions is that of the Laplace operator on a domain in R2. Two such domains are called isospectral if their Laplacians are isospectral.
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Polymeric silsesquioxanes have been reported, first by Brown. High molecular weight tractable polymeric phenyl silsesquioxane featured a ladder-type structure. Brown's findings were the basis for many future investigations. Brown's synthesis proceeded in three- steps: (1) the hydrolysis of phenyltrichlorosilane, (2) equilibration of this hydrolyzate with potassium hydroxide at a low concentration and temperature to give the prepolymer, and (3) equilibration of the prepolymer at a high concentration and temperature to give the final polymer.
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1214–1216, 2012 formulates the augmented Hammerstein model so that it is tractable for use with the 2D nonlinear polynomial model. The augmented Hammerstein model is used to implement memory while maintaining a memoryless polynomial model. The model as a whole becomes a memory model but the polynomial model itself remains memoryless. This reduces the complexity of the polynomial model and has a net reduction on the overall complexity of the composite system.
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The agricultural significance of BPV-1 spurred a successful effort to develop a vaccine against the virus. A few reports have identified papillomaviruses in smaller rodents, such as Syrian hamsters, the African multimammate rat and the Eurasian harvest mouse. However, there are no papillomaviruses known to be capable of infecting laboratory mice. The lack of a tractable mouse model for papillomavirus infection has been a major limitation for laboratory investigation of papillomaviruses.
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Pristionchus pacificus is a species of free-living nematodes (roundworms) in the family Diplogastridae. The species has been established as a satellite model organism to Caenorhabditis elegans, with which it shared a common ancestor 200-300 million years ago. The genome of P. pacificus has been fully sequenced, which in combination with other tools for genetic analysis make this species a tractable model in the laboratory, especially for studies of developmental biology.
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S.R. (1938), p. 8 Previous economic fluctuations had not created the need for federal unemployment programs, and policy and tradition dictated that assistance was a local issue, because traditionally it had been locally tractable. Under the British North America Act of 1867 (BNA), government received most revenue collection powers, and provinces became responsible for social relief, education, and health care. However, 60 years had passed since the BNA, and this was a different economy.
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It is thought to have heralded and inspired the 18th-century Neoclassicism. In the 1640s, Mansart worked on the convent and church of the Val-de-Grâce in Paris, a much coveted commission from Anne of Austria. His alleged profligacy led to his being replaced with a more tractable architect, who basically followed Mansart's design. In the 1650s, Mansart was targeted by political enemies of the prime minister Cardinal Mazarin, for whom Mansart frequently worked.
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The SDS model was intended as a computationally simple version of the full Baer and Rinzel model. It was designed to be analytically tractable and have as few free parameters as possible while retaining those of greatest significance, such as spine neck resistance. The model drops the continuum approximation and instead uses a passive dendrite coupled to excitable spines at discrete points. Membrane dynamics in the spines are modelled using integrate and fire processes.
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Axel Leijonhufvud published a highly influential book in 1968 – 'Keynesian economics and the economics of Keynes' – criticising the direction Keynesian economics had taken under the influence of the IS-LM model. He argued that: > His [Keynes's] followers understandably decided to skip the problematical > dynamic analysis of Chapter 19 and focus on the relatively tractable static > IS-LM model.Peter Howitt, English draft of entry on Leijonhufvud's book for > the Darroz 'Dictionnaire des grandes oeuvres économiques'.
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In game theory, an open-loop model is the one where players cannot observe the play of their opponents, as opposed to a closed-loop model, where all past play is common knowledge. The solution to an open-loop model is called "open- loop equilibrium". Open loop models are more tractable, which is why they are sometimes preferred to closed-loop models even when the latter is a better description of reality.
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After harsh fighting, the 4th Armoured Division captured Soulangy but the gains made were minimal as strong German resistance prevented a breakthrough to Trun.Bercuson, p. 232 On 16 August, the Canadian 2nd Infantry Division broke into Falaise, encountering minor opposition from Waffen-SS units and scattered pockets of German infantry. Although it would take two more days to clear all resistance in the town, the first major objective of Operation Tractable had been achieved.
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A seminal work in SLAM is the research of R.C. Smith and P. Cheeseman on the representation and estimation of spatial uncertainty in 1986. Other pioneering work in this field was conducted by the research group of Hugh F. Durrant-Whyte in the early 1990s. which showed that solutions to SLAM exist in the infinite data limit. This finding motivates the search for algorithms which are computationally tractable and approximate the solution.
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The adopted models must consequently be capable of modeling such a hybrid behavior. It is common in SLS to use 0D —sometimes 1D— equations to model physical phenomena with space variables, instead of 2D or 3D equations. The reason for such a choice is the size of the simulated systems, which is generally too large (i.e. too many elements and/or too large space extension) for the simulation to be computationally tractable.
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The term sub-exponential time is used to express that the running time of some algorithm may grow faster than any polynomial but is still significantly smaller than an exponential. In this sense, problems that have sub-exponential time algorithms are somewhat more tractable than those that only have exponential algorithms. The precise definition of "sub-exponential" is not generally agreed upon, and we list the two most widely used ones below.
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The CBC is based on the presumption that sentience, consciousness followed the same path -- the many ways that species experience events, similarly evolved from prokaryotes. Interestingly, the CBC also allows for a novel perspective on the Hard Problem. Rather that search for the ways in which brains make minds, consciousness is viewed as an integral feature of all life. In short, the emergentist's dilemma is reformulated and in a version that is physiologically more tractable.
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The complexity of raw flow cytometry data (dozens of measurements for thousands to millions of cells) makes answering questions directly using statistical tests or supervised learning difficult. Thus, a critical step in the analysis of flow cytometric data is to reduce this complexity to something more tractable while establishing common features across samples. This usually involves identifying multidimensional regions that contain functionally and phenotypically homogeneous groups of cells. This is a form of cluster analysis.
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A bullock team hitched to two small jinkers (log conveyances) with a dolly in the foreground. Bullockies often chose Devon cattle because they were plentiful, hardy, tractable and readily matched up the team, which was often a source of pride to the owners. Teams had to be educated to perform their respective tasks, too. The first part of a bullock’s education began when the bullocky tied two young bullocks together with two heavy leather collars and a connecting chain.
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Coyotes were probably semidomesticated by various pre-Columbian cultures. Some 19th- century writers wrote of coyotes being kept in native villages in the Great Plains. The coyote is easily tamed as a pup, but can become destructive as an adult. Both full-blooded and hybrid coyotes can be playful and confiding with their owners, but are suspicious and shy of strangers, though coyotes being tractable enough to be used for practical purposes like retrieving and pointing have been recorded.
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This makes analysis much simpler than in a general equilibrium model which includes an entire economy. The dynamic process is that prices adjust until supply equals demand. It is a powerfully simple technique that allows one to study equilibrium, efficiency and comparative statics. The stringency of the simplifying assumptions inherent in this approach make the model considerably more tractable, but it may produce results which while seemingly precise do not effectively model real world economic phenomena.
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Georg Reicherstorffer in "Chorographia Transilvaniae", printed in Vienna in 1550, wrote: > "Orăștie city, which is called Broos by the Saxons, is located a mile away > to the south of the grain fields. It is situated on the river Mureș. The > soil is unusually fertile, liberally yielding wheat, wine, and all kinds of > fruits; the people are very tractable and in clothing style and diet are > closer to the Romanians, who live broadly scattered in the desolate plains > around".
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Administration of Fear, p. 21. For contemporary humanity, fear is also related to speed, which can be seen in scenarios such as a nuclear apocalypse or a stock market crash. Hypotheticals like these are governed by computers, which act at speeds that are not tractable for humans. Virilio also contends that perpetual, instantaneous communication via computers and the internet are disruptive to biological rhythms and historical seasonal patterns of life in human culture, producing both fear and misery.
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This model is based on a distributional assumption about the response error term. Adding a specific distribution assumption into the model can make the model computationally tractable due to the existence of the closed-form representation. But if the distribution of the error term is misspecified, the estimates based on the distribution assumption will be inconsistent. The basic idea of the distribution-free model is to replace the two probability term in the log-likelihood function with other weights.
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Submodular and supermodular set functions are also studied in combinatorial optimization. Many of the results in have analogues in , where submodular functions were first presented as generalizations of matroids. In this context, the core of a convex cost game is called the base polyhedron, because its elements generalize base properties of matroids. However, the optimization community generally considers submodular functions to be the discrete analogues of convex functions , because the minimization of both types of functions is computationally tractable.
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The development of these algorithms led to the method of iterative compression, a more general tool for many other parameterized algorithms. The parameterized algorithms known for these problems take nearly-linear time for any fixed value of k. Alternatively, with polynomial dependence on the graph size, the dependence on k can be made as small as 2.3146^k. In contrast, the analogous problem for directed graphs does not admit a fixed-parameter tractable algorithm under standard complexity- theoretic assumptions.
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An uprated, turbocharged version of the 1.6 L which was developed by Ford Europe for the hugely popular RS Turbo version of the Escort and also later the Ford Fiesta RS Turbo. It made at 6,000 rpm, and of torque at a very tractable 3,000 rpm. The boosted engine was substantially smoother than its normally aspirated cousins, the forced induction helping to damp out unpleasant harmonics. The block was slightly modified to provide an oil return from the turbocharger.
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Mount Bracey, is a mountain in the Miscinchinka Ranges of the Hart Ranges in the Northern Rocky Mountains. Named after Canadian Army Corporal Charles William Bracey, from South Fort George, BC; serving with 4th Armoured Brigade, 4th Canadian (Armoured) Division, Lake Superior Regiment (Motor), R.C.I.C. when he was killed in action 15 August 1944, age 23 during Operation Tractable, in Normandy.. Cpl Bracey is buried at Hottot-les-Bagues War Cemetery, Calvados, France, grave III. A. 5.
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Being a cheap and tractable medium it was highly demanded in contemporary society. It is largely concerned itself with the representation of the scenes of everyday life, and, as such, its social imports appear to be immense. Terracotta, in its varied uses and applications, gives us an idea for constructing the social, cultural, political and religious life of the contemporary people. Terracotta human and animal figurines give us a clear picture of the life-ways during the ancient period.
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This makes analysis much simpler than in a general equilibrium model which includes an entire economy. Here the dynamic process is that prices adjust until supply equals demand. It is a powerfully simple technique that allows one to study equilibrium, efficiency and comparative statics. The stringency of the simplifying assumptions inherent in this approach makes the model considerably more tractable, but may produce results which, while seemingly precise, do not effectively model real world economic phenomena.
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The approximation may provide benefits by being more mathematically tractable than the function being expanded, or by an increase in the speed of computation of the expanded function. Typically, the best approximation is given when the series is truncated at the smallest term. This way of optimally truncating an asymptotic expansion is known as superasymptotics.. The error is then typically of the form where is the expansion parameter. The error is thus beyond all orders in the expansion parameter.
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Thus, such a core is a local minimum, though not necessarily a global one. There are several practical methods of computing minimal unsatisfiable cores.N. Dershowitz, Z. Hanna, and A. Nadel, A Scalable Algorithm for Minimal Unsatisfiable Core ExtractionStefan Szeider, Minimal unsatisfiable formulas with bounded clause-variable difference are fixed- parameter tractable A minimum unsatisfiable core contains the smallest number of the original clauses required to still be unsatisfiable. No practical algorithms for computing the minimum core are known.
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There have been roads in existence in Coorg for many centuries but these roads were not suitable enough for bullock carts and carriages. The first tractable roads in Coorg were built by the British. The two main roads in Coorg constructed in the 19th century were the Eastern Trunk Road and the Northern Trunk Road both meeting at Mercara. The road from Mysore enters Coorg at Fraserpet and runs for nineteen and a half miles to Mercara.
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Although she wanted to be an actress, her mother wanted her to have a practical education, too, and Manon, who had become fluent in French and Italian, prepared for the Austrian state exam as a language teacher and translator. During the 1930s, she became more tractable, even serene. She had a way with animals and was often followed by cats and dogs. She could approach and feed wild roe deer and took a special interest in snakes.
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Although anatomical evidence for such an exclusive relationship is lacking at the level of single receptor and ganglion cells, the relationship between single buds and their innervating ganglion cells is tractable neuroanatomically. In taste, attempts to identify a spatial representation of taste receptors or taste qualities have revealed only an indistinct functional topography in the brain. Nevertheless, taste ganglion cells must distribute peripheral fibers to particular receptor cell types and disseminate impulses centrally in a structurally organized manner.
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The complexity of constraint satisfaction is the application of computational complexity theory on constraint satisfaction. It has mainly been studied for discriminating between tractable and intractable classes of constraint satisfaction problems on finite domains. Solving a constraint satisfaction problem on a finite domain is an NP-complete problem in general. Research has shown a number of polynomial-time subcases, mostly obtained by restricting either the allowed domains or constraints or the way constraints can be placed over the variables.
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This makes analysis much simpler than in a general equilibrium model, which includes an entire economy. Here, the dynamic process is that prices adjust until supply equals demand. It is a powerfully simple technique that allows one to study equilibrium, efficiency and comparative statics. The stringency of the simplifying assumptions inherent in this approach makes the model considerably more tractable, but may produce results which, while seemingly precise, do not effectively model real-world economic phenomena.
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Testing whether the Grundy number of a given graph is at least , for a fixed constant , can be performed in polynomial time, by searching for all possible -atoms that might be subgraphs of the given graph. However, this algorithm is not fixed-parameter tractable, because the exponent in its running time depends on . When is an input variable rather than a parameter, the problem is NP-complete.. The Grundy number is at most one plus the maximum degree of the graph, and it remains NP-complete to test whether it equals one plus the maximum degree.. There exists a constant such that it is NP-hard under randomized reductions to approximate the Grundy number to within an approximation ratio better than .. There is an exact exponential time algorithm for the Grundy number that runs in time . For trees, and graphs of bounded treewidth, the Grundy number may be unboundedly large.. Nevertheless, the Grundy number can be computed in polynomial time for trees, and is fixed-parameter tractable when parameterized by both the treewidth and the Grundy number,.
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The following conditions exploit the primal graph of the problem, which has a vertex for each variable and an edge between two nodes if the corresponding variables are in a constraint. The following are conditions on binary constraint satisfaction problems where enforcing local consistency is tractable and allows establishing satisfiability: # enforcing arc consistency, if the primal graph is acyclic; # enforcing directional arc consistency for an ordering of the variables that makes the ordered graph of constraint having width 1 (such an ordering exists if and only if the primal graph is a tree, but not all orderings of a tree generate width 1); # enforcing strong directional path consistency for an ordering of the variables that makes the primal graph having induced width 2. A condition that extends the last one holds for non-binary constraint satisfaction problems. Namely, for all problems for which there exists an ordering that makes the primal graph having induced width bounded by a constant i, enforcing strong directional i-consistency is tractable and allows establishing satisfiability.
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Vector spaces that are not finite dimensional often require additional structure to be tractable. A normed vector space is a vector space along with a function called a norm, which measures the "size" of elements. The norm induces a metric, which measures the distance between elements, and induces a topology, which allows for a definition of continuous maps. The metric also allows for a definition of limits and completeness - a metric space that is complete is known as a Banach space.
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The hitting set problem is W[2]-complete for the parameter OPT, that is, it is unlikely that there is an algorithm that runs in time f(OPT)nO(1) where OPT is the cardinality of the smallest hitting set. The hitting set problem is fixed-parameter tractable for the parameter OPT + d, where d is the size of the largest edge of the hypergraph. More specifically, there is an algorithm for hitting set that runs in time dOPTnO(1).
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On 14August, the First Canadian Army launched Operation Tractable with the aim of capturing Falaise and achieving a linkup with American forces in Chambois.D'Este, p. 429 A daylight attack was executed after artillery provided smoke-screen cover and medium bombers softened up the German defences. The offensive was largely successful and, although the 2nd Division was not an active participant, divisional troops entered Falaise on 16August as the remainder of First Canadian Army moved south-east towards Trun and Chambois.
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Protein design programs use computer models of the molecular forces that drive proteins in in vivo environments. In order to make the problem tractable, these forces are simplified by protein design models. Although protein design programs vary greatly, they have to address four main modeling questions: What is the target structure of the design, what flexibility is allowed on the target structure, which sequences are included in the search, and which force field will be used to score sequences and structures.
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"with an eye on Anglo- Saxon opinion, Franco made vague promises of forthcoming elections and extremely confusing hints about the installation of a new monarchy", Preston 2011, p. 510 In his trademark style balancing different political groupings, Franco decided to keep supporters of both dynastical options in check by pursuing two paths at the same time. The decreasingly cooperative but still tractable Alfonsist pretender Don Juan was invited to live in Spain, the offer which was ultimately turned down.Payne 2011, p.
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For each set Xi of the tree decomposition, and each partition of the vertices of Xi into color classes, the algorithm determines whether that coloring is valid and can be extended to all descendant nodes in the tree decomposition, by combining information of a similar type computed and stored at those nodes. The resulting algorithm finds an optimal coloring of an n-vertex graph in time O(kk + O(1)n), a time bound that makes this problem fixed-parameter tractable.
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On 14 August, the First Canadian Army launched Operation Tractable with the aim of capturing Falaise and achieving a linkup with American forces in Chambois.D'Este, p. 429 A daylight attack was executed after artillery provided smoke-screen cover and medium bombers softened up the German defenses. The offensive was largely successful and, although the 2nd Division was not an active participant, divisional troops entered Falaise on 16 August as the remainder of First Canadian Army moved south-east towards Trun and Chambois.
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The quadratic loss function is also used in linear-quadratic optimal control problems. In these problems, even in the absence of uncertainty, it may not be possible to achieve the desired values of all target variables. Often loss is expressed as a quadratic form in the deviations of the variables of interest from their desired values; this approach is tractable because it results in linear first-order conditions. In the context of stochastic control, the expected value of the quadratic form is used.
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According to the DeGroot model, each agent takes a weighted average of their neighbors' opinions at each step to update their own belief. The statistician George E. P. Box once said, "All models are wrong; however, some of them are useful." Along the same lines, the DeGroot model is a fairly simple model but it can provide us with useful insights about the learning process in social networks. Indeed, the simplicity of this model makes it tractable for theoretical studies.
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In September 1943, his Italian mainland campaign began: he was later awarded the DSO. He returned to the UK in January 1944, having been transferred to the II Canadian Corps as CCRA, regarded as the "second most senior job for a gunner in the Canadian Forces". II Corps was activated in Normandy on July 11, 1944 and participated in several actions (Operations Atlantic, Spring, Totalize and Tractable) in the Battle of Normandy. Matthews developed the artillery firing plans for each of these operations.
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Key lime (Citrus aurantifolia 'Swingle') is naturalized throughout the Florida Keys. While their thorns make them less tractable, and their thin, yellow rinds more perishable, Key limes are more tart and more aromatic than the common Persian limes seen year-round at grocery stores in the United States. Key limes have not been grown commercially in the U.S. since the 1926 Miami hurricane; they are generally imported from Central or South America. Key lime juice, unlike regular lime juice, is a pale yellow.
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By prefixing a sequence of statements enclosed in curly braces with the keyword `atomic`, the user can indicate that the sequence is to be executed as one indivisible unit, non-interleaved with any other processes. atomic { statements; } Atomic sequences can be an important tool in reducing the complexity of verification models. Note that atomic sequences restrict the amount of interleaving that is allowed in a distributed system. Intractable models can be made tractable by labeling all manipulations of local variables with atomic sequences.
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With the Americans on the southern flank halted and then engaged with Panzer Group Eberbach, and with the British pressing in from the north-west, the First Canadian Army, which included the Polish 1st Armoured Division, was ordered to close the trap.Wilmot, p. 419 After a limited attack by the 2nd Canadian Infantry Division down the Laize valley on 12–13 August, most of the time since Totalize had been spent preparing for Operation Tractable, a set-piece attack on Falaise.
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NMR is particularly amenable to detecting compounds that are less tractable to LC-MS analysis, such as sugars, amines or volatile liquids or GC-MS analysis, such as large molecules (>500 Da) or relatively non-reactive compounds. NMR is not a very sensitive technique with a lower limit of detection of about 5 μM. Typically 50-150 compounds can be identified by NMR-based metabolomic studies. Mass spectrometry is an analytical technique that measures the mass-to-charge ratio of molecules.
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The width of a problem is the width of its minimal- width decomposition. While decompositions of fixed width can be used to efficiently solve a problem, a bound on the width of instances does necessarily produce a tractable structural restriction. Indeed, a fixed width problem has a decomposition of fixed width, but finding it may not be polynomial. In order for a problem of fixed width being efficiently solved by decomposition, one of its decompositions of low width has to be found efficiently.
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Alexis Peak, is a 2,123-metre (6,965-feet) mountain in the Miscinchinka Ranges of the Hart Ranges in Northern British Columbia. Named after Canadian Army Lance Corporal Alexander Alexis, from Prince George, BC. Lance Corporal Alexis was killed in action 18 August 1944, during Operation Tractable, that took place in the final days of the Battle of Falaise Pocket. He was a member of the 3rd Canadian Division, Royal Winnipeg Rifles and is buried in the Beny- Sur-Mer Canadian War Cemetery.
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Connected dominating sets are useful in the computation of routing for mobile ad hoc networks. In this application, a small connected dominating set is used as a backbone for communications, and nodes that are not in this set communicate by passing messages through neighbors that are in the set.. The max leaf number has been employed in the development of fixed-parameter tractable algorithms: several NP-hard optimization problems may be solved in polynomial time for graphs of bounded max leaf number.
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To bolster his offensive, Simonds ordered the Canadian 2nd Infantry Division to move toward the front, with the hope that this reinforcement would be sufficient to enable his divisions to capture the town.Copp. p. 104 Although the first day's progress was slower than expected, Operation Tractable resumed on 15 August; both armoured divisions pushed southeast toward Falaise.Jarymowycz, p. 188 The Canadian 2nd and 3rd Infantry Divisions—with the support of the Canadian 2nd Armoured Brigade—continued their drive south towards the town.
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Wald 1984, p. 4 In spite of the fact that the universe is well described by four-dimensional spacetime, there are several reasons why physicists consider theories in other dimensions. In some cases, by modeling spacetime in a different number of dimensions, a theory becomes more mathematically tractable, and one can perform calculations and gain general insights more easily. There are also situations where theories in two or three spacetime dimensions are useful for describing phenomena in condensed matter physics.
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Although this bound is fixed-parameter tractable, its dependence on the parameter is higher than might be desired. More complex kernelization procedures can improve this bound, by finding smaller kernels, at the expense of greater running time in the kernelization step. In the vertex cover example, kernelization algorithms are known that produce kernels with at most 2k vertices. One algorithm that achieves this improved bound exploits the half- integrality of the linear program relaxation of vertex cover due to Nemhauser and Trotter.
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The horse's groom should be well-trained. He should not tie the halter to the manger where the rope meets the head, as the horse is likely to knock his head on the manger and injure himself. The sores will then make him less tractable when bridled or groomed. He should also tie the horse at a point above the level of his head, so that, when the horse tosses his head, he slackens the rope rather than tightening it.
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For his work on bidimensionality, he was the winner of the Nerode Prize in 2015 along with his co-authors Fedor Fomin, Mohammad T. Hajiaghayi, and Dimitrios Thilikos. The work was the study of a general technique for developing both fixed-parameter tractable exact algorithms and approximation algorithms for a class of algorithmic problems on graphs.. In 2016, he became a fellow at the Association for Computing Machinery."ACM Fellows":Erik Demaine He was given an honorary doctorate by Bard College in 2017.
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Many real-world problems are computationally intractable – for example, making probabilistic inferences using Bayesian belief networks is NP-hard. Many theorists agree that accounts of rationality must not require "[...] capacities, abilities, and skills far beyond those possessed by human beings as they now are." Second, even for problems that are tractable it has been argued that heuristics save effort, even if sometimes this is so at the cost of accuracy. Depending on the structure of the environment, this loss of accuracy might be small.
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The basic idea now known as the Z-transform was known to Laplace, and it was re-introduced in 1947 by W. Hurewicz and others as a way to treat sampled-data control systems used with radar. It gives a tractable way to solve linear, constant-coefficient difference equations. It was later dubbed "the z-transform" by Ragazzini and Zadeh in the sampled-data control group at Columbia University in 1952. The modified or advanced Z-transform was later developed and popularized by E. I. Jury.
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The study of heteroscedasticity has been generalized to the multivariate case, which deals with the covariances of vector observations instead of the variance of scalar observations. One version of this is to use covariance matrices as the multivariate measure of dispersion. Several authors have considered tests in this context, for both regression and grouped-data situations. Bartlett's test for heteroscedasticity between grouped data, used most commonly in the univariate case, has also been extended for the multivariate case, but a tractable solution only exists for 2 groups.
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The problem is also W[1]-hard, meaning that even finding a small induced matching of a given size k is unlikely to have an algorithm significantly faster than the brute force search approach of trying all k-tuples of edges. However, the problem of finding k vertices whose removal leaves an induced matching is fixed-parameter tractable. The problem can also be solved exactly on n-vertex graphs in time O(1.3752^n) with exponential space, or in time O(1.4231^n) with polynomial space.
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Nevertheless, the problem becomes fixed-parameter tractable when restricted to interval graphs , and more generally to graphs of bounded tree-length , such as chordal graphs, permutation graphs or asteroidal-triple-free graphs. Deciding whether the metric dimension of a tree is at most a given integer can be done in linear time (; ). Other linear-time algorithms exist for cographs , chain graphs and cactus block graphs (a class including both cactus graphs and block graphs). The problem may be solved in polynomial time on outerplanar graphs .
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Beverly Wendland is James B. Knapp Dean of the Krieger School of Arts and Sciences at Johns Hopkins University and a professor in the Department of Biology. Wendland previously served as Interim Dean after leading the Johns Hopkins' Department of Biology as its chair from 2009 to 2014. Her laboratory investigates the molecular mechanisms and regulation of endocytic vesicle formation, using cell biology, genetic, and structural biology approaches. Wendland's research has successfully taken advantage of the highly genetically tractable eukaryote, the yeast Saccharomyces cerevisiae.
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But any world model which contains sufficient detail to ensure correct GOFAI output is inevitably too complex, with too many moving parts to be practical, so that by the time world changes are updated, the world has already moved on. PCT avoids the complexity issues of GOFAI by basing its real-time governance on a perceptual window (dimensionally reduced projection) of the world, which is much more tractable than the entire world. Uexküll,, Dyer, and Powers arrived independently at this insight, which is important for robotics.
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Ellis, Volume I, p. 120. When the initial landings in Normandy were launched, the regiment was still based in England, and would join the main forces in mid-June after a beachhead had been established. On 7 and 14 August Operation Totalise and Operation Tractable were launched towards the area of Caen which was key for the Allies to capture if they were to maintain a foothold in the area. During these two operations the regiment participated in the push acting in the ground-support role.
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During this period, large numbers of Anglo-Normans - Thoroughbred-influenced agricultural horses from France - and Arabians were stationed in Zweibrücken. The first organized breeding of Anglo-Arabian horses occurred at Zweibrücken during this time period. The region became widely known for its refined cavalry horses which combined the size and speed of the Thoroughbred with the more tractable temperament of the Arabian. By 1900, the Principal Stud of Zweibrücken comprised more than 250 head of breeding stock and young horses, 74 of which were state-owned stallions.
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Never idle, always on the go, well- > disposed to harmless people, but no cringer, mad on children and always in > love. What could not have become of such a dog, if we only had at that time > military or police service training? His faults were the failings of his > upbringing, and never of his stock. He suffered from a suppressed, or > better, a superfluity of unemployed energy, for he was in heaven when > someone was occupied with him, and then he was the most tractable of dogs.
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DNA damage response: Cell-free extracts have been instrumental to unravel the signaling pathways activated in response to DNA double-strand breaks (ATM), replication fork stalling (ATR) or DNA interstrand crosslinks (FA proteins and ATR). Notably, several mechanisms and components of these signal transduction pathways were first identified in Xenopus. Apoptosis: Xenopus oocytes provide a tractable model for biochemical studies of apoptosis. Recently, oocytes were used recently to study the biochemical mechanisms of caspase-2 activation; importantly, this mechanism turns out to be conserved in mammals.
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He is a Fellow of the American Association for Artificial Intelligence, the American Association for the Advancement of Science and the Association for Computing Machinery. He sits on the advisory board for the DARPA Grand Challenge Cornell Team. His research concepts include tractable inference, knowledge representation, stochastic search methods, theory approximation, knowledge compilation, planning, default reasoning, satisfiability solvers like WalkSAT, and connections between computer science and statistical physics, namely phase transition phenomena. Selman teaches courses on artificial intelligence at Cornell University and advises postdoctoral fellows.
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In London, the board was about to abandon the project and mitigate their losses by selling the cable. Thomson, Cyrus West Field and Curtis M. Lampson argued for another attempt and prevailed, Thomson insisting that the technical problems were tractable. Though employed in an advisory capacity, Thomson had, during the voyages, developed a real engineer's instincts and skill at practical problem-solving under pressure, often taking the lead in dealing with emergencies and being unafraid to assist in manual work. A cable was completed on 5 August.
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The subcase obtained by restricting to a finite constraint language is called a non- uniform problem. These problems are mostly considered when expressing constraint satisfaction in terms of the homomorphism problem, as explained below. Uniform problems were also defined in the settings of homomorphism problems; a uniform problem can be defined as the union of a (possibly infinite) collection of non-uniform problems. A uniform problem made of an infinite set of non-uniform problems can be intractable even if all these non- uniform problems are tractable.
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An algorithm is said to be fixed-parameter tractable if the number of elementary operations it performs has a bound of the form O(n^c)+f(k), where n is some measure of the input size (such as the number of vertices in a graph), k is a parameter describing the complexity of the input (such as the treewidth of the graph), c is a constant that does not depend on n or k, and f is a computable function. Given a time bound of this form, the klam value of the algorithm (or more properly of the time bound) is defined to be the largest value of k such that f(k) does not exceed "some reasonable absolute bound on the maximum number of steps of any computation". More precisely both and use the number 1020 as this bound, and this has been followed by later researchers. To prevent artificially improving the klam value of an algorithm by putting more of its complexity into the O(n^c) part of the time bound, also limit c to be at most three, valid for many known fixed-parameter tractable algorithms.
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Cobham's thesis, also known as Cobham–Edmonds thesis (named after Alan Cobham and Jack Edmonds), asserts that computational problems can be feasibly computed on some computational device only if they can be computed in polynomial time; that is, if they lie in the complexity class P. In modern terms, it identifies tractable problems with the complexity class P. Formally, to say that a problem can be solved in polynomial time is to say that there exists an algorithm that, given an n-bit instance of the problem as input, can produce a solution in time O(nc), the letter O is big-O notation and c is a constant that depends on the problem but not the particular instance of the problem. Alan Cobham's 1965 paper entitled "The intrinsic computational difficulty of functions" is one of the earliest mentions of the concept of the complexity class P, consisting of problems decidable in polynomial time. Cobham theorized that this complexity class was a good way to describe the set of feasibly computable problems. Jack Edmonds's 1965 paper "Paths, trees, and flowers" is also credited with identifying P with tractable problems.
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Alternatively, if it is expected that the planar subgraph will include almost all of the edges of the given graph, leaving only a small number k of non-planar edges for the incremental planarization process, then one can solve the problem exactly by using a fixed-parameter tractable algorithm whose running time is linear in the graph size but non-polynomial in the parameter k.. The problem may also be solved exactly by a branch and cut algorithm, with no guarantees on running time, but with good performance in practice.. This parameter k is known as the skewness of the graph. There has also been some study of a related problem, finding the largest planar induced subgraph of a given graph. Again, this is NP-hard, but fixed-parameter tractable when all but a few vertices belong to the induced subgraph.. proved a tight bound of 3n/(Δ + 1) on the size of the largest planar induced subgraph, as a function of n, the number of vertices in the given graph, and Δ, its maximum degree; their proof leads to a polynomial time algorithm for finding an induced subgraph of this size..
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In algebraic geometry, a toric variety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the action of the torus on itself extends to the whole variety. Some authors also require it to be normal. Toric varieties form an important and rich class of examples in algebraic geometry, which often provide a testing ground for theorems. The geometry of a toric variety is fully determined by the combinatorics of its associated fan, which often makes computations far more tractable.
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At about this time, the surrounding areas experienced recurring fragmentation and reincorporations among a number of feudal secular and ecclesiastical lordships, a common process in the Holy Roman Empire. Alsace experienced great prosperity during the 12th and 13th centuries under Hohenstaufen emperors. Frederick I set up Alsace as a province (a procuratio, not a provincia) to be ruled by ministeriales, a non-noble class of civil servants. The idea was that such men would be more tractable and less likely to alienate the fief from the crown out of their own greed.
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Tlingit grammar at first glance appears to be highly fusional, but this is an incorrect assumption. There are predictable processes by which the basic phonetic shapes of individual morphemes are modified to fit various phonological requirements. These processes can be described with a regular language, and such descriptions are given here on a per morpheme basis by giving rule schemas for the context sensitive phonological modification of base morphemes. Analyzing all the possible combinations of morphemes and phonological contexts in Tlingit and constructing a regular language to describe them is a daunting but tractable task.
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This problem, which was considered before to be mathematically non-tractable was settled in the paper [10] by Bunimovich with Ya.G. Sinai for diffusion of mass in periodic Lorentz gas. In their previous paper was constructed the first infinite Markov partition for chaotic systems with singularities which allowed to transform this deterministic problem into probabilistic one. Then in Bunimovich's paper with H.Spohn [11] diffusion of shear and bulk viscosities in deterministic periodic fluid was rigorously derived. The paper by Bunimovich with Ya.G. Sinai [12] pioneered rigorous studies of the space-time chaos.
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In 1998, Mikkel Thorup claimed that map graphs can be recognized in polynomial time.. However, the high exponent of the algorithm that he sketched makes it impractical, and Thorup has not published the details of his method and its proof. The maximum independent set problem has a polynomial- time approximation scheme for map graphs, and the chromatic number can be approximated to within a factor of two in polynomial time.. The theory of bidimensionality leads to many other approximation algorithms and fixed- parameter tractable algorithms for optimization problems on map graphs....
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Then the satisfying instances of the resulting 2SAT formula encode solutions to the vertex cover problem, and there is a satisfying assignment with true variables if and only if there is a vertex cover with vertices. Therefore, like vertex cover, W2SAT is NP-complete. Moreover, in parameterized complexity W2SAT provides a natural W[1]-complete problem, which implies that W2SAT is not fixed-parameter tractable unless this holds for all problems in W[1]. That is, it is unlikely that there exists an algorithm for W2SAT whose running time takes the form .
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If G is an arbitrary graph, a chordal completion of G (or minimum fill-in) is a chordal graph that contains G as a subgraph. The parameterized version of minimum fill-in is fixed parameter tractable, and moreover, is solvable in parameterized subexponential time. The treewidth of G is one less than the number of vertices in a maximum clique of a chordal completion chosen to minimize this clique size. The k-trees are the graphs to which no additional edges can be added without increasing their treewidth to a number larger than k.
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Stiglitz, together with Avinash Dixit, created a tractable model of monopolistic competition that was an alternative to traditional perfect-competition models of general equilibrium. They showed that in the presence of increasing returns to scale, the entry of firms is socially too small. The model was extended to show that when consumers have a preference for diversity, entry can be socially too large. The modelling approach was also influential in the fields of trade theory, and industrial organisation, and was used by Paul Krugman in his analysis of non comparative advantage trading patterns.
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In February 2017 Pohiva survived a no-confidence motion, with his noble opponents only able to muster 10 votes in favour, against 14 in support of the government. Finance Minister ʻAisake Eke abstained and was fired. On 25 August 2017 King Tupou VI sacked Pohiva and dissolved the Assembly and called fresh elections in the hope of getting a more tractable Prime Minister. The resulting 2017 Tongan general election was a landslide for the DPFI, and Pohiva was re-elected as Prime Minister, defeating former Deputy Prime Minister Siaosi Sovaleni 14 votes to 12.
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The spacetime symmetry group for Special Relativity is the Poincaré group, which is a ten-dimensional group of three Lorentz boosts, three rotations, and four spacetime translations. It is logical to ask what symmetries if any might apply in General Relativity. A tractable case might be to consider the symmetries of spacetime as seen by observers located far away from all sources of the gravitational field. The naive expectation for asymptotically flat spacetime symmetries might be simply to extend and reproduce the symmetries of flat spacetime of special relativity, viz.
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This complicates the study of molecules interacting with high atomic mass unit atoms, such as transitional metals and their catalytic properties. Present algorithms in computational chemistry can routinely calculate the properties of small molecules that contain up to about 40 electrons with errors for energies less than a few kJ/mol. For geometries, bond lengths can be predicted within a few picometres and bond angles within 0.5 degrees. The treatment of larger molecules that contain a few dozen atoms is computationally tractable by more approximate methods such as density functional theory (DFT).
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By 21August the remnants of the battered German Seventh Army had surrendered in the Falaise Pocket, bringing the Battle of Normandy to a close. The German forces committed to Normandy since D-Day had been virtually annihilated—by the end of Operation Tractable, the 12th SS Panzer Division, the main adversary of the Canadians, had lost 80% of its tanks,D'Este, p. 432 70% of its personnel carriers, and 60% of its artillery. Shortly afterwards, the 2nd Division moved to Foret de la Londe, along the valley of the River Seine.
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Poss uses zebrafish to understand how and why tissue regeneration occurs. As a postdoc, he led the first positional cloning of a gene required for regeneration of amputated fins, and he established zebrafish as a model for innate heart regeneration. With the latter discovery, it became clear that heart regeneration occurs and is efficient in some vertebrates, and that it could be dissected using molecular genetics in a tractable model system. Since then, he and his postdocs, students, and staff have innovated many tools to interrogate tissue regeneration.
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A CIR process is a special case of a basic affine jump diffusion, which still permits a closed-form expression for bond prices. Time varying functions replacing coefficients can be introduced in the model in order to make it consistent with a pre-assigned term structure of interest rates and possibly volatilities. The most general approach is in Maghsoodi (1996). A more tractable approach is in Brigo and Mercurio (2001b) where an external time-dependent shift is added to the model for consistency with an input term structure of rates.
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The Poisson model of a cellular network proves to be more tractable than a hexagonal model. Meanwhile, this observation could be argued by the fact that a detailed and precise derivation for the channel attenuation probability distribution function between a random node and a reference base-station for a hexagonal model was explicitly derived in; and this result could be used to tractably derive the outage probability. In the presence of sufficiently strong and independent log-normal shadow fading (or shadowing) and a singular power-law attenuation function, it was observed by simulationT. X. Brown.
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Partial equilibrium analysis examines the effects of policy action in creating equilibrium only in that particular sector or market which is directly affected, ignoring its effect in any other market or industry assuming that they being small will have little impact if any. Hence, this analysis is considered to be useful in constricted markets. Léon Walras first formalised the idea of a one-period economic equilibrium of the general economic system, but it was French economist Antoine Augustin Cournot and English political economist Alfred Marshall who developed tractable models to analyse an economic system.
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Many hard computational problems on graphs have algorithms that are fixed-parameter tractable when parameterized by the tree-depth of their inputs.. Trémaux trees also play a key role in the Fraysseix–Rosenstiehl planarity criterion for testing whether a given graph is planar. According to this criterion, a graph G is planar if, for a given Trémaux tree T of G, the remaining edges can be placed in a consistent way to the left or the right of the tree, subject to constraints that prevent edges with the same placement from crossing each other.; .
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Shepard and Cooper also collaborated on a 1982 book (revised 1986) summarizing past work on mental rotation and other transformations of mental images. Reviewing that work in 1983, Michael Kubovy assessed its importance: > Up to that day in 1968 [Shepard's dream about rotating objects], mental > transformations were no more accessible to psychological experimentation > than were any other so-called private experiences. Shepard transformed a > compelling and familiar experience into an experimentally tractable problem > by injecting it into a problem-task that admits of a correct and incorrect > answer.
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Prolog uses a subset of logic (Horn clauses, closely related to "rules" and "production rules") that permit tractable computation. Rules would continue to be influential, providing a foundation for Edward Feigenbaum's expert systems and the continuing work by Allen Newell and Herbert A. Simon that would lead to Soar and their unified theories of cognition. Critics of the logical approach noted, as Dreyfus had, that human beings rarely used logic when they solved problems. Experiments by psychologists like Peter Wason, Eleanor Rosch, Amos Tversky, Daniel Kahneman and others provided proof.
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In Calcutta, they found that John Andaman recognized none of the words in the vocabulary of the Andamanese compiled by R.H. Colebrooke. He imitated well and learnt to dress (to the point that he began to be ashamed of nudity, his original state), wash and always behaved with propriety. When shown a photograph of himself, he laughed and turned it around to see if his back was seen as well. Lady Canning wrote that he was "gentle and tractable and imitates everything and is amused at everything from a glass of water upwards".
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In 1584 his elder brother Khan Mehmed II Giray refused a Turkish order to lead the Crimeans on a distant campaign to Persia. Murad III recalled Islyam and declared him the new Crimean Khan. The Sultan’s reasons were probably that Islyam was the eldest Giray after Mehmed and that his long stay in Turkey and lack of military experience would make him a tractable vassal. In May 1584 Islyam arrived at Kaffa with Turkish soldiers and was joined by his brothers Alp, Selyamet and Mubarek and most of the Crimean nobles including the Shirin clan.
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Unlike the Hungarians, whom Paul felt would never abandon their claims against Yugoslavia, the Bulgarians were felt to be more tractable. After Germany and Italy, Hungary was the nation that Paul worried about the most as he noted that Danube river valley ran down from the Hungarian plain straight to Belgrade. At the same time, Yugoslavia began staff talks with Greece with the aim of resisting an Italian invasion of either nation. A major problem for Yugoslavia was the lack of modern weapons together with the money to pay for them.
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By 21 August the remnants of the battered German Seventh Army had surrendered in the Falaise Pocket, bringing the Battle of Normandy to a close. The German forces committed to Normandy since D-Day had been virtually annihilated—by the end of Operation Tractable, the 12th SS Panzer Division, the main adversary of the Canadians, had lost 80% of its tanks,D'Este, p. 432 70% of its personnel carriers, and 60% of its artillery. Shortly afterwards, the 2nd Division moved to Foret de la Londe, along the valley of the River Seine.
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The natives of the island of Hispaniola initially approached Columbus and his soldiers with friendliness and generosity. When Columbus arrived in what is today Haiti in December 1492 and met the native Taino Arawak people, they were friendly, exchanging gifts with the Spaniards and volunteering their help. He wrote in a letter to Queen Isabella of Spain that the natives were "tractable, and easily led; they could be made to grow crops and build cities". When Columbus returned to Europe in 1493, 30 Spaniards stayed to build a fort there called La Navidad.
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During seminar presentations, modelers had to defend the existing versions of their models, sometimes quite irrationally, because of time and money considerations. Their models just could not be moved to other environments, because special programming knowledge was needed, and data formats and solution methods were not portable. The idea of an algebraic approach to represent, manipulate, and solve large-scale mathematical models fused old and new paradigms into a consistent and computationally tractable system. Using generator matrices for linear programs revealed the importance of naming rows and columns in a consistent manner.
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At about this time, the surrounding areas experienced recurring fragmentation and reincorporations among a number of feudal secular and ecclesiastical lordships, a common process in the Holy Roman Empire. Alsace experienced great prosperity during the 12th and 13th centuries under Hohenstaufen emperors. Frederick I set up Alsace as a province (a procuratio, not a provincia) to be ruled by ministeriales, a non-noble class of civil servants. The idea was that such men would be more tractable and less likely to alienate the fief from the crown out of their own greed.
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In order to overcome the problems of overrun for the two-stroke engine, a freewheel device was fitted. A 1959 review by Road & Track commented that smooth upshifts of the widely spaced 3-speed manual required revving the engine over 5000 rpm or slipping the clutch. Saab provided a retrofit kit which leaned out the fuel mixture in the carburettor, making the car more tractable at low revs but seriously impacting performance. The magazine also tried a modified GT with , which improved acceleration to from 15.2 seconds (in the GT) to 12 flat.
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Ellis, Normandy, pp. 419–24. The Canadians renewed the advance to Falaise on 14 August in Operation Tractable, with 51st (H) Division attacking towards the Liaison Valley on the left flank. By 21 August the Falaise Pocket had been closed and the division was advancing eastwards towards Lisieux.Ellis, Normandy, pp. 430–1, 449. 51st (H) Division then moved up to and across the Seine for the assault on Le Havre (Operation Astonia). This was a major operation with a massive field artillery preparation alongside support from medium guns and RAF bombers, which cowed the opposition.
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They are also variously referred to as markov random fields (in statistics and signal processing) and energy minimization problems (in physics). While weighted constraint satisfaction problems are NP-hard to solve in general, several subclasses can be solved in polynomial time when their weighted constraints exhibit specific kinds of numerical structure. Tractable subclasses can also be identified by analyzing the way constraints are placed over the variables. Specifically, a weighted constraint satisfaction problem can be solved in time exponential only in the treewidth of its variable- interaction graph (constraint network).
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Ellis, Normandy, pp. 419–24. The Canadians renewed the advance to Falaise on 14 August in Operation Tractable, with 51st (H) Division attacking towards the Liaison Valley on the left flank. By 21 August the Falaise Pocket had been closed and the division was advancing eastwards towards Lisieux.Ellis, Normandy, pp. 430–1, 449. 51st (H) Division then moved up to and across the Seine for the assault on Le Havre (Operation Astonia). This was a major operation with a massive field artillery preparation alongside support from medium guns and RAF bombers, which cowed the opposition.
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Verma was born and grew up partly in Halwara, India; her father was a pilot in the Indian Air Force. She gained her first qualification, a bachelor's degree in electrical engineering at Punjab Engineering College in Chandigarh, India. She went on to gain a masters in robotics from Carnegie Mellon University (CMU) followed by a PhD also in robotics from Carnegie Mellon in 2005, with a thesis entitled Tractable Particle Filters for Robot Fault Diagnosis. At CMU she was involved in a 3-year astrobiology experimental station in the Atacama desert.
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That is, the resulting spin operators for higher spin systems in three spatial dimensions, for arbitrarily large j, can be calculated using this spin operator and ladder operators. They can be found in Rotation group SO(3)#A note on Lie algebra. The analog formula to the above generalization of Euler's formula for Pauli matrices, the group element in terms of spin matrices, is tractable, but less simple. Also useful in the quantum mechanics of multiparticle systems, the general Pauli group is defined to consist of all -fold tensor products of Pauli matrices.
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Although in principle, they were the king's representatives and their charges could be revoked at the king's will, some governors had installed themselves and their heirs as a provincial dynasty. The governors were at the height of their power from the middle of the 16th to the middle of the 17th century, but their role in provincial unrest during the civil wars led Cardinal Richelieu to create the more tractable positions of intendants of finance, policing and justice, and in the 18th century the role of provincial governors was greatly curtailed.
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It was becoming commonplace to view consumption as based on permanent or life-cycle income instead of only current income, unemployment as dependent on inflation expectations, and business investment as dependent on expected path of sales and profits. In the financial realm, share prices were viewed as being based on expected earnings and fixed-income prices as dependent on expectations of short-term interest rates. Translating these concepts into operationally tractable measures required that the expectations formation process be specified. Meiselman articulated this in the term structure realm using an error-learning process.
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A soldier of Gloucestershire. Private G. Mills of the 2nd Battalion, 6 March 1945. In 1944, the 2nd Battalion was transferred to the 56th Independent Infantry Brigade, and at 11:00 on 6 June, during the Normandy landings, the brigade landed without incident in the second wave at Gold Beach. The battalion saw action in the Battle of Normandy: at Tilly-sur- Seulles on 11 June during Operation Perch; along the Saint-Germain d'Ectot ridge on 30 July during Operation Bluecoat; and at Thury-Harcourt on 12 August in the prelude to Operation Tractable.
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The parameter learning task in HMMs is to find, given an output sequence or a set of such sequences, the best set of state transition and emission probabilities. The task is usually to derive the maximum likelihood estimate of the parameters of the HMM given the set of output sequences. No tractable algorithm is known for solving this problem exactly, but a local maximum likelihood can be derived efficiently using the Baum–Welch algorithm or the Baldi–Chauvin algorithm. The Baum–Welch algorithm is a special case of the expectation-maximization algorithm.
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Generalized hypertree decompositions are defined like hypertree decompositions, but the last requirement is dropped; this is the condition "the variables of the constraints of a node that are not variables of the node do not occur in the subtree rooted at the node". A problem can be clearly solved in polynomial time if a fixed-width decomposition of it is given. However, the restriction to a fixed width is not known to being tractable, as the complexity of finding a decomposition of fixed width even if one is known to exist is not known, .
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Despite similar neural areas and evidence from experiments, some scholars remain cautious about comparisons to human episodic memory. Purported episodic-like memory often seems fixed to a particular domain or could be explained in terms of procedural or semantic memory. The problem may be better tractable by studying episodic memory's adaptive counterpart: the capacity to flexibly imagine future events. However, a recent experiment addressed one of Suddendorf and Busby (2003)'s specific criticisms (the Bischof-Köhler hypothesis, which states that nonhuman animals can only take actions based on immediate needs, as opposed to future needs).
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The border cells of the fruit fly Drosophila melanogaster are a cluster of 6–8 migratory cells found in the fly's ovary and derived from the follicular epithelium. Studying cell migration is important from the point of view of metastasis, and for this reason, several model organisms are used to determine what molecules are important in initiating, maintaining and guiding moving cells. Drosophila melanogaster is one of the favorite organisms for studying biological phenomena. The border cells of the Drosophila ovary are a genetically tractable system for studying diverse aspects of moving phenotype.
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In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class. It contains all decision problems that can be solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time. Cobham's thesis holds that P is the class of computational problems that are "efficiently solvable" or "tractable". This is inexact: in practice, some problems not known to be in P have practical solutions, and some that are in P do not, but this is a useful rule of thumb.
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In the 1936 reorganization of the Militia, the Weyburn Regiment and the Saskatchewan Border Regiment (in Estevan) re-amalgamated into a new South Saskatchewan Regiment. During the Second World War, The South Saskatchewan Regiment participated in many major Canadian battles and operations, as part of the 2nd Canadian Infantry Division. The South Saskatchewan Regiment fought in the Dieppe Raid of 1942, Operation Atlantic, Operation Spring, Operation Totalize, Operation Tractable, and the recapture of Dieppe in 1944. They, along with the 8th Reconnaissance Regiment liberated the Westerbork transit camp on 12 April 1945.
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Partial equilibrium analysis examines the effects of policy action in creating equilibrium only in that particular sector or market which is directly affected, ignoring its effect in any other market or industry assuming that they being small will have little impact if any. Hence this analysis is considered to be useful in constricted markets. Léon Walras first formalized the idea of a one-period economic equilibrium of the general economic system, but it was French economist Antoine Augustin Cournot and English political economist Alfred Marshall who developed tractable models to analyze an economic system.
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His research is in the area of knowledge representation and reasoning in artificial intelligence. On the representation side, he has worked on the formalization of a number of concepts pertaining to artificial and natural agents including belief, goals, intentions, ability, and the interaction between knowledge, perception and action. On the reasoning side, his research mainly concerns how automated reasoning can be kept computationally tractable, including the use of greedy local search methods. Hector Levesque has published over 60 research papers, and is the co-author of two books.
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The same result holds for a discrete-time stationary process, with the spectral measure now defined on the unit circle. When processing WSS random signals with linear, time-invariant (LTI) filters, it is helpful to think of the correlation function as a linear operator. Since it is a circulant operator (depends only on the difference between the two arguments), its eigenfunctions are the Fourier complex exponentials. Additionally, since the eigenfunctions of LTI operators are also complex exponentials, LTI processing of WSS random signals is highly tractable—all computations can be performed in the frequency domain.
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Or when his commanders sent him messages of victory, he would hide the messenger and bring out the white fawn wearing celebratory garlands. He would sacrifice to the gods, and tell his men to celebrate because they would soon hear something good had happened. By such stratagems he persuaded his people they were not by the fallible wisdom of some foreigner, but by divine power. So the people were made tractable and all the more ready to help him with his plans, and consequently the extraordinary growth of Sertorius's power led to reinforcing this belief.
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Dantzig's core insight was to realize that most such ground rules can be translated into a linear objective function that needs to be maximized. Development of the simplex method was evolutionary and happened over a period of about a year. After Dantzig included an objective function as part of his formulation during mid-1947, the problem was mathematically more tractable. Dantzig realized that one of the unsolved problems that he had mistaken as homework in his professor Jerzy Neyman's class (and actually later solved), was applicable to finding an algorithm for linear programs.
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The spacetime symmetry group for Special Relativity is the Poincaré group, which is a ten-dimensional group of three Lorentz boosts, three rotations, and four spacetime translations. It is logical to ask what symmetries if any might apply in General Relativity. A tractable case may be to consider the symmetries of spacetime as seen by observers located far away from all sources of the gravitational field. The naive expectation for asymptotically flat spacetime symmetries might be simply to extend and reproduce the symmetries of flat spacetime of special relativity, viz.
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Characterizations of 4-leaf powers are given by and , which also enable linear time recognition. Recognition of the 5-leaf and 6-leaf power graphs are also solved in linear time by Chang and Ko (2007) and Ducoffe (2018), respectively. For k ≥ 7 the recognition problem of k-leaf powers is open, and likewise, it is an open problem whether leaf powers can be recognized in polynomial time. However, it has been proved that recognizing k-leaf powers is fixed-parameter tractable when parameterized by k and the degeneracy of the input graph.
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On arbitrary graphs, or even planar graphs, computing the matching polynomial is #P-complete . However, it can be computed more efficiently when additional structure about the graph is known. In particular, computing the matching polynomial on n-vertex graphs of treewidth k is fixed-parameter tractable: there exists an algorithm whose running time, for any fixed constant k, is a polynomial in n with an exponent that does not depend on k . The matching polynomial of a graph with n vertices and clique-width k may be computed in time nO(k) .
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Constraint satisfaction problems composed of binary constraints only can be viewed as graphs, where the vertices are variables and the edges represent the presence of a constraint between two variables. This graph is called the Gaifman graph or primal constraint graph (or simply primal graph) of the problem. If the primal graph of a problem is acyclic, establishing satisfiability of the problem is a tractable problem. This is a structural restriction, as it can be checked by looking only at the scopes of the constraints, disregarding their relations and the domain.
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Partial equilibrium analysis examines the effects of policy action in creating equilibrium only in that particular sector or market which is directly affected, ignoring its effect in any other market or industry assuming that they being small will have little impact if any; hence, this analysis is considered to be useful in constricted markets. Léon Walras first formalized the idea of a one-period economic equilibrium of the general economic system, but it was French economist Antoine Augustin Cournot and English political economist Alfred Marshall who developed tractable models to analyze an economic system.
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In matroid theory, a mathematical discipline, the girth of a matroid is the size of its smallest circuit or dependent set. The cogirth of a matroid is the girth of its dual matroid. Matroid girth generalizes the notion of the shortest cycle in a graph, the edge connectivity of a graph, Hall sets in bipartite graphs, even sets in families of sets, and general position of point sets. It is hard to compute, but fixed-parameter tractable for linear matroids when parameterized both by the matroid rank and the field size of a linear representation.
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In computational statistics, the pseudo-marginal Metropolis–Hastings algorithm is a Monte Carlo method to sample from a probability distribution. It is an instance of the popular Metropolis–Hastings algorithm that extends its use to cases where the target density is not available analytically. It relies on the fact that the Metropolis–Hastings algorithm can still sample from the correct target distribution if the target density in the acceptance ratio is replaced by an estimate. It is especially popular in Bayesian statistics, where it is applied if the likelihood function is not tractable (see example below).
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Three-dimensional model typically are unmanageable or demand huge computational efforts when applied to natural-scale geophysical mass flows, which can involve masses as large as 10^6 to 10^{13} {m}^3. One way to make the problem more tractable is to assume that flows are long (or wide) relative to their depth, and to use depth-averaging in the direction normal to the sliding surface. This dramatically reduces the complexity associated with the flow from three-dimension to virtually shallow flow so that the computational cost is very low. This is achieved by using the concept of factorization of the mean.
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A typical game that has been solved this way is Hex. A related field of study, drawing from computational complexity theory, is game complexity, which is concerned with estimating the computational difficulty of finding optimal strategies. Research in artificial intelligence has addressed both perfect and imperfect information games that have very complex combinatorial structures (like chess, go, or backgammon) for which no provable optimal strategies have been found. The practical solutions involve computational heuristics, like alpha–beta pruning or use of artificial neural networks trained by reinforcement learning, which make games more tractable in computing practice.
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Telegony held that a female with a history of mating with multiple males would pass on genetic qualities of all previous partners to her offspring. Ewart later bred the mare which had produced zebra-horse hybrids with a pony, and the offspring showed no zebra qualities in either markings or temperament. Ewart's goal was also to produce a draught animal for South African conditions, resistant to African diseases and more tractable than a mule. In 1883 he commissioned George Washington Browne to design a grand new house in Penicuik, finished in 1885, which is where he died on New Year's Eve 1933/34.
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Major General Rod Keller was removed from his command of the 3rd Canadian Infantry Division, after having been badly wounded when his headquarters were hit by American bombs. Keller's poor performance in Totalize lost him the confidence of General Crerar and he received no further command positions for the remainder of the war. Simonds and Crerar mounted a follow-up offensive, Operation Tractable, which took place between 14 and 21 August. On 21 August, the Falaise Pocket was closed when Canadian and Polish units made contact with US troops to the south, ending Commonwealth participation in the Battle of Normandy.
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Kümmel comments: > Considering the fact that the CC method was well understood around the late > fifties[,] it looks strange that nothing happened with it until 1966, as > Jiří Čížek published his first paper on a quantum chemistry problem. He had > looked into the 1957 and 1960 papers published in Nuclear Physics by Fritz > and myself. I always found it quite remarkable that a quantum chemist would > open an issue of a nuclear physics journal. I myself at the time had almost > given up the CC method as not tractable and, of course, I never looked into > the quantum chemistry journals.
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The V12 was detuned to from the Daytona, to provide a more tractable response suited to a GT-oriented Ferrari. In place of the Daytona's downdraft setup, six twin-choke side-draft Weber carburetors were used, whose lower profile made possible the car's lower and sloping hood line.365 GTC/4 engine bay The 5-speed all-synchronised manual transmission was bolted to the engine, another difference from the Daytona which used a transaxle. However the set back placement of the engine and transmission still allowed the car to achieve a near perfect 51:49 weight distribution.
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Using human manufacturing processes, wheeled systems of varying complexity have proven fairly simple to construct, and issues of power transmission and friction have proven tractable. It is not clear, however, that the vastly different processes of embryonic development are suited to—or even capable of—producing a functioning wheel, for reasons described below. The greatest anatomical impediment to wheeled multicellular organisms is the interface between the static and rotating components of the wheel. In either a passive or driven case, the wheel (and possibly axle) must be able to rotate freely relative to the rest of the machine or organism.
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Unrevealed to the crew, the Angels (who are the ship's control computers; their name being an acronym of ANcillary Guardian of Environment and Life ) have their own agenda. They desire absolute control and mastery over any colony resulting from the mission. To this end, they covertly engineered the apparent accident which killed the second-generation crew (who would otherwise have ended the mission before the Angels wanted it to end) and have kept the third-generation crew sexually immature and innocent via drugs and disinformation in order to keep them more tractable. However, their machinations have begun to backfire already.
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The Church of Boyd's adoption, which had given Andrew Melville a chair in one university, and Sharp a chair in another, was not slow to do honour to their brilliant countryman. He was made a professor in the protestant Academy of Saumur; and there for some years he taught theology. He was persuaded, however, in 1614 to come home and accept the Principalship of the Glasgow University. Though he was far from extreme in his Presbyterianism, he was found to be less tractable than the king and his advisers expected, and was obliged to resign his office.
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Approximate polynomial-time algorithms for structural alignment that produce a family of "optimal" solutions within an approximation parameter for a given scoring function have been developed. Although these algorithms theoretically classify the approximate protein structure alignment problem as "tractable", they are still computationally too expensive for large-scale protein structure analysis. As a consequence, practical algorithms that converge to the global solutions of the alignment, given a scoring function, do not exist. Most algorithms are, therefore, heuristic, but algorithms that guarantee the convergence to at least local maximizers of the scoring functions, and are practical, have been developed.
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37, available here a Also the next Iturmendi's assignment kept him busy in Bilbao. In August 1938 the Nationalist Ministry of Interior appointed the 3rd municipal administration, headed by José Lequerica; in a trademark Francoist move of balancing various political groupings, as a tractable Carlist Iturmendi was nominated primero teniente de alcalde, de facto the deputy mayor of the city.Iturmendi Bañales, Antonio entry, [in:] Auñamendi Eusko Entziklopedia service, available here He became president of the Economic and Budgetary CommissionJoseba Agirreazkuenaga, Mikel Urquijo (eds.), Bilbao desde sus alcaldes: Diccionario biográfico de los alcaldes de Bilbao y gestión municipal en la Dictadura vol.
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This approximation approaches continuum QCD as the spacing between lattice sites is reduced to zero. Because the computational cost of numerical simulations can increase dramatically as the lattice spacing decreases, results are often extrapolated to a = 0 by repeated calculations at different lattice spacings a that are large enough to be tractable. Numerical lattice QCD calculations using Monte Carlo methods can be extremely computationally intensive, requiring the use of the largest available supercomputers. To reduce the computational burden, the so-called quenched approximation can be used, in which the quark fields are treated as non-dynamic "frozen" variables.
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Finding a dominating set of size k plays a central role in the theory of parameterized complexity. It is the most well- known problem complete for the class W[2] and used in many reductions to show intractability of other problems. In particular, the problem is not fixed- parameter tractable in the sense that no algorithm with running time f(k)nO(1) for any function f exists unless the W-hierarchy collapses to FPT=W[2]. On the other hand, if the input graph is planar, the problem remains NP-hard, but a fixed-parameter algorithm is known.
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When the cake is 1-dimensional and the pieces must be connected, the simple algorithm of assigning each piece to the agent that values it the most no longer works, even when the pieces are piecewise-constant. In this case, the problem of finding a UM division is NP-hard, and furthermore no FPTAS is possible unless P=NP. There is an 8-factor approximation algorithm, and a fixed-parameter tractable algorithm which is exponential in the number of players. For every set of positive weights, a WUM division exists and can be found in a similar way.
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P450 BM3 (also known as CYP102A1) is a cytochrome P450 enzyme isolated from Bacillus megaterium. BM3 has been extensively studied in the context of enzyme engineering due to its solubility, tractable bacterial isoforms and self-sufficient electron transport system, but also due to its synthetic utility. Engineering studies have revealed that BM3 mutants can 1) be endowed with new and differentiated substrate scopes 2) exhibit regio-/stereoselectivity on new substrates and 3) be engineered to be highly selective and active towards new substrates. BM3 variants have been particularly useful to produce fragrances, flavors, pheromones and pharmaceuticals.
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In order to make this have few enough points to be tractable to calculation in a reasonable time, special coordinate systems can be used such as Boyer- Lindquist coordinates or fish-eye coordinates. Numerical relativity techniques steadily improved from the initial attempts in the 1960s and 1970s. Long-term simulations of orbiting black holes, however, were not possible until three groups independently developed groundbreaking new methods to model the inspiral, merger, and ringdown of binary black holes in 2005. In the full calculations of an entire merger, several of the above methods can be used together.
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When there are no uncertainties in the constraints, it reduces to a constrained utility-maximization problem. (This second equivalence arises because the utility of a function can always be written as the probability of that function exceeding some random variable.) Because it changes the constrained optimization problem associated with reliability-based optimization into an unconstrained optimization problem, it often leads to computationally more tractable problem formulations. In the marketing field there is a huge literature about optimal design for multiattribute products and services, based on experimental analysis to estimate models of consumers' utility functions. These methods are known as Conjoint Analysis.
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The S7 debuted on August 19, 2000 at the Monterey Historic Races. The all-aluminium engine is a proprietary unit developed and built in house, it is a bored-and-stroked derivative of Ford's 351 Windsor small block architecture with Cleveland-style canted valve heads which have been extensively reworked and modified. Having a large displacement of 427 cubic inches the engine is based on and has been developed around the more compact and lighter small-block architecture and is in fact not based on the FE big-block. It proved remarkably tractable and flexible for a high-output requirement— at 6,400 rpm.
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An early structural restriction (that later evolved into that based on induced width) is based on the width of the primal graph of the problem. Given an ordering of the nodes of the graph, the width of a node is the number of nodes that join it and precede it in the order. However, restricting only the width does not lead to a tractable restriction: even restricting this width to 4, establishing satisfiability remains NP- complete. Tractability is obtained by restricting the relations; in particular, if a problem has width k and is strongly k-consistent, it is efficiently solvable.
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If is an arbitrary graph, an interval completion of is an interval graph on the same vertex set that contains as a subgraph. The parameterized version of interval completion (find an interval supergraph with additional edges) is fixed parameter tractable, and moreover, is solvable in parameterized subexponential time. The pathwidth of an interval graph is one less than the size of its maximum clique (or equivalently, one less than its chromatic number), and the pathwidth of any graph G is the same as the smallest pathwidth of an interval graph that contains G as a subgraph..
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During the 19th century, when the road system was modernized, most industrial development moved to the outskirts of the town. During the 20th century, the arrival of new industries continued the outward expansion of Bernay, which now includes the slopes overlooking the historical city centre, which has maintained many of its original buildings. In August 1944, during World War II, the First Canadian Army advanced east towards the Seine following the successful Operation Tractable. The Canadians liberated Bernay, which escaped damage from the Canadian bombardment of the area thanks to a thick layer of cloud, thus preserving the historical city centre.
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However, a two-stage quincunx was constructed by Francis Galton in the late 1800s that can be seen as a physical implementation of an ABC-rejection scheme for a single unknown (parameter) and a single observation.see figure 5 in Another prescient point was made by Rubin when he argued that in Bayesian inference, applied statisticians should not settle for analytically tractable models only, but instead consider computational methods that allow them to estimate the posterior distribution of interest. This way, a wider range of models can be considered. These arguments are particularly relevant in the context of ABC.
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Testing whether the Hadwiger number of a given graph is at least a given value k is NP-complete, from which it follows that determining the Hadwiger number is NP-hard. However, the problem is fixed-parameter tractable: there is an algorithm for finding the largest clique minor in an amount of time that depends only polynomially on the size of the graph, but exponentially in h(G). Additionally, polynomial time algorithms can approximate the Hadwiger number significantly more accurately than the best polynomial-time approximation (assuming P ≠ NP) to the size of the largest complete subgraph.
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Traditionally, enhancers were identified by enhancer trap techniques using a reporter gene or by comparative sequence analysis and computational genomics. In genetically tractable models such as the fruit fly Drosophila melanogaster, for example, a reporter construct such as the lacZ gene can be randomly integrated into the genome using a P element transposon. If the reporter gene integrates near an enhancer, its expression will reflect the expression pattern driven by that enhancer. Thus, staining the flies for LacZ expression or activity and cloning the sequence surrounding the integration site allows the identification of the enhancer sequence.
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The orchestra would play calming music so captives who did not know they were about to die would be more tractable. In December 2019 The New York Times published an article on a previously undocumented aspect of her life in Auschwitz - 25 year old Tichauer had taken a 17 year old lover in Auschwitz, David Wisnia. The pair had been able to engage in monthly liaisons, and had planned to meet, and marry, if they should survive the war. However, they lost track of one another, for several years, and, when they had news of one another, they were both married.
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The MIT economists were thus growthmen in two senses: in seeing growth as an absolutely central policy imperative and in seeing the theory of growth as a focus for economic research. What the MIT growthmen added was a distinctive style of analysis that made it easier to address the dominant policy concerns in tractable formal models. Solow's (1956) model was the perfect exemplar of the MIT style. It provided the central framework for the subsequent developments in growth theory and secured MIT as the center of the universe in the golden age of growth theory in the 1960s (Boianovsky and Hoover 199–200).
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2005 DARPA Grand Challenge winner STANLEY performed SLAM as part of its autonomous driving system A map generated by a SLAM Robot. In computational geometry and robotics, simultaneous localization and mapping (SLAM) is the computational problem of constructing or updating a map of an unknown environment while simultaneously keeping track of an agent's location within it. While this initially appears to be a chicken-and-egg problem there are several algorithms known for solving it, at least approximately, in tractable time for certain environments. Popular approximate solution methods include the particle filter, extended Kalman filter, Covariance intersection, and GraphSLAM.
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By the late 18th century, slaves were increasingly "country born," that is, native to the United States. They were generally considered more tractable than newly enslaved Africans. Connections of kinship and personal relations extended between slaves in the city of Charleston and those on plantations in the Lowcountry, just as those connections existed among the planter class, many of whom had residences (and domestic slaves) in both places. From 1791 to 1803 the Haitian Revolution of slaves and free people of color on Saint-Domingue had embroiled the French colony in violence; blacks gained independence and created the republic of Haiti in 1804.
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In the illustration, every odd cycle in the graph contains the blue (the bottommost) vertices, so removing those vertices kills all odd cycles and leaves a bipartite graph. The edge bipartization problem is the algorithmic problem of deleting as few edges as possible to make a graph bipartite and is also an important problem in graph modification algorithmics. This problem is also fixed-parameter tractable, and can be solved in time O\left(2^k m^2\right), where k is the number of edges to delete and m is the number of edges in the input graph.
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In 1765 a bill was proposed to prevent the importation of Coromantees but was not passed. Edward Long, an anti- Coromantee writer, states: > Such a bill, if passed into law would have struck at very root of evil. No > more Coromantins would have been brought to infest this country, but instead > of their savage race, the island would have been supplied with Blacks of a > more docile tractable disposition and better inclined to peace and > agriculture. Colonists later devised ways of separating Coromantins from each other, by housing them separately, placing them with other slaves, and stricter monitoring of activities.
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His dilemma was like that of Wheelwright, but the difference between the two men was not in their doctrines but in their personalities. Wheelwright was contentious and outspoken, while Cotton was mild and tractable. It was Wheelwright's nature to separate from those who disdained him; it was Cotton's nature to make peace without compromising his essential principles, according to the views of some modern historians. Former Boston magistrate and Hutchinson supporter William Coddington was not happy about the trials, and he began making plans for his own future in consultation with others affected by the Court's decisions.
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If Ladner languages were not expressible in this way, the set of all constraint languages could be divided exactly into those defining polynomial-time and those defining NP-complete problems; that is, this set would exhibit a dichotomy. Partial results are known for some sets of constraint languages. The best known such result is Schaefer's dichotomy theorem, which proves the existence of a dichotomy in the set of constraint languages on a binary domain. More precisely, it proves that a relation restriction on a binary domain is tractable if all its relations belong to one of six classes, and is NP-complete otherwise.
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In the area of artificial intelligence, he is best known for his influential early work on the complexity of nonmonotonic logics and on (generalised) hypertree decompositions, a framework for obtaining tractable structural classes of constraint satisfaction problems, and a generalisation of the notion of tree decomposition from graph theory. This work has also had substantial impact in database theory, since it is known that the problem of evaluating conjunctive queries on relational databases is equivalent to the constraint satisfaction problem. His recent work on XML query languages (notably XPath) has helped create the complexity-theoretical foundations of this area.
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Pathwidth is fixed-parameter tractable: for any constant k, it is possible to test whether the pathwidth is at most k, and if so to find a path-decomposition of width k, in linear time. In general, these algorithms operate in two phases. In the first phase, the assumption that the graph has pathwidth k is used to find a path-decomposition or tree-decomposition that is not optimal, but whose width can be bounded as a function of k. In the second phase, a dynamic programming algorithm is applied to this decomposition in order to find the optimal decomposition.
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For the crew's exercise and entertainment, he introduced regular music and dancing sessions. Bligh's despatches to Campbell and Banks indicated his satisfaction; he had no occasion to administer punishment because, he wrote: "Both men and officers tractable and well disposed, & cheerfulness & content in the countenance of every one". The only adverse feature of the voyage to date, according to Bligh, was the conduct of the surgeon Huggan, who was revealed as an indolent, unhygienic drunkard. From the start of the voyage, Bligh had established warm relations with Christian, according him a status which implied that he was Bligh's second-in-command rather than Fryer.
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One of his most prominent early contributions has been the "Golden Eggs and Hyperbolic Discounting" 1997 paper in QJE where he studied the intertemporal behavior of a time-inconsistent consumer. This work provides a tractable model for self-control problems, in which agents have difficulty sticking to their long-term goals. Agents in Professor Laibson's models generally value "commitment devices," such as 401(k) plans or housing equity, that let them accumulate assets without as much temptation to splurge. These models also explain the "debt puzzle," the idea that American consumers demonstrate both short-run impatience and long-run patience in their lifecycle savings decisions.
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Xammar talked to president Companys about breaking the Anarchist domination in the region. He also demanded that EC people get nominated to high positions in the Generalitat security; Companys did not seem interested. The second-in-command person in the autonomous Catalan structures, the prime minister and the parliament speaker Joan Casanovas, was more tractable; the EC member in the 1920s, later he remained in the ERC mainstream. He started to voice publicly about the need to reinforce the state and assume responsibility for bold action,Josep María Pascual, Un complot desconocido, [in:] Enric Ucelay-Da Cal, Arnau González i Vilalta (ed.), Contra Companys, 1936.
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An important theoretical goal is thus to find an initial approximation to QCD which is both analytically tractable and which can be systematically improved. To address this problem, the light front holography approach maps a confining gauge theory quantized on the light front to a higher-dimensional anti-de Sitter space (AdS) incorporating the AdS/CFT correspondence as a useful guide. The AdS/CFT correspondence is an example of the holographic principle, since it relates gravitation in a five-dimensional AdS space to a conformal quantum field theory at its four-dimensional space- time boundary. Light front quantization was introduced by Paul Dirac to solve relativistic quantum field theories.
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Fractons were originally studied as an analytically tractable realization of quantum glassiness where the immobility of isolated fractons results in a slow relaxation rate . This immobility has also been shown to be capable of producing a partially self-correcting quantum memory, which could be useful for making an analog of a hard drive for a quantum computer . Fractons have also been shown to appear in quantum linearized gravity models and (via a duality) as disclination crystal defects . However, aside from the duality to crystal defects, and although it has been shown to be possible in principle , other experimental realizations of fractons have not yet been realized.
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A conclusion that one can draw is that the neural areas responsible for planning or carrying out certain actions are also responsible for deciding the action to carry out, a decidedly embodied notion. Mathematically, the spike activation pattern, as well as the choice and response time distributions, can be well described by what are known as diffusion models—especially in two-alternative forced choice tasks.For a summary, see Diffusion models, such as the decision field theory, can be viewed as stochastic recurrent neural network models, except that the dynamics are approximated by linear systems. The linear approximation is important for maintaining a mathematically tractable analysis of systems perturbed by noisy inputs.
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Most optical design software has functionality to compute the optical or modulation transfer function of a lens design. Ideal systems such as in the examples here are readily calculated numerically using software such as Julia, GNU Octave or Matlab, and in some specific cases even analytically. The optical transfer function can be calculated following two approaches: # as the Fourier transform of the incoherent point spread function, or # as the auto-correlation of the pupil function of the optical system Mathematically both approaches are equivalent. Numeric calculations are typically most efficiently done via the Fourier transform; however, analytic calculation may be more tractable using the auto-correlation approach.
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"It may seem inapposite that Hazlitt's panorama of the Zeitgeist should end with glimpses of a crotchety bibliophile indulging in an eccentric taste for literary antiquities at a bookstall in an alley off Fleet Street," Kinnaird muses. "But precisely this contrast with the public world of political London serves to make Hazlitt's critical point. The figure of Elia represents in the symbolic landscape of the age those least tractable but deeply natural 'infirmities' of man which, ignored by, when not wholly invisible to, the humorless self-abstraction of modern pride, will never be made to yield to 'the progress of intellectual refinement.'"Kinnaird 1978, p. 323.
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The longest path problem is fixed-parameter tractable when parameterized by the length of the path. For instance, it can be solved in time linear in the size of the input graph (but exponential in the length of the path), by an algorithm that performs the following steps: # Perform a depth-first search of the graph. Let d be the depth of the resulting depth-first search tree. # Use the sequence of root-to- leaf paths of the depth-first search tree, in the order in which they were traversed by the search, to construct a path decomposition of the graph, with pathwidth d.
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It is straightforward to express the monochromatic triangle problem in the monadic second-order logic of graphs (MSO2), by a logical formula that asserts the existence of a partition of the edges into two subsets such that there do not exist three mutually adjacent vertices whose edges all belong to the same side of the partition. It follows from Courcelle's theorem that the monochromatic triangle problem is fixed-parameter tractable on graphs of bounded treewidth. More precisely, there is an algorithm for solving the problem whose running time is the number of vertices of the input graph multiplied by a quickly-growing but computable function of the treewidth..
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Unlike RF band detection, optical frequencies oscillate too rapidly to directly measure and process the electric field electronically. Instead optical photons are (usually) detected by absorbing the photon's energy, thus only revealing the magnitude, and not by following the electric field phase. Hence the primary purpose of heterodyne mixing is to down shift the signal from the optical band to an electronically tractable frequency range. In RF band detection, typically, the electromagnetic field drives oscillatory motion of electrons in an antenna; the captured EMF is subsequently electronically mixed with a local oscillator (LO) by any convenient non-linear circuit element with a quadratic term (most commonly a rectifier).
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Because of the incredible complexity of mammalian systems, yeast are often used as a model organism for working out new pathways. These single-celled organisms are often more genetically tractable than mammalian cells, and strain libraries are available to supply strains harboring almost any non-lethal open reading frame single deletion. The two most commonly used yeasts are Saccharomyces cerevisiae and Schizosaccharomyces pombe, although research is also done in the pathogenic yeast Candida albicans. In addition to the important structural functions of complex sphingolipids (inositol phosphorylceramide and its mannosylated derivatives), the sphingoid bases phytosphingosine and dihydrosphingosine (sphinganine) play vital signaling roles in S. cerevisiae.
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The problem of finding the graph genus is NP-hard (the problem of determining whether an n-vertex graph has genus g is NP-complete). At the same time, the graph genus problem is fixed-parameter tractable, i.e., polynomial time algorithms are known to check whether a graph can be embedded into a surface of a given fixed genus as well as to find the embedding. The first breakthrough in this respect happened in 1979, when algorithms of time complexity O(nO(g)) were independently submitted to the Annual ACM Symposium on Theory of Computing: one by I. Filotti and G.L. Miller and another one by John Reif.
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Operation Cobra began on the same day by coordination and the German high command was unsure which was the main operation. Operation Spring was taken to be the main effort for about two days, because of the importance they gave to holding ground south of Caen, before realising that Cobra was the principal effort and transferred troops westwards. Operation Totalize and Operation Tractable were launched in August and captured more ground against less opposition. The Official History of the Canadian Army, refers to Spring as a "holding attack" in that it was launched with offensive objectives but also firmly with the intent to delay the redeployment of forces westward.
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Kalantiaw, the Hoax Scott's first well known academic work is The Discovery of the Igorots.Scott, William Henry (1974) This is a history of the Cordillera mountain region over several centuries of Spanish contact, constructed from contemporary Spanish sources. Scott argues that the difficulties the Spaniards encountered extending their rule in the face of local resistance resulted in the inhabitants of the region being classified as a 'savage' race separate to the more tractable lowland Filipinos. Scott adopted a similar approach in Cracks in the Parchment Curtain Scott, William Henry (1982) in which he tries to glean a picture of pre-colonial Philippine society from early Spanish sources.
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25 (3): 219 - Journal of Information Science Tools are sometimes needed to make the publishing of link-rich web sites tractable, and many people may lack the technical skills, time, or inclination to engage in hand- crafting new digital document forms.From documents to discourse A link-rich site that is low on content is sometimes referred to as a "gateway site."Project MUSE - American Periodicals: A Journal of History, Criticism, and Bibliography - Review Essay: The Digital Archives Link-rich portals were popular on the Web in 2000. Yahoo! and other sites featuring categories with many links were heavily used and often required fewer than three clicks to reach the content.
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A minor-closed family of graphs that has an apex graph as one of its forbidden minors is known as apex-minor-free. With this terminology, the connection between apex graphs and local treewidth can be restated as the fact that apex-minor-free graph families are the same as minor-closed graph families with bounded local treewidth. The concept of bounded local treewidth forms the basis of the theory of bidimensionality, and allows for many algorithmic problems on apex-minor-free graphs to be solved exactly by a polynomial-time algorithm or a fixed-parameter tractable algorithm, or approximated using a polynomial-time approximation scheme.; ; .
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The property of the GAL1-GAL10 to bind the GAL4 protein is utilised in the GAL4/UAS technique for controlled gene mis-expression in Drosophila. This is the most popular form of binary expression in Drosophila melanogaster, a system which has been adapted for many uses to make Drosophila melanogaster one of the most genetically tractable multicellular organisms. In this technique, four related binding sites between the GAL10 and GAL1 loci in Saccharomyces cerevisiae serve as an Upstream Activating Sequences (UAS) element through GAL4 binding. Several studies have been conducted with Saccharomyces cerevisiae to explore the exact function of upstream activation sequences, often focusing on the aforementioned GAL1-GAL10 intergenic region.
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Due to the critical importance of finding neurotoxins in common environments, specific protocols have been developed by the United States Environmental Protection Agency (EPA) for testing and determining neurotoxic effects of compounds (USEPA 1998). Additionally, in vitro systems have increased in use as they provide significant improvements over the more common in vivo systems of the past. Examples of improvements include tractable, uniform environments, and the elimination of contaminating effects of systemic metabolism. In vitro systems, however, have presented problems as it has been difficult to properly replicate the complexities of the nervous system, such as the interactions between supporting astrocytes and neurons in creating the BBB.
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The application of these theories emerged in Kiyotaki and Wright (1993), when the authors developed a tractable model of the exchange process that captures the "double coincidence of wants problem" in a pure barter setup. In this model, the essential function of money is its role as a medium of exchange. The model can be used to address issues in monetary economics, such as the interaction between specialization and monetary exchange, and the possibility of equilibria with multiple fiat currencies. A shortcoming of search-theoretic models of money is that these models becomes intractable without very strong assumptions, and are therefore impractical for the analysis of monetary policy.
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Grand Challenges are difficult but important problems set by various institutions or professions to encourage solutions or advocate for the application of government or philanthropic funds especially in the most highly developed economies Gould, M. "GIScience grand challenges: How can research and technology in this field address big-picture problems? ArcUser, 13 (4), 64–65." (2010). Accessed at and Grand challenges are more than ordinary research questions or priorities, they are end results or outcomes that are global in scale; very difficult to accomplish, yet offer hope of being ultimately tractable; demand an extensive number of research projects across many technical and non-technical disciplines and accompanied by well-defined metrics.
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Other examples of EXPTIME- complete problems include the problem of evaluating a position in generalized chess, checkers, or Go (with Japanese ko rules). These games have a chance of being EXPTIME-complete because games can last for a number of moves that is exponential in the size of the board. In the Go example, the Japanese ko rule is sufficiently intractable to imply EXPTIME-completeness, but it is not known if the more tractable American or Chinese rules for the game are EXPTIME- complete. By contrast, generalized games that can last for a number of moves that is polynomial in the size of the board are often PSPACE-complete.
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Even after these victories, Sommer did not believe Stump would win the top prize. On February 10, 2009, Stump was named Best in Show, in part because judges felt he had a "cheerful and tractable disposition" in keeping with the breed's standard. Among the finalists Stump defeated were Spirit, a Giant Schnauzer who was ranked the No. 1 show dog in the nation at the time, and Lincoln, a Griffon Bruxellois who was also widely considered a favorite. Other group winners Stump defeated for the top prize included Yes, a standard poodle with 94 Best in Show wins; Sadie, a Scottish terrier; Tiger Woods, a Scottish deerhound; and Conrad, a Puli.
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Tijms et al. believe it is "not likely that computationally tractable methods can be developed to compute the exact numerical values of the steady-state probability in the M/G/k queue." Various approximations for the average queue size, stationary distribution and approximation by a reflected Brownian motion have been offered by different authors. Recently a new approximate approach based on Laplace transform for steady state probabilities has been proposed by Hamzeh Khazaei et al.. This new approach is yet accurate enough in cases of large number of servers and when the distribution of service time has a Coefficient of variation more than one.
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By confining themselves to limiting cases in which sellers or buyers are both "price takers" – so that demand functions ignore supply functions or vice versa – Marshallian marginalists and neoclassical economists produced tractable models of "pure" or "perfect" competition and of various forms of "imperfect" competition, which models are usually captured by relatively simple graphs. Other marginalists have sought to present what they thought of as more realistic explanations,Mund, Vernon Arthur; Monopoly: A History and Theory (1933).Mises, Ludwig Heinrich Edler von; Nationalökonomie: Theorie des Handelns und Wirtschaftens (1940). (See also his Human Action.) but this work has been relatively uninfluential on the mainstream of economic thought.
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Floer homology is the homology of this chain complex. The gradient flow line equation, in a situation where Floer's ideas can be successfully applied, is typically a geometrically meaningful and analytically tractable equation. For symplectic Floer homology, the gradient flow equation for a path in the loopspace is (a perturbed version of) the Cauchy–Riemann equation for a map of a cylinder (the total space of the path of loops) to the symplectic manifold of interest; solutions are known as pseudoholomorphic curves. The Gromov compactness theorem is then used to show that the differential is well-defined and squares to zero, so that the Floer homology is defined.
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In addition, phylogenetic methods rely on explicit models of sequence evolution, which provide a well- understood framework for parameter inference, hypothesis testing, and model selection. This is reflected in the literature, which tends to favour phylogenetic methods as the standard of proof for HGT. The use of phylogenetic methods thus appears to be the preferred standard, especially given that the increase in computational power coupled with algorithmic improvements has made them more tractable, and that the ever denser sampling of genomes lends more power to these tests. Considering phylogenetic methods, several approaches to validating individual HGT inferences and benchmarking methods have been adopted, typically relying on various forms of simulation.
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Probabilistic voting models are usually preferred to traditional Downsian median voter models, as in the former all voters have an influence on the policy outcome, whereas in the latter all power rests in the hands of the pivotal voter or group. For instance, in models where young and old (or rich and poor) voters have conflicting interests, probabilistic voting models predict that the winning candidate strikes a balance between the different interests in her/his policy platform. Due to the smooth mapping between the distribution of policy preferences and the political outcomes, this model has proven to be very tractable and convenient to use in dynamic models with repeated voting.
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Biclique- free graphs have been used in parameterized complexity to develop algorithms that are efficient for sparse graphs with suitably small input parameter values. In particular, finding a dominating set of size , on -biclique-free graphs, is fixed-parameter tractable when parameterized by , even though there is strong evidence that this is not possible using alone as a parameter. Similar results are true for many variations of the dominating set problem. It is also possible to test whether one dominating set of size at most can be converted to another one by a chain of vertex insertions and deletions, preserving the dominating property, with the same parameterization..
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More sophisticated quantum field theories, in particular those that involve a non- abelian gauge group, break the gauge symmetry within the techniques of perturbation theory by introducing additional fields (the Faddeev–Popov ghosts) and counterterms motivated by anomaly cancellation, in an approach known as BRST quantization. While these concerns are in one sense highly technical, they are also closely related to the nature of measurement, the limits on knowledge of a physical situation, and the interactions between incompletely specified experimental conditions and incompletely understood physical theory. The mathematical techniques that have been developed in order to make gauge theories tractable have found many other applications, from solid-state physics and crystallography to low-dimensional topology.
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This theorem has since been extended to the time-dependent domain to develop time-dependent density functional theory (TDDFT), which can be used to describe excited states. The second H–K theorem defines an energy functional for the system and proves that the correct ground-state electron density minimizes this energy functional. In work that later won them the Nobel prize in chemistry, the H–K theorem was further developed by Walter Kohn and Lu Jeu Sham to produce Kohn–Sham DFT (KS DFT). Within this framework, the intractable many-body problem of interacting electrons in a static external potential is reduced to a tractable problem of noninteracting electrons moving in an effective potential.
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One way to construct a fixed-parameter tractable algorithm for the nonblocker problem is to use kernelization, an algorithmic design principle in which a polynomial-time algorithm is used to reduce a larger problem instance to an equivalent instance whose size is bounded by a function of the parameter. For the nonblocker problem, an input to the problem consists of a graph G and a parameter k, and the goal is to determine whether G has a nonblocker with k or more vertices. This problem has an easy kernelization that reduces it to an equivalent problem with at most 2k vertices. First, remove all isolated vertices from G, as they cannot be part of any nonblocker.
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Russell Impagliazzo has described five hypothetical "worlds" that could result from different possible resolutions to the average-case complexity question.R. Impagliazzo, "A personal view of average-case complexity," sct, pp.134, 10th Annual Structure in Complexity Theory Conference (SCT'95), 1995 These range from "Algorithmica", where P = NP and problems like SAT can be solved efficiently in all instances, to "Cryptomania", where P ≠ NP and generating hard instances of problems outside P is easy, with three intermediate possibilities reflecting different possible distributions of difficulty over instances of NP-hard problems. The "world" where P ≠ NP but all problems in NP are tractable in the average case is called "Heuristica" in the paper.
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A final offensive, Operation Tractable, was launched by Canadian forces on 14 August in conjunction with American advances northward toward Chambois; their goal was to encircle and destroy the German 7th Army and 5th Panzer Army near the town of Falaise. In his final order as OB West commander, Kluge issued a full-scale retreat eastward on 16 August. The Allies did not capture Falaise until later that same day, leaving a -gap between Canadian and American forces—known as the Falaise Gap. By 22 August, the gap—desperately maintained by the Germans to allow their trapped forces to escape—was completely sealed, ending the Battle of Normandy with a decisive Allied victory.
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Tyler D. Parry argues the Ghanaian connection is a weak case for its origins, especially considering the ritual used by enslaved people bears far more similarities to the custom in the British Isles. Parry argues that, despite the racial animus that characterized the US South in the nineteenth century, poor white southerners (many of them descendants of people who used irregular forms of matrimony in Britain) and enslaved people exchanged their cultures between one another at far greater rates than commonly acknowledged. Enslavers were faced with a dilemma regarding committed relationships between enslaved people. While some family stability might be desirable as helping to keep enslaved people tractable and pacified, anything approaching a legal marriage was not.
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In March 1944 he returned to England and was promoted again, this time to command of the Canadian First Army. Although it was designated as the Canadian First Army, it contained a significant amount of British and Polish troops, including the entire British I Corps, commanded by Lieutenant- General John Crocker, along with the Polish 1st Armoured Division, and other troops from various European countries. The First Army was withheld by General Sir Bernard Montgomery, commander of the 21st Army Group, during the first few weeks of the Normandy Campaign. The First Army went on to fight in Operation Totalize and Operation Tractable and the Battle of the Falaise Pocket, followed by the clearing the Channel Coast.
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In mathematics, a matrix group is a group G consisting of invertible matrices over a specified field K, with the operation of matrix multiplication, and a linear group is an abstract group that is isomorphic to a matrix group over a field K, in other words, admitting a faithful, finite-dimensional representation over K. Any finite group is linear, because it can be realized by permutation matrices using Cayley's theorem. Among infinite groups, linear groups form an interesting and tractable class. Examples of groups that are not linear include groups which are "too big" (for example, the group of permutations of an infinite set), or which exhibit some pathological behaviour (for example finitely generated infinite torsion groups).
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An exhaustive search algorithm can solve the problem in time 2knO(1), where k is the size of the vertex cover. Vertex cover is therefore fixed-parameter tractable, and if we are only interested in small k, we can solve the problem in polynomial time. One algorithmic technique that works here is called bounded search tree algorithm, and its idea is to repeatedly choose some vertex and recursively branch, with two cases at each step: place either the current vertex or all its neighbours into the vertex cover. The algorithm for solving vertex cover that achieves the best asymptotic dependence on the parameter runs in time O(1.2738^k+(k\cdot n)).
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Because tree-depth is monotonic under graph minors, it is fixed-parameter tractable: there is an algorithm for computing tree-depth running in time where d is the depth of the given graph and n is its number of vertices. Thus, for every fixed value of d, the problem of testing whether the tree-depth is at most d can be solved in polynomial time. More specifically, the dependence on n in this algorithm can be made linear, by the following method: compute a depth first search tree, and test whether this tree's depth is greater than 2d. If so, the tree-depth of the graph is greater than d and the problem is solved.
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Despite the BSA's weight handicap, Banks still managed several top five placings in the world championships against lighter, two stroke motorcycles, including an impressive performance at the 1973 500cc United States Grand Prix in Southern California where, on the hard packed desert terrain, the explosive power delivery of two stroke engines put them at a disadvantage to more tractable power delivery of Banks' BSA. He finished the first moto in third place behind Willy Bauer and Roger De Coster then, finished the second moto in fourth place behind Bauer, Gerrit Wolsink and Jaak van Velthoven. After two seasons riding for Cheney, in 1975 Banks switched to CCM motorcycles, also powered by BSA engines.
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In fact, the problem has a kernel of size linear in k, and running times that are exponential in and cubic in n may be obtained by applying dynamic programming to a branch-decomposition of the kernel. More generally, the dominating set problem and many variants of the problem are fixed-parameter tractable when parameterized by both the size of the dominating set and the size of the smallest forbidden complete bipartite subgraph; that is, the problem is FPT on biclique-free graphs, a very general class of sparse graphs that includes the planar graphs. The complementary set to a dominating set, a nonblocker, can be found by a fixed-parameter algorithm on any graph.
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Games created for humans are considered to have external validity as benchmarks of progress in artificial intelligence. IBM's chess-playing Deep Blue (1997) and DeepMind's AlphaGo (2016) were considered major milestones; some argue that StarCraft would also be a major milestone, due to StarCraft's "real-time play, partial observability, no single dominant strategy, complex rules that make it hard to build a fast forward model, and a particularly large and varied action space." Though difficult, StarCraft may still be tractable with current technology because "its rules are known and the world is discrete with only a few types of objects". StarCraft II is a popular fast-paced online real-time strategy game by Blizzard Entertainment.
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The ears large and tulip shaped, free from creases, carried erect with plenty of width between them. The body should be long and slim, a trifle arched over the loin and racy in appearance; the tail, which must be free from kinks should come well out of the back and be thick at the root or set-on, gradually tapering like a whip lash to a fine end, the length being about equal to that of the mouse's body. Unless the variety standard states otherwise, the coat should be short perfectly smooth, glossy and sleek to the hand. The mouse should be perfectly tractable and free from any vice and not subject to fits or other similar ailments.
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First, if the problem has width bounded by a constant then a decomposition of bounded width can be found in polynomial time. Second, the problem obtained by converting the original problem according to the decomposition is not superpolynomially larger than the original problem, if the decomposition has fixed width. While most tractable structural restrictions derive from fixing the width of a decomposition method, others have been developed. Some can be reformulated in terms of decomposition methods: for example, the restriction to binary acyclic problem can be reformulated as that of problem of treewidth 1; the restriction of induced width (which is not defined in terms of a decomposition) can be reformulated as tree clustering.
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The problem of finding the smallest odd cycle transversal, or equivalently the largest bipartite induced subgraph, is also called odd cycle transversal, and abbreviated as OCT. It is NP-hard, as a special case of the problem of finding the largest induced subgraph with a hereditary property (as the property of being bipartite is hereditary). All such problems for nontrivial properties are NP-hard. The equivalence between the odd cycle transversal and vertex cover problems has been used to develop fixed-parameter tractable algorithms for odd cycle transversal, meaning that there is an algorithm whose running time can be bounded by a polynomial function of the size of the graph multiplied by a larger function of k.
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Combinatorial optimization is a topic that consists of finding an optimal object from a finite set of objects.. In many such problems, exhaustive search is not tractable. It operates on the domain of those optimization problems in which the set of feasible solutions is discrete or can be reduced to discrete, and in which the goal is to find the best solution. Typical problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. Some research literature considers discrete optimization to consist of integer programming together with combinatorial optimization (which in turn is composed of optimization problems dealing with graph structures) although all of these topics have closely intertwined research literature.
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Two divergent approaches to economic modeling, which have later become cornerstones of modeling of economic systems, originated at the Graduate School of Industrial Administration (GSIA) at Carnegie Mellon in the late 1950s and early 1960s. At the same time as John Muth was developing the concept of rational expectations, Herbert A. Simon had been refining his ideas on bounded rationality, emphasizing people's limited computational abilities. Together with their two colleagues at GSIA Charles C. Holt and Franco Modigliani, Muth and Simon collaborated on Planning Production, Inventories, and Work Force (1960), a book on problems of production scheduling and inventory management for the firm. Their goal was to derive tractable, operational rules that could easily be applied in practice.
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Canadian troops with armour support advance cautiously through the streets of Falaise, encountering only light scattered resistance Operation Tractable began at 12:00 on 14 August, when 800 Avro Lancaster and Handley Page Halifax heavy bombers of RAF Bomber Command struck German positions along the front. As with Totalize, many of the bombers mistakenly dropped their bombs short of their targets, causing 400 Polish and Canadian casualties. Covered by a smoke screen laid down by their artillery, two Canadian divisions moved forwards. Although their line of sight was reduced, German units still managed to inflict severe casualties on the Canadian 4th Armoured Division, which included its Armoured Brigade commander Brigadier Leslie Booth, as the division moved south toward Falaise.
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These made 125 voyages from Port Jackson during his thirty or so years involvement in the trade, this in spite of the fact he arrived late on the scene, the industry having peaked in the 1830s.Sydney's whaling fleet, His strategy was to purchase old and inexpensive vessels and crew them with South Sea islanders who were more tractable and prepared to work on the "lay" or share system of payment. He chose experienced and capable masters to command these vessels and keep them at sea in the face of the manifold difficulties routinely experienced on their long and demanding voyages. It was sometimes hard to get insurance for his aged vessels, eight of which were lost at sea.
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Pavol Hell and Jaroslav Nešetřil proved that, for undirected graphs, no other case is tractable: : Hell–Nešetřil theorem (1990): The H-coloring problem is in P when H is bipartite and NP-complete otherwise. This is also known as the dichotomy theorem for (undirected) graph homomorphisms, since it divides H-coloring problems into NP-complete or P problems, with no intermediate cases. For directed graphs, the situation is more complicated and in fact equivalent to the much more general question of characterizing the complexity of constraint satisfaction problems. It turns out that H-coloring problems for directed graphs are just as general and as diverse as CSPs with any other kinds of constraints.
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Her particular areas of research have been in measure- valued processes (especially superprocesses and their generalisations); in theoretical population genetics; and in mathematical ecology. A recent focus has been on the genetics of spatially extended populations, where she has exploited and developed inextricable links with infinite-dimensional stochastic analysis. Her resolution of the so-called 'pain in the torus' is typical of her work in that it draws on ideas from diverse areas, from measure-valued processes to image analysis. The result is a flexible framework for modelling biological populations which, for the first time, combines ecology and genetics in a tractable way, while introducing a novel and mathematically interesting class of stochastic processes.
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Asymptotic freedom can be derived by calculating the beta-function describing the variation of the theory's coupling constant under the renormalization group. For sufficiently short distances or large exchanges of momentum (which probe short-distance behavior, roughly because of the inverse relationship between a quantum's momentum and De Broglie wavelength), an asymptotically free theory is amenable to perturbation theory calculations using Feynman diagrams. Such situations are therefore more theoretically tractable than the long-distance, strong-coupling behavior also often present in such theories, which is thought to produce confinement. Calculating the beta-function is a matter of evaluating Feynman diagrams contributing to the interaction of a quark emitting or absorbing a gluon.
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Phylogenetic networks can be inferred and visualised with software such as SplitsTree, the R-package, phangorn, and, more recently, Dendroscope. A standard format for representing phylogenetic networks is a variant of Newick format which is extended to support networks as well as trees. Many kinds and subclasses of phylogenetic networks have been defined based on the biological phenomenon they represent or which data they are built from (hybridization networks, usually built from rooted trees, recombination networks from binary sequences, median networks from a set of splits, optimal realizations and reticulograms from a distance matrix), or restrictions to get computationally tractable problems (galled trees, and their generalizations level-k phylogenetic networks, tree-child or tree-sibling phylogenetic networks).
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In addition, the large animals provided elevated platforms from which archers could rain down arrows on the enemy, and from which generals could survey the battle. The psychological effect of war elephants was often their main tactical use.John C. Rolfe, Ammianus Marcellinus (Harvard University Press, 1956) After encountering elephant cavalry in the Battle of the Hydaspes River, Alexander the Great's troops mutinied and refused to press further into India.JFC Fuller, The Generalship of Alexander the Great (Da Capo Press, 1989) However, the animals were often not tractable in battle,Flavius Philostratus, The Life of Apollonius of Tyana (Loeb Classical Library translation, 1912) and when faced with determined opponents, would often flee and trample their own infantry in their flight.
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Even a confederate of his opponent Goodman remembered Downham as "a mild, courteous and loving man, wishing well unto all".This description appears in Paul Rogers’s A Breviary or some few Collectiones of the Cittie of Chester, a compilation of papers left by his father, Archdeacon Robert Rogers, who, like Goodman, found an early patron in Sir Edward Fitton: see Mills, "Recycling the Cycle", pp. 52-54. In applying the Uniformity Act he tried to persuade rather than persecute. He considered the laity of his diocese to be inherently tractable, believed in the power of prayer as a unifying force, and regarded skilled preaching as the means of bringing "many obstinate and wilful people into conformity and obedience".
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The optimization version of this problem is called Max Set Splitting and requires finding the partition which maximizes the number of split elements of F. It is an APX-complete problem and hence in NPO. The Set k-Splitting problem is stated as follows: given S, F, and an integer k, does there exist a partition of S which splits at least k subsets of F? The original formulation is the restricted case with k equal to the cardinality of F. The Set k-Splitting is fixed-parameter tractable, i.e., if k taken to be a fixed parameter, rather than a part of the input, then a polynomial algorithm exists for any fixed k.
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For, if the vertex separation number of a topological ordering is at most w, the minimum vertex separation among all orderings can be no larger, so the undirected graph formed by ignoring the orientations of the DAG described above must have pathwith at most w. It is possible to test whether this is the case, using the known fixed-parameter- tractable algorithms for pathwidth, and if so to find a path-decomposition for the undirected graph, in linear time given the assumption that w is a constant. Once a path decomposition has been found, a topological ordering of width w (if one exists) can be found using dynamic programming, again in linear time.
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The Bose-Hubbard model gives a description of the physics of interacting spinless bosons on a lattice. It is closely related to the Hubbard model which originated in solid-state physics as an approximate description of superconducting systems and the motion of electrons between the atoms of a crystalline solid. The model was first introduced by Gersch and Knollman in 1963 in the context of granular superconductors. (The term 'Bose' in its name refers to the fact that the particles in the system are bosonic.) The model rose to prominence in the 1980s after it was found to capture the essence of the superfluid-insulator transition in a way that was much more mathematically tractable than fermionic metal-insulator models.
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In practice, loop variants are often taken to be non-negative integers, or even required to be so, but the requirement that every loop have an integer variant removes the expressive power of unbounded iteration from a programming language. Unless such a (formally verified) language allows a transfinite proof of termination for some other equally powerful construct such as a recursive function call, it is no longer capable of full μ-recursion, but only primitive recursion. Ackermann's function is the canonical example of a recursive function that cannot be computed in a loop with an integer variant. In terms of their computational complexity, however, functions that are not primitive recursive lie far beyond the realm of what is usually considered tractable.
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In 1943 Edith Clarke published a textbook giving a method of use of symmetrical components for three-phase systems that greatly simplified calculations over the original Fortescue paper. Gabriele Kass-Simon, Patricia Farnes, Deborah Nash (ed), Women of Science: Righting the Record , Indiana University Press, 1993, . pages 164-168 In a three-phase system, one set of phasors has the same phase sequence as the system under study (positive sequence; say ABC), the second set has the reverse phase sequence (negative sequence; ACB), and in the third set the phasors A, B and C are in phase with each other (zero sequence, the common-mode signal). Essentially, this method converts three unbalanced phases into three independent sources, which makes asymmetric fault analysis more tractable.
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At the coronation of King James II in April, Ferrers was assistant lord cupbearer. He was also the first colonel of The Princess Anne of Denmark's Regiment of Foot, raised in the summer of 1685, during the Monmouth Rebellion, but was removed in favor of James FitzJames, 1st Duke of Berwick on 1 November 1686. In September 1687, he was appointed Lord Lieutenant of Staffordshire, replacing the Earl of Shrewsbury, who was unwilling to comply with James II's orders for purging the commission of the peace and packing Parliament with royalist candidates (to secure the repeal of the Test Act and the Penal Laws). However, Ferrers proved no more tractable, and was replaced in November by Walter Aston, 3rd Lord Aston of Forfar.
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These are the types of reduction used to prove ♯P-completeness. In parameterized complexity, FPT parsimonious reductions are used; these are parsimonious reductions whose transformation is a fixed-parameter tractable algorithm and that map bounded parameter values to bounded parameter values by a computable function. Polynomial-time parsimonious reductions are a special case of a more general class of reductions for counting problems, the polynomial-time counting reductions.. See in particular pp. 634–635. One common technique used in proving that a reduction R is parsimonious is to show that there is a bijection between the set of solutions to x and the set of solutions to R(x) which guarantees that the number of solutions to both problems is the same.
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Indeed, x can be any predetermined system metric and corresponding mathematical analysis would illustrate some hidden analytical behaviors of the system. The reciprocal-of-polynomial formulation is used for the same reason that computational boundedness is defined as polynomial running time: it has mathematical closure properties that make it tractable in the asymptotic setting (see #Closure properties). For example, if an attack succeeds in violating a security condition only with negligible probability, and the attack is repeated a polynomial number of times, the success probability of the overall attack still remains negligible. In practice one might want to have more concrete functions bounding the adversary's success probability and to choose the security parameter large enough that this probability is smaller than some threshold, say 2−128.
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Equivalently, the vertices correspond to variables, and two variables form an edge if they share an inequality. The sparsity measure d of A is the minimum between the tree-depth of the graph of A and the tree-depth of the graph of the transpose of A. Let a be the numeric measure of A defined as the maximum absolute value of any entry of A. Let n be the number of variables of the integer program. Then it was shown in 2018 that integer programming can be solved in strongly polynomial and fixed-parameter tractable time parameterized by a and d. That is, for some computable function f and some constant k, integer programming can be solved in time f(a,d)n^k.
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The new car's engine provided a top speed and in just under 12 seconds, a little better than the MGB GT. Moreover, the unit was comparatively smooth and tractable, in contrast to the MG's four cylinder BMC B-series engine engine, which produced almost the same power in twin carburettor form, but at higher revs. Fuel economy was very reasonable for the period at , and the interior well up to the competition. The only major criticism was of its rear suspension; the GT6 inherited the swing-axle system from the Spitfire, which in turn was copied from the Herald small saloon. In the saloon it was tolerated, in the little Spitfire it was not liked and in the powerful GT6 it was heavily criticised.
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Historically, projects such as the Cyc knowledge base (1984–) and the massive Japanese Fifth Generation Computer Systems initiative (1982–1992) attempted to cover the breadth of human cognition. These early projects failed to escape the limitations of non- quantitative symbolic logic models and, in retrospect, greatly underestimated the difficulty of cross-domain AI. Nowadays, most current AI researchers work instead on tractable "narrow AI" applications (such as medical diagnosis or automobile navigation). Many researchers predict that such "narrow AI" work in different individual domains will eventually be incorporated into a machine with artificial general intelligence (AGI), combining most of the narrow skills mentioned in this article and at some point even exceeding human ability in most or all these areas. Many advances have general, cross-domain significance.
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Currency mismatches occur when the currency in which debts are denominated is different from the currency in which assets are denominated. In emerging economies, it is often the case that a high proportion of debt is denominated in foreign currency, making them vulnerable to a balance sheet mismatch where debt burdens increase without necessarily increasing in the ability to pay. The difficulty to denominate debt in terms of a currency more tractable to each country's repayment capacity is labeled as the original sin hypothesis, which appears as one of the possible explanations to why emerging countries have trouble handling debt levels that would be otherwise manageable for advanced economies. Capital structure mismatches happen when a government relies more heavily on debt financing rather than on equity.
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Under a strict definition, where helicopter drops are simply transfers from the central bank to the private sector financed with base money a number of economists have argued that they are already occurring. In 2016, the European Central Bank (ECB) launched a TLTRO programme lending money to banks at negative interest rates, which amounts to a transfer to banks. Also, the use of differential interest rates on tiered reserves to support commercial banks' profitability in the face of negative interest rates, opens up another source of helicopter drop - albeit intermediated by banks. In the case of the Eurozone, the use of TLTROs is believed by some economists to provide a legal and administratively tractable means of introducing transfers to households.
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Tractable problems are frequently identified with problems that have polynomial-time solutions (P, PTIME); this is known as the Cobham–Edmonds thesis. Problems that are known to be intractable in this sense include those that are EXPTIME-hard. If NP is not the same as P, then NP-hard problems are also intractable in this sense. However, this identification is inexact: a polynomial-time solution with large degree or large leading coefficient grows quickly, and may be impractical for practical size problems; conversely, an exponential-time solution that grows slowly may be practical on realistic input, or a solution that takes a long time in the worst case may take a short time in most cases or the average case, and thus still be practical.
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The project to unify set theorists behind additional axioms to resolve the Continuum Hypothesis or other meta-mathematical ambiguities is sometimes known as "Gödel's program". Mathematicians currently debate which axioms are the most plausible or "self-evident", which axioms are the most useful in various domains, and about to what degree usefulness should be traded off with plausibility; some "multiverse" set theorists argue that usefulness should be the sole ultimate criterion in which axioms to customarily adopt. One school of thought leans on expanding the "iterative" concept of a set to produce a set-theoretic universe with an interesting and complex but reasonably tractable structure by adopting forcing axioms; another school advocates for a tidier, less cluttered universe, perhaps focused on a "core" inner model.
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L. enzymogenes strain C3 is a genetically tractable strain allowing for easy construction of gene knockouts, supporting its use as a model genetic system for unraveling the molecular basis of pathogenicity, as well as identifying mechanisms of microbial antagonism and biological control. Indeed, a number of derivative strains of L. enzymogenes strain C3 already have been constructed, including mutants affected in structural genes encoding enzyme activities, the regulatory clp gene and various combinations thereof.Palumbo, J. D., G. Y. Yuen, C. C. Jochum, K. Tatum, and D. Y. Kobayashi. 2005. Mutagenesis of β-1,3-glucanase genes in Lysobacter enzymogenes strain C3 results in reduced biological control activity toward Bipolaris leaf spot of tall fescue and Pythium damping-off of sugar beet.
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A 2005 book on Visual Studio notes for instance that a common problem in RTE tools is that the model reversed is not the same as the original one, unless the tools are helped by laborious annotations. The behavioral parts of UML impose even more challenges for RTE. A more tractable form of round-trip engineering is implemented in the context of framework application programming interfaces (APIs), whereby a model describing the usage of a framework API by an application is synchronized with that application's code. In this setting, the API prescribes all correct ways the framework can be used in applications, which allows precise and complete detection of API usages in the code as well as creation of useful code implementing correct API usages.
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By repeating this replacement process one eventually reaches a dominating set no larger than D, so in particular when the starting set D is a minimum dominating set this process forms an equally small independent dominating set., pp. 124–125. Despite this domination perfectness property, it is NP-hard to determine the size of the minimum dominating set in a claw-free graph. However, in contrast to the situation for more general classes of graphs, finding the minimum dominating set or the minimum connected dominating set in a claw-free graph is fixed-parameter tractable: it can be solved in time bounded by a polynomial in the size of the graph multiplied by an exponential function of the dominating set size.
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Barrier thickness may be computed in polynomial time by constructing the arrangement of the barriers (the subdivision of the plane formed by overlaying all barrier boundaries) and computing a shortest path in the dual graph of this subdivision. The complexity of barrier resilience for unit disk barriers is an open problem. It may be solved by a fixed-parameter tractable algorithm whose time is cubic in the total number of barriers and exponential in the square of the resilience, but it is not known whether it has a fully polynomial time solution. The corresponding problem for barriers of some other shapes, including unit-length line segments or axis-aligned rectangles of aspect ratio close to 1, is known to be NP-hard.
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After attending a short course taught by Adrian Smith at Bowling Green State University, Gelfand decided to take a sabbatical to Nottingham, UK with the intention of working on using numerical methods to solve empirical Bayes problems. After studying Tanner and Wong (1987) and being hinted as to its connection to Geman and Geman (1984) by David Clayton, Gelfand was able to realize the computational value of replacing expensive numerical techniques with Monte Carlo sampling-based methods in Bayesian inference. Published as Gelfand and Smith (1990), Gelfand described how the Gibbs sampler can be used for Bayesian inference in a computationally efficient manner. Since its publication, the general methods described in Gelfand and Smith (1990) has revolutionized data analysis allowing previously intractable problems to now be tractable.
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A tree decomposition of a given graph G consists of a tree and, for each tree node, a subset of the vertices of G called a bag. It must satisfy two properties: for each vertex v of G, the bags containing v must be associated with a contiguous subtree of the tree, and for each edge uv of G, there must be a bag containing both u and v. The vertices in a bag can be thought of as the terminals of a subgraph of G, represented by the subtree of the tree decomposition descending from that bag. When G has bounded treewidth, it has a tree decomposition in which all bags have bounded size, and such a decomposition can be found in fixed-parameter tractable time.
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Senior Equitation Over Fences at the 2014 Florida 4H State Horse Show Hunt seat equitation classes judge the rider only, including his or her position on the flat and over fences and overall effectiveness while riding. Therefore, it is not imperative that the horse has perfect movement or jumping form, but it needs good manners and an attractive way of going that does not detract from the rider's performance. Although temperament is not judged, horses with a more tractable temperament are generally easier to ride, and can therefore help riders demonstrate their skills. The ideal equitation mount has less bascule than the show hunter, because it is easier for a rider to maintain the correct jumping position on a "flatter" horse that does not throw the rider out of the saddle when it jumps.
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This is effected by introducing a novel potential function for CRFs that is based on the Sequence Memoizer (SM), a nonparametric Bayesian model for learning infinitely-long dynamics in sequential observations. To render such a model computationally tractable, CRF-infinity employs a mean-field approximation of the postulated novel potential functions (which are driven by an SM). This allows for devising efficient approximate training and inference algorithms for the model, without undermining its capability to capture and model temporal dependencies of arbitrary length. There exists another generalization of CRFs, the semi-Markov conditional random field (semi-CRF), which models variable- length segmentations of the label sequence Y. This provides much of the power of higher-order CRFs to model long-range dependencies of the Y_{i}, at a reasonable computational cost.
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By 1820, the opposition liberals—who, with the ultras, made up half the chamber—proved unmanageable, and Decazes and the king were looking for ways to revise the electoral laws again, to ensure a more tractable conservative majority. In February 1820, the assassination by a Bonapartist of the Duc de Berry, the ultrareactionary son of Louis' ultrareactionary brother and heir-presumptive, the future Charles X, triggered Decazes' fall from power and the triumph of the Ultras. François-René de Chateaubriand, a Romantic writer who sat in the Chamber of Peers Richelieu returned to power for a short interval, from 1820 to 1821. The press was more strongly censored, detention without trial was reintroduced, and Doctrinaire leaders, such as François Guizot, were banned from teaching at the École Normale Supérieure.
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In computer science, iterative compression is an algorithmic technique for the design of fixed-parameter tractable algorithms, in which one element (such as a vertex of a graph) is added to the problem in each step, and a small solution for the problem prior to the addition is used to help find a small solution to the problem after the step. The technique was invented by Reed, Smith and Vetta. to show that the problem of odd cycle transversal was solvable in time , for a graph with vertices, edges, and odd cycle transversal number . Odd cycle transversal is the problem of finding the smallest set of vertices of a graph that include at least one vertex from every odd cycle; its parameterized complexity was a longstanding open question. .
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Repeated application of the separator theorem produces a separator hierarchy which may take the form of either a tree decomposition or a branch- decomposition of the graph. Separator hierarchies may be used to devise efficient divide and conquer algorithms for planar graphs, and dynamic programming on these hierarchies can be used to devise exponential time and fixed-parameter tractable algorithms for solving NP-hard optimization problems on these graphs. Separator hierarchies may also be used in nested dissection, an efficient variant of Gaussian elimination for solving sparse systems of linear equations arising from finite element methods. Bidimensionality theory of Demaine, Fomin, Hajiaghayi, and Thilikos generalizes and greatly expands the applicability of the separator theorem for a vast set of minimization problems on planar graphs and more generally graphs excluding a fixed minor.
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As a more concrete example, it has been observed that the number of boys born to families does not conform faithfully to a binomial distribution as might be expected. Instead, the sex ratios of families seem to skew toward either boys or girls (see, for example the Trivers–Willard hypothesis for one possible explanation) i.e. there are more all-boy families, more all-girl families and not enough families close to the population 51:49 boy-to-girl mean ratio than expected from a binomial distribution, and the resulting empirical variance is larger than specified by a binomial model. In this case, the beta-binomial model distribution is a popular and analytically tractable alternative model to the binomial distribution since it provides a better fit to the observed data.
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It sealed in the importance of there being proofs, or "witnesses", that the answer for an instance is yes and there being proofs, or "witnesses", that the answer for an instance is no. In this blossom algorithm paper, Edmonds also characterizes feasible problems as those solvable in polynomial time; this is one of the origins of the Cobham–Edmonds thesis. A breakthrough of the Cobham–Edmonds thesis, was defining the concept of polynomial time characterising the difference between a practical and an impractical algorithm (in modern terms, a tractable problem or intractable problem). Today, problems solvable in polynomial time are called the complexity class PTIME, or simply P. Edmond's paper “Maximum Matching and a Polyhedron with 0-1 Vertices” along with his previous work gave astonishing polynomial-time algorithms for the construction of maximum matchings.
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Following the battle SS-Aufklärungs-Abteilung 12 deployed to the west of Mohnke's regiment and, by the evening of 8 June the division, while having failed in its assignment to drive the Canadians into the sea, had effectively halted the units of the 3rd Canadian Infantry Division, in the Allied advance on Caen. Men of the Royal Winnipeg Rifles on the march in Normandy, July 1944. Spending much of the next four weeks in static positions, the division participated in the battles to capture Caen in early July, known as Operation Charnwood, followed by Operation Totalize and Operation Tractable and the battles around Verrières Ridge, during the rest of the month. The brigade then took part in the pursuit across France, and clearing the Channel ports, most notably Boulogne, Calais and Cape Gris Nez.
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The science page of Amgen's website prominently features many deCODE publications and projects. The integration with Amgen coincided with the beginning of large-scale whole-genome sequencing at deCODE and the imputation of that data throughout the company's Iceland dataset. With that data, Stefansson and his colleagues at Amgen believed that genomics could be transformative to drug development in a way that was not possible with only SNP-chip and GWAS data.A Kamb, S Harper and K Stefansson, "Human genetics as a foundation for innovative drug development," Nature Biotechnology , Vol 31, pp 975–978, November 2013 Importantly, they could identify rare, high-impact mutations affecting common phenotypes — in brief, the most extreme versions of common diseases — yielding drug targets with potentially better validated and more tractable therapeutic potential.
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For example, yt might refer to the value of income observed in unspecified time period t, y3 to the value of income observed in the third time period, etc. Moreover, when a researcher attempts to develop a theory to explain what is observed in discrete time, often the theory itself is expressed in discrete time in order to facilitate the development of a time series or regression model. On the other hand, it is often more mathematically tractable to construct theoretical models in continuous time, and often in areas such as physics an exact description requires the use of continuous time. In a continuous time context, the value of a variable y at an unspecified point in time is denoted as y(t) or, when the meaning is clear, simply as y.
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This restriction leads to a tractable problem and enables the development of efficient exhaustive enumeration algorithms such as CCC- Biclustering and e-CCC-Biclustering. The approximate patterns in CCC- Biclustering algorithms allow a given number of errors, per gene, relatively to an expression profile representing the expression pattern in the bicluster. The e-CCC-Biclustering algorithm uses approximate expressions to find and report all maximal CCC-Biclusters by a discretized matrix A and efficient string processing techniques. These algorithms find and report all maximal biclusters with coherent and contiguous columns with perfect/approximate expression patterns, in time linear/polynomial which is obtained by manipulating a discretized version of original expression matrix in the size of the time series gene expression matrix using efficient string processing techniques based on suffix trees.
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The use of a quadratic loss function is common, for example when using least squares techniques. It is often more mathematically tractable than other loss functions because of the properties of variances, as well as being symmetric: an error above the target causes the same loss as the same magnitude of error below the target. If the target is t, then a quadratic loss function is :\lambda(x) = C (t-x)^2 \; for some constant C; the value of the constant makes no difference to a decision, and can be ignored by setting it equal to 1. Many common statistics, including t-tests, regression models, design of experiments, and much else, use least squares methods applied using linear regression theory, which is based on the quadratic loss function.
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Philip III of Spain, Philip II of Portugal Philip II's successor, Philip III, made chief minister the capable Francisco Goméz de Sandoval y Rojas, Duke of Lerma as a favourite, the first of the validos ('most worthy'). Philip sought to reduce foreign conflicts, since even the vast revenues could not sustain the nearly bankrupted kingdom. The Kingdom of England, suffering from a series of repulses at sea and from a guerrilla war by Catholics in Ireland, who were supported by Spain, agreed to the Treaty of London, 1604, following the accession of the more tractable Stuart King James I. Philip's chief minister, the duke of Lerma, also steered Spain toward peace with the Netherlands in 1609, although the conflict was to emerge again at a later point.Burkholder, Suzanne Hiles.
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The Ford variable venturi carburettor was replaced by a Weber carburettor 28/30 DFTM which benefited from a manifold vacuum-actuated secondary choke, instead of the more usual sequential linkage which opens the secondary butterfly at 3/4 to full throttle. The theory was to save fuel, especially with lead-footed drivers, but the result was mainly an engine which ran lean under load. This became worse on engines with worn cylinder heads owing to reduced engine vacuum. The 1.4 L version is less responsive to power modification than other CVH engines and some cylinder head parts are not interchangeable with the most common tuning parts; however replacing the carburettor with a Weber 32/34 DMTL and the appropriate inlet manifold makes them more tractable, albeit with a small increase in fuel consumption.
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To prove his new car's ability, in 1997, Alois Ruf entered two special wide-body 'CTR2 Yellowbird' prototype 'Sport' versions, code-named 'CTR2sport' with in the 1997 Pikes Peak Hillclimb race. These cars were stringently built to both FIA and Pikes Peak regulations and driven by brothers Steve Beddor and David Beddor. Unlike the other competitors, both cars were not only race modified, but also duly road registered, tractable, street legal cars. In a demonstration of the Ruf's flexibility, they were street driven to and from the Pikes Peak racecourse, and as a lasting testament to the Ruf CTR2sport's enormous capabilities, Steve Beddor was 1st in overall qualifying (despite driving a legal street car) and finished 2nd overall in the race, while his brother David, (in the second Ruf) finished a close 4th overall.
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It is NP-complete to determine whether a graph G has a branch-decomposition of width at most k, when G and k are both considered as inputs to the problem. However, the graphs with branchwidth at most k form a minor-closed family of graphs,, Theorem 4.1, p. 164. from which it follows that computing the branchwidth is fixed- parameter tractable: there is an algorithm for computing optimal branch- decompositions whose running time, on graphs of branchwidth k for any fixed constant k, is linear in the size of the input graph.. describe an algorithm with improved dependence on k, (2)k, at the expense of an increase in the dependence on the number of vertices from linear to quadratic. For planar graphs, the branchwidth can be computed exactly in polynomial time.
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It is not clear whether Palomino sided with the tractable Rodeznistas or with the intransigent Falcondistas,Manuel Martorell Pérez, La continuidad ideológica del carlismo tras la Guerra Civil [PhD thesis in Historia Contemporanea, Universidad Nacional de Educación a Distancia], Valencia 2009, p. 321 even though for years he remained a close acquaintance of Fal Conde. However, following the Unification Decree Palomino was not listed as member of the FET structures; quite to the opposite, following 1937 he entirely disappeared from politics. If present in the press, it was because of the winegrowing business he kept advertising;in early 1937 Palomino published adverts mostly in Pensamiento Alaves, since September 1937 mostly in Imperio; since early 1938 they appeared in numerous titles indeed, it seems that during the following decades Palomino dedicated his time to commercial activities.
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The Condorcet jury theorem has recently been used to conceptualize score integration when several physician readers (radiologists, endoscopists, etc.) independently evaluate images for disease activity. This task arises in central reading performed during clinical trials and has similarities to voting. According to the authors, the application of the theorem can translate individual reader scores into a final score in a fashion that is both mathematically sound (by avoiding averaging of ordinal data), mathematically tractable for further analysis, and in a manner that is consistent with the scoring task at hand (based on decisions about the presence or absence of features, a subjective classification task) The Condorcet jury theorem is also used in ensemble learning in the field of machine learning. An ensemble method combines the predictions of many individual classifiers by majority voting.
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Due to the increasing human use of coastal waters, Dr. Parish envisioned a program that could provide data on both resident and migrant species of birds; mortality rates after oil spills; levels of chronic oiling, information regarding incidents of entanglement with fishing gear; and causes of death for seabird populations. After deciding that live bird monitoring programs were more difficult, Dr. Parish decided that an efficient, and more tractable program, could monitor carcasses from beached birds. The dead seabirds could be tracked and identified by anyone. In July 1998, Dr. Parrish obtained a grant from the David and Lucile Packard Foundation to fund her vision of creating a seabird monitoring program that would generate baseline data to help assess patterns of seabird mortality due to natural and human-induced events.
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The smallest being the "annual crop of fashions" which he backs up with contemporary and historical patterns, and the largest, which he says are few, are our defined periods in history: "Western Civilization, Asiatic culture, prehistoric to barbarian and primitive societies" (91). The areas of time in-between the smallest and the largest are measured by our calendars and our mathematical methods of measurement. Kubler returns to the manageable interval of a year, thinking that this span is a known and workable measurement of duration as a tractable system of time duration. He explains how different cultures measure in different modes or segments: the Roman lustrum, a census occurring every five years or the Aztec practice of measuring in durations of 52 years (4 sections of 13 years instead of a 100-year century) called Calendar Round.
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Since the early 1990s, Koch has argued that identifying the mechanistic basis of consciousness is a scientifically tractable problem, and has been influential in arguing that consciousness can be approached using the modern tools of neurobiology. He and his student Nao Tsuchiya invented continuous flash suppression, an efficient psychophysical masking technique for rendering images invisible for many seconds. They have used this technique to argue that selective attention and consciousness are distinct phenomena, with distinct biological functions and mechanisms. Koch's primary collaborator in the endeavor of locating the neural correlates of consciousness was the molecular biologist turned neuroscientist, Francis Crick, starting with their first paper in 1990 and their last one, that Crick edited on the day of his death, July 24, 2004, on the relationship between the claustrum, a mysterious anatomical structure situated underneath the insular cortex, and consciousness.
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If a first-order sentence includes distinct variables, then the property it describes can be tested in graphs of vertices by examining all -tuples of vertices; however, this brute force search algorithm is not particularly efficient, taking time . The problem of checking whether a graph models a given first-order sentence includes as special cases the subgraph isomorphism problem (in which the sentence describes the graphs that contain a fixed subgraph) and the clique problem (in which the sentence describes graphs that contain complete subgraphs of a fixed size). The clique problem is hard for W(1), the first level of a hierarchy of hard problems from the point of view of parameterized complexity. Therefore, it is unlikely to have a fixed-parameter tractable algorithm, one whose running time takes the form for a function and constant that are independent of and .
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Usually, a subset of these primitives will be specified by the person operating it, but that's not a requirement of the technique. The symbolic regression problem for mathematical functions has been tackled with a variety of methods, including recombining equations most commonly using genetic programming, as well as more recently methods utilizing Bayesian methods and physics inspired AI. The other non-classical alternative method to SR is called Universal Functions Originator (UFO), which has a different mechanism, search-space, and building strategy. By not requiring a specific model to be specified, symbolic regression isn't affected by human bias, or unknown gaps in domain knowledge. It attempts to uncover the intrinsic relationships of the dataset, by letting the patterns in the data itself reveal the appropriate models, rather than imposing a model structure that is deemed mathematically tractable from a human perspective.
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In 1985 Allshire joined Nicholas Hasties research group at the MRC Human Genetics Unit, Edinburgh (formerly MRC Clinical and Population Cytogentics Unit) as a postdoctoral researcher where he discovered that mammalian telomeres are composed of simple repetitive sequences similar to those of unicellular eukaryotes and that telomere length in blood cells shorten with age and are further eroded in cancerous cells. This work resulted from following the fate of fission yeast (Schizosaccharomyces pombe) telomeres after introdroducing fission yeast chromosomes into mouse cell in collaoration with Peter Fantes. In 1989 he took a position as an independent visiting scientist at Cold Spring Harbor Laboratory (CSHL) for 18 months before joining the MRC Human Genetics Unit as a junior group leader. While at CSHL he decided to switch his focus to investigating chromosomal elements in the genetically tractable fission yeast.
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In the hidden Markov models considered above, the state space of the hidden variables is discrete, while the observations themselves can either be discrete (typically generated from a categorical distribution) or continuous (typically from a Gaussian distribution). Hidden Markov models can also be generalized to allow continuous state spaces. Examples of such models are those where the Markov process over hidden variables is a linear dynamical system, with a linear relationship among related variables and where all hidden and observed variables follow a Gaussian distribution. In simple cases, such as the linear dynamical system just mentioned, exact inference is tractable (in this case, using the Kalman filter); however, in general, exact inference in HMMs with continuous latent variables is infeasible, and approximate methods must be used, such as the extended Kalman filter or the particle filter.
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Although the unphysical axes in the space of detailed configurations are a fundamental property of the physical model, there is no special set of directions "perpendicular" to them. Hence there is an enormous amount of freedom involved in taking a "cross section" representing each physical configuration by a particular detailed configuration (or even a weighted distribution of them). Judicious gauge fixing can simplify calculations immensely, but becomes progressively harder as the physical model becomes more realistic; its application to quantum field theory is fraught with complications related to renormalization, especially when the computation is continued to higher orders. Historically, the search for logically consistent and computationally tractable gauge fixing procedures, and efforts to demonstrate their equivalence in the face of a bewildering variety of technical difficulties, has been a major driver of mathematical physics from the late nineteenth century to the present.
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Many problems in graph algorithms may be solved efficiently on graphs of low pathwidth, by using dynamic programming on a path-decomposition of the graph. For instance, if a linear ordering of the vertices of an n-vertex graph G is given, with vertex separation number w, then it is possible to find the maximum independent set of G in time On graphs of bounded pathwidth, this approach leads to fixed-parameter tractable algorithms, parametrized by the pathwidth. Such results are not frequently found in the literature because they are subsumed by similar algorithms parametrized by the treewidth; however, pathwidth arises even in treewidth- based dynamic programming algorithms in measuring the space complexity of these algorithms. The same dynamic programming method also can be applied to graphs with unbounded pathwidth, leading to algorithms that solve unparametrized graph problems in exponential time.
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By using dynamic programming on a tree decomposition or branch-decomposition of a planar graph, many NP-hard optimization problems may be solved in time exponential in √n or √n log n. For instance, bounds of this form are known for finding maximum independent sets, Steiner trees, and Hamiltonian cycles, and for solving the travelling salesman problem on planar graphs.; ; ; . Similar methods involving separator theorems for geometric graphs may be used to solve Euclidean travelling salesman problem and Steiner tree construction problems in time bounds of the same form.. For parameterized problems that admit a kernelization that preserves planarity and reduces the input graph to a kernel of size linear in the input parameter, this approach can be used to design fixed-parameter tractable algorithms the running time of which depends polynomially on the size of the input graph and exponentially on √k, where k is the parameter of the algorithm.
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The von Mises distribution is a circular distribution which, like any other circular distribution, may be thought of as a wrapping of a certain linear probability distribution around the circle. The underlying linear probability distribution for the von Mises distribution is mathematically intractable; however, for statistical purposes, there is no need to deal with the underlying linear distribution. The usefulness of the von Mises distribution is twofold: it is the most mathematically tractable of all circular distributions, allowing simpler statistical analysis, and it is a close approximation to the wrapped normal distribution, which, analogously to the linear normal distribution, is important because it is the limiting case for the sum of a large number of small angular deviations. In fact, the von Mises distribution is often known as the "circular normal" distribution because of its ease of use and its close relationship to the wrapped normal distribution (Fisher, 1993).
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Early in 1540 Cromwell's religiously conservative, aristocratic enemies, headed by the Duke of Norfolk and assisted by Bishop Gardiner (colloquially known as "Wily Winchester"), decided that the country's decline towards "doctrinal radicalism" in religion, as expressed in a series of parliamentary debates held throughout that Spring, had gone too far. They saw in Catherine Howard, Norfolk's niece, "considerately put in the king's way by that pander, her uncle of Norfolk", an opportunity to displace their foe. Catherine's assignations with the king were openly facilitated by the duke and the bishop and as she "[strode] towards the throne" the two conspirators found themselves edging once more into political power. It would have been a simple matter for Cromwell to arrange an annulment of Henry's marriage to the tractable Anne, but this would have put him in greater jeopardy as it would clear the way for Catherine to marry the king.
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The overall approach in EDIN is to mathematically characterize the rich interactions between composite networks (which may comprise multiple networks with varying levels of coupling between them), and the dynamics that occur within each network or across networks. Examples of key technical approaches within EDIN include the development of formal models for reasoning about interacting networks; development of a theory of composite graphs for modeling interacting networks; modeling and analysis of group behaviors using techniques ranging beyond traditional graph theory; development of community discovery algorithms; characterization of temporal graph properties; development of mathematically tractable tactical mobility models; development of theories of co-evolution of interacting networks, etc. Modeling the evolution and dynamics of a network entails understanding both the structural properties of dynamic networks and understanding the dynamics of processes (or behaviors) of interest embedded in the network. Typically, the dynamics of network structure impacts certain processes (e.g.
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The method of approximation then suitably reduces one aspect of the transient conduction system (spatial temperature variation within the object) to a more mathematically tractable form (that is, it is assumed that the temperature within the object is completely uniform in space, although this spatially uniform temperature value changes over time). The rising uniform temperature within the object or part of a system, can then be treated like a capacitative reservoir which absorbs heat until it reaches a steady thermal state in time (after which temperature does not change within it). An early-discovered example of a lumped-capacitance system which exhibits mathematically simple behavior due to such physical simplifications, are systems which conform to Newton's law of cooling. This law simply states that the temperature of a hot (or cold) object progresses toward the temperature of its environment in a simple exponential fashion.
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A graph with an odd cycle transversal of size 2: removing the two blue bottom vertices leaves a bipartite graph. Odd cycle transversal is an NP-complete algorithmic problem that asks, given a graph G = (V,E) and a number k, whether there exists a set of k vertices whose removal from G would cause the resulting graph to be bipartite. The problem is fixed-parameter tractable, meaning that there is an algorithm whose running time can be bounded by a polynomial function of the size of the graph multiplied by a larger function of k.. The name odd cycle transversal comes from the fact that a graph is bipartite if and only if it has no odd cycles. Hence, to delete vertices from a graph in order to obtain a bipartite graph, one needs to "hit all odd cycle", or find a so-called odd cycle transversal set.
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Second, they proved that no tractable randomized algorithm can approximate probabilistic inference to within an absolute error ɛ < 1/2 with confidence probability greater than 1/2. At about the same time, Roth proved that exact inference in Bayesian networks is in fact #P-complete (and thus as hard as counting the number of satisfying assignments of a conjunctive normal form formula (CNF) and that approximate inference within a factor 2n1−ɛ for every ɛ > 0, even for Bayesian networks with restricted architecture, is NP-hard.D. Roth, On the hardness of approximate reasoning, IJCAI (1993)D. Roth, On the hardness of approximate reasoning, Artificial Intelligence (1996) In practical terms, these complexity results suggested that while Bayesian networks were rich representations for AI and machine learning applications, their use in large real-world applications would need to be tempered by either topological structural constraints, such as naïve Bayes networks, or by restrictions on the conditional probabilities.
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The time complexity of solving some of the applications discussed above, such as multi- dimensional table problems, multicommodity flow problems, and N-fold integer programming problems, is dominated by the cardinality of the relevant Graver basis, which is a polynomial O\left(n^g\right) with typically large degree g which is a suitable Graver complexity of the system. In Raymond Hemmecke, Shmuel Onn, Lyubov Romanchuk: N-fold integer programming in cubic time, Mathematical Programming, 137:325–341, 2013 a much faster algorithm is presented, which finds at each iteration the best improvement x + qg with q positive integer and g element in G(A) without explicitly constructing the Graver basis, in cubic time O\left(n^3\right) regardless of the system. In the terminology of parameterized complexity, this implies that all these problems suitably parameterized, and in particular l × m × n table problems parametrized by l and m, are fixed parameter tractable.
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It is NP-complete to test whether a given graph is 1-planar,.. and it remains NP-complete even for the graphs formed from planar graphs by adding a single edge. Expanded version of a paper from the 17th ACM Symposium on Computational Geometry, 2010. and for graphs of bounded bandwidth.. The problem is fixed-parameter tractable when parameterized by cyclomatic number or by tree-depth, so it may be solved in polynomial time when those parameters are bounded. In contrast to Fáry's theorem for planar graphs, not every 1-planar graph may be drawn 1-planarly with straight line segments for its edges... However, testing whether a 1-planar drawing may be straightened in this way can be done in polynomial time.. Additionally, every 3-vertex-connected 1-planar graph has a 1-planar drawing in which at most one edge, on the outer face of the drawing, has a bend in it.
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There has also been research into the distribution of values of the longest common subsequence, generalizing the study of the expectation of this value. For instance, the standard deviation of the length of the longest common subsequence of random strings of length n is known to be proportional to the square root of n.. One complication in performing this sort of analysis is that the random variables describing whether the characters at different pairs of positions match each other are not independent of each other. For a more mathematically tractable simplification of the longest common subsequence problem, in which the allowed matches between pairs of symbols are not controlled by whether those symbols are equal to each other but instead by independent random variables with probability 1/k of being 1 and (k − 1)/k of being 0, it has been shown that the distribution of the longest common subsequence length is controlled by the Tracy–Widom distribution..
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When practice resumed, Stewart went out on the track in his car on a personal fact-finding mission. His conclusion was that his own preference was to take The Esses complex in fourth gear in the Tyrrell, hence he would be at the low end of the engine's rev range, making the car more tractable and less nervous (in exchange for a bit less throttle response). Cevert, however, preferred to use third gear and be at the top end of his engine's power range: it was always something of a compromise because of the need to accelerate through the combination of corners. Stewart noted that the Tyrrell always felt jumpy through this section of the Watkins Glen track owing to its short wheelbase; he felt that this was somewhat counteracted by driving in the higher gear even though this meant a time penalty if he got his line wrong through the corner.
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301 Strong German defences and indecision and hesitation in the Canadian chain of command hampered Allied efforts and the 4th Canadian and 1st Polish Armoured Divisions suffered many casualties.Reid, pp. 357, 366Bercuson, p. 230 Anglo-Canadian forces reached Hill 195 north of Falaise on 10 August but were unable to make further progress and Totalize was terminated. Lieutenant Kłaptocz of the Polish 1st Armoured Division and Major Leonard Dull of the US 90th Infantry Division, in Chambois, August 1944, after the Allied link-up. The Canadians reorganised and on 14 August began Operation Tractable; three days later Falaise fell.Copp (2006), p. 104 In a meeting with his divisional commanders on 19 August, Simonds emphasised the importance of quickly closing the Falaise Pocket to General Stanisław Maczek. Assigned responsibility for the Moissy–Chambois–Coudehard area, the 1st Polish Armoured Division had split into three battlegroups of an armoured regiment and an infantry battalion each and were sweeping the countryside north of Chambois.
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Knowing via Ultra that Hitler was not planning to retreat from Normandy, Montgomery, on 6 August 1944, ordered an envelopment operation against Army Group B—with the First Canadian Army under Harry Crerar to advance towards Falaise, the Second British Army under Miles Dempsey to advance towards Argentan, and the Third American Army under George S. Patton to advance to Alençon. On 11 August, Montgomery changed his plan, with the Canadians to take Falaise and to meet the Americans at Argentan. The First Canadian Army launched two operations, Operation Totalize on 7 August, which advanced only in four days in the face of fierce German resistance, and Operation Tractable on 14 August, which finally took Falaise on 17 August. In view of the slow Canadian advance, Patton requested permission to take Falaise, but was refused by Bradley on 13 August, which prompted much controversy with many historians arguing that Bradley lacked aggression and that Montgomery should have overruled Bradley.
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The effects of years of clandestine association with the adversary are deep and subtle; the Service B case officer working with a double agent of service A is characterized by an ethnicity or religion may find those bonds run deep, even if the agent hates the government of A. The service B officer may care deeply for the double. Another result of lengthy prior clandestine service is that the agent may be hard to control. In most operations the case officer's superior training and experience give him so decided an edge over the agent that recognition of this superiority makes the agent more tractable. However, added to the fact that the experienced double agent may have been in the business longer than his case officer, his further advantage in having gained a first-hand comparative knowledge of the workings of at least two disparate services, and it is obvious that the case officer's margin of superiority diminishes, vanishes, or even reverses.
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The imprinted brain theory argues that since it is uncertain if a woman's other and future children have and will have the same father, as well as the father generally having lower parental investment, it may be in the father's reproductive interest for his child to maximize usage of the mother's resources while it may be in the mother's interest to limit this in order to have resources for her other and future children. Thus, a genomic imprinting with slight maternal bias would be associated with factors such as decreased growth, more tractable behavior, and an empathizing and less self-centered personality causing less demands on the mother. The opposite would occur for a slight paternal bias. However, an extreme genomic imprinting in favor of maternal genes is argued to cause psychosis such as in schizophrenia spectrum disorders while an extreme genomic imprinting in favor of paternal genes is argued to cause autism spectrum disorders.
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The Canadian horse's origin corresponds to shipments of French horses, some of which came from Louis XIV's own stable and most likely were Baroque horses meant to be gentlemen's mounts. These were ill-suited to farm work and to the hardscrabble life of the New World, so like the Americans, early Canadians crossed their horses with natives escapees. In time they evolved along similar lines as the Quarter Horse to the South as both the US and Canada spread westward and needed a calm and tractable horse versatile enough to carry the farmer's son to school but still capable of running fast and running hard as a cavalry horse, a stockhorse, or a horse to pull a conestoga wagon. Other horses from North America retained a hint of their mustang origins by being either derived from stock that Native Americans bred that came in a rainbow of color, like the Appaloosa and American Paint Horse.
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Lange's most famous and reverberating novel was Vandenberg, a Cold War "near future tale" starring fugitives in the New Mexico wilderness after the successful invasion of the USA by the Soviets. The eponymous hero, an individualist who deserted civilization long before the Russian attack, choosing instead to live alone with his mentally disabled son in a squalid ranch, has several traits in common with the author: he is a World War II veteran, a painter, and an expert survivalist. Sprinkled across the third-person narrative abound inserts headed as "Communications", printed in italics, that transcribe Soviet files, quotations from actual writers on war (especially Robert Ardrey), and Vandenberg's own journals, in which he reflects on the easy defeat of the United States and the sheepish acceptance of the new regime by its people, condemning the American values of the novel's time as materialistic and shallow, which in turn have produced a "tractable, malleable...spineless people". Although the book's undertones, especially the hero's social views and racial profiling, strike as politically incorrect today, some reviewers at the time picked up on Lange's social criticism.
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During the 1990s some researchers such as Geoffrey Hinton and Karl Friston began examining the concept of free energy as a calculably tractable measure of the discrepancy between actual features of the world and representations of those features captured by neural network models.Hinton, G. E. and Zemel, R. S.(1994), Autoencoders, minimum description length, and Helmholtz free energy. Advances in Neural Information Processing Systems 6. J. D. Cowan, G. Tesauro and J. Alspector (Eds.), Morgan Kaufmann: San Mateo, CA. A synthesis has been attempted recentlyFriston K, The free- energy principle: A unified brain theory?, Nat Rev Neurosci. 2010. 11:127–38 by Karl Friston, in which the Bayesian brain emerges from a general principle of free energy minimisation.Friston K, Kilner J, Harrison L. A free energy principle for the brain, J Physiol Paris. 2006. 100:70–87 In this framework, both action and perception are seen as a consequence of suppressing free- energy, leading to perceptualFriston K, A theory of cortical responses, Philos Trans R Soc Lond B Biol Sci. 2005. 360:815–36.
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Although listed as an open problem in the 1979 book Computers and Intractability,, [OPEN4], p. 286; update, p. 339. the computational complexity of the minimum chordal completion problem (also called the minimum fill-in problem) was quickly resolved: showed it to be NP-complete.. If the minimum chordal completion adds edges to a graph , then it is possible to find a chordal completion using at most added edges, in polynomial time.. The problem of finding the optimal set of edges to add can also be solved by a fixed-parameter tractable algorithm, in time polynomial in the graph size and subexponential in .. The treewidth (minimum clique size of a chordal completion) and related parameters including pathwidth and tree-depth are also NP-complete to compute, and (unless P=NP) cannot be approximated in polynomial time to within a constant factor of their optimum values; however, approximation algorithms with logarithmic approximation ratios are known for them.. Both the minimum fill-in and treewidth problems can be solved in exponential time. More precisely, for an -vertex graph, the time is ..
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A combination of novel docking methods and/or its use in the CANDO platform has led to prospectively validated predictions of putative drugs against dengue, dental caries, herpes, lupus, and malaria along with indication-specific collaborators. Other successful areas of application include medicine, predicting HIV drug resistance/susceptibility; nanobiotechnology, where small multifunctional peptides that bind to inorganic substrates are designed computationally; and interactomics of several organisms, including the Nutritious Rice for the World (NRW) projectNutritious Rice for the World web site where protein structure prediction methods are applied to all tractable proteins encoded by the rice genome on the IBM World Community Grid as well as the 1KP project to predict protein structures. functions, and interactions of 1000 plant proteomes. The NRW project harnessed the power of individual PCs via the Grid to perform its computations to help design better rice strains with higher yield and range of bioavailable nutrients, and was covered by more than 200 media outlets worldwide including The New York Times, BusinessWeek, NSF, The Times of India, and Fortune.
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After a third chapter relating the crossing number to graph parameters including skewness, bisection width, thickness, and (via the Albertson conjecture) the chromatic number, the final chapter of part I concerns the computational complexity of finding minimum-crossing graph drawings, including the results that the problem is both NP-complete and fixed-parameter tractable. In the second part of the book, two chapters concern the rectilinear crossing number, describing graph drawings in which the edges must be represented as straight line segments rather than arbitrary curves, and Fáry's theorem that every planar graph can be drawn without crossings in this way. Another chapter concerns 1-planar graphs and the associated local crossing number, the smallest number such that the graph can be drawn with at most crossings per edge. Two chapters concern book embeddings and string graphs, and two more chapters concern variations of the crossing number that count crossings in different ways, for instance by the number of pairs of edges that cross or that cross an odd number of times.
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Grohe's algorithm performs these simplifications until the remaining graph has a small treewidth, and then applies Courcelle's theorem to solve the reduced subproblem... observed that Courcelle's theorem applies to several problems of finding minimum multi-way cuts in a graph, when the structure formed by the graph and the set of cut pairs has bounded treewidth. As a result they obtain a fixed-parameter tractable algorithm for these problems, parameterized by a single parameter, treewidth, improving previous solutions that had combined multiple parameters.. In computational topology, extend Courcelle's theorem from MSO2 to a form of monadic second-order logic on simplicial complexes of bounded dimension that allows quantification over simplices of any fixed dimension. As a consequence, they show how to compute certain quantum invariants of 3-manifolds as well as how to solve certain problems in discrete Morse theory efficiently, when the manifold has a triangulation (avoiding degenerate simplices) whose dual graph has small treewidth.. Short communication, International Congress of Mathematicians, 2014. Methods based on Courcelle's theorem have also been applied to database theory,.
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Mixture densities are complicated densities expressible in terms of simpler densities (the mixture components), and are used both because they provide a good model for certain data sets (where different subsets of the data exhibit different characteristics and can best be modeled separately), and because they can be more mathematically tractable, because the individual mixture components can be more easily studied than the overall mixture density. Mixture densities can be used to model a statistical population with subpopulations, where the mixture components are the densities on the subpopulations, and the weights are the proportions of each subpopulation in the overall population. Mixture densities can also be used to model experimental error or contamination – one assumes that most of the samples measure the desired phenomenon, Parametric statistics that assume no error often fail on such mixture densities – for example, statistics that assume normality often fail disastrously in the presence of even a few outliers – and instead one uses robust statistics. In meta-analysis of separate studies, study heterogeneity causes distribution of results to be a mixture distribution, and leads to overdispersion of results relative to predicted error.
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It is NP-complete to test whether there exists a connected dominating set with size less than a given threshold, or equivalently to test whether there exists a spanning tree with at least a given number of leaves. Therefore, it is believed that the minimum connected dominating set problem and the maximum leaf spanning tree problem cannot be solved in polynomial time. When viewed in terms of approximation algorithms, connected domination and maximum leaf spanning trees are not the same: approximating one to within a given approximation ratio is not the same as approximating the other to the same ratio. There exists an approximation for the minimum connected dominating set that achieves a factor of , where Δ is the maximum degree of a vertex in G.. The maximum leaf spanning tree problem is MAX-SNP hard, implying that no polynomial time approximation scheme is likely.. However, it can be approximated to within a factor of 2 in polynomial time.. Both problems may be solved, on -vertex graphs, in time .. The maximum leaf problem is fixed-parameter tractable, meaning that it can be solved in time exponential in the number of leaves but only polynomial in the input graph size.
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Operation Tractable was the final attack conducted by Canadian and Polish troops, supported by a British tank brigade, during the Battle of Normandy during World War II. The operation was to capture the tactically important French town of Falaise and then the smaller towns of Trun and Chambois. This operation was undertaken by the First Canadian Army with the 1st Polish Armoured Division (Generał brygady Stanisław Maczek) and a British armoured brigade against Army Group B of the Westheer in what became the largest encirclement on the Western Front during the Second World War. Despite a slow start and limited gains north of Falaise, novel tactics by the 1st Polish Armoured Division during the drive for Chambois enabled the Falaise Gap to be partially closed by 19 August 1944, trapping about 150,000 German soldiers in the Falaise Pocket. Although the Falaise Gap was narrowed to a distance of several hundred metres/yards, as a result of attacks and counter-attacks between battle groups of the 1st Polish Armoured Division and the II SS Panzer Corps on Hill 262 (Mont Ormel) the gap was not closed quickly and thousands of German troops escaped on foot.
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Several models, both phenomenological and analytical, have been developed to describe the energetics of Auger transitions. One of the most tractable descriptions, put forth by Jenkins and Chung, estimates the energy of Auger transition ABC as: :E_{ABC}=E_A(Z)-0.5[E_B(Z)+E_B(Z+1)]-0.5[E_C(Z)+E_C(Z+1)] E_i(Z) are the binding energies of the ith level in element of atomic number Z and E_i(Z+1) are the energies of the same levels in the next element up in the periodic table. While useful in practice, a more rigorous model accounting for effects such as screening and relaxation probabilities between energy levels gives the Auger energy as: :E_{ABC}=E_A-E_B-E_C-F(BC:x)+R_{xin}+R_{xex} where F(BC:x) is the energy of interaction between the B and C level holes in a final atomic state x and the R's represent intra- and extra-atomic transition energies accounting for electronic screening. Auger electron energies can be calculated based on measured values of the various E_i and compared to peaks in the secondary electron spectrum in order to identify chemical species.
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Examination of the area after its capture, indicated some destruction of German equipment, including the wreckage of ten of the forty trucks believed to be in the area at the time of the raid. The 48 hours that elapsed between the bombing and the Allied occupation of the area, allowed the Germans time to recover from any shock and disorientation and to salvage some damaged equipment. Examination of the second aiming point, "Northern Caen", failed to reveal a 90 percent zone but it was noted that the obstructive effect of bombing a suburb was significant and had caused substantial delays to vehicles of both sides, by cratering and blocking roads. ORS2 concluded that the success of Charnwood owed little to the bombing and made recommendations including changing to instantly fused bombs, dropping larger numbers of smaller anti-personnel bombs and rapidly following-up a bombardment with ground forces to take advantage of its main effect, which was the temporary suppression of German will to resist. In Operation Goodwood, Operation Bluecoat, Operation Cobra, Operation Totalize and Operation Tractable the 21st Army Group exploited better the effect of preparatory attacks by strategic bombers by following-up the attacks immediately.Copp (2000), pp.
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A first criticism directed towards NCM relates to the rational expectations hypothesis. Under this hypothesis, “people are assumed to know the policy rule used by the monetary (and fiscal) authorities and to have detailed knowledge about the structure of the economy including the size and timing of responses to shocks of various kinds. These assumptions make the models analytically tractable but, taken literally (as they often are), they distort the economist's view of the policy problem by ignoring uncertainty, incomplete knowledge about the structure of the economy and the costs of acquiring information and reducing uncertainty” (Brunner and Meltzer 1993, p. 42). A second criticism addressed by Brunner to NCM concerns the intertemporal concept of equilibrium: “I also have strong reservations about crucial aspects of their 'equilibrium approach' ” (Klamer 1984, p. 191). To the question “So what is wrong with new classical economics?”, Brunner answered: “Their interpretation of equilibrium analysis seems dubious to me. This specific kind of equilibrium analysis implies that all prices are market-clearing relative to all shock-realizations” (p. 192). As a result, NCM cannot explain “the lamented unresponsiveness of prices to current conditions” (Brunner 1980, p.
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Testing whether a given graph has intersection number at most a given number is NP-complete.. As cited by .. Therefore, it is also NP-hard to compute the intersection number of a given graph. The problem of computing the intersection number is, however, fixed-parameter tractable: that is, there is a function such that, when the intersection number is , the time to compute it is at most the product of and a polynomial in n. This may be shown by observing that there are at most distinct closed neighborhoods in the graph – two vertices that belong to the same set of cliques have the same neighborhood – and that the graph formed by selecting one vertex per closed neighbood has the same intersection number as the original graph. Therefore, in polynomial time the input can be reduced to a smaller kernel with at most vertices; applying an exponential time backtracking search procedure to this kernel leads to a function that is double exponential in .. The double- exponential dependence on cannot be reduced to single exponential by a kernelization of polynomial size, unless the polynomial hierarchy collapses,.
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They play a key role in the theory of graph minors: the families of graphs that are closed under graph minors and do not include all forests may be characterized as having bounded pathwidth, and the "vortices" appearing in the general structure theory for minor-closed graph families have bounded pathwidth.. Pathwidth, and graphs of bounded pathwidth, also have applications in VLSI design, graph drawing, and computational linguistics. It is NP-hard to find the pathwidth of arbitrary graphs, or even to approximate it accurately.. However, the problem is fixed-parameter tractable: testing whether a graph has pathwidth k can be solved in an amount of time that depends linearly on the size of the graph but superexponentially on k. Additionally, for several special classes of graphs, such as trees, the pathwidth may be computed in polynomial time without dependence on k.. Many problems in graph algorithms may be solved efficiently on graphs of bounded pathwidth, by using dynamic programming on a path-decomposition of the graph.. Path decomposition may also be used to measure the space complexity of dynamic programming algorithms on graphs of bounded treewidth..
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Minimizing the number of crossings is NP-complete, but may be approximated with an approximation ratio of where is the number of vertices.. Minimizing the one- page or two-page crossing number is fixed-parameter tractable when parameterized by the cyclomatic number of the given graph, or by a combination of the crossing number and the treewidth of the graph... Heuristic methods for reducing the crossing complexity have also been devised, based e.g. on a careful vertex insertion order and on local optimization. Two-page book embeddings with a fixed partition of the edges into pages can be interpreted as a form of clustered planarity, in which the given graph must be drawn in such a way that parts of the graph (the two subsets of edges) are placed in the drawing in a way that reflects their clustering. Two-page book embedding has also been used to find simultaneous embeddings of graphs, in which two graphs are given on the same vertex set and one must find a placement for the vertices in which both graphs are drawn planarly with straight edges.. Book embeddings with more than two pages have also been used to construct three- dimensional drawings of graphs.
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As part of their work on graph minors leading to the Robertson–Seymour theorem and the graph structure theorem, Neil Robertson and Paul Seymour proved that a family F of finite graphs has unbounded treewidth if and only if the minors of graphs in F include arbitrarily large square grid graphs, or equivalently subgraphs of the hexagonal tiling formed by intersecting it with arbitrarily large disks. Although the precise relation between treewidth and grid minor size remains elusive, this result became a cornerstone in the theory of bidimensionality, a characterization of certain graph parameters that have particularly efficient fixed-parameter tractable algorithms and polynomial-time approximation schemes. For finite graphs, the treewidth is always one less than the maximum order of a haven, where a haven describes a certain type of strategy for a robber to escape the police in a pursuit-evasion game played on the graph, and the order of the haven gives the number of police needed to catch a robber using this strategy. Thus, the relation between treewidth and grid minors can be restated: in a family of finite graphs, the order of the havens is unbounded if and only if the size of the grid minors is unbounded.
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