The coming years will mold the calculi on the decisions of this massive summer.
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On the computational power of Brane calculi. Third Workshop on Computational Methods in Systems Biology, 106-117, 2005. 10\. L. Cardelli. Brane Calculi.
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The term is derived from the Greek words sialon (saliva) and lithos (stone), and the Greek -iasis meaning "process" or "morbid condition". A calculus (plural calculi) is a hard, stone-like concretion that forms within an organ or duct inside the body. They are usually made from mineral salts, and other types of calculi include tonsiloliths (tonsil stones) and renal calculi (kidney stones). Sialolithiasis refers to the formation of calculi within a salivary gland.
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In what follows it is shown that mobile membranes have at least the expressive power of mobile ambients and brane calculi by encoding mobile ambients and brane calculi in certain systems of mobile membranes.
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Other process calculi have been developed for describing communication and concurrency.
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The use of channels for communication is one of the features distinguishing the process calculi from other models of concurrency, such as Petri nets and the actor model (see Actor model and process calculi). One of the fundamental motivations for including channels in the process calculi was to enable certain algebraic techniques, thereby making it easier to reason about processes algebraically.
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This is a list of formal systems, also known as logical calculi.
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The tableau calculi mentioned above can be proved complete. A remarkable difference between tableau with unification and the other two calculi is that the latter two calculi only modify a tableau by adding new nodes to it, while the former one allows substitutions to modify the existing part of the tableau. More generally, tableau calculi are classed as destructive or non-destructive depending on whether they only add new nodes to tableau or not. Tableau with unification is therefore destructive, while propositional tableau and tableau without unification are non-destructive.
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For most typed calculi, the type inhabitation problem is very hard. Richard Statman proved that for simply typed lambda calculus the type inhabitation problem is PSPACE-complete. For other calculi, like System F, the problem is even undecidable.
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In 1982 Jan Bergstra and Jan Willem Klop began work on what came to be known as the Algebra of Communicating Processes (ACP), and introduced the term process algebra to describe their work. CCS, CSP, and ACP constitute the three major branches of the process calculi family: the majority of the other process calculi can trace their roots to one of these three calculi.
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The Actor model and process calculi share an interesting history and co- evolution.
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Ugo Montanari and Carolyn Talcott [1998] have contributed to attempting to reconcile Actors with process calculi.
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I introduce a general method, the amphibologization method, to generate amphibologies in pre-existent logical calculi.
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Lambda calculi with dependent types are the base of intuitionistic type theory, the calculus of constructions and the logical framework (LF), a pure lambda calculus with dependent types. Based on work by Berardi on pure type systems, Henk Barendregt proposed the Lambda cube to systematize the relations of pure typed lambda calculi (including simply typed lambda calculus, System F, LF and the calculus of constructions). Some typed lambda calculi introduce a notion of subtyping, i.e. if A is a subtype of B, then all terms of type A also have type B. Typed lambda calculi with subtyping are the simply typed lambda calculus with conjunctive types and System F<:.
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Shows the polynomials presently known as Eulerian polynomials in Euler's work from 1755, Institutiones calculi differentialis, part 2, p. 485/6. The coefficients of these polynomials are known as Eulerian numbers. In 1755 Leonhard Euler investigated in his book Institutiones calculi differentialis polynomials , , , etc. (see the facsimile).
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Scan of first page of L. Eulers book Institutionum Calculi Integralis Vol 1 Institutionum calculi integralis is a three-volume textbook written by Leonhard Euler and published in 1768. It was on the subject of integral calculus and contained many of Euler's discoveries about differential equations.
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There are several types of proof calculi. The most popular are natural deduction, sequent calculi (i.e., Gentzen type systems), Hilbert systems, and semantic tableaux or trees. A given proof procedure will target a specific proof calculus, but can often be reformulated so as to produce proofs in other proof styles.
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Matthew Hennessy is an Irish computer scientist who has contributed especially to concurrency, process calculi and programming language semantics.
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As for intermediate logics, hypersequents have been used to obtain analytic calculi for many substructural logics and fuzzy logics.
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For System LK, System LJ, and System LL, uniform proofs are focused proofs where all the atoms are assigned negative polarity. Many other sequent calculi has been shown to have the focusing property, notably the nested sequent calculi of both the classical and intuitionistic variants of the modal logics in the S5 cube.
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In calculi of communicating processes (like pi- calculus), the vertical bar is used to indicate that processes execute in parallel.
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Therefore many calculi of explicit substitution avoid variable names altogether by using a so-called "name-free" De Bruijn index notation.
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Various prostate pathologies (including prostatitis, calculi (stones), cysts, benign prostatic hyperplasia, bacterial infection, etc.) may result in blood occurring in the ejaculate.
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273, Benjamin C. Pierce Typed lambda calculi are foundational programming languages and are the base of typed functional programming languages such as ML and Haskell and, more indirectly, typed imperative programming languages. Typed lambda calculi play an important role in the design of type systems for programming languages; here typability usually captures desirable properties of the program, e.g. the program will not cause a memory access violation. Typed lambda calculi are closely related to mathematical logic and proof theory via the Curry–Howard isomorphism and they can be considered as the internal language of classes of categories, e.g.
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It may rupture, leading to peritonitis, or it may drain through the umbilicus. Urachal cysts are usually silent clinically until infection, calculi or adenocarcinoma develop.
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An 8-mm kidney stone A calculus (plural calculi), often called a stone, is a concretion of material, usually mineral salts, that forms in an organ or duct of the body. Formation of calculi is known as lithiasis (). Stones can cause a number of medical conditions. Some common principles (below) apply to stones at any location, but for specifics see the particular stone type in question.
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The Romans similarly used pebbles (in Latin: calculi "little stones", whence English calculate). Addition is straightforward, and relatively efficient algorithms for multiplication and division were known.
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A traditional Chinese doctor typically prescribes about 6 to 10 tablets for expelling calculi, and about 4 to 6 tablets for treating inflammation, twice a day.
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Sequent calculi and systems of natural deduction have been developed for several modal logics, but it has proven hard to combine generality with other features expected of good structural proof theories, such as purity (the proof theory does not introduce extra-logical notions such as labels) and analyticity (the logical rules support a clean notion of analytic proof). More complex calculi have been applied to modal logic to achieve generality.
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More so than the other seminal process calculi (CCS and CSP), the development of ACP focused on the algebra of processes, and sought to create an abstract, generalized axiomatic system for processes,Bas Luttik, What is algebraic in process theory, Algebraic Process Calculi: The First Twenty Five Years and Beyond , Bertinoro, Italy, August 1, 2005 and in fact the term process algebra was coined during the research that led to ACP.
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In computer science, the process calculi (or process algebras) are a diverse family of related approaches for formally modelling concurrent systems. Process calculi provide a tool for the high-level description of interactions, communications, and synchronizations between a collection of independent agents or processes. They also provide algebraic laws that allow process descriptions to be manipulated and analyzed, and permit formal reasoning about equivalences between processes (e.g., using bisimulation).
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Typed lambda calculi are weaker than the untyped lambda calculus, which is the primary subject of this article, in the sense that typed lambda calculi can express less than the untyped calculus can, but on the other hand typed lambda calculi allow more things to be proven; in the simply typed lambda calculus it is, for example, a theorem that every evaluation strategy terminates for every simply typed lambda-term, whereas evaluation of untyped lambda-terms need not terminate. One reason there are many different typed lambda calculi has been the desire to do more (of what the untyped calculus can do) without giving up on being able to prove strong theorems about the calculus. Lambda calculus has applications in many different areas in mathematics, philosophy,Coquand, Thierry, "Type Theory", The Stanford Encyclopedia of Philosophy (Summer 2013 Edition), Edward N. Zalta (ed.). linguistics, and computer science.. Lambda calculus has played an important role in the development of the theory of programming languages.
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In 2007, John N. Shutt proposed an extension of lambda calculus that would model without suppressing rewriting of operands, ostensibly avoiding Wand's result.Shutt, "vau-calculi and the theory of fexprs".
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Recipient of the Hari Om Ashram Prerit Award in 1986 for the best piece of Surgical Research on "Newer Aetriopathologoical aspects of Urinary Calculi and means of preventing their recurrence".
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Associated minerals include tanarakite, ardealite, hydroxylapatite, variscite and gypsum. Brushite is the original precipitating material in calcium phosphate kidney stones. It is also one of the minerals present in dental calculi.
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Other concurrency systems (e.g., process calculi) can be modeled in the actor model using a two-phase commit protocol.Frederick Knabe. A Distributed Protocol for Channel-Based Communication with Choice PARLE 1992.
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In a series of seminars in 1961 and 1962 Prawitz gave a comprehensive summary of natural deduction calculi, and transported much of Gentzen's work with sequent calculi into the natural deduction framework. His 1965 monograph Natural deduction: a proof-theoretical study, . was to become a reference work on natural deduction, and included applications for modal and second-order logic. In natural deduction, a proposition is deduced from a collection of premises by applying inference rules repeatedly.
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Typed lambda calculi play an important role in the design of type systems for programming languages; here typability usually captures desirable properties of the program, e.g. the program will not cause a memory access violation. Typed lambda calculi are closely related to mathematical logic and proof theory via the Curry-Howard isomorphism and they can be considered as the internal language of classes of categories, e.g. the simply typed lambda calculus is the language of Cartesian closed categories (CCCs).
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The following year he was commissioned to illustrate the Norwich surgeon John Green Crosse's prize- winning essay on urinary calculi. His paintings usually feature wooded landscapes around Norwich, or rural river scenes.
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Leading examples of process calculi include CSP, CCS, ACP, and LOTOS. More recent additions to the family include the π-calculus, the ambient calculus, PEPA, the fusion calculus and the join-calculus.
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4286-4292, 1989.F. H. Long, N. S. Nishioka, and T. F. Deustch, “Measurement of the optical and thermal properties of biliary calculi using pulsed photothermal radiometry,” Lasers Surg. Med., vol. 7, pp.
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Quantum lambda calculi are extensions of the classical lambda calculus introduced by Alonzo Church and Stephen Cole Kleene in the 1930s. The purpose of quantum lambda calculi is to extend quantum programming languages with a theory of higher-order functions. The first attempt to define a quantum lambda calculus was made by Philip Maymin in 1996.Philip Maymin, "Extending the Lambda Calculus to Express Randomized and Quantumized Algorithms", 1996 His lambda-q calculus is powerful enough to express any quantum computation.
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He was a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, supports, and maintains the programming languages ALGOL 60 and ALGOL 68.
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Logic Journal of the IGPL 22 (2014), pages 982–991. Syntactically, cirquent calculi are deep inference systems with the unique feature of subformula-sharing. This feature has been shown to provide speedup for certain proofs.
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Applicative computing systems, or ACS are the systems of object calculi founded on combinatory logic and lambda calculus.Wolfengagen V.E. Methods and means for computations with objects. Applicative Computational Systems. — M.: JurInfoR Ltd., «Center JurInfoR», 2004.
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Calculi can be distinguished from real egg fossils because when they are broken open, they show the layers of calcium phosphate and the foreign object at the core. Multiple layers of eggshell are known in pathological eggs, but these layers don't go all the way down to its core the way a stomach stone's do. Calculi are often suspiciously intact, unlike fossil eggs, which are usually damaged. Stomach stones also lack distinct shells with their attending structural components like continuous or prismatic layers, mammillae, and pores.
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Thus one is interested in functional calculi more general than polynomials. The subject is closely linked to spectral theory, since for a diagonal matrix or multiplication operator, it is rather clear what the definitions should be.
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Models of concurrency such as the process calculi, Petri nets in 1962, and the actor model in 1973 emerged from this line of inquiry. Research on process calculi began in earnest with Robin Milner's seminal work on the Calculus of Communicating Systems (CCS) during the period from 1973 to 1980. C.A.R. Hoare's Communicating Sequential Processes (CSP) first appeared in 1978, and was subsequently developed into a full-fledged process calculus during the early 1980s. There was much cross-fertilization of ideas between CCS and CSP as they developed.
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It was said to have been played during the Trojan War. The Romans played a derivation of petteia called latrunculi, or the game of the Little Soldiers. The pieces, and sporadically the game itself, were called calculi (pebbles).
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Lithotomy is a surgical method for removal of calculi, stones formed inside certain organs, such as the urinary tract (kidney stones), bladder (bladder stones), and gallbladder (gallstones), that cannot exit naturally through the urinary system or biliary tract.
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JoCaml and Funnel are functional languages supporting declarative join patterns. They present the ideas to direct implement a process calculi in a functional setting. Another extensions to (non-generic) Java, JoinJava, were independently proposed by von Itzstein and Kearney.
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Their bladder is also usually bilobed with a left and right section. The right section is located under the liver, which prevents large stones from remaining in that side while the left section is more likely to have calculi.
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The Scott topology was first defined by Dana Scott for complete lattices and later defined for arbitrary partially ordered sets. Scott-continuous functions show up in the study of models for lambda calculi and the denotational semantics of computer programs.
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The Latin word saxifraga means literally "stone- breaker", from Latin ' ("rock" or "stone") + ' ("to break"). It is usually thought to indicate a medicinal use for treatment of urinary calculi (known as kidney or bladder stones), rather than breaking rocks apart.
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In addition, the increased intracellular calcium has greater time to bind due to the blockage allowing for renal calculi to form.Rodriguez, Eva. Solar, Maria J. et al. “Risk Factors for Acute Kidney Injury in Severe Rhabdomyolsis.” PLOSONE 10.1371 (2013). Web.
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Arbitration is the basis of the indeterminacy in the Actor model of concurrent computation (see History of the Actor model and Actor model theory). It may also play a role in other models of concurrent systems such as process calculi.
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The general notion of sequent introduced here can be specialized in various ways. A sequent is said to be an intuitionistic sequent if there is at most one formula in the succedent (although multi-succedent calculi for intuitionistic logic are also possible). More precisely, the restriction of the general sequent calculus to single-succedent-formula sequents, with the same inference rules as for general sequents, constitutes an intuitionistic sequent calculus. (This restricted sequent calculus is denoted LJ.) Similarly, one can obtain calculi for dual-intuitionistic logic (a type of paraconsistent logic) by requiring that sequents be singular in the antecedent.
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A typed lambda calculus is a typed formalism that uses the lambda-symbol (\lambda) to denote anonymous function abstraction. In this context, types are usually objects of a syntactic nature that are assigned to lambda terms; the exact nature of a type depends on the calculus considered (see Kinds of typed lambda calculi). From a certain point of view, typed lambda calculi can be seen as refinements of the untyped lambda calculus but from another point of view, they can also be considered the more fundamental theory and untyped lambda calculus a special case with only one type.Types and Programming Languages, p.
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It is also used in some toothpastes as a tartar control agent. Heating dicalcium phosphate gives dicalcium diphosphate, a useful polishing agent: :2 CaHPO4 → Ca2P2O7 \+ H2O In the dihydrate (brushite) form it is found in some kidney stones and in dental calculi.
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It has been used both as a framework for a theoretical understanding of computation and as the theoretical basis for several practical implementations of concurrent systems. The relationship of the model to other work is discussed in actor model and process calculi.
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This approach is still under investigation, though early results are favorable. Percutaneous nephrolithotomy or, rarely, anatrophic nephrolithotomy, is the treatment of choice for large or complicated stones (such as calyceal staghorn calculi) or stones that cannot be extracted using less invasive procedures.
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On the Comparative Infrequency of Urinary Calculi in Seafaring People, 1818 Oddly, the study seemed to believe that naval diet destroyed the inevitability of kidney stones, rather than considering that naval diet excluded the causes of kidney stones (being very low in dairy products).
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Other theories suggest that dilatation of a collecting duct may occur, caused by occlusion by uric acid during fetal life or resulting from tubular obstruction due to calcium oxalate calculi secondary to infantile hypercalciuria. A rare, autosomal recessive form is associated with Caroli disease.
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Copy of a Roman abacus The normal method of calculation in ancient Rome, as in Greece, was by moving counters on a smooth table. Originally pebbles (calculi) were used. Later, and in medieval Europe, jetons were manufactured. Marked lines indicated units, fives, tens etc.
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Ultrasound image of sialolithiasis Stone resulting in inflammation and dilation of the duct Diagnosis is usually made by characteristic history and physical examination. Diagnosis can be confirmed by x-ray (80% of salivary gland calculi are visible on x-ray), by sialogram, or by ultrasound.
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The internal language of the cartesian closed category is the simply typed lambda calculus. This view can be extend to other typed lambda calculi. Certain Cartesian closed categories, the topoi, have been proposed as a general setting for mathematics, instead of traditional set theory.
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In computer science, lambda calculi are said to have explicit substitutions if they pay special attention to the formalization of the process of substitution. This is in contrast to the standard lambda calculus where substitutions are performed by beta reductions in an implicit manner which is not expressed within the calculus. The concept of explicit substitutions has become notorious (despite a large number of published calculi of explicit substitutions in the literature with quite different characteristics) because the notion often turns up (implicitly and explicitly) in formal descriptions and implementation of all the mathematical forms of substitution involving variables such as in abstract machines, predicate logic, and symbolic computation.
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Excerpt from p.233 of the E212 — Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum. Euler sums similar series, ca. 1755. The threefold Cauchy product of is the alternating series of triangular numbers; its Abel and Euler sum is .Kline, p.313.
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He was editor-in-chief of the journal for over 25 years. He was a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, supports, and maintains the programming languages ALGOL 60 and ALGOL 68.
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Indirect communication using channels (e.g. Gilles Kahn and David MacQueen [1977]) has been an important issue for communication in parallel and concurrent computation affecting both semantics and performance. Some process calculi differ from the Actor model in their use of channels as opposed to direct communication.
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This can lead to the formation of struvite calculi or renal stones. Risk factors associated with this bacterium include immunosuppression, underlying genitourinary disorders, and antibiotic therapy. There are other urease-producing corynebacteria that are associated with urinary tract infections, but C. urealyticum is the most common.
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There are two different calculi that use the name rho-calculus. The first is a formalism intended to combine the higher-order facilities of lambda calculus with the pattern matching of term rewriting. The second is a reflective higher-order variant of the asynchronous polyadic pi calculus.
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There are several health problems associated with Newfoundlands. Newfoundlands are prone to hip dysplasia (a malformed ball and socket in the hip joint). They also get elbow dysplasia, and cystinuria (a hereditary defect that forms calculi stones in the bladder). Another genetic problem is subvalvular aortic stenosis (SAS).
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Each of these models has been identified as representing a certain numerical value, or a specific type of merchandise. They made it possible to store information for the management of institutions (arrival and departure of goods) or commercial operations, and to send that information to other places. These calculi are perhaps the same type as the tokens found on sites in the Near East for the next few thousand years, whose function remains uncertain. It is thought that notches would be placed on the surface of the clay balls containing the calculi, leading to the creation of numerical tablets which served as an aide-mémoire before the development of true writing (on which, see below).
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Hypersequent calculi based on intuitionistic or single-succedent sequents have been used successfully to capture a large class of intermediate logics, i.e., extensions of intuitionistic propositional logic. Since the hypersequents in this setting are based on single-succedent sequents, they have the following form: : \Gamma_1 \Rightarrow A_1 \mid \dots \mid \Gamma_n \Rightarrow A_n The standard formula interpretation for such an hypersequent is : (\bigwedge\Gamma_1 \to A_1) \lor \dots \lor (\bigwedge\Gamma_n \to A_n) Most hypersequent calculi for intermediate logics include the single-succedent versions of the propositional rules given above, a selection of the structural rules. The characteristics of a particular intermediate logic are mostly captured using a number of additional structural rules. E.g.
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One study came to the conclusion that the presence of salivary calculi is the main indicator for the removal of the submandibular gland, in patients where neoplasia is absent. This was because 82% of glands removed in an ENT department in Stockholm were found to have salivary calculi within them and all of these cases but one had chronic sialadenitis. A mucous retention cyst was found in one patient, but this was not considered to have contributed to the sialadenitis in this case. The duration of the sialadenitis was found to be closely linked to atrophy, fibrosis and the degree of the inflammation in another study, which looked primarily at microliths found in the ducts and glands.
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The π-calculus belongs to the family of process calculi, allows mathematical formalisms for describing and analyzing properties of concurrent computation by using channel names to be communicated along the channels themselves, and in this way it is able to describe concurrent computations whose network configuration may change during the computation.
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In 1966, Sutor was offered a job by Kathleen Lonsdale at University College London. She studied urinary calculi and searched for ways to prevent them. Sutor had good contacts with hospital staff, and even managed to secure Napoléon III's bladder stone. She was supported by a grant from the Nuffield Foundation.
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He was involved with developing international standards in programming and informatics, as a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the programming languages ALGOL 60 and ALGOL 68. and of IFIP Working Group 2.3 on Programming Methodology.
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Concurrency is a property of systems in which several computations are executing simultaneously, and potentially interacting with each other.Jiacun Wang, 2017. Real-Time Embedded Systems. Wiley. p. 12. . A number of mathematical models have been developed for general concurrent computation including Petri nets, process calculi and the Parallel Random Access Machine model.
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He has authored many papers. He is involved with developing international standards in programming and informatics, as an active member of several International Federation for Information Processing (IFIP) working groups, including IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the programming languages ALGOL 60 and ALGOL 68.
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Lidan Paishi Pian () is a sugar-coated tablet or film-coated tablet with a brown core, used in Traditional Chinese medicine to "remove damp-heat, increase the flow of bile and expel calculi".State Pharmacopoeia Commission of the PRC (2005). "Pharmacopoeia of The People's Republic of China (Volume I)". Chemical Industry Press. .
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He was involved with developing international standards in programming and informatics, as a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the programming languages ALGOL 60 and ALGOL 68. He favors and often uses the language Haskell.
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The correspondence has been the starting point of a large spectrum of new research after its discovery, leading in particular to a new class of formal systems designed to act both as a proof system and as a typed functional programming language. This includes Martin-Löf's intuitionistic type theory and Coquand's Calculus of Constructions, two calculi in which proofs are regular objects of the discourse and in which one can state properties of proofs the same way as of any program. This field of research is usually referred to as modern type theory. Such typed lambda calculi derived from the Curry–Howard paradigm led to software like Coq in which proofs seen as programs can be formalized, checked, and run.
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A typed lambda calculus is a typed formalism that uses the lambda-symbol (\lambda) to denote anonymous function abstraction. In this context, types are usually objects of a syntactic nature that are assigned to lambda terms; the exact nature of a type depends on the calculus considered (see kinds below). From a certain point of view, typed lambda calculi can be seen as refinements of the untyped lambda calculus but from another point of view, they can also be considered the more fundamental theory and untyped lambda calculus a special case with only one type. Typed lambda calculi are foundational programming languages and are the base of typed functional programming languages such as ML and Haskell and, more indirectly, typed imperative programming languages.
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The hypersequent structure seem to have appeared first in under the name of cortege to obtain a calculus for modal logic S5. It seems to have been developed independently in, also for treating modal logics, and in the influential, where calculi for modal, intermediate and substructural logics are considered, and the term hypersequent is introduced.
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The most common causes of hydronephrosis in children are anatomical abnormalities. These include vesicoureteral reflux, urethral stricture, and stenosis. The most common cause of hydronephrosis in young adults is kidney stones, or renal calculi. In older adults, the most common cause of hydronephrosis is benign prostate hyperplasia (BPH), or intrapelvic neoplasms such as prostate cancer.
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Petri nets are an attractive and powerful model for reasoning about asynchronous circuits. However, Petri nets have been criticized for their lack of physical realism (see Petri net: Subsequent models of concurrency). Subsequent to Petri nets other models of concurrency have been developed that can model asynchronous circuits including the Actor model and process calculi.
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Other uses include painful spasms of the esophagus such as from cancer or tetanus. It is also used for the small subset of people with pulmonary hypertension. Finally, nifedipine can be used in the treatment of renal calculi, which are commonly referred to as kidney stones. Studies have indicated that it helps to relieve renal colic.
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He has also been engaged in the application of x-ray powder diffraction to solving problems in such diverse fields as urinary calculi, road soils, platinum refining, fossils and breccia; and has taught specialist courses for architecture students on Materials and Failures. For 30 years his annual Christmas Chemical Magic Show has drawn audiences of hundreds.
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Renal causes can be attributed to decreased kidney function. These include acute and chronic kidney failure, acute and chronic glomerulonephritis, tubular necrosis and other kidney diseases. Post renal causes can be due to decreased elimination of urea. These could be due to urinary outflow obstruction such as by calculi, tumours of the bladder or prostate, or a severe infection.
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Excretory calcinosis in American lobsters in Long Island Sound was described in 2002. The disease causes mineralized calculi to form in the antennal glands and gills. These cause a loss of surface area around the gills, and the lobster eventually asphyxiates. Several reasons have been proposed for the cause of a recent outbreak of the disease.
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Java and Ada only have exclusive locks because they are thread based and rely on the compare-and-swap processor instruction. An abstract mathematical foundation for synchronization primitives is given by the history monoid. There are also many higher-level theoretical devices, such as process calculi and Petri nets, which can be built on top of the history monoid.
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Vladimir Aleksandrovich Smirnov (1931 – 12 February 1996, in Moscow) was a Russian philosopher. He worked at both Tomsk University in Siberia and later at the Department of Logic of the Institute of Philosophy, Moscow. He revived interest in the work of Nicolai A. Vasiliev. His doctoral thesis "Formal logic and Logical Calculi" was published in 1972.
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The -calculus belongs to the family of process calculi, mathematical formalisms for describing and analyzing properties of concurrent computation. In fact, the -calculus, like the λ-calculus, is so minimal that it does not contain primitives such as numbers, booleans, data structures, variables, functions, or even the usual control flow statements (such as `if-then-else`, `while`).
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However, states that the assertion symbol in Gentzen-system sequents, which he denotes as ' ⇒ ', is part of the object language, not the metalanguage., defines sequents to have the form U ⇒ V for (possibly non-empty) sets of formulas U and V. Then he writes: : "Intuitively, a sequent represents 'provable from' in the sense that the formulas in U are assumptions for the set of formulas V that are to be proved. The symbol ⇒ is similar to the symbol ⊢ in Hilbert systems, except that ⇒ is part of the object language of the deductive system being formalized, while ⊢ is a metalanguage notation used to reason about deductive systems." According to Prawitz (1965): "The calculi of sequents can be understood as meta-calculi for the deducibility relation in the corresponding systems of natural deduction.".
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Deep inference names a general idea in structural proof theory that breaks with the classical sequent calculus by generalising the notion of structure to permit inference to occur in contexts of high structural complexity. The term deep inference is generally reserved for proof calculi where the structural complexity is unbounded; in this article we will use non-shallow inference to refer to calculi that have structural complexity greater than the sequent calculus, but not unboundedly so, although this is not at present established terminology. Deep inference is not important in logic outside of structural proof theory, since the phenomena that lead to the proposal of formal systems with deep inference are all related to the cut-elimination theorem. The first calculus of deep inference was proposed by Kurt Schütte,Kurt Schütte.
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Later record keeping aids throughout the Fertile Crescent included calculi (clay spheres, cones, etc.) which represented counts of items, probably livestock or grains, sealed in hollow unbaked clay containers.According to , these clay containers contained tokens, the total of which were the count of objects being transferred. The containers thus served as something of a bill of lading or an accounts book.
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Scheme was the first full production system (1969-1970), providing first "catch" and then call/cc. Bruce Duba introduced call/cc into SML. Continuations are also used in models of computation including denotational semantics, the actor model, process calculi, and lambda calculus. These models rely on programmers or semantics engineers to write mathematical functions in the so-called continuation-passing style.
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The calculus of structures is a proof calculus with deep inference for studying the structural proof theory of noncommutative logic. The calculus has since been applied to study linear logic, classical logic, modal logic, and process calculi, and many benefits are claimed to follow in these investigations from the way in which deep inference is made available in the calculus.
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"Multiplicative calculus in biomedical image analysis", Journal of Mathematical Imaging and Vision, DOI: 10.1007/s10851-011-0275-1, 2011. The table below is intended to assist people working with the alternative calculus called the "geometric calculus" (or its discrete analog). Interested readers are encouraged to improve the table by inserting citations for verification, and by inserting more functions and more calculi.
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S.N. Krishna. The Power of Mobility: Four Membranes Suffice. Lecture Notes in Computer Science, vol.3526, 242—251, Springer, 2005. 18\. S.N. Krishna. Membrane computing with transport and embedded proteins. Theoretical Computer Science, vol.410, 355-375, 2009. 19\. S.N. Krishna. Universality results for P systems based on brane calculi operations. Theoretical Computer Science, vol.371, 83-105, 2007. 20\.
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In computer science, a computation is said to diverge if it does not terminate or terminates in an exceptional state. Otherwise it is said to converge. In domains where computations are expected to be infinite, such as process calculi, a computation is said to diverge if it fails to be productive (i.e. to continue producing an action within a finite amount of time).
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He obtained this position without a Doctor of Philosophy (Ph.D.) degree. He was a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the programming languages ALGOL 60 and ALGOL 68. He was elected a Fellow of the American Academy of Arts and Sciences in 1974.
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Dorothy June Sutor (6 June 1929 – 27 May 1990) was a New Zealand-born crystallographer who spent most of her research career in England. She was one of the first scientists to establish that hydrogen bonds could form to hydrogen atoms bonded to carbon atoms. She later worked in the laboratory of Kathleen Lonsdale on the characterisation and prevention of urinary calculi.
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Soon after settling down he elaborated a chart of stethoscopic signs, and carried out an investigation into the solubility of calculi within the body. The former work was favourably reviewed, and passed into a second edition. The latter occupied many years of his life. His results presented to the Royal Society gained his election to a fellowship on 25 May 1843.
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Incidence among wether lambs can be minimized by maintaining a dietary Ca:P intake ratio of 2:1. Alkaline (higher) pH favors formation of carbonate and phosphate calculi. For domestic ruminants, dietary cation: anion balance is sometimes adjusted to assure a slightly acidic urine pH, for prevention of calculus formation. Differing generalizations regarding effects of pH on formation of silicate uroliths may be found.
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On 1 December, Xinhua reported that the Ministry of Health revised the number of victims to more than 290,000 with 51,900 hospitalized; authorities acknowledged receiving reports of 11 suspected deaths from melamine contaminated powdered milk from provinces, but officially confirmed three deaths. On characterisation and treatment of urinary stones in affected infants, the New England Journal of Medicine printed an editorial in March 2009, along with reports on cases from Beijing, Hong Kong and Taipei. Urinary calculi specimens were collected from 15 cases treated in Beijing and were analysed as unknown objects for their components at Beijing Institute of Microchemistry using infrared spectroscopy, nuclear magnetic resonance, and high-performance liquid chromatography. The result of the analyses showed the calculi were composed of melamine and uric acid, and the molecular ratio of uric acid to melamine was around 2:1.
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The Curry-Howard isomorphism between proofs and programs relates to proof theory, especially intuitionistic logic. Formal calculi such as the lambda calculus and combinatory logic are now studied as idealized programming languages. Computer science also contributes to mathematics by developing techniques for the automatic checking or even finding of proofs, such as automated theorem proving and logic programming. Descriptive complexity theory relates logics to computational complexity.
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Transition monoids and syntactic monoids are used in describing finite-state machines. Trace monoids and history monoids provide a foundation for process calculi and concurrent computing. In theoretical computer science, the study of monoids is fundamental for automata theory (Krohn–Rhodes theory), and formal language theory (star height problem). See Semigroup for the history of the subject, and some other general properties of monoids.
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In 1843, lithium carbonate was used as a new solvent for stones in the bladder. In 1859, some doctors recommended a therapy with lithium salts for a number of ailments, including gout, urinary calculi, rheumatism, mania, depression, and headache. In 1948, John Cade discovered the antimanic effects of lithium ions. This finding led lithium, specifically lithium carbonate, to be used to treat mania associated with bipolar disorder.
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Processes are often called "tasks" in embedded operating systems. The sense of "process" (or task) is "something that takes up time", as opposed to "memory", which is "something that takes up space". The above description applies to both processes managed by an operating system, and processes as defined by process calculi. If a process requests something for which it must wait, it will be blocked.
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This basic diversity among the various calculi allows such difference, that the same basic thought (e.g. deduction theorem) must be proven as a metatheorem in Hilbert-style deduction system, while it can be declared explicitly as a rule of inference in natural deduction. In type theory, some analogous notions are used as in mathematical logic (giving rise to connections between the two fields, e.g. Curry–Howard correspondence).
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In computer science, he is known for his work on dialects of the programming language ALGOL. Especially see p. 61. He became involved with developing international standards in programming and informatics, as a Japanese representative on the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, supports, and maintains the languages ALGOL 60 and ALGOL 68.
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Join patterns first appeared in Fournet and Gonthier’s foundational join calculus, an asynchronous process algebra designed for efficient implementation in a distributed setting. The join-calculus is a process calculus as expressive as the full π-calculus. It was developed to provide a formal basis for the design of distributed programming languages, and therefore intentionally avoids communications constructs found in other process calculi, such as rendezvous communications.
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The flow of saliva from the submandibular gland is often against gravity due to variations in the location of the duct orifice. The orifice itself is smaller than that of the parotid. These factors all promote slowing and stasis of saliva in the submandibular duct, making the formation of an obstruction with subsequent calcification more likely. Salivary calculi sometimes are associated with other salivary diseases, e.g.
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In 1982 Roberto Cignoli published some additional constraints that added to LMn-algebras yield proper models for n-valued Łukasiewicz logic; Cignoli called his discovery proper n-valued Łukasiewicz algebras.R. Cignoli, Proper n-Valued Łukasiewicz Algebras as S-Algebras of Łukasiewicz n-Valued Propositional Calculi, Studia Logica, 41, 1982, 3-16, The LMn-algebras that are also MVn-algebras are precisely Cignoli’s proper n-valued Łukasiewicz algebras.
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In 1793 he was a juror of the Revolutionary Tribunal. Known for his work in lithotomy, especially using the suprapubic method. It is believed that he performed over 1200 suprapubic operations for removal of calculi during his career.System of surgery, Volume 1 by Frederic Shepard Dennis, John Shaw As did Jean Baseilhac, he advocated use of a caustic paste containing arsenic for cauterization of cancers.
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About 10–15% of urinary calculi are composed of struvite (ammonium magnesium phosphate, NH4MgPO4·6H2O). Struvite stones (also known as "infection stones," urease, or triple-phosphate stones) form most often in the presence of infection by urea-splitting bacteria. Using the enzyme urease, these organisms metabolize urea into ammonia and carbon dioxide. This alkalinizes the urine, resulting in favorable conditions for the formation of struvite stones.
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Kleene and Rosser were able to show that both systems are able to characterize and enumerate their provably total, definable number-theoretic functions, which enabled them to construct a term that essentially replicates the Richard paradox in formal language. Curry later managed to identify the crucial ingredients of the calculi that allowed the construction of this paradox, and used this to construct a much simpler paradox, now known as Curry's paradox.
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Study of the buildings on this site shows that it was a planned settlement, which would have required significant means. The archaeological material from the site is identical to that of Uruk, consisting of pottery, cylinder-seals, bullae, accounting calculi, and numerical tablets from the end of the period. Thus this new city has every appearance of being an Urukian colony. Around 20 residences of various sorts have been excavated.
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Formal models of legal texts and legal reasoning have been used in AI and Law to clarify issues, to give a more precise understanding and to provide a basis for implementations. A variety of formalisms have been used, including propositional and predicate calculi; deontic, temporal and non-monotonic logics; and state transition diagrams. Prakken and SartorH. Prakken and G.Sartor, Law and logic: A review from an argumentation perspective, Artificial Intelligence.
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A tableau calculus is a set of rules that allows building and modification of a tableau. Propositional tableau rules, tableau rules without unification, and tableau rules with unification, are all tableau calculi. Some important properties a tableau calculus may or may not possess are completeness, destructiveness, and proof confluence. A tableau calculus is called complete if it allows building a tableau proof for every given unsatisfiable set of formulae.
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In a theoretical setting, it is desirable to study the interaction of the two features; a common theoretical setting is system F<:. Various calculi that attempt to capture the theoretical properties of object-oriented programming may be derived from system F<:. The concept of subtyping is related to the linguistic notions of hyponymy and holonymy. It is also related to the concept of bounded quantification in mathematical logic.
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Jackstone calculi are rare bladder stones that have an appearance resembling toy jacks. They are almost always composed of calcium oxalate dihydrate and consist of a dense central core and radiating spicules. They are typically light brown with dark patches and are usually formed in the urinary bladder and rarely in the upper urinary tract. Their appearance on plain radiographs and computed tomography in human patients is usually easily recognizable.
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In 1821, March taught the first anatomy course in the history of New York State. He later founded the Practical School for Anatomy and Surgery in Albany, NY, and held the first chair in surgery at Albany Medical College. Among the devices invented by March were novel methods for removing dead bone and renal calculi. He served as President of the American Medical Association and the New York State Medical Society.
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The Ishango bone, a bone tool dating back to prehistoric Africa. Devices have been used to aid computation for thousands of years, mostly using one-to-one correspondence with fingers. The earliest counting device was probably a form of tally stick. Later record keeping aids throughout the Fertile Crescent included calculi (clay spheres, cones, etc.) which represented counts of items, probably livestock or grains, sealed in hollow unbaked clay containers.
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Turtles have two or more accessory urinary bladders, located lateral to the neck of the urinary bladder and dorsal to the pubis, occupying a significant portion of their body cavity. Their bladder is also usually bilobed with a left and right section. The right section is located under the liver, which prevents large stones from remaining in that side while the left section is more likely to have calculi.
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The most common findings on HRCT are diffuse hyperdense ground- glass attenuation and subpleural linear calcifications, often most predominant in the inferior and posterior portions of the lungs. Additionally, the medial aspects of the lungs appear to be more heavily involved than the lateral aspects. Ground-glass opacities, probably due to small calculi in the air space, are the most common finding in children and in patients with early- stage PAM.
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Ultrasonography can also be used to estimate hepatic volume and vascularity, and to identify related lesions affecting other abdominal structures, such as urinary calculi. Computed tomography (CT) may be considered when ultrasound expertise is lacking or ultrasonography is considered sub-optimal (e.g. because of the conformation of the patient). Control of respiration and careful timing of CT acquisition after contrast injection is necessary for optimal depiction of PSS.
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He improved the rhinoplasty technique. He also developed the syringotome, a special type of scalpel. Among his developments in urology were his technique to puncture the bladder (cytotomy), various methods of removing urinary calculi, external and internal urethrotomies, the subcutaneous ligation of varicocele veins using the fisherman's knot, and genital operations. Argumosa also contributed to the field of arthrology, although it was his students who developed upon his work.
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The calculus of variations may be said to begin with a problem of Johann Bernoulli (1696). It immediately occupied the attention of Jakob Bernoulli but Leonhard Euler first elaborated the subject. His contributions began in 1733, and his Elementa Calculi Variationum gave to the science its name. Joseph Louis Lagrange contributed extensively to the theory, and Adrien-Marie Legendre (1786) laid down a method, not entirely satisfactory, for the discrimination of maxima and minima.
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A formal system (also called a logical calculus, or a logical system) consists of a formal language together with a deductive apparatus (also called a deductive system). The deductive apparatus may consist of a set of transformation rules (also called inference rules) or a set of axioms, or have both. A formal system is used to derive one expression from one or more other expressions. Propositional and predicate calculi are examples of formal systems.
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Since this early work, sequent calculi, also called Gentzen systems,, calls Gentzen systems LC systems. Curry's emphasis is more on theory than on practical logic proofs.. This book is much more concerned with the theoretical, metamathematical implications of Gentzen-style sequent calculus than applications to practical logic proofs., defines Gentzen systems and proves various theorems within these systems, including Gödel's completeness theorem and Gentzen's theorem., gives a brief theoretical presentation of Gentzen systems.
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Today, calculus has widespread uses in science, engineering, and economics. In mathematics education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits. The word calculus (plural calculi) is a Latin word, meaning originally "small pebble" (this meaning is kept in medicine - see Calculus (medicine)). Because such pebbles were used for calculation, the meaning of the word has evolved and today usually means a method of computation.
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Protocol Composition Logic is a formal method that is used for proving security properties of protocols that use symmetric key and Public key cryptography. PCL is designed around a process calculi with actions for possible protocol steps like generating some random number, perform encryption and decryption, send and receive messages and digital signature verification actions. Some problems with the logic have been found implying that some currently claimed proofs cannot be proven within the logic.
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Calculus: Calculi are egg-like objects formed in the stomachs of ruminants such as cattle, deer, elk, and goats. Calculus formation is a defense mechanism protecting the ruminant's stomach from damage if it swallows a foreign object while grazing. After ingestion, the object is covered by the same material composing bone, calcium phosphate, and eventually vomited out of the animal's system. These "stomach stones" tend to range in size from 1 to 6 centimeters.
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A specific feature of the mobile membranes is that this new rule-based model is appropriate to prove computability results in terms of Turing machines rather by reduction to the lambda calculus as in the case of process calculi with mobility. In this section are defined four classes of membranes inspired from biological facts, and it is shown that their computational power depends on the initial configuration and on the set of rules used.
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Without proof confluence, the application of a 'wrong' rule may result in the impossibility of making the tableau complete by applying other rules. Propositional tableaux and tableaux without unification have strongly complete proof procedures. In particular, a complete proof procedure is that of applying the rules in a fair way. This is because the only way such calculi cannot generate a closed tableau from an unsatisfiable set is by not applying some applicable rules.
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The serum uric acid concentration is often normal, as the excess purines are promptly eliminated in the urine. The crystals usually appear as an orange grainy material, or they may coalesce to form either multiple tiny stones or distinct large stones that are difficult to pass. The stones, or calculi, usually cause hematuria (blood in the urine) and increase the risk of urinary tract infection. Some victims suffer kidney damage due to such kidney stones.
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From 1962 until 1988, he was a part time professor at Delft University of Technology. One of his PhD students was Gerard J. Holzmann. He was involved with international standards in programming and informatics, as a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the programming languages ALGOL 60 and ALGOL 68. He the first chairperson, from 1962 to 1968.
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Saxifraga paniculata was first formally described in the eighth edition of The Gardeners Dictionary by the Scottish botanist Philip Miller in 1768 and is placed in the genus Saxifraga (the saxifrages) and in the Saxifragaceae family. The generic name Saxifraga literally means "stone-breaker", from Latin ' ("rock" or "stone") + ' ("to break"). It is usually thought to indicate a medicinal use for treatment of urinary calculi (such as kidney stones), rather than breaking rocks apart.
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As for process calculi, the -calculus allows for a definition of bisimulation equivalence. In the -calculus, the definition of bisimulation equivalence (also known as bisimilarity) may be based on either the reduction semantics or on the labelled transition semantics. There are (at least) three different ways of defining labelled bisimulation equivalence in the -calculus: Early, late and open bisimilarity. This stems from the fact that the -calculus is a value- passing process calculus.
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Apart from viral infection, other infections, such as bacterial, can cause parotitis (acute suppurative parotitis or chronic parotitis). These infections may cause blockage of the duct by salivary duct calculi or external compression. Parotid gland swellings can also be due to benign lymphoepithelial lesions caused by Mikulicz disease and Sjögren syndrome. Swelling of the parotid gland may also indicate the eating disorder bulimia nervosa, creating the look of a heavy jaw line.
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His observations on the climatology of Guernsey were at the time unique. His paper on the origin and progress of cholera and small-pox in 1849 was written at the request of the Epidemiological Society. # A Stethoscopic Chart, in which may be seen at one View the Application of Auscultation and Percussion to the Diagnosis of Thoracic Disease, 1830. # On the Chemical Discrimination of Vesical Calculi, a translation of Scharling's work, 1842.
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Illustration of kidney stones Urolithiasis refers to stones originating anywhere in the urinary system, including the kidneys and bladder. Nephrolithiasis refers to the presence of such stones in the kidneys. Calyceal calculi are aggregations in either the minor or major calyx, parts of the kidney that pass urine into the ureter (the tube connecting the kidneys to the urinary bladder). The condition is called ureterolithiasis when a calculus is located in the ureter.
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Ethilon is a synthetic nonabsorbable nylon suture manufactured by Ethicon in Cornelia, Georgia. Black in color, it is a monofilament suture that is used frequently for soft-tissue approximation and ligation. Even though it is nonabsorbable, the knot security decreases over time (in vivo) and should not be used where permanent retention is required.Johnson & Johnson, Essential Product Information Practitioners should exercise caution using such material in urinary and biliary tracts, as this can lead to calculi formation.
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Vampire's kernel implements the calculi of ordered binary resolution and superposition for handling equality. The splitting rule and negative equality splitting can be simulated by the introduction of new predicate definitions and dynamic folding of such definitions. A DPLL-style algorithm splitting is also supported. A number of standard redundancy criteria and simplification techniques are used for pruning the search space: tautology deletion, subsumption resolution, rewriting by ordered unit equalities, basicness restrictions and irreducibility of substitution terms.
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The castle was constructed by the Atchison, Topeka & Santa Fe Railroad as a luxury hotel, capitalizing on the natural hot springs on the site. These were widely thought to ease the suffering of people with tuberculosis, "chronic rheumatism, gout, biliary, and renal calculi.""The Las Vegas Hot Springs," Harpers Weekly, June 28, 1890 The nearby Gallinas Creek also provided excellent trout fishing. Guests included Theodore Roosevelt,"Splendor on the Frontier," Tom Wiley, New Mexico Magazine, Nov-Dec 1967, p.
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Blockage of the main parotid duct, or one of its branches, is often a primary cause of acute parotitis, with further inflammation secondary to bacterial superinfection. The blockage may be from a salivary stone, a mucous plug, or, more rarely, by a tumor, usually benign. Salivary stones (also called sialolithiasis, or salivary duct calculus) are mainly made of calcium, but do not indicate any kind of calcium disorder.Salivary Gland Stones (Salivary Calculi) Accessed March 20, 2008.
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The received view of theories is a position in the philosophy of science that identifies a scientific theory with a set of propositions which are considered to be linguistic objects, such as axioms. Frederick Suppe describes the position of the received view by saying that it identifies scientific theories with an "axiomatic calculi in which theoretical terms are given a partial observation interpretation by mean of correspondence rules."Suppe, Frederick (1989). The Semantic Conception of Theories and Scientific Realism.
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Yuri Matijasevich, (1967) "Simple examples of undecidable associative calculi", Soviet Mathematics - Doklady 8(2) pp 555–557. The word problem on free Heyting algebras is difficult.Peter T. Johnstone, Stone Spaces, (1982) Cambridge University Press, Cambridge, . (See chapter 1, paragraph 4.11) The only known results are that the free Heyting algebra on one generator is infinite, and that the free complete Heyting algebra on one generator exists (and has one more element than the free Heyting algebra).
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However, vaterite does occur naturally in mineral springs, organic tissue, gallstones, urinary calculi and plants. In those circumstances, some impurities (metal ions or organic matter) may stabilize the vaterite and prevent its transformation into calcite or aragonite. Vaterite is usually colorless, its shape is spherical, and its diameter is small, ranging from 0.05 to 5 μm. Vaterite can be produced as the first mineral deposits repairing natural or experimentally-induced shell damage in some aragonite-shelled mollusks (e.g. gastropods).
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On this machine, he explored list processing methods, and then used these to write a compiler for the language ALGOL 60. This led to an invitation to attend the International Federation for Information Processing (IFIP) congress as Canada's representative. At this time, revisions were being made to ALGOL 60. He became the Canadian member of the IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, supports, and maintains the languages ALGOL 60 and 68.
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Many interesting calculi, logics and programming languages that are commonly seen in computer science feature name binding constructs. For instance, the universal quantifier from first-order logic, the lambda-binder from the lambda-calculus, and the pi-binder from the pi-calculus are all examples of name-binding constructs. Computer scientists often need to manipulate abstract syntax trees. For instance, compiler writers perform many manipulations of abstract syntax trees during the various optimisation and elaboration phases of compiler execution.
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The Euler method is named after Leonhard Euler, who treated it in his book Institutionum calculi integralis (published 1768–1870).; The Euler method is a first-order method, which means that the local error (error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size. The Euler method often serves as the basis to construct more complex methods, e.g., predictor–corrector method.
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The algebra of communicating processes (ACP) is an algebraic approach to reasoning about concurrent systems. It is a member of the family of mathematical theories of concurrency known as process algebras or process calculi. ACP was initially developed by Jan Bergstra and Jan Willem Klop in 1982,J.C.M. Baeten, A brief history of process algebra, Rapport CSR 04-02, Vakgroep Informatica, Technische Universiteit Eindhoven, 2004 as part of an effort to investigate the solutions of unguarded recursive equations.
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These images confirm soft tissue mass (arrows) in the renal pelvis with contrast excretion into the collecting system (arrowheads). CT urography (CTU) is commonly used in the evaluation of hematuria, and specifically tailored to image the renal collecting system, ureters and bladder in addition to the renal parenchyma. Initial imaging includes a noncontrast phase to detect renal calculi as a source of hematuria. Note that dual energy CT may eventually allow the noncontrast phase to be eliminated.
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Drawing from this observation, Girard described directly this operator from the proof and has given a formula, the so-called execution formula, encoding the process of cut elimination at the level of operators. One of the first significant applications of GoI was a better analysis of Lamping's algorithm for optimal reduction for the lambda calculus. GoI had a strong influence on game semantics for linear logic and PCF. GoI has been applied to deep compiler optimisation for lambda calculi.
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The use of these tubes may lead to an infection, which irritates the bladder, resulting in stone formation. Finally, a kidney stone may travel down the ureter into the bladder and become a bladder stone. There is some evidence indicating that chronic irritation of the bladder by retained stones may increase the chance of bladder cancer. Urinary schistosomiasis, a disease caused by the digenean trematode Schistosoma haematobium, has been implicated in the development of vesical calculi.
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There exist, however, typed lambda calculi that are not strongly normalizing. For example the dependently typed lambda calculus with a type of all types (Type : Type) is not normalizing due to Girard's paradox. This system is also the simplest pure type system, a formalism which generalizes the Lambda cube. Systems with explicit recursion combinators, such as Plotkin's "Programming language for Computable Functions" (PCF), are not normalizing, but they are not intended to be interpreted as a logic.
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S. Materazzi, R. Curini, G. D'Ascenzo, and A. D. Magri (1995), TG-FTIR coupled analysis applied to the studies in urolithiasis: characterization of human renal calculi. Termochimica Acta, volume 264, 75--93. The circumstances that lead to their formation, as well as the composition of the substance, are still obscure, and little has been published on the topic. Edward Wagman; Anthony Barbara; James Marquis; Marvin Chirls; Anita Falla (1966), Renal Fat Embolization and Urostealith Formation Complicating Femoral Fracture.
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In computer science, communicating sequential processes (CSP) is a formal language for describing patterns of interaction in concurrent systems. It is a member of the family of mathematical theories of concurrency known as process algebras, or process calculi, based on message passing via channels. CSP was highly influential in the design of the occam programming language, INMOS document 72 occ 45 03. and also influenced the design of programming languages such as Limbo, RaftLib, Go, Crystal, and Clojure's core.async.
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Diagnosis of kidney stones is made on the basis of information obtained from the history, physical examination, urinalysis, and radiographic studies. Clinical diagnosis is usually made on the basis of the location and severity of the pain, which is typically colicky in nature (comes and goes in spasmodic waves). Pain in the back occurs when calculi produce an obstruction in the kidney. Physical examination may reveal fever and tenderness at the costovertebral angle on the affected side.
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In mathematics and computer science, trace theory aims to provide a concrete mathematical underpinning for the study of concurrent computation and process calculi. The underpinning is provided by an algebraic definition of the free partially commutative monoid or trace monoid, or equivalently, the history monoid, which provides a concrete algebraic foundation, analogous to the way that the free monoid provides the underpinning for formal languages. The power of trace theory stems from the fact that the algebra of dependency graphs (such as Petri nets) is isomorphic to that of trace monoids, and thus, one can apply both algebraic formal language tools, as well as tools from graph theory. While the trace monoid had been studied by Pierre Cartier and Dominique Foata for its combinatorics in the 1960s, trace theory was first formulated by Antoni Mazurkiewicz in the 1970s, in an attempt to evade some of the problems in the theory of concurrent computation, including the problems of interleaving and non-deterministic choice with regards to refinement in process calculi.
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The full title of the published work is "Nova methodus pro maximis et minimis, itemque tangentibus, quae nec fractas nec irrationales quantitates moratur, et singulare pro illis calculi genus." In English, the full title can be translated as "A new method for maxima and minima, and for tangents, that is not hindered by fractional or irrational quantities, and a singular kind of calculus for the above mentioned." It is from this title that this branch of mathematics takes the name calculus.
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The superposition calculus is a calculus for reasoning in equational first- order logic. It was developed in the early 1990s and combines concepts from first-order resolution with ordering-based equality handling as developed in the context of (unfailing) Knuth–Bendix completion. It can be seen as a generalization of either resolution (to equational logic) or unfailing completion (to full clausal logic). As most first-order calculi, superposition tries to show the unsatisfiability of a set of first-order clauses, i.e.
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Modestly, Frege did not argue that his logic was more expressive than extant logical calculi, but commentators on Frege's logic regard this as one of his key achievements. Using modern predicate calculus, we quickly discover that the statement is ambiguous. :Some cat is feared by every mouse could mean (Some cat is feared) by every mouse (paraphrasable as Every mouse fears some cat), i.e. :For every mouse m, there exists a cat c, such that c is feared by m, :\forall m.
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The reasons for their success lay in the possibilities that they offered of an image and thus a message with more detail, with a narrative structure, and perhaps an element of magic.; ; The Uruk period also saw the development of what seem to be accounting tools: tokens and clay envelopes containing tokens. These are clay balls on which a cylinder seal has been rolled, which contain tokens (also referred to as calculi). The latter come in various forms: balls, cones, rods, discs, etc.
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Next, it was necessary to identify and prove the equivalence of two notions of effective calculability. Equipped with the λ-calculus and "general" recursion, Stephen Kleene with help of Church and J. Barkley Rosser produced proofs (1933, 1935) to show that the two calculi are equivalent. Church subsequently modified his methods to include use of Herbrand–Gödel recursion and then proved (1936) that the Entscheidungsproblem is unsolvable: there is no algorithm that can determine whether a well formed formula cf. Church 1936 in .
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In proof theory and mathematical logic, sequent calculus is a family of formal systems sharing a certain style of inference and certain formal properties. The first sequent calculi systems, LK and LJ, were introduced in 1934/1935 by Gerhard Gentzen, . as a tool for studying natural deduction in first-order logic (in classical and intuitionistic versions, respectively). Gentzen's so-called "Main Theorem" (Hauptsatz) about LK and LJ was the cut-elimination theorem,, gives a 5-page proof of the elimination theorem.
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Asynchronous message passing may be reliable or unreliable (sometimes referred to as "send and pray"). Message-passing concurrency tends to be far easier to reason about than shared-memory concurrency, and is typically considered a more robust form of concurrent programming. A wide variety of mathematical theories to understand and analyze message-passing systems are available, including the actor model, and various process calculi. Message passing can be efficiently implemented via symmetric multiprocessing, with or without shared memory cache coherence.
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This counterexample works because P can be assumed true in a world and false in another one. If however the same assumption is considered global, eg P is not allowed in any world of the model. These two problems can be combined, so that one can check whether B is a local consequence of A under the global assumption G. Tableaux calculi can deal with global assumption by a rule allowing its addition to every node, regardless of the world it refers to.
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Monotonicity of entailment is a property of many logical systems that states that the hypotheses of any derived fact may be freely extended with additional assumptions. In sequent calculi this property can be captured by an inference rule called weakening, or sometimes thinning, and in such systems one may say that entailment is monotone if and only if the rule is admissible. Logical systems with this property are occasionally called monotonic logics in order to differentiate them from non-monotonic logics.
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This means the area highlighted by the HeNe laser is not precisely the area being affected Nd:YAG laser, and therefore some surgical lasers have an added adjustment to compensate. The first successful use of photodisruption was in 1972, on a case of trabecular meshwork. Photodisruption came to wide use in the early 1980s for the treatment of extracapsular cataract extraction. The technique is most commonly used for lithotripsy of urinary calculi and the treatment of posterior capsulotomy of the lens.
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Board games played in ancient Rome included dice (Tesserae or tali), Roman chess (Latrunculi), Roman Checkers (Calculi), tic-tac-toe (Terni Lapilli), and ludus duodecim scriptorum and tabula, predecessors of backgammon. There were several other activities to keep people engaged like chariot races, musical and theatrical performances, public executions and gladiatorial combat. In the Colosseum, Rome's amphitheatre, 60,000 persons could be accommodated. There are also accounts of the Colosseum's floor being flooded to hold mock naval battles for the public to watch.
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The most common form of SDEs in the literature is an ordinary differential equation with the right hand side perturbed by a term dependent on a white noise variable. In most cases, SDEs are understood as continuous time limit of the corresponding stochastic difference equations. This understanding of SDEs is ambiguous and must be complemented by an "interpretation". The most famous interpretations are provided by Itô and Stratonovich calculi, with the former being most frequently used in mathematics and quantitative finance.
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The actor model has influenced the development of the π-calculus and subsequent process calculi. In his Turing lecture, Robin Milner wrote: > Now, the pure lambda-calculus is built with just two kinds of thing: terms > and variables. Can we achieve the same economy for a process calculus? Carl > Hewitt, with his actors model, responded to this challenge long ago; he > declared that a value, an operator on values, and a process should all be > the same kind of thing: an actor.
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He is credited for producing the first Renaissance manuscript on ophthalmic disorders and eye surgery, "Ophthalmodouleia Das ist Augendienst". It was published in 1583, and discussed ocular diseases, surgical techniques and instruments, and contained an ophthalmic atlas of 92 woodcuts depicting diseases of the eye. Bartisch is also remembered for his work in lithotomy for the removal of urinary calculi. Despite his skill as a surgeon, Bartisch was a superstitious individual, as he believed that magic, astrology and witchcraft played a significant part in medicine.
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Introduced in 1962, Petri nets were an early attempt to codify the rules of consistency models. Dataflow theory later built upon these, and Dataflow architectures were created to physically implement the ideas of dataflow theory. Beginning in the late 1970s, process calculi such as Calculus of Communicating Systems and Communicating Sequential Processes were developed to permit algebraic reasoning about systems composed of interacting components. More recent additions to the process calculus family, such as the π-calculus, have added the capability for reasoning about dynamic topologies.
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In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs. It is a generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and logician William Alvin Howard.The correspondence was first made explicit in . See, for example section 4.6, p.
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Several properties of λ-terms that are difficult to state and prove using the traditional notation are easily expressed in the De Bruijn notation. For example, in a type-theoretic setting, one can easily compute the canonical class of types for a term in a typing context, and restate the type checking problem to one of verifying that the checked type is a member of this class. De Bruijn notation has also been shown to be useful in calculi for explicit substitution in pure type systems..
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Backhouse's career has included Royal Aircraft Establishment (1969–1970), Heriot-Watt University (1973–1982), University of Essex (1982–1986). He was formerly Professor of Computer Science at the University of Groningen (1986–1990) and Eindhoven University of Technology (1990–1999) in the Netherlands, before his position at the University of Nottingham. He was a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the programming languages ALGOL 60 and ALGOL 68.
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Around 1930, Alfred Tarski developed an abstract theory of logical deductions that models some properties of logical calculi. Mathematically, what he described is just a finitary closure operator on a set (the set of sentences). In universal logic and abstract algebraic logic, finitary closure operators are still studied under the name consequence operator, which was coined by Tarski. The set S represents a set of sentences, a subset T of S a theory, and cl(T) is the set of all sentences that follow from the theory.
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Larger sizes are known but very rare. Sometimes tiny dimples cover the surface of a stomach stone, which can fool observers into thinking they are the pores of an egg. Fossil egg expert Ken Carpenter has described stomach stones as the most egg- like natural objects, noting that they are "the trickiest [egg-like] objects to correctly identify". Calculi are so egg-like that on one occasion a detailed description of a stomach stone misidentified as a fossil egg was published in the scientific literature.
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Michel Sintzoff (August 12, 1938 – November 28, 2010) was a Belgian mathematician and computer scientist. He was one of the editors of the Revised Report on the Algorithmic Language Algol 68. He was a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the programming languages ALGOL 60 and ALGOL 68. He was also a member of IFIP Working Group 2.3 on Programming Methodology, of which he was chairperson from 2003–2006.
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He operated on battlefields during the war between Austria and Ottomans, and finally went to Venice. His writings include the Artium et medicine and the very important Libellus Aureus de lapide a vesica per incisionem extrahendo and the De lapide renum. During his life, he diffused in Europe a new surgical technique called "sectio mariana", with the use of a new tool, the "esploratorium", for the extraction of renal calculi. He died in Rome in 1577 and was buried in Santa Maria sopra Minerva church.
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Thus, LOTOS can describe both asynchronous concurrent processes and complex data structures. LOTOS was heavily revised in 2001, leading to the publication of E-LOTOS (Enhanced-Lotos, ISO/IEC standard 15437:2001), which tries to provide a greater expressiveness (for instance, by introducing quantitative time to describe systems with real-time constraints) together with a better user friendliness. Several tools exist to convert descriptions in other process calculi or intermediate format into LOTOS, so that the CADP tools can then be used for verification.
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He began to perform the hysterectomy procedure, again with low mortality compared to other published series. In 1888 Keith moved to London, living at Charles Street, Berkeley Square. His reputation was such that he was consulted by eminent people such as Lady Randolph Churchill (1854-1921), but his years here were dogged by ill health. The congenital cystinuria, which had caused him to pass urinary calculi from childhood and had required operations, now caused a renal abscess which drained by his son and surgical partner Skene Keith (1858–1919.
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After Bell Labs, Bourne worked in senior engineering management positions at Silicon Graphics, Digital Equipment Corporation, Sun Microsystems, and Cisco Systems. He was a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which supports and maintains the programming languages ALGOL 60 and ALGOL 68. From 2000 to 2002 he was president of the Association for Computing Machinery (ACM). For his work on computing, Bourne was awarded the ACM's Presidential Award in 2008 and was made a Fellow of the organization in 2005.
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In single-conclusion sequent calculi, modus ponens is the Cut rule. The cut-elimination theorem for a calculus says that every proof involving Cut can be transformed (generally, by a constructive method) into a proof without Cut, and hence that Cut is admissible. The Curry–Howard correspondence between proofs and programs relates modus ponens to function application: if f is a function of type P → Q and x is of type P, then f x is of type Q. In artificial intelligence, modus ponens is often called forward chaining.
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Dent's disease is a X-linked recessive disorder. The males are prone to manifesting symptoms in early adulthood with symptoms of calculi, rickets or even with kidney failure in more severe cases. In humans, gene CLCN5 is located on chromosome Xp11.22, and has a 2238-bp coding sequence that consists of 11 exons that span 25 to 30 kb of genomic DNA and encode a 746-amino-acid protein. CLCN5 belongs to the family of voltage-gated chloride channel genes (CLCN1-CLCN7, CLCKa and CLCKb) that have about 12 transmembrane domains.
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In the 1960s, Abraham Robinson used model-theoretic techniques to develop calculus and analysis based on infinitesimals, a problem that first had been proposed by Leibniz. In proof theory, the relationship between classical mathematics and intuitionistic mathematics was clarified via tools such as the realizability method invented by Georg Kreisel and Gödel's Dialectica interpretation. This work inspired the contemporary area of proof mining. The Curry–Howard correspondence emerged as a deep analogy between logic and computation, including a correspondence between systems of natural deduction and typed lambda calculi used in computer science.
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A sequent is a formalized statement of provability that is frequently used when specifying calculi for deduction. In the sequent calculus, the name sequent is used for the construct, which can be regarded as a specific kind of judgment, characteristic to this deduction system. The intuitive meaning of the sequent \Gamma\vdash\Sigma is that under the assumption of Γ the conclusion of Σ is provable. Classically, the formulae on the left of the turnstile can be interpreted conjunctively while the formulae on the right can be considered as a disjunction.
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In mathematical logic, structural proof theory is the subdiscipline of proof theory that studies proof calculi that support a notion of analytic proof, a kind of proof whose semantic properties are exposed. When all the theorems of a logic formalised in a structural proof theory have analytic proofs, then the proof theory can be used to demonstrate such things as consistency, provide decision procedures, and allow mathematical or computational witnesses to be extracted as counterparts to theorems, the kind of task that is more often given to model theory.
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Such a logical connective as converse implication "←" is actually the same as material conditional with swapped arguments; thus, the symbol for converse implication is redundant. In some logical calculi (notably, in classical logic), certain essentially different compound statements are logically equivalent. A less trivial example of a redundancy is the classical equivalence between and . Therefore, a classical-based logical system does not need the conditional operator "→" if "¬" (not) and "∨" (or) are already in use, or may use the "→" only as a syntactic sugar for a compound having one negation and one disjunction.
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The most common form of malignant parotid neoplasms are mucoepidermoid carcinomas. The exact cause of malignant parotid tumors is still unknown, however they can be caused by metastasis (spread of cancer) from other areas of the body, certain work exposures, reduced immunity, HIV, as well as radiation exposure. Contrary to other cancers, it is believed that smoking and drinking do not influence salivary gland malignancies. Inflammation ailments of the parotid gland, such as parotid abscesses (collections of pus), deep salivary calculi (mineral deposits), and chronic parotitis (long-term inflammation) may necessitate a total parotidectomy.
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The use of institutions makes it possible to develop concepts of specification languages (like structuring of specifications, parameterization, implementation, refinement, development), proof calculi and even tools in a way completely independent of the underlying logical system. There are also morphisms that allow to relate and translate logical systems. Important applications of this are re-use of logical structure (also called borrowing), heterogeneous specification and combination of logics. The spread of institutional model theory has generalized various notions and results of model theory, and institutions themselves have impacted the progress of universal logic.
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Kehr's sign is the occurrence of acute pain in the tip of the shoulder due to the presence of blood or other irritants in the peritoneal cavity when a person is lying down and the legs are elevated. Kehr's sign in the left shoulder is considered a classic symptom of a ruptured spleen. May result from diaphragmatic or peridiaphragmatic lesions, renal calculi, splenic injury or ruptured ectopic pregnancy. Kehr's sign is a classic example of referred pain: irritation of the diaphragm is signaled by the phrenic nerve as pain in the area above the collarbone.
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As a result, one can always prove unsatisfiability by expanding either eg \Box A only or eg \Box B only; however, if the wrong choice is done the resulting tableau may not be closed. Expanding either subformula leads to tableau calculi that are complete but not proof-confluent. Searching as described in the "Searching for a closed tableau" may therefore be necessary. Depending on whether the precondition and consequence of a tableau expansion rule refer to the same world or not, the rule is called static or transactional.
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Other important topics include reasoning under uncertainty and non-monotonic reasoning. An important part of the uncertainty field is that of argumentation, where further constraints of minimality and consistency are applied on top of the more standard automated deduction. John Pollock's OSCAR systemJohn L. Pollock is an example of an automated argumentation system that is more specific than being just an automated theorem prover. Tools and techniques of automated reasoning include the classical logics and calculi, fuzzy logic, Bayesian inference, reasoning with maximal entropy and many less formal ad hoc techniques.
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He then went to work at Remington Rand, in the UNIVAC division, with Grace Hopper to develop compilers for her A-0 system UNIVAC programming languages starting with A-2, followed by MATH-MATIC and FLOW- MATIC. He then went on to General Electric, Burroughs Corporation, and Xerox. In 1958, he served as one of the original four US members of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, supports, and maintains the languages ALGOL 60 and ALGOL 68.
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Principiorum calculi differentialis et integralis expositio elementaris, 1795 Simon Antoine Jean L'Huilier (or L'Huillier) (24 April 1750 in Geneva - 28 March 1840 in Geneva) was a Swiss mathematician of French Hugenot descent. He is known for his work in mathematical analysis and topology, and in particular the generalization of Euler's formula for planar graphs. He won the mathematics section prize of the Berlin Academy of Sciences for 1784 in response to a question on the foundations of the calculus. The work was published in his 1787 book Exposition elementaire des principes des calculs superieurs.
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S.) in mathematics from the University of Illinois at Urbana-Champaign in 1963. While at Illinois, Gries worked with Manfred Paul and Ruediger Wiehle to write a full compiler for the language ALGOL for the IBM 7090 mainframe computer. He earned his Dr. rer. nat. in 1966 from the Technical University of Munich, studying under Friedrich L. Bauer and Joseph Stoer. He was a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the languages ALGOL 60 and ALGOL 68.
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Eiiti Wada (和田英一, 1 June 1931) is a computer scientist and emeritus professor at the University of Tokyo and the Research Director of Internet Initiative Japan (IIJ), a computer network technology company. He is one of the creators of the Happy Hacking Keyboard. He was involved with developing international standards in programming and informatics. In 1968, the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi (WG2.1) solicited a new version of the programming language ALGOL to succeed ALGOL 60.
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This was the first automated deduction system to demonstrate an ability to solve mathematical problems that were announced in the Notices of the American Mathematical Society before solutions were formally published. First-order theorem proving is one of the most mature subfields of automated theorem proving. The logic is expressive enough to allow the specification of arbitrary problems, often in a reasonably natural and intuitive way. On the other hand, it is still semi-decidable, and a number of sound and complete calculi have been developed, enabling fully automated systems.
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Sialolithiasis (also termed salivary calculi, or salivary stones), is a condition where a calcified mass or sialolith forms within a salivary gland, usually in the duct of the submandibular gland (also termed "Wharton's duct"). Less commonly the parotid gland or rarely the sublingual gland or a minor salivary gland may develop salivary stones. The usual symptoms are pain and swelling of the affected salivary gland, both of which get worse when salivary flow is stimulated, e.g. with the sight, thought, smell or taste of food, or with hunger or chewing.
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A physical object (a possible referent of a concept or word) is considered concrete (not abstract) if it is a particular individual that occupies a particular place and time. However, in the secondary sense of the term 'abstraction', this physical object can carry materially abstracting processes. For example, record-keeping aids throughout the Fertile Crescent included calculi (clay spheres, cones, etc.) which represented counts of items, probably livestock or grains, sealed in containers. According to , these clay containers contained tokens, the total of which were the count of objects being transferred.
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These include: evaluation of renal calculi; assessment for gross intra-abdominal hemorrhage; and post- endostent volume measurements. In addition, non-contrast images are often obtained in conjunction with contrast enhanced images in evaluating potential renal transplant donors and in the evaluation of the pancreas (in combination with contrast phases). Of note, dual-energy CT and the development of virtual “non-contrast” images may ultimately obviate the combination scans. Additionally, CT angiography examinations performed for pathologies like aneurysms and dissection are frequently performed in conjunction with non- contrast imaging.
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Cystolithotomy is a surgical procedure for the removal of bladder stones in the case that one has been deemed too large to pass naturally, such as developed jackstone calculi. This may require open surgery to remove the stone, however robotic cystolithotomy allows for a minimally invasive approach to remove the stone through much smaller incisions than the traditional approach. Most bladder stones can be dealt with by an endoscopic procedure, to avoid the need for a surgical incision. An open cystolithotomy is performed under general anesthesia as an inpatient procedure.
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Various typed lambda calculi have been studied. The simply typed lambda calculus has only one type constructor, the arrow \to, and its only types are basic types and function types \sigma\to\tau. System T extends the simply typed lambda calculus with a type of natural numbers and higher order primitive recursion; in this system all functions provably recursive in Peano arithmetic are definable. System F allows polymorphism by using universal quantification over all types; from a logical perspective it can describe all functions that are provably total in second-order logic.
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Iorgulescu, A.: Connections between MVn-algebras and n-valued Łukasiewicz- Moisil algebras—I. Discrete Math. 181, 155–177 (1998) In 1982 Roberto Cignoli published some additional constraints that added to LMn-algebras produce proper models for n-valued Łukasiewicz logic; Cignoli called his discovery proper Łukasiewicz algebras.R. Cignoli, Proper n-Valued Łukasiewicz Algebras as S-Algebras of Łukasiewicz n-Valued Propositional Calculi, Studia Logica, 41, 1982, 3–16, Moisil however published in 1964 a logic to match his algebra (in the general n ≥ 5 case), now called Moisil logic.
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He was the originator and one of the designers of the programming language ABC, the incidental predecessor of Python. He was chairman of the Dutch Pacifist Socialist Party (PSP) from 1975 until 1981. He was codesigner of the Bird–Meertens formalism, along with Richard Bird, who also gifted him the Meertens number. He became involved with developing international standards in programming and informatics, as a member of IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the languages ALGOL 60 and ALGOL 68.
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To address these concerns, the American Urological Association established the Shock Wave Lithotripsy Task Force to provide an expert opinion on the safety and risk-benefit ratio of ESWL. The task force published a white paper outlining their conclusions in 2009. They concluded the risk-benefit ratio remains favorable for many people. The advantages of ESWL include its noninvasive nature, the fact that it is technically easy to treat most upper urinary tract calculi, and that, at least acutely, it is a well-tolerated, low-morbidity treatment for the vast majority of people.
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The Bulletin of the Section of Logic is a quarterly peer-reviewed academic journal covering logic, published by Lodz University Press in collaboration with the Section of Logic of the Polish Academy of Sciences. It was established in 1972 by Ryszard Wójcicki (Polish Academy of Sciences), as a newsletter-journal designed for the exchange of results among members of the section with their national and international partners, as well as their collaborators. The journal focusses on logical calculi, their methodology, applications, and algebraic interpretations. The editor-in-chief is Andrzej Indrzejczak (University of Łódź).
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John Corcoran considers this terminology unfortunate because it obscures the use of schemata and because such "variables" do not actually range over a domain.. The convention is that a metavariable is to be uniformly substituted with the same instance in all its appearances in a given schema. This is in contrast with nonterminal symbols in formal grammars where the nonterminals on the right of a production can be substituted by different instances.. Attempts to formalize the notion of metavariable result in some kind of type theory.Masahiko Sato, Takafumi Sakurai, Yukiyoshi Kameyama, and Atsushi Igarashi. "Calculi of Meta-variables" in Computer Science Logic.
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This excludes compounds directly and exclusively generated by human activities (anthropogenic) or in living beings (biogenic), such as tungsten carbide, urinary calculi, calcium oxalate crystals in plant tissues, and seashells. However, substances with such origins may qualify if geological processes were involved in their genesis (as is the case of evenkite, derived from plant material; or taranakite, from bat guano; or alpersite, from mine tailings). Hypothetical substances are also excluded, even if they are predicted to occur in currently inaccessible natural environments like the Earth's core or other planets. # It must be a solid substance in its natural occurrence.
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The calculus of variations may be said to begin with Newton's minimal resistance problem in 1687, followed by the brachistochrone curve problem raised by Johann Bernoulli (1696). It immediately occupied the attention of Jakob Bernoulli and the Marquis de l'Hôpital, but Leonhard Euler first elaborated the subject, beginning in 1733. Lagrange was influenced by Euler's work to contribute significantly to the theory. After Euler saw the 1755 work of the 19-year-old Lagrange, Euler dropped his own partly geometric approach in favor of Lagrange's purely analytic approach and renamed the subject the calculus of variations in his 1756 lecture Elementa Calculi Variationum.
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In proof theory, Gerhard Gentzen developed natural deduction and the sequent calculus. The former attempts to model logical reasoning as it 'naturally' occurs in practice and is most easily applied to intuitionistic logic, while the latter was devised to clarify the derivation of logical proofs in any formal system. Since Gentzen's work, natural deduction and sequent calculi have been widely applied in the fields of proof theory, mathematical logic and computer science. Gentzen also proved normalization and cut-elimination theorems for intuitionistic and classical logic which could be used to reduce logical proofs to a normal form.
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For another example consider the Actor for the expression "" which has addresses for two other actors (processes) and . When the composite expression Actor (process) receives an message with addresses for an environment Actor E and a customer C, it sends messages to and with environment E and sends C a new Actor (process) C0. When C0 has received back two values N1 and N2, it sends C the value N1 N2. In this way, the denotational semantics for process calculi and the Actor model provide a denotational semantics for "" in terms of the semantics for and .
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The first signs of a parathyroid adenoma and the resulting primary hyperparathyroidism can include bone fractures and urinary calculi such as kidney stones. Oftentimes parathyroid adenoma is not diagnosed until found on standard blood-tests that reveal high calcium content in the blood, it can appear in urine tests as well.(2012) The New York Times, Health Guide Patients may not be experiencing any noticeable symptoms but could be producing excessive amounts of calcium and eventually experience problems later in life if untreated. However, patients can experience common symptoms that can range from joint, muscle, and abdominal pain to slight discomfort.
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Another approach to graph rewriting is term graph rewriting, which involves the processing or transformation of term graphs (also known as abstract semantic graphs) by a set of syntactic rewrite rules. Term graphs are a prominent topic in programming language research since term graph rewriting rules are capable of formally expressing a compiler's operational semantics. Term graphs are also used as abstract machines capable of modelling chemical and biological computations as well as graphical calculi such as concurrency models. Term graphs can perform automated verification and logical programming since they are well-suited to representing quantified statements in first order logic.
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Not taking into account this would generate wrong results. For example, formula a \wedge eg \Box a states that a is true in the current world and a is false in a world that is accessible from it. Simply applying (\wedge) and the expansion rule above would produce a and eg a, but these two formulae should not in general generate a contradiction, as they hold in different worlds. Modal tableaux calculi do contain rules of the kind of the one above, but include mechanisms to avoid the incorrect interaction of formulae referring to different worlds.
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Impredicative polymorphism (also called first-class polymorphism) is the most powerful form of parametric polymorphism. A definition is said to be impredicative if it is self-referential; in type theory this allows the instantiation of a variable in a type \tau with any type, including polymorphic types, such as \tau itself. An example of this is the System F with the type variable X in the type T = \forall X. X \to X, where X could even refer to T itself. In type theory, the most frequently studied impredicative typed λ-calculi are based on those of the lambda cube, especially System F.
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The subsections above have articulated the following three issues concerned with the use of synchronous channels for process calculi: #Starvation. The use of synchronous channels can cause starvation when a process attempts to get messages from multiple channels in a guarded choice command. #Livelock. The use of synchronous channels can cause a process to be caught in livelock when it attempts to get messages from multiple channels in a guarded choice command. #Efficiency. The use of synchronous channels can require a large number of communications in order to get messages from multiple channels in a guarded choice command.
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Luca Cardelli and Martín Abadi wrote the book A Theory of Objects in 1997 laying out formal calculi for the semantics of object-oriented programming languages. Baby Modula-3 influenced this work according to Luca Cardelli, and guided a calculus of the type of self in Types for object and the type of 'self'. It has opened the way for work on Modula-3 formal semantic checking systems, for object oriented type system programming languages that have been used to model the formal semantics of programming languages such as Ada (programming language) and C (programming language) .
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Phil.) from the University of Oxford. He has held professorships at Queen Mary College, London, University of Texas at Austin and the University of Kent at Canterbury, where he has spent most of his career and retains the title of Emeritus Professor of Computation. He was involved with developing international standards in programming and informatics, as a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the programming languages ALGOL 60 and ALGOL 68. He is also an Emeritus Professor at Middlesex University, England.
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FIGURE 1. Non-contrast CT demonstrating multiple bilateral renal calculi (arrows), which can be obscured on contrast-enhanced images, particularly delayed images when there is excreted contrast in the renal collecting system; axial left, coronal reformat on right. Non-contrast CT scans Figure 1a (left) and 1b (right) are of limited use for the differentiation of soft tissue structures. However, materials like blood, calcium (renal stones, vascular atherosclerosis), bone, and pulmonary parenchyma are highly visible and can usually be adequately assessed with non-contrast CT. For example, in the abdomen and pelvis, there are several indications for non-contrast imaging.
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Maibaum has held academic posts at Imperial College, London, King's College London (UK) and McMaster University (Canada). His research interests have concentrated on the theory of specification, together with its application in different contexts, in the general area of software engineering. From 1996 to 2005, he was a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the programming languages ALGOL 60 and ALGOL 68. He is a Fellow of the Institution of Engineering and Technology and the Royal Society of Arts.
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Following its introduction in the United States in February 1984, ESWL was rapidly and widely accepted as a treatment alternative for renal and ureteral stones. It is currently used in the treatment of uncomplicated stones located in the kidney and upper ureter, provided the aggregate stone burden (stone size and number) is less than and the anatomy of the involved kidney is normal. For a stone greater than , ESWL may not help break the stone in one treatment; instead, two or three treatments may be needed. Some 80-85% of simple renal calculi can be effectively treated with ESWL.
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In mathematics and computer science, a history monoid is a way of representing the histories of concurrently running computer processes as a collection of strings, each string representing the individual history of a process. The history monoid provides a set of synchronization primitives (such as locks, mutexes or thread joins) for providing rendezvous points between a set of independently executing processes or threads. History monoids occur in the theory of concurrent computation, and provide a low-level mathematical foundation for process calculi, such as CSP the language of communicating sequential processes, or CCS, the calculus of communicating systems. History monoids were first presented by M.W. Shields.
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Speculatively, the Curry–Howard correspondence might be expected to lead to a substantial unification between mathematical logic and foundational computer science: Hilbert-style logic and natural deduction are but two kinds of proof systems among a large family of formalisms. Alternative syntaxes include sequent calculus, proof nets, calculus of structures, etc. If one admits the Curry–Howard correspondence as the general principle that any proof system hides a model of computation, a theory of the underlying untyped computational structure of these kinds of proof system should be possible. Then, a natural question is whether something mathematically interesting can be said about these underlying computational calculi.
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ALGOL W is a programming language. It is based on a proposal for ALGOL X by Niklaus Wirth and Tony Hoare as a successor to ALGOL 60 in International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the languages ALGOL 60 and ALGOL 68. When the committee decided that the proposal was an insufficient advance over ALGOL 60, the proposal was published as A contribution to the development of ALGOL. After making small modifications to the language Wirth supervised a high quality implementation for the IBM System/360 at Stanford University that was widely distributed.
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In Berlin, he published the two works for which he would become most renowned: the Introductio in analysin infinitorum, a text on functions published in 1748, and the Institutiones calculi differentialis, published in 1755 on differential calculus. In 1755, he was elected a foreign member of the Royal Swedish Academy of Sciences. In addition, Euler was asked to tutor Friederike Charlotte of Brandenburg- Schwedt, the Princess of Anhalt-Dessau and Frederick's niece. Euler wrote over 200 letters to her in the early 1760s, which were later compiled into a best- selling volume entitled Letters of Euler on different Subjects in Natural Philosophy Addressed to a German Princess.
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He is a member of the Special Interest Group on Computers, Information and Society (SIGCIS) of the Society for the History of Technology CIS, and a founding member of the Editorial Board of the IEEE Annals of the History of Computing journal. He is a Fellow of the Association for Computing Machinery (2008). He is a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 (WG2.1) on Algorithmic Languages and Calculi, which specified, maintains, and supports the programming languages ALGOL 60 and ALGOL 68. He is also a founding member of IFIP WG2.3 on Programming Methodology, and of IFIP WG10.4 on Dependability and Fault Tolerance.
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Appendicolith as seen on plain X-ray In general, plain abdominal radiography (PAR) is not useful in making the diagnosis of appendicitis and should not be routinely obtained from a person being evaluated for appendicitis. Plain abdominal films may be useful for the detection of ureteral calculi, small bowel obstruction, or perforated ulcer, but these conditions are rarely confused with appendicitis.APPENDICITIS from Townsend: Sabiston Textbook of Surgery on MD Consult An opaque fecalith can be identified in the right lower quadrant in fewer than 5% of people being evaluated for appendicitis. A barium enema has proven to be a poor diagnostic tool for appendicitis.
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If any branch of a tableau leads to an evident contradiction, the branch closes. If all branches close, the proof is complete and the original formula is a logical truth. Although the fundamental idea behind the analytic tableau method is derived from the cut-elimination theorem of structural proof theory, the origins of tableau calculi lie in the meaning (or semantics) of the logical connectives, as the connection with proof theory was made only in recent decades. More specifically, a tableau calculus consists of a finite collection of rules with each rule specifying how to break down one logical connective into its constituent parts.
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The primary achievement of ludics is the discovery of a relationship between two natural, but distinct notions of type, or proposition. The first view, which might be termed the proof-theoretic or Gentzen-style interpretation of propositions, says that the meaning of a proposition arises from its introduction and elimination rules. Focalization refines this viewpoint by distinguishing between positive propositions, whose meaning arises from their introduction rules, and negative propositions, whose meaning arises from their elimination rules. In focused calculi, it is possible to define positive connectives by giving only their introduction rules, with the shape of the elimination rules being forced by this choice.
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In some other cases, models have proven to make accurate novel predictions, which can be tested experimentally, thus suggesting new approaches to explore in an experiment that sometimes wouldn't be considered in the design of the protocol of an experimental laboratory. Modeling techniques include differential equations (ODEs), Boolean networks, Petri nets, Bayesian networks, graphical Gaussian network models, Stochastic, and Process Calculi. Conversely, techniques have been proposed for generating models of GRNs that best explain a set of time series observations. Recently it has been shown that ChIP-seq signal of Histone modification are more correlated with transcription factor motifs at promoters in comparison to RNA level.
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Lithotomy from Greek for "lithos" (stone) and "tomos" (cut), is a surgical method for removal of calculi, stones formed inside certain organs, such as the urinary tract (kidney stones), bladder (bladder stones), and gallbladder (gallstones), that cannot exit naturally through the urinary system or biliary tract. The procedure is usually performed by means of a surgical incision (therefore invasive). Lithotomy differs from lithotripsy, where the stones are crushed either by a minimally invasive probe inserted through the exit canal, or by an acoustic pulse (extracorporeal shock wave lithotripsy), which is a non-invasive procedure. Because of these less invasive procedures, the use of lithotomy has decreased significantly in the modern era.
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Proteus also refers to a genus of Gram- negative Proteobacteria, some of which are opportunistic human pathogens known to cause urinary tract infections, most notably. Proteus mirabilis is one of these and is most referenced in its tendency to produce "stag-horn" calculi composed of struvite (magnesium ammonium phosphate) that fill the human renal pelvis. In July 2019 the British professional wrestling company PROGRESS Wrestling announced the introduction of a Proteus Championship. The current holder of the championship will be allowed to declare the type of match they will defend the championship in, with each new champion being able to set their own match type.
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In about 15-20% of cases the sialolith will not be sufficiently calcified to appear radiopaque on a radiograph, and will therefore be difficult to detect. Other sources suggest a retrograde theory of lithogenesis, where food debris, bacteria or foreign bodies from the mouth enter the ducts of a salivary gland and are trapped by abnormalities in the sphincter mechanism of the duct opening (the papilla), which are reported in 90% of cases. Fragments of bacteria from salivary calculi were reported to be Streptococci species which are part of the normal oral microbiota and are present in dental plaque. Stone formation occurs most commonly in the submandibular gland for several reasons.
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Alessio Guglielmi proposed a variation of Retoré's calculus, BV, in which the two noncommutative operations are collapsed onto a single, self-dual, operator, and proposed a novel proof calculus, the calculus of structures to accommodate the calculus. The principal novelty of the calculus of structures was its pervasive use of deep inference, which it was argued is necessary for calculi combining commutative and noncommutative operators; this explanation concurs with the difficulty of designing sequent systems for pomset logic that have cut-elimination. Lutz Strassburger devised a related system, NEL, also in the calculus of structures in which linear logic with the mix rule appears as a subsystem.
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Naur began his career as an astronomer for which he received his Doctor of Philosophy (Ph,D.) degree in 1957, but his encounter with computers led to a change of profession. From 1959 to 1969, he was employed at Regnecentralen, the Danish computing company, while at the same time giving lectures at the Niels Bohr Institute and the Technical University of Denmark. From 1969 to 1998, Naur was a professor of computer science at University of Copenhagen. He was a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, supports, and maintains the languages ALGOL 60 and ALGOL 68.
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For ALGOL 58, Bauer was with the German Gesellschaft für Angewandte Mathematik und Mechanik (GAMM, Society of Applied Mathematics and Mechanics) which worked with the American Association for Computing Machinery (ACM). For ALGOL 60, Bauer was with the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the languages ALGOL 60 and ALGOL 68. In 1968, he coined the term software engineering which has been in widespread use since, and has become a discipline in computer science. Bauer was an influential figure in establishing computer science as an independent subject in German universities.
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Second, the calculus is a sound equational reasoning system with respect to Morris's notion of observational equivalence.Programming languages and lambda calculus by James Morris, MIT 1968 Twenty years later, Crank and Felleisen showed how to scale Plotkin's work to languages with imperative assignment statements.Parameter-Passing and the Lambda Calculus by Crank and Felleisen, Principles of Programming Languages 1991 They define calculi for a language with variables, functions, function application and assignment statement that capture the conventional notions of parameter passing and evaluation strategies of a wide array of programming languages. They show that each calculus satisfies Plotkin's criteria, including traditional Church–Rosser and Curry–Feys theorems respectively.
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Proteus mirabilis, Proteus vulgaris, and Morganella morganii are the most common organisms isolated; less common organisms include Ureaplasma urealyticum and some species of Providencia, Klebsiella, Serratia, and Enterobacter. These infection stones are commonly observed in people who have factors that predispose them to urinary tract infections, such as those with spinal cord injury and other forms of neurogenic bladder, ileal conduit urinary diversion, vesicoureteral reflux, and obstructive uropathies. They are also commonly seen in people with underlying metabolic disorders, such as idiopathic hypercalciuria, hyperparathyroidism, and gout. Infection stones can grow rapidly, forming large calyceal staghorn (antler-shaped) calculi requiring invasive surgery such as percutaneous nephrolithotomy for definitive treatment.
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In the October 2016 Journal of the American Osteopathic Association, a paper entitled "Validation of a Functional Pyelocalyceal Renal Model for the Evaluation of Renal Calculi Passage While Riding a Roller Coaster" was published. The paper's author, Dr. Wartinger, found that patients of his had passed kidney stones after riding Big Thunder Mountain Railroad at Walt Disney World on vacation, including one who passed three stones on three separate occasions. The doctor then tested this result, with the permission of Disney, with a 3D model of a kidney by riding the ride over 20 times. The study found nearly 70% of the time, the kidney stone was passed, with results varying depending on which row they were in.
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In 1959, he became member of the Royal Netherlands Academy of Arts and Sciences. In 1961, he became the director of the Mathematisch Centrum in Amsterdam and remained in that post for the next twenty years. He was one of the designers of the original ALGOL language, and later ALGOL 68, for which he developed a two-level type of formal grammar that became known as a Van Wijngaarden grammar. In 1962, he became involved with developing international standards in programming and informatics, as a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the programming languages ALGOL 60 and ALGOL 68.
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Alexander Copland (or Copeland) Hutchison FRSE (1786–1840) was a British surgeon and medical author remembered for his book Practical Observations in Surgery (1811). In 1818 he made an interesting observation that navy personal suffered exceptionally low levels of kidney stones (Urinary calculi) totalling eight cases over a 15-year period (1800–1815) within a minimum of 145,000 subjects per year. Taking all factors into account he calculated a total rate of approximately 1 in 11,000. Whilst the data was clear the cause was not. It was largely ascribed to the very high proportion of salt beef and pork within the diet, and the rather unattractive issue of sleeping in one’s own sweat within your hammock.
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He worked as Acting Chief of the Office for Information Processing Standards, at the National Bureau of Standards, now National Institute of Standards and Technology (NIST), where he specialized in technical standards for automatic data processing, especially in the technology of fingerprint recognition. He participated in conferences in Zurich in 1958 and Paris in 1960 which developed the programming languages ALGOL 58 and ALGOL 60, respectively. He was involved with international standards in programming and informatics, in at least two groups. He was a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the languages ALGOL 60 and 68.
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In a noted xenotransfusion experiment of November 1667, King with Richard Lower transfused sheep's blood into a man, a direction of research they abandoned in 1668 after reports from France of a death. In 1669 King published further microscopic researches to show that glands consisted of tubes and vessels only. In 1667 King published a paper on ants, and in 1670 one on leaf cutter bees, both in Philosophical Transactions: he had examined the eggs of ants microscopically, and studied anthills. In the Philosophical Transactions for 1686 King published an account of the autopsy of Robert Bacon, a "demented person", who had a calcified pineal gland in his brain, renal and vesical calculi and gallstones.
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Technically, tableaux for modal logics check the satisfiability of a set of formulae: they check whether there exists a model M and world w such that the formulae in the set are true in that model and world. In the example above, while a states the truth of a in w, the formula eg \Box a states the truth of eg a in some world w' that is accessible from w and which may in general be different from w. Tableaux calculi for modal logic take into account that formulae may refer to different worlds. This fact has an important consequence: formulae that hold in a world may imply conditions over different successors of that world.
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Because saliva is stimulated to flow more with the thought, sight or smell of food, or with chewing, pain and swelling will often get suddenly worse just before and during a meal ("peri-prandial"), and then slowly decrease after eating, this is termed meal time syndrome. However, calculi are not the only reasons that a salivary gland may become blocked and give rise to the meal time syndrome. Obstructive salivary gland disease, or obstructive sialadenitis, may also occur due to fibromucinous plugs, duct stenosis, foreign bodies, anatomic variations, or malformations of the duct system leading to a mechanical obstruction associated with stasis of saliva in the duct. Salivary stones may be divided according to which gland they form in.
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He then became involved with developing international standards in programming and informatics, as a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports ALGOL 60 and ALGOL 68. Around 1959, he invented so-called "garbage collection" methods to solve problems in Lisp. He helped to motivate the creation of Project MAC at MIT when he worked there, and at Stanford University, he helped establish the Stanford AI Laboratory, for many years a friendly rival to Project MAC. McCarthy was instrumental in creation of three of the very earliest time-sharing systems (Compatible Time-Sharing System, BBN Time-Sharing System, and Dartmouth Time Sharing System).
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Some proof calculi will only deal with a theory whose formulae are written in prenex normal form. The concept is essential for developing the arithmetical hierarchy and the analytical hierarchy. Gödel's proof of his completeness theorem for first-order logic presupposes that all formulae have been recast in prenex normal form. Tarski's axioms for geometry is a logical system whose sentences can all be written in universal- existential form, a special case of the prenex normal form that has every universal quantifier preceding any existential quantifier, so that all sentences can be rewritten in the form \forall u \forall v \ldots \exists a \exists b \phi, where \phi is a sentence that does not contain any quantifier.
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Samelson was involved with international standards in programming and informatics, and played a key role in the design of ALGOLs 58 and 60, as a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, supports, and maintains the programming languages ALGOL 60 and ALGOL 68. In 1958, he accepted a chair for Mathematics at the University of Mainz, and since 1963 he held a chair at the Technical University of Munich where he and F.L. Bauer, began to develop a university curriculum for Informatics and Computer Science. He became an editor of the journal Acta Informatica when it began in 1971.
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Dunn's research focuses on information based logics, particularly relevance logics and other so-called "substructural" logics. He has an algebraic approach to these under the heading of "gaggle theory" (for generalized galois logics), which he has developed in articles, his book with G. Hardgree Algebraic Methods in Philosophical Logic (Oxford, 2001) , and a book with K. Bimbó, Generalized Galois Logics: Relational Semantics of Nonclassical Logical Calculi. (CSLI Publications, 2008). In his work on relevance logic, he was fortunate to study as a graduate student with the two major figures in relevance logic, Alan Ross Anderson and Nuel D. Belnap, Jr. He was a contributing author to their book Entailment: The Logic of Relevance and Entailment Vol.
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In mathematics, the transcendental law of homogeneity (TLH) is a heuristic principle enunciated by Gottfried Wilhelm Leibniz most clearly in a 1710 text entitled Symbolismus memorabilis calculi algebraici et infinitesimalis in comparatione potentiarum et differentiarum, et de lege homogeneorum transcendentali.Leibniz Mathematische Schriften, (1863), edited by C. I. Gerhardt, volume V, pages 377–382) Henk J. M. Bos describes it as the principle to the effect that in a sum involving infinitesimals of different orders, only the lowest-order term must be retained, and the remainder discarded. Thus, if a is finite and dx is infinitesimal, then one sets :a+dx=a. Similarly, :u\,dv+v\,du+du\,dv=u\,dv+v\,du, where the higher-order term du dv is discarded in accordance with the TLH.
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"Dining Philosophers", a classic problem involving concurrency and shared resources In computer science, concurrency is the ability of different parts or units of a program, algorithm, or problem to be executed out-of-order or in partial order, without affecting the final outcome. This allows for parallel execution of the concurrent units, which can significantly improve overall speed of the execution in multi-processor and multi-core systems. In more technical terms, concurrency refers to the decomposability property of a program, algorithm, or problem into order-independent or partially-ordered components or units. A number of mathematical models have been developed for general concurrent computation including Petri nets, process calculi, the parallel random-access machine model, the actor model and the Reo Coordination Language.
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At the university, she prepared and defended her PhD thesis, Algebraic Treatment of the Functional Calculi of Lewis and Heyting, in 1950 under the guidance of Prof. Andrzej Mostowski. This thesis on algebraic logic initiated her career contributing to the Lwów–Warsaw school of logic: In 1956, she took her second academic degree, doktor nauk (equivalent to habilitation today) in the Institute of Mathematics of the Polish Academy of Sciences, where between 1954 and 1957, she held a post of Associate Professor, becoming a Professor in 1957 and subsequently Full Professor in 1967. For the degree, she submitted two papers, Algebraic Models of Axiomatic Theories and Constructive Theories, which together formed a thesis named Algebraic Models of Elementary Theories and their Applications.
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Sharir was named a Fellow of the Association for Computing Machinery in 1997. He received an honorary doctorate from Utrecht University in 1996, the Feher Foundation Prize in Computer Science from the Jerusalem Institute for Israel Studies in 1999, the Landau Prize for Science and Research in 2002, and the million-dollar The EMET Prize for Art, Science and Culture in the Exact Sciences from the A.M.N. Foundation in 2007. Sharir is an Institute for Scientific Information, ISI Highly Cited researcher. He was involved with developing international standards in programming and informatics, as a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the programming languages ALGOL 60 and ALGOL 68.
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The differential diagnosis for LUTS is broad and includes various medical conditions, neurologic disorders, and other diseases of the bladder, urethra, and prostate such as bladder cancer, urinary tract infection, urethral stricture, urethral calculi (stones), chronic prostatitis, and prostate cancer. Neurogenic bladder can cause urinary retention and cause symptoms similar to those of BPH. This may occur as a result of uncoordinated contraction of the bladder muscle or impairment in the timing of bladder muscle contraction and urethral sphincter relaxation. Notable causes of neurogenic bladder include disorders of the central nervous system such as Parkinson's disease, multiple sclerosis, and spinal cord injuries as well as disorders of the peripheral nervous system such as diabetes mellitus, vitamin B12 deficiency, and alcohol-induced nerve damage.
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There he was one of the editors of the original Report on the Algorithmic Language ALGOL 68, being responsible for the design of ALGOL 68's transput. He became involved with developing international standards in programming and informatics, as a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the programming languages ALGOL 60 and 68. He is the creator of the original Compiler Description Language (CDL), and of affix grammars, which are a variant of Van Wijngaarden grammars. In a sense, CDL is a deterministic executable affix grammar, while Prolog is a non-deterministic executable affix grammar; a link acknowledged by the implementors of the original Prolog interpreter.
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Pliny the Elder is the first writer to mention the Tungri in Gallia Belgica, in his Natural History.Natural History IV.31 and XXXI.8. He notes that their territory > ...has a spring of great renown, which sparkles as it bursts forth with > bubbles innumerable, and has a certain ferruginous taste, only to be > perceived after it has been drunk. This water is strongly purgative, is > curative of tertian fevers, and disperses urinary calculi: upon the > application of fire it assumes a turbid appearance, and finally turns red It has been suggested that this refers to the well-known waters of Spa in the province of Liège, or else to waters found at Tongeren, which are suitably iron-bearing, and today referred to as the "Plinius bron".
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In 1687, Plot was made a notary public by the Archbishop of Canterbury as well as appointed the registrar to the Norfolk Court of Chivalry. Plot resigned from his posts at Oxford in 1690, thereafter marrying Rebecca Burman of London and retiring to his property of Sutton Barne in his hometown of Borden, where he worked on The Natural History of Middlesex and Kent but never completed. The office of Mowbray Herald Extraordinary was created in January 1695 for Plot, who was made registrar of the College of Heralds just two days later. Although able to go on an archaeological tour of Anglia in September 1695, Plot was greatly suffering from urinary calculi (kidney stones), and succumbed to his illness on 30 April 1696 aged 55.
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The monograph "The Philosophical Problems of Multivalued Logic" (1960), soon translated into English, was a significant event in Soviet philosophy, although it had flaws. Classical work became one of the world's first monographs on multi-valued logic and the first in the Soviet bloc. In general, the work of Zinoviev corresponded to the level of scientific achievements in the field of non-classical logic of the time, highly valued by such logicians as Kazimir Aydukevich, Jozef Bohensky, Georg von Wright, but did not attract much attention in the West. Zinoviev gave priority to formal methods over formal calculi, which alienated his work from the main directions and trends of the logic and methodology of science of the second half of the 20th century.
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In order to avoid breaking open the containers, first, clay impressions of the tokens were placed on the outside of the containers, for the count; the shapes of the impressions were abstracted into stylized marks; finally, the abstract marks were systematically used as numerals; these numerals were finally formalized as numbers. Eventually (Schmandt-Besserat estimates it took 5000 years ) the marks on the outside of the containers were all that were needed to convey the count, and the clay containers evolved into clay tablets with marks for the count.. p. 5: calculi were in use in Iraq for primitive accounting systems as early as 3200–3000 BCE, with commodity-specific counting representation systems. Balanced accounting was in use by 3000–2350 BCE, and a sexagesimal number system was in use 2350–2000 BCE.
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In 1960, Hoare left the Soviet Union and began working at Elliott Brothers Ltd, a small computer manufacturing firm located in London. There, he implemented the language ALGOL 60 and began developing major algorithms. He was involved with developing international standards in programming and informatics, as a member of the International Federation for Information Processing (IFIP) IFIP Working Group 2.1 on Algorithmic Languages and Calculi, which specified, maintains, and supports the languages ALGOL 60 and ALGOL 68. He became the Professor of Computing Science at the Queen's University of Belfast in 1968, and in 1977 returned to Oxford as the Professor of Computing to lead the Programming Research Group in the Oxford University Computing Laboratory (now Department of Computer Science, University of Oxford), following the death of Christopher Strachey.
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His next move was to the All India Institute of Medical Sciences, Delhi where he continued till his superannuation in 1972, after which he served as a Scientist Emeritus of the Indian Council of Medical research till 1975. He also worked at Choithram Hospital and Research Centre, Indore, for two years from 1976 to 1978. Rao, who was known to have researched on Neurosciences and Renal calculi, published many articles which included Primary carcinoma of the liver in infancy: report of a case, Active immunization against E. coli as a protective measure against haemorrhagic shock and Bilateral Prefrontal Leucotomy in Indian Patients. He served as the honorary surgeon to the President of India for a number of years and was the president of the Association of Surgeons of India (ASI) for two terms during 1962–63.
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Tuple calculus is a calculus that was created and introduced by Edgar F. Codd as part of the relational model, in order to provide a declarative database- query language for data manipulation in this data model. It formed the inspiration for the database-query languages QUEL and SQL, of which the latter, although far less faithful to the original relational model and calculus, is now the de facto standard database-query language; a dialect of SQL is used by nearly every relational-database-management system. Michel Lacroix and Alain Pirotte proposed domain calculus, which is closer to first- order logic and together with Codd showed that both of these calculi (as well as relational algebra) are equivalent in expressive power. Subsequently, query languages for the relational model were called relationally complete if they could express at least all of these queries.
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Lithium was first used in the 19th century as a treatment for gout after scientists discovered that, at least in the laboratory, lithium could dissolve uric acid crystals isolated from the kidneys. The levels of lithium needed to dissolve urate in the body, however, were toxic. Because of prevalent theories linking excess uric acid to a range of disorders, including depressive and manic disorders, Carl Lange in Denmark and William Alexander Hammond in New York City used lithium to treat mania from the 1870s onwards. By the turn of the 20th century, as theory regarding mood disorders evolved and so-called "brain gout" disappeared as a medical entity, the use of lithium in psychiatry was largely abandoned; however, a number of lithium preparations were still produced for the control of renal calculi and uric acid diathesis.
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Even though most mathematicians do not accept the constructivist's thesis that only mathematics done based on constructive methods is sound, constructive methods are increasingly of interest on non-ideological grounds. For example, constructive proofs in analysis may ensure witness extraction, in such a way that working within the constraints of the constructive methods may make finding witnesses to theories easier than using classical methods. Applications for constructive mathematics have also been found in typed lambda calculi, topos theory and categorical logic, which are notable subjects in foundational mathematics and computer science. In algebra, for such entities as topoi and Hopf algebras, the structure supports an internal language that is a constructive theory; working within the constraints of that language is often more intuitive and flexible than working externally by such means as reasoning about the set of possible concrete algebras and their homomorphisms.
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In addition, they introduce a calculus that reifies ML's notion of reference cell. Ariola and FelleisenThe call-by-need lambda calculus by Ariola and Felleisen, Journal of Functional Programming 1997 and independently Maraist, Odersky and Wadler The call-by-need lambda calculus by Maraist Odersky and Wadler, Journal of Functional Programming 1999 completed this line of work with the design of a lambda calculus that precisely relates the notion of call-by-need aka lazy functional programming to an equational system of calculation. Unlike Plotkin's call-by-value and call-by-name calculi, this call-by-need calculus requires four axioms to characterize function calls. Chang and FelleisenThe call-by-need lambda calculus, revisited by Chang and Felleisen, European Symposium on Programming, 2012 were eventually able to show how to create a by-need calculus with a single, but complex axiom.
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In 1755, however, in his Institutiones Calculi Differentialis, Euler gave a more general concept of a function: :When certain quantities depend on others in such a way that they undergo a change when the latter change, then the first are called functions of the second. This name has an extremely broad character; it encompasses all the ways in which one quantity can be determined in terms of others. Medvedev considers that "In essence this is the definition that became known as Dirichlet's definition." Edwards also credits Euler with a general concept of a function and says further that :The relations among these quantities are not thought of as being given by formulas, but on the other hand they are surely not thought of as being the sort of general set- theoretic, anything-goes subsets of product spaces that modern mathematicians mean when they use the word "function".
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According to , these clay containers contained tokens, the total of which were the count of objects being transferred. The containers thus served as something of a bill of lading or an accounts book. In order to avoid breaking open the containers, first, clay impressions of the tokens were placed on the outside of the containers, for the count; the shapes of the impressions were abstracted into stylized marks; finally, the abstract marks were systematically used as numerals; these numerals were finally formalized as numbers. Eventually (Schmandt-Besserat estimates it took 4000 years ) the marks on the outside of the containers were all that were needed to convey the count, and the clay containers evolved into clay tablets with marks for the count.. p. 5: calculi were in use in Iraq for primitive accounting systems as early as 3200–3000 BCE, with commodity-specific counting representation systems.
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Different species of urinary calculi noted by William Prout Prout is better remembered, however, for his researches into physical chemistry. In 1815, based on the tables of atomic weights available at the time, he anonymously hypothesized that the atomic weight of every element is an integer multiple of that of hydrogen, suggesting that the hydrogen atom is the only truly fundamental particle (which he called protyle), and that the atoms of the other elements are made of groupings of various numbers of hydrogen atoms. While Prout's hypothesis was not borne out by later more-accurate measurements of atomic weights, it was a sufficiently fundamental insight into the structure of the atom that in 1920, Ernest Rutherford chose the name of the newly discovered proton to, among other reasons, give credit to Prout. Prout contributed to the improvement of the barometer, and the Royal Society of London adopted his design as a national standard.
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The Relational calculus consists of two calculi, the tuple relational calculus and the domain relational calculus, that are part of the relational model for databases and provide a declarative way to specify database queries. The relational calculus is similar to the relational algebra, which is also part of the relational model: While the relational calculus is meant as a declarative language which prescribes no execution order on the subexpressions of a relational calculus expression, the relational algebra is meant as an imperative language: the sub-expressions of a relational algebraic expressions are meant to be executed from left-to-right and inside-out following their nesting. A relational algebra expression might prescribe the following steps to retrieve the phone numbers and names of book stores that supply Some Sample Book: # Join book stores and titles over the BookstoreID. # Restrict the result of that join to tuples for the book Some Sample Book.
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Flumequine was associated with severe ocular toxicity, which precluded its use in human patients. Drug-induced calculi (kidney stones) has been associated with such therapy as well. Anaphylactic shock induced by flumequine therapy has also been associated with its use.Allergy to quinolones Eight cases of quinolone allergy F. F. Arboit 1, JC Bessot 2, F. Arboit 1, JC Bessot 2, F. De Blay 2, A. De Blay 2, A. Dietemann 2, C. Dietemann 2, C. Charpentier 2 and G. Carpenter 2 and G. Pauli 2, Pauli 2, 1 Hôpital Belle-Ile, Service de Pneumologie, 57045 METZ Cedex, France 1 Belle-Isle Hospital, Department of Pneumology, 57045 METZ Cedex, France 2 Service de Pneumologie, Pavillon Laennec, Hôpitaux Universitaires de Strasbourg, BP 426, 67091 STRASBOURG Cedex, France 2 Service de Pneumologie, Pavillon Laennec, Hôpitaux Universitaires de Strasbourg, BP 426, 67091 Strasbourg Cedex, France Anaphylactoid reactions such as shock, urticaria, and Quincke’s oedema have been reported to generally appear within two hours after taking the first tablet.
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Other aspects of computer science, informatics, and statistics are also used in systems biology. These include new forms of computational models, such as the use of process calculi to model biological processes (notable approaches include stochastic π-calculus, BioAmbients, Beta Binders, BioPEPA, and Brane calculus) and constraint-based modeling; integration of information from the literature, using techniques of information extraction and text mining; development of online databases and repositories for sharing data and models, approaches to database integration and software interoperability via loose coupling of software, websites and databases, or commercial suits; network-based approaches for analyzing high dimensional genomic data sets. For example, weighted correlation network analysis is often used for identifying clusters (referred to as modules), modeling the relationship between clusters, calculating fuzzy measures of cluster (module) membership, identifying intramodular hubs, and for studying cluster preservation in other data sets; pathway-based methods for omics data analysis, e.g. approaches to identify and score pathways with differential activity of their gene, protein, or metabolite members.
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To perform a proof-search the best thing is to chose the left formula, since \lor is positive, indeed (as discussed above) in some cases there are no proofs where the focus is on the right formula. To overcome this, some focused calculi create a backtracking point such that focusing on the right yields \downarrow \uparrow \phi \lor \psi \implies \langle \phi \lor \psi \rangle, \uparrow \phi \lor \psi, which is still as \phi \lor \psi \implies \phi \lor \psi. The second formula on the right can be removed only when the focused phase has finished, but if proof-search gets stuck before this happens the sequent may remove the focused component thereby returning to the choice e.g., \downarrow \uparrow B \lor A \implies \langle A \rangle, \uparrow A \lor B must be taken to \downarrow \uparrow B \lor A \implies \uparrow A \lor B as no other reductive inference can be made.
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Roughly, a reduction strategy is a function that maps a lambda calculus term with reducible expressions to one particular reducible expression, the one to be reduced next. Mathematical logicians have studied the properties of this system for decades, and the superficial similarity between the description of evaluation strategies and reduction strategies originally misled programming language researchers to speculate that the two were identical, a belief that is still visible in popular textbooks from the early 1980s;Structure and Interpretation of Computer Programs by Abelson and Sussman, MIT Press 1983 these are, however, different concepts. PlotkinCall- by-name, call-by-value, and the lambda calculus showed in 1973, however, that a proper model of an evaluation strategy calls for the formulation of a new axiom for function calls, that is, an entirely new calculus. He validates this idea with two different calculi: one for call-by-name and another one for call-by-value, each for purely functional programming languages.
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The second rule of unit propagation can be seen as a restricted form of resolution, in which one of the two resolvents must always be a unit clause. As for resolution, unit propagation is a correct inference rule, in that it never produces a new clause that was not entailed by the old ones. The differences between unit propagation and resolution are: # resolution is a complete refutation procedure while unit propagation is not; in other words, even if a set of clauses is contradictory, unit propagation may not generate an inconsistency; # the two clauses that are resolved cannot in general be removed after the generated clause is added to the set; on the contrary, the non-unit clause involved in a unit propagation can be removed when its simplification is added to the set; # resolution does not in general include the first rule used in unit propagation. Resolution calculi that include subsumption can model rule one by subsumption and rule two by a unit resolution step, followed by subsumption.
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Indeed, physicist James Crutchfield has constructed a rigorous mathematical theory out of this idea, proving the statistical emergence of "particles" from cellular automata.J. P. Crutchfield, "The Calculi of Emergence: Computation, Dynamics, and Induction", Physica D 75, 11–54, 1994. Then, as the argument goes, one might wonder if our world, which is currently well described, at our current level of understanding, by physics with particle-like objects, could be a CA at its most fundamental level with the gaps in information or incomplete understanding of fundamental data appearing as an arbitrary random order that would seem contrary to CA. While a complete theory along this line has not been developed, entertaining and developing this hypothesis led scholars to interesting speculation and fruitful intuitions on how we can make sense of our world within a discrete framework. Marvin Minsky, the AI pioneer, investigated how to understand particle interaction with a four-dimensional CA lattice; Konrad Zuse—the inventor of the first working computer, the Z3—developed an irregularly organized lattice to address the question of the information content of particles.
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Among other ingredients entering into some of these formulae were the excrements of human beings, dogs, mice, geese, and other animals, calculi, human skull, and moss growing on it, blind puppies, earthworms, etc. Although other editions of the London Pharmacopoeia were issued in 1621, 1632, 1639, and 1677, it was not until the edition of 1721, published under the auspices of Sir Hans Sloane, that any important alterations were made. In this issue many of the remedies previously in use were omitted, although a good number were still retained, such as dogs’ excrement, earthworms, and moss from the human skull; the botanical names of herbal remedies were for the first time added to the official ones; the simple distilled waters were ordered of a uniform strength; sweetened spirits, cordials and ratafias were omitted as well as several compounds no longer used in London, although still in vogue elsewhere. A great improvement was effected in the edition published in 1746, in which only those preparations were retained which had received the approval of the majority of the pharmacopoeia committee; to these was added a list of those drugs only which were supposed to be the most efficacious.
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