That is the ultimate goal; the rhetoric and formalisms of critical thinking are retrofit around it.
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From one point of view, quantum physics is just a set of formalisms, a useful tool kit.
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It had all of those formalisms that you would have come to expect for an invitation to a private event online.
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Trained both as a graphic artist and fine artist at the prestigious JJ School of Arts in Mumbai, Navjot imbibed the formalisms of Western Modernism, which were in vogue in the curricula at the time.
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Adaptive formalisms may be divided into two main categories: full grammar formalisms (adaptive grammars), and adaptive machines, upon which some grammar formalisms have been based.
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The current version of SYNTAX (version 6.0 beta) includes also parser generators for other formalisms, used for natural language processing as well as bio-informatics. These formalisms are context-sensitive formalisms (TAG, RCG or formalisms that rely on context-free grammars and are extended thanks to attribute evaluation, in particular for natural language processing (LFG).
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The following solutions depict how the frame problem is solved in various formalisms. The formalisms themselves are not presented in full: what is presented are simplified versions that are sufficient to explain the full solution.
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42-60, January 1992. These formalisms were classified by Shutt as imperative.
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Formalisms that vary over time (such as adaptive grammars) may rely on these side effects.
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The systematic treatment of the dynamic behavior of interconnected bodies has led to a large number of important multibody formalisms in the field of mechanics. The simplest bodies or elements of a multibody system were treated by Newton (free particle) and Euler (rigid body). Euler introduced reaction forces between bodies. Later, a series of formalisms were derived, only to mention Lagrange’s formalisms based on minimal coordinates and a second formulation that introduces constraints.
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The formalisms listed below, while not grammar formalisms, either serve as the basis of full grammar formalisms, or are included here because they are adaptive in nature. They are listed in their historical order of first mention in the literature. ;Self-modifying finite state automata (Shutt & Rubinstein) :Introduced in 1994 by Shutt and Rubinstein,Shutt, John & Rubinstein, Roy, "Self-Modifying Finite Automata," in B. Pehrson and I. Simon, editors, Technology and Foundations: Information Processing ‘94 Vol. I: Proceedings of 13th IFIP World Computer Congress, Amsterdam: North-Holland, pp.
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The current description of massive, higher spin fields through either Rarita–Schwinger or Fierz–Pauli formalisms is afflicted with several maladies.
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Due to its relation with the most intimate aspects of matter, field theory is the closest branch of theoretical physics to the frontiers of knowledge. Formalisms and other powerful mathematical methods have been developed, in order to solve its problems. The project consists on the application of such formalisms to other branches of physics and, eventually, to other sciences.
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Many raster manipulations map directly onto the mathematical formalisms of linear algebra, where mathematical objects of matrix structure are of central concern.
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" He concludes: "It is surely the emptiest of formalisms to profess respect for Colgate and eviscerate it in application.'362 U.S. at 57.
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Analytical mechanics does not introduce new physics and is not more general than Newtonian mechanics. Rather it is a collection of equivalent formalisms which have broad application. In fact the same principles and formalisms can be used in relativistic mechanics and general relativity, and with some modifications, quantum mechanics and quantum field theory. Analytical mechanics is used widely, from fundamental physics to applied mathematics, particularly chaos theory.
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HFST has been used for writing various linguistic tools, such as spell-checkers, hyphenators, and morphologies. Morphological dictionaries written in other formalisms have also been converted to HFST's formats.
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Glue analyses within other syntactic formalisms have also been proposed; besides LFG, glue analyses have been proposed within HPSG, context-free grammar, categorial grammar, and tree-adjoining grammar. Glue is a theory of the syntax–semantics interface which is compatible not only with various syntactic frameworks, but also with different theories of semantics and meaning representation. Semantic formalisms that have been used as the meaning languages in glue semantics analyses include versions of discourse representation theory, intensional logic, first-order logic, and natural semantic metalanguage.
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Recently Mukherjee has developed a suite of state-specific many-body formalisms like coupled cluster and perturbative theories which bypass the difficulty of the notorious intruder problem for computing potential energy surfaces. These methods do not share the shortcomings of the previously used Effective Hamiltonian formalisms applied to cases warranting a multireference description. The current applications of the methods clearly indicate the potentiality of the developments. This is considered a fundamental contribution to the molecular many-body methods, and it has attracted wide international recognition.
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BAN logic inspired many other similar formalisms, such as GNY logic. Some of these try to repair one weakness of BAN logic: the lack of a good semantics with a clear meaning in terms of knowledge and possible universes. However, starting in the mid-1990s, crypto protocols were analyzed in operational models (assuming perfect cryptography) using model checkers, and numerous bugs were found in protocols that were "verified" with BAN logic and related formalisms. In some cases a protocol was reasoned as secure by the BAN analysis but where in fact insecure.
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Joachim Lambek proposed the first noncommutative logic in his 1958 paper Mathematics of Sentence Structure to model the combinatory possibilities of the syntax of natural languages. His calculus has thus become one of the fundamental formalisms of computational linguistics.
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The semantics of a Reo circuit is a formal description of its behavior. Various semantics for Reo exist.Sung-Shik Jongmans and Farhad Arbab: Overview of Thirty Semantic Formalisms for Reo. Scientific Annals of Computer Science 22(1):201-251, 2012.
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Petri nets are known tools to model manufacturing systems.Silva, M. and Valette, R. (1989); Petri nets and flexible manufacturing. Lecture Notes on Computer Science, 424, 374–417. They are highly expressive and provide good formalisms for the modeling of concurrent systems.
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Here is a short history of applying the formalisms of quantum theory to topics in psychology. Ideas for applying quantum formalisms to cognition first appeared in the 1990s by Diederik Aerts and his collaborators Jan Broekaert, Sonja Smets and Liane Gabora, by Harald Atmanspacher, Robert Bordley, and Andrei Khrennikov. A special issue on Quantum Cognition and Decision appeared in the Journal of Mathematical Psychology (2009, vol 53.), which planted a flag for the field. A few books related to quantum cognition have been published including those by Khrennikov (2004, 2010), Ivancivic and Ivancivic (2010), Busemeyer and Bruza (2012), E. Conte (2012).
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Mukherjee has been the earliest developer of a class of many- body methods for electronic structure which are now standard and highly acclaimed works in the field. These methods, collectively called multireference coupled cluster (MRCC) formalisms, are versatile and powerful methods for predicting with quantitative accuracy the energetics of a vast range of molecular excitations and ionization. The attractive aspects of the formalisms are size-extensivity, compactness and high accuracy. He also developed a linear response theory based on coupled cluster formalism (CCLRT), which is similar in scope to the SAC-CI and done independently of it.
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Petri Nets are established tools used to model manufacturing systems.Silva, M. and Valette, R. (1989); Petri nets and Flexible manufacturing. Lecture Notes on Computer Science, 424, 374–417. They are highly expressive and provide good formalisms for the modeling of concurrent systems.
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Semi-Formal Methods are formalisms and languages that are not considered fully “formal”. It defers the task of completing the semantics to a later stage, which is then done either by human interpretation or by interpretation through software like code or test case generators.
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The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert space which is a kind of linear space. Such are distinguished from mathematical formalisms for physics theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite- dimensional Hilbert spaces(L2 space mainly), and operators on these spaces. In brief, values of physical observables such as energy and momentum were no longer considered as values of functions on phase space, but as eigenvalues; more precisely as spectral values of linear operators in Hilbert space.
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This is the most efficient way to obtain a large range of primes; however, to find individual primes, direct primality tests are more efficient. Furthermore, based on the sieve formalisms, some integer sequences are constructed which also could be used for generating primes in certain intervals.
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The following is a list (by no means complete) of grammar formalisms that, by Shutt's definition above, are considered to be (or have been classified by their own inventors as being) adaptive grammars. They are listed in their historical order of first mention in the literature.
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By Rodrigues' rotation formula, the angle and axis determine a transformation that rotates three-dimensional vectors. The rotation occurs in the sense prescribed by the right-hand rule. The rotation axis is sometimes called the Euler axis. It is one of many rotation formalisms in three dimensions.
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Mathematical Systems Theory 27(6): 511–546. demonstrates that Linear Indexed Grammars, Combinatory Categorial Grammars, Tree-adjoining Grammars, and Head Grammars are weakly equivalent formalisms, in that they all define the same string languages. Kuhlmann et al. (2015)Kuhlmann, M., Koller, A., and Satta, G. 2015.
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Two other entries in this encyclopedia set out particular formalisms involving mathematical modeling of relationships, in one case focusing to a substantial extent on mathematical expressions for relationships Theory of relations and in the other recording suggestions of a universal perspective on modeling and reality Relational theory.
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Concurrency theory has been an active field of research in theoretical computer science. One of the first proposals was Carl Adam Petri's seminal work on Petri nets in the early 1960s. In the years since, a wide variety of formalisms have been developed for modeling and reasoning about concurrency.
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Knowledge representation and reasoning (KR², KR&R;) is the field of artificial intelligence (AI) dedicated to representing information about the world in a form that a computer system can utilize to solve complex tasks such as diagnosing a medical condition or having a dialog in a natural language. Knowledge representation incorporates findings from psychology about how humans solve problems and represent knowledge in order to design formalisms that will make complex systems easier to design and build. Knowledge representation and reasoning also incorporates findings from logic to automate various kinds of reasoning, such as the application of rules or the relations of sets and subsets. Examples of knowledge representation formalisms include semantic nets, systems architecture, frames, rules, and ontologies.
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This work aimed at developing a complete theory of grammar that would fully acknowledge the role of semantics right from the start, while simultaneously adopting constraint- based formalisms as popular in computer science and natural language processing. This theory built on the notion of construction from traditional and pedagogical grammars rather than the rule-based formalisms that dominate most of generative grammar. One of Fillmore's most widely noticed works of the time (with Paul Kay and Cathy O'Connor) appeared in 'Language' in 1988 as "Regularity and Idiomaticity in Grammatical Constructions: The Case of Let Alone". Their paper highlighted the merits of such a theory of by focusing on the 'let alone' construction.
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Minimal recursion semantics (MRS) is a framework for computational semantics. It can be implemented in typed feature structure formalisms such as head- driven phrase structure grammar and lexical functional grammar. It is suitable for computational language parsing and natural language generation.Copestake, A., Flickinger, D. P., Sag, I. A., & Pollard, C. (2005).
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In the same way KIF is meant to facilitate sharing of knowledge across different systems that use different languages, formalisms, platforms, etc. KIF has a declarative semantics. It is meant to describe facts about the world rather than processes or procedures. Knowledge can be described as objects, functions, relations, and rules.
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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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SADL attempts to meet the needs identified above in several ways. The SADL grammar tries to use common words to express formal model relationships. These key words and phrases are mapped unambiguously into the formalisms of OWL, SWRL or Jena Rules, and SPARQL. SADL allows statement combinations for more concise and understandable groupings.
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An important yardstick for describing the relative expressive power of formalisms in this area is the Chomsky hierarchy. It says, for instance, that regular expressions, nondeterministic finite automatons and regular grammars have equal expressive power, while that of context-free grammars is greater; what this means is that the sets of sets of strings described by the first three formalisms are equal, and a proper subset of the set of sets of strings described by context-free grammars. In this area, the cost of expressive power is a central topic of study. It is known, for instance, that deciding whether two arbitrary regular expressions describe the same set of strings is hard, while doing the same for arbitrary context-free grammars is completely impossible.
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There are typically two different ways of mathematically describing how an electromagnetic wave interacts with the elements within an ellipsometer (including the sample): the Jones matrix and the Mueller matrix formalisms. In the Jones matrix formalism, the electromagnetic wave is described by a Jones vector with two orthogonal complex-valued entries for the electric field (typically E_x and E_y), and the effect that an optical element (or sample) has on it is described by the complex-valued 2×2 Jones matrix. In the Mueller matrix formalism, the electromagnetic wave is described by Stokes vectors with four real-valued entries, and their transformation is described by the real-valued 4x4 Mueller matrix. When no depolarization occurs both formalisms are fully consistent.
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See pages 48-58 of Ch. 2 in Henneaux, Marc and Teitelboim, Claudio, Quantization of Gauge Systems. Princeton University Press, 1992. This article assumes familiarity with the standard Lagrangian and Hamiltonian formalisms, and their connection to canonical quantization. Details of Dirac's modified Hamiltonian formalism are also summarized to put the Dirac bracket in context.
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53 (1981) 43. In this Euclidean field theory, real-time observables can be retrieved by analytic continuation. The alternative to the use of fictitious imaginary times is to use a real-time formalism which come in two forms. A path-ordered approach to real-time formalisms includes the Schwinger–Keldysh formalism and more modern variants.
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Vijay-Shanker and Weir (1994)Vijay-Shanker, K. and Weir, David J. 1994. The Equivalence of Four Extensions of Context-Free Grammars. Mathematical Systems Theory 27(6): 511-546. demonstrate that linear indexed grammars, combinatory categorial grammar, tree-adjoining grammars, and head grammars are weakly equivalent formalisms, in that they all define the same string languages.
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Vijay-Shanker and Weir (1994)Vijay-Shanker, K. and Weir, David J. 1994. The Equivalence of Four Extensions of Context-Free Grammars. Mathematical Systems Theory 27(6): 511–546. demonstrate that linear indexed grammars, combinatory categorial grammar, tree-adjoining grammars, and head grammars are weakly equivalent formalisms, in that they all define the same string languages.
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The underlying mathematical formalisms of CIP were first proposed by the physicist, Prof. Dr. Hugo Fierz. The tool was subsequently developed at the Swiss Federal Institute of Technology (Zurich) in a series of research projects during the 1990s. Development and distribution has since been transferred to a commercially operating spin-off company, CIP-Tool, based in Solothurn, Switzerland.
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Francez's current research focuses on proof-theoretic semantics for logic and natural language. He has also carried out work in formal semantics of natural language, type-logical grammar, computational linguistics, unification-based grammar formalisms (LFG, HPSG). In the past he was interested in semantics of programming languages, program verification, concurrent and distributed programming and logic programming.
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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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Kohei Honda and Mario Tokoro 1991, José Meseguer 1992, Ugo Montanari and Carolyn Talcott 1998, M. Gaspari and G. Zavattaro 1999 have attempted to relate Actor semantics to algebra. Also John Darlington and Y. K. Guo 1994 have attempted to relate linear logic to Actor semantics. However, none of the above formalisms addresses the crucial property of guarantee of service (see unbounded nondeterminism).
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"Specification of the legal knowledge interchange format." Estrella, Deliverable 1 (2007). LKIF was designed with two main roles in mind: the translation of legal knowledge bases written in different representation formats and formalisms and to be a knowledge representation formalism which could be part of larger architectures for developing legal knowledge systems.Hoekstra, Rinke, Joost Breuker, Marcello Di Bello, and Alexander Boer.
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He has also been the first to develop a rigorously size-extensive state-specific multi-reference coupled cluster formalism, and its perturbative counterpart which is getting increasingly recognized as a very promising methodological advance. The attractive aspects of Mukherjee's formalisms are compactness and high accuracy. These are now accepted as pioneering and standard works in the field. which has attracted wide international attention.
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Since an infinite result is unphysical, ultraviolet divergences often require special treatment to remove unphysical effects inherent in the perturbative formalisms. In particular, UV divergences can often be removed by regularization and renormalization. Successful resolution of an ultraviolet divergence is known as ultraviolet completion. If they cannot be removed, they imply that the theory is not perturbatively well-defined at very short distances.
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There already exist some approaches to help authors to build adaptive-hypermedia-based systems. However, there is a strong need for high-level approaches, formalisms and tools that support and facilitate the description of reusable adaptive hypermedia and websites. Such models started appearing (see, e.g., the AHAM model of adaptive hypermedia, or the LAOS framework for authoring of adaptive hypermedia).
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Formal language theory mostly studies formalisms to describe sets of strings, such as context-free grammars and regular expressions. Each instance of a formalism, e.g. each grammar and each regular expression, describes a particular set of strings. In this context, the expressive power of a formalism is the set of sets of strings its instances describe, and comparing expressive power is a matter of comparing these sets.
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Most of the large number of human languages use patterns of sound or gesture for symbols which enable communication with others around them. Languages tend to share certain properties, although there are exceptions. There is no defined line between a language and a dialect. Constructed languages such as Esperanto, programming languages, and various mathematical formalisms are not necessarily restricted to the properties shared by human languages.
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In 2008, Kiriushcheva and Kuzmin published a formal disproof of 4 conventional wisdoms surrounding the ADM formalism, most notably that only in the Dirac Hamiltonian formalism, not in the ADM formalism, can proper diffeomorphism invariance be recovered via the canonical transformations. The difference in canonical structure of the Dirac and ADM Hamiltonian formalisms is an ongoing controversy yet to be concluded in the physics literature.
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5, 2010, pp. 629-661. is a logic-based format for presenting mathematical solutions and proofs created by Prof. Ralph-Johan Back and Joakim von Wright at Åbo Akademi University, Turku, Finland. The format was originally introduced as a way for presenting proofs in programming logic, but was later adapted to provide a practical approach to presenting proofs and derivations in mathematics education including exact formalisms.
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In physics, relativistic angular momentum refers to the mathematical formalisms and physical concepts that define angular momentum in special relativity (SR) and general relativity (GR). The relativistic quantity is subtly different from the three-dimensional quantity in classical mechanics. Angular momentum is an important dynamical quantity derived from position and momentum. It is a measure of an object's rotational motion and resistance to stop rotating.
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Some theoreticians have suggested that it would be productive to merge certain features of junction grammar with other models. Millett and Lonsdale, in fact, have proposed an expansion of Tree Adjoining Grammar (TAG) to create junction trees.Millet, Ronald and Lonsdale, Deryle (2005). “Expanding Tree Adjoining Grammar to Create Junction Grammar Trees.” Proceedings of the Seventh International Workshop on Tree Adjoining Grammar and Related Formalisms, pg.
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In quantum mechanics, a raising or lowering operator (collectively known as ladder operators) is an operator that increases or decreases the eigenvalue of another operator. In quantum mechanics, the raising operator is sometimes called the creation operator, and the lowering operator the annihilation operator. Well-known applications of ladder operators in quantum mechanics are in the formalisms of the quantum harmonic oscillator and angular momentum.
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Analytical models based on semantics and discourse pragmatics were rejected by the Bloomfieldian school of linguistics whose derivatives place the object into the verb phrase, following from Wilhelm Wundts Völkerpsychologie. Formalisms based on this convention were constructed in the 1950s by Zellig Harris and Charles Hockett. These gave rise to modern generative grammar. It has been suggested that dependency relations are caused by a random mutation in the human genome.
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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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Though theories of quantum mechanics continue to evolve, there is a basic framework for the mathematical formalism of problems in quantum mechanics underlying most approaches that can be traced back to the mathematical formalisms and techniques first used by von Neumann. In other words, discussions about interpretation of the theory, and extensions to it, are now mostly conducted on the basis of shared assumptions about the mathematical foundations.
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Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability distribution over possible quantum states) is described by a density operator S, which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space H describing the quantum system. This can be shown under various mathematical formalisms for quantum mechanics. One such formalism is provided by quantum logic.
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In linear algebra (and its application to quantum mechanics), a raising or lowering operator (collectively known as ladder operators) is an operator that increases or decreases the eigenvalue of another operator. In quantum mechanics, the raising operator is sometimes called the creation operator, and the lowering operator the annihilation operator. Well-known applications of ladder operators in quantum mechanics are in the formalisms of the quantum harmonic oscillator and angular momentum.
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The repetition of graphic formalisms formed the foundation, which was deliberately blurred and chaotic. These series of works are darkly magical, rigorous and severe. In contrast, the most recent works are free, colorful and expressive. If one looks closely at the opulent, large-format images, though, due to the color rush, the raised streaks reveal themselves similar to the hatching of traditional calligraphy, enriching the composition both stylistically and thematically.
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The λ (lambda) universality class is a group in condensed matter physics. It regroups several systems possessing strong analogies, namely, superfluids, superconductors and smectics (liquid crystals). All these systems are expected to belong to the same universality class for the thermodynamic critical properties of the phase transition. While these systems are quite different at the first glance, they all are described by similar formalisms and their typical phase diagrams are identical.
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Categorial grammar is a term used for a family of formalisms in natural language syntax motivated by the principle of compositionality and organized according to the view that syntactic constituents should generally combine as functions or according to a function-argument relationship. Most versions of categorial grammar analyze sentence structure in terms of constituencies (as opposed to dependencies) and are therefore phrase structure grammars (as opposed to dependency grammars).
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Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability distribution over possible quantum states) is described by a density operator S, which is a non-negative, self-adjoint, trace-class operator of trace 1 on the Hilbert space H describing the quantum system. This can be shown under various mathematical formalisms for quantum mechanics. One such formalism is provided by quantum logic.
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While most grammar formalisms characterise properties of strings of words, in Dynamic Syntax it is propositional structure which is characterised. Propositional structure is modelled through recourse of binary semantic trees. Propositional structure is built up on a strictly incremental manner on a left-to-right basis and is represented through processes of tree growth. Under this framework, syntactic knowledge is considered to be the knowledge to parse/process strings in context.
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First, two lists are made that form two nonintersecting partitions: the list of objects and the list of rules. Objects are denoted by circles. Each rule in a mivar network is an extension of productions, hyper-rules with multi-activators or computational procedures. It is proved that from the perspective of further processing, these formalisms are identical and in fact are nodes of the bipartite graph, denoted by rectangles.
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This is done using LFG formalisms. When applied to ESL, this results in an array of predictions for developmental schedules in syntax and morphology. For instance, word order is predicted to be initially constrained to canonical word order even in questions, as Do-support and auxiliary inversion would require processing resources that are not initially available. PT also includes theoretical modules dealing with L1 transfer, inter-learner variation and the role of linguistic typology.
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The APDA style is generally seen as occupying a middle ground between the styles of CUSID and NPDA. It is somewhat more rule-oriented and structured than the CUSID style, as point-by-point argumentation and careful structure are considered very important. It also emphasizes detailed analysis and de-emphasizes oratory as compared to CUSID. However, APDA style is less structured and theoretical than the NPDA style, and demands less use of technical debate formalisms.
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Colmerauer spent 1967–1970 as assistant professor at the University of Montreal, where he created Q-Systems, one of the earliest linguistic formalisms used in the development of the TAUM-METEO machine translation prototype. Developing Prolog III in 1984, he was one of the main founders of the field of constraint logic programming. Colmerauer became an associate professor at Aix-Marseille University in Luminy in 1970. He was promoted to full professor in 1979.
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As already mentioned, the methods and formalisms of universal algebra are an important tool for many order theoretic considerations. Beside formalizing orders in terms of algebraic structures that satisfy certain identities, one can also establish other connections to algebra. An example is given by the correspondence between Boolean algebras and Boolean rings. Other issues are concerned with the existence of free constructions, such as free lattices based on a given set of generators.
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A Post canonical system, as created by Emil Post, is a string-manipulation system that starts with finitely-many strings and repeatedly transforms them by applying a finite set j of specified rules of a certain form, thus generating a formal language. Today they are mainly of historical relevance because every Post canonical system can be reduced to a string rewriting system (semi-Thue system), which is a simpler formulation. Both formalisms are Turing complete.
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A number of syntactic CG systems have reported F-scores of around 95% for syntactic function labels. CG systems can be used to create full syntactic trees in other formalisms by adding small, non-terminal based phrase structure grammars or dependency grammars, and a number of Treebank projects have used CG for automatic annotation. CG methodology has also been used in a number of language technology applications, such as spell checkers and machine translation systems.
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In general, ligands are viewed as electron donors and the metals as electron acceptors. This is because the ligand and central metal are bonded to one another, and the ligand is providing both electrons to the bond (lone pair of electrons) instead of the metal and ligand each providing one electron. Bonding is often described using the formalisms of molecular orbital theory. The HOMO (Highest Occupied Molecular Orbital) can be mainly of ligands or metal character.
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Basically, the motion of bodies is described by their kinematic behavior. The dynamic behavior results from the equilibrium of applied forces and the rate of change of momentum. Nowadays, the term multibody system is related to a large number of engineering fields of research, especially in robotics and vehicle dynamics. As an important feature, multibody system formalisms usually offer an algorithmic, computer-aided way to model, analyze, simulate and optimize the arbitrary motion of possibly thousands of interconnected bodies.
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In mathematics, a quantum groupoid is any of a number of notions in noncommutative geometry analogous to the notion of groupoid. In usual geometry, the information of a groupoid can be contained in its monoidal category of representations (by a version of Tannaka–Krein duality), in its groupoid algebra or in the commutative Hopf algebroid of functions on the groupoid. Thus formalisms trying to capture quantum groupoids include certain classes of (autonomous) monoidal categories, Hopf algebroids etc.
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On the more experimental side, metabolic flux analysis allows the empirical estimation of reaction rates by stable isotope labelling. Within the kinetic paradigm, kinetic modelling of metabolic networks can be purely theoretical, exploring the potential space of dynamic metabolic fluxes under perturbations away from steady state using formalisms such as biochemical systems theory. Such explorations are most informative when accompanied by empirical measurements of the system under study following actual perturbations, as is the case in metabolic control analysis.
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Herbert identifies eight interpretations of quantum mechanics, all consistent with observation and with the aforementioned mathematical formalisms. He likens these different interpretations to the story of the blind men and an elephant—different approaches to the same underlying reality, which yield remarkably different (but often overlapping) pictures. The interpretations identified by Herbert are: #The Copenhagen interpretation, Part I ("There is no deep reality.") Most notably associated with Niels Bohr and Werner Heisenberg, Herbert identifies this as the most broadly accepted interpretation among physicists.
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YAWL is sometimes seen as an alternative to BPEL. A major advantage of BPEL is that it is driven by a standardization committee supported by several IT industry players. As a result, BPEL is supported by a significant number of tools (both proprietary and open-source) while YAWL has a single implementation at present. Also, several researchers have captured the formal semantics of subsets of BPEL in terms of various formalisms, including Petri nets, process algebra and finite state machine.
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The static semantics defines restrictions on the structure of valid texts that are hard or impossible to express in standard syntactic formalisms. For compiled languages, static semantics essentially include those semantic rules that can be checked at compile time. Examples include checking that every identifier is declared before it is used (in languages that require such declarations) or that the labels on the arms of a case statement are distinct.Michael Lee Scott, Programming language pragmatics, Edition 2, Morgan Kaufmann, 2006, , p.
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Collective intelligence (CI) is shared or group intelligence that emerges from the collaboration, collective efforts, and competition of many individuals and appears in consensus decision making. The term appears in sociobiology, political science and in context of mass peer review and crowdsourcing applications. It may involve consensus, social capital and formalisms such as voting systems, social media and other means of quantifying mass activity. Collective IQ is a measure of collective intelligence, although it is often used interchangeably with the term collective intelligence.
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Deep Linguistic Processing with HPSG - INitiative (DELPH-IN) is a collaboration where computational linguists worldwide develop natural language processing tools for deep linguistic processing of human language.DELPH-IN: Open-Source Deep Processing The goal of DELPH-IN is to combine linguistic and statistical processing methods in order to computationally understand the meaning of texts and utterances. The tools developed by DELPH-IN adopt two linguistic formalisms for deep linguistic analysis, viz. head-driven phrase structure grammar (HPSG) and minimal recursion semantics (MRS).
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James Frederick Allen (born 1950) is a computational linguist recognized for his contributions to temporal logic, in particular Allen's interval algebra. He is interested in knowledge representation, commonsense reasoning, and natural language understanding, believing that "deep language understanding can only currently be achieved by significant hand-engineering of semantically-rich formalisms coupled with statistical preferences".James F. Allen homepage on Rochester He is the John H. Dessaurer Professor of Computer Science at the University of RochesterFaculty listing , linguistics department, Rochester University, retrieved 2011-01-05.
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The transformations between the variables can be very complicated, but the path integral makes them into reasonably straightforward changes of integration variables. For these reasons, the Feynman path integral has made earlier formalisms largely obsolete. The price of a path integral representation is that the unitarity of a theory is no longer self-evident, but it can be proven by changing variables to some canonical representation. The path integral itself also deals with larger mathematical spaces than is usual, which requires more careful mathematics, not all of which has been fully worked out.
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In the 1997 paper "Concepts of the Framework for Enterprise Architecture" Zachman said that the framework should be referred to as a "Framework for Enterprise Architecture", and should have from the beginning. In the early 1980s however, according to Zachman, there was "little interest in the idea of Enterprise Reengineering or Enterprise Modeling and the use of formalisms and models was generally limited to some aspects of application development within the Information Systems community".John A. Zachman (1997). "Concepts of the Framework for Enterprise Architecture: Background, Description and Utility".
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MGS (a General Model of Simulation) is a domain-specific language used for specification and simulation of dynamical systems with dynamical structure, developed at IBISC (Computer Science, Integrative Biology and Complex Systems) at Université d'Évry Val-d'Essonne (University of Évry). MGS is particularly aimed at modelling biological systems. The MGS computational model is a generalisation of cellular automata, Lindenmayer systems, Paun systems and other computational formalisms inspired by chemistry and biology. It manipulates collections - sets of positions, filled with some values, in a lattice with a user-defined topology.
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A large part of research in human-computer interaction involves exploring easier-to- learn or more efficient interaction techniques for common computing tasks. This includes inventing new (post-WIMP) interaction techniques, possibly relying on methods from user interface design, and assessing their efficiency with respect to existing techniques using methods from experimental psychology. Examples of scientific venues in these topics are the UIST and the CHI conferences. Other research focuses on the specification of interaction techniques, sometimes using formalisms such as Petri nets for the purposes of formal verification.
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Obligationes or disputations de obligationibus were a medieval disputation format common in the 13th and 14th centuries. Despite the name, they had nothing to do with ethics or morals but rather dealt with logical formalisms; the name comes from the fact that the participants were "obliged" to follow the rules.Uckelman, Sara L., 2011, "Interactive Logic in the Middle Ages"; Institute for Logic, Language, and Computation Typically, there were two disputants, one Opponens and one Respondens. At the start of a debate, both the disputants would agree on a ‘positum’, usually a false statement.
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Although Montague's work is sometimes regarded as syntactically uninteresting, it helped to bolster interest in categorial grammar by associating it with a highly successful formal treatment of natural language semantics. More recent work in categorial grammar has focused on the improvement of syntactic coverage. One formalism which has received considerable attention in recent years is Steedman and Szabolcsi's combinatory categorial grammar which builds on combinatory logic invented by Moses Schönfinkel and Haskell Curry. There are a number of related formalisms of this kind in linguistics, such as type logical grammar and abstract categorial grammar.
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Runtime verification is a computing system analysis and execution approach based on extracting information from a running system and using it to detect and possibly react to observed behaviors satisfying or violating certain properties . Some very particular properties, such as datarace and deadlock freedom, are typically desired to be satisfied by all systems and may be best implemented algorithmically. Other properties can be more conveniently captured as formal specifications. Runtime verification specifications are typically expressed in trace predicate formalisms, such as finite state machines, regular expressions, context-free patterns, linear temporal logics, etc.
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At first these explanations were not much different than the standard debugging information that developers deal with when debugging any system. However, an active area of research was utilizing natural language technology to ask, understand, and generate questions and explanations using natural languages rather than computer formalisms. An inference engine cycles through three sequential steps: match rules, select rules, and execute rules. The execution of the rules will often result in new facts or goals being added to the knowledge base which will trigger the cycle to repeat.
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Architecture description defines the practices, techniques and types of representations used by software architects to record a software architecture. Architecture description is largely a modeling activity (Software architectural model). Architecture models can take various forms, including text, informal drawings, diagrams or other formalisms (modeling language). An architecture description will often employ several different model kinds to effectively address a variety of audiences, the stakeholders (such as end users, system owners, software developers, system engineers, program managers) and a variety of architectural concerns (such as functionality, safety, delivery, reliability, scalability).
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To describe such recognizers, formal language theory uses separate formalisms, known as automata theory. One of the interesting results of automata theory is that it is not possible to design a recognizer for certain formal languages.. For more on this subject, see undecidable problem. Parsing is the process of recognizing an utterance (a string in natural languages) by breaking it down to a set of symbols and analyzing each one against the grammar of the language. Most languages have the meanings of their utterances structured according to their syntax--a practice known as compositional semantics.
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The rules proposed by Thomas have inspired various mathematicians, who translated them into rigorous theorems, first referring to ordinary differential equations, but also referring to Boolean and multilevel logical formalisms. This is one of the few cases where biological studies led to the formulation and demonstration of general mathematical theorems. The theoretical studies by Thomas on the properties of genetic regulatory circuits were also accompanied by practical considerations regarding the synthesis of novel circuits, with specific properties, in the bacterium E. coli. However, due to various technical problems, the attempts of Thomas' group to build synthetic gene circuits were unsuccessful.
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However, information represented in one syntax may in some cases be accurately translated into a different syntax. Where accurate translation of syntaxes is possible, systems using different syntaxes may also interoperate accurately. In some cases, the ability to accurately translate information among systems using different syntaxes may be limited to one direction, when the formalisms used have different levels of expressivity (ability to express information). A single ontology containing representations of every term used in every application is generally considered impossible, because of the rapid creation of new terms or assignments of new meanings to old terms.
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The formalism, now known as De Donder–Weyl (DW) theory, was developed by Théophile De DonderThéophile De Donder, "Théorie invariantive du calcul des variations," Gauthier-Villars, 1930. Frédéric Hélein: Hamiltonian formalisms for multidimensional calculus of variations and perturbation theory In Haïm Brézis, Felix E. Browder, Abbas Bahri, Sergiu Klainerman, Michael Vogelius (ads.): Noncompact problems at the intersection of geometry, analysis, and topology, American Mathematical Society, 2004, pp. 127–148, p. 131, , and Hermann Weyl. Hermann Weyl made his proposal in 1934 being inspired by the work of Constantin Carathéodory, which in turn was founded on the work of Vito Volterra.
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Systems utilizing Casimir effects have thus far been shown to only create very small forces and are generally considered one-shot devices that would require a subsequent energy to recharge them (i.e. Forward's "vacuum fluctuation battery"). The ability of systems to use the zero-point field continuously as a source of energy or propellant is much more contentious (though peer-reviewed models have been proposed). There is debate over which formalisms of quantum mechanics apply to propulsion physics under such circumstances, the more refined Quantum Electrodynamics (QED), or the relatively undeveloped and controversial Stochastical Quantum Electrodynamics (SED).
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In their 2013 book Quantum Social Science, Emmanuel Haven and Andrei Khrennikov developed mathematical formalisms for the application of quantum models to topics including psychology, economics, finance, and brain science. Most researchers in areas such as quantum cognition view the quantum formalism solely as a mathematical toolbox, and do not assume that human cognition is physically based on quantum mechanics. Separately however, researchers in quantum biology have uncovered evidence of quantum effects being exploited in processes such as photosynthesis and avian navigation; and some authors, notably political scientist Alexander Wendt, have argued that human beings are literally what he calls "walking wave functions".
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The world is moving away from the Church and the Church from the world. The little girl Armelle, his pupil in catechism class, of whom he is very fond and who had always written to him in the trenches, wants to become a model, and he gives her his permission, even if many of his fellow canons disapprove. Marshall masterfully recounts the Catholic Church in France between the two world wars. The more formal people are in approaching her, the more the ecclesiastical hierarchies appear closed in their moralisms, their formalisms, their solipsistic way of thinking.
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Quantum mechanics arose gradually, from theories to explain observations which could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and the correspondence between energy and frequency in Albert Einstein's 1905 paper which explained the photoelectric effect. Early quantum theory was profoundly re-conceived in the mid-1920s by Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Max Born and others. The original interpretation of quantum mechanics is the Copenhagen interpretation, developed by Niels Bohr and Werner Heisenberg in Copenhagen during the 1920s. The modern theory is formulated in various specially developed mathematical formalisms.
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Lafont (1993) first showed how intuitionistic linear logic can be explained as a logic of resources, so providing the logical language with access to formalisms that can be used for reasoning about resources within the logic itself, rather than, as in classical logic, by means of non-logical predicates and relations. Tony Hoare (1985)'s classical example of the vending machine can be used to illustrate this idea. Suppose we represent having a candy bar by the atomic proposition , and having a dollar by . To state the fact that a dollar will buy you one candy bar, we might write the implication .
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The Stanford researchers tried to identify domains where expertise was highly valued and complex, such as diagnosing infectious diseases (Mycin) and identifying unknown organic molecules (Dendral). The idea that "intelligent systems derive their power from the knowledge they possess rather than from the specific formalisms and inference schemes they use"Edward Feigenbaum, 1977. Paraphrased by Hayes-Roth, et al. – as Feigenbaum said – was at the time a significant step forward, since the past research had been focused on heuristic computational methods, culminating in attempts to develop very general-purpose problem solvers (foremostly the conjunct work of Allen Newell and Herbert Simon).
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It has furthermore been neglected in classical information theory that one wants to extract those parts out of a piece of information that are relevant to specific questions. A mathematical phrasing of these operations leads to an algebra of information, describing basic modes of information processing. Such an algebra involves several formalisms of computer science, which seem to be different on the surface: relational databases, multiple systems of formal logic or numerical problems of linear algebra. It allows the development of generic procedures of information processing and thus a unification of basic methods of computer science, in particular of distributed information processing.
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All multi-body simulation formalisms used for code generation create their equations in the form of typical explicit differential equations (ODE). This is especially important in Hardware-in-the- Loop applications where the calculation of simulation results within a specific, defined time frame must be assured. Only then is it possible to implement complex multi-body simulation models for Hardware-in-the-Loop applications under stringent real-time conditions. These constraints cannot be met when using DAE-based methods. Additional “Toolboxes” are available for linear analysis (Eigenvalues, pole-zero analysis, frequency response, etc.) of VRML-based animation.
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Aquamacs is a distribution that includes a number of extensions to GNU Emacs to provide an integrated development environment and to support, among many formalisms, LaTeX, Python, Java, Lisp and Objective C editing, as well as the Emacs Speaks Statistics system for R and S. These packages are installed without the need of further configuration by the end user. Aquamacs is designed to be highly compatible with Emacs, so that extension packages for GNU Emacs can be installed. Users can configure Aquamacs with Emacs customization options. They can also choose to bring back GNU Emacs behaviors.
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OntoWiki is a free and open-source semantic wiki application, meant to serve as an ontology editor and a knowledge acquisition system. It is a web-based application written in PHP and using either a MySQL database or a Virtuoso triple store. OntoWiki is form-based rather than syntax-based, and thus tries to hide as much of the complexity of knowledge representation formalisms from users as possible. OntoWiki is mainly being developed by the Agile Knowledge Engineering and Semantic Web (AKSW) research group at the University of Leipzig, a group also known for the DBpedia project among others, in collaboration with volunteers around the world.
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The air force decided to fund further research on this vision through their Rome Air Development Center laboratory at Griffiss air force base in New York. The majority of the early research was conducted at the Kestrel Institute in Northern California (with Stanford University) and the Information Sciences Institute (ISI) in Southern California (with USC and UCLA). The Kestrel Institute focused primarily on the provably correct transformation of logical models to efficient code. ISI focused primarily on the front end of the process on defining specifications that could map to logical formalisms but were in formats that were intuitive and familiar to systems analysts.
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When university students staged a street demonstration in 1928 (Generation of 1928), they were arrested but were soon released. But Gómez was indeed ruthless in throttling all opposition and he allowed a personality cult, but this was as much his doing as that of his sycophants, who were numerous all over Venezuela.Rourke, Thomas (pseud.), Gomez, Tyrant of the Andes, 1936 Gómez, unlike Guzmán Blanco, never erected a statue of himself anywhere in Venezuela. He was a stickler for legal formalisms, which in essence meant that he introduced new constitutions any time it suited his political ends, although this was also the rule during the 19th century.
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Starting from the need of practical applications, by the mid of nineties, different formalisms have been created, which fit the description of „nets within nets“. Lomazova and Schnoebelen are listingIrina A. Lomazova, Philippe Schnoebelen: Some decidability results for nested Petri nets, Springer LNCS 1755, 2000, pp. 208-220 some of these approaches, namely by Sibertin-Blanc,Christophe Sibertin-Blanc: Cooperative Nets, Springer LNCS 815, 1994, pp. 471-490 Lakos,Charles Lakos: From coloured Petri nets to object Petri nets, Springer LNCS 935, 1995, pp. 278-297 Moldt und WienbergDaniel Moldt und Frank Wienberg: Multi-agent-systems based on coloured Petri nets, Springer LNCS 1248, 1997, pp.
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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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Kurt Gödel (1925) The proof of Gödel's completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 (and a shorter version of the proof, published as an article in 1930, titled "The completeness of the axioms of the functional calculus of logic" (in German)) is not easy to read today; it uses concepts and formalisms that are no longer used and terminology that is often obscure. The version given below attempts to represent all the steps in the proof and all the important ideas faithfully, while restating the proof in the modern language of mathematical logic. This outline should not be considered a rigorous proof of the theorem.
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Other formalisms (besides recursion, the λ-calculus, and the Turing machine) have been proposed for describing effective calculability/computability. Stephen Kleene (1952) adds to the list the functions "reckonable in the system S1" of Kurt Gödel 1936, and Emil Post's (1943, 1946) "canonical [also called normal] systems".Kleene 1952:320 In the 1950s Hao Wang and Martin Davis greatly simplified the one-tape Turing-machine model (see Post–Turing machine). Marvin Minsky expanded the model to two or more tapes and greatly simplified the tapes into "up-down counters", which Melzak and Lambek further evolved into what is now known as the counter machine model.
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The word "superspace" is also used in a completely different and unrelated sense, in the book Gravitation by Misner, Thorne and Wheeler. There, it refers to the configuration space of general relativity, and, in particular, the view of gravitation as geometrodynamics, an interpretation of general relativity as a form of dynamical geometry. In modern terms, this particular idea of "superspace" is captured in one of several different formalisms used in solving the Einstein equations in a variety of settings, both theoretical and practical, such as in numerical simulations. This includes primarily the ADM formalism, as well as ideas surrounding the Hamilton–Jacobi–Einstein equation and the Wheeler–DeWitt equation.
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Debashis Mukherjee is a theoretical chemist, well known for his research in the fields of molecular many body theory, theoretical spectroscopy, finite temperature non-perturbative many body theories. Mukherjee has been the first to develop and implement a class of many-body methods for electronic structure which are now standard works in the field. These methods, collectively called multireference coupled cluster formalisms, are versatile and powerful methods for predicting with quantitative accuracy the energetics and cross-sections of a vast range of molecular excitations and ionization. A long-standing problem of guaranteeing proper scaling of energy for many electron wave-functions of arbitrary complexity has also been first resolved by him.
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The groundbreaking work (that initially used the π-calculus, a process calculus) was later taken over by IBM Cambridge in the UK (Luca Cardelli) that developed SPiM (Stochastic Pi Calculus Machine). In the last decade the field has flourished with a vast variety of applications. More recently, the field even evolved to a synthesis of two different fields molecular computing and molecular programming. The combination of the two exhibits how different mathematical formalisms (such as Chemical Reaction Networks) can serve as 'programming languages' and various molecular architectures (such as DNA molecules architecture) can in principle implement any behavior that can be mathematically expressed by the formalism being used.
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In his 1957 doctoral dissertation, Everett proposed that rather than modeling an isolated quantum system subject to external observation, one could mathematically model an object as well as its observers as purely physical systems within the mathematical framework developed by Paul Dirac, John von Neumann and others, discarding altogether the ad hoc mechanism of wave function collapse. Since Everett's original work, a number of similar formalisms have appeared in the literature. One is the relative state formulation. It makes two assumptions: first, the wavefunction is not simply a description of the object's state, but is entirely equivalent to the object—a claim it has in common with some other interpretations.
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In the first half of the 20th century, various formalisms were proposed to capture the informal concept of a computable function, with μ-recursive functions, Turing machines and the lambda calculus possibly being the best-known examples today. The surprising fact that they are essentially equivalent, in the sense that they are all encodable into each other, supports the Church-Turing thesis. Another shared feature is more rarely commented on: they all are most readily understood as models of sequential computation. The subsequent consolidation of computer science required a more subtle formulation of the notion of computation, in particular explicit representations of concurrency and communication.
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James J. Cimino, is a physician-scientist and biomedical informatician elected in 1992 to the American College of Medical Informatics and in 2014 to the Institute of Medicine of the National Academy of Science. He pioneered the theory and formalisms of medical concept representation underpinning the use of controlled medical vocabularies in electronic medical records in support of clinical decision-making. Training under Octo Barnett at Harvard University, he also contributed to the initiation of the Unified Medical Language System. In addition, he actively practices medicine as an internist and has devoted many years to develop and innovate clinical information systems that have been integrated in the New York–Presbyterian Hospital, and the Columbia University Medical Center.
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Law often concerns issues about time, both relating to the content, such as time periods and deadlines, and those relating to the law itself, such as commencement. Some attempts have been made to model these temporal logics using both computational formalisms such as the Event CalculusR. Hernandez Marin, G. Sartor, Time and norms: a formalisation in the event-calculus, in: Proceedings of the Seventh International Conference on Artificial Intelligence and Law, ACM, New York, 1999, pp. 90–100. and temporal logics such as defeasible temporal logic.G. Governatori, A. Rotolo, G. Sartor, Temporalised normative positions in defeasible logic, in: Proceedings of the Tenth International Conference on Artificial Intelligence and Law, ACM Press, New York, 2005, pp. 25–34.
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Statistical relational learning (SRL) is a subdiscipline of artificial intelligence and machine learning that is concerned with domain models that exhibit both uncertainty (which can be dealt with using statistical methods) and complex, relational structure. Note that SRL is sometimes called Relational Machine Learning (RML) in the literature. Typically, the knowledge representation formalisms developed in SRL use (a subset of) first-order logic to describe relational properties of a domain in a general manner (universal quantification) and draw upon probabilistic graphical models (such as Bayesian networks or Markov networks) to model the uncertainty; some also build upon the methods of inductive logic programming. Significant contributions to the field have been made since the late 1990s.
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A reasonable and effective mathematisation of economics entails Diophantine formalisms. These come with natural undecidabilities and uncomputabilities. In the face of this, [the] conjecture [is] that an economics for the future will be freer to explore experimental methodologies underpinned by alternative mathematical structures.Abstract Sergio M. Focardi and Frank J. Fabozzi, on the other hand, have acknowledged that "economic science is generally considered less viable than the physical sciences" and that "sophisticated mathematical models of the economy have been developed but their accuracy is questionable to the point that the 2007–08 economic crisis is often blamed on an unwarranted faith in faulty mathematical models" (see also: López de Prado, M. and Fabozzi, F. (2018).
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F-logic was developed by Michael Kifer at Stony Brook University and Georg Lausen at the University of Mannheim. F-logic was originally developed for deductive databases, but is now most frequently used for semantic technologies, especially the semantic web. F-logic is considered as one of the formalisms for ontologies, but description logic (DL) is more popular and accepted, as is the DL-based OWL. A development environment for F-logic was developed in the NeOn project and is also used in a range of applications for information integration, question answering and semantic search. Prior to the version 4 of Protégé ontology editor, F-Logic is supported as one of the two kinds of ontology.
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Consequently, Leibniz's quotient notation was re-interpreted to stand for the limit of the modern definition. However, in many instances, the symbol did seem to act as an actual quotient would and its usefulness kept it popular even in the face of several competing notations. Several different formalisms were developed in the 20th century that can give rigorous meaning to notions of infinitesimals and infinitesimal displacements, including nonstandard analysis, tangent space, O notation and others. The derivatives and integrals of calculus can be packaged into the modern theory of differential forms, in which the derivative is genuinely a ratio of two differentials, and the integral likewise behaves in exact accordance with Leibniz notation.
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Physical organic chemists use the mathematical foundation of chemical kinetics to study the rates of reactions and reaction mechanisms. Unlike thermodynamics, which is concerned with the relative stabilities of the products and reactants (ΔG°) and their equilibrium concentrations, the study of kinetics focuses on the free energy of activation (ΔG‡) -- the difference in free energy between the reactant structure and the transition state structure—of a reaction, and therefore allows a chemist to study the process of equilibration. Mathematically derived formalisms such as the Hammond Postulate, the Curtin-Hammett principle, and the theory of microscopic reversibility are often applied to organic chemistry. Chemists have also used the principle of thermodynamic versus kinetic control to influence reaction products.
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Since precise model-based systems development is the primary application area of VIATRA2, it necessitates that (i) the model transformations are specified in a mathematically precise way, and (ii) these transformations are automated so that the target mathematical models can be derived fully automatically. For this purpose, VIATRA2 have chosen to integrate two popular, intuitive, yet mathematically precise rule-based specification formalisms, namely, graph transformation (GT) and Abstract State Machines (ASM) to manipulate graph based models. The basic concept in defining model transformations within VIATRA2 is the (graph) pattern. A pattern is a collection of model elements arranged into a certain structure fulfilling additional constraints (as defined by attribute conditions or other patterns).
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Buchdahl's attempt at making the foundations of thermodynamics more concise was far from advertising the use of the axiomatic method; instead it was an endeavour allowing "physical intuition to take precedence over mathematical niceties". Buchdahl's interest in tensor and spinor analysis was related to dealing with formalisms and calculational procedures, be it spherical and spheroidal harmonics. While working with Weyl's theory and quadratic Lagrangians, he decided to present the Euler–Lagrange derivative of the most general Lagrangian built from the metric, the curvature tensor and its derivatives to arbitrary order.Buchdahl, H.: "Über die Variationsableitung von Fundamentalinvarianten beliebig hoher Ordnung". Acta Mathematica 85 (1951) 63–72 However, he did not use spinors as an important tool in general relativity, e.g.
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The latter involves replacing a straight time contour from (large negative) real initial time t_i to t_i - i\beta by one that first runs to (large positive) real time t_f and then suitably back to t_i - i\beta. In fact all that is needed is one section running along the real time axis as the route to the end point, t_i - i\beta, is less important. The piecewise composition of the resulting complex time contour leads to a doubling of fields and more complicated Feynman rules, but obviates the need of analytic continuations of the imaginary-time formalism. The alternative approach to real-time formalisms is an operator based approach using Bogoliubov transformations, known as thermo field dynamics.
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To address the specification problem, modelers have in recent years moved away from explicit specification of all possible states, and towards rule-based formalisms that allow for implicit model specification, including the κ-calculus, BioNetGen, the Allosteric Network Compiler and others. To tackle the computation problem, they have turned to particle-based methods that have in many cases proved more computationally efficient than population-based methods based on ordinary differential equations, partial differential equations, or the Gillespie stochastic simulation algorithm. Given current computing technology, particle- based methods are sometimes the only possible option. Particle-based simulators further fall into two categories: Non-spatial simulators such as StochSim, DYNSTOC, RuleMonkey, and NFSim and spatial simulators, including Meredys, SRSim and MCell.
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Another advantage is that it is in practice easier to guess the correct form of the Lagrangian of a theory, which naturally enters the path integrals (for interactions of a certain type, these are coordinate space or Feynman path integrals), than the Hamiltonian. Possible downsides of the approach include that unitarity (this is related to conservation of probability; the probabilities of all physically possible outcomes must add up to one) of the S-matrix is obscure in the formulation. The path-integral approach has been proved to be equivalent to the other formalisms of quantum mechanics and quantum field theory. Thus, by deriving either approach from the other, problems associated with one or the other approach (as exemplified by Lorentz covariance or unitarity) go away.
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Music Markup Language (MML) was an early application of XML to describe music objects and events. MML pioneered features commonly used in later music markup formalisms, such as the IEEE 1599 standard. These features included the use of XML as a foundation; the ability to describe a musical object or event comprehensively (as opposed to merely providing a machine-readable format for a traditional musical score, or for a determinate sound recording of one performance); and the division of this comprehensive information into modules (often termed layers in later work), with separate modules for metadata, lyrics, notation, sound, and performance. MML makes it possible to state relationships among written syllables, phonemes, notes in traditional musical notation, pitch, and rhythm in a flexible and extensible way.
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Similar is the situation in the case of charged- particle optics. Let us recall that in relativistic quantum mechanics too one has a similar problem of understanding the relativistic wave equations as the nonrelativistic approximation plus the relativistic correction terms in the quasi-relativistic regime. For the Dirac equation (which is first-order in time) this is done most conveniently using the Foldy–Wouthuysen transformation leading to an iterative diagonalization technique. The main framework of the newly developed formalisms of optics (both light optics and charged-particle optics) is based on the transformation technique of Foldy–Wouthuysen theory which casts the Dirac equation in a form displaying the different interaction terms between the Dirac particle and an applied electromagnetic field in a nonrelativistic and easily interpretable form.
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Since the 1950s, antirealism is more modest, usually instrumentalism, permitting talk of unobservable aspects, but ultimately discarding the very question of realism and posing scientific theory as a tool to help humans make predictions, not to attain metaphysical understanding of the world. The instrumentalist view is carried by the famous quote of David Mermin, "Shut up and calculate", often misattributed to Richard Feynman.For a discussion of the provenance of the phrase "shut up and calculate", see Other approaches to resolve conceptual problems introduce new mathematical formalism, and so propose alternative theories with their interpretations. An example is Bohmian mechanics, whose empirical equivalence with the three standard formalisms—Schrödinger's wave mechanics, Heisenberg's matrix mechanics, and Feynman's path integral formalism—has been demonstrated.
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The research in (iv) had a deep impact on the understanding and initial development of a formalism to obtain semantic information when dealing with concepts, their combinations and variable contexts in a corpus of unstructured documents. This conundrum of natural language processing (NLP) and information retrieval (IR) on the web – and data bases in general – can be addressed using the mathematical formalism of quantum theory. As basic steps, (a) K. Van Rijsbergen introduced a quantum structure approach to IR, (b) Widdows and Peters utilised a quantum logical negation for a concrete search system, and Aerts and Czachor identified quantum structure in semantic space theories, such as latent semantic analysis. Since then, the employment of techniques and procedures induced from the mathematical formalisms of quantum theory – Hilbert space, quantum logic and probability, non-commutative algebras, etc.
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Many aspects of the structure-reactivity relationship in organic chemistry can be rationalized through resonance, electron pushing, induction, the eight electron rule, and s-p hybridization, but these are only helpful formalisms and do not represent physical reality. Due to these limitations, a true understanding of physical organic chemistry requires a more rigorous approach grounded in particle physics. Quantum chemistry provides a rigorous theoretical framework capable of predicting the properties of molecules through calculation of a molecule's electronic structure, and it has become a readily available tool in physical organic chemists in the form of popular software packages. The power of quantum chemistry is built on the wave model of the atom, in which the nucleus is a very small, positively charged sphere surrounded by a diffuse electron cloud.
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Although by no means an exhaustive list, the following parsers and grammar formalisms employ syntactic predicates: ; ANTLR (Parr & Quong) :As originally implemented, syntactic predicates sit on the leftmost edge of a production such that the production to the right of the predicate is attempted if and only if the syntactic predicate first accepts the next portion of the input stream. Although ordered, the predicates are checked first, with parsing of a clause continuing if and only if the predicate is satisfied, and semantic actions only occurring in non-predicates. ; Augmented Pattern Matcher (Balmas) :Balmas refers to syntactic predicates as "multi-step matching" in her paper on APM. As an APM parser parses, it can bind substrings to a variable, and later check this variable against other rules, continuing to parse if and only if that substring is acceptable to further rules.
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The solutions for molecules, such as methane, provide exact representations of their electronic structure which are unobtainable by experimental methods. Instead of four discrete σ-bonds from carbon to each hydrogen atom, theory predicts a set of four bonding molecular orbitals which are delocalized across the entire molecule. Similarly, the true electronic structure of 1,3-butadiene shows delocalized π-bonding molecular orbitals stretching through the entire molecule rather than two isolated double bonds as predicted by a simple Lewis structure. A complete electronic structure offers great predictive power for organic transformations and dynamics, especially in cases concerning aromatic molecules, extended π systems, bonds between metal ions and organic molecules, molecules containing nonstandard heteroatoms like selenium and boron, and the conformational dynamics of large molecules such as proteins wherein the many approximations in chemical formalisms make structure and reactivity prediction impossible.
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Over the course of the 1990s, Butler, Laclau, and Žižek found themselves engaging with each other's work in their own books. In order to focus more closely on their theoretical differences (and similarities), they decided to produce a book in which all three would contribute three essays each, with the authors' respective second and third essays responding to the points of dispute raised by the earlier essays. In this way, the book is structured in three "cycles" of three essays each, with points of dispute and lines of argumentation developed, passed back and forward, and so on. At one point in the exchange, Butler refers to the exercise as an unintentional "comedy of formalisms" (137), with each writer accusing the other two of being too abstract and formalist in relation to the declared themes of contingency, hegemony, and universality.
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The beginnings of the Curry–Howard correspondence lie in several observations: # In 1934 Curry observes that the types of the combinators could be seen as axiom-schemes for intuitionistic implicational logic. # In 1958 he observes that a certain kind of proof system, referred to as Hilbert-style deduction systems, coincides on some fragment to the typed fragment of a standard model of computation known as combinatory logic. # In 1969 Howard observes that another, more "high- level" proof system, referred to as natural deduction, can be directly interpreted in its intuitionistic version as a typed variant of the model of computation known as lambda calculus. In other words, the Curry–Howard correspondence is the observation that two families of seemingly unrelated formalisms—namely, the proof systems on one hand, and the models of computation on the other—are in fact the same kind of mathematical objects.
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Judea Pearl wrote "Haavelmo was the first to recognize the capacity of economic models to guide policies" and "presented a mathematical procedure that takes an arbitrary model and produces quantitative answers to policy questions". According to Pearl, "Haavelmo's paper, 'The Statistical Implications of a System of Simultaneous Equations', marks a pivotal turning point, not in the statistical implications of econometric models, as historians typically presume, but in their causal counterparts." Haavelmo's idea that an economic model depicts a series of hypothetical experiments and that policies can be simulated by modifying equations in the model became the basis of all currently used formalisms of econometric causal inference. (The biostatistics and epidemiology literature on causal inference draws from different sources.) It was first operationalized by Robert H. Strotz and Herman Wold (1960) who advocated "wiping out" selected equations, and then translated into graphical models as "wiping out" incoming arrows.
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The latter became the view of people like Eric Raymond and Linus Torvalds, while Bruce Perens argues that open source was simply meant to popularize free software under a new brand, and even called for a return to the basic ethical principles. Some free software advocates use the terms "Free and Open-Source Software" (FOSS) or "Free/Libre and Open- Source Software" (FLOSS) as a form of inclusive compromise, drawing on both philosophies to bring both free software advocates and open-source software advocates together to work on projects with more cohesion. Some users believe that a compromise term encompassing both aspects is an ideal solution in order to promote both the user's freedom with the software and the pragmatic efficiency of an open-source development model. This eclectic view is reinforced by the fact that the overwhelming majority of OSI-approved licenses and self-avowed open-source programs are also compatible with the free software formalisms and vice versa.
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Fluidized Bed Reactor Graphic Batch reactor Kulkarni's researches were mainly in the fields of Chemical Reaction Engineering, Applied Mathematics and Transport phenomena and he is known for his work on fluidized bed reactors and chemical reactors. He is credited with introducing an integer-solution approach and novel ideas on noise-induced transitions and his work on Artificial Intelligence-based evolutionary formalisms is reported to have assisted in a better understanding of reacting and reactor systems. His work spanned from conventional chemical reaction engineering in gas-liquid and gas-solid catalytic reactions to reactor stability to stochastic analysis of chemically reacting systems as well as inter-disciplinary fields. A model reaction system termed Encillator, an analytical approach for the solving model equations based on arithmetics, use of initial value formalism for modelling fluidized- bed reactors, introduction of normal form theory, evolutionary algorithms and stochastic approximation in analysing reactor behavior and performance are some of the contributions made by him.
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A number of representational phrase structure theories of grammar never acknowledged phrase structure rules, but have pursued instead an understanding of sentence structure in terms the notion of schema. Here phrase structures are not derived from rules that combine words, but from the specification or instantiation of syntactic schemata or configurations, often expressing some kind of semantic content independently of the specific words that appear in them. This approach is essentially equivalent to a system of phrase structure rules combined with a noncompositional semantic theory, since grammatical formalisms based on rewriting rules are generally equivalent in power to those based on substitution into schemata. So in this type of approach, instead of being derived from the application of a number of phrase structure rules, the sentence Colorless green ideas sleep furiously would be generated by filling the words into the slots of a schema having the following structure: ::[NP[ADJ N] VP[V] AP[ADV And which would express the following conceptual content: ::X DOES Y IN THE MANNER OF Z Though they are non-compositional, such models are monotonic.
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In most formalisms that use syntactic predicates, the syntax of the predicate is noncommutative, which is to say that the operation of predication is ordered. For instance, using the above example, consider the following pseudo-grammar, where X ::= Y PRED Z is understood to mean: "Y produces X if and only if Y also satisfies predicate Z": S ::= a X X ::= Y PRED Z Y ::= a+ BNCN Z ::= ANBN c+ BNCN ::= b [BNCN] c ANBN ::= a [ANBN] b Given the string ', in the case where Y must be satisfied first (and assuming a greedy implementation), S will generate aX and X in turn will generate ', thereby generating '. In the case where Z must be satisfied first, ANBN will fail to generate ', and thus ' is not generated by the grammar. Moreover, if either Y or Z (or both) specify any action to be taken upon reduction (as would be the case in many parsers), the order that these productions match determines the order in which those side-effects occur.
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