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Tensor Software
Tensor software is a class of mathematical software designed for manipulation and calculation with tensors. Standalone software * SPLATT is an open source software package for high-performance sparse tensor factorization. SPLATT ships a stand-alone executable, C/C++ library, and Octave/MATLAB API. * Cadabra is a computer algebra system (CAS) designed specifically for the solution of problems encountered in field theory. It has extensive functionality for tensor polynomial simplification including multi-term symmetries, fermions and anti-commuting variables, Clifford algebras and Fierz transformations, implicit coordinate dependence, multiple index types and many more. The input format is a subset of TeX. Both a command-line and a graphical interface are available. * Tela is a software package similar to MATLAB and GNU Octave, but designed specifically for tensors. Software for use with Mathematica * Tensor is a tensor package written for the Mathematica system. It provides many f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Software
Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data. Evolution of mathematical software Numerical analysis and symbolic computation had been in most important place of the subject, but other kind of them is also growing now. A useful mathematical knowledge of such as algorism which exist before the invention of electronic computer, helped to mathematical software developing. On the other hand, by the growth of computing power (such as seeing on Moore's law), the new treatment (for example, a new kind of technique such as data assimilation which combined numerical analysis and statistics) needing conversely the progress of the mathematical science or applied mathematics. The progress of mathematical information presentation such as TeX or MathML will demand to evolution form ''formula manipulation language'' to true ''mathematics manipulation language'' (notwithstanding the problem that whether mathematical theory is inconsistent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bitbucket
Bitbucket is a Git (software), Git-based source code repository (version control), repository shared web hosting service, hosting service owned by Atlassian. Bitbucket offers both commercial plans and free accounts with an unlimited number of private repositories. Services Bitbucket Cloud Bitbucket Cloud (previously known as Bitbucket) is written in Python (programming language), Python using the Django (web framework), Django web framework. Bitbucket is mostly used for code and code review. Bitbucket supports the following features: * Pull requests with code review and comments * Bitbucket Pipelines, a continuous delivery service * Two-step verification and required two-step verification * IP whitelisting * Merge Checks * Code search (Alpha) * Git Large File Storage (LFS) * Documentation, including automatically rendered README files in a variety of Markdown-like file formats * Issue tracking * Wikis * Static sites hosted on Bitbucket Cloud: Static websites have the bitbuc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tensor Decomposition
In multilinear algebra, a tensor decomposition is any scheme for expressing a "data tensor" (M-way array) as a sequence of elementary operations acting on other, often simpler tensors. Many tensor decompositions generalize some matrix decompositions. Tensors are generalizations of matrices to higher dimensions and can consequently be treated as multidimensional fields. The main tensor decompositions are: * Tensor rank decomposition; * Higher-order singular value decomposition; * Tucker decomposition; * matrix product states, and operators or tensor trains; * Online Tensor Decompositions * hierarchical Tucker decomposition A hierarchy (from Greek: , from , 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important ...; * block term decomposition Preliminary Definitions and Notation This section introduces basic notations a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rational Expectations
In economics, "rational expectations" are model-consistent expectations, in that agents inside the model A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models c ... are assumed to "know the model" and on average take the model's predictions as valid. Rational expectations ensure internal consistency in models involving uncertainty. To obtain consistency within a model, the predictions of future values of economically relevant variables from the model are assumed to be the same as that of the decision-makers in the model, given their information set, the nature of the random processes involved, and model structure. The rational expectations assumption is used especially in many contemporary macroeconomic models. Since most macroeconomic models today study decisions under uncertainty and o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Domain-specific Language
A domain-specific language (DSL) is a computer language specialized to a particular application domain. This is in contrast to a general-purpose language (GPL), which is broadly applicable across domains. There are a wide variety of DSLs, ranging from widely used languages for common domains, such as HTML for web pages, down to languages used by only one or a few pieces of software, such as MUSH soft code. DSLs can be further subdivided by the kind of language, and include domain-specific ''markup'' languages, domain-specific ''modeling'' languages (more generally, specification languages), and domain-specific ''programming'' languages. Special-purpose computer languages have always existed in the computer age, but the term "domain-specific language" has become more popular due to the rise of domain-specific modeling. Simpler DSLs, particularly ones used by a single application, are sometimes informally called mini-languages. The line between general-purpose languages and domain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Groovy (programming Language)
Apache Groovy is a Java-syntax-compatible object-oriented programming language for the Java platform. It is both a static and dynamic language with features similar to those of Python, Ruby, and Smalltalk. It can be used as both a programming language and a scripting language for the Java Platform, is compiled to Java virtual machine (JVM) bytecode, and interoperates seamlessly with other Java code and libraries. Groovy uses a curly-bracket syntax similar to Java's. Groovy supports closures, multiline strings, and expressions embedded in strings. Much of Groovy's power lies in its AST transformations, triggered through annotations. Groovy 1.0 was released on January 2, 2007, and Groovy 2.0 in July, 2012. Since version 2, Groovy can be compiled statically, offering type inference and performance near that of Java. Groovy 2.4 was the last major release under Pivotal Software's sponsorship which ended in March 2015. Groovy has since changed its governance structure to a Project ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Java (programming Language)
Java is a high-level, class-based, object-oriented programming language that is designed to have as few implementation dependencies as possible. It is a general-purpose programming language intended to let programmers ''write once, run anywhere'' ( WORA), meaning that compiled Java code can run on all platforms that support Java without the need to recompile. Java applications are typically compiled to bytecode that can run on any Java virtual machine (JVM) regardless of the underlying computer architecture. The syntax of Java is similar to C and C++, but has fewer low-level facilities than either of them. The Java runtime provides dynamic capabilities (such as reflection and runtime code modification) that are typically not available in traditional compiled languages. , Java was one of the most popular programming languages in use according to GitHub, particularly for client–server web applications, with a reported 9 million developers. Java was originally developed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levi-Civita Symbol
In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol or Levi-Civita epsilon represents a collection of numbers; defined from the sign of a permutation of the natural numbers , for some positive integer . It is named after the Italian mathematician and physicist Tullio Levi-Civita. Other names include the permutation symbol, antisymmetric symbol, or alternating symbol, which refer to its antisymmetric property and definition in terms of permutations. The standard letters to denote the Levi-Civita symbol are the Greek lower case epsilon or , or less commonly the Latin lower case . Index notation allows one to display permutations in a way compatible with tensor analysis: \varepsilon_ where ''each'' index takes values . There are indexed values of , which can be arranged into an -dimensional array. The key defining property of the symbol is ''total antisymmetry'' in the indices. When any two indices are interchanged, e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Unitary Group
In mathematics, the special unitary group of degree , denoted , is the Lie group of unitary matrices with determinant 1. The more general unitary matrices may have complex determinants with absolute value 1, rather than real 1 in the special case. The group operation is matrix multiplication. The special unitary group is a normal subgroup of the unitary group , consisting of all unitary matrices. As a compact classical group, is the group that preserves the standard inner product on \mathbb^n. It is itself a subgroup of the general linear group, \operatorname(n) \subset \operatorname(n) \subset \operatorname(n, \mathbb ). The groups find wide application in the Standard Model of particle physics, especially in the electroweak interaction and in quantum chromodynamics. The groups are important in quantum computing, as they represent the possible quantum logic gate operations in a quantum circuit with n qubits and thus 2^n basis states. (Alternatively, the more genera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gamma Matrices
In mathematical physics, the gamma matrices, \left\ , also called the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra Cl1,3(\mathbb). It is also possible to define higher-dimensional gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of spacetime acts. This in turn makes it possible to represent infinitesimal spatial rotations and Lorentz boosts. Spinors facilitate spacetime computations in general, and in particular are fundamental to the Dirac equation for relativistic spin- particles. In Dirac representation, the four contravariant gamma matrices are :\begin \gamma^0 &= \begin 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \en ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feynman Diagrams
In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced the diagrams in 1948. The interaction of subatomic particles can be complex and difficult to understand; Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula. According to David Kaiser, "Since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations. Feynman diagrams have revolutionized nearly every aspect of theoretical physics." While the diagrams are applied primarily to quantum field theory, they can also be used in other fields, such as solid-state theory. Frank Wilczek wrote that the calculations that won him the 2004 Nobel Prize in Physics "would have been literally unthinkable without Feynman diagram ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
High Energy Physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and bosons (force-carrying particles). There are three generations of fermions, but ordinary matter is made only from the first fermion generation. The first generation consists of up and down quarks which form protons and neutrons, and electrons and electron neutrinos. The three fundamental interactions known to be mediated by bosons are electromagnetism, the weak interaction, and the strong interaction. Quarks cannot exist on their own but form hadrons. Hadrons that contain an odd number of quarks are called baryons and those that contain an even number are called mesons. Two baryons, the proton and the neutron, make up most of the mass of ordinary matter. Mesons are unstable and the longest-lived last for only a few hundredths of a mic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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