MatroidIn combinatorics, a branch of mathematics, a matroid ˈmeɪtrɔɪd is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid axiomatically, the most significant being in terms of: independent sets; bases or circuits; rank functions; closure operators; and closed sets or flats. In the language of partially ordered sets, a finite simple matroid is equivalent to a geometric lattice.
Vector spaceIn mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. The terms real vector space and complex vector space are often used to specify the nature of the scalars: real coordinate space or complex coordinate space.
Carathéodory's existence theoremIn mathematics, Carathéodory's existence theorem says that an ordinary differential equation has a solution under relatively mild conditions. It is a generalization of Peano's existence theorem. Peano's theorem requires that the right-hand side of the differential equation be continuous, while Carathéodory's theorem shows existence of solutions (in a more general sense) for some discontinuous equations. The theorem is named after Constantin Carathéodory.
Divergence theoremIn vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem which relates the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed. More precisely, the divergence theorem states that the surface integral of a vector field over a closed surface, which is called the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface.
Kullback–Leibler divergenceIn mathematical statistics, the Kullback–Leibler divergence (also called relative entropy and I-divergence), denoted , is a type of statistical distance: a measure of how one probability distribution P is different from a second, reference probability distribution Q. A simple interpretation of the KL divergence of P from Q is the expected excess surprise from using Q as a model when the actual distribution is P.
Stochastic differential equationA stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.
Concurrent Versions SystemConcurrent Versions System (CVS, also known as the Concurrent Versioning System) is a revision control system originally developed by Dick Grune in July 1986. CVS operates as a front end to RCS, an earlier system which operates on single files. It expands upon RCS by adding support for repository-level change tracking, and a client-server model. Released under the terms of the GNU General Public License, CVS is free software. CVS operates as a front end to Revision Control System (RCS), an older version control system that manages individual files but not whole projects.
Behavioural change theoriesBehavioural change theories are attempts to explain why human behaviours change. These theories cite environmental, personal, and behavioural characteristics as the major factors in behavioural determination. In recent years, there has been increased interest in the application of these theories in the areas of health, education, criminology, energy and international development with the hope that understanding behavioural change will improve the services offered in these areas.
Tietze extension theoremIn topology, the Tietze extension theorem (also known as the Tietze–Urysohn–Brouwer extension theorem or Urysohn-Brouwer lemma) states that continuous functions on a closed subset of a normal topological space can be extended to the entire space, preserving boundedness if necessary. If is a normal space and is a continuous map from a closed subset of into the real numbers carrying the standard topology, then there exists a of to that is, there exists a map continuous on all of with for all Moreover, may be chosen such that that is, if is bounded then may be chosen to be bounded (with the same bound as ).
Distributed version controlIn software development, distributed version control (also known as distributed revision control) is a form of version control in which the complete codebase, including its full history, is mirrored on every developer's computer. Compared to centralized version control, this enables automatic management branching and merging, speeds up most operations (except pushing and pulling), improves the ability to work offline, and does not rely on a single location for backups.
