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A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences and engineering disciplines, as well as in the social sciences.
A Markov chain is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.
Hidden Markov Model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved states.
XSD, a recommendation of the World Wide Web Consortium (W3C), specifies how to formally describe the elements in an Extensible Markup Language (XML) document. It can be used by programmers to verify each piece of item content in a document. They can check if it adheres to the description of the element it is placed in.
A state diagram is a type of diagram used in computer science and related fields to describe the behavior of systems. State diagrams require that the system described is composed of a finite number of states; sometimes, this is indeed the case, while at other times this is a reasonable abstraction. Many forms of state diagrams exist, which differ slightly and have different semantics.
The Object Constraint Language (OCL) is a declarative language describing rules applying to Unified Modeling Language (UML) models developed at IBM and is now part of the UML standard. Initially, OCL was merely a formal specification language extension for UML. OCL may now be used with any Meta-Object Facility (MOF) Object Management Group (OMG) meta-model, including UML. The Object Constraint Language is a precise text language that provides constraint and object query expressions on any MOF model or meta-model that cannot otherwise be expressed by diagrammatic notation. OCL is a key component of the new OMG standard recommendation for transforming models, the Queries/Views/Transformations (QVT) specification.
A marriage license is a document issued, either by a church or state authority, authorizing a couple to marry. The procedure for obtaining a license varies between countries and has changed over time. Marriage licenses began to be issued in the Middle Ages, to permit a marriage which would otherwise be illegal.
Representational State Transfer (REST) is a software architectural style that defines a set of constraints to be used for creating Web services. Web services that conform to the REST architectural style, termed RESTful Web services (RWS), provide interoperability between computer systems on the Internet. RESTful Web services allow the requesting systems to access and manipulate textual representations of Web resources by using a uniform and predefined set of stateless operations. Other kinds of Web services, such as SOAP Web services, expose their own arbitrary sets of operations.
Model-based testing is an application of model-based design for designing and optionally also executing artifacts to perform software testing or system testing. Models can be used to represent the desired behavior of a system under test (SUT), or to represent testing strategies and a test environment. The picture on the right depicts the former approach.
A block cellular automaton or partitioning cellular automaton is a special kind of cellular automaton in which the lattice of cells is divided into non-overlapping blocks and the transition rule is applied to a whole block at a time rather than a single cell. Block cellular automata are useful for simulations of physical quantities, because it is straightforward to choose transition rules that obey physical constraints such as reversibility and conservation laws.
Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted knowledge. It requires selecting and identifying relevant aspects of a situation in the real world and then using different types of models for different aims, such as conceptual models to better understand, operational models to operationalize, mathematical models to quantify, and graphical models to visualize the subject.
This glossary of Unified Modeling Language terms covers all versions of UML. Individual entries will point out any distinctions that exist between versions.
Executable UML is both a software development method and a highly abstract software language. It was described for the first time in 2002 in the book "Executable UML: A Foundation for Model-Driven Architecture". The language "combines a subset of the UML graphical notation with executable semantics and timing rules." The Executable UML method is the successor to the Shlaer–Mellor method.
Kermeta is a modeling and programming language for metamodel engineering.
A standard Sudoku contains 81 cells, in a 9×9 grid, and has 9 boxes, each box being the intersection of the first, middle, or last 3 rows, and the first, middle, or last 3 columns. Each cell may contain a number from one to nine, and each number can only occur once in each row, column, and box. A Sudoku starts with some cells containing numbers (clues), and the goal is to solve the remaining cells. Proper Sudokus have one solution. Players and investigators may use a wide range of computer algorithms to solve Sudokus, study their properties, and make new puzzles, including Sudokus with interesting symmetries and other properties.
The method of covarions, or concomitantly variable codons, is a technique in computational phylogenetics that allows the hypothesized rate of molecular evolution at individual codons in a set of nucleotide sequences to vary in an autocorrelated manner. Under the covarion model, the rates of evolution on different branches of a hypothesized phylogenetic tree vary in an autocorrelated way, and the rates of evolution at different codon sites in an aligned set of DNA or RNA sequences vary in a separate but autocorrelated manner. This provides additional and more realistic constraints on evolutionary rates versus the simpler technique of allowing the rate of evolution on each branch to be selected randomly from a suitable probability distribution such as the gamma distribution. Covarions is a concrete form of the more general concept of heterotachy.
In mathematical logic, satisfiability and validity are elementary concepts of semantics. A formula is satisfiable if it is possible to find an interpretation (model) that makes the formula true. A formula is valid if all interpretations make the formula true. The opposites of these concepts are unsatisfiability and invalidity, that is, a formula is unsatisfiable if none of the interpretations make the formula true, and invalid if some such interpretation makes the formula false. These four concepts are related to each other in a manner exactly analogous to Aristotle's square of opposition.
UML state machine, also known as UML statechart, is a significantly enhanced realization of the mathematical concept of a finite automaton in computer science applications as expressed in the Unified Modeling Language (UML) notation.
Configuration design is a kind of design where a fixed set of predefined components that can be interfaced (connected) in predefined ways is given, and an assembly of components selected from this fixed set is sought that satisfies a set of requirements and obeys a set of constraints.
OptimJ is an extension of the Java with language support for writing optimization models and abstractions for bulk data processing. The extensions and the proprietary product implementing the extensions were developed by Ateji which went out of business in September 2011. OptimJ aims at providing a clear and concise algebraic notation for optimization modeling, removing compatibility barriers between optimization modeling and application programming tools, and bringing software engineering techniques such as object-orientation and modern IDE support to optimization experts.
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