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In mathematics, a field F is algebraically closed if every non-constant polynomial in F[x] (the univariate polynomial ring with coefficients in F) has a root in F. In other words, a field is algebraically closed if the fundamental theorem of algebra holds for it.
Every field
K
{... | Wikipedia/Algebraically_closed |
In the study of the representation theory of Lie groups, the study of representations of SU(2) is fundamental to the study of representations of semisimple Lie groups. It is the first case of a Lie group that is both a compact group and a non-abelian group. The first condition implies the representation theory is disc... | Wikipedia/Representation_theory_of_SU(2) |
In mathematics, a Lie algebra (pronounced LEE) is a vector space
g
{\displaystyle {\mathfrak {g}}}
together with an operation called the Lie bracket, an alternating bilinear map
g
... | Wikipedia/Lie_algebra_homomorphism |
The Lorentz group is a Lie group of symmetries of the spacetime of special relativity. This group can be realized as a collection of matrices, linear transformations, or unitary operators on some Hilbert space; it has a variety of representations. This group is significant because special relativity together with qua... | Wikipedia/Representation_theory_of_the_Lorentz_group |
In abstract algebra, a representation of a Hopf algebra is a representation of its underlying associative algebra. That is, a representation of a Hopf algebra H over a field K is a K-vector space V with an action H × V → V usually denoted by juxtaposition (that is, the image of (h, v) is written hv). The vector space V... | Wikipedia/Representation_theory_of_Hopf_algebras |
In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator. In the language of physics, one looks for a vecto... | Wikipedia/Lie_algebra_representation |
Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups over a field K of positive characteristic p, necessarily a prime number. As well as having applications to group theory, modular representations arise naturally in othe... | Wikipedia/Modular_representation_theory |
In abstract algebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A = A(K) of K. It consists of the points of G having values in A; the definition of the appropriate topology is straightforward only in case G is a linear algebraic group. ... | Wikipedia/Adelic_algebraic_group |
In mathematics, Schur's lemma is an elementary but extremely useful statement in representation theory of groups and algebras. In the group case it says that if M and N are two finite-dimensional irreducible representations
of a group G and φ is a linear map from M to N that commutes with the action of the group, the... | Wikipedia/Schur's_lemma |
In mathematics, a Kac–Moody algebra (named for Victor Kac and Robert Moody, who independently and simultaneously discovered them in 1968) is a Lie algebra, usually infinite-dimensional, that can be defined by generators and relations through a generalized Cartan matrix. These algebras form a generalization of finite-di... | Wikipedia/Kac–Moody_algebra |
In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by reversing all of its edges, under an isomorphism that is an involution without any fixed points. Skew-symmetric graphs are identical to the double covering graphs of b... | Wikipedia/Skew-symmetric_graph |
In mathematics, a Cartan subalgebra, often abbreviated as CSA, is a nilpotent subalgebra
h
{\displaystyle {\mathfrak {h}}}
of a Lie algebra
g
{\dis... | Wikipedia/Cartan_subalgebra |
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals, that its motion is confined to a submanifold
of much smaller d... | Wikipedia/Exactly_solvable_model |
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform ... | Wikipedia/Fourier_transform |
In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras. (A simple Lie algebra is a non-abelian Lie algebra without any non-zero proper ideals.)
Throughout the article, unless otherwise stated, a Lie algebra is a finite-dimensional Lie algebra over a field of characteristic 0. For such ... | Wikipedia/Semisimple_Lie_algebra |
In mathematics, Lie group–Lie algebra correspondence allows one to correspond a Lie group to a Lie algebra or vice versa, and study the conditions for such a relationship. Lie groups that are isomorphic to each other have Lie algebras that are isomorphic to each other, but the converse is not necessarily true. One obvi... | Wikipedia/Lie_group–Lie_algebra_correspondence |
In mathematics, the representation theory of semisimple Lie algebras is one of the crowning achievements of the theory of Lie groups and Lie algebras. The theory was worked out mainly by E. Cartan and H. Weyl and because of that, the theory is also known as the Cartan–Weyl theory. The theory gives the structural descri... | Wikipedia/Representation_theory_of_semisimple_Lie_algebras |
In mathematics, geometric invariant theory (or GIT) is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli spaces. It was developed by David Mumford in 1965, using ideas from the paper (Hilbert 1893) in classical invariant theory.
Geometric invariant theory studies an... | Wikipedia/Geometric_invariant_theory |
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena.
The advancement of science generally d... | Wikipedia/Theoretical_physics |
In the mathematical field of Lie theory, a split Lie algebra is a pair
(
g
,
h
)
{\displaystyle ({\mathfrak {g}},{\mathfrak {h}})}
where
... | Wikipedia/Split_Lie_algebra |
In mathematics, the notion of a real form relates objects defined over the field of real and complex numbers. A real Lie algebra g0 is called a real form of a complex Lie algebra g if g is the complexification of g0:
g
≃
... | Wikipedia/Real_form_(Lie_theory) |
In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a
Z
/
2
Z
{\displaystyle \mathbb {Z} /2\mathbb {Z} }
‑grading. Lie superalgebras are important in theoretical ... | Wikipedia/Lie_superalgebra |
In mathematics, the tensor product of representations is a tensor product of vector spaces underlying representations together with the factor-wise group action on the product. This construction, together with the Clebsch–Gordan procedure, can be used to generate additional irreducible representations if one already kn... | Wikipedia/Tensor_product_of_representations |
In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a one-dimensional representation of A over F. It is the algebra analogue of a multiplicative character of a group. The importance of the concept, however, stems from its a... | Wikipedia/Weight_(representation_theory) |
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping
V
→
W
{\displaystyle V\to W}
between two vector spaces tha... | Wikipedia/Linear_transformations |
In algebra, a simple Lie algebra is a Lie algebra that is non-abelian and contains no nonzero proper ideals. The classification of real simple Lie algebras is one of the major achievements of Wilhelm Killing and Élie Cartan.
A direct sum of simple Lie algebras is called a semisimple Lie algebra.
A simple Lie group is ... | Wikipedia/Simple_Lie_algebra |
In mathematics, the representation theory of the Poincaré group is an example of the representation theory of a Lie group that is neither a compact group nor a semisimple group. It is fundamental in theoretical physics.
In a physical theory having Minkowski space as the underlying spacetime, the space of physical state... | Wikipedia/Representation_theory_of_the_Poincaré_group |
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping
V
→
W
{\displaystyle V\to W}
between two vector spaces tha... | Wikipedia/Linear_transformation |
In mathematics, a linear algebraic group is a subgroup of the group of invertible
n
×
n
{\displaystyle n\times n}
matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, defined by the relation
... | Wikipedia/Linear_algebraic_group |
In the mathematical field of Lie theory, there are two definitions of a compact Lie algebra. Extrinsically and topologically, a compact Lie algebra is the Lie algebra of a compact Lie group; this definition includes tori. Intrinsically and algebraically, a compact Lie algebra is a real Lie algebra whose Killing form is... | Wikipedia/Compact_Lie_algebra |
In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a (not necessarily commutative) ring. The concept of a module also generalizes the notion of an abelian group, since the abelian groups are exactly the modules over the ring of integers.
Like a vector... | Wikipedia/Module_theory |
In mathematics, physics and chemistry, a space group is the symmetry group of a repeating pattern in space, usually in three dimensions. The elements of a space group (its symmetry operations) are the rigid transformations of the pattern that leave it unchanged. In three dimensions, space groups are classified into 219... | Wikipedia/Crystallographic_group |
In nonrelativistic quantum mechanics, an account can be given of the existence of mass and spin (normally explained in Wigner's classification of relativistic mechanics) in terms of the representation theory of the Galilean group, which is the spacetime symmetry group of nonrelativistic quantum mechanics.
== Backgrou... | Wikipedia/Representation_theory_of_the_Galilean_group |
The concept of a system of imprimitivity is used in mathematics, particularly in algebra and analysis, both within the context of the theory of group representations. It was used by George Mackey as the basis for his theory of induced unitary representations of locally compact groups.
The simplest case, and the context... | Wikipedia/Mackey_theory |
In the theory of Lie groups, the exponential map is a map from the Lie algebra
g
{\displaystyle {\mathfrak {g}}}
of a Lie group
G
{\displaystyle G}
to the group, which allows one to recapt... | Wikipedia/Exponential_map_(Lie_theory) |
In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator. In the language of physics, one looks for a vecto... | Wikipedia/Representation_of_a_Lie_algebra |
In the field of mathematics called abstract algebra, a division algebra is, roughly speaking, an algebra over a field in which division, except by zero, is always possible.
== Definitions ==
Formally, we start with a non-zero algebra D over a field. We call D a division algebra if for any element a in D and any non-z... | Wikipedia/Division_algebra |
In mathematics, loop algebras are certain types of Lie algebras, of particular interest in theoretical physics.
== Definition ==
For a Lie algebra
g
{\displaystyle {\mathfrak {g}}}
over a field
K
... | Wikipedia/Loop_algebra |
In mathematics, the main results concerning irreducible unitary representations of the Lie group SL(2, R) are due to Gelfand and Naimark (1946), V. Bargmann (1947), and Harish-Chandra (1952).
== Structure of the complexified Lie algebra ==
We choose a basis H, X, Y for the complexification of the Lie algebra of SL(2,... | Wikipedia/Representation_theory_of_SL2(R) |
In abstract algebra, a representation of an associative algebra is a module for that algebra. Here an associative algebra is a (not necessarily unital) ring. If the algebra is not unital, it may be made so in a standard way (see the adjoint functors page); there is no essential difference between modules for the result... | Wikipedia/Algebra_representation |
In mathematics, an affine Lie algebra is an infinite-dimensional Lie algebra that is constructed in a canonical fashion out of a finite-dimensional simple Lie algebra. Given an affine Lie algebra, one can also form the associated affine Kac-Moody algebra, as described below. From a purely mathematical point of view, af... | Wikipedia/Affine_Lie_algebra |
In abstract algebra, a representation of an associative algebra is a module for that algebra. Here an associative algebra is a (not necessarily unital) ring. If the algebra is not unital, it may be made so in a standard way (see the adjoint functors page); there is no essential difference between modules for the result... | Wikipedia/Representation_of_an_associative_algebra |
In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory.
Many groups of geometric transformations are algebraic groups, including orthog... | Wikipedia/Algebraic_group |
A software system is a system of intercommunicating components based on software forming part of a computer system (a combination of hardware and software). It "consists of a number of separate programs, configuration files, which are used to set up these programs, system documentation, which describes the structure of... | Wikipedia/Software_systems |
A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial control systems which are used for controlling processes or machines. The contro... | Wikipedia/Control_systems |
In system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance; these terms are briefly defined in the overview below. These properties apply (exactly or approximately) to ... | Wikipedia/LTI_system_theory |
Management science (or managerial science) is a wide and interdisciplinary study of solving complex problems and making strategic decisions as it pertains to institutions, corporations, governments and other types of organizational entities. It is closely related to management, economics, business, engineering, managem... | Wikipedia/Management_science |
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations by nature of the ergodicity of dynamic systems. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of... | Wikipedia/Dynamical_systems_theory |
Systems theory in archaeology is the application of systems theory and systems thinking in archaeology. It originated with the work of Ludwig von Bertalanffy in the 1950s, and is introduced in archaeology in the 1960s with the work of Sally R. Binford and Lewis Binford's "New Perspectives in Archaeology" and Kent V. Fl... | Wikipedia/Systems_theory_in_archaeology |
An agent-based model (ABM) is a computational model for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organizations or groups) in order to understand the behavior of a system and what governs its outcomes. It combines elements of game theory, complex system... | Wikipedia/Agent-based_model |
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifu... | Wikipedia/Bifurcation_theory |
A small-world network is a graph characterized by a high clustering coefficient and low distances. In an example of the social network, high clustering implies the high probability that two friends of one person are friends themselves. The low distances, on the other hand, mean that there is a short chain of social con... | Wikipedia/Small-world_network |
System dynamics (SD) is an approach to understanding the nonlinear behaviour of complex systems over time using stocks, flows, internal feedback loops, table functions and time delays.
== Overview ==
System dynamics is a methodology and mathematical modeling technique to frame, understand, and discuss complex issues ... | Wikipedia/System_dynamics |
Michael Christopher Jackson OBE (born 1951) is a British systems scientist, consultant and Emeritus Professor of Management Systems and former Dean of Hull University Business School, known for his work in the field of systems thinking and management.
== Biography ==
Jackson studied Politics, Philosophy and Economics... | Wikipedia/Mike_Jackson_(systems_scientist) |
Dynamic network analysis (DNA) is an emergent scientific field that brings together traditional social network analysis (SNA), link analysis (LA), social simulation and multi-agent systems (MAS) within network science and network theory. Dynamic networks are a function of time (modeled as a subset of the real numbers) ... | Wikipedia/Dynamic_network_analysis |
Systems geology emphasizes the nature of geology as a system – that is, as a set of interacting parts that function as a whole. The systems approach involves study of the linkages or interfaces between the component objects and processes at all levels of detail in order to gain a more comprehensive understanding of the... | Wikipedia/Systems_geology |
System dynamics (SD) is an approach to understanding the nonlinear behaviour of complex systems over time using stocks, flows, internal feedback loops, table functions and time delays.
== Overview ==
System dynamics is a methodology and mathematical modeling technique to frame, understand, and discuss complex issues ... | Wikipedia/Systems_dynamics |
Systems theory is the transdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or artificial. Every system has causal boundaries, is influenced by its context, defined by its structure, function and role, and expressed through its relations with other syste... | Wikipedia/Systems_theory |
A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organi... | Wikipedia/Complex_Systems |
Evolutionary game theory (EGT) is the application of game theory to evolving populations in biology. It defines a framework of contests, strategies, and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Maynard Smith and George R. Price's formalisation of contests, analysed as ... | Wikipedia/Evolutionary_game_theory |
Systems neuroscience is a subdiscipline of neuroscience and systems biology that studies the structure and function of various neural circuits and systems that make up the central nervous system of an organism. Systems neuroscience encompasses a number of areas of study concerned with how nerve cells behave when connec... | Wikipedia/Systems_neuroscience |
Control engineering, also known as control systems engineering and, in some European countries, automation engineering, is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls overlap... | Wikipedia/Control_engineering |
An open system is a system that has external interactions. Such interactions can take the form of information, energy, or material transfers into or out of the system boundary, depending on the discipline which defines the concept. An open system is contrasted with the concept of an isolated system which exchanges neit... | Wikipedia/Environment_(systems) |
Biological systems engineering or biosystems engineering is a broad-based engineering discipline with particular emphasis on non-medical biology. It can be thought of as a subset of the broader notion of biological engineering or bio-technology though not in the respects that pertain to biomedical engineering as biosys... | Wikipedia/Biological_systems_engineering |
Systems pharmacology is the application of systems biology principles to the field of pharmacology. It seeks to understand how drugs affect the human body as a single complex biological system.
Instead of considering the effect of a drug to be the result of one specific drug-protein interaction, systems pharmacology c... | Wikipedia/Systems_pharmacology |
Systems philosophy is a discipline aimed at constructing a new philosophy (in the sense of worldview) by using systems concepts. The discipline was first described by Ervin Laszlo in his 1972 book Introduction to Systems Philosophy: Toward a New Paradigm of Contemporary Thought. It has been described as the "reorientat... | Wikipedia/Systems_philosophy |
Systems chemistry is the science of studying networks of interacting molecules, to create new functions from a set (or library) of molecules with different hierarchical levels and emergent properties.
Systems chemistry is also related to the origin of life (abiogenesis).
== Relations to systems biology ==
Systems che... | Wikipedia/Systems_chemistry |
Systems analysis is "the process of studying a procedure or business to identify its goal and purposes and create systems and procedures that will efficiently achieve them". Another view sees systems analysis as a problem-solving technique that breaks a system down into its component pieces and analyses how well those ... | Wikipedia/Systems_analysis |
Systems immunology is a research field under systems biology that uses mathematical approaches and computational methods to examine the interactions within cellular and molecular networks of the immune system. The immune system has been thoroughly analyzed as regards to its components and function by using a "reduction... | Wikipedia/Systems_immunology |
Living systems are life forms (or, more colloquially known as living things) treated as a system. They are said to be open self-organizing and said to interact with their environment. These systems are maintained by flows of information, energy and matter. Multiple theories of living systems have been proposed. Such th... | Wikipedia/Living_systems |
World-systems theory (also known as world-systems analysis or the world-systems perspective) is a multidisciplinary approach to world history and social change which emphasizes the world-system (and not nation states) as the primary (but not exclusive) unit of social analysis. World-systems theorists argue that their t... | Wikipedia/World-systems_theory |
Conversation theory is a cybernetic approach to the study of conversation, cognition and learning that may occur between two participants who are engaged in conversation with each other. It presents an experimental framework heavily utilizing human-computer interactions and computer theoretic models as a means to prese... | Wikipedia/Conversation_theory |
Systems engineering is an interdisciplinary field of engineering and engineering management that focuses on how to design, integrate, and manage complex systems over their life cycles. At its core, systems engineering utilizes systems thinking principles to organize this body of knowledge. The individual outcome of suc... | Wikipedia/Systems_engineering |
Systems biology is the computational and mathematical analysis and modeling of complex biological systems. It is a biology-based interdisciplinary field of study that focuses on complex interactions within biological systems, using a holistic approach (holism instead of the more traditional reductionism) to biological ... | Wikipedia/Systems_biology |
Modelling biological systems is a significant task of systems biology and mathematical biology. Computational systems biology aims to develop and use efficient algorithms, data structures, visualization and communication tools with the goal of computer modelling of biological systems. It involves the use of computer si... | Wikipedia/Computational_systems_biology |
Systems art is art influenced by cybernetics and systems theory, reflecting on natural systems, social systems, and the social signs of the art world itself.
Systems art emerged as part of the first wave of the conceptual art movement in the 1960s and 1970s. Closely related and overlapping terms include anti-form movem... | Wikipedia/Systems_art |
Developmental systems theory (DST) is an overarching theoretical perspective on biological development, heredity, and evolution. It emphasizes the shared contributions of genes, environment, and epigenetic factors on developmental processes. DST, unlike conventional scientific theories, is not directly used to help mak... | Wikipedia/Developmental_systems_theory |
Earth system science (ESS) is the application of systems science to the Earth. In particular, it considers interactions and 'feedbacks', through material and energy fluxes, between the Earth's sub-systems' cycles, processes and "spheres"—atmosphere, hydrosphere, cryosphere, geosphere, pedosphere, lithosphere, biosphere... | Wikipedia/Earth_system_science |
Systems theory is the transdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or artificial. Every system has causal boundaries, is influenced by its context, defined by its structure, function and role, and expressed through its relations with other syste... | Wikipedia/General_systems_theory |
Sociotechnical systems (STS) in organizational development is an approach to complex organizational work design that recognizes the interaction between people and technology in workplaces. The term also refers to coherent systems of human relations, technical objects, and cybernetic processes that inhere to large, comp... | Wikipedia/Sociotechnical_systems_theory |
Climatology (from Greek κλίμα, klima, "slope"; and -λογία, -logia) or climate science is the scientific study of Earth's climate, typically defined as weather conditions averaged over a period of at least 30 years. Climate concerns the atmospheric condition during an extended to indefinite period of time; weather is th... | Wikipedia/Climate_Science |
Critical systems thinking (CST) is a systems thinking approach designed to aid decision-makers, and other stakeholders, improve complex problem situations that cross departmental and, often, organizational boundaries. CST sees systems thinking as essential to managing multidimensional 'messes' in which technical, econo... | Wikipedia/Critical_systems_thinking |
The prisoner's dilemma is a game theory thought experiment involving two rational agents, each of whom can either cooperate for mutual benefit or betray their partner ("defect") for individual gain. The dilemma arises from the fact that while defecting is rational for each agent, cooperation yields a higher payoff for ... | Wikipedia/Prisoner's_dilemma |
The Internal Family Systems Model (IFS) is an integrative approach to individual psychotherapy developed by Richard C. Schwartz in the 1980s. It combines systems thinking with the view that the mind is made up of relatively discrete subpersonalities, each with its own unique viewpoint and qualities. IFS uses systems ps... | Wikipedia/Family_systems_theory |
Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. Population dynamics is a branch of mathematical biology, and uses mathematical techniques such as differential equations to model behaviour. Population dynamics is also closely relate... | Wikipedia/Population_dynamics |
Living systems are life forms (or, more colloquially known as living things) treated as a system. They are said to be open self-organizing and said to interact with their environment. These systems are maintained by flows of information, energy and matter. Multiple theories of living systems have been proposed. Such th... | Wikipedia/Living_systems_theory |
Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, cognitive and semantic networks, and social networks, considering distinct elements or actors represented by nodes (or vertices) and the connections between the elements or act... | Wikipedia/Network_science |
Earth systems engineering and management (ESEM) is a discipline used to analyze, design, engineer and manage complex environmental systems. It entails a wide range of subject areas including anthropology, engineering, environmental science, ethics and philosophy. At its core, ESEM looks to "rationally design and manage... | Wikipedia/Earth_systems_engineering_and_management |
In machine learning, a neural network (also artificial neural network or neural net, abbreviated ANN or NN) is a computational model inspired by the structure and functions of biological neural networks.
A neural network consists of connected units or nodes called artificial neurons, which loosely model the neurons in ... | Wikipedia/Artificial_neural_network |
Enterprise systems engineering (ESE) is the discipline that applies systems engineering to the design of an enterprise. As a discipline, it includes a body of knowledge, principles, and processes tailored to the design of enterprise systems.
An enterprise is a complex, socio-technical system that comprises interdepen... | Wikipedia/Enterprise_systems_engineering |
Perceptual control theory (PCT) is a model of behavior based on the properties of negative feedback control loops. A control loop maintains a sensed variable at or near a reference value by means of the effects of its outputs upon that variable, as mediated by physical properties of the environment. In engineering cont... | Wikipedia/Perceptual_control_theory |
Soft systems methodology (SSM) is an organised way of thinking applicable to problematic social situations and in the management of change by using action. It was developed in England by academics at the Lancaster Systems Department on the basis of a ten-year action research programme.
== Overview ==
The Soft Systems... | Wikipedia/Soft_systems_methodology |
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations by nature of the ergodicity of dynamic systems. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of... | Wikipedia/Mathematical_system_theory |
Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of info... | Wikipedia/Entropy |
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction P(k) of nodes in the network having k connections to other nodes goes for large values of k as
P
(
k
)
∼
... | Wikipedia/Scale-free_network |
A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial control systems which are used for controlling processes or machines. The contro... | Wikipedia/Control_system |
Rational choice modeling refers to the use of decision theory (the theory of rational choice) as a set of guidelines to help understand economic and social behavior. The theory tries to approximate, predict, or mathematically model human behavior by analyzing the behavior of a rational actor facing the same costs and b... | Wikipedia/Rational_choice_theory |
Biochemical systems theory is a mathematical modelling framework for biochemical systems, based on ordinary differential equations (ODE), in which biochemical processes are represented using power-law expansions in the variables of the system.
This framework, which became known as Biochemical Systems Theory, has been d... | Wikipedia/Biochemical_systems_theory |
System dynamics (SD) is an approach to understanding the nonlinear behaviour of complex systems over time using stocks, flows, internal feedback loops, table functions and time delays.
== Overview ==
System dynamics is a methodology and mathematical modeling technique to frame, understand, and discuss complex issues ... | Wikipedia/System_Dynamics |
The basic study of system design is the understanding of component parts and their subsequent interaction with one another.
Systems design has appeared in a variety of fields, including sustainability, computer/software architecture, and sociology.
== Product Development ==
If the broader topic of product development... | Wikipedia/Systems_design |
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