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Cellular Potts Model
In computational biology, a Cellular Potts model (CPM, also known as the Glazier-Graner-Hogeweg model) is a computational model of cells and tissues. It is used to simulate individual and collective cell behavior, tissue morphogenesis and cancer development. CPM describes cells as deformable objects with a certain volume, that can adhere to each other and to the medium in which they live. The formalism can be extended to include cell behaviours such as cell migration, growth and division, and cell signalling. The first CPM was proposed for the simulation of cell sorting by François Graner and James A. Glazier as a modification of a large-Q Potts model. CPM was then popularized by Paulien Hogeweg for studying morphogenesis. Although the model was developed to describe biological cells, it can also be used to model individual parts of a biological cell, or even regions of fluid. Model description The CPM consists of a rectangular Euclidean lattice, where each cell is a subse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Computational Biology
Computational biology refers to the use of techniques in computer science, data analysis, mathematical modeling and Computer simulation, computational simulations to understand biological systems and relationships. An intersection of computer science, biology, and data science, the field also has foundations in applied mathematics, molecular biology, cell biology, chemistry, and genetics. History Bioinformatics, the analysis of informatics processes in biological systems, began in the early 1970s. At this time, research in artificial intelligence was using network models of the human brain in order to generate new algorithms. This use of biological data pushed biological researchers to use computers to evaluate and compare large data sets in their own field. By 1982, researchers shared information via Punched card, punch cards. The amount of data grew exponentially by the end of the 1980s, requiring new computational methods for quickly interpreting relevant information. Per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Euclidean Space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are ''Euclidean spaces'' of any positive integer dimension ''n'', which are called Euclidean ''n''-spaces when one wants to specify their dimension. For ''n'' equal to one or two, they are commonly called respectively Euclidean lines and Euclidean planes. The qualifier "Euclidean" is used to distinguish Euclidean spaces from other spaces that were later considered in physics and modern mathematics. Ancient Greek geometers introduced Euclidean space for modeling the physical space. Their work was collected by the ancient Greek mathematician Euclid in his ''Elements'', with the great innovation of '' proving'' all properties of the space as theorems, by starting from a few fundamental properties, called '' postulates'', which either were considered as evid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Stochastic Cellular Automata
Stochastic cellular automata or probabilistic cellular automata (PCA) or random cellular automata or locally interacting Markov chains are an important extension of cellular automaton. Cellular automata are a discrete-time dynamical system of interacting entities, whose state is discrete. The state of the collection of entities is updated at each discrete time according to some simple homogeneous rule. All entities' states are updated in parallel or synchronously. Stochastic cellular automata are CA whose updating rule is a stochastic one, which means the new entities' states are chosen according to some probability distributions. It is a discrete-time random dynamical system. From the spatial interaction between the entities, despite the simplicity of the updating rules, complex behaviour may emerge like self-organization. As mathematical object, it may be considered in the framework of stochastic processes as an interacting particle system in discrete-time. See for a more detai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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CompuCell3D
CompuCell3D (CC3D) is an open source software problem solving environment for constructing two- and three-dimensional multiscale agent-based models of multicellular biology, including morphogenesis, homeostasis, disease, therapy and tissue engineering. CompuCell3D was designed to make the development, execution and analysis of complex biological models accessible to non-experts. CompuCell3D is written in C++ and Python. CC3D supports a number of different object classes and modeling methodologies including the Cellular Potts model (CPM) or Glazier-Graner-Hogeweg model (GGH) (originally developed by James A. Glazier, François Graner and Paulien Hogeweg) of the dynamic reorganization of generalized cells (clusters of cells, volumes of extracellular matrix (ECM), cells and their subregions) which can model cell clustering, growth, division, death, adhesion, and volume and surface area constraints; as well as partial differential equation solvers for modeling the diffusion equation a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Chemokine
Chemokines (), or chemotactic cytokines, are a family of small cytokines or signaling proteins secreted by cells that induce directional movement of leukocytes, as well as other cell types, including endothelial and epithelial cells. In addition to playing a major role in the activation of host immune responses, chemokines are important for biological processes, including morphogenesis and wound healing, as well as in the pathogenesis of diseases like cancers. Cytokine proteins are classified as chemokines according to behavior and structural characteristics. In addition to being known for mediating chemotaxis, chemokines are all approximately 8–10 kilodaltons in mass and have four cysteine residues in conserved locations that are key to forming their 3-dimensional shape. These proteins have historically been known under several other names including the ''SIS family of cytokines'', ''SIG family of cytokines'', ''SCY family of cytokines'', ''Platelet factor-4 superfamily'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Haptotaxis
In cellular biology, haptotaxis () is the directional motility or outgrowth of cells, e.g. in the case of axonal outgrowth, usually up a gradient of cellular adhesion sites or substrate-bound chemoattractants (the gradient of the chemoattractant being expressed or bound on a surface, in contrast to the classical model of chemotaxis, in which the gradient develops in a soluble fluid.). These gradients are naturally present in the extracellular matrix (ECM) of the body during processes such as angiogenesis, or artificially present in biomaterials where gradients are established by altering the concentration of adhesion sites on a polymer substrate. Clinical significance Haptotaxis plays a major role in the efficient healing of wounds. For example, when corneal integrity is compromised, epithelial cells quickly cover the damaged area by proliferation and migration (haptotaxis). In the corneal stroma, keratocytes within the wounded area undergo apoptosis, leaving the stroma devoid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Chemotaxis
Chemotaxis (from ''chemical substance, chemo-'' + ''taxis'') is the movement of an organism or entity in response to a chemical stimulus. Somatic cells, bacteria, and other single-cell organism, single-cell or multicellular organisms direct their movements according to certain chemicals in their environment. This is important for bacteria to find food (e.g., glucose) by swimming toward the highest concentration of food molecules, or to flee from poisons (e.g., phenol). In multicellular organisms, chemotaxis is critical to early development (e.g., movement of sperm towards the egg during fertilization) and development (e.g., migration of neurons or lymphocytes) as well as in normal function and health (e.g., migration of White blood cell, leukocytes during injury or infection). In addition, it has been recognized that mechanisms that allow chemotaxis in animals can be subverted during cancer metastasis, and the aberrant change of the overall property of these networks, which contro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Lagrange Multiplier
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function (mathematics), function subject to constraint (mathematics), equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variable (mathematics), variables). It is named after the mathematician Joseph-Louis Lagrange. Summary and rationale The basic idea is to convert a constrained problem into a form such that the derivative test of an unconstrained problem can still be applied. The relationship between the gradient of the function and gradients of the constraints rather naturally leads to a reformulation of the original problem, known as the Lagrangian function or Lagrangian. In the general case, the Lagrangian is defined as \mathcal(x, \lambda) \equiv f(x) + \langle \lambda, g(x)\rangle for functions f, g; the notation \langle \cdot, \cdot \rangle denotes an inner prod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Kronecker Delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: \delta_ = \begin 0 &\text i \neq j, \\ 1 &\text i=j. \end or with use of Iverson brackets: \delta_ = =j, For example, \delta_ = 0 because 1 \ne 2, whereas \delta_ = 1 because 3 = 3. The Kronecker delta appears naturally in many areas of mathematics, physics, engineering and computer science, as a means of compactly expressing its definition above. Generalized versions of the Kronecker delta have found applications in differential geometry and modern tensor calculus, particularly in formulations of gauge theory and topological field models. In linear algebra, the n\times n identity matrix \mathbf has entries equal to the Kronecker delta: I_ = \delta_ where i and j take the values 1,2,\cdots,n, and the inner product of vectors can be written as \mathbf\cdot\mathbf = \sum_^n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Monte Carlo Method In Statistical Physics
Monte may refer to: Places Argentina * Argentine Monte, an ecoregion * Monte Desert * Monte Partido, a ''partido'' in Buenos Aires Province Italy * Monte Bregagno * Monte Cassino * Montecorvino (other) * Montefalcione Portugal * Monte (Funchal), a civil parish in the municipality of Funchal * Monte, a civil parish in the municipality of Fafe * Monte, a civil parish in the municipality of Murtosa * Monte, a civil parish in the municipality of Terras de Bouro Elsewhere * Monte, Haute-Corse, a commune in Corsica, France * Monte, Switzerland, a village in the municipality Castel San Pietro, Ticino, Switzerland * Monte, U.S. Virgin Islands, a neighborhood * Monte Lake, British Columbia, Canada Arts, entertainment, and media * Monte (film), ''Monte'' (film), a 2016 drama film by Amir Naderi * Three-card Monte * Monte Bank or Monte, a card game Other uses * Monte (dessert) a milk cream dessert produced by the German dairy company Zott * Monte (mascot), the mascot of the Uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Metropolis Algorithm
A metropolis () is a large city or conurbation which is a significant economic, political, and cultural area for a country or region, and an important hub for regional or international connections, commerce, and communications. A big city belonging to a larger urban agglomeration, but which is not the core of that agglomeration, is not generally considered a metropolis but a part of it. The plural of the word is ''metropolises'', although the Latin plural is , from the Greek (). For urban areas outside metropolitan areas that generate a similar attraction on a smaller scale for their region, the concept of the regiopolis ("regio" for short) was introduced by urban and regional planning researchers in Germany in 2006. Etymology () is a Greek word, (plural: ) coming from , meaning "mother" and , meaning "city" or "town", which is how the Greek colonies of antiquity referred to their original cities, with whom they retained cultic and political-cultural connections. The wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Principle Of Minimum Energy
A principle may relate to a fundamental truth or proposition that serves as the foundation for a system of beliefs or behavior or a chain of reasoning. They provide a guide for behavior or evaluation. A principle can make values explicit, so they are expressed in the form of rules and standards. Principles unpack the values underlying them more concretely so that the values can be more easily operationalized in policy statements and actions. In law, higher order, overarching principles establish rules to be followed, modified by sentencing guidelines relating to context and proportionality. In science and nature, a principle may define the essential characteristics of the system, or reflect the system's designed purpose. The effective operation would be impossible if any one of the principles was to be ignored. A system may be explicitly based on and implemented from a document of principles as was done in IBM's 360/370 ''Principles of Operation''. It is important to differen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |