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Gradient Pattern Analysis
Gradient pattern analysis (GPA)Rosa, R.R., Pontes, J., Christov, C.I., Ramos, F.M., Rodrigues Neto, C., Rempel, E.L., Walgraef, D. ''Physica A'' 283, 156 (2000). is a geometric computing method for characterizing geometrical bilateral symmetry breaking of an ensemble of symmetric vectors regularly distributed in a square lattice. Usually, the lattice of vectors represent the first-order gradient of a scalar field, here an ''M x M'' square amplitude matrix. An important property of the gradient representation is the following: A given ''M x M'' matrix where all amplitudes are different results in an ''M x M'' gradient lattice containing N_ = M^2 asymmetric vectors. As each vector can be characterized by its norm and phase, variations in the M^2 amplitudes can modify the respective M^2 gradient pattern. The original concept of GPA was introduced by Rosa, Sharma and Valdivia in 1999.Rosa, R.R.; Sharma, A.S.and Valdivia, J.A. ''Int. J. Mod. Phys. C'', 10, 147 (1999), . Usually GPA is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry Breaking
In physics, symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations acting on a system crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observer unaware of the fluctuations (or "noise"), the choice will appear arbitrary. This process is called symmetry "breaking", because such transitions usually bring the system from a symmetric but disorderly state into one or more definite states. The phenomenon is part of most theories of everything. Symmetry breaking is thought to play a major role in pattern formation. In his 1972 ''Science'' paper titled "More is different" Nobel laureate P.W. Anderson used the idea of symmetry breaking to show that even if reductionism is true, its converse, constructionism, which is the idea that scientists can easily predict complex phenomena given theories describing their components, is not. Symmetry breaking can be distinguished into two types, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradient of a function is non-zero at a point , the direction of the gradient is the direction in which the function increases most quickly from , and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to maximize a function by gradient ascent. In coordinate-free terms, the gradient of a function f(\bf) may be defined by: :df=\nabla f \cdot d\bf where ''df'' is the total infinitesimal change in ''f'' for an infinitesimal displacement d\bf, and is seen to be maximal when d\bf is in the direction of the gradi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a "-matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents composition of linear maps. Not all matrices are related to linear algebra. This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. ''This article focuses on matrices related to linear algebra, and, unle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delaunay Triangulation
In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a general position is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). Delaunay triangulations maximize the minimum of all the angles of the triangles in the triangulation; they tend to avoid sliver triangles. The triangulation is named after Boris Delaunay for his work on this topic from 1934. For a set of points on the same line there is no Delaunay triangulation (the notion of triangulation is degenerate for this case). For four or more points on the same circle (e.g., the vertices of a rectangle) the Delaunay triangulation is not unique: each of the two possible triangulations that split the quadrangle into two triangles satisfies the "Delaunay condition", i.e., the requirement that the circumcircles of all triangles have empty interiors. By considering circumscribed spheres, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wave Turbulence
In continuum mechanics, wave turbulence is a set of nonlinear waves deviated far from thermal equilibrium. Such a state is usually accompanied by dissipation. It is either decaying turbulence or requires an external source of energy to sustain it. Examples are waves on a fluid surface excited by winds or ships, and waves in plasma excited by electromagnetic waves etc. Appearance External sources by some resonant mechanism usually excite waves with frequencies and wavelengths in some narrow interval. For example, shaking a container with frequency ω excites surface waves with frequency ω/2 ( parametric resonance, discovered by Michael Faraday). When wave amplitudes are small – which usually means that the wave is far from breaking – only those waves exist that are directly excited by an external source. When, however, wave amplitudes are not very small (for surface waves: when the fluid surface is inclined by more than few degrees) waves with different frequencies start ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Maryland, College Park
The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public land-grant research university in College Park, Maryland. Founded in 1856, UMD is the flagship institution of the University System of Maryland. It is also the largest university in both the state and the Washington metropolitan area, with more than 41,000 students representing all fifty states and 123 countries, and a global alumni network of over 388,000. Together, its 12 schools and colleges offer over 200 degree-granting programs, including 92 undergraduate majors, 107 master's programs, and 83 doctoral programs. UMD is a member of the Association of American Universities and competes in intercollegiate athletics as a member of the Big Ten Conference. The University of Maryland's proximity to the nation's capital has resulted in many research partnerships with the federal government; faculty receive research funding and institutional support from many agencies, such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Institute For Space Research
The National Institute for Space Research ( pt, Instituto Nacional de Pesquisas Espaciais, INPE) is a research unit of the Brazilian Ministry of Science, Technology and Innovations, the main goals of which are fostering scientific research and technological applications and qualifying personnel in the fields of space and atmospheric sciences, space engineering, and space technology. While INPE is the civilian research center for aerospace activities, the Brazilian Air Force's General Command for Aerospace Technology is the military arm. INPE is located in the city of São José dos Campos, São Paulo. History On August 13, 1961, President Jânio Quadros signed a decree which created the Organizing Group for the National Commission on Space Activities (COGNAE). This group would give rise to the current National Institute for Space Research. COGNAE, which shortly after became known as CNAE, started its activities by stimulating, coordinating and supporting studies on space rel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavelet Analysis
A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second. If this wavelet were to be convolved with a signal created from the recording of a melody, then the resulting signal would be useful for determining when the Middle C note appeared in the song. Mathematically, a wavelet correlates with a signal if a portion of the signal is similar. Correlation is at the core of many practical wavelet applications. As a mathematical tool, wavelets can be used to extract information from many different kinds of data, including but not limited to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Algorithms
The following is a list of well-known algorithms along with one-line descriptions for each. Automated planning Combinatorial algorithms General combinatorial algorithms * Brent's algorithm: finds a cycle in function value iterations using only two iterators * Floyd's cycle-finding algorithm: finds a cycle in function value iterations * Gale–Shapley algorithm: solves the stable marriage problem * Pseudorandom number generators (uniformly distributed—see also List of pseudorandom number generators for other PRNGs with varying degrees of convergence and varying statistical quality): ** ACORN generator ** Blum Blum Shub ** Lagged Fibonacci generator ** Linear congruential generator ** Mersenne Twister Graph algorithms * Coloring algorithm: Graph coloring algorithm. * Hopcroft–Karp algorithm: convert a bipartite graph to a maximum cardinality matching * Hungarian algorithm: algorithm for finding a perfect matching * Prüfer coding: conversion between a labeled tree and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
