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Highly Optimized Tolerance
In applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical ..., highly optimized tolerance (HOT) is a method of generating power law behavior in systems by including a global optimization principle. It was developed by Jean M. Carlson and John Doyle in the early 2000s. For some systems that display a characteristic scale, a global optimization term could potentially be added that would then yield power law behavior. It has been used to generate and describe internet-like graphs, forest fire models and may also apply to biological systems. Example The following is taken from Sornette's book. Consider a random variable, X, that takes on values x_i with probability p_i. Furthermore, let’s assume for another parameter r_i :x_i = r_i^ for some fixed \beta. We then ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Mathematics
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. History Historically, applied mathematics consisted principally of applied analysis, most notably differential equations; approximation theory (broadly construed, to include representations, asymptotic methods, variati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Law
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four. Empirical examples The distributions of a wide variety of physical, biological, and man-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, the foraging pattern of various species, the sizes of activity patterns of neuronal populations, the frequencies of words in most languages, frequencies of family names, the species richness in clades of organisms, the sizes of power outages, volcanic eruptions, human judgments of stimulus intensity and many other ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Global Optimization
Global optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function g(x) is equivalent to the minimization of the function f(x):=(-1)\cdot g(x). Given a possibly nonlinear and non-convex continuous function f:\Omega\subset\mathbb^n\to\mathbb with the global minima f^* and the set of all global minimizers X^* in \Omega, the standard minimization problem can be given as :\min_f(x), that is, finding f^* and a global minimizer in X^*; where \Omega is a (not necessarily convex) compact set defined by inequalities g_i(x)\geqslant0, i=1,\ldots,r. Global optimization is distinguished from local optimization by its focus on finding the minimum or maximum over the given set, as opposed to finding ''local'' minima or maxima. Finding an arbitrary local minimum is relatively str ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean M
Jean may refer to: People * Jean (female given name) * Jean (male given name) * Jean (surname) Fictional characters * Jean Grey, a Marvel Comics character * Jean Valjean, fictional character in novel ''Les Misérables'' and its adaptations * Jean Pierre Polnareff, a fictional character from ''JoJo's Bizarre Adventure'' Places * Jean, Nevada, USA; a town * Jean, Oregon Jean is an unincorporated community in Clackamas County, Oregon Oregon () is a U.S. state, state in the Pacific Northwest region of the Western United States. The Columbia River delineates much of Oregon's northern boundary with Washingt ..., USA Entertainment * Jean (dog), a female collie in silent films * "Jean" (song) (1969), by Rod McKuen, also recorded by Oliver * ''Jean Seberg'' (musical), a 1983 musical by Marvin Hamlisch Other uses * JEAN (programming language) * USS ''Jean'' (ID-1308), American cargo ship c. 1918 * Sternwheeler Jean, a 1938 paddleboat of the Willamette River See also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Doyle (engineer)
John Comstock Doyle is the John G Braun Professor of Control and Dynamical Systems, Electrical Engineering, and BioEngineering at the California Institute of Technology. He is known for his work in control theory and his current research interests are in theoretical foundations for complex networks in engineering, biology, and multiscale physics. Education He earned a B.S. and an M.S. in electrical engineering from the Massachusetts Institute of Technology in 1977 and a Ph.D. in Mathematics from the University of California, Berkeley in 1984 with his thesis titled ''Matrix interpolation theory and optimal control''. Work Doyle's early work was in the mathematics of robust control, linear-quadratic-Gaussian control robustness, (structured) singular value analysis, and H-infinity methods. He has co-authored books and software toolboxes, and a control analysis tool for high performance commercial and military aerospace systems, as well as other industrial systems. Awards Doyle earn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forest Fire
A wildfire, forest fire, bushfire, wildland fire or rural fire is an unplanned, uncontrolled and unpredictable fire in an area of combustible vegetation. Depending on the type of vegetation present, a wildfire may be more specifically identified as a bushfire( in Australia), desert fire, grass fire, hill fire, peat fire, prairie fire, vegetation fire, or veld fire. Some natural forest ecosystems depend on wildfire. Wildfires are distinct from beneficial human usage of wildland fire, called controlled burning, although controlled burns can turn into wildfires. Fossil charcoal indicates that wildfires began soon after the appearance of terrestrial plants approximately 419 million years ago during the Silurian period. Earth's carbon-rich vegetation, seasonally dry climates, atmospheric oxygen, and widespread lightning and volcanic ignitions create favorable conditions for fires. The occurrence of wildfires throughout the history of terrestrial life invites conjecture that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads H and tails T) in a sample space (e.g., the set \) to a measurable space, often the real numbers (e.g., \ in which 1 corresponding to H and -1 corresponding to T). Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice; it may also represent uncertainty, such as measurement error. However, the interpretation of probability is philosophically complicated, and even in specific cases is not always straightforward. The purely mathematical analysis of random variables is independent of such interpretational difficulties, and can be based upon a rigorous axiomatic setup. In the formal mathematical language of measure theory, a random ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrange Multipliers
In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). It is named after the mathematician Joseph-Louis Lagrange. 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. The method can be summarized as follows: in order to find the maximum or minimum of a function f(x) subjected to the equality constraint g(x) = 0, form the Lagrangian function :\mathcal(x, \lambda) = f(x) + \lambda g(x) and find the stationary points of \mathcal considered as a function of x and the Lagrange m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-organized Criticality
Self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality. The concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld ("BTW") in a paper Papercore summaryhttp://papercore.org/Bak1987 published in 1987 in ''Physical Review Letters'', and is considered to be one of the mechanisms by which complexity arises in nature. Its concepts have been applied across fields as diverse as geophysics, physical cosmology, evolutionary biology and ecology, bio-inspired computing and optimization (mathematics), economics, quantum gravity, sociology, solar physics, plasma physics, neurobiology and others. SOC is typically observed in slowly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review E
''Physical Review E'' is a peer-reviewed, scientific journal, published monthly by the American Physical Society. The main field of interest is collective phenomena of many-body systems. It is currently edited by Uwe C. Täuber. While original research content requires subscription, editorials, news, and other non-research content is openly accessible. Scope Although the focus of this journal is many-body phenomena, the broad scope of the journal includes quantum chaos, soft matter physics, classical chaos, biological physics and granular materials. Also emphasized are statistical physics, equilibrium and transport properties of fluids, liquid crystals, complex fluids, polymers, chaos, fluid dynamics, plasma physics, classical physics, and computational physics. About Physical Review E APS. July 2010 [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review Letters
''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. As also confirmed by various measurement standards, which include the ''Journal Citation Reports'' impact factor and the journal ''h''-index proposed by Google Scholar, many physicists and other scientists consider ''Physical Review Letters'' to be one of the most prestigious journals in the field of physics. ''According to Google Scholar, PRL is the journal with the 9th journal h-index among all scientific journals'' ''PRL'' is published as a print journal, and is in electronic format, online and CD-ROM. Its focus is rapid dissemination of significant, or notable, results of fundamental research on all topics related to all fields of physics. This is accomplished by rapid publication of short reports, called "Letters". Papers are published and available electronically one article at a time. When published in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science News
''Science News (SN)'' is an American bi-weekly magazine devoted to articles about new scientific and technical developments, typically gleaned from recent scientific and technical journals. History ''Science News'' has been published since 1922 by Society for Science & the Public, a non-profit organization founded by E. W. Scripps in 1920. American chemist Edwin Slosson served as the publication's first editor. From 1922 to 1966, it was called ''Science News Letter''. The title was changed to ''Science News'' with the March 12, 1966 issue (vol. 89, no. 11). Tom Siegfried was the editor from 2007 to 2012. In 2012, Siegfried stepped down, and Eva Emerson became the Editor in Chief of the magazine. In 2017, Eva Emerson stepped down to become the editor of a new digital magazine, Annual Reviews. On February 1, 2018 Nancy Shute became the Editor in Chief of the magazine. In April 2008, the magazine changed from a weekly format to the current biweekly format, and the website w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
