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82,500 | The first fundamental theorem holds under general conditions. A formal statement is as follows: If preferences are locally nonsatiated, and if ( X ∗ , Y ∗ , p ) {\displaystyle (\mathbf {X^{*}} ,\mathbf {Y^{*}} ,\mathbf {p} )} is a price equilibrium with transfers, then the allocation ( X ∗ , Y ∗ ) {\displaystyle (\math... | Second welfare theorem | 0.784162 |
82,501 | Arrow's and Debreu's two papers (written independently and published almost simultaneously) sought to improve on the rigour of Lange's first theorem. Their accounts refer to (short-run) production as well as exchange, expressing the conditions for both through linear functions. Equilibrium for production is expressed b... | Second welfare theorem | 0.784162 |
82,502 | Firstly we have a problem of distribution: how should the goods within a society be shared between its members? And secondly, how should production be organised so that, when goods are so distributed, the members of society obtain the maximum ophelimity? His answer is an informal precursor of the second theorem: Having... | Second welfare theorem | 0.784162 |
82,503 | His own 'indifference curves for obstacles' seem to have been a false path. Shortly after stating the first fundamental theorem, Pareto asks a question about distribution: Consider a collectivist society which seeks to maximise the ophelimity of its members. The problem divides into two parts. | Second welfare theorem | 0.784162 |
82,504 | The following paragraph gives us a theorem: For phenomena of type I , when equilibrium takes place at a point of tangency of indifference curves, the members of the collectivity enjoy a maximum of ophelimity. He adds that 'a rigorous proof cannot be given without the help of mathematics' and refers to his Appendix.Wick... | Second welfare theorem | 0.784162 |
82,505 | Pareto stated the first fundamental theorem in his Manuale (1906) and with more rigour in its French revision (Manuel, 1909). He was the first to claim optimality under his own criterion or to support the claim by convincing arguments.He defines equilibrium more abstractly than Edgeworth as a state which would maintain... | Second welfare theorem | 0.784162 |
82,506 | Lange's paper 'The Foundations of Welfare Economics' is the source of the now-traditional pairing of two theorems, one governing markets, the other distribution. He justified the Pareto definition of optimality for the first theorem by reference to Lionel Robbins's rejection of interpersonal utility comparisons, and su... | Second welfare theorem | 0.784162 |
82,507 | In principle, there are two commonly found versions of the fundamental theorems, one relating to an exchange economy in which endowments are exogenously given, and one relating to an economy in which production occurs. The production economy is more general and entails additional assumptions. The assumptions are all ba... | Second welfare theorem | 0.784162 |
82,508 | The acoustic qualities of a building can be optimised to provide appropriate volume as well as direct sound towards specified areas. The Strait Cultural Center in Fuzhou, China, utilised ADO to optimise the curvature of wall and ceiling structures to facilitate acoustic efficiency. This was achieved through the creatio... | Architectural design optimization | 0.78416 |
82,509 | One potential application of ADO is in the reduction of a building's energy consumption and environmental impact. This might be achieved through the optimisation of the envelope, or façade of a building to ensure ideal thermal properties, which could subsequently reduce the necessity of cooling and heating systems. Oth... | Architectural design optimization | 0.78416 |
82,510 | Architectural design optimization (ADO) is a subfield of engineering that uses optimization methods to study, aid, and solve architectural design problems, such as optimal floorplan layout design, optimal circulation paths between rooms, sustainability and the like. ADO can be achieved through retrofitting, or it can b... | Architectural design optimization | 0.784159 |
82,511 | Topology explores the relationship between structures in a buildings layout while geometry concerns itself more with the placement and dimensions of each structure. Research conducted in 2002 showed that the optimisation of geometry using gradient-based methods yielded successful results, while the optimisation of topo... | Architectural design optimization | 0.784159 |
82,512 | ADO could be employed to reduce travel time between internal areas of a building through the optimisation of its floor plan layout. Ideal circulation paths within a building might also be attained through the considered placement of stairwells, elevators, and escalators in relation to frequently used amenities. This ty... | Architectural design optimization | 0.784159 |
82,513 | Model-based optimisation, unlike metaheuristic and direct search methods, utilises a surrogate model to iteratively refine and optimise architecture. The surrogate model is an explicit representation of implicit mathematical processes, such as statistics or machine learning. Because this method constructs a surrogate m... | Architectural design optimization | 0.784159 |
82,514 | This partition—the set of equivalence classes—is sometimes called the quotient set or the quotient space of S {\displaystyle S} by ∼ , {\displaystyle \,\sim \,,} and is denoted by S / ∼ {\displaystyle S/{\sim }} . When the set S {\displaystyle S} has some structure (such as a group operation or a topology) and the equi... | Canonical projection map | 0.784159 |
82,515 | The curve can be parameterised by the equation x = t − tanh ( t ) , y = 1 / cosh ( t ) {\displaystyle x=t-\tanh(t),y=1/{\cosh(t)}} . Due to the geometrical way it was defined, the tractrix has the property that the segment of its tangent, between the asymptote and the point of tangency, has constant length a. The a... | Tractrix | 0.784159 |
82,516 | Suppose the object is placed at (a, 0) (or (4, 0) in the example shown at right), and the puller at the origin, so a is the length of the pulling thread (4 in the example at right). Then the puller starts to move along the y axis in the positive direction. At every moment, the thread will be tangent to the curve y = y(... | Tractrix | 0.784159 |
82,517 | The curvature radius is r = a cot x/y. A great implication that the tractrix had was the study of its surface of revolution about its asymptote: the pseudosphere. Studied by Eugenio Beltrami in 1868, as a surface of constant negative Gaussian curvature, the pseudosphere is a local model of hyperbolic geometry. The idea... | Tractrix | 0.784158 |
82,518 | In geometry, a tractrix (from Latin trahere 'to pull, drag'; plural: tractrices) is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a pulling point (the tractor) that moves at a right angle to the initial line between the object and... | Tractrix | 0.784158 |
82,519 | In statistics, the principle of marginality is the fact that the average (or main) effects of variables in an analysis are marginal to their interaction effect—that is, the main effect of one explanatory variable captures the effect of that variable averaged over all values of a second explanatory variable whose value ... | Principle of marginality | 0.784158 |
82,520 | Kitaev, Alexei Yu (2003). "Fault-tolerant quantum computation by anyons". Annals of Physics. | Topological phase | 0.784156 |
82,521 | Matter composed of atoms can have different properties and appear in different forms, such as solid, liquid, superfluid, etc. These various forms of matter are often called states of matter or phases. According to condensed matter physics and the principle of emergence, the different properties of materials generally a... | Topological phase | 0.784156 |
82,522 | Their quasi-particle excitations have no fractional charge and fractional statistics. Strictly speaking, topological insulator is an example of symmetry-protected topological (SPT) order, where the first example of SPT order is the Haldane phase of spin-1 chain. But the Haldane phase of spin-2 chain has no SPT order. | Topological phase | 0.784156 |
82,523 | Topological order is robust against any perturbations. It has emergent gauge theory, emergent fractional charge and fractional statistics. In contrast, topological insulators are robust only against perturbations that respect time-reversal and U(1) symmetries. | Topological phase | 0.784156 |
82,524 | This suggests their potential for exciting, novel applications. One theorized application would be to use topologically ordered states as media for quantum computing in a technique known as topological quantum computing. A topologically ordered state is a state with complicated non-local quantum entanglement. | Topological phase | 0.784156 |
82,525 | D. Arovas and J. R. Schrieffer and F. Wilczek, Phys. Rev. Lett., 53, 722 (1984), "Fractional Statistics and the Quantum Hall Effect" Wen, Xiao-Gang; Niu, Qian (1990). "Ground state degeneracy of the FQH states in presence of random potential and on high genus Riemann surfaces" (PDF). | Topological phase | 0.784156 |
82,526 | Traditionally, statisticians have evaluated estimators and designs by considering some summary statistic of the covariance matrix (of an unbiased estimator), usually with positive real values (like the determinant or matrix trace). Working with positive real numbers brings several advantages: If the estimator of a sing... | Singular statistical model | 0.784154 |
82,527 | Because the variance of the estimator of a parameter vector is a matrix, the problem of "minimizing the variance" is complicated. Using statistical theory, statisticians compress the information-matrix using real-valued summary statistics; being real-valued functions, these "information criteria" can be maximized. | Singular statistical model | 0.784154 |
82,528 | The Fisher information is used in machine learning techniques such as elastic weight consolidation, which reduces catastrophic forgetting in artificial neural networks. Fisher information can be used as an alternative to the Hessian of the loss function in second-order gradient descent network training. | Singular statistical model | 0.784154 |
82,529 | It can also be used in the formulation of test statistics, such as the Wald test. In Bayesian statistics, the Fisher information plays a role in the derivation of non-informative prior distributions according to Jeffreys' rule. It also appears as the large-sample covariance of the posterior distribution, provided that ... | Singular statistical model | 0.784154 |
82,530 | In mathematical statistics, the Fisher information (sometimes simply called information) is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the obse... | Singular statistical model | 0.784154 |
82,531 | It also avoids the cost and time required to pressurize and depressurize the exit and entry points of a hyperloop tube. There is also the criticism of design technicalities in the tube system. John Hansman, professor of aeronautics and astronautics at MIT, has pointed out problems, such as how a slight misalignment in ... | Hyperloop | 0.784153 |
82,532 | "Political impediments to the construction of such a project in California may be large due to the "political and reputation capital" invested in the existing mega-project of California High-Speed Rail. Because replacing that with a different design would not be straightforward given California's political economy, Tex... | Hyperloop | 0.784153 |
82,533 | A 40-year operation lifetime would lead to a cost of electricity of 4.8 cents/kWh. LLNL calculated the LCOE of LIFE.2 at 9.1 cents using the discounted cash flow methodology described in the 2009 MIT report "the Future of Nuclear Energy". Using either value, LIFE.2 would be unable to compete with modern renewable energ... | Laser Inertial Fusion Energy | 0.784153 |
82,534 | With the problem of ignition unsolved, the LIFE project was canceled in 2013. The LIFE program was criticized through its development for being based on physics that had not yet been demonstrated. In one pointed assessment, Robert McCrory, director of the Laboratory for Laser Energetics, stated: "In my opinion, the ove... | Laser Inertial Fusion Energy | 0.784153 |
82,535 | NDIs are also redox-active, forming stable radical anions near -1.10 V vs. Fc/Fc+. Their ability to accept electrons reflects the presence of an extended conjugated ring system and the electron withdrawing groups (carbonyl centers). NDIs are used in supramolecular chemistry due to their tendency to form charge-transfer... | Naphthalene tetracarboxylic dianhydride | 0.784153 |
82,536 | 1997 The Walter Boas Medal (1997) of the Australian Institute of Physics, shared with Dr Stephen W. Wilkins. 1992 The Edgeworth David Medal of the Royal Society of New South Wales, shared with Peter James Goadsby. 1989 Pawsey Medal of the Australian Academy of Science. 1988 R&D 100 Award for the development of the penu... | Lobster eye optics | 0.784153 |
82,537 | Nugent was born in Bath, England, where his father was a chocolate chemist for Fry & Sons. The family, including Nugent’s mother and his two brothers, moved to Australia when he was 11, when his father took up a role at Red Tulip (since taken over by Cadbury) in Melbourne. The family moved again to country NSW and Nuge... | Lobster eye optics | 0.784153 |
82,538 | He had previously served as a member of its national scientific advisory board and its board of directors.From 2005-2012, Nugent was director of the ARC Centre of Excellence for Coherent X-ray Science, based at the University of Melbourne, where he drove the development of coherent X-ray diffraction methods for imaging... | Lobster eye optics | 0.784153 |
82,539 | IATIA was awarded the 2006 Australian Technology Showcase Patrons Award.When Nugent's wife Dr Eroia Barone-Nugent developed and instigated the Growing Tall Poppies Program (2008) to increase and sustain girls in science beyond year 10 Nugent quickly included and this program in his scientific endeavors. With a focus on... | Lobster eye optics | 0.784153 |
82,540 | Keith Alexander Nugent FAA (born 28 June 1959) is an Australian physicist. He is the Deputy Vice-Chancellor (Research and Innovation) of the Australian National University (ANU) in Canberra. He was previously Deputy Vice-Chancellor and Vice-President (Research) at La Trobe University, Victoria, and a Laureate Professor... | Lobster eye optics | 0.784153 |
82,541 | The arc converter, sometimes called the arc transmitter, or Poulsen arc after Danish engineer Valdemar Poulsen who invented it in 1903, was a variety of spark transmitter used in early wireless telegraphy. The arc converter used an electric arc to convert direct current electricity into radio frequency alternating curr... | Arc transmitter | 0.784153 |
82,542 | In mathematics, the Cauchy–Hadamard theorem is a result in complex analysis named after the French mathematicians Augustin Louis Cauchy and Jacques Hadamard, describing the radius of convergence of a power series. It was published in 1821 by Cauchy, but remained relatively unknown until Hadamard rediscovered it. Hadama... | Cauchy–Hadamard theorem | 0.784152 |
82,543 | Lis provides facilities for: Automatic program configuration NUMA aware hybrid implementation with MPI and OpenMP Exchangeable dense and sparse matrix storage formats Basic linear algebra operations for dense and sparse matrices Parallel iterative methods for linear equations and eigenvalue problems Parallel preconditi... | Lis (linear algebra library) | 0.784149 |
82,544 | Lis (Library of Iterative Solvers for linear systems, pronounced ) is a scalable parallel software library for solving discretized linear equations and eigenvalue problems that mainly arise in the numerical solution of partial differential equations by using iterative methods. Although it is designed for parallel compu... | Lis (linear algebra library) | 0.784149 |
82,545 | The installation of Lis requires a C compiler. The Fortran interface requires a Fortran compiler, and the algebraic multigrid preconditioner requires a Fortran 90 compiler. For parallel computing environments, an OpenMP or MPI library is required. Both the Matrix Market and Harwell-Boeing formats are supported to impor... | Lis (linear algebra library) | 0.784149 |
82,546 | Shared neural representation for a motor behavior and its observation has been extended into the domains of feelings and emotions. Not only observations of movements but also those of facial expressions activate the same brain regions that are activated by direct experiences. In an fMRI study, the same brain regions ac... | Simulation theory of empathy | 0.784149 |
82,547 | OpenCTM is a 3D geometry technology for storing triangle-based meshes in a compact format. | OpenCTM | 0.784148 |
82,548 | In mathematics and mathematical physics, Slater integrals are certain integrals of products of three spherical harmonics. They occur naturally when applying an orthonormal basis of functions on the unit sphere that transform in a particular way under rotations in three dimensions. Such integrals are particularly useful... | Slater integrals | 0.784146 |
82,549 | During 1996, CASIO worked on the CAS (Computer Algebra System) and studying Geometry. The CAS was first used in the Casio CFX-9970G then the Casio Algebra FX 2.0, and later formed the core math system for the ClassPad. In 1999, the idea of the eActivity emerged. It was intended to allow all applications to interact fro... | Casio ClassPad 300 | 0.784146 |
82,550 | In 2006 CASIO released OS 3.0 for the ClassPad. OS 3.0 featured Laplace and Fourier transform, differential equation graphs, financial functions, AP statistics and parameterized 3D graphs. Subsequent releases were only available for users with OS 3.0 or later. | Casio ClassPad 300 | 0.784146 |
82,551 | The Casio ClassPad 300, ClassPad 330 and fx-CP400 are stylus based touch-screen graphing calculators. It comes with a collection of applications that support self-study, like 3D Graph, Geometry, eActivity, Spreadsheet, etc. A large 160x240 pixel LCD touch screen enables stylus-based operation. It resembles Casio's earl... | Casio ClassPad 300 | 0.784146 |
82,552 | An eActivity application allows the creation of so-called eActivities, which can include figures, expressions, and explanations. In the United States the ClassPad series is banned from standardized tests including the SAT, the ACT, and the AP Calculus test, due to its virtual QWERTY keyboard and stylus usage.In 2017, t... | Casio ClassPad 300 | 0.784146 |
82,553 | A mycorrhiza (from Greek μύκης mýkēs, "fungus", and ῥίζα rhiza, "root"; PL: mycorrhizae, mycorrhiza or mycorrhizas) is a symbiotic association between a fungus and a plant. The term mycorrhiza refers to the role of the fungus in the plant's rhizosphere, its root system. Mycorrhizae play important roles in plant nutriti... | Mycorrhizae and climate change | 0.784144 |
82,554 | Perl Data Language (abbreviated PDL) is a set of free software array programming extensions to the Perl programming language. PDL extends the data structures built into Perl, to include large multidimensional arrays, and adds functionality to manipulate those arrays as vector objects. It also provides tools for image p... | Perl Data Language | 0.784143 |
82,555 | PDL can be used for machine learning. It includes modules that are used to perform classic k-means clustering or general and generalized linear modeling methods such as ANOVA, linear regression, PCA, and logistic regression. Examples of PDL usage for regression modelling tasks include evaluating association between edu... | Perl Data Language | 0.784143 |
82,556 | The Grignard reaction (French: ) is an organometallic chemical reaction in which carbon alkyl, allyl, vinyl, or aryl magnesium halides (Grignard reagent) are added to the carbonyl groups of either an aldehyde or ketone. This reaction is important for the formation of carbon–carbon bonds. (R2 could also be a hydrogen)Gr... | Grignard Reaction | 0.784143 |
82,557 | The classical Grignard reaction typically refers only to the reaction between a ketone or aldehyde group and a Grignard reagent to form a primary or tertiary alcohol. While some chemists understand the definition to mean all reactions from electrophilic molecules with Grignard reagents.So, for the modern definition the... | Grignard Reaction | 0.784143 |
82,558 | The Lefschetz fixed-point theorem generalizes the Brouwer fixed-point theorem, which states that every continuous map from the n {\displaystyle n} -dimensional closed unit disk D n {\displaystyle D^{n}} to D n {\displaystyle D^{n}} must have at least one fixed point. This can be seen as follows: D n {\displaystyle D^{n... | Lefschetz fixed-point theorem | 0.784142 |
82,559 | {\displaystyle \#X(k)=q^{\dim X}\sum _{i}(-1)^{i}\mathrm {tr} ((\Phi _{q}^{-1})^{*}|H^{i}({\bar {X}},\mathbb {Q} _{\ell })).} This formula involves usual cohomology, rather than cohomology with compact supports. The Lefschetz trace formula can also be generalized to algebraic stacks over finite fields. | Lefschetz fixed-point theorem | 0.784142 |
82,560 | Let X {\displaystyle X} be a variety defined over the finite field k {\displaystyle k} with q {\displaystyle q} elements and let X ¯ {\displaystyle {\bar {X}}} be the base change of X {\displaystyle X} to the algebraic closure of k {\displaystyle k} . The Frobenius endomorphism of X ¯ {\displaystyle {\bar {X}}} (often ... | Lefschetz fixed-point theorem | 0.784142 |
82,561 | Adolph Quetelet was a proponent of social physics. In his book Physique sociale he presents distributions of human heights, age of marriage, time of birth and death, time series of human marriages, births and deaths, a survival density for humans and curve describing fecundity as a function of age. He also developed th... | Social statistics | 0.784142 |
82,562 | Social statistics is the use of statistical measurement systems to study human behavior in a social environment. This can be accomplished through polling a group of people, evaluating a subset of data obtained about a group of people, or by observation and statistical analysis of a set of data that relates to people an... | Social statistics | 0.784142 |
82,563 | Probit and logit Item response theory Bayesian statistics Stochastic process Latent class model | Social statistics | 0.784142 |
82,564 | The dish is still actively used today for academic and research purposes. It is owned by the U.S. Government and operated by SRI International. It is used for commanding and calibrating spacecraft and for radio astronomy measurements. | Stanford Dish | 0.784141 |
82,565 | The observatory was originally named Deep Space Station 51 (DSS 51) and was built in 1961 by the National Aeronautics and Space Administration (NASA). In this role the station assisted in tracking many unmanned United States space missions, including the Ranger, Surveyor and Lunar Orbiter spacecraft (which landed on th... | Hartebeesthoek Radio Astronomy Observatory | 0.78414 |
82,566 | The Hartebeesthoek Radio Astronomy Observatory (HartRAO) is a radio astronomy observatory, located in a natural bowl of hills at Hartebeesthoek just south of the Magaliesberg mountain range, and about 50 km west of Johannesburg, Gauteng, South Africa. It is a National Research Facility run by South Africa's National Re... | Hartebeesthoek Radio Astronomy Observatory | 0.78414 |
82,567 | There are various solution approaches, including some using the methods of rotation matrices, and some making a 3D model of the reclined-declined plane and its vertical declined counterpart plane, extracting the geometrical relationships between the hour angle components on both these planes and then reducing the trigo... | Horizontal sundial | 0.78414 |
82,568 | Pegboards are used in games and for educational purposes. Games based on the pegboard concept include peg mosaic boards, where a child may create pictures and lettering by inserting colored pegs in the board, in a way similar to pixel art. These boards are designed so that the pegs do not fall out when the board is til... | Perforated hardboard | 0.784138 |
82,569 | In computer science, polylogarithmic functions occur as the order of time or memory used by some algorithms (e.g., "it has polylogarithmic order"), such as in the definition of QPTAS (see PTAS). All polylogarithmic functions of n are o(nε) for every exponent ε > 0 (for the meaning of this symbol, see small o notation),... | Polylogarithmic function | 0.784133 |
82,570 | Finally, is a theorized link layer cause which is predicated based on physics simulations of packet switching networks on simulated topologies. At a critical packet creation rate, the flow in a network becomes congested and exhibits 1/f noise and long-tail traffic characteristics. There have been criticisms on these so... | Long-tail traffic | 0.784132 |
82,571 | In general, there are three main theories for the causes of long-tail traffic (see a review of all three causes). First, is a cause based in the application layer which theorizes that user session durations vary with a long-tail distribution due to the file size distribution. If the distribution of file sizes is heavy-... | Long-tail traffic | 0.784132 |
82,572 | }}\right)e^{-\mu },} where a is the number of call arrivals and μ {\displaystyle \mu } is the mean number of call arrivals in time T. For this reason, pure-chance traffic is also known as Poisson traffic. The number of call departures in a given time also has a Poisson distribution, i.e.: P ( d ) = ( λ d d ! ) e − λ , ... | Long-tail traffic | 0.784132 |
82,573 | Such power law scaling of the autocorrelation function can be shown to be biconditionally related to a power law relationship between the variance and the mean, when evaluated from sequences by the method of expanding bins. This variance to mean power law is an inherent feature of a family of statistical distributions ... | Long-tail traffic | 0.784132 |
82,574 | Given a topological space X , {\displaystyle X,} the closure can be considered as a map ℘ ( X ) → ℘ ( X ) , {\displaystyle \wp (X)\to \wp (X),} where ℘ ( X ) {\displaystyle \wp (X)} denotes the power set of X . {\displaystyle X.} One has the following Kuratowski closure axioms: A ⊆ cl ( A ) {\displaystyle A\subseteq ... | Neighborhood characterization of topological spaces | 0.784131 |
82,575 | Given a topological space X , {\displaystyle X,} the interior can be considered as a map ℘ ( X ) → ℘ ( X ) , {\displaystyle \wp (X)\to \wp (X),} where ℘ ( X ) {\displaystyle \wp (X)} denotes the power set of X . {\displaystyle X.} It satisfies the following conditions: int ( A ) ⊆ A {\displaystyle \operatorname {int}... | Neighborhood characterization of topological spaces | 0.784131 |
82,576 | If X {\displaystyle X} is a set, then given a notion of net convergence (telling what nets converge to what points) satisfying the above four axioms, a closure operator on X {\displaystyle X} is defined by sending any given set A {\displaystyle A} to the set of all limits of all nets valued in A ; {\displaystyle A;} th... | Neighborhood characterization of topological spaces | 0.784131 |
82,577 | This is to say that a topology can be defined by declaring the closed sets. As such, one can rephrase all definitions to be in terms of closed sets: Given a second topological space Y , {\displaystyle Y,} a function f: X → Y {\displaystyle f:X\to Y} is continuous if and only if for every closed subset U {\displaystyle ... | Neighborhood characterization of topological spaces | 0.784131 |
82,578 | {\displaystyle T.} Now suppose that X {\displaystyle X} is only a set. Given any collection T {\displaystyle T} of subsets of X {\displaystyle X} which satisfy the above axioms, the corresponding set { U: X ∖ U ∈ T } {\displaystyle \{U:X\setminus U\in T\}} is a topology on X , {\displaystyle X,} and it is the only topo... | Neighborhood characterization of topological spaces | 0.784131 |
82,579 | In order to quantify the burst suppression pattern, the EEG signal must be subject to segmentation. The first segmentation used a fixed voltage-threshold, and various methods for segmentation or burst detection have developed in time domain, frequency (Fourier) domain, and both. These processes separates burst and supp... | Burst suppression | 0.784131 |
82,580 | Samuel Orton pioneered the study of learning disabilities, such as dyslexia. where the subject is apt to confound the letter-order of words. He and his assistant Anna Gillingham, an educator and psychologist, evolved the Orton-Gillingham Approach to reading instruction which is language-based, multi-sensory, structured... | Inventive spelling | 0.784129 |
82,581 | Proceedings of the Royal Society B publishes research related to biological sciences. As of 2015 the editor-in-chief is Professor Spencer Barrett. Topics covered in particular include ecology, behavioural ecology and evolutionary biology, as well as epidemiology, human biology, neuroscience, palaeontology, psychology, ... | Proceedings of the Royal Society | 0.784129 |
82,582 | In terms of structure, channelrhodopsins are retinylidene proteins. They are seven-transmembrane proteins like rhodopsin, and contain the light-isomerizable chromophore all-trans-retinal (an aldehyde derivative of vitamin A). The retinal chromophore is covalently linked to the rest of the protein through a protonated S... | Channelrhodopsin | 0.784128 |
82,583 | Using parts of the ChR1 sequence, photocurrent amplitude was later improved to allow excitation of two neuronal populations at two distinct wavelengths.Deisseroth's group has pioneered many applications in live animals such as genetically targeted remote control in rodents in vivo, the optogenetic induction of learning... | Channelrhodopsin | 0.784128 |
82,584 | In 2005, three groups sequentially established ChR2 as a tool for genetically targeted optical remote control (optogenetics) of neurons, neural circuits and behavior. At first, Karl Deisseroth's lab demonstrated that ChR2 could be deployed to control mammalian neurons in vitro, achieving temporal precision on the order... | Channelrhodopsin | 0.784128 |
82,585 | This is useful to study the molecular events during the induction of synaptic plasticity. Transfected cultured neuronal networks can be stimulated to perform some desired behaviors for applications in robotics and control. ChR2 has also been used to map long-range connections from one side of the brain to the other, an... | Channelrhodopsin | 0.784128 |
82,586 | Controlling networks of genetically modified cells with light, an emerging field known as Optogenetics., allows researchers now to explore the causal link between activity in a specific group of neurons and mental events, e.g. decision making. Optical control of behavior has been demonstrated in nematodes, fruit flies,... | Channelrhodopsin | 0.784128 |
82,587 | Channelrhodopsins are key tools in optogenetics. The C-terminal end of Channelrhodopsin-2 extends into the intracellular space and can be replaced by fluorescent proteins without affecting channel function. This kind of fusion construct can be useful to visualize the morphology of ChR2 expressing cells, i.e. simultaneo... | Channelrhodopsin | 0.784128 |
82,588 | Channelrhodopsins are a subfamily of retinylidene proteins (rhodopsins) that function as light-gated ion channels. They serve as sensory photoreceptors in unicellular green algae, controlling phototaxis: movement in response to light. Expressed in cells of other organisms, they enable light to control electrical excita... | Channelrhodopsin | 0.784128 |
82,589 | For example, if I = N , {\displaystyle I=\mathbb {N} ,} then the sequence ( f n ) n ∈ N {\displaystyle (f_{n})_{n\in \mathbb {N} }} with f n = X n + X n + 1 + X n + 2 + ⋯ {\displaystyle f_{n}=X_{n}+X_{n+1}+X_{n+2}+\cdots } does not converge with respect to any J-adic topology on R, but clearly for each monomial the cor... | Power series ring | 0.784128 |
82,590 | The topology on R ] {\displaystyle R]} is such that a sequence of its elements converges only if for each monomial Xα the corresponding coefficient stabilizes. If I is finite, then this the J-adic topology, where J is the ideal of R ] {\displaystyle R]} generated by all the indeterminates in XI. This does not hold if... | Power series ring | 0.784128 |
82,591 | For any natural number n we have where (This formula can only be used if m and a0 are invertible in the ring of coefficients.) In the case of formal power series with complex coefficients, the complex powers are well defined at least for series f with constant term equal to 1. In this case, f α {\displaystyle f^{\alpha... | Power series ring | 0.784128 |
82,592 | {\displaystyle (fg)(x)=f(x)g(x).} Unlike in the case of bona fide functions, these formulas are not definitions but have to be proved. Since the topology on R ] {\displaystyle R]} is the ( X ) {\displaystyle (X)} -adic topology and R ] {\displaystyle R]} is complete, we can in particular apply power series to other p... | Power series ring | 0.784128 |
82,593 | In mathematical analysis, every convergent power series defines a function with values in the real or complex numbers. Formal power series over certain special rings can also be interpreted as functions, but one has to be careful with the domain and codomain. Let f = ∑ a n X n ∈ R ] , {\displaystyle f=\sum a_{n}X^{n}\... | Power series ring | 0.784128 |
82,594 | The functionality comprises decoding (one between many, ASTERIX data format), recording and computation of statistics. TRES (Trajectory Reconstruction and Evaluation Suite) is the core suite of SASS-C, carrying out the reconstruction of reference trajectories from the input data, and doing the evaluation of Surveillanc... | SASS-C | 0.784127 |
82,595 | SASS-C VERIFication is divided into many modules. The key ones are: IRIS: ATC surveillance data recording, decoding and statistics. In supports many framing or coding surveillance data format. One between many: ASTERIX. | SASS-C | 0.784126 |
82,596 | Solenopsins are described as toxic against vertebrates and invertebrates. For example, the compound known as isosolenopsin A has been demonstrated to have strong insecticidal effects which may play a central role in the biology of fire ants. In addition to its toxicity, solenopsis has a number of other biological activ... | Solenopsin | 0.784125 |
82,597 | A more modern classification (Huang & Leung 2010) uniformly classifies the Riemannian symmetric spaces, both compact and non-compact, via a Freudenthal magic square construction. The irreducible compact Riemannian symmetric spaces are, up to finite covers, either a compact simple Lie group, a Grassmannian, a Lagrangian... | Symmetric space | 0.784125 |
82,598 | Selberg's definition can also be phrased equivalently in terms of a generalization of geodesic symmetry. It is required that for every point x in M and tangent vector X at x, there is an isometry s of M, depending on x and X, such that s fixes x; the derivative of s at x sends X to –X.When s is independent of X, M is a... | Symmetric space | 0.784125 |
82,599 | Cloud2Sim extends CloudSim to execute on multiple distributed servers, by leveraging Hazelcast distributed execution framework. RECAP DES extends the CloudSim Plus framework to model synchronous hierarchical architectures (such as ElasticSearch). ThermoSim extends CloudSim toolkit by incorporating thermal characteristi... | CloudSim | 0.784123 |
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