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...ter to encode and decode compared to previous methods that can also handle a large number of errors. ...A real-life adversary cannot spend an indefinite amount of time examining a message in order to find the one error pattern which an algorithm would str ...

...theory; the difference is that approximation-preserving reductions usually make statements on [[Approximation_algorithm|approximation problems]] or [[Optim ...blem B, apply the solver for problem B, and recover a solution for problem A that also has some guarantee of approximation. ...

...an be [[Correlation and dependence|correlated]] and not necessarily follow a [[normal distribution]]. When there are different clusters, that is, groups ...= v(u)</math> is some strictly [[monotone function]] of <math>u</math>. In a hierarchical generalized linear model, the assumption on <math>y|u</math> a ...

...2</sup>''', '''M2''', '''Modigliani–Modigliani measure''' or '''RAP''') is a measure of the risk-adjusted returns of some [[investment portfolio]]. It m ...originally called it "RAP" (risk-adjusted performance). They also defined a related statistic, "RAPA" (presumably, an abbreviation of "risk-adjusted pe ...

...ts at all levels (national, regional and local) need to raise revenue from a variety of sources to finance [[Public expenditure|public-sector expenditur ...f a great nation is like the expense of management to the joint tenants of a great estate, who are all obliged to contribute in proportion to their resp ...

{{Short description|Tool to classify manifolds within a homotopy type in dim > 4}} ...</math> of a compact <math>n</math>-dimensional manifold <math>X</math> is a [[pointed set]] which classifies <math>n</math>-dimensional manifolds withi ...

...d many solutions are available for the general case of {{math|''n'' ≥ 3}}. A solution for {{math|''n'' {{=}} 2}} exists if feature orientations are avai Given a set of {{math|''n''}} 3D points in a world reference frame and their corresponding 2D image projections as well ...

...nzo |author3=Lawrence, Neil D. |title=Kernels for Vector-Valued Functions: A Review|eprint=1106.6251 |date=June 2011|class=stat.ML}}</ref> ...l issues; we will consider here the finite-dimensional case. We start with a brief review of the main ideas underlying kernel methods for scalar learnin ...

...ity density.png|thumb|upright=1.35|The probability density distribution of a quantum particle in three-dimensional space. The points in the image repres ...=P.-L. |date=1983 |title=Nonlinear scalar field equations. I. Existence of a ground state |journal=Arch. Rational Mech. Anal. |volume=82 |issue=4 |pages ...

...ity density.png|thumb|upright=1.35|The probability density distribution of a quantum particle in three-dimensional space. The points in the image repres ...=P.-L. |date=1983 |title=Nonlinear scalar field equations. I. Existence of a ground state |journal=Arch. Rational Mech. Anal. |volume=82 |issue=4 |pages ...

...matics, '''Anderson acceleration''', also called '''Anderson mixing''', is a method for the acceleration of the convergence rate of [[fixed-point iterat ...ionally expensive.<ref name="Quarteroni-Sacco" /> Anderson acceleration is a method to accelerate the convergence of the fixed-point sequence.<ref name= ...

...s.png|thumb|Selected sample questions generated by the query generator for a Visual Turing Test|525x525px]] ...follow a “natural story line”, similar to what humans do when they look at a picture. ...

...(This follows by definition: if the gradient vector is not zero, there is a direction in which we can move to minimize it further – see [[maxima and mi The normal equations can be derived directly from a matrix representation of the problem as follows. The objective is to minimi ...

...e of the novel is based on a [[Riemannian manifold|Riemannian]] instead of a [[Pseudo-Riemannian manifold#lorentzian manifold|Lorentzian manifold]] (whi ...the spacecraft ''Gnat'' to it. Carla, a physicist, studies light and finds a seemingly perfect ratio of five to four in one of her experiments. It has a ...

...on |first2=Bernard | last3= LeGland | first3 = Francois | year=1998 |title=A differential geometric approach to nonlinear filtering: the projection filt ...of the signal given the history of observations. If this distribution has a density, the density satisfies [[Filtering problem (stochastic processes)# ...

...e different. Equivalently, a ''noncommutative ring'' is a ring that is not a [[commutative ring]]. ...restricted to commutative rings, as, in many contexts, ''ring'' is used as a shorthand for ''commutative ring''. ...

...adaraya-Waston kernel estimator to test the nonparametric element to build a least-squares estimator  After that, in 1997, local linear method was found Wolfgang, Liang and Gao (1988) make an assumption that the pair (ß,g) satisfies <math>1/n \textstyle \sum_{i=1} ...

...argaining problem''') are faced by management and labor in the division of a firm's profit, by trade partners in the specification of the terms of trade ...''should'' be shared, by formulating appealing axioms that the solution to a bargaining problem should satisfy. It is useful when both parties are willi ...

.../sub> are 1 if ''i'' divides ''j'' or if ''j''&nbsp;=&nbsp;1; otherwise, ''a''_''ij''&nbsp;=&nbsp;0. It is useful in some contexts to express ...inverse <math>D_n^{-1} = \left[\mu(j/i) M_i(j)\right]</math>. We then have a characterization of the [[invertible matrix|singularity]] of <math>A_n</mat ...

...access-date=30 July 2011}}</ref><ref>{{Cite news|author=T. Rephann|author2=A. Isserman|name-list-style=amp|title=New Highways as Economic Development To ..., New England Economic Review, January/February, pp. 21-48.</ref> there is a positive and statistically significant correlation between investment in [[ ...