15,595 research outputs found

    On the importance of nonlinear modeling in computer performance prediction

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    Computers are nonlinear dynamical systems that exhibit complex and sometimes even chaotic behavior. The models used in the computer systems community, however, are linear. This paper is an exploration of that disconnect: when linear models are adequate for predicting computer performance and when they are not. Specifically, we build linear and nonlinear models of the processor load of an Intel i7-based computer as it executes a range of different programs. We then use those models to predict the processor loads forward in time and compare those forecasts to the true continuations of the time seriesComment: Appeared in "Proceedings of the 12th International Symposium on Intelligent Data Analysis

    Programs with continuations and linear logic

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    AbstractThe purpose of this paper is to investigate the programs with continuations in the framework of classical linear logic which can also be regarded as improvement of traditional classical logic. First, simply typed λ-calculus λ→c with continuation primitives is introduced. Second, a translation from λ→c to linear logic is given. Last, a correspondence between them is presented

    On contractions of classical basic superalgebras

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    We define a class of orthosymplectic osp(m;j2n;ω)osp(m;j|2n;\omega) and unitary sl(m;jn;ϵ)sl(m;j|n;\epsilon) superalgebras which may be obtained from osp(m2n)osp(m|2n) and sl(mn)sl(m|n) by contractions and analytic continuations in a similar way as the special linear, orthogonal and the symplectic Cayley-Klein algebras are obtained from the corresponding classical ones. Casimir operators of Cayley-Klein superalgebras are obtained from the corresponding operators of the basic superalgebras. Contractions of sl(21)sl(2|1) and osp(32)osp(3|2) are regarded as an examples.Comment: 15 pages, Late

    Combining and Relating Control Effects and their Semantics

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    Combining local exceptions and first class continuations leads to programs with complex control flow, as well as the possibility of expressing powerful constructs such as resumable exceptions. We describe and compare games models for a programming language which includes these features, as well as higher-order references. They are obtained by contrasting methodologies: by annotating sequences of moves with "control pointers" indicating where exceptions are thrown and caught, and by composing the exceptions and continuations monads. The former approach allows an explicit representation of control flow in games for exceptions, and hence a straightforward proof of definability (full abstraction) by factorization, as well as offering the possibility of a semantic approach to control flow analysis of exception-handling. However, establishing soundness of such a concrete and complex model is a non-trivial problem. It may be resolved by establishing a correspondence with the monad semantics, based on erasing explicit exception moves and replacing them with control pointers.Comment: In Proceedings COS 2013, arXiv:1309.092

    Continuations of Hermitian indefinite functions and corresponding canonical systems : an example

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    M. G. Krein established a close connection between the continuation problem of positive definite functions from a finite interval to the real axis and the inverse spectral problem for differential operators. In this note we study such a connection for the function f(t) = 1 − |t|, t - R, which is not positive definite on R: its restrictions fa := f|(−2a,2a) are positive definite if a ≤ 1 and have one negative square if a > 1. We show that with f a canonical differential equation or a Sturm-Liouville equation can be associated which have a singularity

    Continuations of the nonlinear Schr\"odinger equation beyond the singularity

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    We present four continuations of the critical nonlinear \schro equation (NLS) beyond the singularity: 1) a sub-threshold power continuation, 2) a shrinking-hole continuation for ring-type solutions, 3) a vanishing nonlinear-damping continuation, and 4) a complex Ginzburg-Landau (CGL) continuation. Using asymptotic analysis, we explicitly calculate the limiting solutions beyond the singularity. These calculations show that for generic initial data that leads to a loglog collapse, the sub-threshold power limit is a Bourgain-Wang solution, both before and after the singularity, and the vanishing nonlinear-damping and CGL limits are a loglog solution before the singularity, and have an infinite-velocity{\rev{expanding core}} after the singularity. Our results suggest that all NLS continuations share the universal feature that after the singularity time TcT_c, the phase of the singular core is only determined up to multiplication by eiθe^{i\theta}. As a result, interactions between post-collapse beams (filaments) become chaotic. We also show that when the continuation model leads to a point singularity and preserves the NLS invariance under the transformation ttt\rightarrow-t and ψψ\psi\rightarrow\psi^\ast, the singular core of the weak solution is symmetric with respect to TcT_c. Therefore, the sub-threshold power and the{\rev{shrinking}}-hole continuations are symmetric with respect to TcT_c, but continuations which are based on perturbations of the NLS equation are generically asymmetric
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