15,595 research outputs found
On the importance of nonlinear modeling in computer performance prediction
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
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
We define a class of orthosymplectic and unitary
superalgebras which may be obtained from and
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 and are regarded as
an examples.Comment: 15 pages, Late
Combining and Relating Control Effects and their Semantics
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
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
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 , the phase of the singular core
is only determined up to multiplication by . 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 and
, the singular core of the weak solution is symmetric
with respect to . Therefore, the sub-threshold power and
the{\rev{shrinking}}-hole continuations are symmetric with respect to ,
but continuations which are based on perturbations of the NLS equation are
generically asymmetric
- …