28,893 research outputs found
Cumulative Step-size Adaptation on Linear Functions
The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation,
where the step size is adapted measuring the length of a so-called cumulative
path. The cumulative path is a combination of the previous steps realized by
the algorithm, where the importance of each step decreases with time. This
article studies the CSA-ES on composites of strictly increasing functions with
affine linear functions through the investigation of its underlying Markov
chains. Rigorous results on the change and the variation of the step size are
derived with and without cumulation. The step-size diverges geometrically fast
in most cases. Furthermore, the influence of the cumulation parameter is
studied.Comment: arXiv admin note: substantial text overlap with arXiv:1206.120
Cumulative Step-size Adaptation on Linear Functions: Technical Report
The CSA-ES is an Evolution Strategy with Cumulative Step size Adaptation,
where the step size is adapted measuring the length of a so-called cumulative
path. The cumulative path is a combination of the previous steps realized by
the algorithm, where the importance of each step decreases with time. This
article studies the CSA-ES on composites of strictly increasing with affine
linear functions through the investigation of its underlying Markov chains.
Rigorous results on the change and the variation of the step size are derived
with and without cumulation. The step-size diverges geometrically fast in most
cases. Furthermore, the influence of the cumulation parameter is studied.Comment: Parallel Problem Solving From Nature (2012
Finite element differential forms on cubical meshes
We develop a family of finite element spaces of differential forms defined on
cubical meshes in any number of dimensions. The family contains elements of all
polynomial degrees and all form degrees. In two dimensions, these include the
serendipity finite elements and the rectangular BDM elements. In three
dimensions they include a recent generalization of the serendipity spaces, and
new H(curl) and H(div) finite element spaces. Spaces in the family can be
combined to give finite element subcomplexes of the de Rham complex which
satisfy the basic hypotheses of the finite element exterior calculus, and hence
can be used for stable discretization of a variety of problems. The
construction and properties of the spaces are established in a uniform manner
using finite element exterior calculus.Comment: v2: as accepted by Mathematics of Computation after minor revisions;
v3: this version corresponds to the final version for Math. Comp., after
copyediting and galley proof
Mathematicians take a stand
We survey the reasons for the ongoing boycott of the publisher Elsevier. We
examine Elsevier's pricing and bundling policies, restrictions on dissemination
by authors, and lapses in ethics and peer review, and we conclude with thoughts
about the future of mathematical publishing.Comment: 5 page
Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations
Specifying boundary conditions continues to be a challenge in numerical
relativity in order to obtain a long time convergent numerical simulation of
Einstein's equations in domains with artificial boundaries. In this paper, we
address this problem for the Einstein--Christoffel (EC) symmetric hyperbolic
formulation of Einstein's equations linearized around flat spacetime. First, we
prescribe simple boundary conditions that make the problem well posed and
preserve the constraints. Next, we indicate boundary conditions for a system
that extends the linearized EC system by including the momentum constraints and
whose solution solves Einstein's equations in a bounded domain
Renormalization-group study of weakly first-order phase transitions
We study the universal critical behaviour near weakly first-order phase
transitions for a three-dimensional model of two coupled scalar fields -- the
cubic anisotropy model. Renormalization-group techniques are employed within
the formalism of the effective average action. We calculate the universal form
of the coarse-grained free energy and deduce the ratio of susceptibilities on
either side of the phase transition. We compare our results with those obtained
through Monte Carlo simulations and the epsilon-expansion.Comment: 8 pages, 4 figures in eps forma
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