57,521 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
Bose-Einstein condensates in `giant' toroidal magnetic traps
The experimental realisation of gaseous Bose-Einstein condensation (BEC) in
1995 sparked considerable interest in this intriguing quantum fluid. Here we
report on progress towards the development of an 87Rb BEC experiment in a large
(~10cm diameter) toroidal storage ring. A BEC will be formed at a localised
region within the toroidal magnetic trap, from whence it can be launched around
the torus. The benefits of the system are many-fold, as it should readily
enable detailed investigations of persistent currents, Josephson effects, phase
fluctuations and high-precision Sagnac or gravitational interferometry.Comment: 5 pages, 3 figures (Figs. 1 and 2 now work
Agriculture in the Clermont Silt Loam Area
Exact date of bulletin unknown.PDF pages: 2
On examples of difference operators for -valued functions over finite sets
Recently V.I.Arnold have formulated a geometrical concept of monads and apply
it to the study of difference operators on the sets of -valued
sequences of length . In the present note we show particular examples of
these monads and indicate one question arising here
Trans-spectral orbital angular momentum transfer via four-wave mixing in Rb vapor
We report the transfer of phase structure and, in particular, of orbital angular momentum from near-infrared pump light to blue light generated in a four-wave-mixing process in Rb-85 vapor. The intensity and phase profile of the two pump lasers at 780 and 776 nm, shaped by a spatial light modulator, influences the phase and intensity profile of light at 420 nm, which is generated in a subsequent coherent cascade. In particular, we observe that the phase profile associated with orbital angular momentum is transferred entirely from the pump light to the blue. Pumping with more complicated light profiles results in the excitation of spatial modes in the blue that depend strongly on phase matching, thus demonstrating the parametric nature of the mode transfer. These results have implications on the inscription and storage of phase information in atomic gases
Finite Temperature Reduction of the SU(2) Higgs-Model with Complete Static Background
Direct evaluation of the 1-loop fluctuation determinant of non-static degrees
of freedom in a complete static background is advocated to be more efficient
for the determination of the effective three-dimensional model of the
electroweak phase transition than the one-by-one evaluation of Feynman
diagrams. The relation of the couplings and fields of the effective model to
those of the four-dimensional finite temperature system is determined in the
general 't Hooft gauge with full implementation of renormalisation effects.
Only field renormalisation constants display dependence on the gauge fixing
parameter. Characteristics of the electroweak transition are computed from the
effective theory in Lorentz-gauge. The dependence of various physical
observables on the three-dimensional gauge fixing parameter is investigated.Comment: 12 pages (LATEX) + 1 table (TEX) appende
A Modified "Bottom-up" Thermalization in Heavy Ion Collisions
In the initial stage of the bottom-up picture of thermalization in heavy ion
collisions, the gluon distribution is highly anisotropic which can give rise to
plasma instability. This has not been taken account in the original paper. It
is shown that in the presence of instability there are scaling solutions, which
depend on one parameter, that match smoothly onto the late stage of bottom-up
when thermalization takes place.Comment: 8 pages and 1 embedded figure, talk presented at the Workshop on
"Quark-Gluon Plasma Thermalization", Vienna, Austria, 10-12 August 200
Error analysis of a space-time finite element method for solving PDEs on evolving surfaces
In this paper we present an error analysis of an Eulerian finite element
method for solving parabolic partial differential equations posed on evolving
hypersurfaces in , . The method employs discontinuous
piecewise linear in time -- continuous piecewise linear in space finite
elements and is based on a space-time weak formulation of a surface PDE
problem. Trial and test surface finite element spaces consist of traces of
standard volumetric elements on a space-time manifold resulting from the
evolution of a surface. We prove first order convergence in space and time of
the method in an energy norm and second order convergence in a weaker norm.
Furthermore, we derive regularity results for solutions of parabolic PDEs on an
evolving surface, which we need in a duality argument used in the proof of the
second order convergence estimate
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