1,870 research outputs found
A C++11 implementation of arbitrary-rank tensors for high-performance computing
This article discusses an efficient implementation of tensors of arbitrary
rank by using some of the idioms introduced by the recently published C++ ISO
Standard (C++11). With the aims at providing a basic building block for
high-performance computing, a single Array class template is carefully crafted,
from which vectors, matrices, and even higher-order tensors can be created. An
expression template facility is also built around the array class template to
provide convenient mathematical syntax. As a result, by using templates, an
extra high-level layer is added to the C++ language when dealing with algebraic
objects and their operations, without compromising performance. The
implementation is tested running on both CPU and GPU.Comment: 21 pages, 6 figures, 1 tabl
Global Behavior of the Douglas-Rachford Method for a Nonconvex Feasibility Problem
In recent times the Douglas-Rachford algorithm has been observed empirically
to solve a variety of nonconvex feasibility problems including those of a
combinatorial nature. For many of these problems current theory is not
sufficient to explain this observed success and is mainly concerned with
questions of local convergence. In this paper we analyze global behavior of the
method for finding a point in the intersection of a half-space and a
potentially non-convex set which is assumed to satisfy a well-quasi-ordering
property or a property weaker than compactness. In particular, the special case
in which the second set is finite is covered by our framework and provides a
prototypical setting for combinatorial optimization problems
Central Stellar Populations of S0 Galaxies in The Fornax Cluster
Based on FORS2-VLT long-slit spectroscopy, the analysis of the central
absorption line indices of 9 S0 galaxies in the Fornax Cluster is presented.
Central indices correlate with central velocity dispersions as observed in
ellipticals. However, the stellar population properties of these S0s indicates
that the observed trends are produced by relative differences in age and
alpha-element abundances and not in metallicity ([Fe/H]) as previous studies
have found in elliptical galaxies. The observed scatter in the line indices vs.
velocity dispersion relations can be partially explained by the
rotationally-supported nature of many of these systems. The presence of tighter
line indices vs. maximum (circular) rotational velocity relations confirms this
statement. It was also confirmed that the dynamical mass is the driving
physical property of all these correlations and in our Fornax S0s it has to be
estimated assuming rotational support.Comment: To appear in the Proceedings of IAU Symposium 241: "Stellar
Populations as Building Blocks of Galaxies", 10-16 December, 2006 at La
Palma, Canary Islands, Spai
How to generate pentagonal symmetry using Turing systems
We explore numerically the formation of Turing patterns in a confined circular domain with small aspect ratio. Our results show that stable fivefold patterns are formed over a well defined range of disk sizes, offering a possible mechanism for inducing the fivefold symmetry observed in early development of regular echinoids. Using this pattern as a seed, more complex biological structures can be mimicked, such as the pigmentation pattern of sea urchins and the plate arrangements of the calyxes of primitive camerate crinoids
A machine learning approach for fighting the curse of dimensionality in global optimization
Finding global optima in high-dimensional optimization problems is extremely
challenging since the number of function evaluations required to sufficiently
explore the search space increases exponentially with its dimensionality.
Furthermore, multimodal cost functions render local gradient-based search
techniques ineffective. To overcome these difficulties, we propose to trim
uninteresting regions of the search space where global optima are unlikely to
be found by means of autoencoders, exploiting the lower intrinsic
dimensionality of certain cost functions; optima are then searched over
lower-dimensional latent spaces. The methodology is tested on benchmark
functions and on multiple variations of a structural topology optimization
problem, where we show that we can estimate this intrinsic lower dimensionality
and based thereon obtain the global optimum at best or superior results
compared to established optimization procedures at worst.Comment: Main text 36 pages, 6 figures, currently submitted to science
advance
Conformal mapping of ultrasonic crystals: confining ultrasound and cochlear-like wave guiding
Conformal mapping of a slab of a two-dimensional ultrasonic crystal generate
a closed geometrical arrangement of ultrasonic scatterers with appealing
acoustic properties. This acoustic shell is able to confine ultrasonic modes.
Some of these internal resonances can be induced from an external wave source.
The mapping of a linear defect produces a wave-guide that exhibits a
spatial-frequency selection analogous to that characteristic of a synthetic
"cochlea". Both, experimental and theoretical results are reported here.Comment: 4 pages, 4 figure
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