15,166 research outputs found
Efficient data structures for masks on 2D grids
This article discusses various methods of representing and manipulating
arbitrary coverage information in two dimensions, with a focus on space- and
time-efficiency when processing such coverages, storing them on disk, and
transmitting them between computers. While these considerations were originally
motivated by the specific tasks of representing sky coverage and cross-matching
catalogues of astronomical surveys, they can be profitably applied in many
other situations as well.Comment: accepted by A&
SL(2,R) Chern-Simons Theories with Rational Charges and Two-dimensional Conformal Field Theories
This paper (completed March 1992) is an extensively revised and expanded
version of work which appeared July 1991 on the initial incarnation of the
hepth bulletin board, and which was published in the Proceedings of the
Workshop on String Theory, Trieste, March 1991. Abstract We present a
hamiltonian quantization of the 3-dimensional Chern-Simons theory
with fractional coupling constant on a space manifold with torus
topology in the ``constrain-first'' framework. By generalizing the ``Weyl-odd''
projection to the fractional charge case, we obtain multi-components
holomorphic wave functions whose components are the Kac-Wakimoto characters of
the modular invariant admissible representations of current
algebra with fractional level. The modular representations carried by the
quantum Hilbert space satisfy both Verlinde's and Vafa's constraints coming
from conformal field theory. They are the ``square-roots'' of the
representations associated to the conformal minimal models. Our results
imply that Chern-Simons theory with as gauge group, which describes
-dimensional gravity with negative cosmological constant, has the modular
properties of the Virasoro discrete series. On the way, we show that the
2-dimensional counterparts of Chern-Simons theories with half-integer
charge Comment: 29 pages, GEF-TH-92-
Approximation numbers of composition operators on the Hardy space of the ball and of the polydisk
We give general estimates for the approximation numbers of composition
operators on the Hardy space on the ball and the polydisk
A Hilbert Space Theory of Generalized Graph Signal Processing
Graph signal processing (GSP) has become an important tool in many areas such
as image processing, networking learning and analysis of social network data.
In this paper, we propose a broader framework that not only encompasses
traditional GSP as a special case, but also includes a hybrid framework of
graph and classical signal processing over a continuous domain. Our framework
relies extensively on concepts and tools from functional analysis to generalize
traditional GSP to graph signals in a separable Hilbert space with infinite
dimensions. We develop a concept analogous to Fourier transform for generalized
GSP and the theory of filtering and sampling such signals
Optimal shape and location of sensors for parabolic equations with random initial data
In this article, we consider parabolic equations on a bounded open connected
subset of . We model and investigate the problem of optimal
shape and location of the observation domain having a prescribed measure. This
problem is motivated by the question of knowing how to shape and place sensors
in some domain in order to maximize the quality of the observation: for
instance, what is the optimal location and shape of a thermometer? We show that
it is relevant to consider a spectral optimal design problem corresponding to
an average of the classical observability inequality over random initial data,
where the unknown ranges over the set of all possible measurable subsets of
of fixed measure. We prove that, under appropriate sufficient spectral
assumptions, this optimal design problem has a unique solution, depending only
on a finite number of modes, and that the optimal domain is semi-analytic and
thus has a finite number of connected components. This result is in strong
contrast with hyperbolic conservative equations (wave and Schr\"odinger)
studied in [56] for which relaxation does occur. We also provide examples of
applications to anomalous diffusion or to the Stokes equations. In the case
where the underlying operator is any positive (possible fractional) power of
the negative of the Dirichlet-Laplacian, we show that, surprisingly enough, the
complexity of the optimal domain may strongly depend on both the geometry of
the domain and on the positive power. The results are illustrated with several
numerical simulations
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Effectiveness of landmark analysis for establishing locality in p2p networks
Locality to other nodes on a peer-to-peer overlay network can be established by means of a set of landmarks shared among the participating nodes. Each node independently collects a set of latency measures to landmark nodes, which are used as a multi-dimensional feature vector. Each peer node uses the feature vector to generate a unique scalar index which is correlated to its topological locality. A popular dimensionality reduction technique is the space filling Hilbert’s curve, as it possesses good locality
preserving properties. However, there exists little comparison between Hilbert’s curve and other techniques for dimensionality reduction. This work carries out a quantitative analysis of their properties. Linear and non-linear techniques for scaling the landmark vectors to a single dimension are investigated. Hilbert’s curve, Sammon’s mapping and Principal Component Analysis
have been used to generate a 1d space with locality preserving properties. This work provides empirical evidence to support the use of Hilbert’s curve in the context of locality preservation when generating peer identifiers by means of landmark vector analysis. A comparative analysis is carried out with an artificial 2d network model and with a realistic network topology model
with a typical power-law distribution of node connectivity in the Internet. Nearest neighbour analysis confirms Hilbert’s curve to be very effective in both artificial and realistic network topologies. Nevertheless, the results in the realistic network model show that there is scope for improvements and better techniques to preserve locality information are required
Conditioning moments of singular measures for entropy optimization. I
In order to process a potential moment sequence by the entropy optimization
method one has to be assured that the original measure is absolutely continuous
with respect to Lebesgue measure. We propose a non-linear exponential transform
of the moment sequence of any measure, including singular ones, so that the
entropy optimization method can still be used in the reconstruction or
approximation of the original. The Cauchy transform in one variable, used for
this very purpose in a classical context by A.\ A.\ Markov and followers, is
replaced in higher dimensions by the Fantappi\`{e} transform. Several
algorithms for reconstruction from moments are sketched, while we intend to
provide the numerical experiments and computational aspects in a subsequent
article. The essentials of complex analysis, harmonic analysis, and entropy
optimization are recalled in some detail, with the goal of making the main
results more accessible to non-expert readers.
Keywords: Fantappi\`e transform; entropy optimization; moment problem; tube
domain; exponential transformComment: Submitted to Indagnationes Mathematicae, I. Gohberg Memorial issu
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