16,674 research outputs found
Multiresolution analysis in statistical mechanics. I. Using wavelets to calculate thermodynamic properties
The wavelet transform, a family of orthonormal bases, is introduced as a
technique for performing multiresolution analysis in statistical mechanics. The
wavelet transform is a hierarchical technique designed to separate data sets
into sets representing local averages and local differences. Although
one-to-one transformations of data sets are possible, the advantage of the
wavelet transform is as an approximation scheme for the efficient calculation
of thermodynamic and ensemble properties. Even under the most drastic of
approximations, the resulting errors in the values obtained for average
absolute magnetization, free energy, and heat capacity are on the order of 10%,
with a corresponding computational efficiency gain of two orders of magnitude
for a system such as a Ising lattice. In addition, the errors in
the results tend toward zero in the neighborhood of fixed points, as determined
by renormalization group theory.Comment: 13 pages plus 7 figures (PNG
Reversible implementation of a disrete linear transformation
Discrete linear transformations form important steps in processing information. Many such transformations are injective and therefore are prime candidates for a physically reversible implementation into hardware. We present here the first steps towards a reversible digital implementation of two different integer transformations on four inputs: The Haar wavelet and the H.264 transform
Sparsity and Incoherence in Compressive Sampling
We consider the problem of reconstructing a sparse signal from a
limited number of linear measurements. Given randomly selected samples of
, where is an orthonormal matrix, we show that minimization
recovers exactly when the number of measurements exceeds where is the number of
nonzero components in , and is the largest entry in properly
normalized: . The smaller ,
the fewer samples needed.
The result holds for ``most'' sparse signals supported on a fixed (but
arbitrary) set . Given , if the sign of for each nonzero entry on
and the observed values of are drawn at random, the signal is
recovered with overwhelming probability. Moreover, there is a sense in which
this is nearly optimal since any method succeeding with the same probability
would require just about this many samples
Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity
We present an in-depth investigation of the momentum
space describing point particles coupled to Einstein gravity in three
space-time dimensions. We introduce different sets of coordinates on the group
manifold and discuss their properties under Lorentz transformations. In
particular we show how a certain set of coordinates exhibits an upper bound on
the energy under deformed Lorentz boosts which saturate at the Planck energy.
We discuss how this deformed symmetry framework is generally described by a
quantum deformation of the Poincar\'e group: the quantum double of . We then illustrate how the space of functions on the group
manifold momentum space has a dual representation on a non-commutative space of
coordinates via a (quantum) group Fourier transform. In this context we explore
the connection between Weyl maps and different notions of (quantum) group
Fourier transform appeared in the literature in the past years and establish
relations between them
An optimal factor analysis approach to improve the wavelet-based image resolution enhancement techniques
The existing wavelet-based image resolution enhancement techniques have many assumptions, such as limitation of the way to generate low-resolution images and the selection of wavelet functions, which limits their applications in different fields. This paper initially identifies the factors that effectively affect the performance of these techniques and quantitatively evaluates the impact of the existing assumptions. An approach called Optimal Factor Analysis employing the genetic algorithm is then introduced to increase the applicability and fidelity of the existing methods. Moreover, a new Figure of Merit is proposed to assist the selection of parameters and better measure the overall performance. The experimental results show that the proposed approach improves the performance of the selected image resolution enhancement methods and has potential to be extended to other methods
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