相关论文: Multiresolution analysis in statistical mechanics.…
In this work, we prove that certain L^2-unbounded transformations of orthogonal wavelet bases generate vaguelets. The L^2-unbounded functions involved in the transformations are assumed to be quasi-homogeneous at high frequencies. We…
We present a preconditioning method for the multi-dimensional Helmholtz equation with smoothly varying coefficient. The method is based on a frame of functions, that approximately separates components associated with different singular…
This paper considers the problem of adaptive estimation of a mean pattern in a randomly shifted curve model. We show that this problem can be transformed into a linear inverse problem, where the density of the random shifts plays the role…
Thermodynamics, introduced over two centuries ago, remains foundational to our understanding of physical, chemical, biological, and engineering systems. Its principles are traditionally grounded in the statistical mechanics framework, which…
A method for computing the Hankel transform is proposed whereby the letter is reduced to a sum by representing the integrand as a smooth function times a Bessel function. The smooth function is replaced by its wavelet decomposition with a…
Using a prime element of a local field K of positive characteristic p, the concepts of multiresolution analysis (MRA) and wavelet can be generalized to such a field. We prove a version of the splitting lemma for this setup and using this…
In a multicellular organism different cell types express a gene in different amounts. Samples from which gene expression levels can be measured typically contain a mixture of different cell types, the resulting measurements thus give only…
Samplets are data adapted multiresolution analyses of localized discrete signed measures. They can be constructed on scattered data sites in arbitrary dimension such that they exhibit vanishing moments with respect to any prescribed set of…
The Density Matrix Renormalization Group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and…
The article considers the nonlinear inverse problem of identifying the material parameters in viscoelastic structures based on a generalized Maxwell model. The aim is to reconstruct the model parameters from stress data acquired from a…
The empirical wavelet transform is a fully adaptive time-scale representation that has been widely used in the last decade. Inspired by the empirical mode decomposition, it consists of filter banks based on harmonic mode supports. Recently,…
We develop the laws of thermodynamics in terms of general exponential families. By casting learning (log-loss minimization) problems in max-entropy and statistical mechanics terms, we translate thermodynamics results to learning scenarios.…
Multiplicative cascades are often used to represent the structure of multiscaling variables in many physical systems, specially turbulent flows. In processes of this kind, these variables can be understood as the result of a successive…
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
We present a novel coarse-to-fine framework that derives a semi-regular multiscale mesh representation of an original input mesh via remeshing. Our approach differs from the conventional mesh wavelet transform strategy in two ways. First,…
The excavation process in mechanized tunneling can be improved by reconnaissance of the geology ahead. A nondestructive exploration can be achieved in means of seismic imaging. A full waveform inversion approach, which works in the…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…
Surface-consistent deconvolution is a standard processing technique in land data to uniformize the wavelet across all sources and receivers. The required wavelet estimation step is generally done in the homomorphic domain since this is a…
With the help of a general expression of the entropies in extensive and nonextensive systems, some important relations between thermodynamics and statistical mechanics are revealed through the views of thermodynamics and statistic physics.…
The multiresolution analysis of Alpert is considered. Explicit formulas for the entries in the matrix coefficients of the refinement equation are given in terms of hypergeometric functions. These entries are shown to solve generalized…