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Can Recent Innovations in Harmonic Analysis ‘Explain’ Key Findings in Natural Image Statistics?
Recent Innovations Natural Image Statistics
2015/8/21
Recently, applied mathematicians have been pursuing the goal of sparse coding of
certain mathematical models of images with edges. They have found by mathematical
analysis that, instead of wavelets ...
15 Years of Reproducible Research in Computational Harmonic Analysis
Computational Harmonic Analysis 15 Years
2015/8/21
Scientific Computation is emerging as absolutely central to the scientific method. Unfortunately, it is error-prone and currently immature: traditional scientific publication is
inc...
It is known that superpositions of ridge functions (single hidden-layer feedforward neural networks) may give good approximations to certain kinds of multivariate functions. It remains unclear, howeve...
New Ties between Computational Harmonic Analysis and Approximation Theory
Computational Harmonic Analysis Approximation Theory
2015/6/17
Is the connection between approximation theory and harmonic analysis genuine? This question may seem a little provocative,especially in light of the recent literature about the significant interaction...
On Measures on Partitions Arising in Harmonic Analysis for Linear and Projective Characters of the Infinite Symmetric Group
Partitions Arising Harmonic Analysis the Infinite Symmetric Group Combinatorics
2011/8/25
Abstract: The z-measures on partitions originated from the problem of harmonic analysis of linear representations of the infinite symmetric group in the works of Kerov, Olshanski and Vershik (1993, 20...
Harmonic analysis and the Riemann-Roch theorem
Harmonic analysis the Riemann-Roch theorem Algebraic Geometry
2011/8/23
Abstract: This paper is a continuation of papers: arXiv:0707.1766 [math.AG] and arXiv:0912.1577 [math.AG]. Using the two-dimensional Poisson formulas from these papers and two-dimensional adelic theor...
Harmonic analysis of spherical sampling in diffusion MRI
Harmonic analysis spherical sampling diffusion MRI
2011/9/9
In the last decade diffusion MRI has become a powerful tool to non-invasively study white-matter integrity in the brain. Recently many research groups have focused their attention on multi-shell spher...
Computer experiments in harmonic analysis
computer experiment experimental mathematics harmonic analysis analysis on fractals
2009/6/24
It is conventionally understood that computers play a rather limited role in theoretical mathematics. While computation is indispensable in applied mathematics and the theory of computing and algorith...
Modelling Geophysical Fields in Source Free Regions by Fourier Series and Rectangular Harmonic Analysis
Source Fourier Series Rectangular Harmonic Analysis
2009/6/15
Modelling Geophysical Fields in Source Free Regions by Fourier Series and Rectangular Harmonic Analysis.
Study of Tides, Setup and Bottom Friction in a Shallow Semi-Enclosed Basin. Part I：Field Experiment and Harmonic Analysis
Bottom Friction Shallow Semi-Enclosed Basin Tides Setup Field Experiment Harmonic Analysis
2009/2/11
This paper is the first in a series reporting the results of a study of tides, setup and bottom friction in the Bight of Abaco, Bahamas. The paper describes three month-long field experiments. employi...
Harmonic analysis, quadratic forms and asymptotic expansions of risk measures
Quadratic form Gaussian model stationary phase
2010/9/10
In this paper we develop asymptotic expansions of Conditional Value at Risk (CVaR), one of the most widely used risk measures in the financial industry, based on harmonic analysis and the method of st...