相关论文: On a new multivariate sampling paradigm and a poly…
In this paper we address sampling and approximation of functions on combinatorial graphs. We develop filtering on graphs by using Schr\"odinger's group of operators generated by combinatorial Laplace operator. Then we construct a sampling…
We study the problem of reconstructing a function on a manifold satisfying some mild conditions, given data on the values and some derivatives of the function at arbitrary points on the manifold. While the problem of finding a polynomial of…
Radial basis functions are a common mathematical tool used to construct a smooth interpolating function from a set of data points. A spatial prior based on thin-plate spline radial basis functions can be easily implemented resulting in a…
Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we…
We formulate an info-clustering paradigm based on a multivariate information measure, called multivariate mutual information, that naturally extends Shannon's mutual information between two random variables to the multivariate case…
Entropy is a fundamental property of both classical and quantum systems, spanning myriad theoretical and practical applications in physics and computer science. We study the problem of obtaining estimates to within a multiplicative factor…
We use an interpolative technique from \cite{abps} to introduce the notion of multiple $N$-separately summing operators. Our approach extends and unifies some recent results; for instance we recover the best known estimates of the…
Successive differences on a sequence of data help to discover some smoothness features of this data. This was one of the main reasons for rewriting the classical interpolation formula in terms of such data differences. The aim of this paper…
Density estimation is a fundamental technique employed in various fields to model and to understand the underlying distribution of data. The primary objective of density estimation is to estimate the probability density function of a random…
It is not obvious how to extend Shannon's original information entropy to higher dimensions, and many different approaches have been tried. We replace the English text symbol sequence originally used to illustrate the theory by a discrete,…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…
We study reduction schemes for functions of "many" variables into system of functions in one variable. Our setting includes infinite-dimensions. Following Cybenko-Kolmogorov, the outline for our results is as follows: We present explicit…
We obtain sampling and interpolation theorems in radial weighted spaces of analytic functions for weights of arbitrary (more rapid than polynomial) growth. We give an application to invariant subspaces of arbitrary index in large weighted…
The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions of two variables. By using these type polynomials, we derive recurrence formulas and some new interesting identities related to the second…
A lemma of Micchelli's, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary linear functionals, as is Schaback's more recent extension of this lemma and Schaback's result concerning…
In this paper we give explicit closed forms for the semi-reproducing kernels associated with thinplate spline interpolation on the sphere. Polyharmonic or thinplate splines for ${\mathbb R}^d$ were introduced by Duchon and have become a…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
The development of high-degree interpolation polynomials which use the values of the function and its subsequent derivatives is reformulated. Also, we present a variant of new formula in barycentric form.
This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as…