相关论文: Decompositions for Sum-of-Power Statistics and the…
We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer…
In a former paper it has been shown that the elliptic Gau{\ss} sums, whose use has been proposed in the context of counting points on elliptic curves and primality tests, can be computed by using modular functions. In this work we give…
Distributed data aggregation is an important task, allowing the decentralized determination of meaningful global properties, that can then be used to direct the execution of other applications. The resulting values result from the…
The paper deals with the construction of images from visibilities acquired using aperture synthesis instruments: Fourier synthesis, deconvolution, and spectral interpolation/extrapolation. Its intended application is to specific situations…
Uniform bin width histograms are widely used so this data graphic should represent data as correctly as possible. Method of moments based on familiar mean, variance and Fisher-Pearson skewness cure this problem.
The Macaulay2 package SumsOfSquares decomposes polynomials as sums of squares. It is based on methods to rationalize sum-of-squares decompositions due to Parrilo and Peyrl. The package features a data type for sums-of-squares polynomials,…
Modern scientific simulations, observations, and large-scale experiments generate data at volumes that often exceed the limits of storage, processing, and analysis. This challenge drives the development of data reduction methods that…
In this thesis, a new class of algorithms based on Sums of Squares Programming is developed. These allow to reduce a degree-$d$ homogeneous polynomial $T = \sum_{i = 1}^m \langle a_i, X \rangle^d $ to a quadratic form being close to a…
One major deficiency of most semantic representation techniques is that they usually model a word type as a single point in the semantic space, hence conflating all the meanings that the word can have. Addressing this issue by learning…
Researchers increasingly use meta-analysis to synthesize the results of several studies in order to estimate a common effect. When the outcome variable is continuous, standard meta-analytic approaches assume that the primary studies report…
We propose a sampling-based method for computing the tensor ring (TR) decomposition of a data tensor. The method uses leverage score sampled alternating least squares to fit the TR cores in an iterative fashion. By taking advantage of the…
We analyze the statistical complexity vs. entropy plane-representation of sampled chaotic attractors as a function of the sampling period {\tau}. It is shown that if the Bandt and Pompe procedure is used to assign a probability distribution…
The negative multinomial distribution appears in many areas of applications such as polarimetric image processing and the analysis of longitudinal count data. In previous studies, Mosimann (1963) derived general formulas for the falling…
We develop a new approach for estimating the expected values of nonlinear functions applied to multivariate random variables with arbitrary distributions. Rather than assuming a particular distribution, we assume that we are only given the…
The purpose of the present paper is to establish moment estimates of Rosenthal type for a rather general class of random variables satisfying certain bounds on the cumulants. We consider sequences of random variables which satisfy a central…
In this article, $q$-regular sequences in the sense of Allouche and Shallit are analysed asymptotically. It is shown that the summatory function of a regular sequence can asymptotically be decomposed as a finite sum of periodic fluctuations…
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is not very realistic in many applications. In addition,…
Let n points be taken at random on a circle of unit circumference and clockwise ordered. Uniform spacings are defined as the clockwise arc-lengths between the successive points from this sample. We are interested in the asymptotic behavior…
We propose an iterative algorithm for the numerical computation of sums of squares of polynomials approximating given data at prescribed interpolation points. The method is based on the definition of a convex functional $G$ arising from the…
Sample coordination, where similar instances have similar samples, was proposed by statisticians four decades ago as a way to maximize overlap in repeated surveys. Coordinated sampling had been since used for summarizing massive data sets.…