相关论文: On a construction method of new moment sequences

In this paper, we investigate certain combinatorial numbers, the \textit{moment generating Stirling numbers}. They are a special case of Hsu's generalized Stirling numbers and satisfy many more properties and combinatorial identities than…

Machine-learning techniques have been recently used with spectacular results to generate artefacts such as music or text. However, these techniques are still unable to capture and generate artefacts that are convincingly structured. In this…

For delta operator $aD-bD^{p+1}$ we find the corresponding polynomial sequence of binomial type and relations with Fuss numbers. In the case $D-\frac{1}{2}D^2$ we show that the corresponding Bessel-Carlitz polynomials are moments of the…

Scattered sequences are a generalization of scattered polynomials. So far, only scattered sequences of order one and two have been constructed. In this paper an infinite family of scattered sequences of order three is obtained. Equivalence…

This paper deals with algorithms for producing and ordering lexical and nonlexical sequences of a given degree. The notion of "elementary operations" on positive integral sequences is introduced. Our main theorem answers the question of…

The dominant approach to sequence generation is to produce a sequence in some predefined order, e.g. left to right. In contrast, we propose a more general model that can generate the output sequence by inserting tokens in any arbitrary…

The main goal of this paper is to study the different definitions of generating sequences appearing in the literature. We present these definitions and show that under certain situations they are equivalent. We also present an example that…

We investigate conditions in order to decide whether a given sequence of real numbers represents expected record values arising from an independent, identically distributed, sequence of random variables. The main result provides a necessary…

In this work, we present a method to generate probability distributions and classes of probability distributions, which broadens a process of probability distribution construction. In this method, distribution classes are built from…

Spectral methods of moments provide a powerful tool for learning the parameters of latent variable models. Despite their theoretical appeal, the applicability of these methods to real data is still limited due to a lack of robustness to…

Linear recurrent sequences are those whose elements are defined as linear combinations of preceding elements, and finding recurrence relations is a fundamental problem in computer algebra. In this paper, we focus on sequences whose elements…

Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step…

The uniform probability measure on a convex polytope induces piecewise polynomial densities on its projections. For a fixed combinatorial type of simplicial polytopes, the moments of these measures are rational functions in the vertex…

Video sequences contain rich dynamic patterns, such as dynamic texture patterns that exhibit stationarity in the temporal domain, and action patterns that are non-stationary in either spatial or temporal domain. We show that a…

We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample…

A polynomial is presented that models a topological knot in a unique manner. It distinguishes all types of knots including the orientation and has a group theory interpretation. The topologies may be labeled via a number, which upon a base…

Using the theory of exponential Riordan arrays and orthogonal polynomials, we demonstrate that the "descending power" Eulerian polynomials, and their once shifted sequence, are moment sequences for simple families of orthogonal polynomials,…

We describe new, simple, recursive methods of construction for orientable sequences over an arbitrary finite alphabet, i.e. periodic sequences in which any sub-sequence of n consecutive elements occurs at most once in a period in either…

A new angular momentum projection for systems of particles with arbitrary spins is formulated based on the Heine-Stieltjes correspondence, which can be regarded as the solutions of the mean-field plus pairing model in the strong pairing…

We introduce a novel method for obtaining a wide variety of moments of any random variable with a well-defined moment-generating function (MGF). We derive new expressions for fractional moments and fractional absolute moments, both central…