相关论文: Three Recitations on Holonomic Systems and Hyperge…

Several methods for generating random Steiner triple systems (STSs) have been proposed in the literature, such as Stinson's hill-climbing algorithm and Cameron's algorithm, but these are not yet completely understood. Those algorithms, as…

These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…

This work builds on earlier work of the first three authors where a notion of congruence modules in higher codimension is introduced. The main new results are a criterion for detecting regularity of local rings in terms of congruence…

We show how to prove the examples of a paper by Chu and Zhang using the WZ-algorithm.

In this paper, we first quickly review the basics of an algebro-geometric method of Karaji's L-summing technique in today's modern language of algebra. Then, we also review the theory of Gosper's algorithm as a decision procedure for…

In an earlier paper we showed that we can improve results by Emmy Noether and Alexander Ostrowski concerning the reducibility modulo p of absolutely irreducible polynomials with integer coefficients by giving the problem a geometric turn…

MM (majorization--minimization) algorithms are an increasingly popular tool for solving optimization problems in machine learning and statistical estimation. This article introduces the MM algorithm framework in general and via three…

Relationships that exist between the classical, Shannon-type, and geometric-based approaches to sampling are investigated. Some aspects of coding and communication through a Gaussian channel are considered. In particular, a constructive…

We propose a systematic method for constructing Wilf-Zeilberger (WZ) seeds and present seven WZ seeds. We also demonstrate how to construct WZ seeds from existing ones. With these WZ seeds, several hypergeometric identities are derived. The…

The work presents an extension of the fuzzy approach to 2-D shape recognition [1] through refinement of initial or coarse classification decisions under a two pass approach. In this approach, an unknown pattern is classified by refining…

These three lectures present some fundamental and classical aspects of microlocal analysis. Starting with the Sato's microlocalization functor and the microsupport of sheaves, we then construct a microlocal analogue of the Hochschild…

10 years ago or so Bill Helton introduced me to some mathematical problems arising from semidefinite programming. This paper is a partial account of what was and what is happening with one of these problems, including many open questions…

We construct the Wess-Zumino-Witten (WZW) term in lattice gauge theory by using a Dirac operator which obeys the Ginsparg-Wilson relation. Topological properties of the WZW term known in the continuum are reproduced on the lattice as a…

This is an introduction to Bayesian inference with a focus on hierarchical models and hyper-parameters. We write primarily for an audience of Bayesian novices, but we hope to provide useful insights for seasoned veterans as well. Examples…

Superintegrable systems are classical and quantum Hamiltonian systems which enjoy much symmetry and structure that permit their solubility via analytic and even, algebraic means. They include such well-known and important models as the…

A powerful approach to computing Feynman integrals or cosmological correlators is to consider them as solution to systems of differential equations. Often these can be chosen to be Gelfand-Kapranov-Zelevinsky (GKZ) systems. However, their…

Holonomy groups and holonomy algebras for connections on locally free sheaves over supermanifolds are introduced. A one-to-one correspondence between parallel sections and holonomy-invariant vectors, and a one-to-one correspondence between…

In this paper, we generalize image (texture) statistical descriptors and propose algorithms that improve their efficacy. Recently, a new method showed how the popular Co-Occurrence Matrix (COM) can be modified into a fuzzy version (FCOM)…

This is an expository article on the techniques of quantization as they are applied to Gromov-Witten theory and related areas.

This article aims to review a selection of central topics and examples in logarithmic conformal field theory. It begins with a pure Virasoro example, critical percolation, then continues with a detailed exposition of symplectic fermions,…