相关论文: SPM Bulletin 1

The Abelian Sandpile Model (ASM) is a game played on a graph realizing the dynamics implicit in the discrete Laplacian matrix of the graph. The purpose of this primer is to apply the theory of lattice ideals from algebraic geometry to the…

Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…

This text arises from teaching advanced undergraduate courses in differential topology for the master curriculum in Mathematics at the University of Pisa. So it is mainly addressed to motivated and collaborative master undergraduate…

Nearly all practical applications of the theory of characteristic modes (CMs) involve the use of computational tools. Here in Paper 2 of this Series on CMs, we review the general transformations that move CMs from a continuous theoretical…

We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between…

MFPS conferences are dedicated to the areas of mathematics, logic, and computer science that are related to models of computation in general, and to semantics of programming languages in particular. This is a forum where researchers in…

The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…

In the first part of this expository paper, we present and discuss the interplay of Dirichlet polynomials in some classical problems of number theory, notably the Lindel\"of Hypothesis. We review some typical properties of their means and…

This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…

Many real world problems naturally appear as constraints satisfaction problems (CSP), for which very efficient algorithms are known. Most of these involve the combination of two techniques: some direct propagation of constraints between…

Representing texts as fixed-length vectors is central to many language processing tasks. Most traditional methods build text representations based on the simple Bag-of-Words (BoW) representation, which loses the rich semantic relations…

This paper is the second in a series of planned papers which provide first bijective proofs of alternating sign matrix results. Based on the main result from the first paper, we construct a bijective proof of the enumeration formula for…

This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non-overlapping circles. The first half of the article is an exposition of…

In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal…

A core problem in statistics and probabilistic machine learning is to compute probability distributions and expectations. This is the fundamental problem of Bayesian statistics and machine learning, which frames all inference as…

We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…

This paper contains selected applications of the new tangential extremal principles and related results developed in Part I to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite…

In the paper "An Abelian Loop for Non-Composites" (arXiv:110.14716), we introduced a group-like structure consisting of odd prime numbers and 1, with properties that allowed us to prove analogous results to well known theorems in Number…

The paper studies the notion of supposition encoded in non-Archimedean conditional probability (and revealed in the acceptance of the so-called indicative conditionals). The notion of qualitative change of view that thus arises is…

We study the set of all pseudoline arrangements with contact points which cover a given support. We define a natural notion of flip between these arrangements and study the graph of these flips. In particular, we provide an enumeration…