Related papers: SPM Bulletin 34
In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.
I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical…
This paper, in French, is a celebration of Max Dehn, and an essay of describing some of his results published in the beginning of the 1910's, and their offspring. It has been written up for a winter school in Les Diablerets, March 7-12,…
This work provides explicit characterizations and formulae for the minimal polynomials of a wide variety of structured $4\times 4$ matrices. These include symmetric, Hamiltonian and orthogonal matrices. Applications such as the complete…
The allocation of scarce spectral resources to support as many user applications as possible while maintaining reasonable quality of service is a fundamental problem in wireless communication. We argue that the problem is best formulated in…
We study the submodular secretary problem with a cardinality constraint. In this problem, $n$ candidates for secretaries appear sequentially in random order. At the arrival of each candidate, a decision maker must irrevocably decide whether…
The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…
Topology optimization facilitates the automated design of high-performance structures across various engineering fields but, if unconstrained, often produces designs that are complex and difficult to manufacture. A key attribute of the…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
We give a self-contained and enriched review about topology properties in the rapidly growing field of topological states of matter (TSM). This review is mainly focus on the beautiful interplay of topology mathematics and condensed matter…
Possibilities for using geometry and topology to analyze statistical problems in biology raise a host of novel questions in geometry, probability, algebra, and combinatorics that demonstrate the power of biology to influence the future of…
The article contains some important classes of multisets. Combinatorial proofs of problems on the number of m-submultisets and m-permutations of multiset elements are considered and effective algorithms for their calculation are given. In…
This chapter reviews the microeconometrics literature on partial identification, focusing on the developments of the last thirty years. The topics presented illustrate that the available data combined with credible maintained assumptions…
This chapter investigates how symmetries can be used to reduce the computational complexity in polynomial optimization problems. A focus will be specifically given on the Moment-SOS hierarchy in polynomial optimization, where results from…
We investigate the optimal configurations of n points on the unit sphere for a class of potential functions. In particular, we characterize these optimal configurations in terms of their approximation properties within frame theory.…
This paper presents a new combinatorial optimisation task, the Subset Sum Matching Problem (SSMP), which is an abstraction of common financial applications such as trades reconciliation. We present three algorithms, two suboptimal and one…
In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.
We give new results for problems in computational and statistical machine learning using tools from high-dimensional geometry and probability. We break up our treatment into two parts. In Part I, we focus on computational considerations in…
We consider methods for aggregating preferences that are based on the resolution of discrete optimization problems. The preferences are represented by arbitrary binary relations (possibly weighted) or incomplete paired comparison matrices.…
During the last decade, the matroid secretary problem (MSP) became one of the most prominent classes of online selection problems. Partially linked to its numerous applications in mechanism design, substantial interest arose also in the…