Related papers: SPM Bulletin 5 (Special issue)

Quantum tunneling across multiple barriers as yet is an unsolved problem for barrier numbers greater than five. The complexity of the mathematical analysis even for small number of barriers pushed it into the realms of Numerical Analysis.…

Solving optimization problems is the key to decision making in many real-life analytics applications. However, the coefficients of the optimization problems are often uncertain and dependent on external factors, such as future demand or…

The main thrust of our current work is to exploit very specific characteristics of a given problem in order to acquire improved compactness for supercritical problems and to prove existence of new types of solutions. To this end, we shall…

We have recently presented a method to solve an overdetermined linear system of equations with multiple right hand side vectors, where the unknown matrix is to be symmetric and positive definite. The coefficient and the right hand side…

In the machine learning system, the hybrid model parallelism combining tensor parallelism (TP) and pipeline parallelism (PP) has become the dominant solution for distributed training of Large Language Models~(LLMs) and Multimodal LLMs…

Contents: 1. Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces, I; 2. Frechet-Urysohn fans in free topological groups; 3. Packing index of subsets in Polish groups; 4.…

We introduce a lower bounding technique for the min max correlation clustering problem and, based on this technique, a combinatorial 4-approximation algorithm for complete graphs. This improves upon the previous best known approximation…

Semiring algebras have been shown to provide a suitable language to formalize many noteworthy combinatorial problems. For instance, the Shortest-Path problem can be seen as a special case of the Algebraic-Path problem when applied to the…

Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for Alternating Minimization have been hard to come by and are still…

In the September 1994 issue of Math Horizons the following problem is given in the Problem Section (p. 33, Problem 5): Lowest Terms - what fraction has the smallest denominator in the interval (19/94, 17/76)? In this paper we develop a…

In this paper we introduce two new methods for constructing injective resolutions of sheaves of finite-dimensional vector spaces on finite posets. Our main result is the existence and uniqueness of a minimal injective resolution of a given…

We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local…

A surprising number of new results in "core" SPM in the last quarter of 2007, and some other beautiful fundamental results are announced.

Semi-Infinite Programming (SIP) has emerged as a powerful framework for modeling problems with infinite constraints, however, its theoretical development in the context of nonconvex and large-scale optimization remains limited. In this…

The Standard Model (SM) of particle physics provides a very successful description of fundamental particles and their interactions but it is incomplete, as neutrino masses, dark matter and the baryon asymmetry of the Universe indicate. In…

This short note describes the tentative form of a finite-dimensional optimization problem that may be of use in a second-generation proof of the Kepler conjecture. In the original 1998 proof of the Kepler conjecture, the form of the…

CONTENTS OF THE ISSUE: Hurewicz-like tests for Borel subsets of the plane; Ordered Spaces, Metric Preimages, and Function Algebras; On the independence of a generalized statement of Egoroff's theorem from ZFC, after T. Weiss; Forty…

In this paper we study the following problems: given a finite number of nonempty closed subsets of a normed space, find a ball with the smallest radius that encloses all of the sets, and find a ball with the smallest radius that intersects…

We consider the problem of revealing a small hidden lattice from the knowledge of a low-rank sublattice modulo a given sufficiently large integer -- the {\em Hidden Lattice Problem}. A central motivation of study for this problem is the…

Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, one converts it into a system of sparse equations, and then…