相关论文: Set Matrices and The Path/Cycle Problem

Periodic and semi periodic patterns are very common in nature. In this paper we introduce a topological toolbox aiming in detecting and quantifying periodicity. The presented technique is of a general nature and may be employed wherever…

Many well-known combinatorial optimization problems can be stated over the set of acyclic orientations of an undirected graph. For example, acyclic orientations with certain diameter constraints are closely related to the optimal solutions…

Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…

The matrix chain problem consists in finding the parenthesization of a matrix product $M := A_1 A_2 \cdots A_n$ that minimizes the number of scalar operations. In practical applications, however, one frequently encounters more complicated…

The present work has been designed for students in secondary school and their teachers in mathematics. We will show how with the help of our knowledge of number systems we can solve problems from other fields of mathematics for example in…

We consider a direct conversion of the, classical, set splitting problem to the directed Hamiltonian cycle problem. A constructive procedure for such a conversion is given, and it is shown that the input size of the converted instance is a…

Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…

We solve the Matrix Completion (MC) problem based on manifold optimization by incorporating the side information under which the columns of the intended matrix are drawn from a union of low dimensional subspaces. It is proved that this side…

We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…

The matrices of spanning rooted forests are studied as a tool for analysing the structure of networks and measuring their properties. The problems of revealing the basic bicomponents, measuring vertex proximity, and ranking from preference…

This book provides an introduction to path integral methods and their application to modeling atomistic processes. The book covers both the foundational theory and recently developed simulation techniques. The text provides a self-contained…

Tensor networks provide extremely powerful tools for the study of complex classical and quantum many-body problems. Over the last two decades, the increment in the number of techniques and applications has been relentless, and especially…

In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…

This is an expository paper. A $1$-cycle in a graph is a set $C$ of edges such that every vertex is contained in an even number of edges from $C$. E.g., a cycle in the sense of graph theory is a $1$-cycle, but not vice versa. It is easy to…

In problem-solving, a path towards solutions can be viewed as a sequence of decisions. The decisions, made by humans or computers, describe a trajectory through a high-dimensional representation space of the problem. By means of…

Primary Cyclic matrices were used (but not named) by Holt and Rees in their version of Parker's MEAT-AXE algorithm to test irreducibility of finite matrix groups and algebras. They are matrices $X$ with at least one cyclic component in the…

Matrix analysis plays a crucial role in the field of control engineering, providing a powerful mathematical framework for the analysis and design of control systems. This research report explores various applications of matrix analysis in…

Linear trajectory models provide mathematical advantages to autonomous driving applications such as motion prediction. However, linear models' expressive power and bias for real-world trajectories have not been thoroughly analyzed. We…

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…

In this article, we establish a class of new projected type iteration methods based on matrix spitting for solving the linear complementarity problem. Also, we provide a sufficient condition for the convergence analysis when the system…