Related papers: Challenges of Matrix Models
We propose to take a look at a new approach to the study of integral polyhedra. The main idea is to give an integral representation, or matrix model representation, for the key combinatorial characteristics of integral polytopes. Based on…
A simple and algorithmic description of matrix shape invariant potentials is presented. The complete lists of generic matrix superpotentials of dimension $2\times2$ and of special superpotentials of dimension $3\times3$ are given…
The paper proposes a logical model of combinatorial problems, also it gives an example of a problem of the class NP that can not be solved in polynomial time on the dimension of the problem.
The spectral problem for matrices with a block-hierarchical structure is often considered in context of the theory of complex systems. In the present article, a new class of matrices with a block-rectangular non-symmetric hierarchical…
In this short paper, we give a complete and affirmative answer to a conjecture on matrix trace inequalities for the sum of positive semidefinite matrices. We also apply the obtained inequality to derive a kind of generalized Golden-Thompson…
We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows…
We give a proposal for future development of the model theory of valued fields. We also summarize some recent results on p-adic numbers.
Cell formation problem is among the first obstacles the designer of cellular production systems must overcome. This paper presents a critical analysis of the various criteria and constraints considered in the literature. The objective is to…
We briefly discuss the current state, and future computational implications, of quantum type theory.
The aim of this paper is to prove an improved version of the bounded differences inequality for matrix valued functions, by developing the methods of Mackey et al.: "Matrix Concentration Inequalities via the Method of Exchangeable Pairs".…
This article is a short review on the relationship between convergent matrix integrals, formal matrix integrals, and combinatorics of maps. We briefly summarize results developed over the last 30 years, as well as more recent discoveries.…
We describe a general approach for computing generators for elimination ideals associated with matrix and hypermatrix spectral decomposition constraints. We derive from these generators iterative procedures for approximating the spectral…
This paper shows the complementary roles of mathematical and engineering points of view when dealing with truss analysis problems involving systems of linear equations and inequalities. After the compatibility condition and the mathematical…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
We consider the reconciliation problem, in which the task is to find a mapping of a gene tree into a species tree, so as to maximize the likelihood of such fitting, given the available data. We describe a model for the evolution of the…
Scaling problems have a rich and diverse history, and thereby have found numerous applications in several fields of science and engineering. For instance, the matrix scaling problem has had applications ranging from theoretical computer…
We survey recent developments in the theory of achievement sets and present a substantial collection of open problems.
It is shown that the world-line can be eliminated in the matrix quantum mechanics conjectured by Banks, Fischler, Shenker and Susskind to describe the light-cone physics of M theory. The resulting matrix model has a form that suggests…
Matrix representations of the Maxwell equations are well-known. However, all these representations lack an exactness or/and are given in terms of a {\em pair} of matrix equations. We present a matrix representation of the Maxwell equation…
This article gives a brief survey of the theory and applications of anomalies.