Related papers: Phenomenological studies in the matrix models
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
We construct six- and four-dimensional toroidal compactifications of the Type I string with magnetic flux on the D-branes. The open strings in this background probe a noncommutative internal geometry. Phenomenologically appealing features…
We review several problems of conventional Grand Unification and some new approaches. In particular, we discuss strongly coupled Grand Unified Theories. Standard Model may emerge as a low energy effective theory of composite particles in…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…
The book is devoted to investigation of arithmetic of the matrix rings over certain classes of commutative finitely generated principal ideals domains. We mainly concentrate on constructing of the matrix factorization theory. We reveal a…
The present work provides an original framework for random matrix analysis based on revisiting the concentration of measure theory from a probabilistic point of view. By providing various notions of vector concentration ($q$-exponential,…
We review for non-experts possible phenomenological scenari in String Theory. In particular we focus on vacuum configurations with intersecting and/or magnetized unoriented D-branes. We will show how a TeV scale tension may be compatible…
Pseudospectral analysis serves as a powerful tool in matrix computation and the study of both linear and nonlinear dynamical systems. Among various numerical strategies, random sampling, especially in the form of rank-$1$ perturbations,…
The recent developments in string theory suggest that the space-time coordinates should be generalized to non-commuting matrices. Postulating this suggestion as the fundamental geometrical principle, we formulate a candidate for covariant…
Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on…
We study compactifications of Matrix theory on twisted tori and non-commutative versions of them. As a first step, we review the construction of multidimensional twisted tori realized as nilmanifolds based on certain nilpotent Lie algebras.…
The perturbation theory based on typicality introduced in Ref. [1] and further refined in Refs. [2, 3] provides a powerful tool since it is intended to be applicable to a wide range of scenarios while relying only on a few parameters. Even…
Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…
After a brief review on Matrix String Theory on flat backgrounds, we formulate matrix string models on different pp-wave backgrounds. This will be done both in the case of constant and variable RR background flux for certain exact string…
We utilize a recently developed topic modeling method called SeNMFk, extending the standard Non-negative Matrix Factorization (NMF) methods by incorporating the semantic structure of the text, and adding a robust system for determining the…
I briefly review the present status of bosonic strings and discretized random surfaces in D>1 which seem to be in a polymer rather than stringy phase. As an explicit example of what happens, I consider the Kazakov-Migdal model with a…
Normalizing Flows are a promising new class of algorithms for unsupervised learning based on maximum likelihood optimization with change of variables. They offer to learn a factorized component representation for complex nonlinear data and,…
A brief discussion is presented assessing the achievements and challenges of string phenomenology: the subfield dedicated to study the potential for string theory to make contact with particle physics and cosmology. Building from the well…
Factorization models express a statistical object of interest in terms of a collection of simpler objects. For example, a matrix or tensor can be expressed as a sum of rank-one components. However, in practice, it can be challenging to…