Related papers: Supermembranes and Super Matrix Models
We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.
The problem of membrane topology in the matrix model of M-theory is considered. The matrix regularization procedure, which makes a correspondence between finite-sized matrices and functions defined on a two-dimensional base space, is…
There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing…
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…
Various aspects of Supersymmetry in 1-dimensional systems are analyzed.
We present a spectral theory of hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of "hyperdeterminants" of hypermatrices, a.k.a.…
Deep learning has received considerable empirical successes in recent years. However, while many ad hoc tricks have been discovered by practitioners, until recently, there has been a lack of theoretical understanding for tricks invented in…
We discuss how to construct open membranes in the recently proposed matrix model of M theory. In order to sustain an open membrane, two boundary terms are needed in the construction. These boundary terms are available in the system of the…
Over algebraically closed fields of characteristic p>2, prolongations of the simple finite dimensional Lie algebras and Lie superalgebras with Cartan matrix are studied for certain simplest gradings of these algebras. Several new simple Lie…
The discussion of enhancement of superconductivity is presented in the framework of the higher-grade hybrid model of layered superconductors. The enhancement is considered from the following two points of view: (i) as a result of long-range…
We discuss current theoretical and experimental issues associated with the recent SuperKamiokande discovery. We survey theoretical models for predictings the new Standard Model parameters needed to explain this discovery, and point out how…
As the deep learning revolution marches on, self-supervised learning has garnered increasing attention in recent years thanks to its remarkable representation learning ability and the low dependence on labeled data. Among these varied…
We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
This article reviews the subject of supersymmetry and its breaking. The emphasis is on recent developments in metastable, dynamical supersymmetry breaking, which permit the construction of promising models of particle physics.
In the last six years remarkable developments have taken place concerning the representation theory of N=2 superconformal algebras. Here we present the highlights of such developments.
The paper describes some recent developments in neural networks and discusses the applicability of neural networks in the development of a machine that mimics the human brain. The paper mentions a new architecture, the pulsed neural network…
In this revised version we correct some mistakes, realizing the supersymmetry algebra on the exact S matrix, taking into account several phase factros. We study the constraint imposed by supersymmetry on the exact $S$-matrix of $\Complex…
This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first order theory of finite groups. The focus is on concepts from stability theory…
Human pluripotent stem cells hold great promise for developments in regenerative medicine and drug design. The mathematical modelling of stem cells and their properties is necessary to understand and quantify key behaviours and develop…