Related papers: Descriptive inner model theory
Statistical learning theory provides the theoretical basis for many of today's machine learning algorithms. In this article we attempt to give a gentle, non-technical overview over the key ideas and insights of statistical learning theory.…
A Short Course on Frame Theory.
In this article, we review the mathematical modeling for the vascular system.
In the sixties,the first author and R.Kasanin have started developing a mean field theory of dense matter.This paper presents a short review of the basic ideas of the theory,and discusses some examples of its applications,which range from…
Politics is everywhere. In this paper, I propose a simple model to demonstrate political behavior in human society.
This is a survey on spectral theory of dynamical systems.
This article introduces patterns of ideals of numerical semigroups, thereby unifying previous definitions of patterns of numerical semigroups. Several results of general interest are proved. More precisely, this article presents results on…
The aim of the paper is to start to develop the most general theory of localizations/inversion. Several new concepts are introduced and studied.
This paper is the extended introduction of a serie of papers about modelling T-homotopy by refinement of observation. The notion of T-homotopy equivalence is discussed. A new one is proposed and its behaviour with respect to other…
This survey paper is an expanded version of lectures given at the Clay Mathematics Academy ; see http://www.claymath.org/programs/outreach/academy/colloquium2005.php These lectures were intended to very young (and motivated) college…
The model is a particular case of causal set. This is a discrete model of spacetime in a microscopic level. In paper the most general properties of the model are investigated without any reference to a dynamics. The dynamics of the model is…
This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed.…
We present an accessible introduction to basic results on groups of intermediate growth.
A survey of tilings in the plane for a general audience.
This text is an introduction to the study of NIP (or dependent) theories. It is meant to serve two purposes. The first is to present various aspects of NIP theories and give the reader the background material needed to understand almost any…
In this paper, we study the structure of a generalized near-group fusion category and classified it when it is slightly degenerate.
We give a characterization of decomposition theory in linear algebra.
The main aim of this work is to present the interpretation of the Ising type models as a kind of field theory in the framework of noncommutative geometry. We present the method and construct sample models of field theory on discrete spaces…
Model theoretic internality provides conditions under which the group of automorphisms of a model over a reduct is itself a definable group. In this paper we formulate a categorical analogue of the condition of internality, and prove an…
This paper has been withdrawn. With the advancement of statistical theory and computing power, data sets are providing a greater amount of insight into the problems of today. Statisticians have an ever increasing number of tools to attack…