Related papers: Selected topics in integrable models
As machine learning systems become ubiquitous, there has been a surge of interest in interpretable machine learning: systems that provide explanation for their outputs. These explanations are often used to qualitatively assess other…
This set of Montreal lectures is an elementary and sketchy introduction to the general field of random matrices. The first half is devoted to combinatorial models, whereas the second half deals with random matrix questions(GUE, etc...).
This is a preliminary version of the textbook on integrable systems. The work has been partly supported by Grant Nr.10/2006-RU, Austrian Academic Exchange Service \"OAD and Grant P20164-N18, Austrian Science Fund FWF
We describe a list of open problems in random matrix theory and the theory of integrable systems that was presented at the conference Asymptotics in Integrable Systems, Random Matrices and Random Processes and Universality, Centre de…
Some aspects of the connection between differential geometry and multidimensional soliton equations are discussed.
We review a surprising correspondence between certain two-dimensional integrable models and the spectral theory of ordinary differential equations. Particular emphasis is given to the relevance of this correspondence to certain problems in…
We discuss the use of methods coming from integrable systems to study problems of enumerative and algebraic combinatorics, and develop two examples: the enumeration of Alternating Sign Matrices and related combinatorial objects, and the…
This introductory paper is structured in the form of an "interview", where the author answers the following questions: Why did you begin working with complex systems? How would you define complexity? What is your favourite aspect/concept of…
We survey a range of models of opinion exchange. From the introduction: "The exchange of opinions between individuals is a fundamental social interaction... Moreover, many models in this field are an excellent playground for mathematicians,…
The purpose of this article is to explore the properties of integrable, purely transmitting, defects placed at the junctions of several one-dimensional domains within a network. The defect sewing conditions turn out to be quite restrictive…
In this short note, we construct a class of models of an extension of homotopy type theory, which we call homotopy type theory with an interval type.
The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit solutions are obtained.
We give a contributed discussion on "Model uncertainty and missing data: An Objective Bayesian Perspective", where we discuss frequentist perspectives on the proposed methodology.
We consider models of CSP based on recording what events are available as possible alternatives to the events that are actually performed. We present many different varieties of such models. For each, we give a compositional semantics,…
Mathematical models are increasingly a part of microbiological research. Here, we share our perspective on how modeling advances the discipline by: (i) enforcing logical consistency, (ii) enabling quantitative prediction, (iii) extracting…
We give an informal introduction to model categories, and treat three important examples in some details: the category of small categories, the category of dg algebras, and the category of small dg categories.
Predictive models are one of the most important techniques that are widely applied in many areas of software engineering. There have been a large number of primary studies that apply predictive models and that present well-preformed studies…
In this note, we investigate some topological properties of probabilistic modular spaces.
A countable class of integrable dynamical systems, with four dimensional phase space and conserved quantities in involution (H\_n,I\_n) are exhibited. For $n=1$ we recover Neumann sytem on T*S^2. All these systems are also integrable at the…
We associate bicomplexes with several integrable models in such a way that conserved currents are obtained by a simple iterative construction. Gauge transformations and dressings are discussed in this framework and several examples are…