Related papers: Introduction to the SK model
Introduction to papers on the modeling and analysis of network data
We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…
This is a survey on stated skein algebras and their representations.
We review recent findings on spin glass models. Both the equilibrium properties and the dynamic properties are covered. We focus on progress in theoretical, in particular numerical, studies, while its relationship to real magnetic materials…
We make some observation on the logarithmic version of K-stability.
In this note, we consider a SK (Sherrington--Kirkpatrick)-type model on Z^d for d greater or equal to 1, weighted by a function allowing to any single spin to interact with a small proportion of the other ones. In the thermodynamical limit,…
This article summarizes the various ways one may use to construct the Skew Brownian motion, and shows their connections. Recent applications of this process in modelling and numerical simulation motivates this survey. This article ends with…
Mathematical induction is a fundamental tool in computer science and mathematics. Henkin initiated the study of formalization of mathematical induction restricted to the setting when the base case B is set to singleton set containing 0 and…
The Mat\'ern model has been a cornerstone of spatial statistics for more than half a century. More recently, the Mat\'ern model has been central to disciplines as diverse as numerical analysis, approximation theory, computational…
Some recent developments in the theory of quantum spin systems are reviewed.
Lecture-notes: introducing and discussing basic kp concepts related to bands interaction at an elementary level to beginners
Mathematical models are an important tool for neuroscientists. During the last thirty years many papers have appeared on single neuron description and specifically on stochastic Integrate and Fire models. Analytical results have been proved…
The evolution of the Sakata model is described on the basis of personal recollections, proceedings of international conferences on high energy physics and some journal articles.
In this paper, we discuss the problem of the software engineering of a class of business spreadsheet models. A methodology for structured software development is proposed, which is based on structured analysis of data, represented as…
In this article we survey some of the recent developments in the structure theory of set addition.
Over the past 50 years, spin glass models have generated a broad range of literature in mathematics, physics, and computer science. There has been much progress in characterizing and proving the limiting free energy of various models,…
This is the draft version of a review paper which is going to appear in "Advances in Imaging and Electron Physics"
This expository article is based on the author's talk at the Kinosaki Algebraic Geometry Symposium 2025. We discuss some recent progress surrounding stable degeneration in algebraic K-stability theory.
This short communication develops a new numerical procedure suitable for a large class of ordinary differential equation systems found in models in physics and engineering. The main numerical procedure is analogous to those concerning the…
This paper is an introduction to the modelling of viscoelastic fluids, with an emphasis on micro-macro (or multiscale) models. Some elements of mathematical and numerical analysis are provided. These notes closely follow the lectures…