Related papers: A lecture on cluster expansions
In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…
In this paper we develop a general theory which provides a unified treatment of two apparently different problems. The weak Gibbs property of measures arising from the application of Renormalization Group maps and the mixing properties of…
We give a precise definition of folded quivers and folded cluster algebras. We give many examples of including some with finite mutation structure that do not have analogues in the unfolded cases. We relate these examples to the finite…
A model is constructed in which pair potentials are combined with the cluster expansion method in order to better describe the energetics of structurally relaxed substitutional alloys. The effect of structural relaxations away from the…
We present two different projects. The first one is related to the development of a semi-analytic model to follow the formation, the evolution and chemical enrichment of cluster galaxies in a hierarchical dark matter model. The second…
This expository paper discusses some conjectures related to visibility and blockers for sets of points in the plane.
In this survey we discuss some combinatorial aspects of higher cluster categories.
The notion of composite system made up of distinguishable parties is investigated in the context of arbitrary convex spaces.
In this research, a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering…
This paper is an overview of my recent work on abstract homomorphisms of algebraic groups. It is based on a talk given at the Conference on Group Actions and Applications in Geometry, Topology, and Analysis held in Kunming in July 2012.
The aim of this paper is to revise the theory of clusters of infinitely near points for arbitrary fields. We describe in particular the intersection matrix of such a cluster, we introduce the notion of curvette over an arbitrary field and…
This manuscript develops the theory of agglomerative clustering with Bregman divergences. Geometric smoothing techniques are developed to deal with degenerate clusters. To allow for cluster models based on exponential families with…
Linked cluster expansions provide a useful tool both for analytical and numerical investigations of lattice field theories. The expansion parameter is the interaction strength fields at neighboured lattice sites are coupled. They result…
In this master's thesis, we introduce expansion systems as a general framework to describe a large variety of approximation algorithms, such as Taylor approximation, decimal expansion and continued fraction. We consider some basic…
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…
We propose a simple abstract version of Calderon--Zygmund theory, which is applicable to spaces with exponential volume growth, and then show that amenable Lie groups can be treated within this framework.
The article presents a method of cluster expansions for groups of operators associated with the von Neumann equations for states and the Heisenberg equations for observables, aiming to construct generating operators for nonperturbative…
We will discuss here how structures observed in clusters of galaxies can provide us insight on the formation and evolution of these objects. We will focus primarily on X-ray observations and results from hydrodynamical $N$-body simulations.…
Partial groups are a natural generalization of discrete groups recently introduced by Chermak in connection with the theory of fusion systems. In this paper we develop an extension theory for partial groups based in the classical theory of…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…