Related papers: Cluster Estimates for Modular Structures
We introduce the notion of modular forms, focusing primarily on the group PSL2Z. We further introduce quasi-modular forms, as wel as discuss their relation to physics and their applications in a variety of enumerative problems. These notes…
We show that conditional expectations, optimal hypotheses, disintegrations, and adjoints of unital completely positive maps, are all instances of Bayesian inverses. We study the existence of the latter by means of the Tomita-Takesaki…
Discussion of the necessity to use the constructive mathematics as the formalism of quantum theory for systems with many particles.
We introduce an approach to partitioning networks into communities that not only determines the best community structure, but also provides a range of characterization techniques to assess how significant that structure is. We study the…
We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of their discrete symmetry groups - the…
In the first part, the second quantization procedure and the free Bosonic scalar field will be introduced, and the axioms for quantum fields and nets of observable algebras will be discussed. The second part is mainly devoted to an…
This lecture is an introduction to cosmological tests with clusters of galaxies. Here I do not intend to provide a complete review of the subject, but rather to describe the basic procedures to set up the fitting machinery to constrain…
It has become increasingly apparent that traditional hydrodynamical simulations of galaxy clusters are unable to reproduce the observed properties of galaxy clusters, in particular overpredicting the mass corresponding to a given cluster…
This is a first step guide to the theory of cluster algebras. We especially focus on basic notions, techniques, and results concerning seeds, cluster patterns, and cluster algebras.
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…
Arclets in clusters of galaxies can be used to determine the lens mapping and not only to constrain the mass density of the cluster. Multiply imaged arclets are therefore easily identified without further modelling.
In this talk I shall try to give an elementary introduction to certain areas of mathematical physics where the idea of moduli space is used to help solve problems or to further our understanding. In the wide area of gauge theory, I shall…
Let $\mathcal{C}$ be a Hom-finite triangulated 2-Calabi-Yau category with a cluster tilting object. Under some constructibility assumptions on $\mathcal{C}$ which are satisfied for instance by cluster categories, by generalized cluster…
A univariate clustering criterion for stationary processes satisfying a $\beta$-mixing condition is proposed extending the work of \cite{KB2} to the dependent setup. The approach is characterized by an alternative sample criterion function…
This paper introduces the notion of co-modularity, to co-cluster observations of bipartite networks into co-communities. The task of co-clustering is to group together nodes of one type with nodes of another type, according to the…
We survey some recent constructions of cluster algebra structures on coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody groups. We also review a quantized version of these results.
In a recent paper ["Cluster Model of Decagonal Tilings" (to be published in Phys. Rev. B)], we have introduced a cluster model for decagonal tilings in two dimensions. This model is now extended to three dimensions. Two-dimensional tilings…
We review the basics of the coupled-cluster expansion formalism for numerical solutions of the many-body problem, and we outline the principles of an approach directed towards an adequate inclusion of continuum effects in the associated…
Let $\CC$ be a Hom-finite triangulated 2-Calabi-Yau category with a cluster-tilting object $T$. Under a constructibility condition we prove the existence of a set $\mathcal G^T(\CC)$ of generic values of the cluster character associated to…
This study focuses on exploring the use of local interpretability methods for explaining time series clustering models. Many of the state-of-the-art clustering models are not directly explainable. To provide explanations for these…