Related papers: A note on clustered cells
As shown by A. Melnikov, the orbits of a Borel subgroup acting by conjugation on upper-triangular matrices with square zero are indexed by involutions in the symmetric group. The inclusion relation among the orbit closures defines a partial…
We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results.
The optimization of the light scattered by photonic cluster made of small particles is studied with the help of the local perturbation method and special optimization algorithm. It was shown that photonic cluster can be optimized in a such…
This note discusses an interesting matrix factorization called the CUR Decomposition. We illustrate various viewpoints of this method by comparing and contrasting them in different situations. Additionally, we offer a new characterization…
We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…
The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the…
We derive and implement a new way of solving coupled cluster equations with lower computational scaling. Our method is based on decomposition of both amplitudes and two electron integrals, using a combination of tensor hypercontraction and…
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.
Optimizing activation and deactivation of base station transmissions provides an instrument for improving energy efficiency in cellular networks. In this paper, we study optimal cell clustering and scheduling of activation duration for each…
This paper presents a novel clustering concept that is based on jointly learned nonlinear transforms (NTs) with priors on the information loss and the discrimination. We introduce a clustering principle that is based on evaluation of a…
In this paper we study the cellularization of classifying spaces of saturated fusion systems with respect to classifying spaces of finite p-groups. We give explicit algebraic criteria to decide when a classifying space is cellular.…
This paper is a survey of our work based on the stratified Morse theory of Goresky and MacPherson. First we discuss the Morse theory of Euclidean space stratified by an arrangement. This is used to show that the complement of a complex…
A semialgebraic bijection from the field of p-adic numbers to itself minus one point is constructed. Semialgebraic p-adic sets are classified up to semialgebraic bijection. A cell decomposition theorem for restricted analytic p-adic maps is…
The computation of a maximal order of an order in a semisimple algebra over a global field is a classical well-studied problem in algorithmic number theory. In this paper we consider the related problems of computing all minimal overorders…
We prove a conjecture of Denef on parameterized $p$-adic analytic integrals using an analytic cell decomposition theorem, which we also prove in this paper. This cell decomposition theorem describes piecewise the valuation of analytic…
We study clustering on graphs with multiple edge types. Our main motivation is that similarities between objects can be measured in many different metrics. For instance similarity between two papers can be based on common authors, where…
Numerous papers ask how difficult it is to cluster data. We suggest that the more relevant and interesting question is how difficult it is to cluster data sets {\em that can be clustered well}. More generally, despite the ubiquity and the…
In nuclear cluster systems, a rigorous structural forbiddenness of virtual nuclear division into unexcited fragments is obtained. We re-analyze the concept of forbiddenness, introduced in Ref. 1 for the understanding of structural effects…
This paper is the second part of a series of two papers dealing with bulking: a way to define quasi-order on cellular automata by comparing space-time diagrams up to rescaling. In the present paper, we introduce three notions of simulation…
Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…