Related papers: A dynamical approach to sampling and interpolation…

We show equivalence of pure point diffraction and pure point dynamical spectrum for measurable dynamical systems build from locally finite measures on locally compact Abelian groups. This generalizes all earlier results of this type. Our…

We obtain sampling and interpolation theorems in radial weighted spaces of analytic functions for weights of arbitrary (more rapid than polynomial) growth. We give an application to invariant subspaces of arbitrary index in large weighted…

We investigate the question of studying spectral clustering in a Hilbert space where the set of points to cluster are drawn i.i.d. according to an unknown probability distribution whose support is a union of compact connected components. We…

Cluster integrable systems are a broad class of integrable systems modelled on bipartite dimer models on the torus. Many discrete integrable dynamics arise by applying sequences of local transformations, which form the cluster modular group…

We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying…

We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…

Multivariate distributions are fundamental to modeling. Discrete copulas can be used to construct diverse multivariate joint distributions over random variables from estimated univariate marginals. The space of discrete copulas admits a…

In this article we extend the notion of $L^p$-measure subgroups couplings, a quantitative asymmetric version of measure equivalence that was introduced by Delabie, Koivisto, Le Ma\^itre and Tessera for finitely generated groups, to the…

We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…

In this paper we present a new dynamical systems algorithm for clustering in hyperspectral images. The main idea of the algorithm is that data points are \`pushed\' in the direction of increasing density and groups of pixels that end up in…

We study uniform and non-uniform model sets in arbitrary locally compact second countable (lcsc) groups, which provide a natural generalization of uniform model sets in locally compact abelian groups as defined by Meyer and used as…

While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…

On a compact group the Haar probability measure plays the role of uniform distribution. The entropy and rate distortion theory for this uniform distribution is studied. New results and simplified proofs on convergence of convolutions on…

In this paper we consider the problem of group invariant subspace clustering where the data is assumed to come from a union of group-invariant subspaces of a vector space, i.e. subspaces which are invariant with respect to action of a given…

We study the emerging collective states in a simple mechanical model of a dense group of self-propelled polar disks with off-centered rotation, confined within a circular arena. Each disk presents self-alignment towards the sum of contact…

We define iterated monodromy groups of more general structures than partial self-covering. This generalization makes it possible to define a natural notion of a combinatorial model of an expanding dynamical system. We prove that a naturally…

Density estimation is a fundamental technique employed in various fields to model and to understand the underlying distribution of data. The primary objective of density estimation is to estimate the probability density function of a random…

In this work, we define the notion of unimodular random measured metric spaces as a common generalization of various other notions. This includes the discrete cases like unimodular graphs and stationary point processes, as well as the…

This paper focuses on flow-adapted point-shifts of point processes on topological groups, which map points of a point process to other points of the point process in a translation invariant way. Foliations and connected components generated…

Through highly non-constructive methods, works by Bestvina, Culler, Feighn, Morgan, Paulin, Rips, Shalen, and Thurston show that if a finitely presented group does not split over a virtually solvable subgroup, then the space of its discrete…