Related papers: Jump sets in local fields
We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials as dynamical systems. This lays the foundation for classification results of more general classes of Newton maps. A fundamental…
We provide descriptions for the moduli spaces $\text{Rep}(\Gamma, PU(m))$, where $\Gamma$ is any finitely generated abelian group and $PU(m)$ is the group of $m\times m$ projective unitary matrices. As an application we show that for any…
The multiplicative Newton-like method developed by the author et al. is extended to the situation where the dynamics is restricted to the orthogonal group. A general framework is constructed without specifying the cost function. Though the…
In this paper, we study a biased version of the nearest-neighbor transposition Markov chain on the set of permutations where neighboring elements $i$ and $j$ are placed in order $(i,j)$ with probability $p_{i,j}$. Our goal is to identify…
We survey the application of a relatively new branch of statistical physics--"community detection"-- to data mining. In particular, we focus on the diagnosis of materials and automated image segmentation. Community detection describes the…
We introduce the notion of Bernstein-Sato polynomial of an arbitrary variety (which is not necessarily reduced nor irreducible), using the theory of V-filtrations of M. Kashiwara and B. Malgrange. We prove that the decreasing filtration by…
We describe a new algorithm for computing the ideal class group, the regulator and a system of fundamental units in number fields under the generalized Riemann hypothesis. We use sieving techniques adapted from the number field sieve…
We study the interaction between two structures on the group of polynomial automorphisms of the affine plane: its structure as an amalgamated free product and as an infinite-dimensional algebraic variety. We introduce a new conjecture, and…
We consider uniform random permutations in classes having a finite combinatorial specification for the substitution decomposition. These classes include (but are not limited to) all permutation classes with a finite number of simple…
We begin by introducing schemes of binoids, invertible $\mathcal{O}_M$-sets and cohomology of sheaves of abelian groups defined on schemes of binoids. We define the so-called punctured combinatorial \v{C}ech-Picard complex, whose first…
We elaborate on a general method that we recently introduced for characterizing the "natural" structures in complex physical systems via a multiscale network based approach for the data mining of such structures. The approach is based on…
In this paper we study the moduli stack of complexes of vector bundles (with chain isomorphisms) over a smooth projective variety $X$ via derived algebraic geometry. We prove that if $X$ is a Calabi-Yau variety of dimension $d$ then this…
We study authomorphisms of $Ind$-groups of polynomial automorphisms (wich are singular) via tame approximations. Such objects were pioneeered in research by B.I.Plotkin We obtain a number of properties of $Aut(Aut(A))$, where $A$ is the…
We introduce the Insertion Chain Complex, a higher-dimensional extension of insertion graphs, as a new framework for analyzing finite sets of words. We study its topological and combinatorial properties, in particular its homology groups,…
The survey is devoted to the combinatorial and metric theory of filtrations, i.\,e., decreasing sequences of $\sigma$-algebras in measure spaces or decreasing sequences of subalgebras of certain algebras. One of the key notions, that of…
The module category of any artin algebra is filtered by the powers of its radical, thus defining an associated graded category. As an extension of the degree of irreducible morphisms, this text introduces the degree of morphisms in the…
Mutually repelling particles form spontaneously ordered clusters when forced into confinement. The clusters may adopt similar spatial arrangements even if the underlying particle interactions are contrastingly different. Here we demonstrate…
We show that any open set in $\R^n$ is a union of an ascending sequence of bounded open sets with analytic boundary. This is just a technical result, which is probably known. We believe, however, that it can be useful for studing BVPs on…
Many vision-related tasks benefit from reasoning over multiple modalities to leverage complementary views of data in an attempt to learn robust embedding spaces. Most deep learning-based methods rely on a late fusion technique whereby…
In this short review we introduce group field theory, a particular class of random tensor models, which represents nowadays one of the candidates for a fundamental theory of quantum gravity. We insist on the combinatorial richness of…