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In this paper, we assess the performance of four iterative algorithms for solving non-symmetric rank-deficient linear systems arising in the FFT-based homogenization of heterogeneous materials defined by digital images. Our framework is…
It is shown that all 3-body quantal integrable systems that emerge in the Hamiltonian reduction method possess the same hidden algebraic structure. All of them are given by a second degree polynomial in generators of an infinite-dimensional…
A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter…
We produce algorithms to detect whether a complex affine variety computed and presented numerically by the machinery of numerical algebraic geometry corresponds to an associated component of a polynomial ideal.
Delorme suggested that the set of all complete intersection numerical semigroups can be computed recursively. We have implemented this algorithm, and particularized it to several subfamilies of this class of numerical semigroups: free and…
We study the two-dimensional continued fraction algorithm introduced in \cite{garr} and the associated \emph{triangle map} $T$, defined on a triangle $\triangle\subset \R^2$. We introduce a slow version of the triangle map, the map $S$,…
In myriad statistical applications, data are collected from related but heterogeneous sources. These sources share some commonalities while containing idiosyncratic characteristics. One of the most fundamental challenges in such scenarios…
Detecting the dimensionality of graphs is a central topic in machine learning. While the problem has been tackled empirically as well as theoretically, existing methods have several drawbacks. On the one hand, empirical tools are…
The iterative absorption method has recently led to major progress in the area of (hyper-)graph decompositions. Amongst other results, a new proof of the Existence conjecture for combinatorial designs, and some generalizations, was…
This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for…
In this article we construct uncountably many new homogeneous locally finite Steiner triple systems of countably infinite order as Fra\"{\i}ss\'{e} limits of classes of finite Steiner triple systems avoiding certain subsystems. The…
Self organizing maps (SOMs) are widely-used for unsupervised classification. For this application, they must be combined with some partitioning scheme that can identify boundaries between distinct regions in the maps they produce. We…
A theorem of A.A. Brudno says that the Kolmogorov-Sinai entropy of a subshift X over $\mathbb{N}$ with respect to an ergodic measure $\mu$ equals the asymptotic Kolmogorov complexity of almost every word $\omega$ in X. The purpose of this…
The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is…
For self-similar sets $X,Y\subseteq \mathbb{R}$, we obtain new results towards the affine embeddings conjecture of Feng-Huang-Rao (2014), and the equivalent weak intersections conjecture. We show that the conjecture holds when the defining…
The eigenvectors of an ergodic semigroup of linear normal positive unital maps on a von Neumann algebra are described. Moreover, it is shown by means of examples, that mere positivity of the maps in question is not sufficient for Frobenius…
In the paper we consider the linear underdetermined system of a special type. Systems of this type appear in non-homogeneous network flow programming problems in the form of systems of constraints and can be characterized as systems with a…
Properties of relative traces and symmetrizing forms on chains of cyclotomic and affine Hecke algebras are studied. The study relies on a use of bases of these algebras which generalize a normal form for elements of the complex reflection…
This paper is a direct continuation of "Functional analysis behind a Family of Multidimensional Continued Fractions: Part I," in which we started the exploration of the functional analysis behind the transfer operators for triangle…
We study quadratic, volume preserving diffeomorphisms whose inverse is also quadratic. Such maps generalize the H\'enon area preserving map and the family of symplectic quadratic maps studied by Moser. In particular, we investigate a family…