Related papers: Backward Iteration Algorithms for Julia sets of M\…
We study asymptotic dynamics in networks of coupled quadratic nodes. While single map complex quadratic iterations have been studied over the past century, considering ensembles of such functions, organized as coupled nodes in a network,…
It is an open problem whether repelling periodic points are dense in the classical Julia set of a non-archimedean rational function of degree more than one. We give a partial positive answer to this question based on a study of a…
The paper addresses for the first time some basic questions in the theory of finite time dynamics and finite time predictions for slowly mixing non-uniformly hyperbolic dynamical systems. It is concerned with transport in phase spaces of…
This paper develops matrix-multiplication-based iterative refinement for diagonalizable non-Hermitian eigendecompositions. The main theory concerns simple eigenvalues and distinguishes two input regimes. In the right-only regime, where only…
The increasing prevalence of neural networks in safety-critical control systems underscores the imperative need for rigorous methods to ensure the reliability and safety of these systems. This work introduces a novel approach employing…
Gibbs-type random probability measures and the exchangeable random partitions they induce represent the subject of a rich and active literature. They provide a probabilistic framework for a wide range of theoretical and applied problems…
Randomized iterative algorithms have attracted much attention in recent years because they can approximately solve large-scale linear systems of equations without accessing the entire coefficient matrix. In this paper, we propose two novel…
We close a gap appearing at the same time in the author's thesis "Iterated rings of bounded elements and generalizations of Schm\"udgen's theorem" [1] and in the author's article "Iterated rings of bounded elements and generalizations of…
The notion of automatic selfadjointness of all ideals in a multiplicative semigroup of the bounded linear operators on a separable Hilbert space B(H) arose in a 2015 discussion with Heydar Radjavi who pointed out that B(H) and the finite…
By a symmetry of the Julia set of a polynomial, also referred as polynomial Julia set, we mean an Euclidean isometry preserving the Julia set. Each such symmetry is in fact a rotation about the centroid of the polynomial. In this article, a…
Our goal is to find classes of convolution semigroups on Lie groups $G$ that give rise to interesting processes in symmetric spaces $G/K$. The $K$-bi-invariant convolution semigroups are a well-studied example. An appealing direction for…
Sparsity learning with known grouping structure has received considerable attention due to wide modern applications in high-dimensional data analysis. Although advantages of using group information have been well-studied by shrinkage-based…
Two types of recurrence sets are introduced for inverse semigroup partial actions in topological spaces. We explore their connections with similar notions for related types of imperfect symmetries (prefix inverse semigroup expansions,…
Using computer graphics and visualization algorithms, we extend in this work the results obtained analytically in [1], on the connectivity domains of alternated Julia sets, defined by switching the dynamics of two quadratic Julia sets. As…
We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of…
The main goal of this note is to suggest an algebraic approach to the quasi-isometric classification of partially commutative groups (alias right-angled Artin groups). More precisely, we conjecture that if the partially commutative groups…
In this paper, we propose a novel approach for computing robust backward reachable sets from noisy data for unknown constrained linear systems subject to bounded disturbances. In particular, we develop an algorithm for obtaining zonotopic…
Many natural systems are organized as networks, in which the nodes interact in a time-dependent fashion. The object of our study is to relate connectivity to the temporal behavior of a network in which the nodes are (real or complex)…
The Backpropagation algorithm has often been criticised for its lack of biological realism. In an attempt to find a more biologically plausible alternative, the recently introduced Forward-Forward algorithm replaces the forward and backward…
Zonotopes are widely used for over-approximating forward reachable sets of uncertain linear systems for verification purposes. In this paper, we use zonotopes to achieve more scalable algorithms that under-approximate backward reachable…