Related papers: Pattern Complexity of Aperiodic Substitutive Subsh…
We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove existence of a tile set that accepts only quasiperiodic and non-recursive tilings. Our construction is based on the…
A fundamental challenge in multiparameter persistent homology is the absence of a complete and discrete invariant. To address this issue, we propose an enhanced framework that realizes a holistic understanding of a fully commutative…
Spatial aperiodicity occurs in various models and material s. Although today the most well-known examples occur in the area of quasicrystals, other applications might also be of interest. Here we discuss some issues related to the notion…
In this note we present a characterisation of all unary and binary patterns that do not only contain variables, but also reversals of their instances. These types of variables were studied recently in either more general or particular…
We prove that a subshift $(X,T)$ is linearly recurrent if and only if it is a primitive and proper $S$-adic subshift. This corrects Proposition 6 in F. Durand ({\it Ergod. Th. & Dynam. Sys. {\bf 20}} (2000), 1061--1078).
We develop a word mechanism applied in knot and link diagrams for the illustration of a diagrammatic property. We also give a necessary condition for determining incompressible and pairwise incompressible surfaces, that are embedded in knot…
In the paper we study aperiodic substitutional dynamical systems arisen from non-primitive substitutions. We prove that the Vershik homeomorphism $\phi$ of a stationary ordered Bratteli diagram is homeomorphic to an aperiodic substitutional…
We study the long time behaviour of the transient before the collapse on the periodic attractors of a discrete deterministic asymmetric neural networks model. The system has a finite number of possible states so it is not possible to use…
The paper studies different variants of almost periodicity notion. We introduce the class of eventually strongly almost periodic sequences where some suffix is strongly almost periodic (=uniformly recurrent). The class of almost periodic…
We consider the alternating sign matrices of the odd order that have some kind of central symmetry. Namely, we deal with matrices invariant under the half-turn, quarter-turn and flips in both diagonals. In all these cases, there are two…
This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching…
We show that static data structure lower bounds in the group (linear) model imply semi-explicit lower bounds on matrix rigidity. In particular, we prove that an explicit lower bound of $t \geq \omega(\log^2 n)$ on the cell-probe complexity…
We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…
We connect the mixing behaviour of random walks over a graph to the power of the local-consistency algorithm for the solution of the corresponding constraint satisfaction problem (CSP). We extend this connection to arbitrary CSPs and their…
Moir\'e patterns are omnipresent. They are important for any overlapping periodic phenomenon, from vibrational and electromagnetic, to condensed matter. Here we show, both theoretically and via experimental simulations by ultracold atoms,…
We study the parameterized complexity of the problems of finding a maximum common (induced) subgraph of two given graphs. Since these problems generalize several NP-complete problems, they are intractable even when parameterized by strongly…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order…
We investigate the stability of maximizing measures for a penalty function of a two-dimensional subshift of finite type, building on the work of Gonschorowski et al. \cite{GQS}. In the one-dimensional case, such measures remain stable under…
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…