Related papers: String attractors of Rote sequences
The palindrome pattern matching (pal-matching) is a kind of generalized pattern matching, in which two strings $x$ and $y$ of same length are considered to match (pal-match) if they have the same palindromic structures, i.e., for any…
The notion of \emph{string attractor} has recently been introduced in [Prezza, 2017] and studied in [Kempa and Prezza, 2018] to provide a unifying framework for known dictionary-based compressors. A string attractor for a word…
We focus on the long time behavior of complex networks of reaction-diffusion (RD) systems. We prove the existence of the global attractor and a $L^{\infty}$-bound for a network of $n$ RD systems with $d$ variables each. This allows us to…
The category of linear algebraic groups admits non-surjective epimorphisms. For simple algebraic groups of rank $2$ defined over algebraically closed fields, we show that the minimal dimension of a closed epimorphic subgroup is $3$.
All rings are commutative, and all modules are unital. The purpose of this paper is to investigate the characterizations of weakly pseudo primary 2-absorbing sub-module in terms of some types of modules. We provide characterizations for the…
We give a new characterization of biinfinite Sturmian sequences in terms of indistinguishable asymptotic pairs. Two asymptotic sequences on a full $\mathbb{Z}$-shift are indistinguishable if the sets of occurrences of every pattern in each…
We investigate the structure and reconstruction complexity of Manacher arrays. First, we establish a combinatorial lower bound, proving that the number of rooted tandem repeat trees with $n+1$ genes exceeds the number of distinct Manacher…
Boolean networks at the critical point have been a matter of debate for many years as, e.g., scaling of number of attractor with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a…
Generalized pseudostandard words have been introduced by de Luca and De Luca in 2006. In comparison to the palindromic and pseudopalindromic closure, only little is known about the generalized pseudopalindromic closure and the associated…
Approximate pattern matching is a natural and well-studied problem on strings: Given a text $T$, a pattern $P$, and a threshold $k$, find (the starting positions of) all substrings of $T$ that are at distance at most $k$ from $P$. We…
Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in…
Generalized pseudostandard word $\bf u$, as introduced in 2006 by de Luca and De Luca, is given by a directive sequence of letters from an alphabet ${\cal A}$ and by a directive sequence of involutory antimorphisms acting on ${\cal A}^*$.…
This text is devoted to simultaneous approximation to $\xi$ and $\xi^2$ by rational numbers with the same denominator, where $\xi$ is a non-quadratic real number. We focus on an exponent $\beta_0(\xi)$ that measures the quality of such…
In these lectures we give a brief introduction to perturbative and non-perturbative string theory. The outline is the following: 1. Introduction to perturbative string theory 1.1 From point particle to extended objects 1.2 Free closed and…
We review the derivation and the basic properties of the perturbative prepotential in N=2 compactifications of the heterotic superstring. We discuss the structure of the perturbative monodromy group and the embedding of rigidly…
Using a $U$-duality symmetry of type II compactification on $T^4$ represented by triality action on the $T$-duality group, and applying the adiabatic argument we construct dual pairs of type II compactifications in lower dimensions. The…
We study the problems of finding a shortest synchronizing word and its length for a given prefix code. This is done in two different settings: when the code is defined by an arbitrary decoder recognizing its star and when the code is…
The classification of all the minimal 1-saturating sets in PG(v, 2) for 2 <= v <= 5, and the classification of the smallest and of the second smallest minimal 1-saturating sets in PG(6, 2) are presented. These results have been found using…
An integer array y = y[1..n] is said to be feasible if and only if y[1] = n and, for every i \in 2..n, i \le i+y[i] \le n+1. A string is said to be indeterminate if and only if at least one of its elements is a subset of cardinality greater…
We refine a uniform algebraic approach for deriving upper bounds on reset thresholds of synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain upper bounds for the reset…