Related papers: On Stricter Reachable Repetitiveness Measures*
Let $N$ be a finite set, let $p \in (0,1)$, and let $N_p$ denote a random binomial subset of $N$ where every element of $N$ is taken to belong to the subset independently with probability $p$ . This defines a product measure $\mu_p$ on the…
For a finite alphabet $\mathcal{A}$ and a sequence $x \in \mathcal{A}^{\mathbb{N}}$, Kamae and Zamboni defined the maximal pattern complexity function $p^*_x(n)$ as a natural generalization of usual word complexity. They defined a…
In this paper we investigate the reachability and observability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a path or a cycle. More in detail, we provide necessary…
It is a common contention that it is an ``impossible mission'' to exactly determine the minimum sample size for the estimation of a binomial parameter with prescribed margin of error and confidence level. In this paper, we investigate such…
Andr\'as Bir\'o and Vera S\'os prove that for any subgroup $G$ of $\T$ generated freely by finitely many generators there is a sequence $A\subset \N$ such that for all $\beta \in \T$ we have ($\|.\|$ denotes the distance to the nearest…
Set cover, over a universe of size $n$, may be modelled as a data-streaming problem, where the $m$ sets that comprise the instance are to be read one by one. A semi-streaming algorithm is allowed only $O(n\, \mathrm{poly}\{\log n, \log…
A superpermutation is a sequence that contains every permutation of $n$ distinct symbols as a contiguous substring. For instance, a valid example for three symbols is a sequence that contains all six permutations. This paper introduces a…
A maximal repetition, or run, in a string, is a maximal periodic substring whose smallest period is at most half the length of the substring. In this paper, we consider runs that correspond to a path on a trie, or in other words, on a…
Generative molecular design has moved from proof-of-concept to real-world applicability, as marked by the surge in very recent papers reporting experimental validation. Key challenges in explainability and sample efficiency present…
The Longest Common Subsequence (LCS) Problem asks for the longest sequence of (non-contiguous) matches between two given strings of characters. Using extensive Monte Carlo simulations, we find a finite size scaling law of the form E(L)/N =C…
In this paper it is proved that if a minimal system has the property that its sequence entropy is uniformly bounded for all sequences, then it has only finitely many ergodic measures and is an almost finite to one extension of its maximal…
The Burrows-Wheeler transform (BWT) is a reversible transform that converts a string $w$ into another string $\mathsf{BWT}(w)$. The size of the run-length encoded BWT (RLBWT) can be interpreted as a measure of repetitiveness in the class of…
A consistent path system in a graph $G$ is an collection of paths, with exactly one path between any two vertices in $G$. A path system is said to be consistent if it is intersection-closed. We say that $G$ is strictly metrizable if every…
Frequent pattern mining is a flagship problem in data mining. In its most basic form, it asks for the set of substrings of a given string $S$ of length $n$ that occur at least $\tau$ times in $S$, for some integer $\tau\in[1,n]$. We…
In 2002, Kamae and Zamboni introduced maximal pattern complexity and determined that any aperiodic sequence must have maximal pattern complexity at least $2k$. In 2006, Kamae and Rao examined the maximal pattern complexity of sequences over…
Suppose $a_n$ is a real, nonnegative sequence that does not increase exponentially. For any $p<1$ we contruct a Lebesgue measurable set $E \subseteq \mathbb{R}$ which has measure at least $p$ in any unit interval and which contains no…
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…
This paper considers the problem of characterizing the simplest discrete point sets that are aperiodic, using invariants based on topological dynamics. A Delone set whose patch-counting function N(T), for radius T, is finite for all T is…
One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…
Twisted permutation codes, introduced recently by the second and third authors, are frequency permutation arrays. They are similar to repetition permutation codes, in that they are obtained by a repetition construction applied to a smaller…