Related papers: Biologically Unavoidable Sequences
An automatic sequence is a letter-to-letter coding of a fixed point of a uniform morphism. More generally, we have morphic sequences, which are letter-to-letter codings of fixed points of arbitrary morphisms. There are many examples where…
We propose a natural, bivariate, generalization of the nonsingular similarity relations considered by T. Fine. We also provide an enumeration formulae and a generating tree for those relations. The latter allow us to give a new bijection…
Large-scale dynamical properties of complete chromosome DNA sequences of eukaryotes are considered. By the proposed deterministic models with intermittency and symbolic dynamics we describe a wide spectrum of large-scale patterns inherent…
The remarkable results of Foster and Vohra was a starting point for a series of papers which show that any sequence of outcomes can be learned (with no prior knowledge) using some universal randomized forecasting algorithm and…
We present a general coalgebraic setting in which we define finite and infinite behaviour with B\"uchi acceptance condition for systems whose type is a monad. The first part of the paper is devoted to presenting a construction of a monad…
Let $ \prod_{i=1}^d (X-\alpha_i Y) \in{\mathbb C}[X,Y]$ be a binary form and let $\epsilon_1,\dots,\epsilon_d$ be nonzero complex numbers. We consider the family of binary forms $ \prod_{i=1}^d (X-\alpha_i \epsilon_i^aY)$, $a\in {\mathbb…
The whole complex process to obtain a protein encoded by a gene is difficult to include in a mathematical model. There are many models for describing different aspects of a genetic network. Finding a better model is one of the most…
The engineered control of cellular function through the design of synthetic genetic networks is becoming plausible. Here we show how a naturally occurring network can be used as a parts list for artificial network design, and how model…
Recent computational experiments have demonstrated the spontaneous emergence of self-replicating programs across universal automata, artificial chemistries, and self-modifying code systems. Remarkably, these results arise without explicit…
A subset $U$ of a set $S$ with a binary operation is called {\it avoidable} if $S$ can be partitioned into two subsets $A$ and $B$ such that no element of $U$ can be written as a product of two distinct elements of $A$ or as the product of…
Randomness (in the sense of being generated in an IID fashion) and exchangeability are standard assumptions in nonparametric statistics and machine learning, and relations between them have been a popular topic of research. This short paper…
It is rigorously proved that quasilinear impulsive systems possess unpredictable solutions when a perturbation generated by an unpredictable sequence is applied. The existence, uniqueness, as well as asymptotic stability of such solutions…
The chase is a ubiquitous algorithm in database theory. However, for existential rules (aka tuple-generating dependencies), its termination is not guaranteed, and even undecidable in general. The problem of termination becomes particularly…
We show that conjugacy of reversible cellular automata is undecidable, whether the conjugacy is to be performed by another reversible cellular automaton or by a general homeomorphism. This gives rise to a new family of finitely-generated…
We study a new type of sequences whose elements are defined in terms of the position, sign and magnitude of another element of the sequence. The name ultra-recursive comes from the fact that these sequences possess terms that are generated…
The generic limit set of a cellular automaton is a topologically dened set of congurations that intends to capture the asymptotic behaviours while avoiding atypical ones. It was dened by Milnor then studied by Djenaoui and Guillon rst, and…
We prove that it is decidable if a finitely based permutation class contains infinitely many simple permutations, and establish an unavoidable substructure result for simple permutations: every sufficiently long simple permutation contains…
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…
Morphic sequences form a natural class of infinite sequences, extending the well-studied class of automatic sequences. Where automatic sequences are known to have several equivalent characterizations and the class of automatic sequences is…
The natural order in the space of binary sequences permits to recover the $U$-sequence. Also the scaling laws of the period-doubling cascade and the intermittency route to chaos defined in that ordered set are explained. These arise as…