Related papers: The Combinatorics of Tandem Duplication
We introduce data structures answering queries concerning the occurrences of patterns from a given dictionary $\mathcal{D}$ in fragments of a given string $T$ of length $n$. The dictionary is internal in the sense that each pattern in…
Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…
We consider the synthesis of deterministic tree transducers from automaton definable specifications, given as binary relations, over finite trees. We consider the case of specifications that are deterministic top-down tree automatic,…
We propose generative models for three types of extra-grammatical word formation phenomena abounding in English slang: Blends, Clippings, and Reduplicatives. Adopting a data-driven approach coupled with linguistic knowledge, we propose…
In this paper, we explore applications of combinatorics on words across various domains, including data compression, error detection, cryptographic protocols, and pseudorandom number generation. The examination of the theoretical…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
A binary tanglegram is a pair <S,T> of binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example in phylogenetics or software engineering, it is required…
A model of pattern formation in living systems is presented. The pattern is achieved by the sequential interaction of two signaling pathways. The coupling of the pattern to the (thick) epithelial sheet changes is given, when the Gauss…
We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…
In this paper, we consider the evolution of an (infinitely large) population under recombination and additional evolutionary forces, modelled by a measure-valued ordinary differential equation. We provide a stochastic representation for the…
The wave of pre-training language models has been continuously improving the quality of the machine-generated conversations, however, some of the generated responses still suffer from excessive repetition, sometimes repeating words from…
Humans have the ability to rapidly understand rich combinatorial concepts from limited data. Here we investigate this ability in the context of auditory signals, which have been evolved in a cultural transmission experiment to study the…
Patterns are fundamental to human cognition, enabling the recognition of structure and regularity across diverse domains. In this work, we focus on structural repeats, patterns that arise from the repetition of hierarchical relations within…
Evolving genomes increase a number of their genes by gene duplications. To escape degradation in a functionless pseudogene, any gene duplicate needs to be guarded by negative (purifying) selection from otherwise inevitable fixation of…
We prime-encode the natural numbers via recursive factorisation, iterated to the exponents, generating a corpus of planar rooted trees equivalently represented as Dyck words. This forms a deterministic text endowed with internal rules.…
Technical signs of progress during the last decades has led to a situation in which the accumulation of genome sequence data is increasingly fast and cheap. The huge amount of molecular data available nowadays can help addressing new and…
With distributed computing and mobile applications becoming ever more prevalent, synchronizing diverging replicas of the same data is a common problem. Reconciliation -- bringing two replicas of the same data structure as close as possible…
In this paper, we try to explore the evolution of language through case calculations. First, we chose the novels of eleven British writers from 1400 to 2005 and found the corresponding works; Then, we use the natural language processing…
The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Hum\'anez \& Bernhardt (power of two). It is well known that Sharkovskii's theorem shows the relationship between the cardinal of the set of…