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Understanding how words change their meanings over time is key to models of language and cultural evolution, but historical data on meaning is scarce, making theories hard to develop and test. Word embeddings show promise as a diachronic…
We consider the enumeration of ordered set partitions avoiding a permutation pattern, as introduced by Godbole, Goyt, Herdan and Pudwell. Let $\op_{n,k}(p)$ be the number of ordered set partitions of $\{1,2,\ldots,n\}$ into $k$ blocks that…
All living languages change over time. The causes for this are many, one being the emergence and borrowing of new linguistic elements. Competition between the new elements and older ones with a similar semantic or grammatical function may…
Word evolution refers to the changing meanings and associations of words throughout time, as a byproduct of human language evolution. By studying word evolution, we can infer social trends and language constructs over different periods of…
Models such as Word2Vec and GloVe construct word embeddings based on the co-occurrence probability $P(i,j)$ of words $i$ and $j$ in text corpora. The resulting vectors $W_i$ not only group semantically similar words but also exhibit a…
We initiate the study of sorting permutations using prefix block-interchanges, which exchange any prefix of a permutation with another non-intersecting interval. The goal is to transform a given permutation into the identity permutation…
Babson and Steingr\'{\i}msson introduced generalized permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We consider n-permutations that avoid the generalized pattern…
Word alignments identify translational correspondences between words in a parallel sentence pair and is used, for instance, to learn bilingual dictionaries, to train statistical machine translation systems , or to perform quality…
The structure of naming systems in natural languages hinges on a trade-off between high informativeness and low complexity. Prior work capitalizes on information theory to formalize these notions; however, these studies generally rely on…
We begin with a new analysis of formal words. Let w be a formal word in letters g_1,...,g_k. The word map associated with w maps the permutations s_1,...,s_k in S_n to the permutation obtained by replacing for each i, every occurrence of…
Inspired by Fisher's geometric approach to study beneficial mutations, we analyse probabilities of beneficial mutation and crossover recombination of strings in a general Hamming space with arbitrary finite alphabet. Mutations and…
The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the…
This article studies some new insertion algorithms that associate pairs of shifted tableaux to finite integer sequences in which certain terms may be primed. When primes are ignored in the input word these algorithms reduce to known…
This article is devoted to the problem of predicting the value taken by a random permutation $\Sigma$, describing the preferences of an individual over a set of numbered items $\{1,\; \ldots,\; n\}$ say, based on the observation of an…
Cooperation is ubiquitous across all levels of biological systems ranging from microbial communities to human societies. It, however, seemingly contradicts the evolutionary theory, since cooperators are exploited by free-riders and thus are…
A wide range of applications, most notably in comparative genomics, involve the computation of a shortest sorting sequence of operations for a given permutation, where the set of allowed operations is fixed beforehand. Such sequences are…
In this paper, we introduce a convergence notion for ordered selections. Our convergence notion is based on subpermutation densities and convergences of the marginal distributions. A particular case of this convergence is the well-known…
Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for…
We consider entailment problems involving powerful constraint languages such as frontier-guarded existential rules in which we impose additional semantic restrictions on a set of distinguished relations. We consider restricting a relation…
In this paper, we study a biased version of the nearest-neighbor transposition Markov chain on the set of permutations where neighboring elements $i$ and $j$ are placed in order $(i,j)$ with probability $p_{i,j}$. Our goal is to identify…