Related papers: Abelian Combinatorics on Words: a Survey
Identifying the relations that exist between words (or entities) is important for various natural language processing tasks such as, relational search, noun-modifier classification and analogy detection. A popular approach to represent the…
The language Eff is an OCaml-like language serving as a prototype implementation of the theory of algebraic effects, intended for experimentation with algebraic effects on a large scale. We present the embedding of Eff into OCaml, using the…
We consider commutative regular and context-free grammars, or, in other words, Parikh images of regular and context-free languages. By using linear algebra and a branching analog of the classic Euler theorem, we show that, under an…
In this paper we undertake the general study of the Abelian complexity of an infinite word on a finite alphabet. We investigate both similarities and differences between the Abelian complexity and the usual subword complexity. While the…
We describe a deterministic process to associate a practical, permanent label to isomorphism classes of abelian varieties defined over finite fields with commutative endomorphism algebra as long as they are ordinary or defined over a prime…
We investigate the structural relationship between prefix-free codes over the binary alphabet and a class of unlabeled rooted trees, which we call \emph{symmetric} trees. We establish a canonical correspondence between prefix-free codes and…
Word embeddings have gained significant attention as learnable representations of semantic relations between words, and have been shown to improve upon the results of traditional word representations. However, little effort has been devoted…
Lexical semantics theories differ in advocating that the meaning of words is represented as an inference graph, a feature mapping or a vector space, thus raising the question: is it the case that one of these approaches is superior to the…
A review of Word Embedding Models through a deconstructive approach reveals their several shortcomings and inconsistencies. These include instability of the vector representations, a distorted analogical reasoning, geometric incompatibility…
A short survey about combinatorics on words and algorithmic methods in a ring. Special attention is given to Shirshov's results. Adopted for undegraduate students.
Defining the biperiodic Fibonacci words as a class of words over the alphabet $\{0,1\}$, and two specializations the $k-$Fibonacci and classical Fibonacci words, we provide a self-similar decomposition of these words into overlapping words…
A challenging task for word embeddings is to capture the emergent meaning or polarity of a combination of individual words. For example, existing approaches in word embeddings will assign high probabilities to the words "Penguin" and "Fly"…
Typical arguments for results like Kleene's Second Recursion Theorem and the existence of self-writing computer programs bear the fingerprints of equational reasoning and combinatory logic. In fact, the connection of combinatory logic and…
The words of a language reflect the structure of the human mind, allowing us to transmit thoughts between individuals. However, language can represent only a subset of our rich and detailed cognitive architecture. Here, we ask what kinds of…
We give combinatorial interpretations of several related identities associated with the names Barrucand, Strehl and Franel, including one for the Apery numbers. The combinatorial constructs employed are derangement-type card deals as…
To a good extent, words can be understood as corresponding to patterns or categories that appeared in order to represent concepts and structures that are particularly important or useful in a given time and space. Words are characterized by…
This dissertation explores the linguistic and computational aspects of the meaning relations that can hold between two or more complex linguistic expressions (phrases, clauses, sentences, paragraphs). In particular, it focuses on…
We give a brief survey of recent results on word maps on simple groups and polynomial maps on simple associative and Lie algebras. Our focus is on parallelism between these theories, allowing one to state many new open problems and giving…
While word embeddings have been shown to implicitly encode various forms of attributional knowledge, the extent to which they capture relational information is far more limited. In previous work, this limitation has been addressed by…
Both algebraic and computational approaches for dealing with similarity spaces are well known in generalized rough set theory. However, these studies may be said to have been confined to particular perspectives of distinguishability in the…