Related papers: Word maps with small image in simple groups
It has been argued that, when learning a first language, babies use a series of small clues to aid recognition and comprehension, and that one of these clues is word length. In this paper we present a statistical part of speech tagger which…
We present a robust approach for linking already existing lexical/semantic hierarchies. We used a constraint satisfaction algorithm (relaxation labeling) to select --among a set of candidates-- the node in a target taxonomy that bests…
We establish the hierarchy among twelve equivalence relations (similarities) on the class of relational structures: the equality, the isomorphism, the equimorphism, the full relation, four similarities of structures induced by similarities…
We study singularity properties of word maps on semisimple algebraic groups and Lie algebras, generalizing the work of Aizenbud-Avni in the case of the commutator map. Given a word $w$ in a free Lie algebra $\mathcal{L}_{r}$, it induces a…
Neural word representations have proven useful in Natural Language Processing (NLP) tasks due to their ability to efficiently model complex semantic and syntactic word relationships. However, most techniques model only one representation…
This work originates from the observation that today's state-of-the-art statistical language models are impressive not only for their performance, but also - and quite crucially - because they are built entirely from correlations in…
Every semigroup which is a finite disjoint union of copies of the free mono- genic semigroup (natural numbers under addition) has soluble word prob- lem and soluble membership problem. Efficient algorithms are given for both problems.
Let $H_{n}^{+}(\mathbb{R})$ be the cone of all positive semidefinite $n\times n$ real matrices. We describe the form of all surjective maps on $H_{n}^{+}(\mathbb{R}) $, $n\geq 3$, that preserve the minus partial order in both directions.
Word maps have been studied for matrix groups over a field. We initiate the study of problems related to word maps in the context of the group $\mathrm{GL}_n(\mathscr O_2)$, where $\mathscr O_2$ is a finite local principal ideal ring of…
As NLP tools become ubiquitous in today's technological landscape, they are increasingly applied to languages with a variety of typological structures. However, NLP research does not focus primarily on typological differences in its…
By describing the features and abstractions of our world, language is a crucial tool for human learning and a promising source of supervision for machine learning models. We use language to improve few-shot visual classification in the…
How do humans learn language, and can the first language be learned at all? These fundamental questions are still hotly debated. In contemporary linguistics, there are two major schools of thought that give completely opposite answers.…
Indian languages are inflectional and agglutinative and typically follow clause-free word order. The structure of sentences across most major Indian languages are similar when their dependency parse trees are considered. While some…
An absent word of a word y of length n is a word that does not occur in y. It is a minimal absent word if all its proper factors occur in y. Minimal absent words have been computed in genomes of organisms from all domains of life; their…
In this document we achieve exact and asymptotic enumeration of words, compositions over a finite group, and/or integer compositions characterized by local restrictions and, separately, subsequence pattern avoidance. We also count…
We present a language independent, unsupervised method for building word embeddings using morphological expansion of text. Our model handles the problem of data sparsity and yields improved word embeddings by relying on training word…
In this note, we establish an equivalence of categories between the category of all eight-dimensional composition algebras with any given quadratic form $n$ over a field $k$ of characteristic not two, and a category arising from an action…
Many networks in natural and human-made systems exhibit scale-free properties and are small worlds. Now we show that people's understanding of complex systems in their cognitive maps also follow a scale-free topology. People focus on a few…
For a word $S$, let $f(S)$ be the largest integer $m$ such that there are two disjoints identical (scattered) subwords of length $m$. Let $f(n, \Sigma) = \min \{f(S): S \text{is of length} n, \text{over alphabet} \Sigma \}$. Here, it is…
We consider the number of occurrences of subwords (non-consecutive sub-sequences) in a given word. We first define the notion of subword entropy of a given word that measures the maximal number of occurrences among all possible subwords. We…