Related papers: Word maps with small image in simple groups
Partial words are sequences over a finite alphabet that may contain wildcard symbols, called holes, which match or are compatible with all letters; partial words without holes are said to be full words (or simply words). Given an infinite…
Many methods have been proposed to find vector representation for words, but most rely on capturing context from the text to find semantic relationships between these vectors. We propose a novel method of using dictionary meanings and image…
We count the number of occurrences of certain patterns in given words. We choose these words to be the set of all finite approximations of a sequence generated by a morphism with certain restrictions. The patterns in our considerations are…
A recent approach for few-shot text classification is to convert textual inputs to cloze questions that contain some form of task description, process them with a pretrained language model and map the predicted words to labels. Manually…
The downward and upward closures of a regular language $L$ are obtained by collecting all the subwords and superwords of its elements, respectively. The downward and upward interiors of $L$ are obtained dually by collecting words having all…
Despite an ever growing number of word representation models introduced for a large number of languages, there is a lack of a standardized technique to provide insights into what is captured by these models. Such insights would help the…
A step-to-step introduction is provided on how to generate a semantic map from a collection of messages (full texts, paragraphs or statements) using freely available software and/or SPSS for the relevant statistics and the visualization.…
Previous research has demonstrated that Distributional Semantic Models (DSMs) are capable of reconstructing maps from news corpora (Louwerse & Zwaan, 2009) and novels (Louwerse & Benesh, 2012). The capacity for reproducing maps is…
We determine the positive integers a,b and the prime powers q for which the word map w(x,y)=x^ay^b is surjective on the group PSL(2,q) (and SL(2,q)). We moreover show that this map is almost equidistributed for the family of groups PSL(2,q)…
Cross-lingual representation learning is an important step in making NLP scale to all the world's languages. Recent work on bilingual lexicon induction suggests that it is possible to learn cross-lingual representations of words based 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…
We continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages…
Let v and w be nontrivial words in two free groups. We prove that, for all sufficiently large finite non-abelian simple groups G, there exist subsets C of v(G) and D of w(G) of size such that every element of G can be realized in at least…
We consider Parikh images of languages accepted by non-deterministic finite automata and context-free grammars; in other words, we treat the languages in a commutative way --- we do not care about the order of letters in the accepted word,…
A pair of letters $x$ and $y$ are said to alternate in a word $w$ if, after removing all letters except for the copies of $x$ and $y$ from $w$, the resulting word is of the form $xyxy\ldots$ (of even or odd length) or $yxyx\ldots$ (of even…
Numerical characteristics of polynomial identities of left nilpotent algebras are examined. Previously, we came up with a construction which, given an infinite binary word, allowed us to build a two-step left nilpotent algebra with…
Recent developments in shape reconstruction and comparison call for the use of many different (topological) descriptor types, such as persistence diagrams and Euler characteristic functions. We establish a framework to quantitatively…
Neural machine translation (NMT) models are typically trained with fixed-size input and output vocabularies, which creates an important bottleneck on their accuracy and generalization capability. As a solution, various studies proposed…
Word embeddings provide an unsupervised way to understand differences in word usage between discursive communities. A number of recent papers have focused on identifying words that are used differently by two or more communities. But word…
We consider bicolored maps, i.e. graphs which are drawn on surfaces, and construct a bijection between (i) oriented maps with arbitary face structure, and (ii) (weighted) non-oriented maps with exactly one face. Above, each non-oriented map…