Related papers: Word maps with small image in simple groups

A word-as-image is a semantic typography technique where a word illustration presents a visualization of the meaning of the word, while also preserving its readability. We present a method to create word-as-image illustrations…

The concept of the {\em half density matrix} is proposed. It unifies the quantum states which are described by density matrices and physical processes which are described by completely positive maps. With the help of the half-density-matrix…

The mapping of lexical meanings to wordforms is a major feature of natural languages. While usage pressures might assign short words to frequent meanings (Zipf's law of abbreviation), the need for a productive and open-ended vocabulary,…

Howie and Duncan observed that a word in a free product with length at least two and which is not a proper power can be decomposed as a product of two cyclic subwords each of which is uniquely positioned. Using this property, they proved…

Viewing Dehn's algorithm as a rewriting system, we generalise to allow an alphabet containing letters which do not necessarily represent group elements. This extends the class of groups for which the algorithm solves the word problem to…

(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal…

Word Embeddings are used widely in multiple Natural Language Processing (NLP) applications. They are coordinates associated with each word in a dictionary, inferred from statistical properties of these words in a large corpus. In this paper…

A morphism h is unambiguous with respect to a word w if there is no other morphism g that maps w to the same image as h. In the present paper we study the question of whether, for any given word, there exists an unambiguous 1-uniform…

Boolean spaces with internal semigroups generalize profinite semigroups and are pertinent for the recognition of not-necessarily regular languages. Via recognition, the study of existential quantification in logic on words amounts to the…

This paper describes an experimental comparison of three unsupervised learning algorithms that distinguish the sense of an ambiguous word in untagged text. The methods described in this paper, McQuitty's similarity analysis, Ward's…

We introduce Trans-gram, a simple and computationally-efficient method to simultaneously learn and align wordembeddings for a variety of languages, using only monolingual data and a smaller set of sentence-aligned data. We use our new…

We present a machine learning algorithm for building classifiers that are comprised of a small number of disjunctions of conjunctions (or's of and's). An example of a classifier of this form is as follows: If X satisfies (x1 = 'blue' AND x3…

We introduce adequate concepts of expansion of a digraph to obtain a sequential construction of minimal strong digraphs. We characterize the class of minimal strong digraphs whose expansion preserves the property of minimality. We prove…

Linguistic similarity is multi-faceted. For instance, two words may be similar with respect to semantics, syntax, or morphology inter alia. Continuous word-embeddings have been shown to capture most of these shades of similarity to some…

Word embeddings are widely used in Natural Language Processing, mainly due to their success in capturing semantic information from massive corpora. However, their creation process does not allow the different meanings of a word to be…

We fill in the details in a procedure outlined by Serre for drawing pictures of compact real Lie groups. In the case of Sp($2n$), the picture generated by the method is connected with abelian varieties over a number field or a finite field.…

Data-driven representation learning for words is a technique of central importance in NLP. While indisputably useful as a source of features in downstream tasks, such vectors tend to consist of uninterpretable components whose relationship…

We seek to better understand the difference in quality of the several publicly released embeddings. We propose several tasks that help to distinguish the characteristics of different embeddings. Our evaluation of sentiment polarity and…

Morpho-syntactic lexicons provide information about the morphological and syntactic roles of words in a language. Such lexicons are not available for all languages and even when available, their coverage can be limited. We present a…

In this work, we show that the class of word-representable graphs is closed under split recomposition and determine the representation number of the graph obtained by recomposing two word-representable graphs. Accordingly, we show that the…