Related papers: Some Results on Digital Segments and Balanced Word…
We construct words with small image in a given finite alternating or unimodular group. This shows that word width in these groups is unbounded in general.
We point out that a sequence of natural numbers is the dimension sequence of a subproduct system if and only if it is the cardinality sequence of a word system (or factorial language). Determining such sequences is, therefore, reduced to a…
A simple yet effective numerical method using orthogonal hybrid functions consisting of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal triangular functions is proposed to solve numerically fractional…
The task of finding a criterion allowing to distinguish a text from an arbitrary set of words is rather relevant in itself, for instance, in the aspect of development of means for internet-content indexing or separating signals and noise in…
Two words $w_1$ and $w_2$ are said to be $k$-binomial equivalent if every non-empty word $x$ of length at most $k$ over the alphabet of $w_1$ and $w_2$ appears as a scattered factor of $w_1$ exactly as many times as it appears as a…
In this paper we describe an algorithm for aligning sentences with their translations in a bilingual corpus using lexical information of the languages. Existing efficient algorithms ignore word identities and consider only the sentence…
Word embeddings provide point representations of words containing useful semantic information. We introduce multimodal word distributions formed from Gaussian mixtures, for multiple word meanings, entailment, and rich uncertainty…
We consider the problem of estimating the support of a measure from a finite, independent, sample. The estimators which are considered are constructed based on the empirical Christoffel function. Such estimators have been proposed for the…
We study an online version of the noisy binary search problem where feedback is generated by a non-stochastic adversary rather than perturbed by random noise. We reframe this as maintaining an accurate estimate for the median of an…
We use the formulation of equilibrium statistical mechanics in order to study some important characteristics of language. Using a simple expression for the Hamiltonian of a language system, which is directly implied by the Zipf law, we are…
Our goal is to build classification models using a combination of free-text and structured data. To do this, we represent structured data by text sentences, DataWords, so that similar data items are mapped into the same sentence. This…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
This article shows that any type of binary data can be defined as a collection from codewords of variable length. This feature helps us to define an Injective and surjective function from the suggested codewords to the required codewords.…
We discuss combining knowledge-based (or rule-based) and statistical part-of-speech taggers. We use two mature taggers, ENGCG and Xerox Tagger, to independently tag the same text and combine the results to produce a fully disambiguated…
Algorithmic fractal dimensions quantify the algorithmic information density of individual points and may be defined in terms of Kolmogorov complexity. This work uses these dimensions to bound the classical Hausdorff and packing dimensions…
We illustrate the potential applications in machine learning of the Christoffel function, or more precisely, its empirical counterpart associated with a counting measure uniformly supported on a finite set of points. Firstly, we provide a…
Although the representation of the real numbers in terms of a base and a set of digits has a long history, new questions arise even in simple situations. This paper concerns binary radix systems, i.e., positional number systems with digits…
There have been many recent advances in the structure and measurement of distributed language models: those that map from words to a vector-space that is rich in information about word choice and composition. This vector-space is the…
We discuss certain matrices associated with Christoffel words, and show that they have a group structure. We compute their determinants and show a relationship between the Zolotareff symbol from number theory.
We introduce a topological approach to words. Words are approximated by Gauss words and then studied up to natural modifications inspired by homotopy transformations of curves on the plane.