Related papers: There Are Fewer Facts Than Words: Communication Wi…
In an incoherent dictionary, most signals that admit a sparse representation admit a unique sparse representation. In other words, there is no way to express the signal without using strictly more atoms. This work demonstrates that sparse…
We show that the laws of autocorrelations decay in texts are closely related to applicability limits of language models. Using distributional semantics we empirically demonstrate that autocorrelations of words in texts decay according to a…
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…
Despite the lack of experimental confirmation and of unambiguous theoretical proof, superstring theory has long been considered by many the only consistent quantized theory of gravity and the unique viable framework for the unification of…
In this paper we introduce and study a new complexity measure for finite words. For positive integer $d$ special scattered subwords, called super-$d$-subwords, in which the gaps are of length at least $(d-1)$, are defined. We give methods…
Lexical ambiguity is widespread in language, allowing for the reuse of economical word forms and therefore making language more efficient. If ambiguous words cannot be disambiguated from context, however, this gain in efficiency might make…
As speakers turn their thoughts into sentences, they maintain a balance between the complexity of words and syntax. However, it is unclear whether this syntax-lexicon tradeoff is unique to the spoken language production that is under the…
In this paper we quantify the consistency of word usage in written texts represented by complex networks, where words were taken as nodes, by measuring the degree of preservation of the node neighborhood.} Words were considered highly…
A quantitative method is suggested, where meanings of words, and grammatic rules about these, of a vocabulary are represented by real numbers. People meet randomly, and average their vocabularies if they are equal; otherwise they either…
Free words are elements of a free monoid, generated over an alphabet via the binary operation of concatenation. Casually speaking, a free word is a finite string of letters. Henceforth, we simply refer to them as words. Motivated by recent…
Zipf (1935) posited that wordforms are optimized to minimize utterances' communicative costs. Under the assumption that cost is given by an utterance's length, he supported this claim by showing that words' lengths are inversely correlated…
The purpose of this paper is to outline a simple set of axioms for basic set theory from which most fundamental facts can be derived. The key to the whole project is a new axiom of set theory which I dubbed "The Law of Extremes". It allows…
Human languages employ constructions that tacitly assume specific properties of the limited range of phenomena they evolved to describe. These assumed properties are true features of that limited context, but may not be general or precise…
Pirillo and Varricchio, and independently, Halbeisen and Hungerbuhler considered the following problem, open since 1994: Does there exist an infinite word w over a finite subset of Z such that w contains no two consecutive blocks of the…
The number of frequencies of factors of length $n+1$ in a recurrent aperiodic infinite word does not exceed $3\Delta \C(n)$, where $\Delta \C (n)$ is the first difference of factor complexity, as shown by Boshernitzan. Pelantov\'a together…
We can measure the complexity of a logical formula by counting the number of alternations between existential and universal quantifiers. Suppose that an elementary first-order formula $\varphi$ (in $\mathcal{L}_{\omega,\omega}$) is…
We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern…
A finite form of de Finetti's representation theorem is established using elementary information-theoretic tools: The distribution of the first $k$ random variables in an exchangeable binary vector of length $n\geq k$ is close to a mixture…
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…
Recent studies have investigated siamese network architectures for learning invariant speech representations using same-different side information at the word level. Here we investigate systematically an often ignored component of siamese…