相关论文: Is space a word, too?
Evidence is given for a systematic text-length dependence of the power-law index gamma of a single book. The estimated gamma values are consistent with a monotonic decrease from 2 to 1 with increasing length of a text. A direct connection…
We explore a probabilistic model of an artistic text: words of the text are chosen independently of each other in accordance with a discrete probability distribution on an infinite dictionary. The words are enumerated 1, 2, $\ldots$, and…
The Subspace Theorem due to Schmidt (1972) is a broad generalisation of Roth's Theorem in Diophantine Approximation (1955) which, in the same way as the latter, suffers a notorious lack of effectivity. This problem is tackled from a…
A key aim in biology and psychology is to identify fundamental principles underpinning the behavior of animals, including humans. Analyses of human language and the behavior of a range of non-human animal species have provided evidence for…
The \emph{word problem} of a group $G = \langle \Sigma \rangle$ can be defined as the set of formal words in $\Sigma^*$ that represent the identity in $G$. When viewed as formal languages, this gives a strong connection between classes of…
A set of data with positive values follows a Pareto distribution if the log-log plot of value versus rank is approximately a straight line. A Pareto distribution satisfies Zipf's law if the log-log plot has a slope of -1. Since many types…
This paper introduces a statistical and other analysis of peer reviewers in order to approach their "quality" through some quantification measure, thereby leading to some quality metrics. Peer reviewer reports for the Journal of the Serbian…
Statistical studies of languages have focused on the rank-frequency distribution of words. Instead, we introduce here a measure of how word ranks change in time and call this distribution \emph{rank diversity}. We calculate this diversity…
We study the hypothesis of information panspermia assigned recently among possible solutions of the Fermi paradox ("where are the aliens?"). It suggests that the expenses of alien signaling can be significantly reduced, if their messages…
Languages are not created randomly but rather to communicate information. There is a strong association between languages and their underlying meanings, resulting in a sparse joint distribution that is heavily peaked according to their…
The density of a rational language can be understood as the frequency of some "pattern" in the shift space, for example a pattern like "words with an even number of a given letter." We study the density of group languages, i.e. rational…
The distributions of the number of occurrences of words (the distributions of words for short) play key roles in information theory, statistics, probability theory, ergodic theory, computer science, and DNA analysis. Bassino et al. 2010 and…
We perform a quantitative analysis of extensive chess databases and show that the frequencies of opening moves are distributed according to a power-law with an exponent that increases linearly with the game depth, whereas the pooled…
We consider expanding maps such that the unit interval can be represented as a full symbolic shift space with bounded distortion. There are already theorems about the Hausdorff dimension for sets defined by the set of accumulation points…
In this work, we leverage the linear algebraic structure of distributed word representations to automatically extend knowledge bases and allow a machine to learn new facts about the world. Our goal is to extract structured facts from…
Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such…
Given a discrete distribution, an interesting problem is to determine the minimum size of a random sample drawn from this distribution, in order to observe a given number of different records. This problem is related with many applied…
A topological space is iso-dense if it has a dense set of isolated points. A topological space is scattered if each of its non-empty subspaces has an isolated point. In $\mathbf{ZF}$, in the absence of the axiom of choice, basic properties…
We consider a system composed of a fixed number of particles with total energy smaller or equal to some prescribed value. The particles are non-interacting, indistinguishable and distributed over fixed number of energy levels. The energy…
The joint probability distribution of many degrees of freedom in biological systems, such as firing patterns in neural networks or antibody sequence composition in zebrafish, often follow Zipf's law, where a power law is observed on a…