Related papers: Snooker Statistics and Zipf's Law
Quantifying the similarity between symbolic sequences is a traditional problem in Information Theory which requires comparing the frequencies of symbols in different sequences. In numerous modern applications, ranging from DNA over music to…
We investigate intra-day foreign exchange (FX) time series using the inverse statistic analysis developed in [1,2]. Specifically, we study the time-averaged distributions of waiting times needed to obtain a certain increase (decrease)…
This paper describes the probabilistic behaviour of a random Sturmian word. It performs the probabilistic analysis of the recurrence function which can be viewed as a waiting time to discover all the factors of length $n$ of the Sturmian…
We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary…
Ranking is used in sport leagues to determine a champion and/or to decide on promotion/relegation of teams. Arguably, the best known ranking method relies on scores obtained by cumulating the points associated with the wins and the draws of…
The problem of compression in standard information theory consists of assigning codes as short as possible to numbers. Here we consider the problem of optimal coding -- under an arbitrary coding scheme -- and show that it predicts Zipf's…
We consider a simple model of firm/city/etc. growth based on a multi-item criterion: whenever entity B fares better that entity A on a subset of $M$ items out of $K$, the agent originally in A moves to B. We solve the model analytically in…
We present empirical data on frequency and pattern of misprints in citations to twelve high-profile papers. We find that the distribution of misprints, ranked by frequency of their repetition, follows Zipf's law. We propose a stochastic…
We study the game of go from a complex network perspective. We construct a directed network using a suitable definition of tactical moves including local patterns, and study this network for different datasets of professional tournaments…
The distribution of frequency counts of distinct words by length in a language's vocabulary will be analyzed using two methods. The first, will look at the empirical distributions of several languages and derive a distribution that…
Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes, or texts as sets of words. On one hand, the joint occurrence of…
Fractals, 1/f noise, Zipf's law, and the occurrence of large catastrophic events are typical ubiquitous general empirical observations across the individual sciences which cannot be understood within the set of references developed within…
We focus on the statistics of word occurrences and of the waiting times between such occurrences in Blogs. Due to the heterogeneity of words' frequencies, the empirical analysis is performed by studying classes of "frequently-equivalent"…
English words and the outputs of many other natural processes are well-known to follow a Zipf distribution. Yet this thoroughly-established property has never been shown to help compress or predict these important processes. We show that…
Zipf's law of city-size distributions can be expressed by three types of mathematical models: one-parameter form, two-parameter form, and three-parameter form. The one-parameter and one of the two-parameter models are familiar to urban…
Traditional linguistic theories have largely regard language as a formal system composed of rigid rules. However, their failures in processing real language, the recent successes in statistical natural language processing, and the findings…
Zipf's law implies the statistical distributions of hyperbolic type, which can describe the properties of stability and entropy loss in linguistics. We present the information theory from which follows that if the system is described by…
The performance of deep learning in natural language processing has been spectacular, but the reasons for this success remain unclear because of the inherent complexity of deep learning. This paper provides empirical evidence of its…
We find the two-variables generating function for the statistic which counts the number of variations in a word bounded by $1$. Thus, we refine and extend previous results concerning staircase words, which are words in which the variation…
According to Benford's Law, many data sets have a bias towards lower leading digits (about $30\%$ are $1$'s). The applications of Benford's Law vary: from detecting tax, voter and image fraud to determining the possibility of match-fixing…