Related papers: A statistical test for the Zipf's law by deviation…
We estimate the $n$-gram entropies of natural language texts in word-length representation and find that these are sensitive to text language and genre. We attribute this sensitivity to changes in the probability distribution of the lengths…
A length dependence of the effective mobility in the form of a power law, B ~ L^(1-1/alpha) is observed in dispersive transport in amorphous substances, with 0 < \alpha < 1. We deduce this behavior as a simple consequence of the statistical…
A collector wishes to collect $m$ complete sets of $N$ distinct coupons. The draws from the population are considered to be independent and identical distributed with replacement, and the probability that a type-$j$ coupon is drawn is noted…
In this work, we study the problem of finding the asymptotic growth rate of the number of of $d$-dimensional arrays with side length $n$ over a given alphabet which avoid a list of one-dimensional "forbidden" words along all cardinal…
In this paper we try to model certain features of human language complexity by means of advanced concepts borrowed from statistical mechanics. We use a time series approach, the diffusion entropy method (DE), to compute the complexity of an…
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 show that the exponent in the inverse power law of word frequencies for the monkey-at-the-typewriter model of Zipf's law will tend towards -1 under broad conditions as the alphabet size increases to infinity and the letter probabilities…
Physics seeks to uncover the laws of Nature and express them through mathematical equations. Despite the vast diversity of natural phenomena, physical equations exhibit structural regularities that set them apart from arbitrary mathematical…
Summation arithmetic functions with asymptotically independent terms are studied in the paper, the limit of which is the law of normal distribution. Assertions about the asymptotic behavior of the indicated functions are proved.
It is proved that the information divergence statistic is infinitely more Bahadur efficient than the power divergence statistics of the orders $\alpha >1$ as long as the sequence of alternatives is contiguous with respect to the sequence of…
We extract the individual names of persons mentioned in news reports from a Philippine-based daily in the English language from 2010-2012. Names are extracted using a learning algorithm that filters adjacent capitalized words and runs it…
Zipf's law for cities is probably the most famous regularity in social sciences. So much that, a hundred years of publication later, its status is not clear: is it a law of social organisation? Is it an instrument of description of city…
A "monkey book" is a book consisting of a random distribution of letters and blanks, where a group of letters surrounded by two blanks is defined as a word. We compare the statistics of the word distribution for a monkey book with the…
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…
For an $n\times n$ random image with independent pixels, black with probability $p(n)$ and white with probability $1-p(n)$, the probability of satisfying any given first-order sentence tends to 0 or 1, provided both $p(n)n^{\frac{2}{k}}$…
Most research related to unithood were conducted as part of a larger effort for the determination of termhood. Consequently, novelties are rare in this small sub-field of term extraction. In addition, existing work were mostly empirically…
We investigate the behavior of the periods and border lengths of random words over a fixed alphabet. We show that the asymptotic probability that a random word has a given maximal border length $k$ is a constant, depending only on $k$ and…
Zipf's law establishes a scaling behavior for word-frequencies in large text corpora. The appearance of Zipfian properties in human language has been previously explained as an optimization problem for the interests of speakers and hearers.…
In recent years, word embeddings have been widely used to measure biases in texts. Even if they have proven to be effective in detecting a wide variety of biases, metrics based on word embeddings lack transparency and interpretability. We…
Data of proportional elections show a striking feature: If the parties are ranked according to the number of their voters, the number of votes grows exponentially with the rank of the party. This so-called Zipf's law has been reported…