Related papers: Citations and the Zipf-Mandelbrot's law
A mere hyperbolic law, like the Zipf's law power function, is often inadequate to describe rank-size relationships. An alternative theoretical distribution is proposed based on theoretical physics arguments starting from the Yule-Simon…
Zipf's law of abbreviation, the tendency of more frequent words to be shorter, is one of the most solid candidates for a linguistic universal, in the sense that it has the potential for being exceptionless or with a number of exceptions…
History-dependent processes are ubiquitous in natural and social systems. Many such stochastic processes, especially those that are associated with complex systems, become more constrained as they unfold, meaning that their sample-space, or…
Human language, the most powerful communication system in history, is closely associated with cognition. Written text is one of the fundamental manifestations of language, and the study of its universal regularities can give clues about how…
Most of various large-size complex systems in nature and society can be well described as complex networks (graphs) to better understand the evolutional mechanisms and dynamical functions behind themselves. Of some part follow scale-free…
We present a general approach to explain the Zipf's law of city distribution. If the simplest interaction (pairwise) is assumed, individuals tend to form cities in agreement with the well-known statistics
It is well known in bibliometrics that the average number of citations per paper differs greatly between the various disciplines. The differing citation culture (in particular the different average number of references per paper and thereby…
We prime-encode the natural numbers via recursive factorisation, iterated to the exponents, generating a corpus of planar rooted trees equivalently represented as Dyck words. This forms a deterministic text endowed with internal rules.…
Power-law distributions with various exponents are studied. We first introduce a simple and generic model that reproduces Zipf's law. We can regard this model both as the time evolution of the population of cities and that of the asset…
We present a simple structure based model of how words are formed from morphemes. The model explains two major empirical facts: the typical distribution of word lengths and the appearance of Zipf like rank frequency curves. In contrast to…
Power laws are a characteristic distribution that are ubiquitous, in that they are found almost everywhere, in both natural as well as in man-made systems. They tend to emerge in large, connected and self-organizing systems, for example,…
Long-range correlations are found in symbolic sequences from human language, music and DNA. Determining the span of correlations in dolphin whistle sequences is crucial for shedding light on their communicative complexity. Dolphin whistles…
Degree distributions of many real networks are known to follow the Mandelbrot law, which can be considered as an extension of the power law and is determined by not only the power-law exponent, but also the shifting coefficient. Although…
To quantify the mechanism of a complex network growth we focus on the network of citations of scientific papers and use a combination of the theoretical and experimental tools to uncover microscopic details of this network growth. Namely,…
It is well known that to estimate the Shannon entropy for symbolic sequences accurately requires a large number of samples. When some aspects of the data are known it is plausible to attempt to use this to more efficiently compute entropy.…
The citations to a set of academic articles are typically unevenly shared, with many articles attracting few citations and few attracting many. It is important to know more precisely how citations are distributed in order to help…
We study the statistical properties of random numbers under the Martin-L\"of definition of randomness, proving that random numbers obey analogues of Strong Law of Large Numbers, the Law of the Iterated Logarithm, and that they are normal.…
The power law is ubiquitous in natural and social phenomena, and is considered as a universal relationship between the frequency and its rank for diverse social systems. However, a general model is still lacking to interpret why these…
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…
We demonstrate a comprehensive framework that accounts for citation dynamics of scientific papers and for the age distribution of references. We show that citation dynamics of scientific papers is nonlinear and this nonlinearity has…