Related papers: Big Data and Large Numbers. Interpreting Zipf's La…
Zipf's law predicts a power-law relationship between word rank and frequency in language communication systems and has been widely reported in a variety of natural language processing applications. However, the emergence of natural language…
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…
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…
We formulate conditions for convergence of Laws of Large Numbers and show its links with of the parts of mathematical analysis such as summation theory, convergence of orthogonal series. We present also applications of the Law of Large…
We present an impossibility result, called a theorem about facts and words, which pertains to a general communication system. The theorem states that the number of distinct words used in a finite text is roughly greater than the number of…
Zipf's law predicts a power-law relationship between word rank and frequency in language communication systems, and is widely reported in texts yet remains enigmatic as to its origins. Computer simulations have shown that language…
Human language, as a typical complex system, its organization and evolution is an attractive topic for both physical and cultural researchers. In this paper, we present the first exhaustive analysis of the text organization of human speech.…
The structure of very complicated irregular "microscopic" (local) entropy fluctuations around a big separated "macroscopic" (global) fluctuation in the statistical equilibrium was studied in numerical experiments on a simple 2--freedom…
This paper studies the limits of language models' statistical learning in the context of Zipf's law. First, we demonstrate that Zipf-law token distribution emerges irrespective of the chosen tokenization. Second, we show that Zipf…
In this paper we will look at the distribution with which passwords are chosen. Zipf's Law is commonly observed in lists of chosen words. Using password lists from four different on-line sources, we will investigate if Zipf's law is a good…
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 study a few dynamical systems composed of many components whose sizes evolve according to multiplicative stochastic rules. We compare them with respect to the emergence of power laws in the size distribution of their components. We show…
We discuss the meaning of Zipf's law in nuclear multifragmentation. We remark that Zipf's law is a consequence of a power law fragment size distribution with exponent $\tau \simeq 2$. We also recall why the presence of such distribution is…
In this article, the relationship between two well-accepted empirical propositions regarding the distribution of population in cities, namely, Gibrat's law and Zipf's law, are rigorously examined using the Chinese census data. Our findings…
We show that statistical criticality, i.e. the occurrence of power law frequency distributions, arises in samples that are maximally informative about the underlying generating process. In order to reach this conclusion, we first identify…
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…
Zipf's law can be used to describe the rank-size distribution of cities in a region. It was seldom employed to research urban internal structure. In this paper, we demonstrate that the space-filling process within a city follows Zipf's law…
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 investigate the average sizes of the $n$ largest fragments in nuclear multifragmentation events near the critical point of the nuclear matter phase diagram. We perform analytic calculations employing Poisson statistics as well as Monte…
This paper presents an extensive survey of regular distributions in natural and social sciences. The survey includes studies from a wide scope of academic disciplines, in order to create an inventory of the different mathematical functions…