Related papers: What can we see from Investment Simulation based o…
We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a…
We demonstrate that large texts, representing human (English, Russian, Ukrainian) and artificial (C++, Java) languages, display quantitative patterns characterized by the Benford-like and Zipf laws. The frequency of a word following the…
Zipf's law states that if words of language are ranked in the order of decreasing frequency in texts, the frequency of a word is inversely proportional to its rank. It is very robust as an experimental observation, but to date it escaped…
By analyzing a large data set of daily returns with data clustering technique, we identify economic sectors as clusters of assets with a similar economic dynamics. The sector size distribution follows Zipf's law. Secondly, we find that…
Here we sketch a new derivation of Zipf's law for word frequencies based on optimal coding. The structure of the derivation is reminiscent of Mandelbrot's random typing model but it has multiple advantages over random typing: (1) it starts…
In this article, I conduct a textual and contextual analysis of the empirical literature on Zipf's law for cities. Building on previous meta-analysis material openly available, I collect full texts and bibliographies of 66 scientific…
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…
Despite renewed interest in emergent language simulations with neural networks, little is known about the basic properties of the induced code, and how they compare to human language. One fundamental characteristic of the latter, known as…
Zipf's law describes the empirical size distribution of the components of many systems in natural and social sciences and humanities. We show, by solving a statistical model, that Zipf's law co-occurs with the maximization of the diversity…
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…
Despite the recent successes of deep learning in natural language processing (NLP), there remains widespread usage of and demand for techniques that do not rely on machine learning. The advantage of these techniques is their…
Despite being a paradigm of quantitative linguistics, Zipf's law for words suffers from three main problems: its formulation is ambiguous, its validity has not been tested rigorously from a statistical point of view, and it has not been…
Zipf's law of abbreviation, namely the tendency of more frequent words to be shorter, has been viewed as a manifestation of compression, i.e. the minimization of the length of forms -- a universal principle of natural communication.…
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…
In a language corpus, the probability that a word occurs $n$ times is often proportional to $1/n^2$. Assigning rank, $s$, to words according to their abundance, $\log s$ vs $\log n$ typically has a slope of minus one. That simple Zipf's law…
It is traditionally assumed that Zipf's law implies the power-law growth of the number of different elements with the total number of elements in a system - the so-called Heaps' law. We show that a careful definition of Zipf's law leads to…
Zipf's law is found when the vocabulary of long written texts is ranked according to the frequency of word occurrences, establishing a power-law decay for the frequency vs rank relation. This law is a robust statistical property observed…
Large Language Models (LLMs) have recently been leveraged for asset pricing tasks and stock trading applications, enabling AI agents to generate investment decisions from unstructured financial data. However, most evaluations of LLM…
Tokenization is a fundamental step in natural language processing (NLP) and other sequence modeling domains, where the choice of vocabulary size significantly impacts model performance. Despite its importance, selecting an optimal…
Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines - from astronomy to demographics to software structure to economics to linguistics to zoology, and even…