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Using the uniform most powerful unbiased test, we observed the sales distribution of consumer electronics in Japan on a daily basis and report that it follows both a lognormal distribution and a power-law distribution and depends on the…
The size that an epidemic can reach, measured in terms of the number of fatalities, is an extremely relevant quantity. It has been recently claimed [Cirillo & Taleb, Nature Physics 2020] that the size distribution of major epidemics in…
In recent years it has been increasing evidence that lognormal distributions are widespread in physical and biological sciences, as well as in various phenomena of economics and social sciences. In social sciences, the appearance of…
The gap between data production and user ability to access, compute and produce meaningful results calls for tools that address the challenges associated with big data volume, velocity and variety. One of the key hurdles is the inability to…
Taylor's law describes the fluctuation characteristics underlying a system in which the variance of an event within a time span grows by a power law with respect to the mean. Although Taylor's law has been applied in many natural and social…
Real-world networks are generally claimed to be scale-free, meaning that the degree distributions follow the classical power-law, at least asymptotically. Yet, closer observation shows that the classical power-law distribution is often…
We present a setup for training, evaluating and interpreting neural language models, that uses artificial, language-like data. The data is generated using a massive probabilistic grammar (based on state-split PCFGs), that is itself derived…
The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been…
City-size distributions follow an approximate power law in various countries despite high volatility in relative city sizes over time. Our empirical evidence for the United States and Japan indicates that the scaling law stems from a…
As the vocabulary size of modern word-based language models becomes ever larger, many sampling-based training criteria are proposed and investigated. The essence of these sampling methods is that the softmax-related traversal over the…
A major problem in the study of large language models is to understand their inherent low-dimensional structure. We introduce an approach to study the low-dimensional structure of language models at a model-agnostic level: as sequential…
There has been a long history of research into the structure and evolution of mankind's scientific endeavor. However, recent progress in applying the tools of science to understand science itself has been unprecedented because only recently…
All living languages change over time. The causes for this are many, one being the emergence and borrowing of new linguistic elements. Competition between the new elements and older ones with a similar semantic or grammatical function may…
We present an overview of possible reasons for the appearance of heavy-tailed distributions in applications to the natural sciences. These distributions include the laws of Pareto, Lotka, and some new ones. The reasons are illustrated using…
We report empirical studies on the personal income distribution, and clarify that the distribution pattern of the lognormal with power law tail is the universal structure. We analyze the temporal change of Pareto index and Gibrat index to…
The frequencies at which individual words occur across languages follow power law distributions, a pattern of findings known as Zipf's law. A vast literature argues over whether this serves to optimize the efficiency of human communication,…
A two-state master equation based decision making model has been shown to generate phase transitions, to be topologically complex and to manifest temporal complexity through an inverse power-law probability distribution function in the…
In this article, we investigate the properties of phoneme N-grams across half of the world's languages. We investigate if the sizes of three different N-gram distributions of the world's language families obey a power law. Further, the…
In this paper, we are analyzing the interactivity time, defined as the duration between two consecutive tasks such as sending emails, collecting friends and followers and writing comments in online social networks (OSNs). The distributions…
Understanding the properties of response time distributions is a long-standing problem in cognitive science. We provide a tutorial overview of several contemporary models that assume power law scaling is a plausible description of the…