Related papers: Taylor's law for Human Linguistic Sequences
Present human languages display slightly asymmetric log-normal (Gauss) distribution for size [1-3], whereas present cities follow power law (Pareto-Zipf law)[4]. Our model considers the competition between languages and that between cities…
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…
According to many phenomenological and theoretical studies the distribution of family name frequencies in a population can be asymptotically described by a power law. We show that the Galton-Watson process corresponding to the dynamics of a…
We report a general technique to study a given experimental time series with superstatistics. Crucial for the applicability of the superstatistics concept is the existence of a parameter $\beta$ that fluctuates on a large time scale as…
For a given distribution, learning algorithm, and performance metric, the rate of convergence (or data-scaling law) is the asymptotic behavior of the algorithm's test performance as a function of number of train samples. Many learning…
We propose an alternate approach to quantifying how well language models learn natural language: we ask how well they match the statistical tendencies of natural language. To answer this question, we analyze whether text generated from…
The current distribution of language size in terms of speaker population is generally described using a lognormal distribution. Analyzing the original real data we show how the double-Pareto lognormal distribution can give an alternative…
For the study of information propagation, one fundamental problem is uncovering universal laws governing the dynamics of information propagation. This problem, from the microscopic perspective, is formulated as estimating the propagation…
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…
Many languages' inflectional morphological systems are replete with irregulars, i.e., words that do not seem to follow standard inflectional rules. In this work, we quantitatively investigate the conditions under which irregulars can…
The technique of Pad\'e Approximants, introduced in a previous work, is applied to extended recent data on the distribution of variations of interest rates compiled by the Federal Reserve System in the US. It is shown that new power laws…
We constructed an analog circuit generating fluctuations of which a probability density function has power law tails. In the circuit fluctuations with an arbitrary exponent of the power law can be obtained by tuning the resistance. A theory…
The theory of regularity is a philosophical perspective in which laws of nature are just descriptions, that is to say, laws of nature do not govern the world. Moreover, according to the theory of regularity, the number of laws of nature…
A novel approach to analyzing time series generated by complex systems, such as markets, is presented. The basic idea of the approach is the {\it Law of Self-Similar Evolution}, according to which any complex system develops self-similarly.…
We study frequency linear-time temporal logic (fLTL) which extends the linear-time temporal logic (LTL) with a path operator $G^p$ expressing that on a path, certain formula holds with at least a given frequency p, thus relaxing the…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
Statistical fluctuations of the light emitted from amplifying random media are studied theoretically and numerically. The characteristic scales of the diffusive motion of light lead to Gaussian or power-law (Levy) distributed fluctuations…
We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the…
Variational inference has become one of the most widely used methods in latent variable modeling. In its basic form, variational inference employs a fully factorized variational distribution and minimizes its KL divergence to the posterior.…
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…