Related papers: Structural Foundations for Leading Digit Laws: Bey…
We show that the information gained in spectroscopic experiments regarding the number and distribution of atomic environments can be used as a valuable constraint in the refinement of the atomic-scale structures of nanostructured or…
We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable simple example of information processing in complex systems. In this problem, multiple inputs map to the same output,…
One aim of data mining is the identification of interesting structures in data. For better analytical results, the basic properties of an empirical distribution, such as skewness and eventual clipping, i.e. hard limits in value ranges, need…
The present communication addresses a set of observations, obeying both deterministic as well as statistical formal requirements, and serving to operate within the framework of the dynamical systems theory, with a certain emphasis placed on…
The scope of this paper is twofold. First, to emphasize the use of the mod 1 map in exploring the digit distribution of random variables. We show that the well-known base- and scale-invariance of Benford variables are consequences of their…
We present the first prediction of the probability distribution function (PDF) for self-organization of shear flows modeled by a nonlinear diffusion equation with a stochastic forcing. A novel non-perturbative method based on a coherent…
Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…
The mechanism that controls digit formation has long intrigued developmental and theoretical biologists, and many different models and mechanisms have been proposed. Here we review models of limb development with a specific focus on digit…
Existing music generation models are mostly language-based, neglecting the frequency continuity property of notes, resulting in inadequate fitting of rare or never-used notes and thus reducing the diversity of generated samples. We argue…
Benford's law describes a common phenomenon among many naturally occurring data sets and distributions in which the leading digits of the data are distributed with the probability of a first digit of $d$ base $B$ being…
Distribution shifts have long been regarded as troublesome external forces that a decision-maker should either counteract or conform to. An intriguing feedback phenomenon termed decision dependence arises when the deployed decision affects…
Nature and our world have a bias! Roughly $30\%$ of the time the number $1$ occurs as the leading digit in many datasets base $10$. This phenomenon is known as Benford's law and it arrises in diverse fields such as the stock market,…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
Spreading phenomena essentially underlie the dynamics of various natural and technological networked systems, yet how spatiotemporal propagation patterns emerge from such networks remains largely unknown. Here we propose a novel approach…
Denoising Diffusion Probabilistic Models (DDPMs) have significantly advanced generative AI, achieving impressive results in high-quality image and data generation. However, enhancing fidelity without compromising semantic content remains a…
Benford's law states that in data sets from different phenomena leading digits tend to be distributed logarithmically such that the numbers beginning with smaller digits occur more often than those with larger ones. Particularly, the law is…
We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalized fluctuation process of the digit sums converges strongly distributional to a random variable…
Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…
The cosmic large scale structure encodes the formation and evolution of a weblike network of dark matter and galaxies within the Universe. The cosmological information is wrapped up in non-Gaussian statistics requiring characterisation…
The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows,…