Related papers: Fractional stochastic model of citation dynamics w…
We analyze the citation time-series of manuscripts in three different fields of science; physics, social science and technology. The evolution of the time-series of the yearly number of citations, namely the citation trajectories, diffuse…
This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we…
Although higher-order interactions are known to affect the typical state of dynamical processes giving rise to new collective behavior, how they drive the emergence of rare events and fluctuations is still an open problem. We investigate…
This is a set of four lectures devoted to simple ideas about turbulent transport, a ubiquitous non-equilibrium phenomenon. In the course similar to that given by the author in 2006 in Warwick [45], we discuss lessons which have been learned…
Stochastic mechanics is based on the hypothesis that all matter is subject to universal modified Brownian motion. In this report, we calculated probability density distributions using concepts of stochastic mechanics independent of…
Stochasticity is a defining feature of the pairwise forces governing interactions in biological systems-from molecular motors to cell-cell adhesion-yet its consequences on large-scale dynamics remain poorly understood. Here, we show that…
The recent interest in human dynamics has led researchers to investigate the stochastic processes that explain human behaviour in different contexts. Here we propose a generative model to capture the essential dynamics of survival analysis,…
With the rapid development of computational techniques and scientific tools, great progress of data-driven analysis has been made to extract governing laws of dynamical systems from data. Despite the wide occurrences of non-Gaussian…
The goal of this paper is to establish a general framework for dynamic behaviors of coupled fractional-order stochastic dynamic systems of particles by using star-coupled models. In particular, the general mechanics on the dynamic behaviors…
Learning the underlying potential energy of stochastic gradient systems from partial and noisy observations is a fundamental problem arising in physics, chemistry, and data-driven modeling. Classical approaches often rely on direct…
Science is a growing system, exhibiting ~4% annual growth in publications and ~1.8% annual growth in the number of references per publication. Combined these trends correspond to a 12-year doubling period in the total supply of references,…
The ARCH process (R. F. Engle, 1982) constitutes a paradigmatic generator of stochastic time series with time-dependent variance like it appears on a wide broad of systems besides economics in which ARCH was born. Although the ARCH process…
Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the…
Scoring patent documents is very useful for technology management. However, conventional methods are based on static models and, thus, do not reflect the growth potential of the technology cluster of the patent. Because even if the cluster…
Stochastic processes with multiplicative noise have been studied independently in several different contexts over the past decades. We focus on the regime, found for a generic set of control parameters, in which stochastic processes with…
Brownian ratchet like stochastic theory for the electrochemical membrane system of Hodgkin-Huxley (HH) is developed. The system is characterized by a continuous variable $Q_m(t)$, representing mobile membrane charge density, and a discrete…
Long-range correlated processes are ubiquitous, ranging from climate variables to financial time series. One paradigmatic example for such processes is fractional Brownian motion (fBm). In this work, we highlight the potentials and…
A stochastic model, the product of a circulant matrix and a random normal vector, is shown to produce an evolutive long memory time series with a power law spectral density. The distribution of the time series, a beta location scale family…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
Transformer-based scientific foundation models are increasingly deployed in high-stakes settings, but current architectures give deterministic outputs and provide limited support for calibrated predictive uncertainty. We propose Stochastic…