Related papers: Fractional stochastic model of citation dynamics w…
We uncover a universal scaling law governing the dispersion of collective attention and identify its underlying stochastic criticality. By analysing large-scale ensembles of Wikipedia page views, we find that the variance of logarithmic…
This work develops a comprehensive mathematical theory for a class of stochastic processes whose local regularity adapts dynamically in response to their own state. We first introduce and rigorously analyze a time-varying fractional…
Citation distributions are crucial for the analysis and modeling of the activity of scientists. We investigated bibliometric data of papers published in journals of the American Physical Society, searching for the type of function which…
We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the…
We perform experimental verification of the preferential attachment model that is commonly accepted as a generating mechanism of the scale-free complex networks. To this end we chose citation network of Physics papers and traced citation…
The records statistics in stationary and non-stationary fractal time series is studied extensively. By calculating various concepts in record dynamics, we find some interesting results. In stationary fractional Gaussian noises, we observe a…
Scholarly communications have been rapidly integrated into digitised and networked open ecosystems, where preprint servers have played a pivotal role in accelerating the knowledge transfer processes. However, quantitative evidence is scarce…
We propose a new class of rough stochastic volatility models obtained by modulating the power-law kernel defining the fractional Brownian motion (fBm) by a logarithmic term, such that the kernel retains square integrability even in the…
Data from the social-media site, Twitter, is used to study the fluctuations in tweet rates of brand names. The tweet rates are the result of a strongly correlated user behavior, which leads to bursty collective dynamics with a…
Modeling and forecasting forward citations to a patent is a central task for the discovery of emerging technologies and for measuring the pulse of inventive progress. Conventional methods for forecasting these forward citations cast the…
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on…
A mass of traces of human activities show diverse dynamic patterns. In this paper, we comprehensively investigate the dynamic pattern of human attention defined by the quantity of interests on subdisciplines in an online academic…
In these lecture notes, we explore the mathematical preliminaries and foundational concepts that connect stochastic processes with partial differential equations. We begin by investigating Brownian motion, which serves as a model for random…
We analyze time evolution of statistical distributions of citations to scientific papers published in one year. While these distributions can be fitted by a power-law dependence we find that they are nonstationary and the exponent of the…
We investigate the dynamics of a broad class of stochastic copying processes on a network that includes examples from population genetics (spatially-structured Wright-Fisher models), ecology (Hubbell-type models), linguistics (the utterance…
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability…
The origin of the long-range memory in the non-equilibrium systems is still an open problem as the phenomenon can be reproduced using models based on Markov processes. In these cases a notion of spurious memory is introduced. A good example…
Efficiency of search for randomly distributed targets is a prominent problem in many branches of the sciences. For the stochastic process of L\'evy walks, a specific range of optimal efficiencies was suggested under variation of search…
In this paper we prove, for small Hurst parameters, the higher order differentiability of a stochastic flow associated with a stochastic differential equation driven by an additive multi-dimensional fractional Brownian noise, where the…
We propose a single chunk model of long-term memory that combines the basic features of the ACT-R theory and the multiple trace memory architecture. The pivot point of the developed theory is a mathematical description of the creation of…