Related papers: Anomalous diffusions induced by enhancement of mem…
Strong anomalous diffusion is {often} characterized by a piecewise-linear spectrum of the moments of displacement. The spectrum is characterized by slopes $\xi$ and $\zeta$ for small and large moments, respectively, and by the critical…
Anomalous diffusions arise as scaling limits of continuous-time random walks (CTRWs) whose innovation times are distributed according to a power law. The impact of a non-exponential waiting time does not vanish with time and leads to…
The memory effect in disordered systems is a key physical phenomenon that has been employed for optical imaging, metrology, and communication through opaque media. Under the conventional memory effect, when the incident beam is tilted…
We investigate the long-term diffusion transport and chaos properties of single and coupled standard maps. We consider model parameters that are known to induce anomalous diffusion in the maps' phase spaces, as opposed to normal diffusion…
Disordered and amorphous materials often retain memories of perturbations they have experienced since preparation. Studying such memories is a gateway to understanding this challenging class of systems, yet it often requires the ability to…
Diffusion probabilistic models have become a cornerstone of modern generative AI, yet the mechanisms underlying their generalization remain poorly understood. In fact, if these models were perfectly minimizing their training loss, they…
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…
We introduce Pairwise Distance-Diffusion Analysis (PDDA), a geometric framework for estimating the Hurst exponent from distance plots of long-memory stochastic processes. A single construction yields two complementary routes: R/S-PDDA, a…
We perform an extensive and detailed analysis of the generalized diffusion processes in deterministic area preserving maps with noncompact phase space, exemplified by the standard map, with the special emphasis on understanding the…
The study of the dynamics of natural and artificial systems has provided several examples of deviations from Brownian behavior, generally defined as anomalous diffusion. The investigation of these dynamics can provide a better understanding…
We present a theory for the coagulation reaction A+A -> A for particles moving subdiffusively in one dimension. Our theory is tested against numerical simulations of the concentration of $A$ particles as a function of time (``anomalous…
We consider a class of dynamic advertising problems under uncertainty in the presence of carryover and distributed forgetting effects, generalizing a classical model of Nerlove and Arrow. In particular, we allow the dynamics of the product…
The deviation from pure Brownian motion generally referred to as anomalous diffusion has received large attention in the scientific literature to describe many physical scenarios. Several methods, based on classical statistics and machine…
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…
We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with…
Fractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean squared particle displacement following a power law, $\langle {\Delta r}^2 \rangle \sim…
We introduce a one-dimensional random walk, which at each step performs a reinforced dynamics with probability $\theta$ and with probability $1 - \theta$, the random walk performs a step independent of the past. We analyse its asymptotic…
The self-exciting Hawkes process is widely used to model events which occur in bursts. However, many real world data sets contain missing events and/or noisily observed event times, which we refer to as data distortion. The presence of such…
We introduce a simple stochastic system able to generate anomalous diffusion both for position and velocity. The model represents a viable description of the Fermi's acceleration mechanism and it is amenable to analytical treatment through…
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…