Related papers: Memory loss for time-dependent dynamical systems

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…

We propose a model of Sinai billiards with moving scatterers, in which the locations and shapes of the scatterers may change by small amounts between collisions. Our main result is the exponential loss of memory of initial data at uniform…

In this paper we introduce the concept of random time changes in dynamical systems. The subordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…

The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…

Evaluating robustness under temporal distribution shift remains an open challenge. Existing metrics quantify the average decline in performance, but fail to capture how models adapt to evolving data. As a result, temporal degradation is…

In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential…

Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving…

This work focuses on the training dynamics of one associative memory module storing outer products of token embeddings. We reduce this problem to the study of a system of particles, which interact according to properties of the data…

Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…

The dynamics of a wide range of real systems, from email patterns to earthquakes, display a bursty, intermittent nature, characterized by short timeframes of intensive activity followed by long times of no or reduced activity. The…

Memory effects are ubiquitous in small-scale systems. They emerge from interactions between accessible and inaccessible degrees of freedom and give rise to evolution equations that are non-local in time. If the characteristic time scales of…

We prove a concentration inequality for sequential dynamical systems of the unit interval enjoying an exponential loss of memory in the BV norm, and we investigate several of its consequences. In particular, this covers compositions of…

This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…

We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…

Human close-range proximity interactions are the key determinant for spreading processes like knowledge diffusion, norm adoption, and infectious disease transmission. These dynamical processes can be modeled with time-respecting paths on…

We investigate the statistics of recurrences to finite size intervals for chaotic dynamical systems. We find that the typical distribution presents an exponential decay for almost all recurrence times except for a few short times affected…

Machine learning-based performance models are increasingly being used to build critical job scheduling and application optimization decisions. Traditionally, these models assume that data distribution does not change as more samples are…

The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…

Various features of the development of individual living species, including individual humans, are programmed. Is death also programmed, and if yes, how is it implemented and what can be the underlying mechanism providing the inevitability…

Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. Individual's…