Related papers: Memory loss for time-dependent dynamical systems

We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…

Evolution equations are derived for the amplitudes of associative memories: heterogeneous states stored in the connectivity of distributed systems with non-local interactions. The resulting coupled amplitude equations describe the…

This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…

While tabular machine learning has achieved remarkable success, temporal distribution shifts pose significant challenges in real-world deployment, as the relationships between features and labels continuously evolve. Static models assume…

Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…

Moving average models, linear or nonlinear, are characterized by their short memory. This paper shows that, in the presence of feedback in the dynamics, the above characteristic can disappear.

This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one…

Populations of replicating entities frequently experience sudden or cyclical changes in environment. We explore the implications of this phenomenon via a environmental switching parameter in several common evolutionary dynamics models…

In the first half of the paper, some recent advances in coupled dynamical systems, in particular, a globally coupled map are surveyed. First, dominance of Milnor attractors in partially ordered phase is demonstrated. Second, chaotic…

We study the use of Temporal-Difference learning for estimating the structural parameters in dynamic discrete choice models. Our algorithms are based on the conditional choice probability approach but use functional approximations to…

This article develops a periodic version of a time varying parameter fractional process in the stationary region. It is a partial extension of Hosking (1981)'s article which dealt with the case where the coefficients are invariant in time.…

A time-dependent global fiber-bundle model of fracture with continuous damage is formulated in terms of a set of coupled non-linear differential equations. A first integral of this set is analytically obtained. The time evolution of the…

We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…

We show how a recently introduced statistics [Patil et al, Phys. Rev. Lett. 81 5878 (2001)] provides a direct relationship between dimension and predictability in spatiotemporal chaotic systems. Regions of low dimension are identified as…

Memory effects are a key feature in the description of the dynamical systems governed by the generalized Langevin equation, which presents an exact reformulation of the equation of motion. A simple measure for the estimation of memory…

The study of immune system aging, i.e. immunosenescence, is a relatively new research topic. It deals with understanding the processes of immunodegradation that indicate signs of functionality loss possibly leading to death. Even though it…

We consider a discrete-time random walk where the random increment at time step $t$ depends on the full history of the process. We calculate exactly the mean and variance of the position and discuss its dependence on the initial condition…

Divisibility of dynamical maps is visualized by trajectories in the parameter space and analyzed within the framework of collision models. We introduce ultimate completely positive (CP) divisible processes, which lose CP divisibility under…

Regime shifts in biology, ecology, and other complex systems are often interpreted through stability landscapes and early warning signals that implicitly assume dynamics without memory effects. Yet many real systems exhibit these effects,…

We develop and generalize the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical…