Related papers: Memory loss for time-dependent dynamical systems
We study the time evolution of the mutual information between the mass distributions in spatially separated but casually connected regions in an expanding universe. The evolution of the mutual information is primarily determined by the…
We analyse large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time t depends itself on the value q_t of the time-averaged quantity. First we consider the elephant random walk…
This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
We introduce a novel loss function, Covariance Loss, which is conceptually equivalent to conditional neural processes and has a form of regularization so that is applicable to many kinds of neural networks. With the proposed loss, mappings…
This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic evolutionary equations. Under suitable…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
We analyze the transport properties of a set of symmetry-breaking extensions %, both spatial and temporal, of the Chirikov--Taylor Map. The spatial and temporal asymmetries result in the loss of periodicity in momentum direction in the…
For any linear system with unreduced dynamics governed by invertible propagators, we derive a closed, time-delayed, linear system for a reduced-dimensional quantity of interest. This method does not target dimensionality reduction: rather,…
We analyze the fate of dynamical systems that consist of two kind of processes. The first type is supposed to perform a certain function by processing information at a required high accuracy, which is, however, limited to less than 100…
Resistance switching memory cells such as electrochemical metallization cells and valence change mechanism cells have the potential to revolutionize information processing and storage. However, the creation of deterministic resistance…
The impact of quenched disorder on deterministic diffusion in chaotic dynamical systems is studied. As a simple example, we consider piecewise linear maps on the line. In computer simulations we find a complicated scenario of multiple…
In this work we investigate the information loss in (nonlinear) dynamical input-output systems and provide some general results. In particular, we present an upper bound on the information loss rate, defined as the (non-negative) difference…
In this paper we study the distribution of hitting times for a class of random dynamical systems. We prove that for invariant measures with super-polynomial decay of correlations hitting times to dynamically defined cylinders satisfy…
In this doctoral thesis, we investigate the complex interplay between temporal dynamics associated with aging and memory and their effects on social and economic systems. To do so, we combine theoretical modeling, to explore the aging…
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…
This paper proposes a formal approach to online learning and planning for agents operating in a priori unknown, time-varying environments. The proposed method computes the maximally likely model of the environment, given the observations…
We study a model of stochastic evolutionary game dynamics in which the probabilities that agents choose suboptimal actions are dependent on payoff consequences. We prove a sample path large deviation principle, characterizing the rate of…
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
Use of machine learning to perform database operations, such as indexing, cardinality estimation, and sorting, is shown to provide substantial performance benefits. However, when datasets change and data distribution shifts, empirical…