Related papers: Memory loss for time-dependent dynamical systems
Widespread deployment of societal-scale machine learning systems necessitates a thorough understanding of the resulting long-term effects these systems have on their environment, including loss of trustworthiness, bias amplification, and…
We investigate how the time evolution of different kinetic Ising models depends on the initial conditions of the dynamics. To this end we consider the simultaneous evolution of two identical systems subjected to the same thermal noise. We…
In this work, we propose a method to learn multivariate probability distributions using sample path data from stochastic differential equations. Specifically, we consider temporally evolving probability distributions (e.g., those produced…
We introduce a random dynamical system related to continued fraction expansions. It uses random combination of the Gauss map and the R\'enyi (or backwards) continued fraction map. We explore the continued fraction expansions that this…
Memory has a great impact on the evolution of every process related to human societies. Among them, the evolution of an epidemic is directly related to the individuals' experiences. Indeed, any real epidemic process is clearly sustained by…
Dynamical systems are often time-varying, whose modeling requires a function that evolves with respect to time. Recent studies such as the neural ordinary differential equation proposed a time-dependent neural network, which provides a…
We introduce a two-dimensional discrete-time dynamical system which represents the evolution of an angle and angular velocity. While the angle evolves by a fixed amount in every step, the evolution of the angular velocity is governed by a…
Certain intriguing consequences of the discreteness of time on the time evolution of dynamical systems are discussed. In the discrete-time classical mechanics proposed here, there is an {\it arrow of time} that follows from the fact that…
In this work, we consider a fully dynamic Biot model that includes memory effects due to evolving permeability. Time integrals are used to account for the change in structure. We propose an iterative splitting scheme for this model,…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
Despite their deterministic nature, dynamical systems often exhibit seemingly random behaviour. Consequently, a dynamical system is usually represented by a probabilistic model of which the unknown parameters must be estimated using…
We use freeness assumptions of random matrix theory to analyze the dynamical behavior of inference algorithms for probabilistic models with dense coupling matrices in the limit of large systems. For a toy Ising model, we are able to recover…
Discrete time evolution of one-dimensional maps is embedded in continuous time by truncating the Taylor series expansion of the time evolution operator to a finite order N. Truncations with N > 4 leads to unconditional instability.…
Machine learning models often require large datasets and struggle to generalize beyond their training distribution. These limitations pose significant challenges in scientific and engineering contexts, where generating exhaustive datasets…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of…
The problem of error growth due to the incomplete knowledge of the evolution law which rules the dynamics of a given physical system is addressed. Major interest is devoted to the analysis of error amplification in systems with many…
In the paper the memory effect in the system consisting from a trajectory of process and an environment is considered. The environment is presented by scalar potential and noise. The evolution of system is interpreted as process of the…
We consider a dynamical system to have memory if it remembers the current state as well as the state before that. The dynamics is defined as follows: $x_{n+1}=T_{\alpha}(x_{n-1},x_{n})=\tau (\alpha \cdot x_{n}+(1-\alpha)\cdot x_{n-1}),$…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…