Related papers: Stability and Memory-loss go Hand-in-Hand: Three R…
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 living organism as an observer of the evolution of its environment recording sensory information about the state space X of the environment in real time. Sensory information is sampled and then processed on two levels. On the…
Jamming is a phenomenon shared by a wide variety of systems, such as granular materials, foams, and glasses in their high density regime. This has motivated the development of a theoretical framework capable of explaining many of their…
Deficits in working memory, which includes both the ability to learn and to retain information short-term, are a hallmark of many cognitive disorders. Our study analyzes data from a neuroscience experiment on animal subjects, where…
What is the physiological basis of long-term memory? The prevailing view in neuroscience attributes changes in synaptic efficacy to memory acquisition. This view implies that stable memories correspond to stable connectivity patterns.…
Dynamical compensation (DC) has been recently defined as the ability of a biological system to keep its output dynamics unchanged in the face of varying parameters. This concept is purported to describe a design principle that provides…
Using recently proposed measures for non-Markovianity [H. P. Breuer, E. M. Laine, and J. Piilo, Phys. Rev. Lett. {\bf 103}, 210401 (2009)], we study the dynamics of a qubit coupled to a spin environment via an energy-exchange mechanism. We…
Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
Time-dependent data-generating distributions have proven to be difficult for gradient-based training of neural networks, as the greedy updates result in catastrophic forgetting of previously learned knowledge. Despite the progress in the…
The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect…
We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…
The abundance of process operating data in modern industries, along with the rapid advancement of learning techniques, has led to a paradigm shift towards data-centric analysis and control. However, integrating machine learning with control…
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…
Time-dependently driven stochastic systems form a vast and manifold class of non-equilibrium systems used to model important applications on small length scales such as bit erasure protocols or microscopic heat engines. One property that…
Solids are rigid, which means that when left undisturbed, their structures are nearly static. It follows that these structures depend on history -- but it is surprising that they hold readable memories of past events. Here we review the…
The increasing interest in understanding the behavior of the biological neural networks, and the increasing utilization of artificial neural networks in different fields and scales, both require a thorough understanding of how neuromorphic…
Interrelations between dynamical and statistical laws in physics, on the one hand, and between the classical and quantum mechanics, on the other hand, are discussed with emphasis on the new phenomenon of dynamical chaos. The principal…
This paper discusses the evolution of probability distributions for certain time-dependent dynamical systems. Exponential loss of memory is proved for expanding maps and for one-dimensional piecewise expanding maps with slowly varying…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…