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We introduce an statistical mechanical formalism for the study of discrete-time stochastic processes with which we prove: (i) General properties of extremal chains, including triviality on the tail $\sigma$-algebra, short-range…

This paper presents the design of an associative memory with feedback that is capable of on-line temporal sequence learning. A framework for on-line sequence learning has been proposed, and different sequence learning models have been…

This paper discusses a system that accelerates reinforcement learning by using transfer from related tasks. Without such transfer, even if two tasks are very similar at some abstract level, an extensive re-learning effort is required. The…

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…

In this paper, it is presented a methodology for implementing arbitrarily constructed time-homogenous Markov chains with biochemical systems. Not only discrete but also continuous-time Markov chains are allowed to be computed. By employing…

In multi-state life insurance, an adequate balance between analytic tractability, computational efficiency, and statistical flexibility is of great importance. This might explain the popularity of Markov chain modelling, where matrix…

Additive models form a widely popular class of regression models which represent the relation between covariates and response variables as the sum of low-dimensional transfer functions. Besides flexibility and accuracy, a key benefit of…

We examine a previouly introduced attractor neural network model that explains the persistent activities of neurons in the anterior ventral temporal cortex of the brain. In this model, the coexistence of several attractors including…

The primate heteromodal cortex presents an evident functional modularity at a mesoscopic level, with physiological and anatomical evidence pointing to it as likely substrate of long-term memory. In order to investigate some of its…

Machine learning techniques not only offer efficient tools for modelling dynamical systems from data, but can also be employed as frontline investigative instruments for the underlying physics. Nontrivial information about the original…

Modeling long sequences is crucial for various large-scale models; however, extending existing architectures to handle longer sequences presents significant technical and resource challenges. In this paper, we propose an efficient and…

Non-Markovian quantum processes exhibit different memory effects when measured in different ways; an unambiguous characterization of memory length requires accounting for the sequence of instruments applied to probe the system dynamics.…

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 propose a conceptually novel method of reconstructing the topology of dynamical networks. By examining the correlation between the variable of one node and the derivative of another node, we derive a simple matrix equation yielding the…

One important problem in constructing the reduced dynamics of molecular systems is the accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved variables. The main complication emerges from the lack of scale…

Firing rate models are dynamical systems widely used in applied and theoretical neuroscience to describe local cortical dynamics in neuronal populations. By providing a macroscopic perspective of neuronal activity, these models are…

Many scientific areas, from computer science to the environmental sciences and finance, give rise to multivariate time series which exhibit long memory, or loosely put, a slow decay in their autocorrelation structure. Efficient modelling…

Markov chains in random environments (MCREs) have recently attracted renewed interest, as these processes naturally arise in many applications, such as econometrics and machine learning. Although specific asymptotic results, such as the law…

Markov chains are a common framework for individual-based state and time discrete models in ecology and evolution. Their use, however, is largely limited to systems with a low number of states, since the transition matrices involved pose…

It is well-known that the aggregated time series might have very different properties from those of the individual series, in particular, long memory. At the present time, aggregation has become one of the main tools for modelling of long…