相关论文: Memory Functions of the Additive Markov chains: Ap…

In this study, a new extension of the Markov Renewal theory is introduced by allowing time to evolve in multiple dimensions. The resulting chains are referred to as multi-time Markov Renewal chains and since this extension is new, the state…

We consider additive functionals of Markov processes in continuous time with general (metric) state spaces. We derive concentration bounds for their exponential moments and moments of finite order. Applications include diffusions,…

Learning to remember long sequences remains a challenging task for recurrent neural networks. Register memory and attention mechanisms were both proposed to resolve the issue with either high computational cost to retain memory…

In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has…

The main goal of the paper is to develop an estimate for the conditional probability function of random stationary ergodic symbolic sequences with elements belonging to a finite alphabet. We elaborate a decomposition procedure for the…

In this paper we study the additive functionals of Markov chains via conditioning with respect to both past and future of the chain. We shall point out new sufficient projective conditions, which assure that the variance of partial sums of…

We consider the evolution of correlation functions in a non-Markov version of the contact model in the continuum. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. This leads to a…

Recurrent neural networks (RNN) are simple dynamical systems whose computational power has been attributed to their short-term memory. Short-term memory of RNNs has been previously studied analytically only for the case of orthogonal…

Stochastic processes with long memories, known as long memory processes, are ubiquitous in various science and engineering problems. Superposing Markovian stochastic processes generates a non-Markovian long memory process serving as…

A new object of the probability theory, two-sided chain of events (symbols), is introduced. A theory of multi-steps Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to establish…

Given a description of the stacking statistics of layered close-packed structures in the form of a hidden Markov model, we develop analytical expressions for the pairwise correlation functions between the layers. These may be calculated…

We introduce a hybrid approach for computing dynamical observables in strongly correlated systems using higher-order moments. This method integrates memory kernel coupling theory (MKCT) with the density matrix renormalization group (DMRG),…

Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…

We describe a new algorithm for the perfect simulation of variable length Markov chains and random systems with perfect connections. This algorithm, which generalizes Propp and Wilson's simulation scheme, is based on the idea of coupling…

Neuron models of associative memory provide a new and prospective technology for reliable date storage and patterns recognition. However, even when the patterns are uncorrelated, the efficiency of most known models of associative memory is…

We develop an instanton technique for calculations of correlation functions characterizing statistical behavior of the elastic string in disordered media and apply the proposed approach to correlations of string free energies corresponding…

We describe a new class of learning models called memory networks. Memory networks reason with inference components combined with a long-term memory component; they learn how to use these jointly. The long-term memory can be read and…

Many real-world complex systems are characterized by interactions in groups that change in time. Current temporal network approaches, however, are unable to describe group dynamics, as they are based on pairwise interactions only. Here, we…

Contextual memory integration remains a high challenge in the development of language models, particularly in tasks that require maintaining coherence over extended sequences. Traditional approaches, such as self-attention mechanisms and…

This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…