Related papers: Memory functions and Correlations in Additive Bina…

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…

Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…

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…

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…

Many complex systems exhibit interactions that depend not only on pairwise connections, but also group structures and memory effects. To capture such effects, we develop a unified tensor framework for modeling higher-order Markov chains…

Temporal networks are widely used models for describing the architecture of complex systems. Network memory -- that is the dependence of a temporal network's structure on its past -- has been shown to play a prominent role in diffusion,…

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 propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many…

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…

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…

Conversion of temporal to spatial correlations in the cortex is one of the most intriguing functions in the brain. The learning at synapses triggering the correlation conversion can take place in a wide integration window, whose influence…

We augment recurrent neural networks with an external memory mechanism that builds upon recent progress in metalearning. We conceptualize this memory as a rapidly adaptable function that we parameterize as a deep neural network. Reading…

In the paper, the law of the iterated logarithm for additive functionals of Markov chains is obtained under some weak conditions, which are weaker than the conditions of invariance principle of additive functionals of Markov chains in M.…

We investigate a new method to augment recurrent neural networks with extra memory without increasing the number of network parameters. The system has an associative memory based on complex-valued vectors and is closely related to…

Long range dependence or long memory is a feature of many processes in the natural world, which provides important insights on the underlying mechanisms that generate the observed data. The usual tools available to characterize the…

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…

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…

Temporal correlations are fundamental in quantum physics, yet their computation is often challenging. The regression theorem (or hypothesis) serves as a key tool in this context, offering a seemingly straightforward approach. However, it…

Sequential recommendation refers to recommending the next item of interest for a specific user based on his/her historical behavior sequence up to a certain time. While previous research has extensively examined Markov chain-based…

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,…