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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…

A new method to study the long-range correlations in multiparticle production is developped. It is proposed to study the joint factorial moments or cumulants of multiplicity distributions in several (more than two) bins. It is shown that…

We study the statistical performance of a continual learning problem with two linear regression tasks in a well-specified random design setting. We consider a structural regularization algorithm that incorporates a generalized…

We investigate correlation functions in a periodic box-ball system. For the second and the third nearest neighbor correlation functions, we give explicit formulae obtained by combinatorial methods. A recursion formula for a specific…

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,…

This paper explores Memory-Augmented Neural Networks (MANNs), delving into how they blend human-like memory processes into AI. It covers different memory types, like sensory, short-term, and long-term memory, linking psychological theories…

We propose machine learning (ML) methods to characterize the memristive properties of single and coupled quantum memristors. We show that maximizing the memristivity leads to large values in the degree of entanglement of two quantum…

One stylized feature of financial volatility impacting the modeling process is long memory. This paper examines long memory for alternative risk measures, observed absolute and squared returns for Daily REITs and compares the findings for a…

This paper proposes a method for sequential data mining using correlation matrix memory. Here, we use the concept of the Logical Match to mine the indices of the sequential pattern. We demonstrate the uniqueness of the method with both the…

Network datasets typically exhibit certain types of statistical dependencies, such as within-dyad correlation, row and column heterogeneity, and third-order dependence patterns such as transitivity and clustering. The first two of these can…

This paper presents a graded hierarchy or chain of binary operations on the reals and the complex numbers. The operations are related distributively in the sense that any one of them distributes over the next lower operation in the chain.…

We study a model of associative memory based on a neural network with small-world structure. The efficacy of the network to retrieve one of the stored patterns exhibits a phase transition at a finite value of the disorder. The more ordered…

Correlated fluctuations in the activity of neural populations reflect the network's dynamics and connectivity. The temporal and spatial dimensions of neural correlations are interdependent. However, prior theoretical work mainly analyzed…

Classical models of memory in psychology and neuroscience rely on similarity-based retrieval of stored patterns, where similarity is a function of retrieval cues and the stored patterns. While parsimonious, these models do not allow…

We investigate from a computational perspective the efficiency of the Willshaw synaptic update rule in the context of familiarity discrimination, a binary-answer, memory-related task that has been linked through psychophysical experiments…

Motivated by multiple applications in social networks, nervous systems, and financial risk analysis, we consider the problem of learning the underlying (directed) influence graph or causal graph of a high-dimensional multivariate…

Memory is the fundamental form of temporal complexity: when present but uncontrollable, it manifests as non-Markovian noise; conversely, if controllable, memory can be a powerful resource for information processing. Memory effects arise…

A notion of a coring extension is defined and it is related to the existence of an additive functor between comodule categories that factorises through forgetful functors. This correspondence between coring extensions and factorisable…

We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. We discuss this new property and describe certain classes of associative string…

An associative memory is a framework of content-addressable memory that stores a collection of message vectors (or a dataset) over a neural network while enabling a neurally feasible mechanism to recover any message in the dataset from its…