Related papers: Memory functions and Correlations in Additive Bina…

Associative memories are structures that store data in such a way that it can later be retrieved given only a part of its content -- a sort-of error/erasure-resilience property. They are used in applications ranging from caches and memory…

We study a dephasing channel with memory, modelled by a Markov chain. We show that even weak memory effects have a detrimental impact on the performance of quantum error correcting schemes designed for uncorrelated errors. We also discuss…

To better understand the flows of ideas or information through social and biological systems, researchers develop maps that reveal important patterns in network flows. In practice, network flow models have implied memoryless first-order…

Time delays increase the effective dimensionality of reservoirs, thus suggesting that time delays in reservoirs can enhance their performance, particularly their memory and prediction abilities. We find new closed-form expressions for…

A central question in neuroscience is to understand how noisy firing patterns are used to transmit information. Because neural spiking is noisy, spiking patterns are often quantified via pairwise correlations, or the probability that two…

We consider the problem of neural association for a network of non-binary neurons. Here, the task is to first memorize a set of patterns using a network of neurons whose states assume values from a finite number of integer levels. Later,…

We consider a Markov control model in discrete time with countable both state space and action space. Using the value function of a suitable long-run average reward problem, we study various reachability/controllability problems. First, we…

Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…

Multivariate Hawkes processes are past-dependant point processes originally introduced to model excitation effects, later extended to a nonlinear framework to account for the opposite effect, known as inhibition. Motivated by applications…

Given a sequence of i.i.d. random functions $\Psi_{n}:\mathbb{R}\to\mathbb{R}$, $n\in\mathbb{N}$, we consider the iterated function system and Markov chain which is recursively defined by $X_{0}^{x}:=x$ and…

In this research paper, the relationship between finite / countable state space stochastic processes and point processes is explored. Utilizing the known relationship between Poisson processes and continuous time Markov chains, finite /…

Causal relationships play a fundamental role in understanding the world around us. The ability to identify and understand cause-effect relationships is critical to making informed decisions, predicting outcomes, and developing effective…

This article introduces autocorrelograms for time series of point processes. Such time series usually arise when a longer temporal or spatio-temporal point process is sliced into smaller time units; for example, when an annual process is…

The goal of this paper is to develop an estimate for the entropy of random long-range correlated symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov…

Recent empirical studies have demonstrated long-memory in the signs of orders to buy or sell in financial markets [2, 19]. We show how this can be caused by delays in market clearing. Under the common practice of order splitting, large…

We discuss the efficient computation of performance, reliability, and availability measures for Markov chains; these metrics, and the ones obtained by combining them, are often called performability measures. We show that this computational…

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…

The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…

The synapses of real neural systems seem to have delays. Therefore, it is worthwhile to analyze associative memory models with delayed synapses. Thus, a sequential associative memory model with delayed synapses is discussed, where a…

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…