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We describe how to analyze the wide class of non stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability…
Neurons in the central nervous system communicate with each other with the help of series of Action Potentials, or spike trains. Various studies have shown that neurons encode information in different features of spike trains, such as the…
Information processing in the brain is conducted by a concerted action of multiple neural populations. Gaining insights in the organization and dynamics of such populations can best be studied with broadband intracranial recordings of…
We propose to examine the predictability and the complexity characteristics of the Standard&Poor500 dynamics behaviors in a coarse-grained way using the symbolic dynamics method and under the prism of the Information theory through the…
Multivariate time series analysis is extensively used in neurophysiology with the aim of studying the relationship between simultaneously recorded signals. Recently, advances on information theory and nonlinear dynamical systems theory have…
Many empirical time series are genuinely symbolic: examples range from link activation patterns in network science, DNA coding or firing patterns in neuroscience to cryptography or combinatorics on words. In some other contexts, the…
A well-interpretable measure of information has been recently proposed based on a partition obtained by intersecting a random sequence with its moving average. The partition yields disjoint sets of the sequence, which are then ranked…
The paper presents a time-series-based classification approach to identify similarities in pairs of simulated human-generated patterns. An example for a pattern is a time-series representing a heart rate during a specific time-range,…
Sampling considerations limit the experimental conditions under which information theoretic analyses of neurophysiological data yield reliable results. We develop a procedure for computing the full temporal entropy and information of…
Entropy has been a common index to quantify the complexity of time series in a variety of fields. Here, we introduce increment entropy to measure the complexity of time series in which each increment is mapped into a word of two letters,…
Maximum Entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a…
Understanding the interaction patterns among simultaneous recordings of spike trains from multiple neuronal units is a key topic in neuroscience. However, an optimal approach of assessing these interactions has not been established, as…
One of the main challenges in the study of time-varying networks is the interplay of memory effects with structural heterogeneity. In particular, different nodes and dyads can have very different statistical properties in terms of both link…
Information theory is a powerful framework for quantifying complexity, uncertainty, and dynamical structure in time-series data, with widespread applicability across disciplines such as physics, finance, and neuroscience. However, the…
A new model for stocks markets using integer values for each stock price is presented. In contrast with previously reported models, the variables used in the model are not of binary type, but of more general integer type. It is shown how…
Appealing to several multivariate information measures---some familiar, some new here---we analyze the information embedded in discrete-valued stochastic time series. We dissect the uncertainty of a single observation to demonstrate how the…
The aim of this paper is to investigate various information-theoretic measures, including entropy, mutual information, and some systematic measures that based on mutual information, for a class of structured spiking neuronal network. In…
We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it…
Models of social learning feature either binary signals or abstract signal structures often deprived of micro-foundations. Both models are limited when analyzing interim results or performing empirical analysis. We present a method of…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…