Search results for " Entropy"

Relations frequency hypermatrices in mutual, conditional and joint entropy-based information indices.

2012

Graph-theoretic matrix representations constitute the most popular and significant source of topological molecular descriptors (MDs). Recently, we have introduced a novel matrix representation, named the duplex relations frequency matrix, F, derived from the generalization of an incidence matrix whose row entries are connected subgraphs of a given molecular graph G. Using this matrix, a series of information indices (IFIs) were proposed. In this report, an extension of F is presented, introducing for the first time the concept of a hypermatrix in graph-theoretic chemistry. The hypermatrix representation explores the n-tuple participation frequencies of vertices in a set of connected subgrap…

Assessing Transfer Entropy in cardiovascular and respiratory time series under long-range correlations.

2021

Heart Period (H) results from the activity of several coexisting control mechanisms, involving Systolic Arterial Pressure (S) and Respiration (R), which operate across multiple time scales encompassing not only short-term dynamics but also long-range correlations. In this work, multiscale representation of Transfer Entropy (TE) and of its decomposition in the network of these three interacting processes is obtained by extending the multivariate approach based on linear parametric VAR models to the Vector AutoRegressive Fractionally Integrated (VARFI) framework for Gaussian processes. This approach allows to dissect the different contributions to cardiac dynamics accounting for the simultane…

Localification of variable-basis topological systems

2011

The paper provides another approach to the notion of variable-basis topological system generalizing the fixed-basis concept of S. Vickers, considers functorial relationships between the categories of modified variable-basis topological systems and variable-basis fuzzy topological spaces in the sense of S.E. Rodabaugh and shows that the procedure of localification is possible in the new setting. Quaestiones Mathematicae 33(2010), 11–33

Fuzzy Multi-Criteria Decision Making: An entropy-based approach to assess tourism sustainability

2019

In this article, we propose a method for ranking tourist destinations and evaluating their performances under a sustainability perspective: a fuzzy multiple criteria decision-making method is applied for determining sustainability performance values and ranking destinations accordingly. We select a set of sustainability evaluation criteria and use a fuzzy analytic hierarchy process to weight the selected criteria. We also optimize each evaluator’s membership function support by means of a fuzzy entropy maximization criteria. A case study is illustrated and results are compared with two data envelopment analysis–based models. The simplicity of the proposed approach along with the easy reada…

Robust existence of nonhyperbolic ergodic measures with positive entropy and full support

2021

We prove that for some manifolds $M$ the set of robustly transitive partially hyperbolic diffeomorphisms of $M$ with one-dimensional nonhyperbolic centre direction contains a $C^1$-open and dense subset of diffeomorphisms with nonhyperbolic measures which are ergodic, fully supported and have positive entropy. To do so, we formulate abstract conditions sufficient for the construction of an ergodic, fully supported measure $\mu$ which has positive entropy and is such that for a continuous function $\phi\colon X\to\mathbb{R}$ the integral $\int\phi\,d\mu$ vanishes. The criterion is an extended version of the control at any scale with a long and sparse tail technique coming from the previous w…

Machinery Failure Approach and Spectral Analysis to Study the Reaction Time Dynamics over Consecutive Visual Stimuli: An Entropy-Based Model.

2020

[EN] The reaction times of individuals over consecutive visual stimuli have been studied using an entropy-based model and a failure machinery approach. The used tools include the fast Fourier transform and a spectral entropy analysis. The results indicate that the reaction times produced by the independently responding individuals to visual stimuli appear to be correlated. The spectral analysis and the entropy of the spectrum yield that there are features of similarity in the response times of each participant and among them. Furthermore, the analysis of the mistakes made by the participants during the reaction time experiments concluded that they follow a behavior which is consistent with …

Answering Schrödinger's "What Is Life?"

2020

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A thread through challenging questions

2015

In the pages which follow I shall try to present a network relating some challenging different problems and questions; questions and problems which in different forms have been discussed with Enric along the years. The thread, of course, is constructed by me and now, and is based on my memory, choices and preferences. For these reasons I am not sure that Enric will totally agree with the particular way in which I have intertwined the different elements composing the thread as well as the pieces it connects. However I presume that this thread - also in the specific subjective form as it appears - will show, anyway, some elements of Enric’s activity and the way in which we have interacted alo…

Quantifying attentional demand of a lane-keeping task as the minimum required information in predictive processing

2021

Information Decomposition in Bivariate Systems: Theory and Application to Cardiorespiratory Dynamics

2015

In the framework of information dynamics, the temporal evolution of coupled systems can be studied by decomposing the predictive information about an assigned target system into amounts quantifying the information stored inside the system and the information transferred to it. While information storage and transfer are computed through the known self-entropy (SE) and transfer entropy (TE), an alternative decomposition evidences the so-called cross entropy (CE) and conditional SE (cSE), quantifying the cross information and internal information of the target system, respectively. This study presents a thorough evaluation of SE, TE, CE and cSE as quantities related to the causal statistical s…