Search results for "entropy"

ON THE STAR HEIGHT OF RATIONAL LANGUAGES

1994

Two problems concerning the star height of a rational language are investigated: the star height one problem and the relationships between the unambiguity of an expression and its star height. For this purpose we consider the class of factorial, transitive and rational (FTR) languages. From the algebraic point of view a FTR language is the set of factors of a rational submonoid M. Two subclasses of FTR languages are introduced: renewal languages, corresponding to the case of M finitely generated, and unambiguous renewal languages, corresponding to the case of M finitely generated and free. We prove that a FTR language has star height one if and only if it is renewal. This gives a simple de…

Balancing and clustering of words in the Burrows–Wheeler transform

2011

AbstractCompression algorithms based on Burrows–Wheeler transform (BWT) take advantage of the fact that the word output of BWT shows a local similarity and then turns out to be highly compressible. The aim of the present paper is to study such “clustering effect” by using notions and methods from Combinatorics on Words.The notion of balance of a word plays a central role in our investigation. Empirical observations suggest that balance is actually the combinatorial property of input word that ensure optimal BWT compression. Moreover, it is reasonable to assume that the more balanced the input word is, the more local similarity we have after BWT (and therefore the better the compression is).…

Developing and Integrating Advanced Movement Features Improves Automated Classification of Ciliate Species

2015

Recent advances in tracking technologies such as GPS or video tracking systems describe the movement paths of individuals in unprecedented details and are increasingly used in different fields, including ecology. However, extracting information from raw movement data requires advanced analysis techniques, for instance to infer behaviors expressed during a certain period of the recorded trajectory, or gender or species identity in case data is obtained from remote tracking. In this paper, we address how different movement features affect the ability to automatically classify the species identity, using a dataset of unicellular microbes (i.e., ciliates). Previously, morphological attributes a…

Hydration entropy of BaZrO3 from first principles phonon calculations

2015

The impact of phonons on the hydration and defect thermodynamics of undoped and acceptor (Sc, In, Y and Gd) doped BaZrO3 is addressed by means of first principles supercell calculations. In contrast to previous, similar investigations, we evaluate contributions from all phonon modes, and also pressure/volume effects on the phonon properties. The calculations are performed at the GGA-level with the PBE and RPBE functionals, both of which predict for BaZrO3 a stable cubic perovskite structure. For all dopants, the vibrational formation entropy of the doubly positively charged oxygen vacancy is significantly lower than that of the protonic defect , which therefore also is the dominant contribu…

Feasibility of Linear Parametric Estimation of Dynamic Information Measures to assess Physiological Stress from Short-Term Cardiovascular Variability

2021

Extensive efforts have been recently devoted to implement fast and reliable algorithms capable of assessing the physiological response of the organism to physiological stress. In this study, we propose the comparison between model-free and linear parametric methods as regards their ability to detect alterations in the dynamics and in the complexity of cardiovascular and respiratory variability evoked by postural and mental stress. Dynamic entropy (DE) and information storage (IS) measures were calculated on three physiological time-series, i.e. heart period, respiratory volume and systolic arterial pressure, on 61 healthy subjects monitored in resting conditions as well as during head-up ti…

Network Entropy for the Sequence Analysis of Functional Connectivity Graphs of the Brain

2018

Dynamic representation of functional brain networks involved in the sequence analysis of functional connectivity graphs of the brain (FCGB) gains advances in uncovering evolved interaction mechanisms. However, most of the networks, even the event-related ones, are highly heterogeneous due to spurious interactions, which bring challenges to revealing the change patterns of interactive information in the complex dynamic process. In this paper, we propose a network entropy (NE) method to measure connectivity uncertainty of FCGB sequences to alleviate the spurious interaction problem in dynamic network analysis to realize associations with different events during a complex cognitive task. The p…

Information Decomposition: A Tool to Dissect Cardiovascular and Cardiorespiratory Complexity

2017

This chapter reports some recent developments of information-theoretic concepts applied to the description of coupled dynamical systems, which allow to decompose the entropy of an assigned target system into components reflecting the information stored in the system and the information transferred to it from the other systems, as well as the nature (synergistic or redundant) of the information transferred to the target. The decomposition leads to well-defined measures of information dynamics which in the chapter will be defined theoretically, computed in simulations of linear Gaussian systems and implemented in practice through the application to heart period, arterial pressure and respirat…

Analytical properties of horizontal visibility graphs in the Feigenbaum scenario

2012

Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [1] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-doubling and band-splitting attractor cascades that characterize unimodal maps transform into families of graphs that turn out to be independent of map nonlinearity or other particulars. Here we provide an in depth description of the HV treatment of the Feigenbaum scenario, together with analytical derivations that relate to the degree di…

Feigenbaum graphs: a complex network perspective of chaos

2011

The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map…

Entropy

2008