Test-retest reliability of electromyographic variables of masseter and temporal muscles in patients with cerebral palsy

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Linear and nonlinear measures of fetal heart rate patterns evaluated on very short fetal magnetocardiograms

We analyzed the effectiveness of linear short- and long-term variability time domain parameters, an index of sympatho-vagal balance (SDNN/RMSSD) and entropy in differentiating fetal heart rate patterns (fHRPs) on the fetal heart rate (fHR) series of 5, 3 and 2 min duration reconstructed from 46 fetal magnetocardiograms. Gestational age (GA) varied from 21 to 38 weeks. FHRPs were classified based on the fHR standard deviation. In sleep states, we observed that vagal influence increased with GA, and entropy significantly increased (decreased) with GA (SDNN/RMSSD), demonstrating that a prevalence of vagal activity with autonomous nervous system maturation may be associated with increased sleep state complexity. In active wakefulness, we observed a significant negative (positive) correlation of short-term (long-term) variability parameters with SDNN/RMSSD. ANOVA statistics demonstrated that long-term irregularity and standard deviation of normal-to-normal beat intervals (SDNN) best differentiated among fHRPs. Our results confirm that short-and long-term variability parameters are useful to differentiate between quiet and active states, and that entropy improves the characterization of sleep states. All measures differentiated fHRPs more effectively on very short HR series, as a result of the fMCG high temporal resolution and of the intrinsic timescales of the events that originate the different fHRPs.

Sensitivity, specificity and predictive values of linear and nonlinear indices of heart rate variability in stable angina patients

Abstract Background Decreased heart rate variability (HRV) is related to higher morbidity and mortality. In this study we evaluated the linear and nonlinear indices of the HRV in stable angina patients submitted to coronary angiography. Methods We studied 77 unselected patients for elective coronary angiography, which were divided into two groups: coronary artery disease (CAD) and non-CAD groups. For analysis of HRV indices, HRV was recorded beat by beat with the volunteers in the supine position for 40 minutes. We analyzed the linear indices in the time (SDNN [standard deviation of normal to normal], NN50 [total number of adjacent RR intervals with a difference of duration greater than 50ms] and RMSSD [root-mean square of differences]) and frequency domains ultra-low frequency (ULF) ≤ 0,003 Hz, very low frequency (VLF) 0,003 – 0,04 Hz, low frequency (LF) (0.04–0.15 Hz), and high frequency (HF) (0.15–0.40 Hz) as well as the ratio between LF and HF components (LF/HF). In relation to the nonlinear indices we evaluated SD1, SD2, SD1/SD2, approximate entropy (−ApEn), α1, α2, Lyapunov Exponent, Hurst Exponent, autocorrelation and dimension correlation. The definition of the cutoff point of the variables for predictive tests was obtained by the Receiver Operating Characteristic curve (ROC). The area under the ROC curve was calculated by the extended trapezoidal rule, assuming as relevant areas under the curve ≥ 0.650. Results Coronary arterial disease patients presented reduced values of SDNN, RMSSD, NN50, HF, SD1, SD2 and -ApEn. HF ≤ 66 ms2, RMSSD ≤ 23.9 ms, ApEn ≤−0.296 and NN50 ≤ 16 presented the best discriminatory power for the presence of significant coronary obstruction. Conclusion We suggest the use of Heart Rate Variability Analysis in linear and nonlinear domains, for prognostic purposes in patients with stable angina pectoris, in view of their overall impairment.

Indicatori di correlazione e di disordine basati sul concetto di entropia

The aim of this work is to carry out an applicative, comparative and exhaustive study between several entropy based indicators of independence and correlation. We considered some indicators characterized by a wide and consolidate literature, like mutual information, joint entropy, relative entropy or Kullback Leibler distance, and others, more recently introduced, like Granger, Maasoumi and racine entropy, also called Sρ, or utilized in more restricted domains, like Pincus approximate entropy or ApEn. We studied the behaviour of such indicators applying them to binary series. The series was designed to simulate a wide range of situations in order to characterize indicators limit and capability and to identify, case by case, the more useful and trustworthy ones. Our target was not only to study if such indicators were able to discriminate between dependence and independence because, especially for mutual information and Granger, Maasoumi and Racine, that was already demonstrated and reported in literature, but also to verify if and how they were able to provide information about structure, complexity and disorder of the series they were applied to. Special attention was paid on Pincus approximate entropy, that is said by the author to be able to provide information regarding the level of randomness, regularity and complexity of a series. By means of a focused and extensive research, we furthermore tried to clear the meaning of ApEn applied to a couple of different series. In such situation the indicator is named in literature as cross-ApEn. The cross-ApEn meaning and the interpretation of its results is often not simple nor univocal and the matter is scarcely delved into by literature, thereby users can easily leaded up to a misleading conclusion, especially if the indicator is employed, as often unfortunately it happens, in uncritical manner. In order to plug some cross-ApEn gaps and limits clearly brought out during the experimentation, we developed and applied to the already considered cases a further indicator we called “correspondence index”. The correspondence index is perfectly integrated into the cross-ApEn computational algorithm and it is able to provide, at least for binary data, accurate information about the intensity and the direction of an eventual correlation, even not linear, existing between two different series allowing, in the meanwhile, to detect an eventual condition of independence between the series themselves.

A recipe for randomness

Despite many diverse theories that address closely related themes—e.g., probability theory, algorithmic complexity, cryptoanalysis, and pseudorandom number generation—a near-void remains in constructive methods certified to yield the desired “random” output. Herein, we provide explicit techniques to produce broad sets of both highly irregular finite and normal infinite sequences, based on constructions and properties derived from approximate entropy (ApEn), a computable formulation of sequential irregularity. Furthermore, for infinite sequences, we considerably refine normality, by providing methods for constructing diverse classes of normal numbers, classified by the extent to which initial segments deviate from maximal irregularity.

Randomness and degrees of irregularity.

The fundamental question "Are sequential data random?" arises in myriad contexts, often with severe data length constraints. Furthermore, there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness--e.g., to evaluate the efficacy of therapy in medicine. We address both these issues from a computable framework via a quantification of regularity. ApEn (approximate entropy), defining maximal randomness for sequences of arbitrary length, indicating the applicability to sequences as short as N = 5 points. An infinite sequence formulation of randomness is introduced that retains the operational (and computable) features of the finite case. In the infinite sequence setting, we indicate how the "foundational" definition of independence in probability theory, and the definition of normality in number theory, reduce to limit theorems without rates of convergence, from which we utilize ApEn to address rates of convergence (of a deficit from maximal randomness), refining the aforementioned concepts in a computationally essential manner. Representative applications among many are indicated to assess (i) random number generation output; (ii) well-shuffled arrangements; and (iii) (the quality of) bootstrap replicates.

Regularity analysis of nocturnal oximetry recordings to assist in the diagnosis of sleep apnoea syndrome

The relationship between sleep apnoea–hypopnoea syndrome (SAHS) severity and the regularity of nocturnal oxygen saturation (SaO2) recordings was analysed. Three different methods were proposed to quantify regularity: approximate entropy (AEn), sample entropy (SEn) and kernel entropy (KEn). A total of 240 subjects suspected of suffering from SAHS took part in the study. They were randomly divided into a training set (96 subjects) and a test set (144 subjects) for the adjustment and assessment of the proposed methods, respectively. According to the measurements provided by AEn, SEn and KEn, higher irregularity of oximetry signals is associated with SAHS-positive patients. Receiver operating characteristic (ROC) and Pearson correlation analyses showed that KEn was the most reliable predictor of SAHS. It provided an area under the ROC curve of 0.91 in two-class classification of subjects as SAHS-negative or SAHS-positive. Moreover, KEn measurements from oximetry data exhibited a linear dependence on the apnoea–hypopnoea index, as shown by a correlation coefficient of 0.87. Therefore, these measurements could be used for the development of simplified diagnostic techniques in order to reduce the demand for polysomnographies. Furthermore, KEn represents a convincing alternative to AEn and SEn for the diagnostic analysis of noisy biomedical signals.

Análise não linear de séries temporais e aplicações à Psicologia

Nesta dissertação estudámos as séries temporais que representam a complexa dinâmica do comportamento. Demos especial atenção às técnicas de dinâmica não linear. As técnicas fornecem-nos uma quantidade de índices quantitativos que servem para descrever as propriedades dinâmicas do sistema. Estes índices têm sido intensivamente usados nos últimos anos em aplicações práticas em Psicologia. Estudámos alguns conceitos básicos de dinâmica não linear, as características dos sistemas caóticos e algumas grandezas que caracterizam os sistemas dinâmicos, que incluem a dimensão fractal, que indica a complexidade de informação contida na série temporal, os expoentes de Lyapunov, que indicam a taxa com que pontos arbitrariamente próximos no espaço de fases da representação do espaço dinâmico, divergem ao longo do tempo, ou a entropia aproximada, que mede o grau de imprevisibilidade de uma série temporal. Esta informação pode então ser usada para compreender, e possivelmente prever, o comportamento. ABSTRACT: ln this thesis we studied the time series that represent the complex dynamic behavior. We focused on techniques of nonlinear dynamics. The techniques provide us a number of quantitative indices used to describe the dynamic properties of the system. These indices have been extensively used in recent years in practical applications in psychology. We studied some basic concepts of nonlinear dynamics, the characteristics of chaotic systems and some quantities that characterize the dynamic systems, including fractal dimension, indicating the complexity of information in the series, the Lyapunov exponents, which indicate the rate at that arbitrarily dose points in phase space representation of a dynamic, vary over time, or the approximate entropy, which measures the degree of unpredictability of a series. This information can then be used to understand and possibly predict the behavior.

Effects of pitch area-restrictions on tactical behavior, physical and physiological performances in soccer large-sided games

The aim of this study was to identify how pitch area-restrictions affects the tactical behavior, physical and physiological performances of players during soccer large-sided games. A 10 vs. 9 large-sided game was performed under three experimental conditions: (i) restricted-spacing, the pitch was divided into specific areas where players were assigned and they should not leave it; (ii) contiguous-spacing, the pitch was divided into specific areas where the players were only allowed to move to a neighboring one; (iii) free-spacing, the players had no restrictions in space occupation. The positional data were used to compute players’ spatial exploration index and also the distance, coefficient of variation, approximate entropy and frequency of near-in-phase displacements synchronization of players’ dyads formed by the outfield teammates. Players’ physical and physiological performances were assessed by the distance covered at different speed categories, game pace and heart rate. Most likely higher values were found in players’ spatial exploration index under free-spacing conditions. The synchronization between dyads’ displacements showed higher values for contiguous-spacing and free-spacing conditions. In contrast, for the jogging and running intensity zones, restricted-spacing demanded a moderate effect and most likely decrease compared to other scenarios (~20-50% to jogging and ~60-90% to running). Overall, the effects of limiting players’ spatial exploration greatly impaired the co-adaptation between teammates’ positioning while decreasing the physical and physiological performances. These results allow for a better understanding of players’ decision-making process according to specific task rules and can be relevant to enrich practice task design, such that coaches acknowledge the differential effect by using specific pitch-position areas restrictions.

Analysis of heat transfer and entropy generation for a thermally developing Brinkman–Brinkman forced convection problem in a rectangular duct with isoflux walls

Heat transfer and entropy generation analysis of the thermally developing forced convection in a porous-saturated duct of rectangular cross-section, with walls maintained at a constant and uniform heat flux, is investigated based on the Brinkman flow model. The classical Galerkin method is used to obtain the fully developed velocity distribution. To solve the thermal energy equation, with the effects of viscous dissipation being included, the Extended Weighted Residuals Method (EWRM) is applied. The local (three dimensional) temperature field is solved by utilizing the Green’s function solution based on the EWRM where symbolic algebra is being used for convenience in presentation. Following the computation of the temperature field, expressions are presented for the local Nusselt number and the bulk temperature as a function of the dimensionless longitudinal coordinate, the aspect ratio, the Darcy number, the viscosity ratio, and the Brinkman number. With the velocity and temperature field being determined, the Second Law (of Thermodynamics) aspect of the problem is also investigated. Approximate closed form solutions are also presented for two limiting cases of MDa values. It is observed that decreasing the aspect ratio and MDa values increases the entropy generation rate.

Power law and entropy analysis of catastrophic phenomena

Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, tsunamis, floods and landslides, are always accompanied by a large number of casualties. The size distribution of these casualties has separately been shown to follow approximate power law (PL) distributions. In this paper, we analyze the statistical distributions of the number of victims of catastrophic phenomena, in particular, terrorism, and find double PL behavior. This means that the data sets are better approximated by two PLs instead of a single one. We plot the PL parameters, corresponding to several events, and observe an interesting pattern in the charts, where the lines that connect each pair of points defining the double PLs are almost parallel to each other. A complementary data analysis is performed by means of the computation of the entropy. The results reveal relationships hidden in the data that may trigger a future comprehensive explanation of this type of phenomena.

Climate entropy budget of the HadCM3 atmosphere-ocean general circulation model and of FAMOUS, its low resolution version

The entropy budget is calculated of the coupled atmosphere–ocean general circulation model HadCM3. Estimates of the different entropy sources and sinks of the climate system are obtained directly from the diabatic heating terms, and an approximate estimate of the planetary entropy production is also provided. The rate of material entropy production of the climate system is found to be ∼50 mW m−2 K−1, a value intermediate in the range 30–70 mW m−2 K−1 previously reported from different models. The largest part of this is due to sensible and latent heat transport (∼38 mW m−2 K−1). Another 13 mW m−2 K−1 is due to dissipation of kinetic energy in the atmosphere by friction and Reynolds stresses. Numerical entropy production in the atmosphere dynamical core is found to be about 0.7 mW m−2 K−1. The material entropy production within the ocean due to turbulent mixing is ∼1 mW m−2 K−1, a very small contribution to the material entropy production of the climate system. The rate of change of entropy of the model climate system is about 1 mW m−2 K−1 or less, which is comparable with the typical size of the fluctuations of the entropy sources due to interannual variability, and a more accurate closure of the budget than achieved by previous analyses. Results are similar for FAMOUS, which has a lower spatial resolution but similar formulation to HadCM3, while more substantial differences are found with respect to other models, suggesting that the formulation of the model has an important influence on the climate entropy budget. Since this is the first diagnosis of the entropy budget in a climate model of the type and complexity used for projection of twenty-first century climate change, it would be valuable if similar analyses were carried out for other such models.

Entropy production in the early-cosmology pionic phase

We point out that in the early universe, for temperatures in the approximate interval 150-80 MeV (after the quark-gluon plasma), pions carried a large share of the entropy and supported the largest inhomogeneities. Its thermal conductivity (previously calculated) allows the characterization of entropy production due to equilibration (damping) of thermal fluctuations. Simple model distributions of thermal fluctuations are considered and the associated entropy production evaluated.

Entropy production in irreversible systems described by a Fokker-Planck equation

We analyze the irreversibility and the entropy production in nonequilibrium interacting particle systems described by a Fokker-Planck equation by the use of a suitable master equation representation. The irreversible character is provided either by nonconservative forces or by the contact with heat baths at distinct temperatures. The expression for the entropy production is deduced from a general definition, which is related to the probability of a trajectory in phase space and its time reversal, that makes no reference a priori to the dissipated power. Our formalism is applied to calculate the heat conductance in a simple system consisting of two Brownian particles each one in contact to a heat reservoir. We show also the connection between the definition of entropy production rate and the Jarzynski equality.