Shannon entropy analysis of the genome code

This paper studies the chromosome information of twenty five species, namely, mammals, fishes, birds, insects, nematodes, fungus, and one plant. A quantifying scheme inspired in the state space representation of dynamical systems is formulated. Based on this algorithm, the information of each chromosome is converted into a bidimensional distribution. The plots are then analyzed and characterized by means of Shannon entropy. The large volume of information is integrated by averaging the lengths and entropy quantities of each species. The results can be easily visualized revealing quantitative global genomic information.

Isolated and synergistic effects of PM10 and average temperature on cardiovascular and respiratory mortality

OBJECTIVE To analyze the effect of air pollution and temperature on mortality due to cardiovascular and respiratory diseases. METHODS We evaluated the isolated and synergistic effects of temperature and particulate matter with aerodynamic diameter < 10 µm (PM10) on the mortality of individuals > 40 years old due to cardiovascular disease and that of individuals > 60 years old due to respiratory diseases in Sao Paulo, SP, Southeastern Brazil, between 1998 and 2008. Three methodologies were used to evaluate the isolated association: time-series analysis using Poisson regression model, bidirectional case-crossover analysis matched by period, and case-crossover analysis matched by the confounding factor, i.e., average temperature or pollutant concentration. The graphical representation of the response surface, generated by the interaction term between these factors added to the Poisson regression model, was interpreted to evaluate the synergistic effect of the risk factors. RESULTS No differences were observed between the results of the case-crossover and time-series analyses. The percentage change in the relative risk of cardiovascular and respiratory mortality was 0.85% (0.45;1.25) and 1.60% (0.74;2.46), respectively, due to an increase of 10 μg/m3 in the PM10 concentration. The pattern of correlation of the temperature with cardiovascular mortality was U-shaped and that with respiratory mortality was J-shaped, indicating an increased relative risk at high temperatures. The values for the interaction term indicated a higher relative risk for cardiovascular and respiratory mortalities at low temperatures and high temperatures, respectively, when the pollution levels reached approximately 60 μg/m3. CONCLUSIONS The positive association standardized in the Poisson regression model for pollutant concentration is not confounded by temperature, and the effect of temperature is not confounded by the pollutant levels in the time-series analysis. The simultaneous exposure to different levels of environmental factors can create synergistic effects that are as disturbing as those caused by extreme concentrations.

Entropy analysis of integer and fractional dynamical systems

This paper investigates the adoption of entropy for analyzing the dynamics of a multiple independent particles system. Several entropy definitions and types of particle dynamics with integer and fractional behavior are studied. The results reveal the adequacy of the entropy concept in the analysis of complex dynamical systems.

Approximate entropy normalized measures for analyzing social neurobiological systems

When considering time series data of variables describing agent interactions in social neurobiological systems, measures of regularity can provide a global understanding of such system behaviors. Approximate entropy (ApEn) was introduced as a nonlinear measure to assess the complexity of a system behavior by quantifying the regularity of the generated time series. However, ApEn is not reliable when assessing and comparing the regularity of data series with short or inconsistent lengths, which often occur in studies of social neurobiological systems, particularly in dyadic human movement systems. Here, the authors present two normalized, nonmodified measures of regularity derived from the original ApEn, which are less dependent on time series length. The validity of the suggested measures was tested in well-established series (random and sine) prior to their empirical application, describing the dyadic behavior of athletes in team games. The authors consider one of the ApEn normalized measures to generate the 95th percentile envelopes that can be used to test whether a particular social neurobiological system is highly complex (i.e., generates highly unpredictable time series). Results demonstrated that suggested measures may be considered as valid instruments for measuring and comparing complexity in systems that produce time series with inconsistent lengths.

Topological entropy of catalytic sets: Hypercycles revisited

The dynamics of catalytic networks have been widely studied over the last decades because of their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One of the most studied mathematical bodies for catalytic networks was initially formulated in the context of prebiotic evolution, by means of the hypercycle theory. The hypercycle is a set of self-replicating species able to catalyze other replicator species within a cyclic architecture. Hypercyclic organization might arise from a quasispecies as a way to increase the informational containt surpassing the so-called error threshold. The catalytic coupling between replicators makes all the species to behave like a single and coherent evolutionary multimolecular unit. The inherent nonlinearities of catalytic interactions are responsible for the emergence of several types of dynamics, among them, chaos. In this article we begin with a brief review of the hypercycle theory focusing on its evolutionary implications as well as on different dynamics associated to different types of small catalytic networks. Then we study the properties of chaotic hypercycles with error-prone replication with symbolic dynamics theory, characterizing, by means of the theory of topological Markov chains, the topological entropy and the periods of the orbits of unimodal-like iterated maps obtained from the strange attractor. We will focus our study on some key parameters responsible for the structure of the catalytic network: mutation rates, autocatalytic and cross-catalytic interactions.

Nonautonomous Graphs and Topological Entropy of Nonautonomous Lorenz Systems

In this work, we associate a p-periodic nonautonomous graph to each p-periodic nonautonomous Lorenz system with finite critical orbits. We develop Perron-Frobenius theory for nonautonomous graphs and use it to calculate their entropy. Finally, we prove that the topological entropy of a p-periodic nonautonomous Lorenz system is equal to the entropy of its associated nonautonomous graph.

Quantificação da complexidade do ritmo cardíaco usando o método da Multiscale Entropy

Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

Multidimensional Scaling Visualization using Parametric Similarity Indices

In this paper, we apply multidimensional scaling (MDS) and parametric similarity indices (PSI) in the analysis of complex systems (CS). Each CS is viewed as a dynamical system, exhibiting an output time-series to be interpreted as a manifestation of its behavior. We start by adopting a sliding window to sample the original data into several consecutive time periods. Second, we define a given PSI for tracking pieces of data. We then compare the windows for different values of the parameter, and we generate the corresponding MDS maps of ‘points’. Third, we use Procrustes analysis to linearly transform the MDS charts for maximum superposition and to build a global MDS map of “shapes”. This final plot captures the time evolution of the phenomena and is sensitive to the PSI adopted. The generalized correlation, the Minkowski distance and four entropy-based indices are tested. The proposed approach is applied to the Dow Jones Industrial Average stock market index and the Europe Brent Spot Price FOB time-series.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

Entropy Analysis of Industrial Accident Data Series

Complex industrial plants exhibit multiple interactions among smaller parts and with human operators. Failure in one part can propagate across subsystem boundaries causing a serious disaster. This paper analyzes the industrial accident data series in the perspective of dynamical systems. First, we process real world data and show that the statistics of the number of fatalities reveal features that are well described by power law (PL) distributions. For early years, the data reveal double PL behavior, while, for more recent time periods, a single PL fits better into the experimental data. Second, we analyze the entropy of the data series statistics over time. Third, we use the Kullback–Leibler divergence to compare the empirical data and multidimensional scaling (MDS) techniques for data analysis and visualization. Entropy-based analysis is adopted to assess complexity, having the advantage of yielding a single parameter to express relationships between the data. The classical and the generalized (fractional) entropy and Kullback–Leibler divergence are used. The generalized measures allow a clear identification of patterns embedded in the data.

Portuguese average cost of capital

The oldest Portuguese share index still being calculated is the BVL/PSI-General, one which started the daily series on 5/Jan/1988 with a base value of 1000 points. Everyday a single value is computed based on the closing prices of all the shares included in the sample. Also, all corporate events affecting the price of any share beyond market sentiment are taken into account through proper adjustments, either in the numerator or the denominator of the formula. However, for dates before January 1988, there is nothing comparable to this index since the two different series known either never disclosed the methodology adopted to calculate the index or followed solutions not compatible with the above index. The present paper explains the solutions adopted to replicate as closely as possible the methodology of the BVL-General index to the main market of the Lisbon Exchange for the period 1978 – 1987. This is the first estimate of the historical Equity Risk Premium in Portugal above short-term risk-free rate from the re-opening of the market following the Carnation Revolution (and the accompanying nationalizations), to the present. In showing a value of the same order of magnitude found in other countries, the paper invites further studies on the effects of political decisions such as privatizations and joining the European Union.

Rényi entropy and the thermodynamic stability of black holes

Thermodynamic stability of black holes, described by the Rényi formula as equilibrium compatible entropy function, is investigated. It is shown that within this approach, asymptotically flat, Schwarzschild black holes can be in stable equilibrium with thermal radiation at a fixed temperature. This implies that the canonical ensemble exists just like in anti-de Sitter space, and nonextensive effects can stabilize the black holes in a very similar way as it is done by the gravitational potential of an anti-de Sitter space. Furthermore, it is also shown that a Hawking–Page-like black hole phase transition occurs at a critical temperature which depends on the q-parameter of the Rényi formula.

Predicting the distribution of forest tree species using topographic variables and vegetation index in eastern Acre, Brazil

Species distribution modeling has relevant implications for the studies of biodiversity, decision making about conservation and knowledge about ecological requirements of the species. The aim of this study was to evaluate if the use of forest inventories can improve the estimation of occurrence probability, identify the limits of the potential distribution and habitat preference of a group of timber tree species. The environmental predictor variables were: elevation, slope, aspect, normalized difference vegetation index (NDVI) and height above the nearest drainage (HAND). To estimate the distribution of species we used the maximum entropy method (Maxent). In comparison with a random distribution, using topographic variables and vegetation index as features, the Maxent method predicted with an average accuracy of 86% the geographical distribution of studied species. The altitude and NDVI were the most important variables. There were limitations to the interpolation of the models for non-sampled locations and that are outside of the elevation gradient associated with the occurrence data in approximately 7% of the basin area. Ceiba pentandra (samaúma), Castilla ulei (caucho) and Hura crepitans (assacu) is more likely to occur in nearby water course areas. Clarisia racemosa (guariúba), Amburana acreana (cerejeira), Aspidosperma macrocarpon (pereiro), Apuleia leiocarpa (cumaru cetim), Aspidosperma parvifolium (amarelão) and Astronium lecointei (aroeira) can also occur in upland forest and well drained soils. This modeling approach has potential for application on other tropical species still less studied, especially those that are under pressure from logging.

Sex differences in the fetal heart rate variability indices of twins

Aims: To evaluate the differences in linear and complex heart rate dynamics in twin pairs according to fetal sex combination [male-female (MF), male-male (MM), and female-female (FF)]. Methods: Fourteen twin pairs (6 MF, 3 MM, and 5 FF) were monitored between 31 and 36.4 weeks of gestation. Twenty-six fetal heart rate (FHR) recordings of both twins were simultaneously acquired and analyzed with a system for computerized analysis of cardiotocograms. Linear and nonlinear FHR indices were calculated. Results: Overall, MM twins presented higher intrapair average in linear indices than the other pairs, whereas FF twins showed higher sympathetic-vagal balance. MF twins exhibited higher intrapair average in entropy indices and MM twins presented lower entropy values than FF twins considering the (automatically selected) threshold rLu. MM twin pairs showed higher intrapair differences in linear heart rate indices than MF and FF twins, whereas FF twins exhibited lower intrapair differences in entropy indices. Conclusions: The results of this exploratory study suggest that twins have sex-specific differences in linear and nonlinear indices of FHR. MM twins expressed signs of a more active autonomic nervous system and MF twins showed the most active complexity control system. These results suggest that fetal sex combination should be taken into consideration when performing detailed evaluation of the FHR in twins.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.