The Persistence of Memory

This paper analyzes several natural and man-made complex phenomena in the perspective of dynamical systems. Such phenomena are often characterized by the absence of a characteristic length-scale, long range correlations and persistent memory, which are features also associated to fractional order systems. For each system, the output, interpreted as a manifestation of the system dynamics, is analyzed by means of the Fourier transform. The amplitude spectrum is approximated by a power law function and the parameters are interpreted as an underlying signature of the system dynamics. The complex systems under analysis are then compared in a global perspective in order to unveil and visualize hidden relationships among them.

Dynamical Analysis and Visualization of Tornadoes Time Series

In this paper we analyze the behavior of tornado time-series in the U.S. from the perspective of dynamical systems. A tornado is a violently rotating column of air extending from a cumulonimbus cloud down to the ground. Such phenomena reveal features that are well described by power law functions and unveil characteristics found in systems with long range memory effects. Tornado time series are viewed as the output of a complex system and are interpreted as a manifestation of its dynamics. Tornadoes are modeled as sequences of Dirac impulses with amplitude proportional to the events size. First, a collection of time series involving 64 years is analyzed in the frequency domain by means of the Fourier transform. The amplitude spectra are approximated by power law functions and their parameters are read as an underlying signature of the system dynamics. Second, it is adopted the concept of circular time and the collective behavior of tornadoes analyzed. Clustering techniques are then adopted to identify and visualize the emerging patterns.

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.

Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

In this paper we study several natural and man-made complex phenomena in the perspective of dynamical systems. For each class of phenomena, the system outputs are time-series records obtained in identical conditions. The time-series are viewed as manifestations of the system behavior and are processed for analyzing the system dynamics. First, we use the Fourier transform to process the data and we approximate the amplitude spectra by means of power law functions. We interpret the power law parameters as a phenomenological signature of the system dynamics. Second, we adopt the techniques of non-hierarchical clustering and multidimensional scaling to visualize hidden relationships between the complex phenomena. Third, we propose a vector field based analogy to interpret the patterns unveiled by the PL parameters.

The electoral dynamics of human development

This paper analyses the impact of elections on the dynamics of human development in a panel of 82 countries over the period 1980-2013. The incidence of partisan and political support effects is also taken into account. A GMM estimator is employed in the empirical analysis and the results point out to the presence of an electoral cycle in the growth rate of human development. Majority governments also influence it, but no clear evidence is found regarding partisan effects. The electoral cycles have proved to be stronger in non-OECD countries, in countries with less frequent elections, with lower levels of income and human development, in presidential and non-plurality systems and in proportional representation regimes. They have also become more intense in this millennium.

Species distribution models reveal apparent competitive and facilitative effects of a dominant species on the distribution of tundra plants

Abiotic factors are considered strong drivers of species distribution and assemblages. Yet these spatial patterns are also influenced by biotic interactions. Accounting for competitors or facilitators may improve both the fit and the predictive power of species distribution models (SDMs). We investigated the influence of a dominant species, Empetrum nigrum ssp. hermaphroditum, on the distribution of 34 subordinate species in the tundra of northern Norway. We related SDM parameters of those subordinate species to their functional traits and their co-occurrence patterns with E. hermaphroditum across three spatial scales. By combining both approaches, we sought to understand whether these species may be limited by competitive interactions and/or benefit from habitat conditions created by the dominant species. The model fit and predictive power increased for most species when the frequency of occurrence of E. hermaphroditum was included in the SDMs as a predictor. The largest increase was found for species that 1) co-occur most of the time with E. hermaphroditum, both at large (i.e. 750 m) and small spatial scale (i.e. 2 m) or co-occur with E. hermaphroditum at large scale but not at small scale and 2) have particularly low or high leaf dry matter content (LDMC). Species that do not co-occur with E. hermaphroditum at the smallest scale are generally palatable herbaceous species with low LDMC, thus showing a weak ability to tolerate resource depletion that is directly or indirectly induced by E. hermaphroditum. Species with high LDMC, showing a better aptitude to face resource depletion and grazing, are often found in the proximity of E. hermaphroditum. Our results are consistent with previous findings that both competition and facilitation structure plant distribution and assemblages in the Arctic tundra. The functional and co-occurrence approaches used were complementary and provided a deeper understanding of the observed patterns by refinement of the pool of potential direct and indirect ecological effects of E. hermaphroditum on the distribution of subordinate species. Our correlative study would benefit being complemented by experimental approaches.

Predicting trabecular bone microdamage initiation and accumulation using a non-linear perfect damage model

Studies evaluating the mechanical behavior of the trabecular microstructure play an important role in our understanding of pathologies such as osteoporosis, and in increasing our understanding of bone fracture and bone adaptation. Understanding of such behavior in bone is important for predicting and providing early treatment of fractures. The objective of this study is to present a numerical model for studying the initiation and accumulation of trabecular bone microdamage in both the pre- and post-yield regions. A sub-region of human vertebral trabecular bone was analyzed using a uniformly loaded anatomically accurate microstructural three-dimensional finite element model. The evolution of trabecular bone microdamage was governed using a non-linear, modulus reduction, perfect damage approach derived from a generalized plasticity stress-strain law. The model introduced in this paper establishes a history of microdamage evolution in both the pre- and post-yield regions

Power laws and scaling of rain events and dry spells in the Catalonia region

We analyze the statistics of rain-event sizes, rain-event durations, and dry-spell durations in a network of 20 rain gauges scattered in an area situated close to the NW Mediterranean coast. Power-law distributions emerge clearly for the dryspell durations, with an exponent around 1.50 ± 0.05, although for event sizes and durations the power-law ranges are rather limited, in some cases. Deviations from power-law behavior are attributed to finite-size effects. A scaling analysis helps to elucidate the situation, providing support for the existence of scale invariance in these distributions. It is remarkable that rain data of not very high resolution yield findings in agreement with self-organized critical phenomena.

Variability of North Atlantic hurricanes: seasonal versus individual-event features

Tropical cyclones are affected by a large number of climatic factors, which translates into complex patterns of occurrence. The variability of annual metrics of tropical-cyclone activity has been intensively studied, in particular since the sudden activation of the North Atlantic in the mid 1990’s. We provide first a swift overview on previous work by diverse authors about these annual metrics for the North-Atlantic basin, where the natural variability of the phenomenon, the existence of trends, the drawbacks of the records, and the influence of global warming have been the subject of interesting debates. Next, we present an alternative approach that does not focus on seasonal features but on the characteristics of single events [Corral et al., Nature Phys. 6, 693 (2010)]. It is argued that the individual-storm power dissipation index (PDI) constitutes a natural way to describe each event, and further, that the PDI statistics yields a robust law for the occurrence of tropical cyclones in terms of a power law. In this context, methods of fitting these distributions are discussed. As an important extension to this work we introduce a distribution function that models the whole range of the PDI density (excluding incompleteness effects at the smallest values), the gamma distribution, consisting in a powerlaw with an exponential decay at the tail. The characteristic scale of this decay, represented by the cutoff parameter, provides very valuable information on the finiteness size of the basin, via the largest values of the PDIs that the basin can sustain. We use the gamma fit to evaluate the influence of sea surface temperature (SST) on the occurrence of extreme PDI values, for which we find an increase around 50 % in the values of these basin-wide events for a 0.49 C SST average difference. Similar findings are observed for the effects of the positive phase of the Atlantic multidecadal oscillation and the number of hurricanes in a season on the PDI distribution. In the case of the El Niño Southern oscillation (ENSO), positive and negative values of the multivariate ENSO index do not have a significant effect on the PDI distribution; however, when only extreme values of the index are used, it is found that the presence of El Niño decreases the PDI of the most extreme hurricanes.

Sex-biased dispersal in a migratory bat: a characterization using sex-specific demographic parameters.

We studied the noctule bat (Nyctalus noctula), in which the mitochondrial F(ST) is about 10 times that revealed by nuclear markers, to address two questions. We first verified whether random dispersal of one sex is compatible with highly contrasted mitochondrial and nuclear population structures. Using computer simulations, we then assessed the power of multilocus population differentiation tests when the expected population structure departs only slightly from panmixia. Using an island model with sex-specific demographic parameters, we found that random male dispersal is consistent with the population structure observed in the noctule. However, other parameter combinations are also compatible with the data. We computed the minimum sex bias in dispersal (at least 69% of the dispersing individuals are males), a result that would not be available if we had used more classical population genetic models. The power of multilocus population differentiation tests was unexpectedly high, the tests being significant in almost 100% of the replicates, although the observed population structure infered from nuclear markers was extremely low (F(ST) = 0.6%).

Adéquation et choix de modele de marche aléatoire des trajectoires des navires de peches

L'étude du mouvement des organismes est essentiel pour la compréhension du fonctionnement des écosystèmes. Dans le cas des écosystèmes marins exploités, cela amène à s'intéresser aux stratégies spatiales des pêcheurs. L'une des approches les plus utilisées pour la modélisation du mouvement des prédateurs supé- rieurs est la marche aléatoire de Lévy. Une marche aléatoire est un modèle mathématique composé par des déplacements aléatoires. Dans le cas de Lévy, les longueurs des déplacements suivent une loi stable de Lévy. Dans ce cas également, les longueurs, lorsqu'elles tendent vers l'in ni (in praxy lorsqu'elles sont grandes, grandes par rapport à la médiane ou au troisième quartile par exemple), suivent une loi puissance caractéristique du type de marche aléatoire de Lévy (Cauchy, Brownien ou strictement Lévy). Dans la pratique, outre que cette propriété est utilisée de façon réciproque sans fondement théorique, les queues de distribution, notion par ailleurs imprécise, sont modélisée par des lois puissances sans que soient discutées la sensibilité des résultats à la dé nition de la queue de distribution, et la pertinence des tests d'ajustement et des critères de choix de modèle. Dans ce travail portant sur les déplacements observés de trois bateaux de pêche à l'anchois du Pérou, plusieurs modèles de queues de distribution (log-normal, exponentiel, exponentiel tronqué, puissance et puissance tronqué) ont été comparés ainsi que deux dé nitions possible de queues de distribution (de la médiane à l'in ni ou du troisième quartile à l'in ni). Au plan des critères et tests statistiques utilisés, les lois tronquées (exponentielle et puissance) sont apparues les meilleures. Elles intègrent en outre le fait que, dans la pratique, les bateaux ne dépassent pas une certaine limite de longueur de déplacement. Le choix de modèle est apparu sensible au choix du début de la queue de distribution : pour un même bateau, le choix d'un modèle tronqué ou l'autre dépend de l'intervalle des valeurs de la variable sur lequel le modèle est ajusté. Pour nir, nous discutons les implications en écologie des résultats de ce travail.

Drift compensation of gas sensor array data by Orthogonal Signal Correction

Drift is an important issue that impairs the reliability of gas sensing systems. Sensor aging, memory effects and environmental disturbances produce shifts in sensor responses that make initial statistical models for gas or odor recognition useless after a relatively short period (typically few weeks). Frequent recalibrations are needed to preserve system accuracy. However, when recalibrations involve numerous samples they become expensive and laborious. An interesting and lower cost alternative is drift counteraction by signal processing techniques. Orthogonal Signal Correction (OSC) is proposed for drift compensation in chemical sensor arrays. The performance of OSC is also compared with Component Correction (CC). A simple classification algorithm has been employed for assessing the performance of the algorithms on a dataset composed by measurements of three analytes using an array of seventeen conductive polymer gas sensors over a ten month period.

Monte Carlo simulation of interface alloying

An Ising-like model, with interactions ranging up to next-nearest-neighbor pairs, is used to simulate the process of interface alloying. Interactions are chosen to stabilize an intermediate "antiferromagnetic" ordered structure. The dynamics proceeds exclusively by atom-vacancy exchanges. In order to characterize the process, the time evolution of the width of the intermediate ordered region and the diffusion length is studied. Both lengths are found to follow a power-law evolution with exponents depending on the characteristic features of the model.

Wave propagation in a medium with disordered excitability

The effect of quenched disorder on the propagation of autowaves in excitable media is studied both experimentally and numerically in relation to the light-sensitive Belousov-Zhabotinsky reaction. The spatial disorder is introduced through a random distribution with two different levels of transmittance. In one dimension the (time-averaged) wave speed is smaller than the corresponding to a homogeneous medium with the mean excitability. Contrarily, in two dimensions the velocity increases due to the roughening of the front. Results are interpreted using kinematic and scaling arguments. In particular, for d = 2 we verify a theoretical prediction of a power-law dependence for the relative change of the propagation speed on the disorder amplitude.

Distributions of avalanches in martensitic transformations

An experimental study of the acoustic emission generated during a martensitic transformation is presented. A statistical analysis of the amplitude and lifetime of a large number of signals has revealed power-law behavior for both magnitudes. The exponents of these distributions have been evaluated and, through independent measurements of the statistical lifetime to amplitude dependence, we have checked the scaling relation between the exponents. Our results are discussed in terms of current ideas on avalanche dynamics.