Statistical mixing and aggregation in Feller diffusion

We consider Feller mean-reverting square-root diffusion, which has been applied to model a wide variety of processes with linearly state-dependent diffusion, such as stochastic volatility and interest rates in finance, and neuronal and populations dynamics in natural sciences. We focus on the statistical mixing (or superstatistical) process in which the parameter related to the mean value can fluctuate - a plausible mechanism for the emergence of heavy-tailed distributions. We obtain analytical results for the associated probability density function (both stationary and time dependent), its correlation structure and aggregation properties. Our results are applied to explain the statistics of stock traded volume at different aggregation scales.Comment: 16 pages, 3 figures. To be published in Journal of Statistical Mechanics: Theory and Experimen

Minding impacting events in a model of stochastic variance

We introduce a generalisation of the well-known ARCH process, widely used for generating uncorrelated stochastic time series with long-term non-Gaussian distributions and long-lasting correlations in the (instantaneous) standard deviation exhibiting a clustering profile. Specifically, inspired by the fact that in a variety of systems impacting events are hardly forgot, we split the process into two different regimes: a first one for regular periods where the average volatility of the fluctuations within a certain period of time is below a certain threshold and another one when the local standard deviation outnumbers it. In the former situation we use standard rules for heteroscedastic processes whereas in the latter case the system starts recalling past values that surpassed the threshold. Our results show that for appropriate parameter values the model is able to provide fat tailed probability density functions and strong persistence of the instantaneous variance characterised by large values of the Hurst exponent is greater than 0.8, which are ubiquitous features in complex systems.Comment: 18 pages, 5 figures, 1 table. To published in PLoS on

On a generalised model for time-dependent variance with long-term memory

The ARCH process (R. F. Engle, 1982) constitutes a paradigmatic generator of stochastic time series with time-dependent variance like it appears on a wide broad of systems besides economics in which ARCH was born. Although the ARCH process captures the so-called "volatility clustering" and the asymptotic power-law probability density distribution of the random variable, it is not capable to reproduce further statistical properties of many of these time series such as: the strong persistence of the instantaneous variance characterised by large values of the Hurst exponent (H > 0.8), and asymptotic power-law decay of the absolute values self-correlation function. By means of considering an effective return obtained from a correlation of past returns that has a q-exponential form we are able to fix the limitations of the original model. Moreover, this improvement can be obtained through the correct choice of a sole additional parameter, $q_{m}$. The assessment of its validity and usefulness is made by mimicking daily fluctuations of SP500 financial index.Comment: 6 pages, 4 figure

Components of multifractality in the Central England Temperature anomaly series

We study the multifractal nature of the Central England Temperature (CET) anomaly, a time series that spans more than 200 years. The series is analyzed as a complete data set and considering a sliding window of 11 years. In both cases, we quantify the broadness of the multifractal spectrum as well as its components defined by the deviations from the Gaussian distribution and the influence of the dependence between measurements. The results show that the chief contribution to the multifractal structure comes from the dynamical dependencies, mainly the weak ones, followed by a residual contribution of the deviations from Gaussianity. However, using the sliding window, we verify that the spikes in the non-Gaussian contribution occur at very close dates associated with climate changes determined in previous works by component analysis methods. Moreover, the strong non-Gaussian contribution found in the multifractal measures from the 1960s onwards is in agreement with global results very recently proposed in the literature.Comment: 21 pages, 10 figure

The dynamics of financial stability in complex networks

We address the problem of banking system resilience by applying off-equilibrium statistical physics to a system of particles, representing the economic agents, modelled according to the theoretical foundation of the current banking regulation, the so called Merton-Vasicek model. Economic agents are attracted to each other to exchange `economic energy', forming a network of trades. When the capital level of one economic agent drops below a minimum, the economic agent becomes insolvent. The insolvency of one single economic agent affects the economic energy of all its neighbours which thus become susceptible to insolvency, being able to trigger a chain of insolvencies (avalanche). We show that the distribution of avalanche sizes follows a power-law whose exponent depends on the minimum capital level. Furthermore, we present evidence that under an increase in the minimum capital level, large crashes will be avoided only if one assumes that agents will accept a drop in business levels, while keeping their trading attitudes and policies unchanged. The alternative assumption, that agents will try to restore their business levels, may lead to the unexpected consequence that large crises occur with higher probability

Process enhancement at near neutral pH of a homogeneous photo-Fenton reaction using ferricarboxylate complexes: Application to oxytetracycline degradation

This work demonstrates the application at near neutral pH of a photo-Fenton reaction mediated by ferricarboxylates on the treatment of aqueous solutions containing the antibiotic Oxytetracycline (OTC) under solar irradiation. The formation of a Fe:OTC complex after Fe2+ oxidation to Fe3+, in the presence of H2O2, showed the inconvenience of using the conventional Fe2+/H2O2/UV-Vis process at near neutral pH levels, as the complex is retained in the filter. To overcome this, a Fe3+/Oxalate/UV-Vis or Fe3+/Citrate/H2O2/UV-Vis process was proposed. The higher tendency of Fe3+ to form complexes with carboxylates avoids the formation of Fe:OTC complexes and allows for proper OTC detection along reaction times. The photo-Fenton process itself is improved by the extension of the iron solubility to higher and more practical pH values, by the increase of the quantum yield of Fe2+ production and by presenting stronger radiation absorption at wavelengths up to 580 nm. In this way, process efficiency was evaluated for different variables such as Fe3+ concentration, pH, temperature and irradiance, using a compound parabolic collector (CPC) photoreactor at lab-scale under simulated solar radiation. Reaction rates were compared in the presence of different inorganic anions and humic acids, and in two different real wastewater matrixes. Results obtained in a CPC pilot-scale plant under natural solar light, using an iron/oxalate molar rati

Competition and fragmentation: a simple model generating lognormal-like distributions

The current distribution of language size in terms of speaker population is generally described using a lognormal distribution. Analyzing the original real data we show how the double-Pareto lognormal distribution can give an alternative fit that indicates the existence of a power law tail. A simple Monte Carlo model is constructed based on the processes of competition and fragmentation. The results reproduce the power law tails of the real distribution well and give better results for a poorly connected topology of interactions.Comment: 14 pages, 11 figure

Forecasting the dynamics of a complex microbial community using integrated meta-omics.

peer reviewedPredicting the behaviour of complex microbial communities is challenging. However, this is essential for complex biotechnological processes such as those in biological wastewater treatment plants (BWWTPs), which require sustainable operation. Here we summarize 14 months of longitudinal meta-omics data from a BWWTP anaerobic tank into 17 temporal signals, explaining 91.1% of the temporal variance, and link those signals to ecological events within the community. We forecast the signals over the subsequent five years and use 21 extra samples collected at defined time intervals for testing and validation. Our forecasts are correct for six signals and hint on phenomena such as predation cycles. Using all the 17 forecasts and the environmental variables, we predict gene abundance and expression, with a coefficient of determination ≥0.87 for the subsequent three years. Our study demonstrates the ability to forecast the dynamics of open microbial ecosystems using interactions between community cycles and environmental parameters.R-AGR-0369 - ATTRACT A09/03 Sysbionama (01/02/2010 - 31/01/2015) - WILMES Pau

Componentes da dieta artificial de Anthonomus grandis (Coleoptera: Curculionidae) afetam a viabilidade dos conídios de Metarhizium anisopliae (Hypocreales: Clavicipitaceae)?

Estudos tem demonstrado que Metarhizium anisopliae (Hypocreales: Clavicipitaceae) é altamente virulento a Anthonomus grandis (Coleoptera: Curculionidae) quando os adultos se alimentam de botões florais, mas quando se alimentam de dieta artificial a mortalidade dos adultos pelo fungo reduz significativamente. Desta forma, o objetivo deste trabalho foi determinar se componentes da dieta artificial de A. grandis podem afetar a germinação de M. anisopliae