The extreme vulnerability of interdependent spatially embedded networks

Recent studies show that in interdependent networks a very small failure in one network may lead to catastrophic consequences. Above a critical fraction of interdependent nodes, even a single node failure can invoke cascading failures that may abruptly fragment the system, while below this "critical dependency" (CD) a failure of few nodes leads only to small damage to the system. So far, the research has been focused on interdependent random networks without space limitations. However, many real systems, such as power grids and the Internet, are not random but are spatially embedded. Here we analytically and numerically analyze the stability of systems consisting of interdependent spatially embedded networks modeled as lattice networks. Surprisingly, we find that in lattice systems, in contrast to non-embedded systems, there is no CD and \textit{any} small fraction of interdependent nodes leads to an abrupt collapse. We show that this extreme vulnerability of very weakly coupled lattices is a consequence of the critical exponent describing the percolation transition of a single lattice. Our results are important for understanding the vulnerabilities and for designing robust interdependent spatial embedded networks.Comment: 13 pages, 5 figure

The robustness of interdependent clustered networks

It was recently found that cascading failures can cause the abrupt breakdown of a system of interdependent networks. Using the percolation method developed for single clustered networks by Newman [Phys. Rev. Lett. {\bf 103}, 058701 (2009)], we develop an analytical method for studying how clustering within the networks of a system of interdependent networks affects the system's robustness. We find that clustering significantly increases the vulnerability of the system, which is represented by the increased value of the percolation threshold $p_c$ in interdependent networks.Comment: 6 pages, 6 figure

Assessment of long-range correlation in animal behaviour time series: the temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus)

The aim of this study was to evaluate the performance of a classical method of fractal analysis, Detrended Fluctuation Analysis (DFA), in the analysis of the dynamics of animal behavior time series. In order to correctly use DFA to assess the presence of long-range correlation, previous authors using statistical model systems have stated that different aspects should be taken into account such as: 1) the establishment by hypothesis testing of the absence of short term correlation, 2) an accurate estimation of a straight line in the log-log plot of the fluctuation function, 3) the elimination of artificial crossovers in the fluctuation function, and 4) the length of the time series. Taking into consideration these factors, herein we evaluated the presence of long-range correlation in the temporal pattern of locomotor activity of Japanese quail ({\sl Coturnix coturnix}) and mosquito larva ({\sl Culex quinquefasciatus}). In our study, modeling the data with the general ARFIMA model, we rejected the hypothesis of short range correlations (d=0) in all cases. We also observed that DFA was able to distinguish between the artificial crossover observed in the temporal pattern of locomotion of Japanese quail, and the crossovers in the correlation behavior observed in mosquito larvae locomotion. Although the test duration can slightly influence the parameter estimation, no qualitative differences were observed between different test durations

Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series

Notwithstanding the significant efforts to develop estimators of long-range correlations (LRC) and to compare their performance, no clear consensus exists on what is the best method and under which conditions. In addition, synthetic tests suggest that the performance of LRC estimators varies when using different generators of LRC time series. Here, we compare the performances of four estimators [Fluctuation Analysis (FA), Detrended Fluctuation Analysis (DFA), Backward Detrending Moving Average (BDMA), and centred Detrending Moving Average (CDMA)]. We use three different generators [Fractional Gaussian Noises, and two ways of generating Fractional Brownian Motions]. We find that CDMA has the best performance and DFA is only slightly worse in some situations, while FA performs the worst. In addition, CDMA and DFA are less sensitive to the scaling range than FA. Hence, CDMA and DFA remain "The Methods of Choice" in determining the Hurst index of time series.Comment: 6 pages (including 3 figures) + 3 supplementary figure

Population dynamics and identification of efficient strains of Azospirillum in maize ecosystems of Bihar (India)

Information on inoculum load and diversity of native microbial community is an important prerequisite for crop management of microbial origin. Azospirillum has a proven role in benefiting the maize (Zea mays) crop in terms of nutrient (nitrogen) supply as well as plant growth enhancement. Bihar state has highest average national maize productivity although fertilizer consumption is minimum, indicating richness of Azospirillum both in terms of population and diversity in soils. An experiment was planned to generate basic information on Azospirillum population variation in maize soils under different agricultural practices and soil types of Bihar, to identify suitable agricultural practices supporting the target microorganism and efficient Azospirillum strain(s). No tillage, growing traditional maize cultivar, land use history (diara soil having history of maize cultivation), soil organic carbon (>1%) and intercrop with oat supported prevalence of Azospirillum in maize rhizosphere. Native Azospirillum population varied from 1 million to 1 billion/g soil under diverse agricultural practices and soil types. Such richness, however, does not necessarily mean that artificial inoculation of Azospirillum is not required in Bihar soils as 92% of Azospirillum isolates (50 isolates) were poor in nitrogen-fixing ability and 88% were poor on IAA production. Efficient strains of Azospirillum based on growth (three), acetylene reduction assay (three), IAA production (three), broad range of pH (two) and temperature tolerance were identified. The findings suggested that maize crop in Bihar should be inoculated in universal mode rather than site-specific mode

Microalgae cultivation in wastewater: nutrient removal from anaerobic membrane bioreactor effluent

This study investigated the removal of nitrogen and phosphorus from the effluent of a submerged anaerobic membrane bioreactor (SAnMBR) by means of a lab-scale photobioreactor in which algae biomass was cultured in a semi-continuous mode for a period of 42 days. Solids retention time was 2 days and a stable pH value in the system was maintained by adding CO2. Nitrogen and phosphorus concentrations in the SAnMBR effluent fluctuated according to the operating performance of the bioreactor and the properties of its actual wastewater load. Despite these variations, the anaerobic effluent proved to be a suitable growth medium for microalgae (mean biomass productivity was 234 mgl(-1) d(-1)), achieving a nutrient removal efficiency of 67.2% for ammonium (NH4+-N) and 97.8% for phosphate (PO4-3-P). When conditions were optimum, excellent water quality with very low ammonium and phosphate concentrations was obtained.This research project has been supported by the Spanish Research Foundation (CICYT, projects CTM2011-28595-C02-01 and CTM2011-28595-C02-02), whose support is gratefully acknowledged.Ruiz Martínez, A.; Martin Garcia, N.; Romero Gil, I.; Seco, A.; Ferrer, J. (2012). Microalgae cultivation in wastewater: nutrient removal from anaerobic membrane bioreactor effluent. Bioresource Technology. 126:247-253. https://doi.org/10.1016/j.biortech.2012.09.022S24725312