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

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

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

Production of a potential liquid plant bio-stimulant by immobilized Piriformospora indica in repeated-batch fermentation process

Piriformospora indica, a mycorrhizal-like fungus able to establish associations with roots of a wide range of plants, supporting plant nutrition and increasing plant resistance and tolerance to stress, was shown to solubilise phosphate applied in the form of animal bone char (HABO) in fermentation systems. The process of P solubilisation was caused most likely by proton extrusion and medium pH lowering. The fungal mycelium was successfully immobilized/retained in a polyurethane foam carrier. Further employment of the immobilized mycelium in repeated-batch fermentation process resulted in at least 5 cycles of P solubilization. The concentration of soluble P increased during the experiment with 1.0 and 3.0 g HABO l−1 and at the end of the 5th batch cycle reached 40.8 and 120 mg l−1, respectively. The resulting final liquid product, without or with solubilized phosphate, was found to significantly increase plant growth and P plant uptake. It can be used as a biostimulant containing microbial plant growth-promoting substances and soluble P derived from renewable sources (HABO) thus supporting the development of sustainable agro-ecosystems.This work was supported by Project CTM2014-53186-R, Ministerio de Economia y Competitividad-ES/EC FEDER Fund and the sabbatical Grant PRX16/00277 to NV