Scaling in the structure of directory trees in a computer cluster

We describe the topological structure and the underlying organization principles of the directories created by users of a computer cluster when storing his/her own files. We analyze degree distributions, average distance between files, distribution of communities and allometric scaling exponents of the directory trees. We find that users create trees with a broad, scale-free degree distribution. The structure of the directories is well captured by a growth model with a single parameter. The degree distribution of the different trees has a non-universal exponent associated with different values of the parameter of the model. However, the distribution of community sizes has a universal exponent analytically obtained from our model.Comment: refined data analysis and modeling, completely reorganized version, 4 pages, 2 figure

Point rainfall statistics for ecohydrological analyses derived from satellite integrated rainfall measurements

ABSTRACT: Satellite rainfall measurements, nowadays commonly available, provide valuable information about the spatial structure of rainfall. In areas with low-density rain gage networks, or where these networks are nonexistent, satellite rainfall measurements can also provide useful estimates to be used as virtual rain gages. However, satellite and rain gage measurements are statistically different in nature and cannot be directly compared to one another. In the present paper, we develop a methodology to downscale satellite rainfall measurements to generate rain-gage-equivalent statistics. We apply the methodology to four locations along a strong rainfall gradient in the Kalahari transect, southern Africa, to validate the methodology. We show that the method allows the estimation of point rainfall statistics where only satellite measurements exist. Point rainfall statistics are key descriptors for ecohydrologic studies linking the response of vegetation to rainfall dynamics

Tailoring the frictional properties of granular media

A method of modifying the roughness of soda-lime glass spheres is presented, with the purpose of tuning inter-particle friction. The effect of chemical etching on the surface topography and the bulk frictional properties of grains is systematically investigated. The surface roughness of the grains is measured using white light interferometry and characterised by the lateral and vertical roughness length scales. The underwater angle of repose is measured to characterise the bulk frictional behaviour. We observe that the co-efficient of friction depends on the vertical roughness length scale. We also demonstrate a bulk surface roughness measurement using a carbonated soft drink.Comment: 10 pages, 17 figures, submitted to Phys. Rev.

Damage and fluctuations induce loops in optimal transport networks

Leaf venation is a pervasive example of a complex biological network, endowing leaves with a transport system and mechanical resilience. Transport networks optimized for efficiency have been shown to be trees, i.e. loopless. However, dicotyledon leaf venation has a large number of closed loops, which are functional and able to transport fluid in the event of damage to any vein, including the primary veins. Inspired by leaf venation, we study two possible reasons for the existence of a high density of loops in transport networks: resilience to damage and fluctuations in load. In the first case, we seek the optimal transport network in the presence of random damage by averaging over damage to each link. In the second case, we seek the network that optimizes transport when the load is sparsely distributed: at any given time most sinks are closed. We find that both criteria lead to the presence of loops in the optimum state

Topological reversibility and causality in feed-forward networks

Systems whose organization displays causal asymmetry constraints, from evolutionary trees to river basins or transport networks, can be often described in terms of directed paths (causal flows) on a discrete state space. Such a set of paths defines a feed-forward, acyclic network. A key problem associated with these systems involves characterizing their intrinsic degree of path reversibility: given an end node in the graph, what is the uncertainty of recovering the process backwards until the origin? Here we propose a novel concept, \textit{topological reversibility}, which rigorously weigths such uncertainty in path dependency quantified as the minimum amount of information required to successfully revert a causal path. Within the proposed framework we also analytically characterize limit cases for both topologically reversible and maximally entropic structures. The relevance of these measures within the context of evolutionary dynamics is highlighted.Comment: 9 pages, 3 figure

Beyond the SCS-CN method : A theoretical framework for spatially lumped rainfall-runoff response

Acknowledgments This work was supported through the USDA Agricultural Research Service cooperative agreement 58-6408-3-027; and National Science Foundation (NSF) grants CBET-1033467, EAR-1331846, FESD-1338694, EAR-1316258, and the Duke WISeNet grant DGE-1068871. The data used for Figure 9 are reproduced from Tedela et al. [2011, 2008]. Processed data and code are available by e-mail from the corresponding author. We thank the reviewers for their useful and constructive comments that helped improve the paper.Peer reviewedPublisher PD

Mandelbrot's stochastic time series models

I survey and illustrate the main time series models that Mandelbrot introduced into time series analysis in the 1960s and 1970s. I focus particularly on the members of the additive fractional stable family including Lévy flights and fractional Brownian motion (fBm), noting some of the less well‐known aspects of this family, such as the cases when the self‐similarity exponent H and the Hurst exponent J differ. I briefly discuss the role of multiplicative models in modeling the physics of cascades. I then recount the still little‐known story of Mandelbrot's work on fractional renewal models in the late 1960s, explaining how these differ from their more familiar fBm counterpart and form a “missing link” between fBm and the problem of random change points. I conclude by highlighting the frontier problem of damped fractional models

Resistance and inactivation kinetics of bacterial strains isolated from the Non-chlorinated and chlorinated effluents of a WWTP

The microbiological quality of water from a wastewater treatment plant that uses sodium hypochlorite as a disinfectant was assessed. Mesophilic aerobic bacteria were not removed efficiently. This fact allowed for the isolation of several bacterial strains from the effluents. Molecular identification indicated that the strains were related to Aeromonas hydrophila, Escherichia coli (three strains), Enterobacter cloacae, Kluyvera cryocrescens (three strains), Kluyvera intermedia, Citrobacter freundii (two strains), Bacillus sp. and Enterobacter sp. The first five strains, which were isolated from the non-chlorinated effluent, were used to test resistance to chlorine disinfection using three sets of variables: disinfectant concentration (8, 20 and 30 mg·L−1), contact time (0, 15 and 30 min) and water temperature (20, 25 and 30 °C). The results demonstrated that the strains have independent responses to experimental conditions and that the most efficient treatment was an 8 mg·L−1 dose of disinfectant at a temperature of 20 °C for 30 min. The other eight strains, which were isolated from the chlorinated effluent, were used to analyze inactivation kinetics using the disinfectant at a dose of 15 mg·L−1 with various retention times (0, 10, 20, 30, 60 and 90 min). The results indicated that during the inactivation process, there was no relationship between removal percentage and retention time and that the strains have no common response to the treatmentsThe work of SM-H was supported by a graduate scholarship (number 217745) that was kindly provided by CONACyT, Mexico. Some chemical reagents were generously provided by the Administration of the B.A. in Biology at UAEH, Mexico. We thank the Instituto Tecnológico de Estudios Superiores de Monterrey, Hidalgo campus, for allowing us to sample from its WWTP. The authors recognize Jose A. Rodriguez-Ávila for his comments on the procedure for analyzing inactivation kineticsS

Space-Time Diffusion of Ground and Its Fractal Nature

We present evidences of the diffusive motion of the ground and tunnels and show that if systematic movements are excluded then the remaining uncorrelated component of the motion obeys a characteristic fractal law with the displacement variance dY^2 scaling with time- and spatial intervals T and L as dY^2 \propto T^(Alpha)L^(Gamma) with both exponents close to 1. We briefly describe experimental methods of the mesa- and microscopic ground motion detection used in the measurements at the physics research facilities sensitive to the motion, particularly, large high energy elementary particle accelerators. A simple mathematical model of the fractal motion demonstrating the observed scaling law is also presented and discussed.Comment: 83 pages, 46 fig

Geometry of River Networks II: Distributions of Component Size and Number

The structure of a river network may be seen as a discrete set of nested sub-networks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method. Exponential relationships, known as Horton's laws, between stream order and ensemble-averaged quantities pertaining to network components are observed. We extend these observations to incorporate fluctuations and all higher moments by developing functional relationships between distributions. The relationships determined are drawn from a combination of theoretical analysis, analysis of real river networks including the Mississippi, Amazon and Nile, and numerical simulations on a model of directed, random networks. Underlying distributions of stream segment lengths are identified as exponential. Combinations of these distributions form single-humped distributions with exponential tails, the sums of which are in turn shown to give power law distributions of stream lengths. Distributions of basin area and stream segment frequency are also addressed. The calculations identify a single length-scale as a measure of size fluctuations in network components. This article is the second in a series of three addressing the geometry of river networks.Comment: 16 pages, 13 figures, 4 tables, Revtex4, submitted to PR