Quasiperiodic graphs: structural design, scaling and entropic properties

A novel class of graphs, here named quasiperiodic, are constructed via application of the Horizontal Visibility algorithm to the time series generated along the quasiperiodic route to chaos. We show how the hierarchy of mode-locked regions represented by the Farey tree is inherited by their associated graphs. We are able to establish, via Renormalization Group (RG) theory, the architecture of the quasiperiodic graphs produced by irrational winding numbers with pure periodic continued fraction. And finally, we demonstrate that the RG fixed-point degree distributions are recovered via optimization of a suitably defined graph entropy

Cloud system resolving model study of the roles of deep convection for photo-chemistry in the TOGA COARE/CEPEX region

International audienceA cloud system resolving model including photo-chemistry (CSRMC) has been developed based on a prototype version of the Weather Research and Forecasting (WRF) model and is used to study influences of deep convection on chemistry in the TOGA COARE/CEPEX region. Lateral boundary conditions for trace gases are prescribed from global chemistry-transport simulations, and the vertical advection of trace gases by large scale dynamics, which is not reproduced in a limited area cloud system resolving model, is taken into account. The influences of deep convective transport and of lightning on NOx, O3, and HOx(=HO2+OH), in the vicinity of the deep convective systems are investigated in a 7-day 3-D 248×248 km2 horizontal domain simulation and several 2-D sensitivity runs with a 500 km horizontal domain. Mid-tropospheric entrainment is more important on average for the upward transport of O3 in the 3-D run than in the 2-D runs, but at the same time undiluted O3-poor air from the marine boundary layer reaches the upper troposphere more frequently in the 3-D run than in the 2-D runs, indicating the presence of undiluted convective cores. In all runs, in situ lightning is found to have only minor impacts on the local O3 budget. Near zero O3 volume mixing ratios due to the reaction with lightning-produced NO are only simulated in a 2-D sensitivity run with an extremely high number of NO molecules per flash, which is outside the range of current estimates. The fraction of NOx chemically lost within the domain varies between 20 and 24% in the 2-D runs, but is negligible in the 3-D run, in agreement with a lower average NOx concentration in the 3-D run despite a greater number of flashes. Stratosphere to troposphere transport of O3 is simulated to occur episodically in thin filaments in the 2-D runs, but on average net upward transport of O3 from below ~16 km is simulated in association with mean large scale ascent in the region. Ozone profiles in the TOGA COARE/CEPEX region are suggested to be strongly influenced by the intra-seasonal (Madden-Julian) oscillation

Modelling tracer transport by a cumulus ensemble: lateral boundary conditions and large-scale ascent

International audienceThe vertical transport of tracers by a cumulus ensemble at the TOGA-COARE site is modelled during a 7 day episode using 2-D and 3-D cloud-resolving setups of the Weather Research and Forecast (WRF) model. Lateral boundary conditions (LBC) for tracers, water vapour, and wind are specified and the horizontal advection of trace gases across the lateral domain boundaries is considered. Furthermore, the vertical advection of trace gases by the large-scale motion (short: vertical large-scale advection of tracers, VLSAT) is considered. It is shown, that including VLSAT partially compensates the calculated net downward transport from the middle and upper troposphere (UT) due to the mass balancing mesoscale subsidence induced by deep convection. Depending on whether the VLSAT term is added or not, modelled domain averaged vertical tracer profiles can differ significantly. Differences between a 2-D and a 3-D model run were mainly attributed to an increase in horizontal advection across the lateral domain boundaries due to the meridional wind component not considered in the 2-D setup

Model sensitivity studies regarding the role of the retention coefficient for the scavenging and redistribution of highly soluble trace gases by deep convective cloud systems

International audienceThe role of the retention coefficient (i.e. the fraction of a dissolved trace gas which is retained in hydrometeors during freezing) for the scavenging and redistribution of highly soluble trace gases by deep convective cloud systems is investigated using a modified version of the Weather Research and Forecasting (WRF) model. Results from cloud system resolving model runs (in which deep convection is initiated by small random perturbations in association with so-called "large scale forcings (LSF)") for a tropical oceanic (TOGA COARE) and a mid-latitude continental case (ARM) are compared to two runs in which bubbles are used to initiate deep convection (STERAO, ARM). In the LSF runs, scavenging is found to almost entirely prevent a highly soluble tracer initially located in the lowest 1.5 km of the troposphere from reaching the upper troposphere, independent of the retention coefficient. The release of gases from freezing hydrometeors leads to mixing ratio increases in the upper troposphere comparable to those calculated for insoluble trace gases only in the two runs in which bubbles are used to initiate deep convection. A comparison of the two ARM runs indicates that using bubbles to initiate deep convection may result in an overestimate of the influence of the retention coefficient on the vertical transport of highly soluble tracers. It is, however, found that the retention coefficient plays an important role for the scavenging and redistribution of highly soluble trace gases with a (chemical) source in the free troposphere and also for trace gases for which even relatively inefficient transport may be important. The large difference between LSF and bubble runs is attributed to differences in dynamics and microphysics in the inflow regions of the storms. The dependence of the results on the model setup indicates the need for additional model studies with a more realistic initiation of deep convection, e.g., considering effects of orography in a nested model setup

Topological properties and fractal analysis of recurrence network constructed from fractional Brownian motions

Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the relationship between $H$ and $$can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e. the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension$$ of recurrence networks decreases with the Hurst index $H$ of the associated FBMs, and their dependence approximately satisfies the linear formula $\approx 2 - H$. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index $H=0.5$ possess the strongest multifractality. In addition, the dependence relationships of the average information dimension $$and the average correlation dimension$$ on the Hurst index $H$ can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated FBM series.Comment: 25 pages, 1 table, 15 figures. accepted by Phys. Rev.

Sample size calculations for cluster randomised controlled trials with a fixed number of clusters

Background\ud Cluster randomised controlled trials (CRCTs) are frequently used in health service evaluation. Assuming an average cluster size, required sample sizes are readily computed for both binary and continuous outcomes, by estimating a design effect or inflation factor. However, where the number of clusters are fixed in advance, but where it is possible to increase the number of individuals within each cluster, as is frequently the case in health service evaluation, sample size formulae have been less well studied. \ud \ud Methods\ud We systematically outline sample size formulae (including required number of randomisation units, detectable difference and power) for CRCTs with a fixed number of clusters, to provide a concise summary for both binary and continuous outcomes. Extensions to the case of unequal cluster sizes are provided. \ud \ud Results\ud For trials with a fixed number of equal sized clusters (k), the trial will be feasible provided the number of clusters is greater than the product of the number of individuals required under individual randomisation ($n_i$) and the estimated intra-cluster correlation ($\rho$). So, a simple rule is that the number of clusters ($\kappa$) will be sufficient provided: \ud \ud $\kappa$ > $n_i$ x $\rho$\ud \ud Where this is not the case, investigators can determine the maximum available power to detect the pre-specified difference, or the minimum detectable difference under the pre-specified value for power. \ud \ud Conclusions\ud Designing a CRCT with a fixed number of clusters might mean that the study will not be feasible, leading to the notion of a minimum detectable difference (or a maximum achievable power), irrespective of how many individuals are included within each cluster. \ud \u

A Strategy for Detecting Natural Anthelmintic Constituents of the Grassland Species \u3ci\u3ePlantago lanceolata\u3c/i\u3e

A strategy to detect anthelmintic constituents in plantain (Plantago lanceolata) using a bioassay-driven purification approach was tested. Plantain consumed by cattle may control or reduce internal parasite titers, possibly due to the iridoid glucoside aucubin. Lyophilized, ground leaves of wild P. lanceolata were extracted with 95 % ethanol or boiling water containing calcium carbonate. Partially purified extracts (0 to 250 mg ml-1), 5 μg ml-1 of the anthelmintic levamisole, or 5 mg ml-1 of aucubin were tested with sheathed bovine parasites (Ostertagia ostertagi). The percent moving worms was unchanged for water controls and reduced to 0 % for anthelmintic levamisole. Aucubin significantly reduced the number of swimming worms at day 2, but they returned to starting values at day 3. Extracts from tall fescue and white clover foliage did not show anthelmintic effects. Treatment of extract or aucubin with ß-glucosidase did not alter their activity. Beneficial anthelmintic action of ingested plantain is not due to aucubin

Feigenbaum graphs: a complex network perspective of chaos

The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos.Comment: Published in PLoS ONE (Sep 2011

Ecology and Genetic Structure of a Northern Temperate Vibrio cholerae Population Related to Toxigenic Isolates

Although Vibrio cholerae is an important human pathogen, little is known about its populations in regions where the organism is endemic but where cholera disease is rare. A total of 31 independent isolates confirmed as V. cholerae were collected from water, sediment, and oysters in 2008 and 2009 from the Great Bay Estuary (GBE) in New Hampshire, a location where the organism has never been detected. Environmental analyses suggested that abundance correlates most strongly with rainfall events, as determined from data averaged over several days prior to collection. Phenotyping, genotyping, and multilocus sequence analysis (MLSA) revealed a highly diverse endemic population, with clones recurring in both years. Certain isolates were closely related to toxigenic O1 strains, yet no virulence genes were detected. Multiple statistical tests revealed evidence of recombination among strains that contributed to allelic diversity equally as mutation. This relatively isolated population discovered on the northern limit of detection for V. cholerae can serve as a model of natural population dynamics that augments predictive models for disease emergence