Pattern Formation on Trees

Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the nodes of a tree is described by a nonlinear map, given rise to a coupled map lattice system. The coupling is expressed by a matrix whose eigenvectors constitute a basis on which spatial patterns on trees can be expressed by linear combination. The spectrum of eigenvalues of the coupling matrix exhibit a nonuniform distribution which manifest itself in the bifurcation structure of the spatially synchronized modes. These models may describe reaction-diffusion processes and several other phenomena occurring on heterogeneous media with hierarchical structure.Comment: Submitted to Phys. Rev. E, 15 pages, 9 fig

Statistical Complexity and Nontrivial Collective Behavior in Electroencephalografic Signals

We calculate a measure of statistical complexity from the global dynamics of electroencephalographic (EEG) signals from healthy subjects and epileptic patients, and are able to stablish a criterion to characterize the collective behavior in both groups of individuals. It is found that the collective dynamics of EEG signals possess relative higher values of complexity for healthy subjects in comparison to that for epileptic patients. To interpret these results, we propose a model of a network of coupled chaotic maps where we calculate the complexity as a function of a parameter and relate this measure with the emergence of nontrivial collective behavior in the system. Our results show that the presence of nontrivial collective behavior is associated to high values of complexity; thus suggesting that similar dynamical collective process may take place in the human brain. Our findings also suggest that epilepsy is a degenerative illness related to the loss of complexity in the brain.Comment: 13 pages, 3 figure

Characterization of two new alleles at the goat CSN1S2 locus.

Two novel alleles at the goat CSN1S2 locus have been identified: CSN1S2(F) and CSN1S2(D). Sequence analyses revealed that the CSN1S2(F) allele is characterized by a G --> A transition at the 13th nucleotide in exon 3 changing the seventh amino acid of the mature protein from Val to Ile. The CSN1S2(D) allele, apparently associated with a decreased synthesis of alpha s2-casein, is characterized by a 106-bp deletion, involving the last 11 bp of the exon 11 and the first 95 bp of the following intron. Methods (PCR-RFLP and PCR) for identification of carriers of these alleles have been developed

Global sensitivity analysis for urban water quality modelling: Terminology, convergence and comparison of different methods

Sensitivity analysis represents an important step in improving the understanding and use of environmental models. Indeed, by means of global sensitivity analysis (GSA), modellers may identify both important (factor prioritisation) and non-influential (factor fixing) model factors. No general rule has yet been defined for verifying the convergence of the GSA methods. In order to fill this gap this paper presents a convergence analysis of three widely used GSA methods (SRC, Extended FAST and Morris screening) for an urban drainage stormwater quality-quantity model. After the convergence was achieved the results of each method were compared. In particular, a discussion on peculiarities, applicability, and reliability of the three methods is presented. Moreover, a graphical Venn diagram based classification scheme and a precise terminology for better identifying important, interacting and non-influential factors for each method is proposed. In terms of convergence, it was shown that sensitivity indices related to factors of the quantity model achieve convergence faster. Results for the Morris screening method deviated considerably from the other methods. Factors related to the quality model require a much higher number of simulations than the number suggested in literature for achieving convergence with this method. In fact, the results have shown that the term "screening" is improperly used as the method may exclude important factors from further analysis. Moreover, for the presented application the convergence analysis shows more stable sensitivity coefficients for the Extended-FAST method compared to SRC and Morris screening. Substantial agreement in terms of factor fixing was found between the Morris screening and Extended FAST methods. In general, the water quality related factors exhibited more important interactions than factors related to water quantity. Furthermore, in contrast to water quantity model outputs, water quality model outputs were found to be characterised by high non-linearity

Dynamics of Coupling Functions in Globally Coupled Maps: Size, Periodicity and Stability of Clusters

It is shown how different globally coupled map systems can be analyzed under a common framework by focusing on the dynamics of their respective global coupling functions. We investigate how the functional form of the coupling determines the formation of clusters in a globally coupled map system and the resulting periodicity of the global interaction. The allowed distributions of elements among periodic clusters is also found to depend on the functional form of the coupling. Through the analogy between globally coupled maps and a single driven map, the clustering behavior of the former systems can be characterized. By using this analogy, the dynamics of periodic clusters in systems displaying a constant global coupling are predicted; and for a particular family of coupling functions, it is shown that the stability condition of these clustered states can straightforwardly be derived.Comment: 12 pp, 5 figs, to appear in PR

Modelling the induced polarization of bentonite-sand mixtures

International audienceSpectral induced polarization (SIP) has become an increasingly popular geophysical method for hydrogeological and environmental applications. These applications include for instance the non-intrusive characterization of the textural and interfacial physicochemical properties of bentonites used as permeability barriers in landfills or to store various types of contaminants including radioactive wastes. Bentonites are mainly constituted of smectites, which have very high specific surface areas (SSA) and cation exchange capacities (CEC). Therefore, these minerals have very high electromigration and polarization current densities responsible for very high in phase and quadrature conductivities, respectively. In addition, in diluted water, the diffuse layer of smectites occupies a large fraction of the pore space and may be therefore considered as part of the pore space. In our approach [1], complex electrical conductivities of saturated unconsolidated bentonite and bentonite-sand mixtures are modeled at different salinities (NaCl) of the bulk pore water using a Donnan equilibrium model coupled to the revisited SIP model of Leroy and Revil [2]. Our complex surface conductivity model considers the DC contribution of the diffuse and Stern layers as well as the electrochemical polarization of the Stern layer coating the grains with different sizes. The macroscopic SIP model is based on the differential effective medium theory and considers the complex surface conductivity of the sand and smectite grains and the complex conductivity of the pore space. In our model, the diffuse layer of quartz sands occupies a small fraction of the pore space and is considered therefore as part of the surface of the grains. Our SIP model predicts very well the low frequency (0.1 Hz - kHz) complex electrical conductivities of bentonite and bentonite-sand mixtures, except for very low frequencies (< 0.1 Hz) where membrane polarization may occur (Figure 1). The in phase conductivity of the sample with a high clay content (20 % in volume) increases slowly with salinity because of the very high DC surface conductivity of smectite. The observed large increase of the in phase and quadrature conductivity of the samples with the clay content (1, 20 and 100% in volume) is also predicted by our model. The quadrature conductivity of the samples with a high clay content is fairly independent on the pore fluid salinity because it is strongly connected with the SSA, CEC and Stern layer of smectite (Figure 1). The in phase conductivity of the sample with a low clay content (1% in volume) increases quickly with the salinity because of its low DC surface conductivity. Its quadrature conductivity also increases quickly with salinity because of the formation of the Stern layer at the surface of quartz sand. Nevertheless, our SIP model can't predict the quadrature conductivity spectra observed at very low frequencies (< 10-1 Hz). The missing polarization mechanism may correspond to membrane polarization and there is an effort to be done to incorporate this contribution in a unified model

Periodic Neural Activity Induced by Network Complexity

We study a model for neural activity on the small-world topology of Watts and Strogatz and on the scale-free topology of Barab\'asi and Albert. We find that the topology of the network connections may spontaneously induce periodic neural activity, contrasting with chaotic neural activities exhibited by regular topologies. Periodic activity exists only for relatively small networks and occurs with higher probability when the rewiring probability is larger. The average length of the periods increases with the square root of the network size.Comment: 4 pages, 5 figure

Genetic variability detected at the lactoferrin locus (LTF) in the Italian Mediterranean river buffalo

Lactoferrin (LTF) is multi-functional protein belonging to the whey protein fractions of the milk. The gene LTF encoding for such protein is considered a potential candidate for body measurement, milk composition and yield. This study reports on the genetic variability at LTF locus in the Italian Mediterranean river buffalo and its possible association with milk yield. Eleven polymorphic sites were found in the DNA fragment spanning the exons 15-16. In particular, the intron 15 was extremely polymorphic with 9 SNPs detected, whereas the remaining 2 SNPs were exonic mutations (g.88G>A at the exon 15 and g.1351G>A at the exon 16) and both synonymous. The genotyping of the informative samples evidenced 3 haplotypes, whose frequencies were 0.6; 0.3 and 0.1 respectively, whereas the analysis of the exonic SNPs showed a perfect condition of linkage disequilibrium (g.88A/g.1351G and g.88G/g.1351A). The association study carried out by using the SNP g.88G>A showed that buffalo LTF gene has no statistically significant influence on daily milk yield. This study adds knowledge to the genetic variability of a species less investigated than the other ruminant species, that may serve as a useful tool for large-scale screening of buffalo populations