Anderson transition on the Cayley tree as a traveling wave critical point for various probability distributions

For Anderson localization on the Cayley tree, we study the statistics of various observables as a function of the disorder strength $W$ and the number $N$ of generations. We first consider the Landauer transmission $T_N$. In the localized phase, its logarithm follows the traveling wave form $\ln T_N \simeq \bar{\ln T_N} + \ln t^*$ where (i) the disorder-averaged value moves linearly $\bar{\ln (T_N)} \simeq - \frac{N}{\xi_{loc}}$ and the localization length diverges as $\xi_{loc} \sim (W-W_c)^{-\nu_{loc}}$ with $\nu_{loc}=1$ (ii) the variable $t^*$ is a fixed random variable with a power-law tail $P^*(t^*) \sim 1/(t^*)^{1+\beta(W)}$ for large $t^*$ with $0<\beta(W) \leq 1/2$, so that all integer moments of $T_N$ are governed by rare events. In the delocalized phase, the transmission $T_N$ remains a finite random variable as $N \to \infty$, and we measure near criticality the essential singularity $\bar{\ln (T)} \sim - | W_c-W |^{-\kappa_T}$ with $\kappa_T \sim 0.25$. We then consider the statistical properties of normalized eigenstates, in particular the entropy and the Inverse Participation Ratios (I.P.R.). In the localized phase, the typical entropy diverges as $(W-W_c)^{- \nu_S}$ with $\nu_S \sim 1.5$, whereas it grows linearly in $N$ in the delocalized phase. Finally for the I.P.R., we explain how closely related variables propagate as traveling waves in the delocalized phase. In conclusion, both the localized phase and the delocalized phase are characterized by the traveling wave propagation of some probability distributions, and the Anderson localization/delocalization transition then corresponds to a traveling/non-traveling critical point. Moreover, our results point towards the existence of several exponents $\nu$ at criticality.Comment: 28 pages, 21 figures, comments welcom

Anderson localization on the Cayley tree : multifractal statistics of the transmission at criticality and off criticality

In contrast to finite dimensions where disordered systems display multifractal statistics only at criticality, the tree geometry induces multifractal statistics for disordered systems also off criticality. For the Anderson tight-binding localization model defined on a tree of branching ratio K=2 with $N$ generations, we consider the Miller-Derrida scattering geometry [J. Stat. Phys. 75, 357 (1994)], where an incoming wire is attached to the root of the tree, and where $K^{N}$ outcoming wires are attached to the leaves of the tree. In terms of the $K^{N}$ transmission amplitudes $t_j$, the total Landauer transmission is $T \equiv \sum_j | t_j |^2$, so that each channel $j$ is characterized by the weight $w_j=| t_j |^2/T$. We numerically measure the typical multifractal singularity spectrum $f(\alpha)$ of these weights as a function of the disorder strength $W$ and we obtain the following conclusions for its left-termination point $\alpha_+(W)$. In the delocalized phase $W<W_c$, $\alpha_+(W)$ is strictly positive $\alpha_+(W)>0$ and is associated with a moment index $q_+(W)>1$. At criticality, it vanishes $\alpha_+(W_c)=0$ and is associated with the moment index $q_+(W_c)=1$. In the localized phase $W>W_c$, $\alpha_+(W)=0$ is associated with some moment index $q_+(W)<1$. We discuss the similarities with the exact results concerning the multifractal properties of the Directed Polymer on the Cayley tree.Comment: v2=final version (16 pages

Structure of the French farm-to-table surveillance system for Salmonella

The French surveillance system for Salmonella is based on a national system which can be traced back to 1947 for human cases and to the late 1980s for the main animal reservoirs. This system has evolved with regard to both European regulations and changes in the observed prevalence of Salmonella. European regulations establish a solid foundation on which to build an active harmonised surveillance system at the production level and for integrating data from the whole food chain. There are also passive surveillance networks in the agri-food and veterinary sectors and these allow complementary information to be obtained from other sectors or sources. The main strengths and weaknesses of these systems are described and a comparison of the different approaches is presented using a grid analysis. The results show that passive systems are very useful for detecting emerging or unusual events and for early warning of outbreaks. They also produce time series of cases or can determine the number of strains that should be used to assess the impact of interventions. Active surveillance data, due to their representativeness and reliability, are key elements in the application of risk analysis tools such as quantitative risk assessment or attribution. Thus, although data is collected and analysed by various organisations, these organisations all collaborate at a national level. Furthermore, their implication in European and international projects is effective and the main objectives of a surveillance system can be met

Localization of a polymer in random media: Relation to the localization of a quantum particle

In this paper we consider in detail the connection between the problem of a polymer in a random medium and that of a quantum particle in a random potential. We are interested in a system of finite volume where the polymer is known to be {\it localized} inside a low minimum of the potential. We show how the end-to-end distance of a polymer which is free to move can be obtained from the density of states of the quantum particle using extreme value statistics. We give a physical interpretation to the recently discovered one-step replica-symmetry-breaking solution for the polymer (Phys. Rev. E{\bf 61}, 1729 (2000)) in terms of the statistics of localized tail states. Numerical solutions of the variational equations for chains of different length are performed and compared with quenched averages computed directly by using the eigenfunctions and eigenenergies of the Schr\"odinger equation for a particle in a one-dimensional random potential. The quantities investigated are the radius of gyration of a free gaussian chain, its mean square distance from the origin and the end-to-end distance of a tethered chain. The probability distribution for the position of the chain is also investigated. The glassiness of the system is explained and is estimated from the variance of the measured quantities.Comment: RevTex, 44 pages, 13 figure

Comparison of two recombinant erythropoietin formulations in patients with anemia due to end-stage renal disease on hemodialysis: A parallel, randomized, double blind study

BACKGROUND: Recombinant human erythropoietin (EPO) is used for the treatment of last stage renal anemia. A new EPO preparation was obtained in Cuba in order to make this treatment fully nationally available. The aim of this study was to compare the pharmacokinetic, pharmacodynamic and safety properties of two recombinant EPO formulations in patients with anemia due to end-stage renal disease on hemodialysis. METHODS: A parallel, randomized, double blind study was performed. A single 100 IU/Kg EPO dose was administered subcutaneously. Heberitro (Heber Biotec, Havana, formulation A), a newly developed product and Eprex (CILAG AG, Switzerland, formulation B), as reference treatment were compared. Thirty-four patients with anemia due to end-stage renal disease on hemodialysis were included. Patients had not received EPO previously. Serum EPO level was measured by enzyme immunoassay (EIA) during 120 hours after administration. Clinical and laboratory variables were determined as pharmacodynamic and safety criteria until 216 hours. RESULTS: Both groups of patients were similar regarding all demographic and baseline characteristics. EPO kinetics profiles were similar for both formulations; the pharmacokinetic parameters were very close (i.e., AUC: 4667 vs. 4918 mIU.h/mL; Cmax: 119.1 vs. 119.7 mIU/mL; Tmax: 13.9 vs. 18.1 h; half-life, 20.0 vs. 22.5 h for formulations A and B, respectively). The 90% confidence intervals for the ratio between both products regarding these metrics were close to the 0.8 – 1.25 range, considered necessary for bioequivalence. Differences did not reach 20% in any case and were not determined by a formulation effect, but probably by a patients' variability effect. Concerning pharmacodynamic features, a high similitude in reticulocyte counts increments until 216 hours and the percentage decrease in serum iron until 120 hours was observed. There were no differences between formulations regarding the adverse events and their intensity. The more frequent events were pain at injection site (35.3%) and hypertension (29%). Additionally, further treatment of the patients with the study product yielded satisfactory increases in hemoglobin and hematocrit values. CONCLUSION: The formulations are comparable. The newly developed product should be acceptable for long-term application

Avian diseases which affect egg production and quality

This chapter addresses diseases and syndromes which have been shown, or are reported, to have adverse effects on egg production and quality. However, any disease of poultry can adversely affect egg production and quality indirectly, by affecting the health of the bird. The main topics are the effect on egg production and quality of bacteria ('Salmonella', 'Mycoplasma', 'Escherichia coli', infectious coryza, 'Ornithobacterium', 'Gallibacterium', spirochaetosis), viruses (infectious bronchitis virus, egg drop syndrome, swollen head syndrome, avian encephalomyelitis, influenza, Newcastle disease, laryngotracheitis), syndromes (fatty liver haemorrhagic syndrome, cage layer osteoporosis) and toxic agents. A short section on clinical perspectives reports on information obtained from practising poultry veterinarians as such observations can provide valuable starting points for future research

Dynamic mechanical relaxation of cross-linked styrene-butadiene polymers containing free chains: Possibility of reptation

cited By 5International audienceThe structure of styrene-butadiene rubbers (SBRs) consists of chains attached to cross-links of relatively small number density. These rubbers show an α-relaxation process that is attributed to segmental motions of the attached chains. To investigate how an SBR's rubber-like behavior would change when free chains interpenetrate its structure, we prepared one SBR of mol wt 120 × 103containing 3-4% free chains of identical mol wt, and studied its dynamic mechanical relaxation. For 0.1 Hz frequency measurements, the α-relaxation peak appeared at 210 K, and a second relaxation peak, which we refer to as αR-relaxation, at 300 K. A third relaxation of small magnitude was resolved at temperatures between the αR- and the α-relaxation peaks, and its origin was discussed in relation to other studies. Spectral features of the αR-and the α-relaxations were found similar. We investigated the merits of the time-temperature superposition of the α- and of the αR-relaxations. The αRrelaxation vanished when the free chains were extracted from the SBR by swelling-extraction procedure. The features of α-relaxation can be interpreted as segmental motions of the SBR, but the features of the αR-relaxation is be interpretable only in terms of tube model for diffusion of free chains in a lightly cross-linked structure. We estimated the mol wt of these free chains and the mass between entanglements, and then used these quantities to calculate, by using the Doi-Edwards formalism, the relaxation time of the αR-process at 293 K. This relaxation time agrees with the experimental value. The αR-relaxation seems consistent with the tube model for diffusion of free chains in the cross-linked structure of SBR. © 2014 Elsevier Ltd. All rights reserved