Generation of uncorrelated random scale-free networks

Uncorrelated random scale-free networks are useful null models to check the accuracy and the analytical solutions of dynamical processes defined on complex networks. We propose and analyze a model capable of generating random uncorrelated scale-free networks with no multiple and self-connections. The model is based on the classical configuration model, with an additional restriction on the maximum possible degree of the vertices. We check numerically that the proposed model indeed generates scale-free networks with no two- and three-vertex correlations, as measured by the average degree of the nearest neighbors and the clustering coefficient of the vertices of degree k, respectively.

Random diffusion and leverage effect in financial markets

We prove that Brownian market models with random diffusion coefficients provide an exact measure of the leverage effect [J-P. Bouchaud et al., Phys. Rev. Lett. 87, 228701 (2001)]. This empirical fact asserts that past returns are anticorrelated with future diffusion coefficient. Several models with random diffusion have been suggested but without a quantitative study of the leverage effect. Our analysis lets us to fully estimate all parameters involved and allows a deeper study of correlated random diffusion models that may have practical implications for many aspects of financial markets.

Class of correlated random networks with hidden variables

We study a class of models of correlated random networks in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices. The expressions obtained are checked by means of numerical simulations in a particular example. The general model is extended to describe a practical algorithm to generate random networks with an a priori specified correlation structure. We also present an extension of the class, to map nonequilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system.

Exact long-time behavior of a network of oscillators under random fields

We present an exact solution for the order parameters that characterize the stationary behavior of a population of Kuramotos phase oscillators under random external fields [Y. Kuramoto, in International Symposium on Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, Vol. 39 (Springer, Berlin, 1975), p. 420]. From these results it is possible to generate the phase diagram of models with an arbitrary distribution of random frequencies and random fields.

Generalization of the persistent random walk to dimensions greater than 1

We propose a generalization of the persistent random walk for dimensions greater than 1. Based on a cubic lattice, the model is suitable for an arbitrary dimension d. We study the continuum limit and obtain the equation satisfied by the probability density function for the position of the random walker. An exact solution is obtained for the projected motion along an axis. This solution, which is written in terms of the free-space solution of the one-dimensional telegraphers equation, may open a new way to address the problem of light propagation through thin slabs.

Non independent continuous-time random walks

The usual development of the continuous-time random walk (CTRW) assumes that jumps and time intervals are a two-dimensional set of independent and identically distributed random variables. In this paper, we address the theoretical setting of nonindependent CTRWs where consecutive jumps and/or time intervals are correlated. An exact solution to the problem is obtained for the special but relevant case in which the correlation solely depends on the signs of consecutive jumps. Even in this simple case, some interesting features arise, such as transitions from unimodal to bimodal distributions due to correlation. We also develop the necessary analytical techniques and approximations to handle more general situations that can appear in practice.

Random mixtures with orientational order, and the anisotropic resistivity tensor of high Tc superconductors

By generalizing effective-medium theory to the case of orientationally ordered but positionally disordered two component mixtures, it is shown that the anisotropic dielectric tensor of oxide superconductors can be extracted from microwave measurements on oriented crystallites of YBa2Cu3O7¿x embedded in epoxy. Surprisingly, this technique appears to be the only one which can access the resistivity perpendicular to the copper¿oxide planes in crystallites that are too small for depositing electrodes. This possibility arises in part because the real part of the dielectric constant of oxide superconductors has a large magnitude. The validity of the effective-medium approach for orientationally ordered mixtures is corroborated by simulations on two¿dimensional anisotropic random resistor networks. Analysis of the experimental data suggests that the zero-temperature limit of the finite frequency resistivity does not vanish along the c axis, a result which would simply the existence of states at the Fermi surface, even in the superconducting state

Parrondo-like behavior in continuous-time random walks with memory

The continuous-time random walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this paper we will show how the random combination of two different unbiased CTRWs can give rise to a process with clear drift, if one of them is a CTRW with memory. If one identifies the other one as noise, the effect can be thought of as a kind of stochastic resonance. The ultimate origin of this phenomenon is the same as that of the Parrondo paradox in game theory.

Quantum relaxation in random magnets

We present a comprehensive study of the low-temperature magnetic relaxation in random magnets. The first part of the paper contains theoretical analysis of the expected features of the relaxation, based upon current theories of quantum tunneling of magnetization. Models of tunneling, dissipation, the crossover from the thermal to the quantum regime, and the effect of barrier distribution on the relaxation rate are discussed. It is argued that relaxation-type experiments are ideally suited for the observation of magnetic tunneling, since they automatically provide the condition of very low barriers. The second part of the paper contains experimental results on transition-metal¿rare-earth amorphous magnets. Structural and magnetic characterization of materials is presented. The temperature and field dependence of the magnetic relaxation is studied. Our key observation is a nonthermal character of the relaxation below a few kelvin. The observed features are in agreement with theoretical suggestions on quantum tunneling of magnetization.

Structural disorder in two-dimensional random magnets: Very thin films of rare earths and transition metals

The low-temperature isothermal magnetization curves, M(H), of SmCo4 and Fe3Tb thin films are studied according to the two-dimensional correlated spin-glass model of Chudnovsky. We have calculated the magnetization law in approach to saturation and shown that the M(H) data fit well the theory at high and low fields. In our fit procedure we have used three different correlation functions. The Gaussian decay correlation function fits well the experimental data for both samples.

Growth and Nutrition of Eucalypt Rooted Cuttings Promoted by Ectomycorrhizal Fungi in Commercial Nurseries

ABSTRACT Ectomycorrhizal fungi (EMF) may improve the adaptation of eucalypts saplings to field conditions and allow more efficient fertilizer use. The effectiveness of EMF inoculum application in promoting fungal colonization, plant growth, nutrient uptake, and the quality of rooted cuttings was evaluated forEucalyptus urophylla under commercial nursery conditions. For inoculated treatments, fertilization of the sapling substrate was reduced by 50 %. The experiment was carried out in a completely randomized design in a 4 × 4 factorial arrangement, wherein the factors were inoculum application rates of 0 (control), 5, 10, and 15 gel beads of calcium alginate containing the vegetative mycelium of Amanita muscaria, Elaphomyces antracinus, Pisolithus microcarpus, andScleroderma areolatum, plus a non-inoculated treatment without fertilization reduction in the substrate (commercial). Ectomycorrhizal fungi increased plant growth and fungal colonization as well as N and K uptake evenly. The best plant growth and fungal colonization were observed for the highest application rate. The greatest growth and fungal colonization and contents of P, N, and K were observed at the 10-bead rate. Plant inoculation with Amanita muscaria, Elaphomyces anthracinus, and Scleroderma areolatum increased P concentrations and contents in a differential manner. The Dickson Quality Index was not affected by the type of fungi or by inoculum application rates. Eucalypt rooted cuttings inoculated with ectomycorrhizal fungi and under half the amount of commercial fertilization had P, N, and K concentrations and contents greater than or equal to those of commercial plants and have high enough quality to be transplanted after 90 days.

Rhizobia Isolated from Coal Mining Areas in the Nodulation and Growth of Leguminous Trees

ABSTRACT An alternative for recovery of areas degraded by coal mining is revegetation with rapidly growing leguminous trees, which often do not establish in low fertility soils. The objective of this study was to evaluate the efficiency of native rhizobia isolated from coal mining areas in the nodulation and growth of leguminous trees. We isolated 19 strains of rhizobia from a degraded soil near Criciúma, SC, Brazil, and evaluated the nodulation and growth-promoting capacity of the inoculated isolates for bracatinga (Mimosa scabrella), maricá (M. bimucronata) and angico-vermelho (Parapiptadenia rigida). Isolates UFSC-B2, B6, B8, B9, B11 and B16 were able to nodulate bracatinga, providing average increases of 165 % in shoot dry matter, with a significant contribution to N accumulation. Isolates UFSC-B5, B12, and M8 favored nodulation and growth of maricá, especially isolate UFSC-B12, which promoted increases of 370 % in N accumulation compared to treatment with N fertilizer. All strains were inefficient in promoting growth and N uptake by angico-vermelho. In conclusion, isolation and use of selected rhizobia for bracatinga and maricá plant inoculation can contribute to the growth and accumulation of N, with prospects for use in programs for revegetation of degraded soils in coal mining areas.

Non-random autosome segregation: a stepping stone for the evolution of sex chromosome complexes?

A new study in Caenorhabditis elegans shows that homologous autosomes segregate non-randomly with the sex chromosome in the heterogametic sex. Segregation occurs according to size, small autosomes segregating with, and large autosomes segregating away from the X-chromosome. Such sex-biased transmission of autosomes could facilitate the spread of sexually antagonistic alleles whose effects favor the fitness of one sex at the expense of the other. This may provide a first step toward the evolution of new sex determination systems.