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.

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

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.

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.

Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of the Stratonovich integral.

Photodynamic Diagnosis of Non-muscle-invasive Bladder Cancer with Hexaminolevulinate Cystoscopy: A Meta-analysis of Detection and Recurrence Based on Raw Data.

BACKGROUND: Studies on hexaminolevulinate (HAL) cystoscopy report improved detection of bladder tumours. However, recent meta-analyses report conflicting effects on recurrence. OBJECTIVE: To assess available clinical data for blue light (BL) HAL cystoscopy on the detection of Ta/T1 and carcinoma in situ (CIS) tumours, and on tumour recurrence. DESIGN, SETTING, AND PARTICIPANTS: This meta-analysis reviewed raw data from prospective studies on 1345 patients with known or suspected non-muscle-invasive bladder cancer (NMIBC). INTERVENTION: A single application of HAL cystoscopy was used as an adjunct to white light (WL) cystoscopy. OUTCOME MEASUREMENTS AND STATISTICAL ANALYSIS: We studied the detection of NMIBC (intention to treat [ITT]: n=831; six studies) and recurrence (per protocol: n=634; three studies) up to 1 yr. DerSimonian and Laird's random-effects model was used to obtain pooled relative risks (RRs) and associated 95% confidence intervals (CIs) for outcomes for detection. RESULTS AND LIMITATIONS: BL cystoscopy detected significantly more Ta tumours (14.7%; p<0.001; odds ratio [OR]: 4.898; 95% CI, 1.937-12.390) and CIS lesions (40.8%; p<0.001; OR: 12.372; 95% CI, 6.343-24.133) than WL. There were 24.9% patients with at least one additional Ta/T1 tumour seen with BL (p<0.001), significant also in patients with primary (20.7%; p<0.001) and recurrent cancer (27.7%; p<0.001), and in patients at high risk (27.0%; p<0.001) and intermediate risk (35.7%; p=0.004). In 26.7% of patients, CIS was detected only by BL (p<0.001) and was also significant in patients with primary (28.0%; p<0.001) and recurrent cancer (25.0%; p<0.001). Recurrence rates up to 12 mo were significantly lower overall with BL, 34.5% versus 45.4% (p=0.006; RR: 0.761 [0.627-0.924]), and lower in patients with T1 or CIS (p=0.052; RR: 0.696 [0.482-1.003]), Ta (p=0.040; RR: 0.804 [0.653-0.991]), and in high-risk (p=0.050) and low-risk (p=0.029) subgroups. Some subgroups had too few patients to allow statistically meaningful analysis. Heterogeneity was minimised by the statistical analysis method used. CONCLUSIONS: This meta-analysis confirms that HAL BL cystoscopy significantly improves the detection of bladder tumours leading to a reduction of recurrence at 9-12 mo. The benefit is independent of the level of risk and is evident in patients with Ta, T1, CIS, primary, and recurrent cancer.