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.

The Effect of a threshold proportional reinsurance strategy on ruin probabilities

[spa] En un modelo de Poisson compuesto, definimos una estrategia de reaseguro proporcional de umbral : se aplica un nivel de retención k1 siempre que las reservas sean inferiores a un determinado umbral b, y un nivel de retención k2 en caso contrario. Obtenemos la ecuación íntegro-diferencial para la función Gerber-Shiu, definida en Gerber-Shiu -1998- en este modelo, que nos permite obtener las expresiones de la probabilidad de ruina y de la transformada de Laplace del momento de ruina para distintas distribuciones de la cuantía individual de los siniestros. Finalmente presentamos algunos resultados numéricos.

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.

Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

Random assignment of intervention points in two phase single-case designs: data-division-specific distributions

The present study explores the statistical properties of a randomization test based on the random assignment of the intervention point in a two-phase (AB) single-case design. The focus is on randomization distributions constructed with the values of the test statistic for all possible random assignments and used to obtain p-values. The shape of those distributions is investigated for each specific data division defined by the moment in which the intervention is introduced. Another aim of the study consisted in testing the detection of inexistent effects (i.e., production of false alarms) in autocorrelated data series, in which the assumption of exchangeability between observations may be untenable. In this way, it was possible to compare nominal and empirical Type I error rates in order to obtain evidence on the statistical validity of the randomization test for each individual data division. The results suggest that when either of the two phases has considerably less measurement times, Type I errors may be too probable and, hence, the decision making process to be carried out by applied researchers may be jeopardized.

Reconeixement de punts clau en imatges mitjançant l'algorisme Random Ferns

Treball final de carrera basat en el reconeixement de punts clau en imatges mitjançant l'algorisme Random Ferns.

Aplicació en línia d'un sistema variable de control multivariable en un Reactor ..

L’objecte del present treball és la realització d’una aplicació que permeti portar a terme el control estadístic multivariable en línia d’una planta SBR.Aquesta eina ha de permetre realitzar un anàlisi estadístic multivariable complet del lot en procés, de l’últim lot finalitzat i de la resta de lots processats a la planta.L’aplicació s’ha de realitzar en l’entorn LabVIEW. L’elecció d’aquest programa vecondicionada per l’actualització del mòdul de monitorització de la planta que s’estàdesenvolupant en aquest mateix entorn

Application of Multi-SNP Approaches Bayesian LASSO and AUC-RF to Detect Main Effects of Inflammatory-Gene Variants Associated with Bladder Cancer Risk

The relationship between inflammation and cancer is well established in several tumor types, including bladder cancer. We performed an association study between 886 inflammatory-gene variants and bladder cancer risk in 1,047 cases and 988 controls from the Spanish Bladder Cancer (SBC)/EPICURO Study. A preliminary exploration with the widely used univariate logistic regression approach did not identify any significant SNP after correcting for multiple testing. We further applied two more comprehensive methods to capture the complexity of bladder cancer genetic susceptibility: Bayesian Threshold LASSO (BTL), a regularized regression method, and AUC-Random Forest, a machine-learning algorithm. Both approaches explore the joint effect of markers. BTL analysis identified a signature of 37 SNPs in 34 genes showing an association with bladder cancer. AUC-RF detected an optimal predictive subset of 56 SNPs. 13 SNPs were identified by both methods in the total population. Using resources from the Texas Bladder Cancer study we were able to replicate 30% of the SNPs assessed. The associations between inflammatory SNPs and bladder cancer were reexamined among non-smokers to eliminate the effect of tobacco, one of the strongest and most prevalent environmental risk factor for this tumor. A 9 SNP-signature was detected by BTL. Here we report, for the first time, a set of SNP in inflammatory genes jointly associated with bladder cancer risk. These results highlight the importance of the complex structure of genetic susceptibility associated with cancer risk.