Mutual information on the fuzzy sphere

We numerically calculate entanglement entropy and mutual information for a massive free scalar field on commutative (ordinary) and noncommutative (fuzzy) spheres. We regularize the theory on the commutative geometry by discretizing the polar coordinate, whereas the theory on the noncommutative geometry naturally posseses a finite and adjustable number of degrees of freedom. Our results show that the UV-divergent part of the entanglement entropy on a fuzzy sphere does not follow an area law, while the entanglement entropy on a commutative sphere does. Nonetheless, we find that mutual information (which is UV-finite) is the same in both theories. This suggests that nonlocality at short distances does not affect quantum correlations over large distances in a free field theory.Comment: 16 pages, 10 figures. Fixed minor typos, references updated, discussion slightly expande

Correction to Black-Scholes formula due to fractional stochastic volatility

Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in terms of a fractional Ornstein Uhlenbeck process to have such correlations. It is shown how the associated implied volatility has a term structure that is a function of maturity to a fractional power

Coupled paraxial wave equations in random media in the white-noise regime

In this paper the reflection and transmission of waves by a three-dimensional random medium are studied in a white-noise and paraxial regime. The limit system derives from the acoustic wave equations and is described by a coupled system of random Schr\"{o}dinger equations driven by a Brownian field whose covariance is determined by the two-point statistics of the fluctuations of the random medium. For the reflected and transmitted fields the associated Wigner distributions and the autocorrelation functions are determined by a closed system of transport equations. The Wigner distribution is then used to describe the enhanced backscattering phenomenon for the reflected field.Comment: Published in at http://dx.doi.org/10.1214/08-AAP543 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Regularity dependence of the rate of convergence of the learning curve for Gaussian process regression

This paper deals with the speed of convergence of the learning curve in a Gaussian process regression framework. The learning curve describes the average generalization error of the Gaussian process used for the regression. More specifically, it is defined in this paper as the integral of the mean squared error over the input parameter space with respect to the probability measure of the input parameters. The main result is the proof of a theorem giving the mean squared error in function of the number of observations for a large class of kernels and for any dimension when the number of observations is large. From this result, we can deduce the asymptotic behavior of the generalization error. The presented proof generalizes previous ones that were limited to more specific kernels or to small dimensions (one or two). The result can be used to build an optimal strategy for resources allocation. This strategy is applied successfully to a nuclear safety problem

Genealogical particle analysis of rare events

In this paper an original interacting particle system approach is developed for studying Markov chains in rare event regimes. The proposed particle system is theoretically studied through a genealogical tree interpretation of Feynman--Kac path measures. The algorithmic implementation of the particle system is presented. An estimator for the probability of occurrence of a rare event is proposed and its variance is computed, which allows to compare and to optimize different versions of the algorithm. Applications and numerical implementations are discussed. First, we apply the particle system technique to a toy model (a Gaussian random walk), which permits to illustrate the theoretical predictions. Second, we address a physically relevant problem consisting in the estimation of the outage probability due to polarization-mode dispersion in optical fibers.Comment: Published at http://dx.doi.org/10.1214/105051605000000566 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Topological superconductivity with deformable magnetic skyrmions

Magnetic skyrmions are nanoscale spin configurations that can be efficiently created and manipulated. They hold great promises for next-generation spintronics applications. In parallel to these developments, the interplay of magnetism, superconductivity and spin-orbit coupling has proved to be a versatile platform for engineering topological superconductivity predicted to host non-abelian excitations, Majorana zero modes. We show that topological superconductivity can be induced by proximitizing magnetic skyrmions and conventional superconductors, without need for additional ingredients. Apart from a previously reported Majorana zero mode in the core of the skyrmion, we find a more universal chiral band of Majorana modes on the edge of the skyrmion. We show that the chiral Majorana band is effectively flat in the physically relevant regime of parameters, leading to interesting robustness and scaling properties. In particular, the number of Majorana modes in the (nearly-)flat band scales with the perimeter length of a deformed skyrmion configuration, while being robust to local disorder.Comment: 16 + 3 pages, 3 figures + Supplementary Material

Influence of Process and Material Parameters on Impact Response in Composite Structure: Methodology Using Design of Experiments

Even if the mechanical performances of composite materials give new perspectives for the aircraft and space design, the variability of their behavior, linked to the presence of initial microscopic defects or led in service, constitute however a still important brake in their development. As regards particularly the response to fatigue loads or ageing, the behavior of these materials is affected by several sources of uncertainties, notably on the nature of the physical mechanisms of degradation, which are translated by a strong dispersion in life time. In aerospace industry, low energy impact phenomenon is not well known concerning composite materials and composite structures. Many manufacturers use important safety factors to design structures. The aim of this work is to define the most predominant parameters which permit a good response of damage using experiences plans. The differences of these parameters by using Resin Transfer Molding (RTM) or Liquid Resin Infusion (LRI) process than prepreg one is also studied in this work