Fractional backward stochastic differential euqations and fractional backward variational inequalities

In the framework of fractional stochastic calculus, we study the existence and the uniqueness of the solution for a backward stochastic differential equation, formally written as: [{[c]{l}% -dY(t)= f(t,\eta(t),Y(t),Z(t))dt-Z(t)\delta B^{H}(t), \quad t\in[0,T], Y(T)=\xi,.] where $\eta$ is a stochastic process given by $\eta(t)=\eta(0) +\int_{0}^{t}\sigma(s) \delta B^{H}(s)$, $t\in[0,T]$, and $B^{H}$ is a fractional Brownian motion with Hurst parameter greater than 1/2. The stochastic integral used in above equation is the divergence-type integral. Based on Hu and Peng's paper, \textit{BDSEs driven by fBm}, SIAM J Control Optim. (2009), we develop a rigorous approach for this equation. Moreover, we study the existence of the solution for the multivalued backward stochastic differential equation [{[c]{l} -dY(t)+\partial\varphi(Y(t))dt\ni f(t,\eta(t),Y(t),Z(t))dt-Z(t)\delta B^{H}(t),\quad t\in[0,T], Y(T)=\xi,.] where $\partial\varphi$ is a multivalued operator of subdifferential type associated with the convex function $\varphi$.Comment: 41 page

A new MRI rating scale for progressive supranuclear palsy and multiple system atrophy: validity and reliability

AIM To evaluate a standardised MRI acquisition protocol and a new image rating scale for disease severity in patients with progressive supranuclear palsy (PSP) and multiple systems atrophy (MSA) in a large multicentre study. METHODS The MRI protocol consisted of two-dimensional sagittal and axial T1, axial PD, and axial and coronal T2 weighted acquisitions. The 32 item ordinal scale evaluated abnormalities within the basal ganglia and posterior fossa, blind to diagnosis. Among 760 patients in the study population (PSP = 362, MSA = 398), 627 had per protocol images (PSP = 297, MSA = 330). Intra-rater (n = 60) and inter-rater (n = 555) reliability were assessed through Cohen's statistic, and scale structure through principal component analysis (PCA) (n = 441). Internal consistency and reliability were checked. Discriminant and predictive validity of extracted factors and total scores were tested for disease severity as per clinical diagnosis. RESULTS Intra-rater and inter-rater reliability were acceptable for 25 (78%) of the items scored (≥ 0.41). PCA revealed four meaningful clusters of covarying parameters (factor (F) F1: brainstem and cerebellum; F2: midbrain; F3: putamen; F4: other basal ganglia) with good to excellent internal consistency (Cronbach α 0.75-0.93) and moderate to excellent reliability (intraclass coefficient: F1: 0.92; F2: 0.79; F3: 0.71; F4: 0.49). The total score significantly discriminated for disease severity or diagnosis; factorial scores differentially discriminated for disease severity according to diagnosis (PSP: F1-F2; MSA: F2-F3). The total score was significantly related to survival in PSP (p<0.0007) or MSA (p<0.0005), indicating good predictive validity. CONCLUSIONS The scale is suitable for use in the context of multicentre studies and can reliably and consistently measure MRI abnormalities in PSP and MSA. Clinical Trial Registration Number The study protocol was filed in the open clinical trial registry (http://www.clinicaltrials.gov) with ID No NCT00211224

Champs de Markov multirésolution et algorithme multigrille pour l'estimation de mouvement

Nous nous intéressons dans cet article à l'estimation de champs denses de déplacement entre deux images consécutives d'une séquence. Cet estimateur multirésolution, formulé dans un cadre markovien, s'exprime comme l'optimisation globale d'une fonction d'énergie. Celle-ci intègre des estimateurs robustes permettant d'une part d'extraire les discontinuités spatiales du champ à estimer et d'autre part de s'affranchir de données aberrantes. Définie dans un contexte multirésolution afin d'accéder de façon incrémentale aux mouvements de grande amplitude, la minimisation est menée au moyen d'un algorithme multigrille très efficace

Parallélisation des algorithmes d'analyse d'images par champs markoviens dans un contexte pyramidal

L'émergence, ces dernières années, de nombreuses applications de traitement d'image bas niveau utilisant une modélisation statistique par champ markovien et les problèmes d'optimisation globale qui leur sont associés ont motivé l'étude d'algorithmes de relaxation parallèles. Dans cet article, différents modes de parallélisation pour les algorithmes de relaxation sont décrits. La comparaison, pour une application de mesure du mouvement, de trois algorithme (monorésolution, multigrille, multiéchelle) nous permet de dégager un algorithme de relaxation efficace et se parallélisant de façon naturelle

Stochastic modelling of turbulent flows for numerical simulations

Numerical simulations are a powerful tool to investigate turbulent flows, both for theoretical studies and practical applications. The reliability of a simulation is mainly dependent on the turbulence model adopted, and improving its accuracy is a crucial issue. In this study, we investigated the potential for an alternative formulation of the Navier-Stokes equations, based on the stochastic representation of the velocity field. The new approach, named pseudo-stochastic simulation (PSS), is a generalisation of the widespread classical eddy-viscosity model, where the contribution of the unresolved scales of motion is expressed by a variance tensor, modelled following different paradigms. The PSS models were compared with the classical ones mathematically and numerically in the turbulent channel flow at Re\u3c4 = 590. The PSS and the classical models are equivalent when the variance tensor is shaped through a molecular dissipation analogy, while it is more accurate when the tensor is defined by the way of a local variance model. A near-wall damping function derived from recent advancement in the field is also proposed and was successfully validated. The analyses demonstrate the relevance of the approach proposed and provide a basis for the development of an alternative turbulence model

Adaptative Multigrid And Variable Parameterization For Optical-Flow Estimation

We investigate the use of adaptative multigrid minimization algorithms for the estimation of the apparent motion field. The proposed approach provides a coherent and efficient framework for estimating piecewise smooth flow fields for different parameterizations relative to adaptative partitions of the image. The performances of the resulting algorithms are demonstrated in the difficult context of a non convex global energy formulation