A Pathwise Fractional one Compartment Intra-Veinous Bolus Model

Extending deterministic compartments pharmacokinetic models as diffusions seems not realistic on biological side because paths of these stochastic processes are not smooth enough. In order to extend one compartment intra-veinous bolus models, this paper suggests to modelize the concentration process $C$ by a class of stochastic differential equations driven by a fractional Brownian motion of Hurst parameter belonging to $]1/2,1[$. The first part of the paper provides probabilistic and statistical results on the concentration process $C$ : the distribution of $C$, a control of the uniform distance between $C$ and the solution of the associated ordinary differential equation, an ergodic theorem for the concentration process and its application to the estimation of the elimination constant, and consistent estimators of the driving signal's Hurst parameter and of the volatility constant. The second part of the paper provides applications of these theoretical results on simulated concentration datas : a qualitative procedure for choosing parameters on small sets of observations, and simulations of the estimators of the elimination constant and of the driving signal's Hurst parameter. The relationship between the estimations quality and the size/length of the sample is discussed.Comment: 16 pages, 6 figure

Sensitivities via Rough Paths

Motivated by a problematic coming from mathematical finance, this paper is devoted to existing and additional results of continuity and differentiability of the It\^o map associated to rough differential equations. These regularity results together with Malliavin calculus are applied to sensitivities analysis for stochastic differential equations driven by multidimensional Gaussian processes with continuous paths, especially fractional Brownian motions. Precisely, in that framework, results on computation of greeks for It\^o's stochastic differential equations are extended. An application in mathematical finance, and simulations, are provided.Comment: 36 pages, 1 figur

Ergodicity of a Generalized Jacobi's Equation and Applications

Consider a $1$-dimensional centered Gaussian process $W$ with $\alpha$-H\"older continuous paths on the compact intervals of $\mathbb R_+$ ($\alpha\in ]0,1[$) and $W_0 = 0$, and $X$ the local solution in rough paths sense of Jacobi's equation driven by the signal $W$. The global existence and the uniqueness of the solution are proved via a change of variable taking into account the singularities of the vector field, because it doesn't satisfy the non-explosion condition. The regularity of the associated It\^o map is studied. By using these deterministic results, Jacobi's equation is studied on probabilistic side : an ergodic theorem in L. Arnold's random dynamical systems framework, and the existence of an explicit density with respect to Lebesgue's measure for each $X_t$, $t > 0$ are proved. The paper concludes on a generalization of Morris-Lecar's neuron model, where the normalized conductance of the $\textrm{K}^+$ current is the solution of a generalized Jacobi's equation.Comment: 32 pages, 4 figures. Stochastic Processes and their Applications, 201

An energy-consistent depth-averaged Euler system: derivation and properties

In this paper, we present an original derivation process of a non-hydrostatic shallow water-type model which aims at approximating the incompressible Euler and Navier-Stokes systems with free surface. The closure relations are obtained by aminimal energy constraint instead of an asymptotic expansion. The model slightly differs from thewell-known Green-Naghdi model and is confronted with stationary andanalytical solutions of the Euler system corresponding to rotationalflows. At the end of the paper, we givetime-dependent analytical solutions for the Euler system that are alsoanalytical solutions for the proposed model but that are not solutionsof the Green-Naghdi model. We also give and compare analytical solutions of thetwo non-hydrostatic shallow water models

Change detection in SAR time-series based on the coefficient of variation

This paper discusses change detection in SAR time-series. Firstly, several statistical properties of the coefficient of variation highlight its pertinence for change detection. Then several criteria are proposed. The coefficient of variation is suggested to detect any kind of change. Then other criteria based on ratios of coefficients of variations are proposed to detect long events such as construction test sites, or point-event such as vehicles. These detection methods are evaluated first on theoretical statistical simulations to determine the scenarios where they can deliver the best results. Then detection performance is assessed on real data for different types of scenes and sensors (Sentinel-1, UAVSAR). In particular, a quantitative evaluation is performed with a comparison of our solutions with state-of-the-art methods

Fabricating management practices : "Responsible Care" and Corporate Social Responsibility.

Purpose this study focuses on the policy of Corporate Social Responsibility (CSR) launched in the chemical industry in the 1980s and known as “Responsible Care”. The debate surrounding this issue prompts us to question the ever-changing nature of this policy and the way to measure the performance achieved. Methodology Our findings are drawn from analysis of a double set of data including a longitudinal survey and a current case study. Blending these two data sets allows a better understanding of the ongoing building process of “Responsible Care” and, more broadly, of corporate social responsibility. Findings this paper asserts that, contrary to the common wisdom developed in research, companies do not simply react to stakeholder pressure. Companies autonomously develop ways to protect their environment and so contribute to changing Society's expectations. Thus, performance cannot be read without a dynamic perspective in mind. Research limitations/implications Our findings lead us to reconsider the assessment of companies' sustainable performances by taking into account the fabricating process of sustainable activities. The main limitation of this research stems from the single unit of analysis considered. Broader studies will be necessary to enrich our understanding of corporate policies. Originality/value of the paper Our paper stands apart from the traditional view of organizations as cynical actors and attempts to provide a more complex picture of the behaviours observed.Performance management; Performance measurement; “Responsible Care”; Corporate Social Responsibility;