Optimization of an Alkylpolyglucoside-Based Dishwashing Detergent Formulation.

The aim of this work was to formulate and optimize the washing performance of an alkylpolyglucoside-based dishwashing detergent. The liquid detergent was formulated with five ingredients of commercial origin: anionic (linear sodium alkylbenzenesulfonate and sodium laurylethersulfate), nonionic (C12–C14 alkylpolyglucoside) and zwitterionic (a fatty acid amide derivative with a betaine structure) surfactants, and NaCl for viscosity control. In addition to the plate test, other properties were investigated including ‘‘cloud point’’, viscosity, and emulsion stability. Statistical analysis software was used to generate a central composite experimental design. Then, a second order design and analysis of experiments approach, known as the Response Surface Methodology, was set up to investigate the effects of the five components of the formulation on the studied properties in the region covering plausible component ranges. The method proved to be efficient for locating the domains of concentrations where the desired properties were met

Mass Transportation on Sub-Riemannian Manifolds

We study the optimal transport problem in sub-Riemannian manifolds where the cost function is given by the square of the sub-Riemannian distance. Under appropriate assumptions, we generalize Brenier-McCann's Theorem proving existence and uniqueness of the optimal transport map. We show the absolute continuity property of Wassertein geodesics, and we address the regularity issue of the optimal map. In particular, we are able to show its approximate differentiability a.e. in the Heisenberg group (and under some weak assumptions on the measures the differentiability a.e.), which allows to write a weak form of the Monge-Amp\`ere equation

Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page

Global stability of enzymatic chain of full reversible Michaelis-Menten reactions

International audienceWe consider a chain of metabolic reactions catalyzed by enzymes, of reversible Michaelis-Menten type with full dynamics, i.e. not reduced with any quasi- steady state approximations. We study the corresponding dynamical system and show its global stability if the equilibrium exists. If the system is open, the equilibrium may not exist. The main tool is monotone systems theory. Finally we study the implications of these results for the study of coupled genetic-metabolic systems

Conditioned Pain Modulation Is Associated with Common Polymorphisms in the Serotonin Transporter Gene

BACKGROUND: Variation in the serotonin transporter (5-HTT) gene (SLC6A4) has been shown to influence a wide range of affective processes. Low 5-HTT gene-expression has also been suggested to increase the risk of chronic pain. Conditioned pain modulation (CPM)--i.e. 'pain inhibits pain'--is impaired in chronic pain states and, reciprocally, aberrations of CPM may predict the development of chronic pain. Therefore we hypothesized that a common variation in the SLC6A4 is associated with inter-individual variation in CPM. Forty-five healthy subjects recruited on the basis of tri-allelic 5-HTTLPR genotype, with inferred high or low 5-HTT-expression, were included in a double-blind study. A submaximal-effort tourniquet test was used to provide a standardized degree of conditioning ischemic pain. Individualized noxious heat and pressure pain thresholds (PPTs) were used as subjective test-modalities and the nociceptive flexion reflex (NFR) was used to provide an objective neurophysiological window into spinal processing. RESULTS: The low, as compared to the high, 5-HTT-expressing group exhibited significantly reduced CPM-mediated pain inhibition for PPTs (p = 0.02) and heat-pain (p = 0.02). The CPM-mediated inhibition of the NFR, gauged by increases in NFR-threshold, did not differ significantly between groups (p = 0.75). Inhibition of PPTs and heat-pain were correlated (Spearman's rho = 0.35, p = 0.02), whereas the NFR-threshold increase was not significantly correlated with degree of inhibition of these subjectively reported modalities. CONCLUSIONS: Our results demonstrate the involvement of the tri-allelic 5-HTTLPR genotype in explaining clinically relevant inter-individual differences in pain perception and regulation. Our results also illustrate that shifts in NFR-thresholds do not necessarily correlate to the modulation of experienced pain. We discuss various possible mechanisms underlying these findings and suggest a role of regulation of 5-HT receptors along the neuraxis as a function of differential 5-HTT-expression

Algebraic estimation in partial derivatives systems: parameters and differentiation problems

International audienceTwo goals are sought in this paper: namely, to provide a succinct overview on algebraic techniques for numerical differentiation and parameter estimation for linear systems and to present novel algebraic methods in the case of several variables. The state-of-art in the introduction is followed by a brief description of the methodology in the subsequent sections. Our new algebraic methods are illustrated by two examples in the multidimensional case. Some algebraic preliminaries are given in the appendix

Generic properties of the spectrum of the Stokes system with Dirichlet boundary condition in R-3

International audienceLet (S D-Omega) be the Stokes operator defined in a bounded domain Omega of R-3 with Dirichlet boundary conditions. We prove that, generically with respect to the domain Omega with C-5 boundary, the spectrum of (S D-Omega) satisfies a non-resonant property introduced by C. Foias and J.C. Saut in [17] to linearize the Navier-Stokes system in a bounded domain Omega of R-3 with Dirichlet boundary conditions. For that purpose, we first prove that, generically with respect to the domain Omega with C-5 boundary, all the eigenvalues of (SD Omega) are simple. That answers positively a question raised by J.H. Ortega and E. Zuazua in [27, Section 6]. The proofs of these results follow a standard strategy based on a contradiction argument requiring shape differentiation. One needs to shape differentiate at least twice the initial problem in the direction of carefully chosen domain variations. The main step of the contradiction argument amounts to study the evaluation of Dirichlet-to-Neumann operators associated to these domain variations. (C) 2014 Elsevier Masson SAS. All rights reserved

Robust Stabilization by Saturated Feedback

In this paper we deal with the problem of stabilization of uncertain systems in the presence of input constraint. First algebraic conditions are derived for input-to-state stability of linear system with saturated linear feedback of low dimension. Then a recursive design procedure is derived for robust stabilization of block upper triangular nonlinear systems with feedforward structure