Un algorithme pour la détermination de perméabilités relatives triphasiques satisfaisant une condition de différentielle totale

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Nonparametric instrumental regression with non-convex constraints

This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. A classical example in microeconomics considers the consumer demand function as a function of the price of goods and the income, both variables often considered as endogenous. In this framework, the economic theory also imposes shape restrictions on the demand function, like integrability conditions. Motivated by this illustration in microeconomics, we study an estimator of a nonparametric constrained regression function using instrumental variables by means of Tikhonov regularization. We derive rates of convergence for the regularized model both in a deterministic and stochastic setting under the assumption that the true regression function satisfies a projected source condition including, because of the non-convexity of the imposed constraints, an additional smallness condition

Refinement indicators for estimating hydrogeologic parameters

We identify simultaneously the hydraulic transmissivity and the storage coefficient in a ground water flow governed by a linear parabolic equation. Both coefficients are assumed to be functions which are piecewise constant in space and constant in time. Therefore the unknowns are the coefficient values as well as the geometry of the zones where these parameters are constant. The identification problem is formulated as the minimization of a misfit least-square function. Using refinement indicators, we refine the parameterization locally and iteratively. We distinguish the cases where the two parameters have the same parameterization or different parameterizations

Discretization of variational regularization in Banach spaces

Consider a nonlinear ill-posed operator equation $F(u)=y$ where $F$ is defined on a Banach space $X$. In general, for solving this equation numerically, a finite dimensional approximation of $X$ and an approximation of $F$ are required. Moreover, in general the given data \yd of $y$ are noisy. In this paper we analyze finite dimensional variational regularization, which takes into account operator approximations and noisy data: We show (semi-)convergence of the regularized solution of the finite dimensional problems and establish convergence rates in terms of Bregman distances under appropriate sourcewise representation of a solution of the equation. The more involved case of regularization in nonseparable Banach spaces is discussed in detail. In particular we consider the space of finite total variation functions, the space of functions of finite bounded deformation, and the $L^\infty$--space

Structural Basis of Teneurin-Latrophilin Interaction in Repulsive Guidance of Migrating Neurons

Teneurins are ancient metazoan cell adhesion receptors that control brain development and neuronal wiring in higher animals. The extracellular C terminus binds the adhesion GPCR Latrophilin, forming a trans-cellular complex with synaptogenic functions. However, Teneurins, Latrophilins, and FLRT proteins are also expressed during murine cortical cell migration at earlier developmental stages. Here, we present crystal structures of Teneurin-Latrophilin complexes that reveal how the lectin and olfactomedin domains of Latrophilin bind across a spiraling beta-barrel domain of Teneurin, the YD shell. We couple structure-based protein engineering to biophysical analysis, cell migration assays, and in utero electroporation experiments to probe the importance of the interaction in cortical neuron migration. We show that binding of Latrophilins to Teneurins and FLRTs directs the migration of neurons using a contact repulsion-dependent mechanism. The effect is observed with cell bodies and small neurites rather than their processes. The results exemplify how a structure-encoded synaptogenic protein complex is also used for repulsive cell guidance

The Iteratively Regularized Gau{\ss}-Newton Method with Convex Constraints and Applications in 4Pi-Microscopy

This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to the Newton equations in each iteration step. Convergence of this iterative regularization method is analyzed if both the operator and the right hand side are given with errors and all error levels tend to zero. Our study has been motivated by the joint estimation of object and phase in 4Pi microscopy, which leads to a semi-blind deconvolution problem with nonnegativity constraints. The performance of the proposed algorithm is illustrated both for simulated and for three-dimensional experimental data