Discrete Approximations of a Controlled Sweeping Process

The paper is devoted to the study of a new class of optimal control problems governed by the classical Moreau sweeping process with the new feature that the polyhe- dral moving set is not fixed while controlled by time-dependent functions. The dynamics of such problems is described by dissipative non-Lipschitzian differential inclusions with state constraints of equality and inequality types. It makes challenging and difficult their anal- ysis and optimization. In this paper we establish some existence results for the sweeping process under consideration and develop the method of discrete approximations that allows us to strongly approximate, in the W^{1,2} topology, optimal solutions of the continuous-type sweeping process by their discrete counterparts

Finding largest small polygons with GloptiPoly

A small polygon is a convex polygon of unit diameter. We are interested in small polygons which have the largest area for a given number of vertices $n$. Many instances are already solved in the literature, namely for all odd $n$, and for $n=4, 6$ and 8. Thus, for even $n\geq 10$, instances of this problem remain open. Finding those largest small polygons can be formulated as nonconvex quadratic programming problems which can challenge state-of-the-art global optimization algorithms. We show that a recently developed technique for global polynomial optimization, based on a semidefinite programming approach to the generalized problem of moments and implemented in the public-domain Matlab package GloptiPoly, can successfully find largest small polygons for $n=10$ and $n=12$. Therefore this significantly improves existing results in the domain. When coupled with accurate convex conic solvers, GloptiPoly can provide numerical guarantees of global optimality, as well as rigorous guarantees relying on interval arithmetic

Composition pour retarder l'initiation tumorale de cellules cancereuses chez un mammifère à risque

La présente invention concerne une composition préventive antitumorale comprenant une quantité pharmaceutiquement efficace d\u27au moins un antagoniste du récepteur AT2 de l\u27angiotensine II pour son application comme médicament afin de prévenir le développement de cancers chez un mammifère à risque. La présente invention concerne également un procédé de prévention du développement de cancer chez un mammifère à risque, ainsi qu\u27un kit de prévention du développement de cancers

Semidefinite approximations of projections and polynomial images of semialgebraic sets

Given a compact semialgebraic set S of R^n and a polynomial map f from R^n to R^m, we consider the problem of approximating the image set F = f(S) in R^m. This includes in particular the projection of S on R^m for n greater than m. Assuming that F is included in a set B which is simple (e.g. a box or a ball), we provide two methods to compute certified outer approximations of F. Method 1 exploits the fact that F can be defined with an existential quantifier, while Method 2 computes approximations of the support of image measures.The two methods output a sequence of superlevel sets defined with a single polynomial that yield explicit outer approximations of F. Finding the coefficients of this polynomial boils down to computing an optimal solution of a convex semidefinite program. We provide guarantees of strong convergence to F in L^1 norm on B, when the degree of the polynomial approximation tends to infinity. Several examples of applications are provided, together with numerical experiments

Keeping the Extracellular Matrix Well Structured to Keep Healthy Vessels

Commentaire sur l\u27importance de la matrice extracellulaire dans la mécanotransduction vasculair

Emerging role of G protein-coupled receptors in microvascular myogenic tone

Blood flow autoregulation results from the ability of resistance arteries to reduce or increase their diameters in response to changes in intravascular pressure. The mechanism by which arteries maintain a constant blood flow to organs over a range of pressures relies on this myogenic response, which defines the intrinsic property of the smooth muscle to contract in response to stretch. The resistance to flow created by myogenic tone (MT) prevents tissue damage and allows the maintenance of a constant perfusion, despite fluctuations in arterial pressure. Interventions targeting MT may provide a more rational therapeutic approach in vascular disorders, such as hypertension, vasospasm, chronic heart failure, or diabetes. Despite its early description by Bayliss in 1902, the cellular and molecular mechanisms underlying MT remain poorly understood. We now appreciate that MT requires a complex mechanotransduction converting a physical stimulus (pressure) into a biological response (change in vessel diameter). Although smooth muscle cell depolarization and a rise in intracellular calcium concentration are recognized as cornerstones of the myogenic response, the role of wall strain-induced formation of vasoactive mediators is less well established. The vascular system expresses a large variety of Class 1 G protein-coupled receptors (GPCR) activated by an eclectic range of chemical entities, including peptides, lipids, nucleotides, and amines. These messengers can function in blood vessels as vasoconstrictors. This review focuses on locally generated GPCR agonists and their proposed contributions to MT. Their interplay with pivotal G(q-11) and G(12-13) protein signalling is also discussed

Optimal control of the sweeping process

We formulate and study an optimal control problem for the sweeping (Moreau) process, where control functions enter the moving sweeping set. To the best of our knowledge, this is the first study in the literature devoted to optimal control of the sweeping process. We first establish an existence theorem of optimal solutions and then derive necessary optimality conditions for this optimal control problem of a new type, where the dynamics is governed by discontinuous differential inclusions with variable right-hand sides. Our approach to necessary optimality conditions is based on the method of discrete approximations and advanced tools of variational analysis and generalized differentiation. The final results obtained are given in terms of the initial data of the controlled sweeping process and are illustrated by nontrivial examples