First and second order optimality conditions for optimal control problems of state constrained integral equations

This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with constraints of arbitrary high orders. First and second-order necessary conditions of optimality are obtained, as well as second-order sufficient conditions

Volume-controlled buckling of thin elastic shells: Application to crusts formed on evaporating partially-wetted droplets

Motivated by the buckling of glassy crusts formed on evaporating droplets of polymer and colloid solutions, we numerically model the deformation and buckling of spherical elastic caps controlled by varying the volume between the shell and the substrate. This volume constraint mimics the incompressibility of the unevaporated solvent. Discontinuous buckling is found to occur for sufficiently thin and/or large contact angle shells, and robustly takes the form of a single circular region near the boundary that `snaps' to an inverted shape, in contrast to externally pressurised shells. Scaling theory for shallow shells is shown to well approximate the critical buckling volume, the subsequent enlargement of the inverted region and the contact line force.Comment: 7 pages in J. Phys. Cond. Mat. spec; 4 figs (2 low-quality to reach LANL's over-restrictive size limits; ask for high-detailed versions if required

Strong duality in conic linear programming: facial reduction and extended duals

The facial reduction algorithm of Borwein and Wolkowicz and the extended dual of Ramana provide a strong dual for the conic linear program $$(P) \sup {<c, x> | Ax \leq_K b}$$ in the absence of any constraint qualification. The facial reduction algorithm solves a sequence of auxiliary optimization problems to obtain such a dual. Ramana's dual is applicable when (P) is a semidefinite program (SDP) and is an explicit SDP itself. Ramana, Tuncel, and Wolkowicz showed that these approaches are closely related; in particular, they proved the correctness of Ramana's dual using certificates from a facial reduction algorithm. Here we give a clear and self-contained exposition of facial reduction, of extended duals, and generalize Ramana's dual: -- we state a simple facial reduction algorithm and prove its correctness; and -- building on this algorithm we construct a family of extended duals when $K$ is a {\em nice} cone. This class of cones includes the semidefinite cone and other important cones.Comment: A previous version of this paper appeared as "A simple derivation of a facial reduction algorithm and extended dual systems", technical report, Columbia University, 2000, available from http://www.unc.edu/~pataki/papers/fr.pdf Jonfest, a conference in honor of Jonathan Borwein's 60th birthday, 201

Structured Sparsity: Discrete and Convex approaches

Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics applications: While the ambient dimension is vast in modern data analysis problems, the relevant information therein typically resides in a much lower dimensional space. However, many solutions proposed nowadays do not leverage the true underlying structure. Recent results in CS extend the simple sparsity idea to more sophisticated {\em structured} sparsity models, which describe the interdependency between the nonzero components of a signal, allowing to increase the interpretability of the results and lead to better recovery performance. In order to better understand the impact of structured sparsity, in this chapter we analyze the connections between the discrete models and their convex relaxations, highlighting their relative advantages. We start with the general group sparse model and then elaborate on two important special cases: the dispersive and the hierarchical models. For each, we present the models in their discrete nature, discuss how to solve the ensuing discrete problems and then describe convex relaxations. We also consider more general structures as defined by set functions and present their convex proxies. Further, we discuss efficient optimization solutions for structured sparsity problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure

Controle de domaines temporels

Cet article étudie des problème de contrôle optimal d'une équation parabolique linéaire, lorsque l'observation est l'ensemble des instants pour lesquels un critère de qualité (local en temps) sur l'état n'est pas vérifié

A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World

International audienceEngineering sciences and applications of mathematics show unambiguously that positive semidefiniteness of matrices is the most important generalization of non-negative real num- bers. This notion of non-negativity for matrices has been well-studied in the literature; it has been the subject of review papers and entire chapters of books. This paper reviews some of the nice, useful properties of positive (semi)definite matrices, and insists in particular on (i) characterizations of positive (semi)definiteness and (ii) the geometrical properties of the set of positive semidefinite matrices. Some properties that turn out to be less well-known have here a special treatment. The use of these properties in optimization, as well as various references to applications, are spread all the way through. The "raison d'être" of this paper is essentially pedagogical; it adopts the viewpoint of variational analysis, shedding new light on the topic. Important, fruitful, and subtle, the positive semidefinite world is a good place to start with this domain of applied mathematics

Bilevel Parameter Learning for Higher-Order Total Variation Regularisation Models.

We consider a bilevel optimisation approach for parameter learning in higher-order total variation image reconstruction models. Apart from the least squares cost functional, naturally used in bilevel learning, we propose and analyse an alternative cost based on a Huber-regularised TV seminorm. Differentiability properties of the solution operator are verified and a first-order optimality system is derived. Based on the adjoint information, a combined quasi-Newton/semismooth Newton algorithm is proposed for the numerical solution of the bilevel problems. Numerical experiments are carried out to show the suitability of our approach and the improved performance of the new cost functional. Thanks to the bilevel optimisation framework, also a detailed comparison between TGV 2 and ICTV is carried out, showing the advantages and shortcomings of both regularisers, depending on the structure of the processed images and their noise level.King Abdullah University of Science and Technology (KAUST) (Grant ID: KUKI1-007-43), Engineering and Physical Sciences Research Council (Grant IDs: Nr. EP/J009539/1 “Sparse & Higher-order Image Restoration” and Nr. EP/M00483X/1 “Efficient computational tools for inverse imaging problems”), Escuela Politécnica Nacional de Quito (Grant ID: PIS 12-14, MATHAmSud project SOCDE “Sparse Optimal Control of Differential Equations”), Leverhulme Trust (project on “Breaking the non-convexity barrier”), SENESCYT (Ecuadorian Ministry of Higher Education, Science, Technology and Innovation) (Prometeo Fellowship)This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s10851-016-0662-

Identification and characterization of a rich population of CD34mesenchymal stem/stromal cells in human parotid, sublingual and submandibular glands

Mesenchymal stem/stromal cells (MSCs) play crucial roles in maintaining tissue homeostasis during physiological turnovers and injuries. Very little is known about the phenotype, distribution and molecular nature of MSCs in freshly isolated human salivary glands (SGs) as most reports have focused on the analysis of cultured MSCs. Our results demonstrate that the cell adhesion molecule CD34 was widely expressed by the MSCs of human major SGs, namely parotid (PAG), sublingual (SLG) and submandibular (SMG) glands. Further, gene expression analysis of CD34+ cells derived from fetal SMGs showed significant upregulation of genes involved in cellular adhesion, proliferation, branching, extracellular matrix remodeling and organ development. Moreover, CD34+ SMG cells exhibited elevated expression of genes encoding extracellular matrix, basement membrane proteins, and members of ERK, FGF and PDGF signaling pathways, which play key roles in glandular development, branching and homeostasis. In vitro CD34+ cell derived SG-MSCs revealed multilineage differentiation potential. Intraglandular transplantation of cultured MSCs in immunodeficient mice led to their engraftment in the injected and uninjected contralateral and ipsilateral glands. Engrafted cells could be localized to the stroma surrounding acini and ducts. In summary, our data show that CD34+ derived SG-MSCs could be a promising cell source for adoptive cell-based SG therapies, and bioengineering of artificial SGs

Lipoxin A4 Stimulates Calcium-Activated Chloride Currents and Increases Airway Surface Liquid Height in Normal and Cystic Fibrosis Airway Epithelia

Cystic Fibrosis (CF) is a genetic disease characterised by a deficit in epithelial Cl− secretion which in the lung leads to airway dehydration and a reduced Airway Surface Liquid (ASL) height. The endogenous lipoxin LXA4 is a member of the newly identified eicosanoids playing a key role in ending the inflammatory process. Levels of LXA4 are reported to be decreased in the airways of patients with CF. We have previously shown that in normal human bronchial epithelial cells, LXA4 produced a rapid and transient increase in intracellular Ca2+. We have investigated, the effect of LXA4 on Cl− secretion and the functional consequences on ASL generation in bronchial epithelial cells obtained from CF and non-CF patient biopsies and in bronchial epithelial cell lines. We found that LXA4 stimulated a rapid intracellular Ca2+ increase in all of the different CF bronchial epithelial cells tested. In non-CF and CF bronchial epithelia, LXA4 stimulated whole-cell Cl− currents which were inhibited by NPPB (calcium-activated Cl− channel inhibitor), BAPTA-AM (chelator of intracellular Ca2+) but not by CFTRinh-172 (CFTR inhibitor). We found, using confocal imaging, that LXA4 increased the ASL height in non-CF and in CF airway bronchial epithelia. The LXA4 effect on ASL height was sensitive to bumetanide, an inhibitor of transepithelial Cl− secretion. The LXA4 stimulation of intracellular Ca2+, whole-cell Cl− currents, conductances and ASL height were inhibited by Boc-2, a specific antagonist of the ALX/FPR2 receptor. Our results provide, for the first time, evidence for a novel role of LXA4 in the stimulation of intracellular Ca2+ signalling leading to Ca2+-activated Cl− secretion and enhanced ASL height in non-CF and CF bronchial epithelia