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

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

Exploiting symmetries in SDP-relaxations for polynomial optimization

In this paper we study various approaches for exploiting symmetries in polynomial optimization problems within the framework of semi definite programming relaxations. Our special focus is on constrained problems especially when the symmetric group is acting on the variables. In particular, we investigate the concept of block decomposition within the framework of constrained polynomial optimization problems, show how the degree principle for the symmetric group can be computationally exploited and also propose some methods to efficiently compute in the geometric quotient.Comment: (v3) Minor revision. To appear in Math. of Operations Researc

AMPK alpha 1-induced RhoA phosphorylation mediates vasoprotective effect of estradiol

OBJECTIVE: Estradiol (E2) mediates numerous beneficial effects assigned to estrogens, but whereas mechanisms have been described at the endothelial level, direct effects on vascular smooth muscle cells (VSMC) are poorly documented. As evidence accumulates regarding the role of RhoA in vascular pathophysiology and the benefit of RhoA-Rho associated protein kinase (Rock) pathway inhibition, we analyzed if E2 could inhibit it in VSMC. METHODS AND RESULTS: We show that in VSMC, E2 inhibits the RhoA-Rock pathway in a time- and concentration-dependent manner. The inhibition of RhoA-Rock pathway results from E2-induced phosphorylation of the Ser188 of RhoA. Using pharmacological, transfection, and in vitro phosphorylation experiments, we demonstrate that AMP-activated protein kinase subunit alpha 1 (AMPKalpha1) is activated by estrogen receptor stimulation and catalyzes RhoA phosphorylation induced by E2. Ex vivo, ovariectomy leads to an increase in the amplitude of phenylephrine- or serotonine-induced contractions of aortic rings in wild-type mice but not in AMPKalpha1-knock-out mice or E2-supplemented animals. These functional effects were correlated with a reduced level of RhoA phosphorylation in the aorta of ovariectomized female, male, and AMPKalpha1 knock-out mice. CONCLUSION: Our work thus defines AMPKalpha1 as (1) a new kinase for RhoA and (2) a new mediator of the vasoprotective effects of estrogen

Heme oxygenase 1 is differentially involved in blood flow-dependent arterial remodeling: role of inflammation, oxidative stress, and nitric oxide

Heme oxygenase 1 is induced by hemodynamic forces in vascular smooth muscle and endothelial cells. We investigated the involvement of heme oxygenase 1 in flow (shear stress)-dependent remodeling. Two or 14 days after ligation of mesenteric resistance arteries, vessels were isolated. In rats, at 14 days, diameter increased by 23% in high-flow arteries and decreased by 22% in low-flow arteries compared with normal flow vessels. Heme oxygenase activity inhibition using Tin-protoporphyrin abolished diameter enlargement in high-flow arteries and accentuated arterial narrowing in low-flow arteries (32% diameter decrease versus 22% in control). Two days after ligation, heme oxygenase 1 expression increased in high-flow and low-flow vessels, in association with a reduced mitochondrial aconitase activity (marker of oxidative stress) in high-flow arteries only. Inhibition of macrophage infiltration (clodronate) decreased heme oxygenase 1 induction in low-flow but not in high-flow arteries. Similarly, inhibition of NADPH oxidase activity (apocynin) decreased heme oxygenase 1 induction in low-flow but not high-flow arteries. However, dihydroethidium staining was higher in high-flow and low-flow compared with normal flow arteries. In arteries cannulated in an arteriograph, heme oxygenase 1 mRNA increased in a flow-dependent manner and was abolished by N(G)-nitro-l-arginine methyl ester, catalase, or mitochondrial electron transport chain inhibition. Furthermore, heme oxygenase 1 induction using cobalt-protoporphyrin restored altered high-flow remodeling in endothelial NO synthase knockout mice. Thus, in high-flow remodeling, heme oxygenase 1 induction depends on shear stress-generated NO and mitochondria-derived hydrogen peroxide. In low-flow remodeling, heme oxygenase 1 induction requires macrophage infiltration and is mediated by NADPH oxidase-derived superoxide

Cyclooxygenase-2 preserves flow-mediated remodelling in old obese Zucker rat mesenteric arteries

AIMS: Resistance arteries have a key role in the control of local blood flow and pressure, and chronic increases in blood flow induce endothelium-dependent outward hypertrophic remodelling. The incidence of metabolic syndrome increases with age, and the combination of these two risk factors impairs endothelium integrity, in part through an inflammatory process. We hypothesized that cyclooxygenase-2 (COX2) would affect remodelling in 12-month-old obese rats compared with young rats. METHODS AND RESULTS: Mesenteric arteries of obese and lean Zucker rats were alternatively ligated to generate high flow (HF) in the median artery. After 21 days, arteries were isolated for in vitro analysis. After 21 days, outward hypertrophic remodelling occurred in HF arteries in obese (498 +/- 20 vs. 443 +/- 18 mum intraluminal diameter in normal flow (NF) arteries, P < 0.01), but not in lean rats (454 +/- 17 vs. 432 +/- 14, NS; n = 12 per group). Endothelium-dependent (acetylcholine)-mediated relaxation (AMR) was lower in obese than in lean rats. AMR was reduced by NO-synthase blockade in all groups, and eNOS expression was higher in HF than in NF arteries without difference between lean and obese rats. Indomethacin further reduced AMR in HF arteries from obese rats only. Obesity increased COX2 immunostaining in mesenteric arteries. Acute COX2 inhibition (NS398) significantly reduced AMR in HF arteries from obese rats only, suggesting production of vasodilator prostanoid(s). In obese rats chronically treated with the COX2 inhibitor celecoxib, outward remodelling did not occur in HF arteries and AMR was improved without reaching the level found in lean rats. CONCLUSION: COX2 preserved in part flow-mediated arterial remodelling in old obese rats. Nevertheless, this effect was not sufficient to keep endothelium-dependent relaxation to the level obtained in lean rats

In Vitro Effects of the Endocrine Disruptor p,p’-DDT on Human Follitropin Receptor

BACKGROUND: 1-chloro-4-[2,2,2-trichloro-1-(4-chlorophenyl)ethyl]benzene (p,p\u27-DDT) is a persistent environmental endocrine disruptor (ED). Several studies have shown an association between p,p\u27-DDT exposure and reproductive abnormalities. OBJECTIVES: To investigate the putative effects of p,p\u27-DDT on the human follitropin receptor (FSHR) function. METHODS AND RESULTS: We used Chinese hamster ovary (CHO) cells stably expressing human FSHR to investigate the impact of p,p\u27-DDT on FSHR activity and its interaction with the receptor. At a concentration of 5 μM p,p\u27-DDT increased the maximum response of the FSHR to follitropin by 32 ± 7.45%. However, 5 μM p,p\u27-DDT decreased the basal activity and did not influence the maximal response of the closely related LH/hCG receptor to human chorionic gonadotropin (hCG). The potentiating effect of p,p\u27-DDT was specific for the FSHR. Moreover, in cells that did not express FSHR, p,p\u27-DDT had no effect on cAMP response. Thus, the potentiating effect of p,p\u27-DDT was dependent on the FSHR. In addition, p,p\u27-DDT increased the sensitivity of FSHR to hCG and to a low molecular weight agonist of the FSHR, 3-((5methyl)-2-(4-benzyloxy-phenyl)-5-{[2-[3-ethoxy-4-methoxy-phenyl)-ethylcarbamoyl]-methyl}-4-oxo-thiazolidin-3-yl)-benzamide (16a). Basal activity in response to p,p\u27-DDT and potentiation of the FSHR response to FSH by p,p\u27-DDT varied among FSHR mutants with altered transmembrane domains (TMDs), consistent with an effect of p,p\u27-DDT via TMD binding. This finding was corroborated by the results of simultaneously docking p,p\u27-DDT and 16a into the FSHR transmembrane bundle. CONCLUSION:p,p\u27-DDT acted as a positive allosteric modulator of the FSHR in our experimental model. These findings suggest that G protein-coupled receptors are additional targets of endocrine disruptor

Involvement of angiotensin II in the remodeling induced by a chronic decrease in blood flow in rat mesenteric resistance arteries

Blood flow reduction induces inward remodeling of resistance arteries (RAs). This remodeling occurs in ischemic diseases, diabetes and hypertension. Nonetheless, the effect of flow reduction per se, independent of the effect of pressure or metabolic influences, is not well understood in RA. As angiotensin II is involved in the response to flow in RA, we hypothesized that angiotensin II may also be involved in the remodeling induced by a chronic flow reduction. We analyzed the effect of angiotensin I-converting enzyme inhibition (perindopril) and angiotensin II type 1 receptor blockade (candesartan) on inward remodeling induced by blood flow reduction in vivo in rat mesenteric RAs (low flow (LF) arteries). After 1 week, diameter reduction in LF arteries was associated with reduced endothelium-dependent relaxation and lower levels of eNOS expression. Superoxide production and extracellular signal-regulated kinases 1/2 (ERK1/2 phosphorylation were higher in LF than in normal flow arteries. Nevertheless, the absence of eNOS or superoxide level reduction (tempol or apocynin) did not prevent LF remodeling. Perindopril and candesartan prevented inward remodeling in LF arteries. Contractility to angiotensin II was reduced in LF vessels by perindopril, candesartan and the ERK1/2 blocker PD98059. ERK1/2 activation (ratio phospho-ERK/ERK) was higher in LF arteries, and this activation was prevented by perindopril and candesartan. ERK1/2 inhibition in vivo (U0126) prevented LF-induced diameter reduction. Thus, inward remodeling because of blood flow reduction in mesenteric RA depends on unopposed angiotensin II-induced contraction and ERK1/2 activation, independent of superoxide production. These findings might be of importance in the treatment of vascular disorders