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

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

One-step synthesis of a highly homogeneous SBA-NHC hybrid material: En route to single-site NHC-metal heterogeneous catalysts with high loadings

The one-step synthesis of a mesoporous silica of SBA type, functionalized with a 1-(2,6-diisopropylphenyl)-3-propyl-imidazolium (iPr2Ar-NHC-propyl) cation located in the pore channels, is described. This material was obtained by the direct hydrolysis and co-condensation of tetraethylorthosilicate (TEOS) and 1-(2,6-diisopropylphenyl)-3-[3-(triethoxysilyl)propyl]-imidazolium iodide in the presence of Pluronic P123 as a non-ionic structure-directing agent and aqueous HCl (37%) as an acid catalyst. Small-angle X-ray diffraction measurements, scanning and transmission electron microscopies, as well as dinitrogen sorption analyses revealed that the synthesized material is highly mesoporous with a 2D hexagonal arrangement of the porous network. 13C and 29Si CP-MAS NMR spectroscopy confirmed that the material contains intact iPr2Ar-NHC-propyl cations, which are covalently anchored via silicon atoms fused into the silica matrix. Moreover, comparison of the latter data with those of an analogous post-synthetic grafted SBA–NHC material allowed us to establish that, as expected, (i) it is most probably more homogeneous and (ii) it shows a more robust anchoring of the organic units. Finally, elemental mapping by energy dispersive X-ray spectroscopy in the scanning electron microscope demonstrated a very homogeneous distribution of the imidazolium units within the one-pot material, moreover with a high content. This study thus demonstrates that a relatively bulky and hydrophilic imidazolium unit can be directly co-condensed with TEOS in the presence of a structure-directing agent to provide in a single step a highly ordered and homogeneous mesoporous hybrid SBA–NHC material, possessing a significant number of cationic NHC sites

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

Effectiveness and tolerability of pegylated interferon alfa-2b in combination with ribavirin for treatment of chronic hepatitis C: the PegIntrust Study

Background and study aims : Large international clinical trials conducted in the past 5 years rapidly improved the treatment of chronic hepatitis C; however, it is unclear whether the advances seen in clinical trials are being paralleled by similar improvements in routine clinical practice. PegIntrust is a Belgian community-based trial evaluating the sustained virological response. Patients and Methods : Observational study of 219 patients receiving pegylated interferon alfa-2b (1.5 mu g/kg/wk) and weight. based ribavirin (800-1200 mg/day) for 48 weeks. Primary study end point was sustained virological response (SVR), defined as undetectable HCV RNA 6 months after the completion of treatment. Results : In total, 108 patients (49.3 %) had undetectable HCV RNA at the end of therapy, 91(41.6%) attaining SVR. Of the 111 patients without an end-of-treatment response, 28 were non-responders, and 21 had virological breakthrough. In total, 134 patients attained early virological response (EVR); 88 (65.7%) of those patients attained SVR. In contrast, 82 (96.5 %) of the 85 patients who did not attain EVR also did not attain SVR. Age, fibrosis score and baseline viral load were identified as important predictors of treatment outcome. The most frequently reported serious adverse events resulting in treatment discontinuation were anemia (n = 10), fatigue/asthenia/malaise (n = 6) and fever (n = 3). Conclusion : Our data indicate that treatment of chronic hepatitis C with PEG-IFN alfa-2b plus weight-based ribavirin results in favourable treatment outcomes in a Belgian cohort of patients treated in community-based clinical practice. (Ada gastroenterol. belg., 2010, 73, 5-11)

Approximate volume and integration for basic semi-algebraic sets

Given a basic compact semi-algebraic set \K\subset\R^n, we introduce a methodology that generates a sequence converging to the volume of \K. This sequence is obtained from optimal values of a hierarchy of either semidefinite or linear programs. Not only the volume but also every finite vector of moments of the probability measure that is uniformly distributed on \K can be approximated as closely as desired, and so permits to approximate the integral on \K of any given polynomial; extension to integration against some weight functions is also provided. Finally, some numerical issues associated with the algorithms involved are briefly discussed

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