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

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

Iron deficiency without anemia is responsible for decreased left ventricular function and reduced mitochondrial complex I activity in a mouse model

BACKGROUND: Iron deficiency (ID), with or without anemia, is frequent in heart failure patients, and iron supplementation improves patient condition. However, the link between ID (independently of anemia) and cardiac function is poorly understood, but could be explained by an impaired mitochondrial metabolism. Our aim was to explore this hypothesis in a mouse model. METHODS AND RESULTS: We developed a mouse model of ID without anemia, using a blood withdrawal followed by 3-weeks low iron diet. ID was confirmed by low spleen, liver and heart iron contents and the repression of HAMP gene coding for hepcidin. ID was corrected by a single ferric carboxymaltose (FCM) injection (ID + FCM mice). Hemoglobin levels were similar in ID, ID + FCM and control mice. ID mice had impaired physical performances and left ventricular function (echocardiography). Mitochondrial complex I activity of cardiomyocytes was significantly decreased in ID mice, but not complexes II, III and IV activities. ID + FCM mice had improved physical performance, cardiac function and complex I activity compared to ID mice. Using BN-PAGE, we did not observe complex I disassembly, but a reduced quantity of the whole enzyme complex I in ID mice, that was restored in ID + FCM mice. CONCLUSIONS: ID, independently of anemia, is responsible for a decreased left ventricular function, through a reduction in mitochondrial complex I activity, probably secondary to a decrease in complex I quantity. These abnormalities are reversed after iron treatment, and may explain, at least in part, the benefit of iron supplementation in heart failure patients with ID

Computation with Polynomial Equations and Inequalities arising in Combinatorial Optimization

The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear algebra or semidefinite programming relaxations of many kinds of feasibility or optimization questions. We are particularly interested in problems arising in combinatorial optimization.Comment: 28 pages, survey pape

Determinants of flow-mediated outward remodeling in female rodents: respective roles of age, estrogens, and timing

OBJECTIVE: Flow (shear stress)-mediated outward remodeling (FMR) of resistance arteries is a key adaptive process allowing collateral growth after arterial occlusion but declining with age. 17-beta-estradiol (E2) has a key role in this process through activation of estrogen receptor alpha (ERalpha). Thus, we investigated the impact of age and timing for estrogen efficacy on FMR. APPROACH AND RESULTS: Female rats, 3 to 18 months old, were submitted to surgery to increase blood flow locally in 1 mesenteric artery in vivo. High-flow and normal-flow arteries were collected 2 weeks later for in vitro analysis. Diameter increased by 27% in high-flow arteries compared with normal-flow arteries in 3-month-old rats. The amplitude of remodeling declined with age (12% in 18-month-old rats) in parallel with E2 blood level and E2 substitution failed restoring remodeling in 18-month-old rats. Ovariectomy of 3-, 9-, and 12-month-old rats abolished FMR, which was restored by immediate E2 replacement. Nevertheless, this effect of E2 was absent 9 months after ovariectomy. In this latter group, ERalpha and endothelial nitric oxide synthase expression were reduced by half compared with age-matched rats recently ovariectomized. FMR did not occur in ERalpha(-/-) mice, whereas it was decreased by 50% in ERalpha(+/-) mice, emphasizing the importance of gene dosage in high-flow remodeling. CONCLUSIONS: E2 deprivation, rather than age, leads to decline in FMR, which can be prevented by early exogenous E2. However, delayed E2 replacement was ineffective on FMR, underlining the importance of timing of this estrogen action

Influence of the scattering potential model on low energy electron diffraction from Cu(001)−c(2 × 2)-Pb

A dynamical LEED intensity analysis is reported for Cu(001)−c(2 × 2)-Pb. The adsorbate layer distance from the substrate is determined as 2.29 Å, and the topmost interlayer spacing for the substrate is the same as in bulk Cu, in contrast to a contraction for clean Cu(001). This structural result is, within the accuracy reached, insensitive to changes in the assumed scattering potential models. The r-factors suggest a weak preference for an energy-dependent exchange correlation and a moderate one for adding a localized adsorption part inside the muffin-tin spheres. The sensitivity of spectra and r-factors to changes in the assumed isotropic Debye temperature for Pb suggests that vibrational anisotropy should be taken into account in order to improve the accuracy of the analysis. Calculated spin polarization spectra are very sensitive to the exchange approximation, the localized absorption and the Debye temperature. Together with experimental data, they should be useful in particular for determining the vibrational anisotropy

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

Resveratrol Decreases TXNIP mRNA and Protein Nuclear Expressions With an Arterial Function Improvement in Old Mice

Aging leads to a high prevalence of glucose intolerance and cardiovascular diseases, with oxidative stress playing a potential role. Resveratrol has shown promising effects on glucose tolerance and tends to improve endothelial function in elderly patients. Thioredoxin-interacting protein (TXNIP) was recently proposed as a potential link connecting glucose metabolism to oxidative stress. Here, we investigated the resveratrol-induced improvement of arterial aging phenotype in old mice and the expression of aortic TXNIP. Using an in vivo model of old mice with or without 3-month resveratrol treatment, we investigated the effects of resveratrol on age-related impairments from a cardiovascular Doppler analysis, to a molecular level, by studying inflammation and oxidative stress factors. We found a dual effect of resveratrol, with a decrease of age-related glucose intolerance and oxidative stress imbalance leading to reduced matrix remodeling that forestalls arterial aging phenotype in terms of intima-media thickness and arterial distensibility. These results provide the first evidence that aortic TXNIP mRNA and protein nuclear expressions are increased in the arterial aging and decreased by resveratrol treatment. In conclusion, we demonstrated that resveratrol helped to restore several aging impaired processes in old mice, with a decrease of aortic TXNIP mRNA and protein nuclear expression