Exponential Lower Bounds for Polytopes in Combinatorial Optimization

We solve a 20-year old problem posed by Yannakakis and prove that there exists no polynomial-size linear program (LP) whose associated polytope projects to the traveling salesman polytope, even if the LP is not required to be symmetric. Moreover, we prove that this holds also for the cut polytope and the stable set polytope. These results were discovered through a new connection that we make between one-way quantum communication protocols and semidefinite programming reformulations of LPs.Comment: 19 pages, 4 figures. This version of the paper will appear in the Journal of the ACM. The earlier conference version in STOC'12 had the title "Linear vs. Semidefinite Extended Formulations: Exponential Separation and Strong Lower Bounds

Marcel Duchamp, Alain Jouffroy, Gustave Courbet et ces quelques lignes qui dérangent

L’Histoire des quelques documents conservés aux Archives de la critique d’art nous ramène en France au début des années 1960. On y rencontre Alain Jouffroy, un jeune critique d’art perspicace, dont l’action semble être motivée par la recherche et l’accompagnement des protagonistes d’une véritable avant-garde dans le domaine de l’art. Au sein du milieu artistique parisien de cette période, considéré comme immobile, autoréférentiel et conservateur, les jeunes artistes qu’Alain Jouffroy fréquent..

Sleep apnea and the impact on cardiovascular risk in patients with Marfan syndrome

Background: Marfan syndrome (MFS) is an inherited connective tissue disorder characterized by ectopia lentis, aortic root dilation and dissection and specific skeletal features. Obstructive sleep apnea (OSA) in MFS has been described earlier but the prevalence and its relation with the cardiovascular risk is still controversial. This study aimed to further investigate these aspects. Methods: In this prospective longitudinal study, we performed an attended polysomnography in 40 MFS patients (60% women, 37 +/- 12.8 years) and evaluated several cardiovascular parameters through echocardiography, resting electrocardiogram, 24 hr-Holter monitoring and serum NT-ProBNP measurements. Results: We found that OSA was present in 42.5% of the patients and that higher body mass index was the most important factor associated with the presence of OSA. We observed that overweight was present in 27.5% of the patients in the whole cohort and in 55.6% if >40 years. Furthermore, when evaluating the impact of OSA on the cardiovascular system, we observed that patients with OSA tended to have higher systolic blood pressure, larger distal aortic diameters and a higher prevalence of ventricular arrhythmia. These differences were, however, not significant after adjusting for confounders. Conclusions: Our study shows a high prevalence of OSA and a high prevalence of overweight in MFS patients. We found some trends between OSA and cardiovascular features but we could not establish a solid association. Our study, however might be underpowered, and a multicenter collaborative study could be very useful to answer some important open questions

Different patterns of cerebral and muscular tissue oxygenation 10 years after coarctation repair

The purpose of this study was to assess whether the lower exercise tolerance in children after coarctation repair is associated with alterations in peripheral tissue oxygenation during exercise. A total of 16 children after coarctation repair and 20 healthy control subjects performed an incremental ramp exercise test to exhaustion. Cerebral and locomotor muscle oxygenation were measured by means of near infrared spectroscopy. The responses of cerebral and muscle tissue oxygenation index (cTOI, mTOI), oxygenated (O(2)Hb), and deoxygenated hemoglobin (HHb) as a function of work rate were compared. Correlations between residual continuous wave Doppler gradients at rest, arm-leg blood pressure difference and local oxygenation responses were evaluated. Age, length, and weight was similar in both groups. Patients with aortic coarctation had lower peak power output (Ppeak) (72.3 +/- 20.2% vs. 106 +/- 18.7%, P < 0.001), VO(2)peak/kg (37.3 +/- 9.1 vs. 44.2 +/- 7.6 ml/kg, P = 0.019) and %VO(2)peak/kg (85.7 +/- 21.9% vs. 112.1 +/- 15.5%, P < 0.001). Cerebral O(2)Hb and HHb had a lower increase in patients vs. controls during exercise, with significant differences from 60 to 90% Ppeak (O(2)Hb) and 70% to 100% Ppeak (HHb). Muscle TOI was significantly lower in patients from 10 to 70% Ppeak and muscle HHb was significantly higher in patients vs. controls from 20 to 80% Ppeak. Muscle O(2)Hb was not different between both groups. There was a significant correlation between residual resting blood pressure gradient and Delta muscle HHb/Delta P at 10-20W and 20-30W (r = 0.40, P = 0.039 and r = 0.43, P = 0.034). Children after coarctation repair have different oxygenation responses at muscular and cerebral level. This reflects a different balance between O-2 supply to O-2 demand which might contribute to the reduced exercise tolerance in this patient population

Myocardial disease and ventricular arrhythmia in Marfan syndrome : a prospective study

Background Aortic root dilatation and-dissection and mitral valve prolapse are established cardiovascular manifestations in Marfan syndrome (MFS). Heart failure and arrhythmic sudden cardiac death have emerged as additional causes of morbidity and mortality. Methods To characterize myocardial dysfunction and arrhythmia in MFS we conducted a prospective longitudinal case-control study including 86 patients with MFS (55.8% women, mean age 36.3 yr-range 13-70 yr-) and 40 age-and sex-matched healthy controls. Cardiac ultrasound, resting and ambulatory ECG (AECG) and NT-proBNP measurements were performed in all subjects at baseline. Additionally, patients with MFS underwent 2 extra evaluations during 30 +/- 7 months follow-up. To study primary versus secondary myocardial involvement, patients with MFS were divided in 2 groups: without previous surgery and normal/mild valvular function (MFS-1; N = 55) and with previous surgery or valvular dysfunction (MFS-2; N = 31). Results Compared to controls, patients in MFS-1 showed mild myocardial disease reflected in a larger left ventricular end-diastolic diameter (LVEDD), lower TAPSE and higher amount of (supra) ventricular extrasystoles [(S)VES]. Patients in MFS-2 were more severely affected. Seven patients (five in MFS-2) presented decreased LV ejection fraction. Twenty patients (twelve in MFS-2) had non-sustained ventricular tachycardia (NSVT) in at least one AECG. Larger LVEDD and higher amount of VES were independently associated with NSVT. Conclusion Our study shows mild but significant myocardial involvement in patients with MFS. Patients with previous surgery or valvular dysfunction are more severely affected. Evaluation of myocardial function with echocardiography and AECG should be considered in all patients with MFS, especially in those with valvular disease and a history of cardiac surgery

Water-induced modifications of GaP(100) and InP(100) surfaces studied by photoelectron spectroscopy and reflection anisotropy spectroscopy

In this work, we investigate the initial interaction of water and oxygen with different surface reconstructions of GaP(100) applying photoelectron spectroscopy, low-energy electron diffraction, and reflection anisotropy spectroscopy. Surfaces were prepared by metal-organic vapour phase epitaxy, transferred to ultra-high vacuum, and exposed to oxygen or water vapour at room temperature. The (2 4) reconstructed, Ga-rich surface is more sensitive and reactive to adsorption, bearing a less ordered surface reconstruction upon exposure and indicating a mixture of dissociative and molecular water adsorption. The p(2 2)=c(4 2) P-rich surface, on the other hand, is less reactive, but shows a new surface symmetry after water adsorption. Correlating findings of photoelectron spectroscopy with reflection anisotropy spectroscopy could pave the way towards optical in-situ monitoring of electrochemical surface modifications with reflection anisotropy spectroscopy

HIV-1 Phenotypic Reverse Transcriptase Inhibitor Drug Resistance Test Interpretation Is Not Dependent on the Subtype of the Virus Backbone

To date, the majority of HIV-1 phenotypic resistance testing has been performed with subtype B virus backbones (e.g. HXB2). However, the relevance of using this backbone to determine resistance in non-subtype B HIV-1 viruses still needs to be assessed. From 114 HIV-1 subtype C clinical samples (36 ARV-naïve, 78 ARV-exposed), pol amplicons were produced and analyzed for phenotypic resistance using both a subtype B- and C-backbone in which the pol fragment was deleted. Phenotypic resistance was assessed in resulting recombinant virus stocks (RVS) for a series of antiretroviral drugs (ARV's) and expressed as fold change (FC), yielding 1660 FC comparisons. These Antivirogram® derived FC values were categorized as having resistant or sensitive susceptibility based on biological cut-off values (BCOs). The concordance between resistance calls obtained for the same clinical sample but derived from two different backbones (i.e. B and C) accounted for 86.1% (1429/1660) of the FC comparisons. However, when taking the assay variability into account, 95.8% (1590/1660) of the phenotypic data could be considered as being concordant with respect to their resistance call. No difference in the capacity to detect resistance associated with M184V, K103N and V106M mutations was noted between the two backbones. The following was concluded: (i) A high level of concordance was shown between the two backbone phenotypic resistance profiles; (ii) Assay variability is largely responsible for discordant results (i.e. for FC values close to BCO); (iii) Confidence intervals should be given around the BCO's, when assessing resistance in HIV-1 subtype C; (iv) No systematic resistance under- or overcalling of subtype C amplicons in the B-backbone was observed; (v) Virus backbone subtype sequence variability outside the pol region does not contribute to phenotypic FC values. In conclusion the HXB2 virus backbone remains an acceptable vector for phenotyping HIV-1 subtype C pol amplicons

Analysis of the recovery phase after maximal exercise in children with repaired tetralogy of Fallot and the relationship with ventricular function

Background Few studies demonstrate delayed recovery after exercise in children and adults with heart disease. We assess the recovery patterns of gas exchange parameters and heart rate (HR) in children with repaired Tetralogy of Fallot (rToF) compared to healthy peers and investigate the correlation with ventricular function and QRS duration. Methods 45 children after rToF and 45 controls performed a maximal incremental cardiopulmonary exercise test. In the subsequent recovery period, patterns of VO2, VCO2 and HR were analysed. Half-life time (T-1/2) of the exponential decay and drop per minute (Rec(min)) were compared between groups. In the rToF group, correlations were examined between the recovery parameters and QRS-duration and ventricular function, described by fractional shortening (FS) and tricuspid annular plane systolic excursion (TAPSE) measured at baseline prior to exercise. Results Recovery of VO2 and VCO2 was delayed in rToF patients, half-life time values were higher compared to controls (T1/2VO2 52.51 11.29 s vs. 44.31 +/- 10.47 s; p = 0.001 and T1/2VCO2 68.28 +/- 13.84 s vs. 59.41 +/- 12.06 s; p = 0.002) and percentage drop from maximal value was slower at each minute of recovery (p<0.05). Correlations were found with FS (T1/2VO2: r = -0.517; p<0.001; Rec(1min)VO(2): r = -0.636, p<0.001; Rec(1min)VCO(2): r = -0.373, p = 0.012) and TAPSE (T1/2VO2: r = -0.505; p<0.001; Rec(1min)VO(2): r = -0.566, p<0.001; T1/2VCO2: r = -0.466; p = 0.001; Rec(1min)VCO(2): r = -0.507, p<0.001), not with QRS-duration. No difference was found in HR recovery between patients and controls. Conclusions Children after rToF show a delayed gas exchange recovery after exercise. This delay correlates to ventricular function, demonstrating its importance in recovery after physical activity