On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

On p-optimal proof systems and logics for PTIME

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On slicewise monotone parameterized problems and optimal proof systems for TAUT

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Optimal asymptotic bounds for spherical designs

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Protein intake and exercise for optimal muscle function with aging: recommendations from the ESPEN Expert Group.

The aging process is associated with gradual and progressive loss of muscle mass along with lowered strength and physical endurance. This condition, sarcopenia, has been widely observed with aging in sedentary adults. Regular aerobic and resistance exercise programs have been shown to counteract most aspects of sarcopenia. In addition, good nutrition, especially adequate protein and energy intake, can help limit and treat age-related declines in muscle mass, strength, and functional abilities. Protein nutrition in combination with exercise is considered optimal for maintaining muscle function. With the goal of providing recommendations for health care professionals to help older adults sustain muscle strength and function into older age, the European Society for Clinical Nutrition and Metabolism (ESPEN) hosted a Workshop on Protein Requirements in the Elderly, held in Dubrovnik on November 24 and 25, 2013. Based on the evidence presented and discussed, the following recommendations are made (a) for healthy older people, the diet should provide at least 1.0-1.2 g protein/kg body weight/day, (b) for older people who are malnourished or at risk of malnutrition because they have acute or chronic illness, the diet should provide 1.2-1.5 g protein/kg body weight/day, with even higher intake for individuals with severe illness or injury, and (c) daily physical activity or exercise (resistance training, aerobic exercise) should be undertaken by all older people, for as long as possible.

Designing the Optimal Conservativeness of the Central Bank

In this paper we propose a new measure of the degree of conservativeness of an inde- pendent central bank and we derive the optimal value from the social welfare perspective. We show that the mere appointment of an independent central bank is not enough to achieve lower inflation, which may explain the mixed results found between central bank independence and inflation in the empirical literature. Further, the optimal central bank should not be too conservative. For instance, we will show that in some circumstances it will be optimal that the central bank is less conservative than society in the Rogoff sense. JEL classification: E58, E63. Keywords: Central bank; Conservativeness; Independence.

Optimal 3-T MRI for depiction of the finger A2 pulley: comparison between T1-weighted, fat-saturated T2-weighted and gadolinium-enhanced fat-saturated T1-weighted sequences

OBJECTIVE: To compare three spin-echo sequences, transverse T1-weighted (T1WI), transverse fat-saturated (FS) T2-weighted (T2WI), and transverse gadolinium-enhanced (Gd) FS T1WI, for the visualisation of normal and abnormal finger A2 pulley with magnetic resonance (MR) imaging at 3 tesla (T). MATERIALS AND METHODS: Sixty-three fingers from 21 patients were consecutively investigated. Two musculoskeletal radiologists retrospectively compared all sequences to assess the visibility of normal and abnormal A2 pulleys and the presence of motion or ghost artefacts. RESULTS: Normal and abnormal A2 pulleys were visible in 94% (59/63) and 95% (60/63) on T1WI sequences, in 63% (40/63) and 60% (38/63) on FS T2WI sequences, and in 87% (55/63) and 73% (46/63) on Gd FS T1WI sequences when read by the first and second observer, respectively. Motion and ghost artefacts were higher on FS T2WI sequences. Seven among eight abnormal A2 pulleys were detected, and were best depicted with Gd FS T1WI sequences in 71% (5/7) and 86% (6/7) by the first and the second observer, respectively. CONCLUSION: In 3-T MRI, the comparison between transverse T1WI, FS T2WI, and Gd FS T1WI sequences shows that transverse T1WI allows excellent depiction of the A2 pulley, that FS T2WI suffers from a higher rate of motion and ghost artefacts, and transverse Gd FS T1WI is the best sequence for the depiction of abnormal A2 pulley.

The composition of mineral waters sourced from Europe and North America in respect to bone health: composition of mineral water optimal for bone.

The consumption of mineral waters is increasing in industrialised countries. High intakes of Ca and other alkalising cations as well as a low acid intake are beneficial to bone. We examined which components of mineral waters are conditioning their Ca content and their alkalinising power, in order to define the optimal profile. European mineral waters were randomly selected on the Internet: 100 waters with less than 200 mg Ca/l (9.98 mEq/l) and fifty with more than 200 mg/l, all with complete data for SO4, P, Cl, Na, K, Mg and Ca, and most also for HCO3. For comparison, forty North American mineral waters were randomly chosen. The potential renal acid load (PRAL) was calculated for each mineral water. North American waters did not reveal significant results because of their low mineralisation. We performed correlations between all eight components in order to explore the properties of the mineral waters. In the European waters, twenty-six out of twenty-eight correlations showed a P value of <or= 0.01. In waters with PRAL >0 (acidifying waters), PRAL was positively correlated with SO4, Ca, K and Mg (P < 0.001). In those with PRAL < 0 (alkalinising waters), PRAL was negatively correlated with HCO3, Na, Mg, Ca, K, Cl and SO4 (P < 0.001). SO4 and HCO3 were not found together in high quantities in the same water for geochemical reasons. A high Ca content is associated with either a high SO4 or a high HCO3 content. SO4 theoretically increases Ca excretion, while HCO3 and low PRAL values are associated with positive effects on bone. Therefore, the best waters for bone health are rich in both HCO3 and Ca, and by consequence low in SO4.

Is PaCO2 management optimal under controlled mechanical ventilation (CMV) during neuro-resuscitation?

INTRODUCTION. Both hypocapnia and hypercapnia can be deleterious to brain injured patients. Strict PaCO2 control is difficult to achieve because of patient's instability and unpredictable effects of ventilator settings changes. OBJECTIVE. The aim of this study was to evaluate our ability to comply with a protocol of controlled mechanical ventilation (CMV) aiming at a PaCO2 between 35 and 40 mmHg in patients requiring neuro-resuscitation. METHODS. Retrospective analysis of consecutive patients (2005-2011) requiring intracranial pressure (ICP) monitoring for traumatic brain injury (TBI), subarachnoid haemorrhage (SAH), intracranial haemorrhage (ICH) or ischemic stroke (IS). Demographic data, GCS, SAPS II, hospital mortality, PaCO2 and ICP values were recorded. During CMV in the first 48 h after admission, we analyzed the time spent within the PaCO2 target in relation to the presence or absence of intracranial hypertension (ICP[20 mmHg, by periods of 30 min) (Table 1). We also compared the fraction of time (determined by linear interpolation) spent with normal, low or high PaCO2 in hospital survivors and non-survivors (Wilcoxon, Bonferroni correction, p\0.05) (Table 2). PaCO2 samples collected during and after apnoea tests were excluded. Results given as median [IQR]. RESULTS. 436 patients were included (TBI: 51.2 %, SAH: 20.6 %, ICH: 23.2 %, IS: 5.0 %), age: 54 [39-64], SAPS II score: 52 [41-62], GCS: 5 [3-8]. 8744 PaCO2 samples were collected during 150611 h of CMV. CONCLUSIONS. Despite a high number of PaCO2 samples collected (in average one sample every 107 min), our results show that patients undergoing CMV for neuro- resuscitation spent less than half of the time within the pre-defined PaCO2 range. During documented intracranial hypertension, hypercapnia was observed in 17.4 % of the time. Since non-survivors spent more time with hypocapnia, further analysis is required to determine whether hypocapnia was detrimental per se, or merely reflects increased severity of brain insult.

Performance of OptiMAL® in the diagnosis of Plasmodium vivax and Plasmodium falciparum infections in a malaria referral center in Colombia

Alternative, non-microscopic methods for the diagnosis of malaria have recently become available. Among these, rapid dipstick methods stand out. One such test, OptiMAL®, is based on the immunochromatographic detection of Plasmodium lactate dehydrogenase (pLDH) and has the capacity to detect and distinguish infections caused by P. falciparum and Plasmodium sp. This capacity is particularly important in countries where different species of Plasmodium co-exist. In this study we evaluated the performance of OptiMAL® in an urban referral center for malaria diagnosis. Two sets of patients were included: one (n = 112) having predetermined infections with P. falciparum or P. vivax and individuals with negative blood smears; and another consisting of all eligible consecutive patients (n = 80) consulting for diagnosis at the referral center during one month. The overall diagnostic efficiency of OptiMAL® for both sets of patients was 96.9%. Efficiency was higher for P. vivax (98.1%) than for P. falciparum (94.9%). These results corroborate the diagnostic utility of OptiMAL® in settings where P. vivax and P. falciparum co-exist and support its implementation where microscopic diagnosis is unavailable and in circumstances that exceed the capacity of the local microscopic diagnosis facility.

Assessment of left coronary artery beat-to-beat repositioning in order to propose an optimal acquisition window for coronary MRA

Introduction: Coronary magnetic resonance angiography (MRA) is a medical imaging technique that involves collecting data from consecutive heartbeats, always at the same time in the cardiac cycle, in order to minimize heart motion artifacts. This technique relies on the assumption that coronary arteries always follow the same trajectory from heartbeat to heartbeat. Until now, choosing the acquisition window in the cardiac cycle was based exclusively on the position of minimal coronary motion. The goal of this study was to test the hypothesis that there are time intervals during the cardiac cycle when coronary beat-to-beat repositioning is optimal. The repositioning uncertainty values in these time intervals were then compared with the intervals of low coronary motion in order to propose an optimal acquisition window for coronary MRA. Methods: Cine breath-hold x-ray angiograms with synchronous ECG were collected from 11 patients who underwent elective routine diagnostic coronarography. Twenty-three bifurcations of the left coronary artery were selected as markers to evaluate repositioning uncertainty and velocity during cardiac cycle. Each bifurcation was tracked by two observers, with the help of a user-assisted algorithm implemented in Matlab (The Mathworks, Natick, MA, USA) that compared the trajectories of the markers coming from consecutive heartbeats and computed the coronary repositioning uncertainty with steps of 50ms until 650ms after the R-wave. Repositioning uncertainty was defined as the diameter of the smallest circle encompassing the points to be compared at the same time after the R-wave. Student's t-tests with a false discovery rate (FDR, q=0.1) correction for multiple comparison were applied to see whether coronary repositioning and velocity vary statistically during cardiac cycle. Bland-Altman plots and linear regression were used to assess intra- and inter-observer agreement. Results: The analysis of left coronary artery beat-to-beat repositioning uncertainty shows a tendency to have better repositioning in mid systole (less than 0.84±0.58mm) and mid diastole (less than 0.89±0.6mm) than in the rest of the cardiac cycle (highest value at 50ms=1.35±0.64mm). According to Student's t-tests with FDR correction for multiple comparison (q=0.1), two intervals, in mid systole (150-200ms) and mid diastole (550-600ms), provide statistically better repositioning in comparison with the early systole and the early diastole. Coronary velocity analysis reveals that left coronary artery moves more slowly in end systole (14.35±11.35mm/s at 225ms) and mid diastole (11.78±11.62mm/s at 625ms) than in the rest of the cardiac cycle (highest value at 25ms: 55.96±22.34mm/s). This was confirmed by Student's t-tests with FDR correction for multiple comparison (q=0.1, FDR-corrected p-value=0.054): coronary velocity values at 225, 575 and 625ms are not much different between them but they are statistically inferior to all others. Bland-Altman plots and linear regression show that intra-observer agreement (y=0.97x+0.02 with R²=0.93 at 150ms) is better than inter-observer (y=0.8x+0.11 with R²=0.67 at 150ms). Discussion: The present study has demonstrated that there are two time intervals in the cardiac cycle, one in mid systole and one in mid diastole, where left coronary artery repositioning uncertainty reaches points of local minima. It has also been calculated that the velocity is the lowest in end systole and mid diastole. Since systole is less influenced by heart rate variability than diastole, it was finally proposed to test an acquisition window between 150 and 200ms after the R-wave.