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).

Could Hyperglycaemia and Troponin I predict outcome in intensive care after congenital heart surgery in children?

Objective: To establish if hyperglycaemia and cardiac Troponin I (cTnI) after congenital heart surgery on cardiopulmonary bypass in children could predict outcome in intensive care unit. Methods: retrospective cohort study including 274 children (mean age 4.6 years; range 0 - 17 years-old). CTnI and glucose values were retrieved from our database. Integrated values (area under the curve (AUC)) were calculated for evaluation of sustained hyperglycaemia and then normalised per hour (48h-Gluc/h). Maximal cTnI, fi rst glucose value (Gluc1) and 48h-Gluc/h were then correlated with duration of mechanical ventilation, ICU stay and mortality using cut-off values. Results: The mean duration of mechanical ventilation was 5.1 ± 7.2 days and ICU stay was 11.0 ± 13.3 days, 11 patients (3.9%) died. Hyperglycaemia (>6.1 mmol/l) was present in 68% of children at admission and was sustained in 85% for 48 hours. The mean value of Gluc1 (7.3 ± 2.7 vs. 11.8 ± 6.4 mmol/l, p < 0.0001), 48h-Gluc/h (7.4 ± 1.4 vs. 9.9 ± 4.6 mmol/l/h, p < 0.0001) and cTnI max (16.7 ± 21.8 vs. 59.2 ± 41.4 mcg/l, p < 0.0001) were signifi cantly lower in survivors vs. non survivors. Cut-off values and odds ratio are summarised in Table 1. Analyses for duration of mechanical ventilation and for length of stay in ICU are depicted in Table 2. Conclusions: Hyperglycaemia is frequent after cardiopulmonary bypass and sustained in the fi rst 48 hours. Admission glycaemia and cTnI max are associated with a high risk of mortality, prolonged duration of mechanical ventilation and prolonged length of stay in ICU.

On slicewise monotone parameterized problems and optimal proof systems for TAUT

"Vegeu el resum a l'inici del document del fitxer adjunt"

Active mitral ring for post-surgical remote correction of residual mitral regurgitation on the beating heart.

OBJECTIVES: Residual mitral regurgitation after valve repair worsens patients' clinical outcome. Postimplant adjustable mitral rings potentially address this issue, allowing the reshaping of the annulus on the beating heart under echocardiography control. We developed an original mitral ring allowing valve geometry remodelling after the implantation and designed an animal study to assess device effectiveness in correcting residual mitral regurgitation. METHODS: The device consists of two concentric rings: one internal and flexible, sutured to the mitral annulus and a second external and rigid. A third conic element slides between the two rings, modifying the shape of the flexible ring. This sliding element is remotely activated with a rotating tool. Animal model: in adult swine, under cardio pulmonary bypass and cardiac arrest, we shortened the primary chordae of P2 segment to reproduce Type III regurgitation and implanted the active ring. We used intracardiac ultrasound to assess mitral regurgitation and the efficacy of the active ring to correct it. RESULTS: Severe mitral regurgitation (3+ and 4+) was induced in eight animals, 54 ± 6 kg in weight. Vena contracta width decreased from 0.8 ± 0.2 to 0.1 cm; proximal isovelocity surface area radius decreased from 0.8 ± 0.2 to 0.1 cm and effective regurgitant orifice area decreased from 0.50 ± 0.1 to 0.1 ± 0.1 cm(2). Six animals had a reversal of systolic pulmonary flow that normalized following the activation of the device. All corrections were reversible. CONCLUSIONS: Postimplant adjustable mitral ring corrects severe mitral regurgitation through the reversible modification of the annulus geometry on the beating heart. It addresses the frequent and morbid issue of recurrent mitral valve regurgitation.

Application of the combined integral method to Stefan problems

In this paper we present a new, accurate form of the heat balance integral method, termed the Combined Integral Method (or CIM). The application of this method to Stefan problems is discussed. For simple test cases the results are compared with exact and asymptotic limits. In particular, it is shown that the CIM is more accurate than the second order, large Stefan number, perturbation solution for a wide range of Stefan numbers. In the initial examples it is shown that the CIM reduces the standard problem, consisting of a PDE defined over a domain specified by an ODE, to the solution of one or two algebraic equations. The latter examples, where the boundary temperature varies with time, reduce to a set of three first order ODEs.

Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions

In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the Heat Balance and Refined Integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t & 0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions.

An axiomatic justification of mediation in bankruptcy problems.

This paper provides a natural way of reaching an agreement between two prominent proposals in a bankruptcy problem. Particularly, using the fact that such problems can be faced from two different points of views, awards and losses, we justify the average of any pair of dual bankruptcy rules through the definition a double recursive process. Finally, by considering three posible sets of equity principles that a particular society may agree on, we retrieve the average of old and well known bankruptcy rules, the Constrained Equal Awards and the Constrained Equal Losses rules, Piniles’ rule and its dual rule, and the Constrained Egalitarian rule and its dual rule. Keywords: Bankruptcy problems, Midpoint, Bounds, Duality, Recursivity. JEL classification: C71, D63, D71.

A way to play bankruptcy problems.

The commitment among agents has always been a difficult task, especially when they have to decide how to distribute the available amount of a scarce resource among all. On the one hand, there are a multiplicity of possible ways for assigning the available amount; and, on the other hand, each agent is going to propose that distribution which provides her the highest possible award. In this paper, with the purpose of making this agreement easier, firstly we use two different sets of basic properties, called Commonly Accepted Equity Principles, to delimit what agents can propose as reasonable allocations. Secondly, we extend the results obtained by Chun (1989) and Herrero (2003), obtaining new characterizations of old and well known bankruptcy rules. Finally, using the fact that bankruptcy problems can be analyzed from awards and losses, we define a mechanism which provides a new justification of the convex combinations of bankruptcy rules. Keywords: Bankruptcy problems, Unanimous Concessions procedure, Diminishing Claims mechanism, Piniles’ rule, Constrained Egalitarian rule. JEL classification: C71, D63, D71.

Effets hémodynamiques d'un inhibiteur de l'effet vasculaire de la vasopressine chez des patients avec insuffisance cardiaque congestive [Hemodynamic effects of an inhibitor of the vascular effects of vasopressin in patients with congestive heart failure]

To assess the role of vasopressin (AVP) in congestive heart failure (CHF), we investigated 10 patients with CHF refractory to conventional treatment, before and 60 minutes after intravenous administration of 5 micrograms/kg of d(CH2)5Tyr(Me)AVP, a specific antagonist of AVP at the vascular receptor level. Heart rate, systemic arterial pressure, pulmonary arterial pressure, pulmonary capillary wedge pressure, cardiac index by thermodilution, and cutaneous blood flow by laser-Doppler technique were measured. In 9 patients there was no significant hemodynamic and cutaneous blood flow response to the AVP antagonist. Plasma AVP was 2.3 +/- 0.8 pg/ml and plasma osmolality 284 +/- 14 mosm/kg H2O. The tenth patient had the most severe CHF. His plasma AVP was 55 pg/ml and plasma osmolality 290 mosm/kg. He responded to the AVP antagonist with a marked decrease in systemic arterial pressure from 115/61 to 79/41 mm Hg, in pulmonary arterial pressure from 58/31 to 33/13 mm Hg and in pulmonary capillary wedge pressure from 28 to 15 mm Hg. Simultaneously cardiac index increased from 1.1 to 2.21 X min-1 X m-2 and cutaneous blood flow rose 5-fold. Thus, most patients with CHF have only moderately elevated plasma AVP and its role in determining peripheral vascular resistance appears to be limited. AVP may become important in rare patients presenting with marked hemodynamic instability and very high plasma AVP.

Atrial arrhythmias in adults with congenital heart disease.

BACKGROUND: Atrial arrhythmias increase disease burden in the general adult population. Adults with congenital heart lesions constitute a rapidly growing group of patients with cardiovascular disease. We hypothesized that atrial arrhythmias increase with age and impair health outcomes in this population. METHODS AND RESULTS: We conducted a population-based analysis of prevalence, lifetime risk, mortality, and morbidity associated with atrial arrhythmias in adults with congenital heart disease from l983 to 2005. In 38 428 adults with congenital heart disease in 2005, 5812 had atrial arrhythmias. Overall, the 20-year risk of developing atrial arrhythmia was 7% in a 20-year-old subject and 38% in a 50-year-old subject. More than 50% of patients with severe congenital heart disease reaching age 18 years developed atrial arrhythmias by age 65 years. In patients with congenital heart disease, the hazard ratio of any adverse event in those with atrial arrhythmias compared with those without was 2.50 (95% confidence interval, 2.38 to 2.62; P<0.0001), with a near 50% increase in mortality (hazard ratio, 1.47; 95% confidence interval, 1.37 to 1.58; P<0.001), more than double the risk of morbidity (stroke or heart failure) (hazard ratio, 2.21; 95% confidence interval, 2.07 to 2.36; P<0.001), and 3 times the risk of cardiac interventions (hazard ratio, 3.00; 95% confidence interval, 2.81 to 3.20; P<0.001). CONCLUSIONS: Atrial arrhythmias occurred in 15% of adults with congenital heart disease. The lifetime incidence increased steadily with age and was associated with a doubling of the risk of adverse events. An increase in resource allocation should be anticipated to deal with this increasing burden.

Reversible congestive heart failure associated with primary carnitin deficiency: report of a case and review of the literature.

A 5-year-old previously healthy boy was admitted for abdominal pain and vomiting. Physical examination showed tachypnoe (32/min), hepatomegaly and painful palpation of the upper right abdominal quadrant. Laboratory tests were normal except for elevated ammonium (202mcmol/l). Chest X-ray was performed, showing cardiomegaly and interstitial edema. Transthoracic echocardiography revealed dilated left cavities and LV hypertrophy together with a diffuse hypokinesia and LVEF of 30-40%. Diuretics and ACE-inhibitors were introduced. At that time, the differential diagnosis for the DCM included myocarditis, congenital or genetic, metabolic or autoimmune disease. The next day, the boy underwent cardiac magnetic resonance (CMR) examination, showing a severe dilatation of the LV with an end-diastolic diameter of 50mm and a volume of 150ml. LVEF was 20% with diffuse LV hypokinesia (Fig. 1). No late enhancement was present after Gadolinium injection, ruling out myocarditis. Further laboratory metabolic analysis indicated severely decreased total and free carnitin levels and low renal carnitin reabsorption, corroborating the diagnosis of primary carnitin deficiency (PCD). Carnitin substitution was initiated. The clinical condition rapidly improved. No symptoms of heart failure were present anymore. A follow-up CMR performed 9 months later confirmed the recovery. LV end-diastolic volume decreased from 150ml to 66ml, LVEF increased from 20% to 55% (Fig. 2). Late enhancement was absent after Gadolinum injection (Fig. 3).Carnitin is required for the transport of fatty acids from the cytosol into mitochondria during lipid breakdown. 75% of carnitin is obtained from food, 25% is endogenously synthesized. PCD is an autosomal recessive disorder resulting from impairment of a transporter activity, caused by mutation of the SLC22A5 gene. Incidence is about 1 in 40'000 newborns. Diagnosis is usually made at age 1 to 7. Three forms of PCD are described. In the form associated with cardiomyopathy, the disease is progressive and patient die from heart failure if not treated. Substitution of L-Carnitin leads to a dramatic improvement of disease course.This case underlines the crucial role of etiologic diagnostics in this reversible form of DCM. Early diagnostics and therapy are critical for the prognosis of the patient. This is furthermore an example of a role played by CMR in the diagnostic work-up of heart failure and its follow-up under therapy.

Confounding effects of heart rate on pulse wave velocity in paced patients with a low degree of atherosclerosis.

BACKGROUND: Pulse wave velocity (PWV), an index of arterial wall stiffness, is modulated by blood pressure (BP). Whether heart rate (HR) is also a modulator of PWV is controversial. Recent research involving mainly patients with high aortic PWV have found either no change or a positive correlation between the two. Given that PWV is increasingly being measured in cardiovascular studies, the relationship between HR and PWV should be known in patients with preserved arterial wall elasticity. OBJECTIVE: The aim of this study was to evaluate the importance of HR as a determinant of the variability in PWV in patients with a low degree of atherosclerosis. DESIGN AND METHODS: Fourteen patients (five female, nine male; aged 68 +/- 8 years) were evaluated post pacemaker implantation due to sick sinus or carotid hypersensitivity syndromes. Carotid-femoral PWV was measured at rest and during atrial pacing at 80, 90 and 100 bpm (paced HR). Arterial femoral blood flow (AFBF) was measured by echodoppler. RESULTS: PWV increased from 6.2 +/- 1.5 m/s (mean +/- SD) during resting sinus rhythm (HR 62 +/- 8 bpm; mean +/- SD) to 6.8 +/- 1.0, 7.0 +/- 0.9, and 7.6 +/- 1.1 m/s at pacing rates of 80, 90 and 100 bpm, respectively (P < 0.0001). Systolic (SBP) and mean blood pressure (MBP) remained constant at all HR levels, whereas AFBF increased in a linear fashion. CONCLUSIONS: These results demonstrate that even in patients with a low degree of atherosclerosis, HR is a potential modulator of carotid-femoral PWV.

Postinfarction heart failure in rats is associated with upregulation of GLUT-1 and downregulation of genes of fatty acid metabolism.

OBJECTIVES: Increasing evidence suggests that left ventricular remodeling is associated with a shift from fatty acid to glucose metabolism for energy production. The aim of this study was to determine whether left ventricular remodeling with and without late-onset heart failure after myocardial infarction is associated with regional changes in the expression of regulatory proteins of glucose or fatty acid metabolism. METHODS: Myocardial infarction was induced in rats by ligation of the left anterior descending coronary artery (LAD). In infarcted and sham-operated hearts the peri-infarction region (5-mm zone surrounding the region at risk), the interventricular septum and the right ventricular free wall were separated for analysis. RESULTS: At 8 and 20 weeks after LAD ligation, the peri-infarction region and the septum exhibited marked re-expression of atrial natriuretic factor [+252+/-37 and +1093+/-279%, respectively, in the septum (P<0.05)] and of alpha-smooth muscle actin [+34+/-10 and +43+/-14%, respectively, in the septum (P<0.05)]. At 8 weeks, when left ventricular hypertrophy was present without signs of heart failure, myocardial mRNA expression of glucose transporters (GLUT-1 and GLUT-4) was not altered, whereas mRNA expression of medium-chain acyl-CoA dehydrogenase (MCAD) was significantly reduced in the peri-infarction region (-25+/-7%; P<0.05). In hearts exhibiting heart failure 20 weeks after infarct-induction there was a change in all three ventricular regions of both mRNA and protein content of GLUT-1 [+72+/-28 and +121+/-15%, respectively, in the peri-infarction region (P<0.05)] and MCAD [-29+/-9 and -56+/-4%, respectively, in the peri-infarction region (P<0.05)]. CONCLUSION: In rats with large myocardial infarction, progression from compensated remodeling to overt heart failure is associated with upregulation of GLUT-1 and downregulation of MCAD in both the peri-infarction region and the septum.