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).

Solving higher-dimensional continuous time stochastic control problems by value function regression

The paper develops a method to solve higher-dimensional stochasticcontrol problems in continuous time. A finite difference typeapproximation scheme is used on a coarse grid of low discrepancypoints, while the value function at intermediate points is obtainedby regression. The stability properties of the method are discussed,and applications are given to test problems of up to 10 dimensions.Accurate solutions to these problems can be obtained on a personalcomputer.

Missing Value and Comparison Problems : what Pupils Know before the Teaching of Proportion. 'Problemas de valor ausente y de comparación : qué saben los alumnos antes de la enseñanza de la proporción'.

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An integral equation method for a boundary value problem arising in unsteady water wave problems

In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem. Keywords. Boundary integral equation method, Water waves, Laplace’s

A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.

Mixed initial-boundary value problem in particle modeling of microelectronic devices

The Boltzmann equation in presence of boundary and initial conditions, which describes the general case of carrier transport in microelectronic devices is analysed in terms of Monte Carlo theory. The classical Ensemble Monte Carlo algorithm which has been devised by merely phenomenological considerations of the initial and boundary carrier contributions is now derived in a formal way. The approach allows to suggest a set of event-biasing algorithms for statistical enhancement as an alternative of the population control technique, which is virtually the only algorithm currently used in particle simulators. The scheme of the self-consistent coupling of Boltzmann and Poisson equation is considered for the case of weighted particles. It is shown that particles survive the successive iteration steps.

On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.

The diagnostic value of Gram stain for initial identification of the etiologic agent of peritonitis in CAPD patients

Objective: To evaluate the effectiveness of the Gram stain in the initial diagnosis of the etiologic agent of peritonitis in continuous ambulatory peritoneal dialysis (CAPD). Design: Retrospective study analyzing the sensitivity (S), specificity (SS), positive predictive value (+PV), and negative predictive value (-PV) of the Gram stain relating to the results of cultures in 149 episodes of peritonitis in CAPD. The data were analyzed in two studies. In the first, only the cases with detection of a single agent by Gram stain were taken (Study 1). In the second, only the cases with two agents in Gram stain were evaluated (Study 2). Setting: Dialysis Unit and Laboratory of Microbiology of a tertiary medical center. Patients: Sixty-three patients on regular CAPD who presented one or more episodes of peritonitis from May 1992 to May 1995. Results: The positivity of Gram stain was 93.2% and the sensitivity was 95.7%. The values of S, SS, +PV, and -PV were respectively: 94.9%, 53.5%, 68.3%, and 90.9% for gram-positive cocci and 83.3%, 98.8%, 95.2%, and 95.6% for gram-negative bacilli. The association of gram-positive cocci plus gram-negative bacilli were predictive of growth of both in 6.8%, growth of gram-positive cocci in 13.7%, and growth of gram-negative bacilli in 72.5%. Conclusions: The Gram stain is a method of great value in the initial diagnosis of the etiologic agent of peritonitis in CAPD, especially for gram-negative bacilli.

Statistical problems related to excitation threshold and reset value of membrane potentials

Die vorliegende Arbeit ist motiviert durch biologische Fragestellungen bezüglich des Verhaltens von Membranpotentialen in Neuronen. Ein vielfach betrachtetes Modell für spikende Neuronen ist das Folgende. Zwischen den Spikes verhält sich das Membranpotential wie ein Diffusionsprozess X der durch die SDGL dX_t= beta(X_t) dt+ sigma(X_t) dB_t gegeben ist, wobei (B_t) eine Standard-Brown'sche Bewegung bezeichnet. Spikes erklärt man wie folgt. Sobald das Potential X eine gewisse Exzitationsschwelle S überschreitet entsteht ein Spike. Danach wird das Potential wieder auf einen bestimmten Wert x_0 zurückgesetzt. In Anwendungen ist es manchmal möglich, einen Diffusionsprozess X zwischen den Spikes zu beobachten und die Koeffizienten der SDGL beta() und sigma() zu schätzen. Dennoch ist es nötig, die Schwellen x_0 und S zu bestimmen um das Modell festzulegen. Eine Möglichkeit, dieses Problem anzugehen, ist x_0 und S als Parameter eines statistischen Modells aufzufassen und diese zu schätzen. In der vorliegenden Arbeit werden vier verschiedene Fälle diskutiert, in denen wir jeweils annehmen, dass das Membranpotential X zwischen den Spikes eine Brown'sche Bewegung mit Drift, eine geometrische Brown'sche Bewegung, ein Ornstein-Uhlenbeck Prozess oder ein Cox-Ingersoll-Ross Prozess ist. Darüber hinaus beobachten wir die Zeiten zwischen aufeinander folgenden Spikes, die wir als iid Treffzeiten der Schwelle S von X gestartet in x_0 auffassen. Die ersten beiden Fälle ähneln sich sehr und man kann jeweils den Maximum-Likelihood-Schätzer explizit angeben. Darüber hinaus wird, unter Verwendung der LAN-Theorie, die Optimalität dieser Schätzer gezeigt. In den Fällen OU- und CIR-Prozess wählen wir eine Minimum-Distanz-Methode, die auf dem Vergleich von empirischer und wahrer Laplace-Transformation bezüglich einer Hilbertraumnorm beruht. Wir werden beweisen, dass alle Schätzer stark konsistent und asymptotisch normalverteilt sind. Im letzten Kapitel werden wir die Effizienz der Minimum-Distanz-Schätzer anhand simulierter Daten überprüfen. Ferner, werden Anwendungen auf reale Datensätze und deren Resultate ausführlich diskutiert.

Predictive value of the Acute Low Back Pain Screening Questionnaire and the Örebro Musculoskeletal Pain Screening Questionnaire for persisting problems

A small proportion of individuals with non-specific low back pain (NSLBP) develop persistent problems. Up to 80% of the total costs for NSLBP are owing to chronic NSLBP. Psychosocial factors have been described to be important in the transition from acute to chronic NSLBP. Guidelines recommend the use of the Acute Low Back Pain Screening Questionnaire (ALBPSQ) and the Örebro Musculoskeletal Pain Screening Questionnaire (ÖMPSQ) to identify individuals at risk of developing persistent problems, such as long-term absence of work, persistent restriction in function or persistent pain. These instruments can be used with a cutoff value, where patients with values above the threshold are further assessed with a more comprehensive examination.

Effects of Initial Body Condition, Frame Size and Concentration of Dietary Energy on Carcass Value of Finished Steers

Yearling steers were sorted into four groups based on hip height and fat cover at the start of the finishing period. Each group of sorted steers was fed diets containing 0.59 or 0.64 Mcal NEg per pound of diet. The value of each carcass was determined by use of the Oklahoma State University Boxed Beef Calculator. Sorting to increase hip height decreased the percentage of Choice carcasses and fat cover, increased ribeye area, and had no effect on carcass weight or yield grades 1 and 2. Sorting to decrease initial fat cover decreased carcass weight, carcass fat cover, and percentage of choice carcasses and increased the proportion of yield grades 1 and 2 carcasses. Concentration of energy in the finishing diet had no effect on carcass measurements. Increasing the percentage of yield grades 1 and 2 carcasses did not result in increased economic value of the carcasses when quality grades were lower and when there was a wide spread between Choice and Select carcasses, as occurred in 1996. With less spread between Choice and Select, as in 1997, sorting the cattle to increase yield grades 1 and 2 resulted in increased value, especially for close-trim boxed beef. The results of this study emphasize the importance of knowing how carcasses will grade before selecting a valuebased market for selling cattle.

Prognostic value of PCSK9 levels in patients with acute coronary syndromes.

AIMS Proprotein convertase subtilisin kexin 9 (PCSK9) is an emerging target for the treatment of hypercholesterolaemia, but the clinical utility of PCSK9 levels to guide treatment is unknown. We aimed to prospectively assess the prognostic value of plasma PCSK9 levels in patients with acute coronary syndromes (ACS). METHODS AND RESULTS Plasma PCSK9 levels were measured in 2030 ACS patients undergoing coronary angiography in a Swiss prospective cohort. At 1 year, the association between PCSK9 tertiles and all-cause death was assessed adjusting for the Global Registry of Acute Coronary Events (GRACE) variables, as well as the achievement of LDL cholesterol targets of <1.8 mmol/L. Patients with higher PCSK9 levels at angiography were more likely to have clinical familial hypercholesterolaemia (rate ratio, RR 1.21, 95% confidence interval, CI 1.09-1.53), be treated with lipid-lowering therapy (RR 1.46, 95% CI 1.30-1.63), present with longer time interval of chest pain (RR 1.29, 95% CI 1.09-1.53) and higher C-reactive protein levels (RR 1.22, 95% CI 1.16-1.30). PCSK9 increased 12-24 h after ACS (374 ± 149 vs. 323 ± 134 ng/mL, P < 0.001). At 1 year follow-up, HRs for upper vs. lower PCSK9-level tertiles were 1.13 (95% CI 0.69-1.85) for all-cause death and remained similar after adjustment for the GRACE score. Patients with higher PCSK9 levels were less likely to reach the recommended LDL cholesterol targets (RR 0.81, 95% CI 0.66-0.99). CONCLUSION In ACS patients, high initial PCSK9 plasma levels were associated with inflammation in the acute phase and hypercholesterolaemia, but did not predict mortality at 1 year.

Unbalanced value chain in perishable agricultural products.

Value chain in agriculture is a current issue affecting from farmers to consumers. It questions important issues as profitability, and even though continuity of certain sectors. Although there has been an evolution along time in the structure and concentration of intermediate and final levels of the value chain between distribution and retail sector, a similar evolution seems not to arrive at the initial level of the chain, the production sector. This produces large imbalances in power and leverage between levels of the value chain that could imply several problems for rural actors. Relatively little attention has been paid to possible market distortions caused by the high level of concentration distribution side of the agrifood system.