Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

An Actor-Critic based controller for glucose regulation in type 1 diabetes

A novel adaptive approach for glucose control in individuals with type 1 diabetes under sensor-augmented pump therapy is proposed. The controller, is based on Actor-Critic (AC) learning and is inspired by the principles of reinforcement learning and optimal control theory. The main characteristics of the proposed controller are (i) simultaneous adjustment of both the insulin basal rate and the bolus dose, (ii) initialization based on clinical procedures, and (iii) real-time personalization. The effectiveness of the proposed algorithm in terms of glycemic control has been investigated in silico in adults, adolescents and children under open-loop and closed-loop approaches, using announced meals with uncertainties in the order of ±25% in the estimation of carbohydrates. The results show that glucose regulation is efficient in all three groups of patients, even with uncertainties in the level of carbohydrates in the meal. The percentages in the A+B zones of the Control Variability Grid Analysis (CVGA) were 100% for adults, and 93% for both adolescents and children. The AC based controller seems to be a promising approach for the automatic adjustment of insulin infusion in order to improve glycemic control. After optimization of the algorithm, the controller will be tested in a clinical trial.

Adaptive Algorithms for Personalized Diabetes Treatment

Dynamic systems, especially in real-life applications, are often determined by inter-/intra-variability, uncertainties and time-varying components. Physiological systems are probably the most representative example in which population variability, vital signal measurement noise and uncertain dynamics render their explicit representation and optimization a rather difficult task. Systems characterized by such challenges often require the use of adaptive algorithmic solutions able to perform an iterative structural and/or parametrical update process towards optimized behavior. Adaptive optimization presents the advantages of (i) individualization through learning of basic system characteristics, (ii) ability to follow time-varying dynamics and (iii) low computational cost. In this chapter, the use of online adaptive algorithms is investigated in two basic research areas related to diabetes management: (i) real-time glucose regulation and (ii) real-time prediction of hypo-/hyperglycemia. The applicability of these methods is illustrated through the design and development of an adaptive glucose control algorithm based on reinforcement learning and optimal control and an adaptive, personalized early-warning system for the recognition and alarm generation against hypo- and hyperglycemic events.

The inverse problem for Schwinger pair production

The production of electron–positron pairs in time-dependent electric fields (Schwinger mechanism) depends non-linearly on the applied field profile. Accordingly, the resulting momentum spectrum is extremely sensitive to small variations of the field parameters. Owing to this non-linear dependence it is so far unpredictable how to choose a field configuration such that a predetermined momentum distribution is generated. We show that quantum kinetic theory along with optimal control theory can be used to approximately solve this inverse problem for Schwinger pair production. We exemplify this by studying the superposition of a small number of harmonic components resulting in predetermined signatures in the asymptotic momentum spectrum. In the long run, our results could facilitate the observation of this yet unobserved pair production mechanism in quantum electrodynamics by providing suggestions for tailored field configurations.

Consensus Document of the International Union of Angiology (IUA)-2013. Current concept on the management of arterio-venous management

Arterio-venous malformations (AVMs) are congenital vascular malformations (CVMs) that result from birth defects involving the vessels of both arterial and venous origins, resulting in direct communications between the different size vessels or a meshwork of primitive reticular networks of dysplastic minute vessels which have failed to mature to become 'capillary' vessels termed "nidus". These lesions are defined by shunting of high velocity, low resistance flow from the arterial vasculature into the venous system in a variety of fistulous conditions. A systematic classification system developed by various groups of experts (Hamburg classification, ISSVA classification, Schobinger classification, angiographic classification of AVMs,) has resulted in a better understanding of the biology and natural history of these lesions and improved management of CVMs and AVMs. The Hamburg classification, based on the embryological differentiation between extratruncular and truncular type of lesions, allows the determination of the potential of progression and recurrence of these lesions. The majority of all AVMs are extra-truncular lesions with persistent proliferative potential, whereas truncular AVM lesions are exceedingly rare. Regardless of the type, AV shunting may ultimately result in significant anatomical, pathophysiological and hemodynamic consequences. Therefore, despite their relative rarity (10-20% of all CVMs), AVMs remain the most challenging and potentially limb or life-threatening form of vascular anomalies. The initial diagnosis and assessment may be facilitated by non- to minimally invasive investigations such as duplex ultrasound, magnetic resonance imaging (MRI), MR angiography (MRA), computerized tomography (CT) and CT angiography (CTA). Arteriography remains the diagnostic gold standard, and is required for planning subsequent treatment. A multidisciplinary team approach should be utilized to integrate surgical and non-surgical interventions for optimum care. Currently available treatments are associated with significant risk of complications and morbidity. However, an early aggressive approach to elimiate the nidus (if present) may be undertaken if the benefits exceed the risks. Trans-arterial coil embolization or ligation of feeding arteries where the nidus is left intact, are incorrect approaches and may result in proliferation of the lesion. Furthermore, such procedures would prevent future endovascular access to the lesions via the arterial route. Surgically inaccessible, infiltrating, extra-truncular AVMs can be treated with endovascular therapy as an independent modality. Among various embolo-sclerotherapy agents, ethanol sclerotherapy produces the best long term outcomes with minimum recurrence. However, this procedure requires extensive training and sufficient experience to minimize complications and associated morbidity. For the surgically accessible lesions, surgical resection may be the treatment of choice with a chance of optimal control. Preoperative sclerotherapy or embolization may supplement the subsequent surgical excision by reducing the morbidity (e.g. operative bleeding) and defining the lesion borders. Such a combined approach may provide an excellent potential for a curative result. Conclusion. AVMs are high flow congenital vascular malformations that may occur in any part of the body. The clinical presentation depends on the extent and size of the lesion and can range from an asymptomatic birthmark to congestive heart failure. Detailed investigations including duplex ultrasound, MRI/MRA and CT/CTA are required to develop an appropriate treatment plan. Appropriate management is best achieved via a multi-disciplinary approach and interventions should be undertaken by appropriately trained physicians.

Hyperaldosteronism in pregnancy

Aldosterone is a key regulator of electrolyte and water homeostasis and plays a central role in blood pressure regulation. Hormonal changes during pregnancy, among them increased progesterone and aldosterone production, lead to the required plasma volume expansion of the maternal body as an accommodation mechanism for fetus growth. This review discusses the regulation of aldosterone production by aldosterone synthase (CYP11B2); the impact on aldosterone secretion due to the presence of a chimeric gene originating from a crossover between CYP11B1 and CYP11B2 in glucocorticoid remediable aldosteronism (GRA) - the inherited form of hypertension; enhanced aldosterone production in aldosterone-producing adenoma (APA); and idiopathic hyperaldosteronism (IHA). Features of hyperaldosteronism are also found in patients with apparent mineralocorticoid excess (AME), in which glucocorticoids exacerbate activation of the mineralocorticoid receptor (MR) because of a defect in the 11beta-hydroxysteroid dehydrogenase type 2 enzyme. Regulation of aldosterone production and tissue-specific activation of the mineralocorticoid receptor are prerequisites for optimal control of body fluids and blood pressure during pregnancy and contribute largely to the wellbeing of the mother-to-be.

Strategies for reducing fumigant loss to the atmosphere

A model is developed to describe transport and loss of methyl bromide (MeBr) in soil following application as a soil fumigant. The model is used to investigate the effect of soil and management factors on MeBr volatilization. Factors studied include depth of injection, soil water content, presence or absence of tarp, depth to downward barrier, and irrigation after injection. Of these factors, the most important was irrigation after injection followed by covering with the tarp, which increased the diffusive resistance of the soil and prevented early loss of MeBr. The model offers an explanation for the apparently contradictory observations of earlier field studies of MeBr volatilization from soils under different conditions. The model was also used to calculate the concentration-time index for various management alternatives, showing that the irrigation application did not make the surface soil more difficult to fumigate, except at very early times. Therefore, irrigation shows promise for reducing fumigant loss while at the same time permitting control of target organisms during fumigation.

What are the metacognitive costs of young children's overconfidence?

Children typically hold very optimistic views of their own skills but so far, only a few studies have investigated possible correlates of the ability to predict performance accurately. Therefore, this study examined the role of individual differences in performance estimation accuracy as a global metacognitive index for different monitoring and control skills (item-level judgments of learning [JOLs] and confidence judgments [CJs]), metacognitive control processes (allocation of study time and control of answers), and executive functions (cognitive flexibility, inhibition, working memory) in 6-year-olds (N=93). The three groups of under estimators, realists and over estimators differed significantly in their monitoring and control abilities: the under estimators outperformed the over estimators by showing a higher discrimination in CJs between correct and incorrect recognition. Also, the under estimators scored higher on the adequate control of incorrectly recognized items. Regarding the interplay of monitoring and control processes, under estimators spent more time studying items with low JOLs, and relied more systematically on their monitoring when controlling their recognition compared to over estimators. At the same time, the three groups did not differ significantly from each other in their executive functions. Overall, results indicate that differences in performance estimation accuracy are systematically related to other global and item-level metacognitive monitoring and control abilities in children as young as six years of age, while no meaningful association between performance estimation accuracy and executive functions was found.

Optimization of Schwinger pair production in colliding laser pulses

Recent studies of Schwinger pair production have demonstrated that the asymptotic particle spectrum is extremely sensitive to the applied field profile. We extend the idea of the dynamically assisted Schwinger effect from single pulse profiles to more realistic field configurations to be generated in an all-optical experiment searching for pair creation. We use the quantum kinetic approach to study the particle production and employ a multi-start method, combined with optimal control theory, to determine a set of parameters for which the particle yield in the forward direction in momentum space is maximized. We argue that this strategy can be used to enhance the signal of pair production on a given detector in an experimental setup.

Optimal time for initiating antiretroviral therapy (ART) in HIV-infected, treatment-naive children aged 2 to 5 years old

BACKGROUND The use of combination antiretroviral therapy (cART) comprising three antiretroviral medications from at least two classes of drugs is the current standard treatment for HIV infection in adults and children. Current World Health Organization (WHO) guidelines for antiretroviral therapy recommend early treatment regardless of immunologic thresholds or the clinical condition for all infants (less than one years of age) and children under the age of two years. For children aged two to five years current WHO guidelines recommend (based on low quality evidence) that clinical and immunological thresholds be used to identify those who need to start cART (advanced clinical stage or CD4 counts ≤ 750 cells/mm(3) or per cent CD4 ≤ 25%). This Cochrane review will inform the current available evidence regarding the optimal time for treatment initiation in children aged two to five years with the goal of informing the revision of WHO 2013 recommendations on when to initiate cART in children. OBJECTIVES To assess the evidence for the optimal time to initiate cART in treatment-naive, HIV-infected children aged 2 to 5 years. SEARCH METHODS We searched the Cochrane Central Register of Controlled Trials (CENTRAL), MEDLINE, EMBASE, the AEGIS conference database, specific relevant conferences, www.clinicaltrials.gov, the World Health Organization International Clinical Trials Registry platform and reference lists of articles. The date of the most recent search was 30 September 2012. SELECTION CRITERIA Randomised controlled trials (RCTs) that compared immediate with deferred initiation of cART, and prospective cohort studies which followed children from enrolment to start of cART and on cART. DATA COLLECTION AND ANALYSIS Two review authors considered studies for inclusion in the review, assessed the risk of bias, and extracted data on the primary outcome of death from all causes and several secondary outcomes, including incidence of CDC category C and B clinical events and per cent CD4 cells (CD4%) at study end. For RCTs we calculated relative risks (RR) or mean differences with 95% confidence intervals (95% CI). For cohort data, we extracted relative risks with 95% CI from adjusted analyses. We combined results from RCTs using a random effects model and examined statistical heterogeneity. MAIN RESULTS Two RCTs in HIV-positive children aged 1 to 12 years were identified. One trial was the pilot study for the larger second trial and both compared initiation of cART regardless of clinical-immunological conditions with deferred initiation until per cent CD4 dropped to <15%. The two trials were conducted in Thailand, and Thailand and Cambodia, respectively. Unpublished analyses of the 122 children enrolled at ages 2 to 5 years were included in this review. There was one death in the immediate cART group and no deaths in the deferred group (RR 2.9; 95% CI 0.12 to 68.9). In the subgroup analysis of children aged 24 to 59 months, there was one CDC C event in each group (RR 0.96; 95% CI 0.06 to 14.87) and 8 and 11 CDC B events in the immediate and deferred groups respectively (RR 0.95; 95% CI 0.24 to 3.73). In this subgroup, the mean difference in CD4 per cent at study end was 5.9% (95% CI 2.7 to 9.1). One cohort study from South Africa, which compared the effect of delaying cART for up to 60 days in 573 HIV-positive children starting tuberculosis treatment (median age 3.5 years), was also included. The adjusted hazard ratios for the effect on mortality of delaying ART for more than 60 days was 1.32 (95% CI 0.55 to 3.16). AUTHORS' CONCLUSIONS This systematic review shows that there is insufficient evidence from clinical trials in support of either early or CD4-guided initiation of ART in HIV-infected children aged 2 to 5 years. Programmatic issues such as the retention in care of children in ART programmes in resource-limited settings will need to be considered when formulating WHO 2013 recommendations.

Evaluating the optimal timing of surgical antimicrobial prophylaxis: study protocol for a randomized controlled trial

BACKGROUND Surgical site infections are the most common hospital-acquired infections among surgical patients. The administration of surgical antimicrobial prophylaxis reduces the risk of surgical site infections . The optimal timing of this procedure is still a matter of debate. While most studies suggest that it should be given as close to the incision time as possible, others conclude that this may be too late for optimal prevention of surgical site infections. A large observational study suggests that surgical antimicrobial prophylaxis should be administered 74 to 30 minutes before surgery. The aim of this article is to report the design and protocol of a randomized controlled trial investigating the optimal timing of surgical antimicrobial prophylaxis.Methods/design: In this bi-center randomized controlled trial conducted at two tertiary referral centers in Switzerland, we plan to include 5,000 patients undergoing general, oncologic, vascular and orthopedic trauma procedures. Patients are randomized in a 1:1 ratio into two groups: one receiving surgical antimicrobial prophylaxis in the anesthesia room (75 to 30 minutes before incision) and the other receiving surgical antimicrobial prophylaxis in the operating room (less than 30 minutes before incision). We expect a significantly lower rate of surgical site infections with surgical antimicrobial prophylaxis administered more than 30 minutes before the scheduled incision. The primary outcome is the occurrence of surgical site infections during a 30-day follow-up period (one year with an implant in place). When assuming a 5 surgical site infection risk with administration of surgical antimicrobial prophylaxis in the operating room, the planned sample size has an 80% power to detect a relative risk reduction for surgical site infections of 33% when administering surgical antimicrobial prophylaxis in the anesthesia room (with a two-sided type I error of 5%). We expect the study to be completed within three years. DISCUSSION The results of this randomized controlled trial will have an important impact on current international guidelines for infection control strategies in the hospital. Moreover, the results of this randomized controlled trial are of significant interest for patient safety and healthcare economics.Trial registration: This trial is registered on ClinicalTrials.gov under the identifier NCT01790529.

Population-based analysis of 4113 patients with acute cholecystitis: defining the optimal time-point for laparoscopic cholecystectomy

Objective: To compare clinical outcomes after laparoscopic cholecystectomy (LC) for acute cholecystitis performed at various time-points after hospital admission. Background: Symptomatic gallstones represent an important public health problem with LC the treatment of choice. LC is increasingly offered for acute cholecystitis, however, the optimal time-point for LC in this setting remains a matter of debate. Methods: Analysis was based on the prospective database of the Swiss Association of Laparoscopic and Thoracoscopic Surgery and included patients undergoing emergency LC for acute cholecystitis between 1995 and 2006, grouped according to the time-points of LC since hospital admission (admission day (d0), d1, d2, d3, d4/5, d ≥6). Linear and generalized linear regression models assessed the effect of timing of LC on intra- or postoperative complications, conversion and reoperation rates and length of postoperative hospital stay. Results: Of 4113 patients, 52.8% were female, median age was 59.8 years. Delaying LC resulted in significantly higher conversion rates (from 11.9% at d0 to 27.9% at d ≥6 days after admission, P < 0.001), surgical postoperative complications (5.7% to 13%, P < 0.001) and re-operation rates (0.9% to 3%, P = 0.007), with a significantly longer postoperative hospital stay (P < 0.001). Conclusions: Delaying LC for acute cholecystitis has no advantages, resulting in significantly increased conversion/re-operation rate, postoperative complications and longer postoperative hospital stay. This investigation—one of the largest in the literature—provides compelling evidence that acute cholecystitis merits surgery within 48 hours of hospital admission if impact on the patient and health care system is to be minimized.