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.

Continuous monitoring of bovine spongiform encephalopathy rapid test performance by weak positive tissue controls and quality control charts

Bovine spongiform encephalopathy (BSE) rapid tests and routine BSE-testing laboratories underlie strict regulations for approval. Due to the lack of BSE-positive control samples, however, full assay validation at the level of individual test runs and continuous monitoring of test performance on-site is difficult. Most rapid tests use synthetic prion protein peptides, but it is not known to which extend they reflect the assay performance on field samples, and whether they are sufficient to indicate on-site assay quality problems. To address this question we compared the test scores of the provided kit peptide controls to those of standardized weak BSE-positive tissue samples in individual test runs as well as continuously over time by quality control charts in two widely used BSE rapid tests. Our results reveal only a weak correlation between the weak positive tissue control and the peptide control scores. We identified kit-lot related shifts in the assay performances that were not reflected by the peptide control scores. Vice versa, not all shifts indicated by the peptide control scores indeed reflected a shift in the assay performance. In conclusion these data highlight that the use of the kit peptide controls for continuous quality control purposes may result in unjustified rejection or acceptance of test runs. However, standardized weak positive tissue controls in combination with Shewhart-CUSUM control charts appear to be reliable in continuously monitoring assay performance on-site to identify undesired deviations.

Improving bovine udder health: a national mastitis control program in the Netherlands

Because of increasing bulk milk somatic cell counts and continuous clinical mastitis problems in a substantial number of herds, a national mastitis control program was started in 2005 to improve udder health in the Netherlands. The program started with founding the Dutch Udder Health Centre (UGCN), which had the task to coordinate the program. The program consisted of 2 parts: a research part and a knowledge-transfer part, which were integrated as much as possible. The knowledge-transfer part comprised 2 communication strategies: a central and a peripheral approach. The central approach was based on educating farmers using comprehensive science-based and rational argumentation about mastitis prevention and included on-farm study group meetings. Comprehensive education materials were developed for farmers that were internally motivated to improve udder health. In the peripheral approach it was tried to motivate farmers to implement certain management measures using nontechnical arguments. Mass media campaigns were used that focused on one single aspect of mastitis prevention. These communication strategies, as well as an integrated approach between various stakeholders and different scientific disciplines were used to reach as many farmers as possible. It should be noted that, because this intervention took place at a national level, no control group was available, as it would be impossible to isolate farmers from all forms of communication for 5 years. Based on several studies executed during and after the program, however, the results suggest that udder health seemed to have improved on a national level during the course of the program from 2005 to 2010. Within a cohort of dairy herds monitored during the program, the prevalence of subclinical mastitis did not change significantly (23.0 in 2004 vs. 22.2 in 2009). The incidence rate of clinical mastitis, however, decreased significantly, from 33.5 to 28.1 quarter cases per 100 cow years at risk. The most important elements of the farmers' mindset toward mastitis control also changed favorably. The simulated costs of mastitis per farm were reduced compared with a situation in which the mastitis would not have changed, with € 400 per year. When this amount is extrapolated to all Dutch farms, the sector as a whole reduced the total costs of mastitis by € 8 million per year. It is difficult to assign the improved udder health completely to the efforts of the program due to the lack of a control group. Nevertheless, investing € 8 million by the Dutch dairy industry in a 5-yr national mastitis control program likely improved udder health and seemed to pay for itself financially.

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.

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.

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.

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.

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.

Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems

This article centers on the computational performance of the continuous and discontinuous Galerkin time stepping schemes for general first-order initial value problems in R n , with continuous nonlinearities. We briefly review a recent existence result for discrete solutions from [6], and provide a numerical comparison of the two time discretization methods.

Establishing glycaemic control with continuous subcutaneous insulin infusion in children and adolescents with type 1 diabetes: experience of the PedPump Study in 17 countries

AIMS/HYPOTHESIS: To assess the use of paediatric continuous subcutaneous infusion (CSII) under real-life conditions by analysing data recorded for up to 90 days and relating them to outcome. METHODS: Pump programming data from patients aged 0-18 years treated with CSII in 30 centres from 16 European countries and Israel were recorded during routine clinical visits. HbA(1c) was measured centrally. RESULTS: A total of 1,041 patients (age: 11.8 +/- 4.2 years; diabetes duration: 6.0 +/- 3.6 years; average CSII duration: 2.0 +/- 1.3 years; HbA(1c): 8.0 +/- 1.3% [means +/- SD]) participated. Glycaemic control was better in preschool (n = 142; 7.5 +/- 0.9%) and pre-adolescent (6-11 years, n = 321; 7.7 +/- 1.0%) children than in adolescent patients (12-18 years, n = 578; 8.3 +/- 1.4%). There was a significant negative correlation between HbA(1c) and daily bolus number, but not between HbA(1c) and total daily insulin dose. The use of <6.7 daily boluses was a significant predictor of an HbA(1c) level >7.5%. The incidence of severe hypoglycaemia and ketoacidosis was 6.63 and 6.26 events per 100 patient-years, respectively. CONCLUSIONS/INTERPRETATION: This large paediatric survey of CSII shows that glycaemic targets can be frequently achieved, particularly in young children, and the incidence of acute complications is low. Adequate substitution of basal and prandial insulin is associated with a better HbA(1c).

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.