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.

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.

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.

ATMOSPHERIC RETRIEVAL ANALYSIS OF THE DIRECTLY IMAGED EXOPLANET HR 8799b

Directly imaged exoplanets are unexplored laboratories for the application of the spectral and temperature retrieval method, where the chemistry and composition of their atmospheres are inferred from inverse modeling of the available data. As a pilot study, we focus on the extrasolar gas giant HR 8799b, for which more than 50 data points are available. We upgrade our non-linear optimal estimation retrieval method to include a phenomenological model of clouds that requires the cloud optical depth and monodisperse particle size to be specified. Previous studies have focused on forward models with assumed values of the exoplanetary properties; there is no consensus on the best-fit values of the radius, mass, surface gravity, and effective temperature of HR 8799b. We show that cloud-free models produce reasonable fits to the data if the atmosphere is of super-solar metallicity and non-solar elemental abundances. Intermediate cloudy models with moderate values of the cloud optical depth and micron-sized particles provide an equally reasonable fit to the data and require a lower mean molecular weight. We report our best-fit values for the radius, mass, surface gravity, and effective temperature of HR 8799b. The mean molecular weight is about 3.8, while the carbon-to-oxygen ratio is about unity due to the prevalence of carbon monoxide. Our study emphasizes the need for robust claims about the nature of an exoplanetary atmosphere to be based on analyses involving both photometry and spectroscopy and inferred from beyond a few photometric data points, such as are typically reported for hot Jupiters.

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.

Preliminary Experience in Treatment of Papillary and Macular Retinoblastoma: Evaluation of Local Control and Local Complications After Treatment with Linear Accelerator-Based Stereotactic Radiotherapy with Micromultileaf Collimator as Second-Line or Salvage Treatment after chemotherapy

To determine the local control and complication rates for children with papillary and/or macular retinoblastoma progressing after chemotherapy and undergoing stereotactic radiotherapy (SRT) with a micromultileaf collimator.

Genetic diversity in an indigenous horse breed: implications for mating strategies and the control of future inbreeding

The Franches-Montagnes is an indigenous Swiss horse breed, with approximately 2500 foalings per year. The stud book is closed, and no introgression from other horse breeds was conducted since 1998. Since 2006, breeding values for 43 different traits (conformation, performance and coat colour) are estimated with a best linear unbiased prediction (BLUP) multiple trait animal model. In this study, we evaluated the genetic diversity for the breeding population, considering the years from 2003 to 2008. Only horses with at least one progeny during that time span were included. Results were obtained based on pedigree information as well as from molecular markers. A series of software packages were screened to combine best the best linear unbiased prediction (BLUP) methodology with optimal genetic contribution theory. We looked for stallions with highest breeding values and lowest average relationship to the dam population. Breeding with such stallions is expected to lead to a selection gain, while lowering the future increase in inbreeding within the breed.

An insulin infusion advisory system for type 1 diabetes patients based on non-linear model predictive control methods

In this paper, an Insulin Infusion Advisory System (IIAS) for Type 1 diabetes patients, which use insulin pumps for the Continuous Subcutaneous Insulin Infusion (CSII) is presented. The purpose of the system is to estimate the appropriate insulin infusion rates. The system is based on a Non-Linear Model Predictive Controller (NMPC) which uses a hybrid model. The model comprises a Compartmental Model (CM), which simulates the absorption of the glucose to the blood due to meal intakes, and a Neural Network (NN), which simulates the glucose-insulin kinetics. The NN is a Recurrent NN (RNN) trained with the Real Time Recurrent Learning (RTRL) algorithm. The output of the model consists of short term glucose predictions and provides input to the NMPC, in order for the latter to estimate the optimum insulin infusion rates. For the development and the evaluation of the IIAS, data generated from a Mathematical Model (MM) of a Type 1 diabetes patient have been used. The proposed control strategy is evaluated at multiple meal disturbances, various noise levels and additional time delays. The results indicate that the implemented IIAS is capable of handling multiple meals, which correspond to realistic meal profiles, large noise levels and time delays.

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.