Contributions to exact approaches in combinatorial optimization

The focus of this thesis is to contribute to the development of new, exact solution approaches to different combinatorial optimization problems. In particular, we derive dedicated algorithms for a special class of Traveling Tournament Problems (TTPs), the Dial-A-Ride Problem (DARP), and the Vehicle Routing Problem with Time Windows and Temporal Synchronized Pickup and Delivery (VRPTWTSPD). Furthermore, we extend the concept of using dual-optimal inequalities for stabilized Column Generation (CG) and detail its application to improved CG algorithms for the cutting stock problem, the bin packing problem, the vertex coloring problem, and the bin packing problem with conflicts. In all approaches, we make use of some knowledge about the structure of the problem at hand to individualize and enhance existing algorithms. Specifically, we utilize knowledge about the input data (TTP), problem-specific constraints (DARP and VRPTWTSPD), and the dual solution space (stabilized CG). Extensive computational results proving the usefulness of the proposed methods are reported.

Analysis and numerical solution of the Peterlin viscoelastic model

Liquids and gasses form a vital part of nature. Many of these are complex fluids with non-Newtonian behaviour. We introduce a mathematical model describing the unsteady motion of an incompressible polymeric fluid. Each polymer molecule is treated as two beads connected by a spring. For the nonlinear spring force it is not possible to obtain a closed system of equations, unless we approximate the force law. The Peterlin approximation replaces the length of the spring by the length of the average spring. Consequently, the macroscopic dumbbell-based model for dilute polymer solutions is obtained. The model consists of the conservation of mass and momentum and time evolution of the symmetric positive definite conformation tensor, where the diffusive effects are taken into account. In two space dimensions we prove global in time existence of weak solutions. Assuming more regular data we show higher regularity and consequently uniqueness of the weak solution. For the Oseen-type Peterlin model we propose a linear pressure-stabilized characteristics finite element scheme. We derive the corresponding error estimates and we prove, for linear finite elements, the optimal first order accuracy. Theoretical error of the pressure-stabilized characteristic finite element scheme is confirmed by a series of numerical experiments.

Computing primal solutions with exact arithmetics in SCIP.

The research for exact solutions of mixed integer problems is an active topic in the scientific community. State-of-the-art MIP solvers exploit a floating- point numerical representation, therefore introducing small approximations. Although such MIP solvers yield reliable results for the majority of problems, there are cases in which a higher accuracy is required. Indeed, it is known that for some applications floating-point solvers provide falsely feasible solutions, i.e. solutions marked as feasible because of approximations that would not pass a check with exact arithmetic and cannot be practically implemented. The framework of the current dissertation is SCIP, a mixed integer programs solver mainly developed at Zuse Institute Berlin. In the same site we considered a new approach for exactly solving MIPs. Specifically, we developed a constraint handler to plug into SCIP, with the aim to analyze the accuracy of provided floating-point solutions and compute exact primal solutions starting from floating-point ones. We conducted a few computational experiments to test the exact primal constraint handler through the adoption of two main settings. Analysis mode allowed to collect statistics about current SCIP solutions' reliability. Our results confirm that floating-point solutions are accurate enough with respect to many instances. However, our analysis highlighted the presence of numerical errors of variable entity. By using the enforce mode, our constraint handler is able to suggest exact solutions starting from the integer part of a floating-point solution. With the latter setting, results show a general improvement of the quality of provided final solutions, without a significant loss of performances.

Retinal vascular occlusion after vitrectomy with retrobulbar anesthesia-observational case series and survey of literature

BACKGROUND: Severe postoperative loss of vision has been occasionally reported as a rare complication of retrobulbar anesthesia, and several possible causes have been proposed in the literature. In this work, our own and other investigators' experiences with these complications are surveyed with a view to identifying its pathophysiology. PATIENTS: This observational case series refers to six patients who presented during a 3-month period with occlusion of either the central artery itself (n = 3) or a branch thereof (n = 3) 2-14 days after uneventful vitreoretinal surgery following retrobulbar anesthesia with a commercial preparation of mepivacaine (1% Scandicain®, Astra Chemicals, Sweden) containing methyl- and propyl parahydroxybenzoate as preservatives. RESULTS: Three of the patients carried risk factors, which were medically controlled. In three individuals, vasoocclusion was observed after a second vitreoretinal intervention, which was performed 3-12 months after uneventful primary surgery. Good visual recovery was observed in only one instance. CONCLUSIONS: In patients who were anesthetized with preservative-free mepivacaine, no vasoocclusion occurred. In individuals who were anesthetized with mepivacaine containing the preservatives methyl- and propyl parahydroxybenzoate, a tenfold increase in the incidence of eyes requiring re-operation was documented, with a 2- to 14-day lapse in the onset of vasoocclusion. These findings reveal a possible implication of preservatives contained in the local anesthetic solution for the vasoocclusive events. Due to this potential hazard, the use of preservative-free preparations of local anesthesia in ocular surgery is emphasized in order to prevent this sight-threatening complication.

Educational case series: Mechanisms of drug allergy

Once administered, a drug can activate the immune system by various mechanisms and lead to a large range of clinical manifestations closely related to the type of immune reaction elicited. Administration of the drug can classically result in an immunoglobulin E (IgE)-type sensitization, but can also result in more complex activation of the immune system potentially resulting in severe syndromes, such as the drug-induced hypersensitivity syndrome (DIHS). Although there has been a major increase in our knowledge over the last years, the exact mechanisms of drug allergy are not well understood for most clinical manifestations. A complex interaction between individual characteristics, environmental factors, and the drug itself is usually responsible for adverse reactions to drugs. In this educational review series, we described three cases of drug allergy: first, a child with a typical IgE-mediated drug allergy, second, a child with a non-immediate reaction to penicillin, and in the third patient, we will discuss the drug-induced hypersensitivity syndrome, which is rare but potentially fatal. These cases are correlated to the immune mechanism potentially involved.

A multivariate approach for processing magnetization effects in triggered event-related functional magnetic resonance imaging time series

Triggered event-related functional magnetic resonance imaging requires sparse intervals of temporally resolved functional data acquisitions, whose initiation corresponds to the occurrence of an event, typically an epileptic spike in the electroencephalographic trace. However, conventional fMRI time series are greatly affected by non-steady-state magnetization effects, which obscure initial blood oxygen level-dependent (BOLD) signals. Here, conventional echo-planar imaging and a post-processing solution based on principal component analysis were employed to remove the dominant eigenimages of the time series, to filter out the global signal changes induced by magnetization decay and to recover BOLD signals starting with the first functional volume. This approach was compared with a physical solution using radiofrequency preparation, which nullifies magnetization effects. As an application of the method, the detectability of the initial transient BOLD response in the auditory cortex, which is elicited by the onset of acoustic scanner noise, was used to demonstrate that post-processing-based removal of magnetization effects allows to detect brain activity patterns identical with those obtained using the radiofrequency preparation. Using the auditory responses as an ideal experimental model of triggered brain activity, our results suggest that reducing the initial magnetization effects by removing a few principal components from fMRI data may be potentially useful in the analysis of triggered event-related echo-planar time series. The implications of this study are discussed with special caution to remaining technical limitations and the additional neurophysiological issues of the triggered acquisition.

RAPID SPACE TRAJECTORY GENERATION USING A FOURIER SERIES SHAPE-BASED APPROACH

With the insatiable curiosity of human beings to explore the universe and our solar system, it is essential to benefit from larger propulsion capabilities to execute efficient transfers and carry more scientific equipment. In the field of space trajectory optimization the fundamental advances in using low-thrust propulsion and exploiting the multi-body dynamics has played pivotal role in designing efficient space mission trajectories. The former provides larger cumulative momentum change in comparison with the conventional chemical propulsion whereas the latter results in almost ballistic trajectories with negligible amount of propellant. However, the problem of space trajectory design translates into an optimal control problem which is, in general, time-consuming and very difficult to solve. Therefore, the goal of the thesis is to address the above problem by developing a methodology to simplify and facilitate the process of finding initial low-thrust trajectories in both two-body and multi-body environments. This initial solution will not only provide mission designers with a better understanding of the problem and solution but also serves as a good initial guess for high-fidelity optimal control solvers and increases their convergence rate. Almost all of the high-fidelity solvers enjoy the existence of an initial guess that already satisfies the equations of motion and some of the most important constraints. Despite the nonlinear nature of the problem, it is sought to find a robust technique for a wide range of typical low-thrust transfers with reduced computational intensity. Another important aspect of our developed methodology is the representation of low-thrust trajectories by Fourier series with which the number of design variables reduces significantly. Emphasis is given on simplifying the equations of motion to the possible extent and avoid approximating the controls. These facts contribute to speeding up the solution finding procedure. Several example applications of two and three-dimensional two-body low-thrust transfers are considered. In addition, in the multi-body dynamic, and in particular the restricted-three-body dynamic, several Earth-to-Moon low-thrust transfers are investigated.

Auswirkung des anisotropen Gefüges strahlgeschmolzener Bauteile auf mechanische Eigenschaftswerte

Die Strahlschmelztechnologie entwickelt sich in vielen Anwendungsbereichen zu einer echten Alternative zu den konventionellen Fertigungsverfahren. Dieser Trend wird gerade durch die Verarbeitung von serienidentischen, einkomponentigen Pulvern zur Herstellung metallischer Bauteile verstärkt, wodurch sich wiederum neue Entwicklungs- und Einsatzpotentiale ergeben. Allerdings weisen die Strahlschmelzbauteile keine vollkommen übereinstimmenden Werkstoffkennwerte im Vergleich zu herkömmlich hergestellten Bauteilen auf, wodurch die Akzeptanz durch Industrie und Forschung eingeschränkt wird. Eine exakte Beschreibung (Nachweis) der Materialeigenschaften von strahlgeschmolzenen Bauteilen wird in dem Maße wichtiger, mit dem diese Verfahren zur Fertigung von Endprodukten herangezogen werden. Weiterhin spielt die Anisotropie des Gefüges strahlgeschmolzener Bauteile eine große Rolle. Aus diesem Grund wurden im RTC Duisburg umfangreiche Festigkeitsuntersuchungen (statisch und dynamisch) in Abhängigkeit von der Baulage, des Oberflächenzustandes und verschiedener Belichtungsstrategien durchgeführt. In diesem Vortrag werden ausgewählte Ergebnisse zu den Untersuchungen vorgestellt.

Multinomial goodness-of-fit: large sample tests with survey design correction and exact tests for small samples

I introduce the new mgof command to compute distributional tests for discrete (categorical, multinomial) variables. The command supports largesample tests for complex survey designs and exact tests for small samples as well as classic large-sample x2-approximation tests based on Pearson’s X2, the likelihood ratio, or any other statistic from the power-divergence family (Cressie and Read, 1984, Journal of the Royal Statistical Society, Series B (Methodological) 46: 440–464). The complex survey correction is based on the approach by Rao and Scott (1981, Journal of the American Statistical Association 76: 221–230) and parallels the survey design correction used for independence tests in svy: tabulate. mgof computes the exact tests by using Monte Carlo methods or exhaustive enumeration. mgof also provides an exact one-sample Kolmogorov–Smirnov test for discrete data.

Supersymmetric quantum mechanics on the lattice: II. Exact results

Simulations of supersymmetric field theories with spontaneously broken supersymmetry require in addition to the ultraviolet regularisation also an infrared one, due to the emergence of the massless Goldstino. The intricate interplay between ultraviolet and infrared effects towards the continuum and infinite volume limit demands careful investigations to avoid potential problems. In this paper – the second in a series of three – we present such an investigation for N=2 supersymmetric quantum mechanics formulated on the lattice in terms of bosonic and fermionic bonds. In one dimension, the bond formulation allows to solve the system exactly, even at finite lattice spacing, through the construction and analysis of transfer matrices. In the present paper we elaborate on this approach and discuss a range of exact results for observables such as the Witten index, the mass spectra and Ward identities.

CODE ultra-rapid product series for the IGS

CODE, the Center for Orbit Determination in Europe, is a joint venture of the following four institutions: Astronomical Institute, University of Bern (AIUB), Bern, Switzerland; Federal Office of Topography swisstopo, Wabern, Switzerland; Federal Agency of Cartography and Geodesy (BKG), Frankfurt a. M., Germany; Institut für Astronomische und Physikalische Geodäsie, Technische Universität München (IAPG, TUM), Munich, Germany. It acts as a global analysis center of the International GNSS Service (IGS). The operational computations are performed at AIUB using the latest development version of the Bernese GNSS Software. In this context an ultra-rapid solution series is generated considering GPS and GLONASS satellites. It is updated several times per day and contains 24 hours of observed and 24 hours of predicted orbit interval. More details are available in: Lutz, S., G. Beutler, S. Schaer, R. Dach, A. Jäggi; 2014: CODE's new ultra-rapid orbit and ERP products for the IGS. GPS Solutions. DOI 10.1007/s10291-014-0432-2

CODE rapid product series for the IGS

CODE, the Center for Orbit Determination in Europe, is a joint venture of the following four institutions: Astronomical Institute, University of Bern (AIUB), Bern, Switzerland;Federal Office of Topography swisstopo, Wabern, Switzerland; Federal Agency of Cartography and Geodesy (BKG), Frankfurt a. M., Germany; Institut für Astronomische und Physikalische Geodäsie, Technische Universität München (IAPG, TUM), Munich, Germany. It acts as a global analysis center of the International GNSS Service (IGS). The operational computations are performed at AIUB using the latest development version of the Bernese GNSS Software (Dach et al., 2015). In this context a rapid solution series is generated considering all active GPS and GLONASS satellites. It contains 24 hours of observed orbits and published at the day after the observations.

CODE final product series for the IGS

CODE, the Center for Orbit Determination in Europe, is a joint venture of the following four institutions:Astronomical Institute, University of Bern (AIUB), Bern, Switzerland; Federal Office of Topography swisstopo, Wabern, Switzerland; Federal Agency of Cartography and Geodesy (BKG), Frankfurt a. M., Germany; Institut für Astronomische und Physikalische Geodäsie, Technische Universität München (IAPG, TUM), Munich, Germany. It acts as a global analysis center of the International GNSS Service (IGS). The operational computations are performed at AIUB using the latest development version of the Bernese GNSS Software. In this context a final solution series is generated considering all active GPS and GLONASS satellites. It is published in daily files with a delay of about two weeks.

CODE product series for the IGS-MGEX project

CODE, the Center for Orbit Determination in Europe, is a joint venture of the following four institutions: Astronomical Institute, University of Bern (AIUB), Bern, Switzerland; Federal Office of Topography swisstopo, Wabern, Switzerland; Federal Agency of Cartography and Geodesy (BKG), Frankfurt a. M., Germany; Institut für Astronomische und Physikalische Geodäsie, Technische Universität München (IAPG, TUM), Munich, Germany. It acts as a global analysis center of the International GNSS Service (IGS). The operational computations are performed at AIUB using the latest development version of the Bernese GNSS Software. In this context a multi-GNSS solution is generated considering all active GPS, GLONASS, Galileo, BeiDou (expect for GEOs), and QZSS satellites as a contribution to the IGS-MGEX project. The results are published with a delay of about two weeks.