Library

Description: Consolidation of commodities and coordination of vehicle routes are fundamental features of supply chain management problems. While locations for consolidation and coordination are typically known a priori, in adaptive transportation networks this is not the case. The identification of such consolidation locations forms part of the decision making process. Supply chain management problems integrating the designation of consolidation locations with the coordination of long haul and local vehicle routing is not only challenging to solve, but also very difficult to formulate mathematically. In this paper, the first mathematical model integrating location clustering with long haul and local vehicle routing is proposed. This mathematical formulation is used to develop algorithms to find high quality solutions. A novel parallel framework is developed that combines exact and heuristic methods to improve the search for high quality solutions and provide valid bounds. The results demonstrate that using exact methods to guide heuristic search is an effective approach to find high quality solutions for difficult supply chain management problems.

Description: We previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. The design process of NFEPP was based on mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands, recognizing that GPCRs function differently under pathological versus healthy conditions. We now present an additional and novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels and their dependence on parameters of inflamed and healthy tissue (pH, radicals). The model is validated against in vitro experimental data for the ligands NFEPP and fentanyl at different pH values and radical concentrations. We observe markedly reduced binding affinity and calcium channel inhibition for NFEPP at normal pH compared to lower pH, in contrast to the effect of fentanyl. For increasing radical concentrations, we find enhanced constitutive G-protein activation but reduced ligand binding affinity. Assessing the different effects, the results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.

Description: The chemical diffusion master equation (CDME) describes the probabilistic dynamics of reaction--diffusion systems at the molecular level [del Razo et al., Lett. Math. Phys. 112:49, 2022]; it can be considered the master equation for reaction--diffusion processes. The CDME consists of an infinite ordered family of Fokker--Planck equations, where each level of the ordered family corresponds to a certain number of particles and each particle represents a molecule. The equations at each level describe the spatial diffusion of the corresponding set of particles, and they are coupled to each other via reaction operators --linear operators representing chemical reactions. These operators change the number of particles in the system, and thus transport probability between different levels in the family. In this work, we present three approaches to formulate the CDME and show the relations between them. We further deduce the non-trivial combinatorial factors contained in the reaction operators, and we elucidate the relation to the original formulation of the CDME, which is based on creation and annihilation operators acting on many-particle probability density functions. Finally we discuss applications to multiscale simulations of biochemical systems among other future prospects.

Description: We performed a citation analysis on the Web of Science publications consisting of more than 63 million articles and 1.45 billion citations on 254 subjects from 1981 to 2020. We proposed the Article’s Scientific Prestige (ASP) metric and compared this metric to number of citations (#Cit) and journal grade in measuring the scientific impact of individual articles in the large-scale hierarchical and multi-disciplined citation network. In contrast to #Cit, ASP, that is computed based on the eigenvector centrality, considers both direct and indirect citations, and provides steady-state evaluation cross different disciplines. We found that ASP and #Cit are not aligned for most articles, with a growing mismatch amongst the less cited articles. While both metrics are reliable for evaluating the prestige of articles such as Nobel Prize winning articles, ASP tends to provide more persuasive rankings than #Cit when the articles are not highly cited. The journal grade, that is eventually determined by a few highly cited articles, is unable to properly reflect the scientific impact of individual articles. The number of references and coauthors are less relevant to scientific impact, but subjects do make a difference.

Description: Reaction coordinates (RCs) are indicators of hidden, low-dimensional mechanisms that govern the long-term behavior of high-dimensional stochastic processes. We present a novel and general variational characterization of optimal RCs and provide conditions for their existence. Optimal RCs are minimizers of a certain loss function, and reduced models based on them guarantee a good approximation of the statistical long-term properties of the original high-dimensional process. We show that for slow-fast systems, metastable systems, and other systems with known good RCs, the novel theory reproduces previous insight. Remarkably, for reversible systems, the numerical effort required to evaluate the loss function scales only with the variability of the underlying, low-dimensional mechanism, and not with that of the full system. The theory provided lays the foundation for an efficient and data-sparse computation of RCs via modern machine learning techniques.

Description: This theoretical study concerns a pH oscillator based on the urea-urease reaction confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyse the structure of the phase flow and of the limit cycle, which controls the dynamics for giant vesicles and dominates the pronouncedly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, which are amenable to analytic treatments that are complemented by numerical solutions, and obtain the period and amplitude of the oscillations as well as the parameter domain, where oscillatory behavior persists. We show that the accuracy of these predictions is highly sensitive to the employed reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The faithful modeling of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms.

Description: Tackling societal challenges relating to sustainability requires both an understanding of the underlying complex socio-ecological systems and participation of scientists as well as relevant stakeholders, such as practice experts, decision makers, and citizens. This paper introduces the Decision Theatre Triangle, a method which combines empirical information, mathematical modelling and simulation, and a format for dialogue between scientists and stakeholders. While it builds on previous Decision Theatre work, the new structuring into these three elements emphasizes what is needed for setting up a Decision Theatre for a given challenge. Based on experience with a specific example – sustainable mobility in Germany – it is argued that agent-based models are particularly suitable for Decision Theatres and that the method is useful not only for decision support but also for science communication and co-creation of a deeper knowledge of the system under discussion. As a step towards facilitating a broader use of the Decision Theatre Triangle method, the paper then sketches research needs for each of its three elements, with a focus on mathematical modelling and simulation.

Description: The remarkably complex skeletal systems of the sea stars (Echinodermata, Asteroidea), consisting of hundreds to thousands of individual elements (ossicles), have intrigued investigators for more than 150 years. While the general features and structural diversity of isolated asteroid ossicles have been well documented in the literature, the task of mapping the spatial organization of these constituent skeletal elements in a whole-animal context represents an incredibly laborious process, and as such, has remained largely unexplored. To address this unmet need, particularly in the context of understanding structure-function relationships in these complex skeletal systems, we present an integrated approach that combines micro-computed tomography, semi-automated ossicle segmentation, data visualization tools, and the production of additively manufactured tangible models to reveal biologically relevant structural data that can be rapidly analyzed in an intuitive manner. In the present study, we demonstrate this high-throughput workflow by segmenting and analyzing entire skeletal systems of the giant knobby star, Pisaster giganteus, at four different stages of growth. The in-depth analysis, presented herein, provides a fundamental understanding of the three-dimensional skeletal architecture of the sea star body wall, the process of skeletal maturation during growth, and the relationship between skeletal organization and morphological characteristics of individual ossicles. The widespread implementation of this approach for investigating other species, subspecies, and growth series has the potential to fundamentally improve our understanding of asteroid skeletal architecture and biodiversity in relation to mobility, feeding habits, and environmental specialization in this fascinating group of echinoderms.

Description: For over ten years, the constraint integer programming framework SCIP has been extended by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs (MINLPs). With the recently published version~8.0, these capabilities have been largely reworked and extended. This paper discusses the motivations for recent changes and provides an overview of features that are particular to MINLP solving in SCIP. Further, difficulties in benchmarking global MINLP solvers are discussed and a comparison with several state-of-the-art global MINLP solvers is provided.

Description: Existing planning approaches for onshore wind farm siting and network integration often do not meet minimum cost solutions or social and environmental considerations. In this paper, we develop an approach for the multi-objective optimization of turbine locations and their network connection using a Quota Steiner tree problem. Applying a novel transformation on a known directed cut formulation, reduction techniques, and heuristics, we design an exact solver that makes large problem instances solvable and outperforms generic MIP solvers. Although our case studies in selected regions of Germany show large trade-offs between the objective criteria of cost and landscape impact, small burdens on one criterion can significantly improve the other criteria. In addition, we demonstrate that contrary to many approaches for exclusive turbine siting, network integration must be simultaneously optimized in order to avoid excessive costs or landscape impacts in the course of a wind farm project. Our novel problem formulation and the developed solver can assist planners in decision making and help optimize wind farms in large regions in the future.

Description: The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit of an infinitely large population, may be described by means of reaction-diffusion partial differential equations. Analyzing and understanding the relation between different mathematical models for reaction-diffusion dynamics is a research topic of steady interest. In this work, we explore a route to the hydrodynamic limit of the RDME which uses gradient structures. Specifically, we elaborate on a method introduced in [J. Maas and A. Mielke, J. Stat. Phys., 181 (2020), pp. 2257–2303] in the context of well-mixed reaction networks by showing that, once it is complemented with an appropriate limit procedure, it can be applied to spatially extended systems with diffusion. Under the assumption of detailed balance, we write down a gradient structure for the RDME and use the method in order to produce a gradient structure for its hydrodynamic limit, namely, for the corresponding RDPDE.

Description: With the emergence of ”Big Data” the analysis of large data sets of high-dimensional energy time series in network structures have become feasible. However, building large-scale data-driven and computationally efficient models to accurately capture the underlying spatial and temporal dynamics and forecast the multivariate time series data remains a great challenge. Additional constraints make the problem more challenging to solve with conventional methods. For example, to ensure the security of supply, energy networks require the demand and supply to be balanced. This paper introduces a novel large-scale Hierarchical Network Regression model with Relaxed Balance constraint (HNR-RB) to investigate the network dynamics and predict multistep-ahead flows in the natural gas transmission network, where the total in- and out-flows of the network have to be balanced over a period of time. We concurrently address three main challenges: high dimensionality of networks with more than 100 nodes, unknown network dynamics, and constraint of balanced supply and demand in the network. The effectiveness of the proposed model is demonstrated through a real-world case study of forecasting demand and supply in a large-scale natural gas transmission network. The results demonstrate that HNR-RB outperforms alternative models for short- and mid-term horizons.

Description: This thesis considers the transient gas network control optimization problem for on-shore pipeline-based transmission networks with numerous gas routing options. As input, the problem is given the network's topology, its initial state, and future demands at the boundaries of the network, which prescribe the gas flow exchange and potentially the pressure values. The task is to find a set of future control measures for all the active, i.e., controllable, elements in the network that minimizes a combination of different penalty functions. The problem is examined in the context of a decision support tool for gas network dispatchers. This results in detailed models featuring a diverse set of constraints, large and challenging real-world instances, and demanding time limit requirements. All these factors further complicate the problem, which is already difficult to solve in theory due to the inherent combination of non-linear and combinatorial aspects. Our contributions concern different steps of the process of solving the problem. Regarding the model formulation, we investigate the validity of two common approximations of the gas flow description in transport pipes: neglecting the inertia term and assuming a friction term that linearly depends on the gas flow and the pressure. For both, we examine if they can be applied under real-world conditions by evaluating a large amount of historical state data of the network of our project partner, the gas network operator Open Grid Europe. While we can confirm that it is reasonable to ignore the influence of the inertia term, the friction term linearization leads to significant errors and, as a consequence, cannot be used for describing the general gas flow behavior in transport pipes. As another topic of this thesis, we introduce the target value concept as a more realistic approach to express control actions of dispatchers regarding regulators and compressor stations. Here, we derive the mechanisms defined for target values based on the gas flow principles in pipes and develop a mixed-integer programming model capturing their behavior. The accuracy of this model is demonstrated in comparison to a target-value-based industry-standard simulator. Furthermore, we present two heuristics for the transient gas network control optimization problem featuring target values that are based on approximative models for the target-value-based control and determine the final decisions in a post-processing step. To compare the performance of the two heuristics with the approach of directly solving the corresponding model, we evaluate them on a set of artificially created test instances. Finally, we develop problem-specific algorithms for two variants of the described problem. One considers the control optimization for a single network station, which represents a local operation site featuring a large number of active elements. The used transient model is very detailed and includes a sophisticated representation of the compressor stations. Based on the shortness of the pipes in the station, the corresponding algorithm finds valid solutions by solving a series of stationary model variants as well as a transient rolling horizon approach. As the second variant, we consider the problem on the entire network but assume an approximative model representing the control capabilities of network stations. Aside from a new description of the compression capabilities, we introduce an algorithm that uses a combination of sequential mixed-integer programming, two heuristics based on reduced time horizons, and a specialized dynamic branch-and-bound node limit to determine promising values for the binary variables of the model. Complete solutions for the problem are obtained by fixing the binary values and solving the remaining non-linear program. Both algorithms are investigated in extensive empirical studies based on real-world instances of the corresponding model variants.

Description: Diese Arbeit behandelt das Optimierungsproblem der transienten Gasnetzwerksteuerung von Fernleitungsnetzen auf dem Festland mit einer großen Anzahl möglicher Gastransportrouten. Die Eingabedaten bestehen aus der Netzwerktopologie, dem Anfangszustand des Netzes und zukünftigen Vorgaben an den Randknoten des Netzes, welche den Gaseinfluss und Gasausfluss sowie eine potenzielle Vorgabe von Druckwerten umfassen. Gegeben diese Daten besteht die Aufgabe besteht darin, eine Menge an zukünftigen Steuerungsentscheidungen für alle aktiven, also steuerbaren, Elemente des Netzes zu finden, sodass eine Kombination von Straffunktionen minimiert wird. Das Problem wird in dieser Arbeit im Rahmen der Erstellung eines entscheidungsunterstützenden Systems für Dispatcher betrachtet, welche das Gasnetz steuern. Dies resultiert in einer detaillierten Modellierung mit einer Vielzahl von Nebenbedingungen, großen und herausfordernden realistischen Instanzen sowie anspruchsvollen Vorgaben zur maximalen Laufzeit. Diese Eigenschaften erhöhen die Komplexität des Problems, welches bereits in der Theorie auf Grund der inhärenten Kombination von nichtlinearen und kombinatorischen Aspekten schwierig zu lösen ist. Die Beiträge dieser Arbeit betreffen verschiedene Schritte des Prozesses zur Lösung des Problems. Bezüglich der Modellformulierung werden zwei übliche Approximationen der Gasflussbeschreibung in Fernleitungsrohren auf Validität überprüft: die Vernachlässigung des Trägheitsterms und die Annahme einer linearisierten Beschreibung des Reibungsterms. Für beide Approximationen wird untersucht, ob sie für reale Gasflussbedingungen zulässig sind. Dazu wird eine große Anzahl historischer Netzzustandsdaten des Gasnetzbetreibers Open Grid Europe ausgewertet. Während bestätigt werden kann, dass eine Vernachlässigung des Trägheitsterms unter Realbedingungen angemessen ist, führt die Linearisierung des Reibungsterms zu signifikanten Fehlern und kann daher nicht für die allgemeine Beschreibung des Gasflusses in Fernleitungsrohren verwendet werden. In einem weiteren Teil dieser Arbeit wird das Konzept der Sollwerte eingeführt. Mit diesen ist eine realistischere Beschreibung der Steuerungsbefehle möglich, welche den Dispatchern für Regler und Verdichterstationen zur Verfügung stehen. Der Sollwertmechanismus wird basierend auf den Gasflussprinzipien in Rohrleitungen hergeleitet, um anschließend ein gemischt-ganzzahliges Programm zu entwickeln, welches das entsprechende Verhalten erzeugt. Die Präzision dieses Modells wird durch einen Vergleich mit einem Simulator von Industriestandard sichergestellt, welcher auf Sollwerten basiert. Außerdem werden zwei Heuristiken für das Optimierungsproblem der transienten Gasnetzwerksteuerung mit Sollwertmodellierung vorgestellt. Diese basieren auf approximativen Modellen für die Sollwertsteuerung und ermitteln die letztendlichen Steuerungsentscheidungen in einer nachgelagerten Routine. Basierend auf künstlich erzeugten Testinstanzen werden die Heuristiken schließlich mit dem direkten Lösen des entsprechenden Modells verglichen. Zudem werden in dieser Arbeit problemspezifische Algorithmen für zwei Varianten des beschriebenen Optimierungsproblems entwickelt. Die erste Variante betrachtet das Gasnetzwerksteuerungsproblem beschränkt auf eine einzelne Netzstation, die lokale Betriebsstellen darstellen und über eine Vielzahl an aktiven Steuerungselementen verfügen. Das entsprechende transiente Modell ist sehr detailliert und beinhaltet eine differenzierte Beschreibung der Verdichterstationen. Der problemspezifische Algorithmus basiert auf der Kürze der Rohre innerhalb der Station und findet zulässige Lösungen durch das Lösen von stationären Varianten des Modells sowie der Nutzung eines transienten Rolling-Horizon Ansatzes. In der zweiten Problemvariante wird das gesamte Gasnetz betrachtet, wobei eine vereinfachte Modellierung der Steuerungsmöglichkeiten innerhalb von Netzstationen angenommen wird. Neben einer neuen Beschreibung der Verdichtungsmöglichkeiten einer Station wird ebenfalls ein problemspezifischer Algorithmus entwickelt. Dieser erstellt aussichtsreiche Werte für die Binärvariablen und nutzt dafür eine Kombination aus sequenzieller gemischt-ganzzahliger Programmierung, zwei auf verkürzten Zeithorizonten basierenden Heuristiken und eine spezialisierte dynamische Obergrenze für die Anzahl der Branch-and-Bound-Knoten. Diese Teillösungen werden durch eine Fixierung der binären Variablen und das anschließende Lösen des restlichen nichtlinearen Programms komplettiert. Die Güte beider Algorithmen wird in umfangreichen empirischen Experimenten untersucht, welche reale Instanzen der jeweiligen Problemvarianten betrachten.

Description: Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a 4% decrease in solve time, and an 8% decrease in number of nodes over affected instances of MIPLIB 2017.

Description: The concept of shape correspondence describes a relation between two or more shapes of the same class. It often consists of a mapping between points on semantically similar locations of all shapes. One possible application for shape correspondence in medicine is the automatic location of anatomical landmarks. Another popular application is the construction of statistical shape models. These models are an established way to represent geometric variation of anatomical shapes in a compact way. Possible applications range from the generation of shapes and reconstruction tasks to disease classification. This thesis aims to investigate unsupervised methods that can be used to estimate such a correspondence on anatomical shapes. While most methods used in the medical domain focus on classical optimization algorithms to establish correspondence, the broader computer vision domain developed a versatile field of data-driven methods. Recently, the new shape model FlowSSM was introduced, which does not require predefined correspondences for training as it generates them itself. As the performance of the shape model is quite competitive, it is natural to assume that the generated correspondences are of high quality as well. For this reason, we evaluate the quality of the correspondences generated by FlowSSM within this thesis. Furthermore, we modify the method by adding a second loss term that minimizes geodesic distortions. This is done to favor isometric deformations which can lead to better correspondences. We compare the results with two established methods from the medical domain, LDDMM and Meshmonk. Furthermore, we investigate the performance of a fourth method called Neuromoph. This data-driven method comes from the wider computer vision field and was not tested on anatomical data yet. All methods are evaluated with a set of different metrics. This includes metrics to assess the quality of the resulting meshes, a sparse correspondence error on anatomical landmarks, and metrics to measure the quality of the resulting shape models. Furthermore, we test all methods on three datasets with different degrees of geometric variation, namely liver, distal femur and face. We show that FlowSSM produces correspondences with state-of-the-art quality. Moreover, our modification further improved the quality of correspondences at a global level. Nevertheless, there is no clear ranking between all methods, as the results differ between metrics and datasets. Thereby, we can show that there are different qualities to a proper correspondence which are reflected in the different metrics. It is therefore strongly recommendable to choose a correspondence estimation method specifically for the problem at hand.

Description: Das Konzept der Formkorrespondenz zwischen 3D-Objekten einer Klasse beschreibt eine Beziehung zwischen den Instanzen (oft Punkten) der unterschiedlichen Objekten. Hierbei werden Punkte, die an semantisch gleichwertigen Orten liegen, miteinander in Verbindung gebracht. Eine mögliche Anwednung der Formkorrespondenz im medizinischen Bereich ist daher die automatisierte Lokalisierung von anatomischen Landmarken. Eine weitere Anwendung ist das Erstellen von statistischen Formmodellen. Mit diesen kann die geometrische Variation anatomischer Formen kompakt abgebildet werden. Medizinische Anwendungen reichen dabei von der einfachen Formgenerierung zu komplexeren Rekonstruktionsaufgaben und der Klassifizierung von gesunden und pathologischen Formen. In dieser Arbeit werden unterschiedliche Methoden zur Erzeugung von Formkorrespondenzen untersucht. Die entsprechende Literatur im medizinischen Bereich verwendet hierzu meist Methoden, die das klassische Optimierungsproblem einer nichtrigiden Transformation lösen. Im Computer Vision Bereich wurden in den letzten Jahren auch einige datengetriebene Methoden zur Korrespondenzgenerierung veröffentlicht. Im letzten Jahr wurde außerdem die Methode FlowSSM zur Erstellung statistischer Formmodelle vorgestellt, die nicht auf korrespondierenden Oberflächen basiert, sondern diese selbst erzeugt. Da FlowSSM trotzdem konkurenzfähige Ergebnisse erzielt, ist naheliegend, dass auch die zugrundeliegenden, selbst generierten Korrespondenzen von hoher Qualität sind. Innerhalb dieser Arbeit wird daher die Qualität der von FlowSSM erzeugten Korrespondenzen evaluiert. Außerdem wird die Methode um eine zusätzliche Kostenfunktion erweitert, die geod#tische Verzerrungen verhindern soll. Dadurch sollen nichtisometrische Deformationen vermieden werden, wodurch die Qualität der resultierenden Korrenspondenzen gesteigert werden kann. Die Ergebnisse von FlowSSM werden mit zwei etablierten Methoden aus dem medizinischen Bereich, LDDMM und Meshmonk, verglichen. Außerdem wird NeuroMorph, eine aktuelle, datengetriebene Methode aus dem Bereich des maschinellen Sehens getestet. Letztere wurde bisher noch nicht auf medizinischen Daten evaluiert. Die Bewertung aller generierten Korrespondenzen basiert auf ausgewählten indirekten Metriken. Hierzu gehört auch die Performance bei konkreten Anwendungsfällen wie der Lokalisierung von Landmarken und dem Erstellen von statistischen Formmodellen. Im Rahmen der Arbeit wird gezeigt, dass FlowSSM Korrespondenzen produziert, deren Qualität dem aktuellen State-of-the-art entspricht. Durch das Hinzufügen der zweiten Kostenfunktion wird die Qualität der Korrespondenzen auf einem globalen Level noch weiter gesteigert. Prinzipiell lässt sich jedoch keine Hierarchie zwischen den Methoden ableiten, da die Performance stark innerhalb der untersuchten Metriken und Datensätzen schwankt. Die Auswahl einer passenden Methode sollte sich daher vor allem am Anwendungsfall orientieren.

Description: The Periodic Event Scheduling Problem (PESP) is the central mathematical tool for periodic timetable optimization in public transport. PESP can be formulated in several ways as a mixed-integer linear program with typically general integer variables. We investigate the split closure of these formulations and show that split inequalities are identical with the recently introduced flip inequalities. While split inequalities are a general mixed-integer programming technique, flip inequalities are defined in purely combinatorial terms, namely cycles and arc sets of the digraph underlying the PESP instance. It is known that flip inequalities can be separated in pseudo-polynomial time. We prove that this is best possible unless P $=$ NP, but also observe that the complexity becomes linear-time if the cycle defining the flip inequality is fixed. Moreover, introducing mixed-integer-compatible maps, we compare the split closures of different formulations, and show that reformulation or binarization by subdivision do not lead to stronger split closures. Finally, we estimate computationally how much of the optimality gap of the instances of the benchmark library PESPlib can be closed exclusively by split cuts, and provide better dual bounds for five instances.

Description: The current cut selection algorithm used in mixed-integer programming solvers has remained largely unchanged since its creation. In this paper, we propose a set of new cut scoring measures, cut filtering techniques, and stopping criteria, extending the current state-of-the-art algorithm and obtaining a 5\% performance improvement for SCIP over the MIPLIB 2017 benchmark set.

Description: Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a $4\%$ decrease in solve time, and an $8\%$ decrease in number of nodes over affected instances of MIPLIB 2017.

Description: Solving high-dimensional partial differential equations is a recurrent challenge in economics, science and engineering. In recent years, a great number of computational approaches have been developed, most of them relying on a combination of Monte Carlo sampling and deep learning based approximation. For elliptic and parabolic problems, existing methods can broadly be classified into those resting on reformulations in terms of backward stochastic differential equations (BSDEs) and those aiming to minimize a regression-type L2-error (physics-informed neural networks, PINNs). In this paper, we review the literature and suggest a methodology based on the novel diffusion loss that interpolates between BSDEs and PINNs. Our contribution opens the door towards a unified understanding of numerical approaches for high-dimensional PDEs, as well as for implementations that combine the strengths of BSDEs and PINNs. The diffusion loss furthermore bears close similarities to (least squares) temporal difference objectives found in reinforcement learning. We also discuss eigenvalue problems and perform extensive numerical studies, including calculations of the ground state for nonlinear Schr ¨odinger operators and committor functions relevant in molecular dynamics.

Description: Using the recently proposed maximal quadratic-free sets and the well-known monoidal strengthening procedure, we show how to improve inter- section cuts for quadratically-constrained optimization problems by exploiting integrality requirements. We provide an explicit construction that allows an efficient implementation of the strengthened cuts along with computational results showing their improvements over the standard intersection cuts. We also show that, in our setting, there is unique lifting which implies that our strengthening procedure is generating the best possible cut coefficients for the integer variables.

Description: Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method.

Description: In this article, we propose a deep learning-based algorithm for the classification of crop types from Sentinel-1 and Sentinel-2 time series data which is based on the celebrated transformer architecture. Crucially, we enable our algorithm to do early classification, i.e., predict crop types at arbitrary time points early in the year with a single trained model (progressive intra-season classification). Such early season predictions are of practical relevance for instance for yield forecasts or the modeling of agricultural water balances, therefore being important for the public as well as the private sector. Furthermore, we improve the mechanism of combining different data sources for the prediction task, allowing for both optical and radar data as inputs (multi-modal data fusion) without the need for temporal interpolation. We can demonstrate the effectiveness of our approach on an extensive data set from three federal states of Germany reaching an average F1 score of 0.92 using data of a complete growing season to predict the eight most important crop types and an F1 score above 0.8 when doing early classification at least one month before harvest time. In carefully chosen experiments, we can show that our model generalizes well in time and space.

Description: Recently, a series of papers proposed deep learning-based approaches to sample from unnormalized target densities using controlled diffusion processes. In this work, we identify these approaches as special cases of the Schrödinger bridge problem, seeking the most likely stochastic evolution between a given prior distribution and the specified target. We further generalize this framework by introducing a variational formulation based on divergences between path space measures of time-reversed diffusion processes. This abstract perspective leads to practical losses that can be optimized by gradient-based algorithms and includes previous objectives as special cases. At the same time, it allows us to consider divergences other than the reverse Kullback-Leibler divergence that is known to suffer from mode collapse. In particular, we propose the so-called log-variance loss, which exhibits favorable numerical properties and leads to significantly improved performance across all considered approaches.

Description: This Package implements a variation of the Voronoi Graph Traversal algorithm by Polianskii and Pokorny [1]. It constructs a Voronoi Diagram from a set of points by performing a random walk on the graph of the vertices of the diagram. Unlike many other Voronoi implementations this algorithm is not limited to 2 or 3 dimensions and promises good performance even in higher dimensions.

Description: The optical inspection of the surfaces of diode lasers, especially the p-sides and facets, is an essential part of the quality control in the laser fabrication procedure. With reliable, fast, and flexible optical inspection processes, it is possible to identify and eliminate defects, accelerate device selection, reduce production costs, and shorten the cycle time for product development. Due to a vast range of rapidly changing designs, structures, and coatings, however, it is impossible to realize a practical inspection with conventional software. In this work, we therefore suggest a deep learning based defect detection algorithm that builds on a Faster Regional Convolutional Neural Network (Faster R-CNN) as a core component. While for related, more general object detection problems, the application of such models is straightforward, it turns out that our task exhibits some additional challenges. On the one hand, a sophisticated pre- and postprocessing of the data has to be deployed to make the application of the deep learning model feasible. On the other hand, we find that creating labeled training data is not a trivial task in our scenario, and one has to be extra careful with model evaluation. We can demonstrate in multiple empirical assessments that our algorithm can detect defects in diode lasers accurately and reliably in most cases. We analyze the results of our production-ready pipeline in detail, discuss its limitations and provide some proposals for further improvements.

Description: It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95\% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest.

Description: A depinning transition is observed in a variety of contexts when a certain threshold force must be applied to drive a system out of an immobile state. A well-studied example is the depinning of colloidal particles from a corrugated landscape, whereas its active-matter analogue has remained unexplored. We discuss how active noise due to self-propulsion impacts the nature of the transition: it causes a change of the critical exponent from 1/2 for quickly reorienting particles to 3/2 for slowly reorienting ones. In between these analytically tractable limits, the drift velocity exhibits a superexponential behavior as is corroborated by high-precision data. Giant diffusion phenomena occur in the two different regimes. Our predictions appear amenable to experimental tests, lay foundations for insight into the depinning of collective variables in active matter, and are relevant for any system with a saddle-node bifurcation in the presence of a bounded noise.

Description: We present a data-driven method to learn and understand collective variables for noisy voter model dynamics on networks. A collective variable (CV) is a projection of the high-dimensional system state into a low-dimensional space that preserves the essential dynamical information. Thus, CVs can be used to improve our understanding of complex emergent behaviors and to enable an easier analysis and prediction. We demonstrate our method using three example networks: the stochastic block model, a ring-shaped graph, and a scale-free network generated by the Albert--Barabási model. Our method combines the recent transition manifold approach with a linear regression step to produce interpretable CVs that describe the role and importance of each network node.

Description: Agent-based models (ABMs) provide an intuitive and powerful framework for studying social dynamics by modeling the interactions of individuals from the perspective of each individual. In addition to simulating and forecasting the dynamics of ABMs, the demand to solve optimization problems to support, for example, decision-making processes naturally arises. Most ABMs, however, are non-deterministic, high-dimensional dynamical systems, so objectives defined in terms of their behavior are computationally expensive. In particular, if the number of agents is large, evaluating the objective functions often becomes prohibitively time-consuming. We consider data-driven reduced models based on the Koopman generator to enable the efficient solution of multi-objective optimization problems involving ABMs. In a first step, we show how to obtain data-driven reduced models of non-deterministic dynamical systems (such as ABMs) that depend on potentially nonlinear control inputs. We then use them in the second step as surrogate models to solve multi-objective optimal control problems. We first illustrate our approach using the example of a voter model, where we compute optimal controls to steer the agents to a predetermined majority, and then using the example of an epidemic ABM, where we compute optimal containment strategies in a prototypical situation. We demonstrate that the surrogate models effectively approximate the Pareto-optimal points of the ABM dynamics by comparing the surrogate-based results with test points, where the objectives are evaluated using the ABM. Our results show that when objectives are defined by the dynamic behavior of ABMs, data-driven surrogate models support or even enable the solution of multi-objective optimization problems.

Description: It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95\% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest.

Description: We develop a functional framework suitable for the treatment of partial differential equations and variational problems posed on evolving families of Banach spaces. We propose a definition for the weak time derivative which does not rely on the availability of an inner product or Hilbertian structure and explore conditions under which the spaces of weakly differentiable functions (with values in an evolving Banach space) relate to the classical Sobolev--Bochner spaces. An Aubin--Lions compactness result in this setting is also proved. We then analyse several concrete examples of function spaces over time-evolving spatial domains and hypersurfaces for which we explicitly provide the definition of the time derivative and verify isomorphism properties with the aforementioned Sobolev--Bochner spaces. We conclude with the formulation and proof of well posedness for a class of nonlinear monotone problems on an abstract evolving space (generalising in particular the evolutionary p-Laplace equation on a moving domain or surface) and identify some additional evolutionary problems that can be appropriately formulated with the abstract setting developed in this work.

Description: The Feasibility Pump (FP) is one of the best-known primal heuristics for mixed-integer programming (MIP): more than 15 papers suggested various modifications of all of its steps. So far, no variant considered information across multiple iterations, but all instead maintained the principle to optimize towards a single reference integer point. In this paper, we evaluate the usage of multiple reference vectors in all stages of the FP algorithm. In particular, we use LP-feasible vectors obtained during the main loop to tighten the variable domains before entering the computationally expensive enumeration stage. Moreover, we consider multiple integer reference vectors to explore further optimizing directions and introduce alternative objective scaling terms to balance the contributions of the distance functions and the original MIP objective. Our computational experiments demonstrate that the new method can improve performance on general MIP test sets. In detail, our modifications provide a 29.3% solution quality improvement and 4.0% running time improvement in an embedded setting, needing 16.0% fewer iterations over a large test set of MIP instances. In addition, the method’s success rate increases considerably within the first few iterations. In a standalone setting, we also observe a moderate performance improvement, which makes our version of FP suitable for the two main use-cases of the algorithm.

Description: We present a fully computer-assisted proof system for solving a particular family of problems in Extremal Combinatorics. Existing techniques using Flag Algebras have proven powerful in the past, but have so far lacked a computational counterpart to derive matching constructive bounds. We demonstrate that common search heuristics are capable of finding constructions far beyond the reach of human intuition. Additionally, the most obvious downside of such heuristics, namely a missing guarantee of global optimality, can often be fully eliminated in this case through lower bounds and stability results coming from the Flag Algebra approach. To illustrate the potential of this approach, we study two related and well-known problems in Extremal Graph Theory that go back to questions of Erdős from the 60s. Most notably, we present the first major improvement in the upper bound of the Ramsey multiplicity of the complete graph on 4 vertices in 25 years, precisely determine the first off-diagonal Ramsey multiplicity number, and settle the minimum number of independent sets of size four in graphs with clique number strictly less than five.

Description: Fibrotic tissue is one of the main risk factors for cardiac arrhythmias. It is therefore a key component in computational studies. In this work, we compare the monodomain equation to two eikonal models for cardiac electrophysiology in the presence of fibrosis. We show that discontinuities in the conductivity field, due to the presence of fibrosis, introduce a delay in the activation times. The monodomain equation and eikonal-diffusion model correctly capture these delays, contrarily to the classical eikonal equation. Importantly, a coarse space discretization of the monodomain equation amplifies these delays, even after accounting for numerical error in conduction velocity. The numerical discretization may also introduce artificial conduction blocks and hence increase propagation complexity. Therefore, some care is required when comparing eikonal models to the discretized monodomain equation.

Description: The maximum-cut problem is one of the fundamental problems in combinatorial optimization. With the advent of quantum computers, both the maximum-cut and the equivalent quadratic unconstrained binary optimization problem have experienced much interest in recent years. This article aims to advance the state of the art in the exact solution of both problems—by using mathematical programming techniques. The main focus lies on sparse problem instances, although also dense ones can be solved. We enhance several algorithmic components such as reduction techniques and cutting-plane separation algorithms, and combine them in an exact branch-and-cut solver. Furthermore, we provide a parallel implementation. The new solver is shown to significantly outperform existing state-of-the-art software for sparse maximum-cut and quadratic unconstrained binary optimization instances. Furthermore, we improve the best known bounds for several instances from the 7th DIMACS Challenge and the QPLIB, and solve some of them (for the first time) to optimality.

Description: Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017 and a neural network verification data set. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP.

Description: Concrete plays a central role as the standard building material in civil engineering. Experimental characterization of the concrete microstructure and a description of failure mechanisms are important to understand the concrete’s mechanical properties. Computed tomography is a powerful source of information as it yields 3d images of concrete specimens. However, complete visual inspection is often infeasible due to very large image sizes. Hence, automatic methods for crack detection and segmentation are needed. A region-growing algorithm and a 3d U-Net showed promising results in a previous study. Cracks in normal concrete and high-performance concrete that were initiated via tensile tests were investigated. Here, the methods are validated on a more diverse set of concrete types and crack characteristics. Adequate adaptions of the methods are necessary to deal with the complex crack structures. The segmentation results are assessed qualitatively and compared to those of a template matching algorithm which is well-established in industry.

Description: Data are often subject to some degree of uncertainty, whether aleatory or epistemic. This applies both to experimental data acquired with sensors as well as to simulation data. Displaying these data and their uncertainty faithfully is crucial for gaining knowledge. Specifically, the effective communication of the uncertainty can influence the interpretation of the data and the user’s trust in the visualization. However, uncertainty-aware visualization has gotten little attention in molecular visualization. When using the established molecular representations, the physicochemical attributes of the molecular data usually already occupy the common visual channels like shape, size, and color. Consequently, to encode uncertainty information, we need to open up another channel by using feature lines. Even though various line variables have been proposed for uncertainty visualizations, they have so far been primarily used for two-dimensional data and there has been little perceptual evaluation. Thus, we conducted two perceptual studies to determine the suitability of the line variables blur, dashing, grayscale, sketchiness, and width for distinguishing several values in molecular visualizations. While our work was motivated by uncertainty visualization, our techniques and study results also apply to other types of scalar data.

Description: Mixed-integer linear programming (MILP) plays a crucial role in the field of mathematical optimization and is especially relevant for practical applications due to the broad range of problems that can be modeled in that fashion. The vast majority of MILP solvers employ the LP-based branch-and-cut approach. As the name suggests, the linear programming (LP) subproblems that need to be solved therein influence their behavior and performance significantly. This thesis explores the impact of various LP solvers as well as LP solving techniques on the constraint integer programming framework SCIP Optimization Suite. SCIP allows for comparisons between academic and open-source LP solvers like Clp and SoPlex, as well as commercially developed, high-end codes like CPLEX, Gurobi, and Xpress. We investigate how the overall performance and stability of an MILP solver can be improved by new algorithmic enhancements like LP solution polishing and persistent scaling that we have implemented in the LP solver SoPlex. The former decreases the fractionality of LP solutions by selecting another vertex on the optimal hyperplane of the LP relaxation, exploiting degeneracy. The latter provides better numerical properties for the LP solver throughout the MILP solving process by preserving and extending the initial scaling factors, effectively also improving the overall performance of SCIP. Both enhancement techniques are activated by default in the SCIP Optimization Suite. Additionally, we provide an analysis of numerical conditions in SCIP through the lens of the LP solver by comparing different measures and how these evolve during the different stages of the solving process. A side effect of our work on this topic was the development of TreeD: a new and convenient way of presenting the search tree interactively and animated in the three-dimensional space. This visualization technique facilitates a better understanding of the MILP solving process of SCIP. Furthermore, this thesis presents the various algorithmic techniques like the row representation and iterative refinement that are implemented in SoPlex and that distinguish the solver from other simplex-based codes. Although it is often not as performant as its competitors, SoPlex demonstrates the ongoing research efforts in the field of linear programming with the simplex method. Aside from that, we demonstrate the rapid prototyping of algorithmic ideas and modeling approaches via PySCIPOpt, the Python interface to the SCIP Optimization Suite. This tool allows for convenient access to SCIP's internal data structures from the user-friendly Python programming language to implement custom algorithms and extensions without any prior knowledge of SCIP's programming language C. TreeD is one such example, demonstrating the use of several Python libraries on top of SCIP. PySCIPOpt also provides an intuitive modeling layer to formulate problems directly in the code without having to utilize another modeling language or framework. All contributions presented in this thesis are readily accessible in source code in SCIP Optimization Suite or as separate projects on the public code-sharing platform GitHub.

Description: Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case.

Description: Presolving has become an essential component of modern mixed integer program (MIP) solvers, both in terms of computational performance and numerical robustness. In this paper, we present PaPILO, a new C++ header-only library that provides a large set of presolving routines for MIP and linear programming problems from the literature. The creation of PaPILO was motivated by the current lack of (a) solver-independent implementations that (b) exploit parallel hardware and (c) support multiprecision arithmetic. Traditionally, presolving is designed to be fast. Whenever necessary, its low computational overhead is usually achieved by strict working limits. PaPILO’s parallelization framework aims at reducing the computational overhead also when presolving is executed more aggressively or is applied to large-scale problems. To rule out conflicts between parallel presolve reductions, PaPILO uses a transaction-based design. This helps to avoid both the memory-intensive allocation of multiple copies of the problem and special synchronization between presolvers. Additionally, the use of Intel’s Threading Building Blocks library aids PaPILO in efficiently exploiting recursive parallelism within expensive presolving routines, such as probing, dominated columns, or constraint sparsification. We provide an overview of PaPILO’s capabilities and insights into important design choices.

Description: It has recently been shown that ISTA, an unaccelerated optimization method, presents sparse updates for the ℓ1-regularized undirected personalized PageRank problem (Fountoulakis et al., 2019), leading to cheap iteration complexity and providing the same guarantees as the approximate personalized PageRank algorithm (APPR) (Andersen et al., 2006). In this work, we design an accelerated optimization algorithm for this problem that also performs sparse updates, providing an affirmative answer to the COLT 2022 open question of Fountoulakis and Yang (2022). Acceleration provides a reduced dependence on the condition number, while the dependence on the sparsity in our updates differs from the ISTA approach. Further, we design another algorithm by using conjugate directions to achieve an exact solution while exploiting sparsity. Both algorithms lead to faster convergence for certain parameter regimes. Our findings apply beyond PageRank and work for any quadratic objective whose Hessian is a positive-definite 푀-matrix.

Description: Stochastic optimization (SO) is a classical approach for optimization under uncertainty that typically requires knowledge about the probability distribution of uncertain parameters. Because the latter is often unknown, distributionally robust optimization (DRO) provides a strong alternative that determines the best guaranteed solution over a set of distributions (ambiguity set). In this work, we present an approach for DRO over time that uses online learning and scenario observations arriving as a data stream to learn more about the uncertainty. Our robust solutions adapt over time and reduce the cost of protection with shrinking ambiguity. For various kinds of ambiguity sets, the robust solutions converge to the SO solution. Our algorithm achieves the optimization and learning goals without solving the DRO problem exactly at any step. We also provide a regret bound for the quality of the online strategy that converges at a rate of O(log T/T−−√), where T is the number of iterations. Furthermore, we illustrate the effectiveness of our procedure by numerical experiments on mixed-integer optimization instances from popular benchmark libraries and give practical examples stemming from telecommunications and routing. Our algorithm is able to solve the DRO over time problem significantly faster than standard reformulations.

Description: Small ring nitrogen heterocycles, azabicyclobutanes and azirines, were investigated by computational methods in order to address the discrepancy between their regioisomers 1- and 2-azabicyclobutane and 1H- and 2H-azirines. Both 1-azabicyclobutane and 2H-azirine are well known synthetic starting points to larger nitrogen heterocycles whereas 2-azabicyclobutane and 1H-azirine and their derivatives have yet to be reported as isolable compounds. Calculated parameters such as structure, base strength (proton affinities), NICS values and enthalpies of formation from which strain energies are derived are reported. The destabilization of the less stable regioisomers is attributed to homoantiaromaticity in 2-azabicyclobutane and antiaromaticity in 1H-azirine. Two stereoisomers exist for 2-azabicyclobutane with the endo- stereoisomer being more stable. This phenomenon is indicative of the hydrogen bond acceptor properties of the neighboring cyclpropane and the π-bond character of the central bond in 2-azabicyclobutane.

Description: It is important to design multi-energy supply systems optimally in consideration of their operations for variations in energy demands. An approach for efficiently solving such an optimal design problem with a large number of periods for variations in energy demands is to derive an approximate optimal design solution by time series aggregation. However, such an approach does not provide any information on the accuracy for the optimal value of the objective function. In this paper, an effective approach for time series aggregation is proposed to derive an approximate optimal design solution and evaluate a proper gap between the upper and lower bounds for the optimal value of the objective function based on a mixed-integer linear model. In accordance with aggregation, energy demands are relaxed to uncertain parameters and the problem for deriving an approximate optimal design solution and evaluating it is transformed to a three-level optimization problem, and it is solved by applying both the robust and hierarchical optimization methods. A case study is conducted on a cogeneration system with a practical configuration, and it turns out that the proposed approach enables one to derive much smaller gaps as compared with those obtained by a conventional approach.

Description: We propose a globally-accelerated, first-order method for the optimization of smooth and (strongly or not) geodesically-convex functions in a wide class of Hadamard manifolds. We achieve the same convergence rates as Nesterov’s accelerated gradient descent, up to a multiplicative geometric penalty and log factors. Crucially, we can enforce our method to stay within a compact set we define. Prior fully accelerated works \emph{resort to assuming} that the iterates of their algorithms stay in some pre-specified compact set, except for two previous methods of limited applicability. For our manifolds, this solves the open question in (Kim and Yang, 2022) about obtaining global general acceleration without iterates assumptively staying in the feasible set.In our solution, we design an accelerated Riemannian inexact proximal point algorithm, which is a result that was unknown even with exact access to the proximal operator, and is of independent interest. For smooth functions, we show we can implement the prox step inexactly with first-order methods in Riemannian balls of certain diameter that is enough for global accelerated optimization.

Description: Due to the current and foreseeable shifts towards carbon dioxide neutral energy production, which will likely result in balancing fluctuating renewable energy generation by transforming power-to-gas-to-power as well as building a large-scale hydrogen transport infrastructure, the trading and transport operations of gas will become more dynamic, volatile, and hence also less predictable. Therefore, computer-aided support in terms of rapid simulation and control optimization will further broaden its importance for gas network dispatching. In this paper, we aim to contribute and openly publish two new mathematical models for regulators, also referred to as control valves, which together with compressors make up the most complex and involved types of active elements in gas network infrastructures. They provide direct control over gas networks but are in turn controlled via target values, also known as set-point values, themselves. Our models incorporate up to six dynamical target values to define desired transient states for the elements' local vicinity within the network. That is, each pair of every two target values defines a bounding box for the inlet pressure, outlet pressure as well as the passing mass flow of gas. In the proposed models, those target values are prioritized differently and are constantly in competition with each other, which can only be resolved dynamically at run-time of either a simulation or optimization process. Besides careful derivation, we compare simulation and optimization results with predictions of the widely adopted commercial simulation tool SIMONE, serving as our substitute for actual real-world transport operations.

Description: Tooth enamel is the hardest tissue in human organism, formed by prism layers in regularly alternating directions. These prisms form the Hunter-Schreger Bands (HSB) pattern when under side illumination, which is composed of light and dark stripes resembling fingerprints. We have shown in previous works that HSB pattern is highly variable, seems to be unique for each tooth and can be used as a biometric method for human identification. Since this pattern cannot be acquired with sensors, the HSB region in the digital photograph must be identified and correctly segmented from the rest of the tooth and background. Although these areas can be manually removed, this process is not reliable as excluded areas can vary according to the individual‘s subjective impression. Therefore, the aim of this work was to develop an algorithm that automatically selects the region of interest (ROI), thus, making the entire biometric process straightforward. We used two different approaches: a classical image processing method which we called anisotropy-based segmentation (ABS) and a machine learning method known as U-Net, a fully convolutional neural network. Both approaches were applied to a set of extracted tooth images. U-Net with some post processing outperformed ABS in the segmentation task with an Intersection Over Union (IOU) of 0.837 against 0.766. Even with a small dataset, U-Net proved to be a potential candidate for fully automated in-mouth application. However, the ABS technique has several parameters which allow a more flexible segmentation with interactive adjustments specific to image properties.

Description: Classic models to derive a timetable for public transport often face a chicken-and-egg situation: A good timetable should offer passengers routes with small travel times, but the route choice of passengers depends on the timetable. While models that fix passenger routes were frequently considered in the literature, integrated models that simultaneously optimize timetables and passenger routes have seen increasing attention lately. This creates a growing need for a set of instances that allows to test and compare new algorithmic developments for the integrated problem. Our paper addresses this requirement by presenting TimPassLib, a new benchmark library of instances for integrated periodic timetabling and passenger routing.

Description: Manual processing of tomographic data volumes, such as interactive image segmentation in medicine or paleontology, is considered a time-consuming and cumbersome endeavor. Immersive volume sculpting stands as a potential solution to improve its efficiency and intuitiveness. However, current open-source software solutions do not yield the required performance and functionalities. We address this issue by contributing a novel open-source game engine voxel library that supports real-time immersive volume sculpting. Our design leverages GPU instancing, parallel computing, and a chunk-based data structure to optimize collision detection and rendering. We have implemented features that enable fast voxel interaction and improve precision. Our benchmark evaluation indicates that our implementation offers a significant improvement over the state-of-the-art and can render and modify millions of visible voxels while maintaining stable performance for real-time interaction in virtual reality.

Description: We consider maintenance sites for urban rail systems, where unavailable tracks typically require changes to the regular timetable, and often even to the line plan. In this paper, we present an integrated mixed-integer linear optimization model to compute an optimal line plan that makes best use of the available tracks, together with a periodic timetable, including its detailed routing on the tracks within the stations. The key component is a flexible, turn-sensitive event-activity network that allows to integrate line planning and train routing using a track choice extension of the Periodic Event Scheduling Problem (PESP). Major goals are to maintain as much of the regular service as possible, and to keep the necessary changes rather local. Moreover, we present computational results on real construction site scenarios on the S-Bahn Berlin network. We demonstrate that this integrated problem is indeed solvable on practically relevant instances.

Description: Periodic timetabling for highly utilized railway networks is a demanding challenge. We formulate an infrastructure-aware extension of the Periodic Event Scheduling Problem (PESP) by requiring that not only events, but also activities using the same infrastructure must be separated by a minimum headway time. This extended problem can be modeled as a mixed-integer program by adding constraints on the sum of periodic tensions along certain cycles, so that it shares some structural properties with standard PESP. We further refine this problem by fixing cyclic orders at each infrastructure element. Although the computational complexity remains unchanged, the mixed-integer programming model then becomes much smaller. Furthermore, we also discuss how to find a minimal subset of infrastructure elements whose cyclic order already prescribes the order for the remaining parts of the network, and how cyclic order information can be modeled in a mixed-integer programming context. In practice, we evaluate the impact of cyclic orders on a real-world instance on the S-Bahn Berlin network, which turns out to be computationally fruitful.

Description: The ongoing electrification of logistics systems and vehicle fleets increases the complexity of associated vehicle routing or scheduling problems. Battery-powered vehicles have to be scheduled to recharge in-service, and the relationship between charging time and replenished driving range is non-linear. In order to access the powerful toolkit offered by mixed-integer and linear programming techniques, this battery behavior has to be linearized. Moreover, as electric fleets grow, power draw peaks have to be avoided to save on electricity costs or to adhere to hard grid capacity limits, such that it becomes desirable to keep recharge rates dynamic. We suggest a novel linearization approach of battery charging behavior for vehicle scheduling problems, in which the recharge rates are optimization variables and not model parameters.

Description: Flight planning, the computation of optimal routes in view of flight time and fuel consumption under given weather conditions, is traditionally done by finding globally shortest paths in a predefined airway network. Free flight trajectories, not restricted to a network, have the potential to reduce the costs significantly, and can be computed using locally convergent continuous optimal control methods. Hybrid methods that start with a discrete global search and refine with a fast continuous local optimization combine the best properties of both approaches, but rely on a good switchover, which requires error estimates for discrete paths relative to continuous trajectories. Based on vertex density and local complete connectivity, we derive localized and a priori bounds for the flight time of discrete paths relative to the optimal continuous trajectory, and illustrate their properties on a set of benchmark problems. It turns out that localization improves the error bound by four orders of magnitude, but still leaves ample opportunities for tighter bounds using a posteriori error estimators.

Description: In optical nano metrology numerical models are used widely for parameter reconstructions. Using the Bayesian target vector optimization method we fit a finite element numerical model to a Grazing Incidence x-ray fluorescence data set in order to obtain the geometrical parameters of a nano structured line grating. Gaussian process, stochastic machine learning surrogate models, were trained during the reconstruction and afterwards sampled with a Markov chain Monte Carlo sampler to determine the distribution of the reconstructed model parameters. The numerical discretization parameters of the used finite element model impact the numerical discretization error of the forward model. We investigated the impact of the polynomial order of the finite element ansatz functions on the reconstructed parameters as well as on the model parameter distributions. We showed that such a convergence study allows to determine numerical parameters which allows for efficient and accurate reconstruction results.

Description: Purpose: To investigate the influence of teeth and dental restorations on the facial skeleton's gray value distributions in cone-beam computed tomography (CBCT). Methods: Gray value selection for the upper and lower jaw segmentation was performed in 40 patients. In total, CBCT data of 20 maxillae and 20 mandibles, ten partial edentulous and ten fully edentulous in each jaw, respectively, were evaluated using two different gray value selection procedures: manual lower threshold selection and automated lower threshold selection. Two sample t tests, linear regression models, linear mixed models, and Pearson's correlation coefficients were computed to evaluate the influence of teeth, dental restorations, and threshold selection procedures on gray value distributions. Results: Manual threshold selection resulted in significantly different gray values in the fully and partially edentulous mandible. (p = 0.015, difference 123). In automated threshold selection, only tendencies to different gray values in fully edentulous compared to partially edentulous jaws were observed (difference: 58–75). Significantly different gray values were evaluated for threshold selection approaches, independent of the dental situation of the analyzed jaw. No significant correlation between the number of teeth and gray values was assessed, but a trend towards higher gray values in patients with more teeth was noted. Conclusions: Standard gray values derived from CT imaging do not apply for threshold-based bone segmentation in CBCT. Teeth influence gray values and segmentation results. Inaccurate bone segmentation may result in ill-fitting surgical guides produced on CBCT data and misinterpreting bone density, which is crucial for selecting surgical protocols.

Description: High-dimensional metastable molecular dynamics (MD) can often be characterised by a few features of the system, that is, collective variables (CVs). Thanks to the rapid advance in the area of machine learning and deep learning, various deep learning-based CV identification techniques have been developed in recent years, allowing accurate modelling and efficient simulation of complex molecular systems. In this paper, we look at two different categories of deep learning-based approaches for finding CVs, either by computing leading eigenfunctions of transfer operator associated to the underlying dynamics, or by learning an autoencoder via minimisation of reconstruction error. We present a concise overview of the mathematics behind these two approaches and conduct a comparative numerical study of these two approaches on illustrative examples.