Library

Description: This paper studies time-inhomogeneous nonequilibrium diffusion processes, including both Brownian dynamics and Langevin dynamics. We derive upper bounds of the relative entropy production of the time-inhomogeneous process with respect to the transient invariant probability measures. We also study the time reversal of the reverse process in Crooks' fluctuation theorem. We show that the time reversal of the reverse process coincides with the optimally controlled forward process that leads to zero variance importance sampling estimator based on Jarzynski's equality.

Description: Calculating averages with respect to probability measures on submanifolds is often necessary in various application areas such as molecular dynamics, computational statistical mechanics and Bayesian statistics. In recent years, various numerical schemes have been proposed in the literature to study this problem based on appropriate reversible constrained stochastic dynamics. In this paper we present and analyse a non-reversible generalisation of the projection-based scheme developed by one of the authors [ESAIM: M2AN, 54 (2020), pp. 391-430]. This scheme consists of two steps - starting from a state on the submanifold, we first update the state using a non-reversible stochastic differential equation which takes the state away from the submanifold, and in the second step we project the state back onto the manifold using the long-time limit of a ordinary differential equation. We prove the consistency of this numerical scheme and provide quantitative error estimates for estimators based on finite-time running averages. Furthermore, we present theoretical analysis which shows that this scheme outperforms its reversible counterpart in terms of asymptotic variance. We demonstrate our findings on an illustrative test example.

Description: We present a method based on a generative model for detection of disturbances such as prosthesis, screws, zippers, and metals in 2D radiographs. The generative model is trained in an unsupervised fashion using clinical radiographs as well as simulated data, none of which contain disturbances. Our approach employs a latent space consistency loss which has the benefit of identifying similarities, and is enforced to reconstruct X-rays without disturbances. In order to detect images with disturbances, an anomaly score is computed also employing the Frechet distance between the input X-ray and the reconstructed one using our generative model. Validation was performed using clinical pelvis radiographs. We achieved an AUC of 0.77 and 0.83 with clinical and synthetic data, respectively. The results demonstrated a good accuracy of our method for detecting outliers as well as the advantage of utilizing synthetic data.

Description: Three-dimensional medical imaging enables detailed understanding of osteoarthritis structural status. However, there remains a vast need for automatic, thus, reader-independent measures that provide reliable assessment of subject-specific clinical outcomes. To this end, we derive a consistent generalization of the recently proposed B-score to Riemannian shape spaces. We further present an algorithmic treatment yielding simple, yet efficient computations allowing for analysis of large shape populations with several thousand samples. Our intrinsic formulation exhibits improved discrimination ability over its Euclidean counterpart, which we demonstrate for predictive validity on assessing risks of total knee replacement. This result highlights the potential of the geodesic B-score to enable improved personalized assessment and stratification for interventions.

Description: We present a method for the quantification of knee alignment from full-leg X-Rays. A state-of-the-art object detector, YOLOv4, was trained to locate regions of interests (ROIs) in full-leg X-Ray images for the hip joint, the knee, and the ankle. Residual neural networks (ResNets) were trained to regress landmark coordinates for each ROI.Based on the detected landmarks the knee alignment, i.e., the hip-knee-ankle (HKA) angle, was computed. The accuracy of landmark detection was evaluated by a comparison to manually placed landmarks for 360 legs in 180 X-Rays. The accuracy of HKA angle computations was assessed on the basis of 2,943 X-Rays. Results of YARLA were compared to the results of two independent image reading studies(Cooke; Duryea) both publicly accessible via the Osteoarthritis Initiative. The agreement was evaluated using Spearman's Rho, and weighted kappa as well as regarding the correspondence of the class assignment (varus/neutral/valgus). The average difference between YARLA and manually placed landmarks was less than 2.0+- 1.5 mm for all structures (hip, knee, ankle). The average mismatch between HKA angle determinations of Cooke and Duryea was 0.09 +- 0.63°; YARLA resulted in a mismatch of 0.10 +- 0.74° compared to Cooke and of 0.18 +- 0.64° compared to Duryea. Cooke and Duryea agreed almost perfectly with respect to a weighted kappa value of 0.86, and showed an excellent reliability as measured by a Spearman's Rho value of 0.99. Similar values were achieved by YARLA, i.e., a weighted kappa value of0.83 and 0.87 and a Spearman's Rho value of 0.98 and 0.99 to Cooke and Duryea,respectively. Cooke and Duryea agreed in 92% of all class assignments and YARLA did so in 90% against Cooke and 92% against Duryea. In conclusion, YARLA achieved results comparable to those of human experts and thus provides a basis for an automated assessment of knee alignment in full-leg X-Rays.

Description: Three-dimensional medical imaging enables detailed understanding of osteoarthritis structural status. However, there remains a vast need for automatic, thus, reader-independent measures that provide reliable assessment of subject-specific clinical outcomes. To this end, we derive a consistent generalization of the recently proposed B-score to Riemannian shape spaces. We further present an algorithmic treatment yielding simple, yet efficient computations allowing for analysis of large shape populations with several thousand samples. Our intrinsic formulation exhibits improved discrimination ability over its Euclidean counterpart, which we demonstrate for predictive validity on assessing risks of total knee replacement. This result highlights the potential of the geodesic B-score to enable improved personalized assessment and stratification for interventions.

Description: We present a novel approach for nonlinear statistical shape modeling that is invariant under Euclidean motion and thus alignment-free. By analyzing metric distortion and curvature of shapes as elements of Lie groups in a consistent Riemannian setting, we construct a framework that reliably handles large deformations. Due to the explicit character of Lie group operations, our non-Euclidean method is very efficient allowing for fast and numerically robust processing. This facilitates Riemannian analysis of large shape populations accessible through longitudinal and multi-site imaging studies providing increased statistical power. Additionally, as planar configurations form a submanifold in shape space, our representation allows for effective estimation of quasi-isometric surfaces flattenings. We evaluate the performance of our model w.r.t. shape-based classification of hippocampus and femur malformations due to Alzheimer's disease and osteoarthritis, respectively. In particular, we achieve state-of-the-art accuracies outperforming the standard Euclidean as well as a recent nonlinear approach especially in presence of sparse training data. To provide insight into the model's ability of capturing biological shape variability, we carry out an analysis of specificity and generalization ability.

Description: Currently, new materials for knee implants need to be extensively and expensive tested in a knee wear simulator in a realized design. However, using a rolling-sliding test bench, these materials can be examined under the same test conditions but with simplified geometries. In the present study, the test bench was optimized, and forces were adapted to the physiological contact pressure in the knee joint using the available geometric parameters. Various polymers made of polyethylene and polyurethane articulating against test wheels made of cobalt-chromium and aluminum titanate were tested in the test bench using adapted forces based on ISO 14243-1. Polyurethane materials showed distinctly higher wear rates than polyethylene materials and showed inadequate wear resistance for use as knee implant material. Thus, the rolling-sliding test bench is an adaptable test setup for evaluating newly developed bearing materials for knee implants. It combines the advantages of screening and simulator tests and allows testing of various bearing materials under physiological load and tribological conditions of the human knee joint. The wear behavior of different material compositions and the influence of surface geometry and quality can be initially investigated without the need to produce complex implant prototypes of total knee endoprosthesis or interpositional spacers.

Description: Long-lived flow patterns in the atmosphere such as weather fronts, mid-latitude blockings or tropical cyclones often induce extreme weather conditions. As a consequence, their description, detection, and tracking has received increasing attention in recent years. Similar objectives also arise in diverse fields such as turbulence and combustion research, image analysis, and medical diagnostics under the headlines of "feature tracking", "coherent structure detection" or "image registration" - to name just a few. A host of different approaches to addressing the underlying, often very similar, tasks have been developed and successfully used. Here, several typical examples of such approaches are summarized, further developed and applied to meteorological data sets. Common abstract operational steps form the basis for a unifying framework for the specification of "persistent structures" involving the definition of the physical state of a system, the features of interest, and means of measuring their persistence.

Description: Convolutional neural networks (CNNs) are the state-of-the-art for automated assessment of knee osteoarthritis (KOA) from medical image data. However, these methods lack interpretability, mainly focus on image texture, and cannot completely grasp the analyzed anatomies’ shapes. In this study we assess the informative value of quantitative features derived from segmentations in order to assess their potential as an alternative or extension to CNN-based approaches regarding multiple aspects of KOA. Six anatomical structures around the knee (femoral and tibial bones, femoral and tibial cartilages, and both menisci) are segmented in 46,996 MRI scans. Based on these segmentations, quantitative features are computed, i.e., measurements such as cartilage volume, meniscal extrusion and tibial coverage, as well as geometric features based on a statistical shape encoding of the anatomies. The feature quality is assessed by investigating their association to the Kellgren-Lawrence grade (KLG), joint space narrowing (JSN), incident KOA, and total knee replacement (TKR). Using gold standard labels from the Osteoarthritis Initiative database the balanced accuracy (BA), the area under the Receiver Operating Characteristic curve (AUC), and weighted kappa statistics are evaluated. Features based on shape encodings of femur, tibia, and menisci plus the performed measurements showed most potential as KOA biomarkers. Differentiation between non-arthritic and severely arthritic knees yielded BAs of up to 99%, 84% were achieved for diagnosis of early KOA. Weighted kappa values of 0.73, 0.72, and 0.78 were achieved for classification of the grade of medial JSN, lateral JSN, and KLG, respectively. The AUC was 0.61 and 0.76 for prediction of incident KOA and TKR within one year, respectively. Quantitative features from automated segmentations provide novel biomarkers for KLG and JSN classification and show potential for incident KOA and TKR prediction. The validity of these features should be further evaluated, especially as extensions of CNN- based approaches. To foster such developments we make all segmentations publicly available together with this publication.

Description: Morphomatics is an open-source Python library for (statistical) shape analysis developed within the geometric data analysis and processing research group at Zuse Institute Berlin. It contains prototype implementations of intrinsic manifold-based methods that are highly consistent and avoid the influence of unwanted effects such as bias due to arbitrary choices of coordinates.

Description: Purpose Segmentation of surgical instruments in endoscopic video streams is essential for automated surgical scene understanding and process modeling. However, relying on fully supervised deep learning for this task is challenging because manual annotation occupies valuable time of the clinical experts. Methods We introduce a teacher–student learning approach that learns jointly from annotated simulation data and unlabeled real data to tackle the challenges in simulation-to-real unsupervised domain adaptation for endoscopic image segmentation. Results Empirical results on three datasets highlight the effectiveness of the proposed framework over current approaches for the endoscopic instrument segmentation task. Additionally, we provide analysis of major factors affecting the performance on all datasets to highlight the strengths and failure modes of our approach. Conclusions We show that our proposed approach can successfully exploit the unlabeled real endoscopic video frames and improve generalization performance over pure simulation-based training and the previous state-of-the-art. This takes us one step closer to effective segmentation of surgical instrument in the annotation scarce setting.

Description: This article revisits a complexly folded silver scroll excavated in Jerash, Jordan in 2014 that was digitally examined in 2015. In this article we apply, examine and discuss a new virtual unfolding technique that results in a clearer image of the scroll’s 17 lines of writing. We also compare it to the earlier unfolding and discuss progress in general analytical tools. We publish the original and the new images as well as the unfolded volume data open access in order to make these available to researchers interested in optimising unfolding processes of various complexly folded materials.

Description: Balanced separators are node sets that split the graph into size bounded components. They find applications in different theoretical and practical problems. In this paper we discuss how to find a minimum set of balanced separators in node weighted graphs. Our contribution is a new and exact algorithm that solves Minimum Balanced Separators by a sequence of Hitting Set problems. The only other exact method appears to be a mixed-integer program (MIP) for the edge weighted case. We adapt this model to node weighted graphs and compare it to our approach on a set of instances, resembling transit networks. It shows that our algorithm is far superior on almost all test instances.

Description: Agent based models (ABMs) are a useful tool for modeling spatio-temporal population dynamics, where many details can be included in the model description. Their computational cost though is very high and for stochastic ABMs a lot of individual simulations are required to sample quantities of interest. Especially, large numbers of agents render the sampling infeasible. Model reduction to a metapopulation model leads to a significant gain in computational efficiency, while preserving important dynamical properties. Based on a precise mathematical description of spatio-temporal ABMs, we present two different metapopulation approaches (stochastic and piecewise deterministic) and discuss the approximation steps between the different models within this framework. Especially, we show how the stochastic metapopulation model results from a Galerkin projection of the underlying ABM onto a finite-dimensional ansatz space. Finally, we utilize our modeling framework to provide a conceptual model for the spreading of COVID-19 that can be scaled to real-world scenarios.

Description: Convolutional neural networks (CNNs) are the state-of-the-art for automated assessment of knee osteoarthritis (KOA) from medical image data. However, these methods lack interpretability, mainly focus on image texture, and cannot completely grasp the analyzed anatomies’ shapes. In this study we assess the informative value of quantitative features derived from segmentations in order to assess their potential as an alternative or extension to CNN-based approaches regarding multiple aspects of KOA A fully automated method is employed to segment six anatomical structures around the knee (femoral and tibial bones, femoral and tibial cartilages, and both menisci) in 46,996 MRI scans. Based on these segmentations, quantitative features are computed, i.e., measurements such as cartilage volume, meniscal extrusion and tibial coverage, as well as geometric features based on a statistical shape encoding of the anatomies. The feature quality is assessed by investigating their association to the Kellgren-Lawrence grade (KLG), joint space narrowing (JSN), incident KOA, and total knee replacement (TKR). Using gold standard labels from the Osteoarthritis Initiative database the balanced accuracy (BA), the area under the Receiver Operating Characteristic curve (AUC), and weighted kappa statistics are evaluated. Features based on shape encodings of femur, tibia, and menisci plus the performed measurements showed most potential as KOA biomarkers. Differentiation between healthy and severely arthritic knees yielded BAs of up to 99%, 84% were achieved for diagnosis of early KOA. Substantial agreement with weighted kappa values of 0.73, 0.73, and 0.79 were achieved for classification of the grade of medial JSN, lateral JSN, and KLG, respectively. The AUC was 0.60 and 0.75 for prediction of incident KOA and TKR within 5 years, respectively. Quantitative features from automated segmentations yield excellent results for KLG and JSN classification and show potential for incident KOA and TKR prediction. The validity of these features as KOA biomarkers should be further evaluated, especially as extensions of CNN-based approaches. To foster such developments we make all segmentations publicly available together with this publication.

Description: The Periodic Event Scheduling Problem (PESP) is the central mathematical model behind the optimization of periodic timetables in public transport. We apply Benders decomposition to the incidence-based MIP formulation of PESP. The resulting formulation exhibits particularly nice features: The subproblem is a minimum cost network flow problem, and feasibility cuts are equivalent to the well-known cycle inequalities by Odijk. We integrate the Benders approach into a branch-and-cut framework, and assess the performance of this method on instances derived from the benchmarking library PESPlib.

Description: About 23% of the German energy demand is supplied by natural gas. Additionally, for about the same amount Germany serves as a transit country. Thereby, the German network represents a central hub in the European natural gas transport network. The transport infrastructure is operated by transmissions system operators (TSOs). The number one priority of the TSOs is to ensure the security of supply. However, the TSOs have only very limited knowledge about the intentions and planned actions of the shippers (traders). Open Grid Europe (OGE), one of Germany’s largest TSO, operates a high-pressure transport network of about 12,000 km length. With the introduction of peak-load gas power stations, it is of great importance to predict in- and out-flow of the network to ensure the necessary flexibility and security of supply for the German Energy Transition (“Energiewende”). In this paper, we introduce a novel hybrid forecast method applied to gas flows at the boundary nodes of a transport network. This method employs an optimized feature selection and minimization. We use a combination of a FAR, LSTM and mathematical programming to achieve robust high-quality forecasts on real-world data for different types of network nodes.

Description: We evaluated how plasma proteomic signatures in patients with suspected COVID-19 can unravel the pathophysiology, and determine kinetics and clinical outcome of the infection. We identified distinct plasma proteins linked to the presence and course of COVID-19. These plasma proteomic findings may translate to a protein fingerprint, helping to assist clinical management decisions.

Description: Solving PDEs on unstructured grids is a cornerstone of engineering and scientific computing. Heterogeneous parallel platforms, including CPUs, GPUs, and FPGAs, enable energy-efficient and computationally demanding simulations. In this article, we introduce the HPM C++-embedded DSL that bridges the abstraction gap between the mathematical formulation of mesh-based algorithms for PDE problems on the one hand and an increasing number of heterogeneous platforms with their different programming models on the other hand. Thus, the HPM DSL aims at higher productivity in the code development process for multiple target platforms. We introduce the concepts as well as the basic structure of the HPM DSL, and demonstrate its usage with three examples. The mapping of the abstract algorithmic description onto parallel hardware, including distributed memory compute clusters, is presented. A code generator and a matching back end allow the acceleration of HPM code with GPUs. Finally, the achievable performance and scalability are demonstrated for different example problems.

Description: Solving partial differential equations on unstructured grids is a cornerstone of engineering and scientific computing. Nowadays, heterogeneous parallel platforms with CPUs, GPUs, and FPGAs enable energy-efficient and computationally demanding simulations. We developed the HighPerMeshes C++-embedded Domain-Specific Language (DSL) for bridging the abstraction gap between the mathematical and algorithmic formulation of mesh-based algorithms for PDE problems on the one hand and an increasing number of heterogeneous platforms with their different parallel programming and runtime models on the other hand. Thus, the HighPerMeshes DSL aims at higher productivity in the code development process for multiple target platforms. We introduce the concepts as well as the basic structure of the HighPer-Meshes DSL, and demonstrate its usage with three examples, a Poisson and monodomain problem, respectively, solved by the continuous finite element method, and the discontinuous Galerkin method for Maxwell’s equation. The mapping of the abstract algorithmic description onto parallel hardware, including distributed memory compute clusters is presented. Finally, the achievable performance and scalability are demonstrated for a typical example problem on a multi-core CPU cluster.

Description: When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the nonparametric case, the maximum likelihood estimate is known to overfit the data, an issue that is commonly tackled by regularization. However, the majority of regularizations are ad hoc choices which lack invariance under reparametrization of the model and result in inconsistent estimates for equivalent models. We introduce a nonparametric, transformation-invariant estimator for the prior distribution. Being defined in terms of the missing information similar to the reference prior, it can be seen as an extension of the latter to the data-driven setting. This implies a natural interpretation as a trade-off between choosing the least informative prior and incorporating the information provided by the data, a symbiosis between the objective and empirical Bayes methodologies.

Description: It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that the decision-theoretic framework is neither appropriate nor sufficient. To this end, we consider an alternative optimality criterion from Bayesian experimental design and study its implied optimal information in the numerical context. This information is demonstrated to differ, in general, from the information that would be used in an average-case-optimal numerical method. The explicit connection to Bayesian experimental design suggests several distinct regimes in which optimal probabilistic numerical methods can be developed.

Description: This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the Convex Quadratic relaxation of the Optimal Transmission Switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. We then introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the Optimal Transmission Switching problem in Power Systems. Using the proposed improvements, along with bound propagation, on 23 medium-size test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on 5 instances. The tightened model has promising computational results when compared to state-of-the-art formulations.

Description: Conflict-driven Pseudo-Boolean (PB) solvers optimize 0-1 integer linear programs by extending the conflict-driven clause learning (CDCL) paradigm from SAT solving. Though PB solvers have the potential to be exponentially more efficient than CDCL solvers in theory, in practice they can sometimes get hopelessly stuck even when the linear program (LP) relaxation is infeasible over the reals. Inspired by mixed integer programming (MIP), we address this problem by interleaving incremental LP solving with cut generation within the conflict-driven PB search. This hybrid approach, which for the first time combines MIP techniques with full-blown conflict analysis over linear inequalities using the cutting planes method, significantly improves performance on a wide range of benchmarks, approaching a "best of two worlds" scenario between SAT-style conflict-driven search and MIP-style branch-and-cut.

Description: The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation. Due to both theoretical and practical considerations, relaxations of MINLPs are usually required to be convex. Nonetheless, current optimization solver can often successfully handle a moderate presence of nonconvexities, which opens the door for the use of potentially tighter nonconvex relaxations. In this work, we exploit this fact and make use of a nonconvex relaxation obtained via aggregation of constraints: a surrogate relaxation. These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since. We revisit these relaxations in an MINLP setting and show the computational benefits and challenges they can have. Additionally, we study a generalization of such relaxation that allows for multiple aggregations simultaneously and present the first algorithm that is capable of computing the best set of aggregations. We propose a multitude of computational enhancements for improving its practical performance and evaluate the algorithm’s ability to generate strong dual bounds through extensive computational experiments.

Description: The motion of celestial bodies in astronomy is closely related to the orbits of electrons encircling an atomic nucleus. Bohr and Sommerfeld presented a quantization scheme of the classical orbits to analyze the eigenstates of the hydrogen atom. Here we discuss another close connection of classical trajectories and quantum mechanical states: the transient dynamics of objects around a nucleus. In this setup a comet (or an electron) is trapped for a while in the vicinity of parent object (Jupiter or an atomic nucleus), but eventually escapes after many revolutions around the center of attraction.

Description: For providing railway services the company’s railway rolling stock is one if not the most important ingredient. It decides about the number of passenger or cargo trips the company can offer, about the quality a passenger experiences the train ride and it is often related to the image of the company itself. Thus, it is highly desired to have the available rolling stock in the best shape possible. Moreover, in many countries, as Germany where our industrial partner DB Fernverkehr AG (DBF) is located, laws enforce regular vehicle inspections to ensure the safety of the passengers. This leads to rolling stock optimization problems with complex rules for vehicle maintenance. This problem is well studied in the literature for example see Maroti and Kroon 2005, or Cordeau et. al. 2001 for applications including vehicle maintenance. The contribution of this paper is a new algorithmic approach to solve the Rolling Stock Rotation Problem for the ICE high speed train fleet of DBF with included vehicle maintenance. It is based on a relaxation of a mixed integer linear programming model with an iterative cut generation to enforce the feasibility of a solution of the relaxation in the solution space of the original problem. The resulting mixed integer linear programming model is based on a hypergraph approach presented in Borndörfer et. al. 2015. The new approach is tested on real world instances modeling different scenarios for the ICE high speed train network in Germany and compared to the approaches of Reuther 2017 that are in operation at DB Fernverkehr AG. The approach shows a significant reduction of the run time to produce solutions with comparable or even better objective function values.

Description: We investigate the directional locking effects that arise when a monolayer of paramagnetic colloidal particles is driven across a triangular lattice of magnetic bubbles. We use an external rotating magnetic field to generate a two-dimensional traveling wave ratchet forcing the transport of particles along a direction that intersects two crystallographic axes of the lattice. We find that, while single particles show no preferred direction, collective effects induce transversal current and directional locking at high density via a spontaneous symmetry breaking. The colloidal current may be polarized via an additional bias field that makes one transport direction energetically preferred.

Description: Historische Fotos online zu stellen, ist rechtlich betrachtet in vielfacher Hinsicht problematisch. Zum einen ist dies nur zulässig, wenn hierfür entsprechende urheberrechtliche Nutzungsrechte vorliegen oder die Fotos inzwischen gemeinfrei sind. Allerdings unterscheidet das Recht zwischen Fotos als Werken und bloßen „Knipsbildern“, was sich vor allem darauf auswirkt, wie lange Fotos urheberrechtlich geschützt sind. Auf die urheberrechtlichen Fragen bei der Online-Veröffentlichung von Fotos wird im ersten Teil eingegangen. Sind auf Fotos Personen erkennbar, so sind auch die Persönlichkeitsrechte der Abgebildeten zu beachten. In der Regel ist die Online-Veröffentlichung nur mit Zustimmung der Abgebildeten zulässig. Nur in bestimmten Ausnahmefällen dürfen solche Fotos auch ohne ausdrückliche Zustimmung genutzt werden. Hiermit beschäftigt sich der zweite Teil dieser kleinen Handreichung

Description: The intersection cut paradigm is a powerful framework that facilitates the generation of valid linear inequalities, or cutting planes, for a potentially complex set S. The key ingredients in this construction are a simplicial conic relaxation of S and an S-free set: a convex zone whose interior does not intersect S. Ideally, such S-free set would be maximal inclusion-wise, as it would generate a deeper cutting plane. However, maximality can be a challenging goal in general. In this work, we show how to construct maximal S-free sets when S is defined as a general quadratic inequality. Our maximal S-free sets are such that efficient separation of a vertex in LP-based approaches to quadratically constrained problems is guaranteed. To the best of our knowledge, this work is the first to provide maximal quadratic-free sets.

Description: We consider the problem of verifying linear properties of neural networks. Despite their success in many classification and prediction tasks, neural networks may return unexpected results for certain inputs. This is highly problematic with respect to the application of neural networks for safety-critical tasks, e.g. in autonomous driving. We provide an overview of algorithmic approaches that aim to provide formal guarantees on the behavior of neural networks. Moreover, we present new theoretical results with respect to the approximation of ReLU neural networks. On the other hand, we implement a solver for verification of ReLU neural networks which combines mixed integer programming (MIP) with specialized branching and approximation techniques. To evaluate its performance, we conduct an extensive computational study. For that we use test instances based on the ACAS Xu System and the MNIST handwritten digit data set. Our solver is publicly available and able to solve the verification problem for instances which do not have independent bounds for each input neuron.

Description: Research software has become a central asset in academic research. It optimizes existing and enables new research methods, implements and embeds research knowledge, and constitutes an essential research product in itself. Research software must be sustainable in order to understand, replicate, reproduce, and build upon existing research or conduct new research effectively. In other words, software must be available, discoverable, usable, and adaptable to new needs, both now and in the future. Research software therefore requires an environment that supports sustainability. Hence, a change is needed in the way research software development and maintenance are currently motivated, incentivized, funded, structurally and infrastructurally supported, and legally treated. Failing to do so will threaten the quality and validity of research. In this paper, we identify challenges for research software sustainability in Germany and beyond, in terms of motivation, selection, research software engineering personnel, funding, infrastructure, and legal aspects. Besides researchers, we specifically address political and academic decision-makers to increase awareness of the importance and needs of sustainable research software practices. In particular, we recommend strategies and measures to create an environment for sustainable research software, with the ultimate goal to ensure that software-driven research is valid, reproducible and sustainable, and that software is recognized as a first class citizen in research. This paper is the outcome of two workshops run in Germany in 2019, at deRSE19 - the first International Conference of Research Software Engineers in Germany - and a dedicated DFG-supported follow-up workshop in Berlin.

Description: Friction in liquids arises from conservative forces between molecules and atoms. Although the hydrodynamics at the nanoscale is subject of intense research and despite the enormous interest in the non-Markovian dynamics of single molecules and solutes, the onset of friction from the atomistic scale so far could not be demonstrated. Here, we fill this gap based on frequency-resolved friction data from high-precision simulations of three prototypical liquids, including water. Combining with theory, we show that friction in liquids emerges abruptly at a characteristic frequency, beyond which viscous liquids appear as non-dissipative, elastic solids. Concomitantly, the molecules experience Brownian forces that display persistent correlations. A critical test of the generalised Stokes–Einstein relation, mapping the friction of single molecules to the visco-elastic response of the macroscopic sample, disproves the relation for Newtonian fluids, but substantiates it exemplarily for water and a moderately supercooled liquid. The employed approach is suitable to yield insights into vitrification mechanisms and the intriguing mechanical properties of soft materials.

Description: We investigate polyhedral aspects of the Periodic Event Scheduling Problem (PESP), the mathematical basis for periodic timetabling problems in public transport. Flipping the orientation of arcs, we obtain a new class of valid inequalities, the flip inequalities, comprising both the known cycle and change-cycle inequalities. For a point of the LP relaxation, a violated flip inequality can be found in pseudo-polynomial time, and even in linear time for a spanning tree solution. Our main result is that the integer vertices of the polytope described by the flip inequalities are exactly the vertices of the PESP polytope, i.e., the convex hull of all feasible periodic slacks with corresponding modulo parameters. Moreover, we show that this flip polytope equals the PESP polytope in some special cases. On the computational side, we devise several heuristic approaches concerning the separation of cutting planes from flip inequalities. These produce better dual bounds for the smallest and largest instance of the benchmarking library PESPlib.

Description: The coma of comet 67P/Churyumov-Gerasimenko has been probed by the Rosetta spacecraft and shows a variety of different molecules. The ROSINA COmet Pressure Sensor and the Double Focusing Mass Spectrometer provide in-situ densities for many volatile compounds including the 14 gas species H2O, CO2, CO, H2S, O2, C2H6, CH3OH, H2CO, CH4, NH3, HCN, C2H5OH, OCS, and CS2. We fit the observed densities during the entire comet mission between August 2014 and September 2016 to an inverse coma model. We retrieve surface emissions on a cometary shape with 3996 triangular elements for 50 separated time intervals. For each gas we derive systematic error bounds and report the temporal evolution of the production, peak production, and the time-integrated total production. We discuss the production for the two lobes of the nucleus and for the northern and southern hemispheres. Moreover we provide a comparison of the gas production with the seasonal illumination.

Description: While graph covering is a fundamental and well-studied problem, this field lacks a broad and unified literature review. The holistic overview of graph covering given in this article attempts to close this gap. The focus lies on a characterization and classification of the different problems discussed in the literature. In addition, notable results and common approaches are also included. Whenever appropriate, our review extends to the corresponding partioning problems.

Description: We present the tamper-resistant broadcast abstraction of the Bitcoin blockchain, and show how it can be used to implement tamper-resistant replicated state machines. The tamper-resistant broadcast abstraction provides functionality to: broadcast, deliver, and verify messages. The tamper-resistant property ensures: 1) the probabilistic protection against byzantine behaviour, and 2) the probabilistic verifiability that no tampering has occurred. In this work, we study various tamper-resistant broadcast protocols for: different environmental models (public/permissioned, bounded/unbounded, byzantine fault tolerant (BFT)/non-BFT, native/non-native); as well as different properties, such as ordering guarantees (FIFO-order, causal-order, total-order), and delivery guarantees (validity, agreement, uniform). This way, we can match the protocol to the required environment model and consistency model of the replicated state machine. We implemented the tamper-resistant broadcast abstraction as a proof of concept. The results show that the implemented tamper-resistant broadcast protocols can compete on throughput and latency with other state-of-the-art broadcast technologies. Use cases, such as a tamper-resistant file system, supply chain tracking, and a timestamp server highlight the expressiveness of the abstraction. In conclusion, the tamper-resistant broadcast protocols provide a powerful interface, with clear semantics and tunable settings, enabling the design of tamper-resistant applications.

Description: A new ion mobility (IM) spectrometer, enabling mobility measurements in the pressure range between 5 and 500 mbar and in the reduced field strength range E/N of 5–90 Td, was developed and characterized. Reduced mobility (K0) values were studied under low E/N (constant value) as well as high E/N (deviation from low field K0) for a series of molecular ions in nitrogen. Infrared matrix-assisted laser desorption ionization (IR-MALDI) was used in two configurations: a source working at atmospheric pressure (AP) and, for the first time, an IR-MALDI source working with a liquid (aqueous) matrix at sub-ambient/reduced pressure (RP). The influence of RP on IR-MALDI was examined and new insights into the dispersion process were gained. This enabled the optimization of the IM spectrometer for best analytical performance. While ion desolvation is less efficient at RP, the transport of ions is more efficient, leading to intensity enhancement and an increased number of oligomer ions. When deciding between AP and RP IR-MALDI, a trade-off between intensity and resolving power has to be considered. Here, the low field mobility of peptide ions was first measured and compared with reference values from ESI-IM spectrometry (at AP) as well as collision cross sections obtained from molecular dynamics simulations. The second application was the determination of the reduced mobility of various substituted ammonium ions as a function of E/N in nitrogen. The mobility is constant up to a threshold at high E/N. Beyond this threshold, mobility increases were observed. This behavior can be explained by the loss of hydrated water molecules.

Description: The mixed-integer linear programming (MILP) method has been applied widely to optimal design of energy supply systems. A hierarchical MILP method has been proposed to solve such optimal design problems effi- ciently. As one of the strategies to enhance the computation efficiency furthermore, a method of reducing model by time aggregation has been proposed to search design candidates accurately and efficiently in the relaxed optimal design problem at the upper level. In this paper, the hierarchical MILP method and model reduction by time aggregation are applied to the multiobjective optimal design. In applying the model reduc- tion, the methods of clustering periods by the order of time series, based on an operational strategy, and by the k-medoids method are applied. As a case study, the multiobjective optimal design of a gas turbine cogeneration system with a practical configuration is investigated by adopting the annual total cost and pri- mary energy consumption as the objective functions to be minimized simultaneously, and the clustering methods are compared with one another in terms of the computation efficiency. It turns out that the model reduction by any clustering method is effective to enhance the computation efficiency when importance is given to minimizing the first objective function. It also turns out that the model reduction only by the k- medoids method is effective very limitedly when importance is given to minimizing the second objective function.

Description: This study examines the usability of a real-world, large-scale natural gas transport infrastructure for hydrogen transport. We investigate whether a converted network can transport the amounts of hydrogen necessary to satisfy current energy demands. After introducing an optimization model for the robust transient control of hydrogen networks, we conduct computational experiments based on real-world demand scenarios. Using a representative network, we demonstrate that replacing each turbo compressor unit by four parallel hydrogen compressors, each of them comprising multiple serial compression stages, and imposing stricter rules regarding the balancing of in- and outflow suffices to realize transport in a majority of scenarios. However, due to the reduced linepack there is an increased need for technical and non-technical measures leading to a more dynamic network control. Furthermore, the amount of energy needed for compression increases by 364% on average.

Description: The identification of sound sources is a common problem in acoustics. Different parameters are sought, among these are signal and position of the sources. We present an adjoint-based approach for sound source identification, which employs computational aeroacoustic techniques. Two different applications are presented as a proof-of-concept: optimization of a sound reinforcement setup and the localization of (moving) sound sources.

Description: Die Bestimmung optimaler Treiberfunktionen von Lautsprechern in beliebiger Anordnung ist ein schlecht gestelltes Optimierungsproblem, da die Anzahl der Quellen immer erheblich kleiner als die Anzahl der Empfänger ist. Typischerweise werden frequenz-basierte Löser eingesetzt. In einem vorangegangenen Beitrag haben die Autoren einen Adjungierten-basierten Ansatz vorgestellt, um optimale Treiberfunktionen im Zeitbereich zu bestimmen. Die Methode erlaubt es, inhomogene Windprofile und Temperaturschichtungen einzubeziehen, die typischerweise bei auf der Wellengleichung beruhenden Lösungen nicht berücksichtigt werden. Daru ̈ber hinaus können komplexe Geometrien und Randbedingungen berücksichtigt werden. Bisher war diese Methode auf Monopolquellen beschränkt. Hier stellen die Autoren eine Erweiterung des Ansatzes in Bezug auf eine Adjungierten-basierte Monopolsynthese vor, die es ermöglicht, auch Quellen mit komplexen Richtcharakteristiken zu betrachten. Das Verfahren wird für typische Quellsignale und ein repräsentatives Lautsprechermodell mit komplexer Richtcharakteristik validiert.

Description: An adjoint-based approach for synthesizing complex sound sources by discrete, grid-based monopoles in finite-difference time-domain simulations is presented. Previously [Stein et al., 2019a, J. Acoust. Soc. Am. 146(3), 1774–1785] demonstrated that the approach allows to consider unsteady and non-uniform ambient conditions such as wind flow and thermal gradient in contrast to standard methods of numerical sound field simulation. In this work, it is proven that not only ideal monopoles but also realistic sound sources with complex directivity characteristics can be synthesized. In detail, an oscillating circular piston and a real 2-way near-field monitor are modeled. The required number of monopoles in terms of the SPL deviation between the directivity of the original and the synthesized source is analyzed. Since the computational effort is independent of the number of monopoles used for the synthesis, also more complex sources can be reproduced by increasing the number of monopoles utilized. In contrast to classical least-square problem solvers, this does not increase the computational effort, which makes the method attractive for predicting the effect of sound reinforcement systems with highly directional sources under difficult acoustic boundary conditions.

Description: Lattice-based cryptography has received attention as a next-generation encryption technique, because it is believed to be secure against attacks by classical and quantum computers. Its essential security depends on the hardness of solving the shortest vector problem (SVP). In the cryptography, to determine security levels, it is becoming significantly more important to estimate the hardness of the SVP by high-performance computing. In this study, we develop the world’s first distributed and asynchronous parallel SVP solver, the MAssively Parallel solver for SVP (MAP-SVP). It can parallelize algorithms for solving the SVP by applying the Ubiquity Generator framework, which is a generic framework for branch-and-bound algorithms. The MAP-SVP is suitable for massive-scale parallelization, owing to its small memory footprint, low communication overhead, and rapid checkpoint and restart mechanisms. We demonstrate its performance and scalability of the MAP-SVP by using up to 100,032 cores to solve instances of the Darmstadt SVP Challenge.

Description: In this article, we discuss the Length-Constrained Cycle Partition Problem (LCCP). Besides edge weights, the undirected graph in LCCP features an individual critical weight value for each vertex. A cycle partition, i.e., a vertex disjoint cycle cover, is a feasible solution if the length of each cycle is not greater than the critical weight of each of the vertices in the cycle. The goal is to find a feasible partition with the minimum number of cycles. In this article, we discuss theoretical properties, preprocessing techniques, and two mixed-integer programming models (MIP) for LCCP both inspired by formulations for the closely related Travelling Salesperson Problem (TSP). Further, we introduce conflict hypergraphs, whose cliques yield valid constraints for the MIP models. We conclude with a report on computational experiments conducted on (A)TSPLIB-based instances. As an example, we use a routing problem in which a fleet of uncrewed aerial vehicles (UAVs) patrols a set of areas.

Description: A projective hypersurface X⊆P^n has defect if h^i(X) ≠ h^i(P^n) for some i∈{n,…,2n−2} in a suitable cohomology theory. This occurs for example when X⊆P^4 is not Q-factorial. We show that hypersurfaces with defect tend to be very singular: In characteristic 0, we present a lower bound on the Tjurina number, where X is allowed to have arbitrary isolated singularities. For X with mild singularities, we prove a similar result in positive characteristic. As an application, we obtain an estimate on the asymptotic density of hypersurfaces without defect over a finite field.

Description: We investigate polyhedral aspects of the Periodic Event Scheduling Problem (PESP), the mathematical basis for periodic timetabling problems in public transport. Flipping the orientation of arcs, we obtain a new class of valid inequalities, the flip inequalities, comprising both the known cycle and change-cycle inequalities. For a point of the LP relaxation, a violated flip inequality can be found in pseudo-polynomial time, and even in linear time for a spanning tree solution. Our main result is that the integer vertices of the polytope described by the flip inequalities are exactly the vertices of the PESP polytope, i.e., the convex hull of all feasible periodic slacks with corresponding modulo parameters. Moreover, we show that this flip polytope equals the PESP polytope in some special cases. On the computational side, we devise several heuristic approaches concerning the separation of cutting planes from flip inequalities. We finally present better dual bounds for the smallest and largest instance of the benchmarking library PESPlib.

Description: A design point is inessential when it does not contribute to an optimal design, and can therefore be safely discarded from the design space. We derive three inequalities for the detection of such inessential points in c-optimal design: the first two are direct consequences of the equivalence theorem for c-optimality; the third one is derived from a second-order cone programming formulation of c-optimal design. Elimination rules for A-optimal design are obtained as a byproduct. When implemented within an optimization algorithm, each inequality gives a screening test that may provide a substantial acceleration by reducing the size of the problem online. Several examples are presented with a multiplicative algorithm to illustrate the effectiveness of the approach.

Description: We consider the theoretical model of Bergmann and Lebowitz for open systems out of equilibrium and translate its principles in the adaptive resolution simulation molecular dynamics technique. We simulate Lennard-Jones fluids with open boundaries in a thermal gradient and find excellent agreement of the stationary responses with the results obtained from the simulation of a larger locally forced closed system. The encouraging results pave the way for a computational treatment of open systems far from equilibrium framed in a well-established theoretical model that avoids possible numerical artifacts and physical misinterpretations.

Description: This paper studies the empirical efficacy and benefits of using projection-free first-order methods in the form of Conditional Gradients, a.k.a. Frank-Wolfe methods, for training Neural Networks with constrained parameters. We draw comparisons both to current state-of-the-art stochastic Gradient Descent methods as well as across different variants of stochastic Conditional Gradients. In particular, we show the general feasibility of training Neural Networks whose parameters are constrained by a convex feasible region using Frank-Wolfe algorithms and compare different stochastic variants. We then show that, by choosing an appropriate region, one can achieve performance exceeding that of unconstrained stochastic Gradient Descent and matching state-of-the-art results relying on L2-regularization. Lastly, we also demonstrate that, besides impacting performance, the particular choice of constraints can have a drastic impact on the learned representations.

Description: The complexity in large-scale optimization can lie in both handling the objective function and handling the constraint set. In this respect, stochastic Frank-Wolfe algorithms occupy a unique position as they alleviate both computational burdens, by querying only approximate first-order information from the objective and by maintaining feasibility of the iterates without using projections. In this paper, we improve the quality of their first-order information by blending in adaptive gradients. We derive convergence rates and demonstrate the computational advantage of our method over the state-of-the-art stochastic Frank-Wolfe algorithms on both convex and nonconvex objectives. The experiments further show that our method can improve the performance of adaptive gradient algorithms for constrained optimization.

Description: Constrained second-order convex optimization algorithms are the method of choice when a high accuracy solution to a problem is needed, due to their local quadratic convergence. These algorithms require the solution of a constrained quadratic subproblem at every iteration. We present the \emph{Second-Order Conditional Gradient Sliding} (SOCGS) algorithm, which uses a projection-free algorithm to solve the constrained quadratic subproblems inexactly. When the feasible region is a polytope the algorithm converges quadratically in primal gap after a finite number of linearly convergent iterations. Once in the quadratic regime the SOCGS algorithm requires O(log(log1/ε)) first-order and Hessian oracle calls and O(log(1/ε)log(log1/ε)) linear minimization oracle calls to achieve an ε-optimal solution. This algorithm is useful when the feasible region can only be accessed efficiently through a linear optimization oracle, and computing first-order information of the function, although possible, is costly.

Description: In graphical representations of public transportation networks, there is often some degree of uncertainty in the arc values, due to delays or transfer times. This uncertainty can be expressed as a parameterized weight on the transfer arcs. Classical shortest path algorithms often have difficulty handling parameterized arc weights and a tropical geometry approach has been shown as a possible solution. The connection between the classical shortest path problem and tropical geometry is well establish: Tropically multiplying the n × n adjacency matrix of a graph with itself n − 1 times results in the so-called Kleene star, and is a matrix-form solution to the all-pairs shortest path problem. Michael Joswig and Benjamin Schröter showed in their paper The Tropical Geometry of Shortest Paths that the same method can be used to find the solution to the all-pairs shortest path problem even in the case of variable arc weights and they proposed an algorithm to solve the single-target shortest path problem in such a case. The solution takes the form of a polyhedral subdivision of the parameter space. As the number of variable arc weights grows, the time needed to execute an implementation of this algorithm grows exponentially. As the size of a public transportation network grows, the number of variable arc weights grows exponentially as well. However, it has been observed that in public transportation networks, there are usually only a few possible shortest routes. Geometrically, this means that there should be few polyhedra in the polyhedral subdivision. This algorithm is used on an example of a real-world public transportation network and an analysis of the polyhedral subdivision is made. Then a geometrical approach is used to analyze the impact of limiting the number of transfers, and thereby limiting the number of parameterized arcs used, as an estimation of the solution to the all-pairs shortest path problem

Description: One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well- known McCormick relaxation for a product of two variables x and y over a box-constrained domain. The starting point of this paper is the fact that the convex hull of the graph of xy can be much tighter when computed over a strict, non-rectangular subset of the box. In order to exploit this in practice, we propose to compute valid linear inequalities for the projection of the feasible region onto the x-y-space by solving a sequence of linear programs akin to optimization-based bound tightening. These valid inequalities allow us to employ results from the literature to strengthen the classical McCormick relaxation. As a consequence, we obtain a stronger convexification procedure that exploits problem structure and can benefit from supplementary information obtained during the branch-and bound algorithm such as an objective cutoff. We complement this by a new bound tightening procedure that efficiently computes the best possible bounds for x, y, and xy over the available projections. Our computational evaluation using the academic solver SCIP exhibit that the proposed methods are applicable to a large portion of the public test library MINLPLib and help to improve performance significantly.

Description: In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware implementations of presolving as part of a parallel interior-point method to solve linear programs with block-diagonal structure, including both linking variables and linking constraints. While presolving reductions are often mathematically simple, their implementation in a high-performance computing environment is a complex endeavor. We report results on impact, performance, and scalability of the resulting presolving routines on real-world energy system models with up to 700 million nonzero entries in the constraint matrix.

Description: We consider event-based Mixed-Integer Programming (MIP) models for the Resource-Constrained Project Scheduling Problem (RCPSP) that represent an alternative to the common time-indexed model (DDT) of Pritsker et al. (1969) for the case where the underlying time horizon is large or job processing times are subject to huge variations. In contrast to the time-indexed model, the size of event-based models does not depend on the time horizon. For two event-based formulations OOE and SEE of Koné et al. (2011) we present new valid inequalities that dominate the original formulation. Additionally, we introduce a new event-based model: the Interval Event-Based Model (IEE). We deduce linear transformations between all three models that yield the strict domination order IEE 〉 SEE 〉 OOE for their linear programming (LP) relaxations, meaning that IEE has the strongest linear relaxation among the event-based models. We further show that the popular DDT formulation can be retrieved from IEE by certain polyhedral operations, thus giving a unifying view on a complete branch of MIP formulations for the RCPSP. In addition, we analyze the computational performance of all presented models on test instances of the PSPLIB (Kolisch and Sprecher 1997).

Description: This paper focuses on a special case of vehicle routing problem where perishable goods are considered. Deliveries have to be performed until a due date date, which may vary for different products. Storing products is prohibited. Since late deliveries have a direct impact on the revenues for these products, a precise demand prediction is important. In our practical case the product demands and vehicle driving times for the product delivery are dependent on weather conditions, i.e., temperatures, wind, and precipitation. In this paper the definition and a solution approach to the Vehicle Routing Problem with Perishable Goods is presented. The approach includes a procedure how historical weather data is used to predict demands and driving times. Its run time and solution quality is evaluated on different data sets given by the MOPTA Competition 2018.

Description: Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of partial differential equations, aimed at supporting application-oriented research in numerical analysis and scientific computing. The library is written in C++ and is based on the \textsc{Dune} interface. The code is independent of spatial dimension and works with different grid managers. An important feature is the mix-and-match approach to discretizing systems of PDEs with different ansatz and test spaces for all variables. We describe the mathematical concepts behind the library as well as its structure, illustrating its use at several examples on the way.

Description: This thesis presents a method for interpolating data using a neural network. The data is sparse and perturbed and is used as training data for a small neural network. For severely perturbed data, the network does not manage to find a smooth interpolation. But as the data resembles the solution to the one-dimensional and time-independent heat equation, the weak form of this PDE and subsequently its functional can be written down. If the functional is minimized, a solution to the weak form of the heat equation is found. The functional is now added to the traditional loss function of a neural network, the mean squared error between the network prediction and the given data, in order to smooth out fluctuations and interpolate between distanced grid points. This way, the network minimizes both the mean squared error and the functional, resulting in a smoother curve that can be used to predict u(x) for any grid point x.

Description: Project plan4res (www.plan4res.eu) involves the development of a modular framework for the modeling and analysis of energy system strategies at the European level. It will include models describing the investment and operation decisions for a wide variety of technologies related to electricity and non-electricity energy sectors across generation, consumption, transmission and distribution. The modularity of the framework allows for detailed modelling of major areas of energy systems that can help stakeholders from different backgrounds to focus on specific topics related to the energy landscape in Europe and to receive relevant outputs and insights tailored to their needs. The current paper presents a qualitative description of key concepts and methods of the novel modular optimization framework and provides insights into the corresponding energy landscape.

Description: This paper investigates the estimation of the size of Branch-and-Bound (B&B) trees for solving mixed-integer programs. We first prove that the size of the B&B tree cannot be approximated within a factor of~2 for general binary programs, unless P equals NP. Second, we review measures of the progress of the B&B search, such as the gap, and propose a new measure, which we call leaf frequency. We study two simple ways to transform these progress measures into B&B tree size estimates, either as a direct projection, or via double-exponential smoothing, a standard time-series forecasting technique. We then combine different progress measures and their trends into nontrivial estimates using Machine Learning techniques, which yields more precise estimates than any individual measure. The best method we have identified uses all individual measures as features of a random forest model. In a large computational study, we train and validate all methods on the publicly available MIPLIB and Coral general purpose benchmark sets. On average, the best method estimates B&B tree sizes within a factor of 3 on the set of unseen test instances even during the early stage of the search, and improves in accuracy as the search progresses. It also achieves a factor 2 over the entire search on each out of six additional sets of homogeneous instances we have tested. All techniques are available in version 7 of the branch-and-cut framework SCIP.

Description: The German high-pressure natural gas transport network consists of thousands of interconnected elements spread over more than 120,000 km of pipelines built during the last 100 years. During the last decade, we have spent many person-years to extract consistent data out of the available sources, both public and private. Based on two case studies, we present some of the challenges we encountered. Preparing consistent, high-quality data is surprisingly hard, and the effort necessary can hardly be overestimated. Thus, it is particularly important to decide which strategy regarding data curation to adopt. Which precision of the data is necessary? When is it more efficient to work with data that is just sufficiently correct on average? In the case studies we describe our experiences and the strategies we adopted to deal with the obstacles and to minimize future effort. Finally, we would like to emphasize that well-compiled data sets, publicly available for research purposes, provide the grounds for building innovative algorithmic solutions to the challenges of the future.

Description: Recently, Intel released the oneAPI programming environment. With Data Parallel C++ (DPC++), oneAPI enables codes to target multiple hardware architectures like multi-core CPUs, GPUs, and even FPGAs or other hardware using a single source. For legacy codes that were written for Nvidia GPUs, a compatibility tool is provided which facilitates the transition to the SYCL-based DPC++ programming language. This paper presents early experiences when using both the compatibility tool and oneAPI as well the employed extension to the SYCL programming standard for the tsunami simulation code easyWave. A performance study compares the original code running on Xeon processors using OpenMP as well as CUDA with the performance of the DPC++ counter part on multicore CPUs as well as integrated GPUs.

Description: In designing energy supply systems, designers should heighten the robustness in performance criteria against the uncertainty in energy demands. In this paper, a robust optimal design method using a hierarchi- cal mixed-integer linear programming (MILP) method is proposed to maximize the robustness of energy sup- ply systems under uncertain energy demands based on a mixed-integer linear model. A robust optimal design problem is formulated as a three-level min-max-min MILP one by expressing uncertain energy demands by intervals, evaluating the robustness in a performance criterion based on the minimax regret cri- terion, and considering relationships among integer design variables, uncertain energy demands, and inte- ger and continuous operation variables. This problem is solved by evaluating upper and lower bounds for the minimum of the maximum regret of the performance criterion repeatedly outside, and evaluating lower and upper bounds for the maximum regret repeatedly inside. Since these different types of optimization problems are difficult to solve even using commercial MILP solvers, they are solved by applying a hierarchi- cal MILP method developed for ordinary optimal design problems with its modifications. In a case study, the proposed approach is applied to the robust optimal design of a cogeneration system. Through the study, its validity and effectiveness are ascertained, and some features of the obtained robust designs are clarified.

Description: The well-known network simplex algorithm is a powerful tool to solve flow problems on graphs. Based on a recent dissertation by Isabel Beckenbach, we develop the necessary theory to extend the network simplex to capacitated flow problems on hypergraphs and implement this new variant. We then attempt to solve instances arising from real-life vehicle rotation planning problems.

Description: The determination of non-gravitational forces based on precise astrometry is one of the main tools to establish the cometary character of interstellar and solar-system objects. The Rosetta mission to comet 67P/C-G provided the unique opportunity to benchmark Earth-bound estimates of non-gravitational forces with in-situ data. We determine the accuracy of the standard Marsden and Sekanina parametrization of non-gravitational forces with respect to the observed dynamics. Additionally we analyse the rotation-axis changes (orientation and period) of 67P/C-G. This comparison provides a reference case for future cometary missions and sublimation models for non-gravitational forces.