Library

Description: This is the documentation on current results of a research project jointly conducted by Stiftung Deutsche Kinemathek (SDK) and Zuse Institute Berlin (ZIB). In this project, we are working on a practical yet sustainable archiving solution for audiovisual material. In the course of the project two major obstacles were identified: 1) Metadata is collected according to standards established in the community but lacking a prescribed serialisation format. 2) Storage size of audiovisual material and time scales of production processes make it often impractical to defer submission for archival storage until all components have arrived and can be processed in one go.

Description: Kunst- und Kulturinstitutionen beschäftigen sich zunehmend mit der Digitalisierung ihrer Sammlungen, auch und gerade im Angesicht der Pandemie 2020. Dabei spielen nicht nur technische und organisatorische Fragen eine Rolle, vor allem rechtliche Aspekte führen oft zu Unsicherheit bei der digitalen Zugänglichmachung der Daten. Um diesen Unsicherheiten kompakt zu begegnen, gibt digiS die "Rechtsfibel" in Zusammenarbeit mit iRights und Paul Klimpel als Autor heraus. Darin werden unter anderem konkrete Fragen des Urheberrechts zu verschiedenen Objektgattungen, Lizenzfragen, Persönlichkeitsrecht und Datenschutz, die Online-Präsentation von Digitalisaten und zur Archivierung behandelt. Die Handreichung soll Mitarbeiter*innen in Kultur(-erbe)einrichtungen ermutigen, sich mit den rechtlichen Fragen bei der Digitalisierung auseinanderzusetzen, indem sie die vielen Facetten dieses Bereichs verständlich darstellt.

Description: As the natural gas market is moving towards short-term planning, accurate and robust short-term forecasts of the demand and supply of natural gas is of fundamental importance for a stable energy supply, a natural gas control schedule, and transport operation on a daily basis. We propose a hybrid forecast model, Functional AutoRegressive and Convolutional Neural Network model, based on state-of-the-art statistical modeling and artificial neural networks. We conduct short-term forecasting of the hourly natural gas flows of 92 distribution nodes in the German high-pressure gas pipeline network, showing that the proposed model provides nice and stable accuracy for different types of nodes. It outperforms all the alternative models, with an improved relative accuracy up to twofold for plant nodes and up to fourfold for municipal nodes. For the border nodes with rather flat gas flows, it has an accuracy that is comparable to the best performing alternative model.

Description: The choice of solvents influences crystalline solid formed during the crystallization of active pharmaceutical ingredients (API). The underlying effects are not always well understood because of the complexity of the systems. Theoretical models are often insufficient to describe this phenomenon. In this study, the crystallization behavior of the model drug paracetamol in different solvents was studied based on experimental and molecular dynamics data. The crystallization process was followed in situ using time-resolved Raman spectroscopy. Molecular dynamics with simulated annealing algorithm was used for an atomistic understanding of the underlying processes. The experimental and theoretical data indicate that paracetamol molecules adopt a particular geometry in a given solvent predefining the crystallization of certain polymorphs.

Description: We present an extension of Taylor's Theorem for the piecewise polynomial expansion of non-smooth evaluation procedures involving absolute value operations. Evaluation procedures are computer programs of mathematical functions in closed form expression and allow a different treatment of smooth operations or calls to the absolute value function. The well known classical Theorem of Taylor defines polynomial approximations of sufficiently smooth functions and is widely used for the derivation and analysis of numerical integrators for systems of ordinary differential- or differential-algebraic equations, for the construction of solvers for continuous non-linear optimization of finite dimensional objective functions and for root solving of non-linear systems of equations. The long term goal is the stabilization and acceleration of already known methods and the derivation of new methods by incorporating piecewise polynomial Taylor expansions. The herein provided proof of the higher order approximation quality of the new generalized expansions is constructive and allows efficiently designed algorithms for the execution and computation of the piecewise polynomial expansions. As a demonstration towards the ultimate goal we will derive a prototype of a {\$}{\$}k{\$}{\$}k-step method on the basis of polynomial interpolation and the proposed generalized expansions.

Description: Tom Streubel has observed that for functions in abs-normal form, generalized Taylor expansions of arbitrary order $\bar d-1$ can be generated by algorithmic piecewise differentiation. Abs-normal form means that the real or vector valued function is defined by an evaluation procedure that involves the absolute value function $|...|$ apart from arithmetic operations and $\bar d$ times continuously differentiable univariate intrinsic functions. The additive terms in Streubel's expansion are abs-polynomial, i.e. involve neither divisions nor intrinsics. When and where no absolute values occur, Moore's recurrences can be used to propagate univariate Taylor polynomials through the evaluation procedure with a computational effort of $\mathcal O({\bar d}^2)$, provided all univariate intrinsics are defined as solutions of linear ODEs. This regularity assumption holds for all standard intrinsics, but for irregular elementaries one has to resort to Faa di Bruno's formula, which has exponential complexity in $\bar d$. As already conjectured we show that the Moore recurrences can be adapted for regular intrinsics to the abs-normal case. Finally, we observe that where the intrinsics are real analytic the expansions can be extended to infinite series that converge absolutely on spherical domains.

Description: Tom Streubel has observed that for functions in abs-normal form, generalized Taylor expansions of arbitrary order $\bar d-1$ can be generated by algorithmic piecewise differentiation. Abs-normal form means that the real or vector valued function is defined by an evaluation procedure that involves the absolute value function $|...|$ apart from arithmetic operations and $\bar d$ times continuously differentiable univariate intrinsic functions. The additive terms in Streubel's expansion are abs-polynomial, i.e. involve neither divisions nor intrinsics. When and where no absolute values occur, Moore's recurrences can be used to propagate univariate Taylor polynomials through the evaluation procedure with a computational effort of $\mathcal O({\bar d}^2)$, provided all univariate intrinsics are defined as solutions of linear ODEs. This regularity assumption holds for all standard intrinsics, but for irregular elementaries one has to resort to Faa di Bruno's formula, which has exponential complexity in $\bar d$. As already conjectured we show that the Moore recurrences can be adapted for regular intrinsics to the abs-normal case. Finally, we observe that where the intrinsics are real analytic the expansions can be extended to infinite series that converge absolutely on spherical domains.

Description: 混合整数計画法 (Mixed Integer Programming: MIP) は，MIP を解くソフトウェアである MIP ソルバが大規模な現実問題を解けるようになったこともあり，現実問題を解く有用な OR の手法として広く知られるようになった．しかしながら，MIP ソルバの開発に欠かせないベンチマーク・データセットおよび性能測定方法についてはそれほど広く知られているとは言い難い．ベンチマーク・データセットは注意を払って作成しないと，多くのバイアスがかかってしまう．それらのバイアスを可能な限りのぞき，真に有用なベンチマーク・テストの結果を得るためには複数の人数で多大な労力を割く必要がある．本稿では，そのような MIP ソルバ開発の背景として重要な役割を果たしてきた MIPLIB と Hans Mittelmann’s benchmarks について解説する．また，本稿において Hans Mittelmann’s benchmarks は，BENCHMARKS FOR OPTIMIZATION SOFTWAREのページ (http://plato.asu.edu/bench.html) に示されているベンチマークである．

Description: We present a transductive learning approach for morphometric osteophyte grading based on geometric deep learning. We formulate the grading task as semi-supervised node classification problem on a graph embedded in shape space. To account for the high-dimensionality and non-Euclidean structure of shape space we employ a combination of an intrinsic dimension reduction together with a graph convolutional neural network. We demonstrate the performance of our derived classifier in comparisons to an alternative extrinsic approach.

Description: A decision support system relies on frequent re-solving of similar problem instances. While the general structure remains the same in corresponding applications, the input parameters are updated on a regular basis. We propose a generative neural network design for learning integer decision variables of mixed-integer linear programming (MILP) formulations of these problems. We utilise a deep neural network discriminator and a MILP solver as our oracle to train our generative neural network. In this article, we present the results of our design applied to the transient gas optimisation problem. With the trained network we produce a feasible solution in 2.5s, use it as a warm-start solution, and thereby decrease global optimal solution solve time by 60.5%.

Description: In order to better understand the relationship between shape of the nasal cavity and to find objective classification for breathing obstruction, a population of 25 cases of healthy nasal cavity and 27 cases with diagnosed nasal airway obstruction (NAO) was examined for correlations between morphological, clinical and CFD parameters. For this purpose a workflow was implemented in Tcl to perform automatic measurements of morphological parameters of nasal cavity surfaces in Amira, which has as output a table with all estimated values. Furthermore, the statistical analysis was designed using Python to find the most probable subset of parameters that are predictors of nasal cavity pathology and consisted of correlation analysis, the selection of the best possible subset of parameters that could be used as predictors of clinically stated pathology of the nasal cavity by a logistic regression classifier. As a result, 10 most promising parameters were identified: mean distance between the two isthmuses, left isthmus contour, area ratio between the two isthmuses, left isthmus height, height ratio between the two isthmuses, left isthmus width, right isthmus width, right isthmus hydraulic diameter, mean distance of septal curvature between the septum enclosing walls of the nasal cavity, velocities volume average by expiration. As it turns out, most parameters refer to the isthmus region. This was to be expected since this region plays an important role in the airflow system of the nasal cavity.

Description: The growing importance of mathematical software in everyday life—in applications such as internet communication, traffic, and artificial intelligence—necessitates advances in software documentation services to raise awareness of existing packages and their usage. Such information helps potential software developers and users make informed choices about packages that could advance their work in modeling, simulation, and analysis. At the same time, software presents novel challenges to information services that require the development of new methods and means of processing. swMATH provides users with an overview of a broad range of mathematical software and extends documentation services for publications related to such software. It acts as a counterpart to the established abstracting and reviewing services for mathematical publications and has nearly 30,000 entries, making it one of the most comprehensive documentation services in mathematics.

Description: More and more diseases have been found to be strongly correlated with disturbances in the microbiome constitution, e.g., obesity, diabetes, or some cancer types. Thanks to modern high-throughput omics technologies, it becomes possible to directly analyze human microbiome and its influence on the health status. Microbial communities are monitored over long periods of time and the associations between their members are explored. These relationships can be described by a time-evolving graph. In order to understand responses of the microbial community members to a distinct range of perturbations such as antibiotics exposure or diseases and general dynamical properties, the time-evolving graph of the human microbial communities has to be analyzed. This becomes especially challenging due to dozens of complex interactions among microbes and metastable dynamics. The key to solving this problem is the representation of the time-evolving graphs as fixed-length feature vectors preserving the original dynamics. We propose a method for learning the embedding of the time-evolving graph that is based on the spectral analysis of transfer operators and graph kernels. We demonstrate that our method can capture temporary changes in the time-evolving graph on both synthetic data and real-world data. Our experiments demonstrate the efficacy of the method. Furthermore, we show that our method can be applied to human microbiome data to study dynamic processes.

Description: Urban transportation systems are subject to a high level of variation and fluctuation in demand over the day. When this variation and fluctuation are observed in both time and space, it is crucial to develop line plans that are responsive to demand. A multi-period line planning approach that considers a changing demand during the planning horizon is proposed. If such systems are also subject to limitations of resources, a dynamic transfer of resources from one line to another throughout the planning horizon should also be considered. A mathematical modelling framework is developed to solve the line planning problem with a cost-oriented approach considering transfer of resources during a finite length planning horizon of multiple periods. We use real-life public transportation network data for our computational results. We analyze whether or not multi-period solutions outperform single period solutions in terms of feasibility and relevant costs. The importance of demand variation on multi-period solutions is investigated. We evaluate the impact of resource transfer constraints on the effectiveness of solutions. We also study the effect of period lengths along with the problem parameters that are significant for and sensitive to the optimality of solutions.

Description: Public transportation networks are typically operated with a periodic timetable. The Periodic Event Scheduling Problem (PESP) is the standard mathematical modelling tool for periodic timetabling. Since PESP can be solved in linear time on trees, it is a natural question to ask whether there are polynomial-time algorithms for input networks of bounded treewidth. We show that deciding the feasibility of a PESP instance is NP-hard even when the treewidth is 2, the branchwidth is 2, or the carvingwidth is 3. Analogous results hold for the optimization of reduced PESP instances, where the feasibility problem is trivial. To complete the picture, we present two pseudo-polynomial-time dynamic programming algorithms solving PESP on input networks with bounded tree- or branchwidth. We further analyze the parameterized complexity of PESP with bounded cyclomatic number, diameter, or vertex cover number. For event-activity networks with a special -- but standard -- structure, we give explicit and sharp bounds on the branchwidth in terms of the maximum degree and the carvingwidth of an underlying line network. Finally, we investigate several parameters on the smallest instance of the benchmarking library PESPlib.

Description: Conformational dynamics is essential to biomolecular processes. Markov State Models (MSMs) are widely used to elucidate dynamic properties of molecular systems from unbiased Molecular Dynamics (MD). However, the implementation of reweighting schemes for MSMs to analyze biased simulations is still at an early stage of development. Several dynamical reweighing approaches have been proposed, which can be classified as approaches based on (i) Kramers rate theory, (ii) rescaling of the probability density flux, (iii) reweighting by formulating a likelihood function, (iv) path reweighting. We present the state-of-the-art and discuss the methodological differences of these methods, their limitations and recent applications.

Description: Phage display biopanning with Illumina next-generation sequencing (NGS) is applied to reveal insights into peptide-based adhesion domains for polypropylene (PP). One biopanning round followed by NGS selects robust PP-binding peptides that are not evident by Sanger sequencing. NGS provides a significant statistical base that enables motif analysis, statistics on positional residue depletion/enrichment, and data analysis to suppress false-positive sequences from amplification bias. The selected sequences are employed as water-based primers for PP?metal adhesion to condition PP surfaces and increase adhesive strength by 100\% relative to nonprimed PP.

Description: The temporally and spatially resolved tracking of lithium intercalation and electrode degradation processes are crucial for detecting and understanding performance losses during the operation of lithium-batteries. Here, high-throughput X-ray computed tomography has enabled the identification of mechanical degradation processes in a commercial Li/MnO2 primary battery and the indirect tracking of lithium diffusion; furthermore, complementary neutron computed tomography has identified the direct lithium diffusion process and the electrode wetting by the electrolyte. Virtual electrode unrolling techniques provide a deeper view inside the electrode layers and are used to detect minor fluctuations which are difficult to observe using conventional three dimensional rendering tools. Moreover, the ‘unrolling’ provides a platform for correlating multi-modal image data which is expected to find wider application in battery science and engineering to study diverse effects e.g. electrode degradation or lithium diffusion blocking during battery cycling.

Description: On average, an approved drug today costs $2-3 billion and takes over ten years to develop1. In part, this is due to expensive and time-consuming wet-lab experiments, poor initial hit compounds, and the high attrition rates in the (pre-)clinical phases. Structure-based virtual screening (SBVS) has the potential to mitigate these problems. With SBVS, the quality of the hits improves with the number of compounds screened2. However, despite the fact that large compound databases exist, the ability to carry out large-scale SBVSs on computer clusters in an accessible, efficient, and flexible manner has remained elusive. Here we designed VirtualFlow, a highly automated and versatile open-source platform with perfect scaling behaviour that is able to prepare and efficiently screen ultra-large ligand libraries of compounds. VirtualFlow is able to use a variety of the most powerful docking programs. Using VirtualFlow, we have prepared the largest and freely available ready-to-dock ligand library available, with over 1.4 billion commercially available molecules. To demonstrate the power of VirtualFlow, we screened over 1 billion compounds and discovered a small molecule inhibitor (iKeap1) that engages KEAP1 with nanomolar affinity (Kd = 114 nM) and disrupts the interaction between KEAP1 and the transcription factor NRF2. We also identified a set of structurally diverse molecules that bind to KEAP1 with submicromolar affinity. This illustrates the potential of VirtualFlow to access vast regions of the chemical space and identify binders with high affinity for target proteins.

Description: Fast domain propagation of linear constraints has become a crucial component of today's best algorithms and solvers for mixed integer programming and pseudo-boolean optimization to achieve peak solving performance. Irregularities in the form of dynamic algorithmic behaviour, dependency structures, and sparsity patterns in the input data make efficient implementations of domain propagation on GPUs and, more generally, on parallel architectures challenging. This is one of the main reasons why domain propagation in state-of-the-art solvers is single thread only. In this paper, we present a new algorithm for domain propagation which (a) avoids these problems and allows for an efficient implementation on GPUs, and is (b) capable of running propagation rounds entirely on the GPU, without any need for synchronization or communication with the CPU. We present extensive computational results which demonstrate the effectiveness of our approach and show that ample speedups are possible on practically relevant problems: on state-of-the-art GPUs, our geometric mean speed-up for reasonably-large instances is around 10x to 20x and can be as high as 195x on favorably-large instances.

Description: Structure-based virtual screening approaches have the ability to dramatically reduce the time and costs associated to the discovery of new drug candidates. Studies have shown that the true hit rate of virtual screenings improves with the scale of the screened ligand libraries. Therefore, we have recently developed an open source drug discovery platform (VirtualFlow), which is able to routinely carry out ultra-large virtual screenings. One of the primary challenges of molecular docking is the circumstance when the protein is highly dynamic or when the structure of the protein cannot be captured by a static pose. To accommodate protein dynamics, we report the extension of VirtualFlow to allow the docking of ligands using a grey wolf optimization algorithm using the docking program GWOVina, which substantially improves the quality and efficiency of flexible receptor docking compared to AutoDock Vina. We demonstrate the linear scaling behavior of VirtualFlow utilizing GWOVina up to 128 000 CPUs. The newly supported docking method will be valuable for drug discovery projects in which protein dynamics and flexibility play a significant role.

Description: The determination of time of death is one of the central tasks in forensic medicine. A standard method of time of death estimation elies on matching temperature measurements of the corpse with a post-mortem cooling model. In addition to widely used empirical post-mortem models, modelling based on a precise mathematical simulation of the cooling process have been gaining popularity. The simulation based cooling models and the resulting time of death estimates dependon a large variety of parameters. These include hermal properties for different body tissue types, environmental conditions such as temperature and air flow, and the presence of clothing and coverings. In this thesis we focus on a specific arameter - the contact between corpse and underground - and investigate its influence on the time of death estimation. Resulting we aim to answer the question whether it is necessary to consider contact mechanics in the underlying mathematical cooling model.

Description: Though gait asymmetry is used as a metric of functional recovery in clinical rehabilitation, there is no consensus on an ideal method for its evaluation. Various methods have been proposed but are limited in scope, as they can often use only positive signals or discrete values extracted from time-scale data as input. By defining five symmetry axioms, a framework for benchmarking existing methods was established and a new method was described here for the first time: the weighted universal symmetry index (wUSI), which overcomes limitations of other methods. Both existing methods and the wUSI were mathematically compared to each other and in respect to their ability to fulfill the proposed symmetry axioms. Eligible methods that fulfilled these axioms were then applied using both discrete and continuous approaches to ground reaction force (GRF) data collected from healthy gait, both with and without artificially induced asymmetry using a single instrumented elbow crutch. The wUSI with a continuous approach was the only symmetry method capable of determining GRF asymmetries in different walking conditions in all three planes of motion. When used with a continuous approach, the wUSI method was able to detect asymmetries while avoiding artificial inflation, a common problem reported in other methods. In conclusion, the wUSI is proposed as a universal method to quantify three-dimensional GRF asymmetries, which may also be expanded to other biomechanical signals.

Description: In state-of-the-art mixed-integer programming solvers, a large array of reduction techniques are applied to simplify the problem and strengthen the model formulation before starting the actual branch-and-cut phase. Despite their mathematical simplicity, these methods can have significant impact on the solvability of a given problem. However, a crucial property for employing presolve techniques successfully is their speed. Hence, most methods inspect constraints or variables individually in order to guarantee linear complexity. In this paper, we present new hashing-based pairing mechanisms that help to overcome known performance limitations of more powerful presolve techniques that consider pairs of rows or columns. Additionally, we develop an enhancement to one of these presolve techniques by exploiting the presence of set-packing structures on binary variables in order to strengthen the resulting reductions without increasing runtime. We analyze the impact of these methods on the MIPLIB 2017 benchmark set based on an implementation in the MIP solver SCIP.

Description: In this paper, we introduce the Maximum Diversity Assortment Selection Problem (MADASS), which is a generalization of the 2-dimensional Cutting Stock Problem (2CSP). Given a set of rectangles and a rectangular container, the goal of 2CSP is to determine a subset of rectangles that can be placed in the container without overlapping, i.e., a feasible assortment, such that a maximum area is covered. In MADASS, we need to determine a set of feasible assortments, each of them covering a certain minimum threshold of the container, such that the diversity among them is maximized. Thereby, diversity is defined as minimum or average normalized Hamming-Distance of all assortment pairs. The MADASS Problem was used in the 11th AIMMS-MOPTA Competition in 2019. The methods we describe in this article and the computational results won the contest. In the following, we give a definition of the problem, introduce a mathematical model and solution approaches, determine upper bounds on the diversity, and conclude with computational experiments conducted on test instances derived from the 2CSP literature.

Description: We present visual methods for the analysis and comparison of the results of curved fibre reconstruction algorithms, i.e., of algorithms extracting characteristics of curved fibres from X-ray computed tomography scans. In this work, we extend previous methods for the analysis and comparison of results of different fibre reconstruction algorithms or parametrisations to the analysis of curved fibres. We propose fibre dissimilarity measures for such curved fibres and apply these to compare multiple results to a specified reference. We further propose visualisation methods to analyse differences between multiple results quantitatively and qualitatively. In two case studies, we show that the presented methods provide valuable insights for advancing and parametrising fibre reconstruction algorithms, and support in improving their results in characterising curved fibres.

Description: Two essential ingredients of modern mixed-integer programming (MIP) solvers are diving heuristics that simulate a partial depth-first search in a branch-and-bound search tree and conflict analysis of infeasible subproblems to learn valid constraints. So far, these techniques have mostly been studied independently: primal heuristics under the aspect of finding high-quality feasible solutions early during the solving process and conflict analysis for fathoming nodes of the search tree and improving the dual bound. Here, we combine both concepts in two different ways. First, we develop a diving heuristic that targets the generation of valid conflict constraints from the Farkas dual. We show that in the primal this is equivalent to the optimistic strategy of diving towards the best bound with respect to the objective function. Secondly, we use information derived from conflict analysis to enhance the search of a diving heuristic akin to classical coefficient diving. The computational performance of both methods is evaluated using an implementation in the source-open MIP solver SCIP. Experiments are carried out on publicly available test sets including Miplib 2010 and Cor@l.

Description: Conflict learning plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. A major step for MIP conflict learning is to aggregate the LP relaxation of an infeasible subproblem to a single globally valid constraint, the dual proof, that proves infeasibility within the local bounds. Among others, one way of learning is to add these constraints to the problem formulation for the remainder of the search. We suggest to not restrict this procedure to infeasible subproblems, but to also use global proof constraints from subproblems that are not (yet) infeasible, but can be expected to be pruned soon. As a special case, we also consider learning from integer feasible LP solutions. First experiments of this conflict-free learning strategy show promising results on the MIPLIB2017 benchmark set.

Description: The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming frame- work SCIP. This paper discusses enhancements and extensions contained in version 7.0 of the SCIP Optimization Suite. The new version features the parallel presolving library PaPILO as a new addition to the suite. PaPILO 1.0 simplifies mixed-integer linear op- timization problems and can be used stand-alone or integrated into SCIP via a presolver plugin. SCIP 7.0 provides additional support for decomposition algorithms. Besides im- provements in the Benders’ decomposition solver of SCIP, user-defined decomposition structures can be read, which are used by the automated Benders’ decomposition solver and two primal heuristics. Additionally, SCIP 7.0 comes with a tree size estimation that is used to predict the completion of the overall solving process and potentially trigger restarts. Moreover, substantial performance improvements of the MIP core were achieved by new developments in presolving, primal heuristics, branching rules, conflict analysis, and symmetry handling. Last, not least, the report presents updates to other components and extensions of the SCIP Optimization Suite, in particular, the LP solver SoPlex and the mixed-integer semidefinite programming solver SCIP-SDP.

Description: The generalization of MIP techniques to deal with nonlinear, potentially non-convex, constraints have been a fruitful direction of research for computational MINLP in the last decade. In this paper, we follow that path in order to extend another essential subroutine of modern MIP solvers towards the case of nonlinear optimization: the analysis of infeasible subproblems for learning additional valid constraints. To this end, we derive two different strategies, geared towards two different solution approaches. These are using local dual proofs of infeasibility for LP-based branch-and-bound and the creation of nonlinear dual proofs for NLP-based branch-and-bound, respectively. We discuss implementation details of both approaches and present an extensive computational study, showing that both techniques can significantly enhance performance when solving MINLPs to global optimality.

Description: We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach.

Description: We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach.

Description: Due to the increase in accessibility and robustness of sequencing technology, single cell RNA-seq (scRNA-seq) data has become abundant. The technology has made significant contributions to discovering novel phenotypes and heterogeneities of cells. Recently, there has been a push for using single-- or multiple scRNA-seq snapshots to infer the underlying gene regulatory networks (GRNs) steering the cells' biological functions. To date, this aspiration remains unrealised. In this paper, we took a bottom-up approach and curated a stochastic two gene interaction model capturing the dynamics of a complete system of genes, mRNAs, and proteins. In the model, the regulation was placed upstream from the mRNA on the gene level. We then inferred the underlying regulatory interactions from only the observation of the mRNA population through~time. We could detect signatures of the regulation by combining information of the mean, covariance, and the skewness of the mRNA counts through time. We also saw that reordering the observations using pseudo-time did not conserve the covariance and skewness of the true time course. The underlying GRN could be captured consistently when we fitted the moments up to degree three; however, this required a computationally expensive non-linear least squares minimisation solver. There are still major numerical challenges to overcome for inference of GRNs from scRNA-seq data. These challenges entail finding informative summary statistics of the data which capture the critical regulatory information. Furthermore, the statistics have to evolve linearly or piece-wise linearly through time to achieve computational feasibility and scalability.

Description: Molecular simulations of ligand–receptor interactions are a computational challenge, especially when their association- (‘on’-rate) and dissociation- (‘off’-rate) mechanisms are working on vastly differing timescales. One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)-N-phenyl propionamide (NFEPP) in a μ-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab.

Description: The problem of determining the rate of rare events in dynamical systems is quite well-known but still difficult to solve. Recent attempts to overcome this problem exploit the fact that dynamic systems can be represented by a linear operator, such as the Koopman operator. Mathematically, the rare event problem comes down to the difficulty in finding invariant subspaces of these Koopman operators K. In this article, we describe a method to learn basis functions of invariant subspaces using an artificial neural Network.

Description: Molecular simulations of ligand-receptor interactions are a computational challenge, especially when their association- (``on''-rate) and dissociation- (``off''-rate) mechanisms are working on vastly differing timescales. In addition, the timescale of the simulations themselves is, in practice, orders of magnitudes smaller than that of the mechanisms; which further adds to the complexity of observing these mechanisms, and of drawing meaningful and significant biological insights from the simulation. One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)- N-phenyl propionamide (NFEPP) in a $\mu$-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab, who investigated the influence of pH on the inhibitory constant of fentanyl and NFEPP (Spahn et al. 2017). MD simulations are far more accessible and cost-effective than in vitro and in vivo studies. Especially in the context of the current opioid crisis, MD simulations can aid in unravelling molecular functionality and assist in clinical decision-making; the approaches presented in this paper are a pertinent step forward in this direction.

Description: Growing demand, distributed generation, such as renewable energy sources (RES), and the increasing role of storage systems to mitigate the volatility of RES on a medium voltage level, push existing distribution grids to their limits. Therefore, necessary network expansion needs to be evaluated to guarantee a safe and reliable electricity supply in the future taking these challenges into account. This problem is formulated as an optimal power flow (OPF) problem which combines network expansion, volatile generation and storage systems, minimizing network expansion and generation costs. As storage systems introduce a temporal coupling into the system, a multiperiod OPF problem is needed and analysed in this thesis. To reduce complexity, the network expansion problem is represented in a continuous nonlinear programming formulation by using fundamental properties of electrical engeneering. This formulation is validated succesfully against a common mixed integer programming approach on a 30 and 57 bus network with respect to solution and computing time. As the OPF problem is, in general, a nonconvex, nonlinear problem and, thus, hard to solve, convex relaxations of the power flow equations have gained increasing interest. Sufficient conditions are represented which guarantee exactness of a second-order cone (SOC) relaxation of an operational OPF in radial networks. In this thesis, these conditions are enhanced for the network expansion planning problem. Additionally, nonconvexities introduced by the choice of network expansion variables are relaxed by using McCormick envelopes. These relaxations are then applied on the multiperiod OPF and compared to the original problem on a 30 and a 57 bus network. In particular, the computational time is decreased by an order up to 10^2 by the SOC relaxation while it provides either an exact solution or a sufficient lower bound on the original problem. Finally, a sensitivity study is performed on weights of network expansion costs showing strong dependency of both the solution of performed expansion and solution time on the chosen weights.

Description: Demand Side Management (DSM) is usually considered as a process of energy consumption shifting from peak hours to off-peak times. DSM does not always reduce total energy consumption, but it helps to meet energy demand and supply. For example, it balances variable generation from renewables (such as solar and wind) when energy demand differs from renewable generation.

Description: Natural gas is considered by many to be the most important energy source for the future. The objectives of energy commodities strategic problems can be mainly related to natural gas and deal with the definition of the “optimal” gas pipelines design which includes a number of related sub problems such as: Gas stations (compression) location and Gas storage locations, as well as compression station design and optimal operation.

Description: To attain the highest performance of energy supply systems, it is necessary to determine design specifications optimally in consideration of operational strategies corresponding to seasonal and hourly variations in energy demands. A hierarchical mixed-integer linear programming method has been proposed to solve such an optimal design problem efficiently. In this paper, a method of reducing model by clustering periods with the k-medoids method is applied to the relaxed optimal design problem at the upper level. Through a case study, it is clarified how the proposed method is effective to enhance the computation efficiency in a large scale optimal design problem.

Description: To attain the highest performance of energy supply systems, it is necessary to determine design specifications optimally in consideration of operational strategies corresponding to seasonal and hourly variations in energy demands. Mixed-integer linear programming (MILP) methods have been applied widely to such optimal design problems. A hierarchical MILP method has been proposed to solve the problems very efficiently. In addition, by utilizing features of the hierarchical MILP method, a method of reducing model by clustering periods based on the optimal operational strategies of equipment has been proposed to search design solution candidates efficiently in the relaxed optimal design problem at the upper level. In this paper, these methods are applied to the multiobjective optimal design of a cogeneration system by considering the annual total cost and primary energy consumption as the objective functions to be minimized. Through a case study, it turns out that the model reduction by the operation-based time-period clustering is effective in terms of the computation efficiency when importance is given to the first objective function, while it is not when importance is given to the second objective function.

Description: A robust optimal design method of energy supply systems under uncertain energy demands has been proposed using a mixed-integer linear model for constituent equipment. However, this method takes a long computation time, and thus it can be applied only to small-scale problems. In this paper, a hierarchical optimization method is applied to two types of optimization problems for evaluating robustness to solve them efficiently. In a case study, the proposed method is applied to a cogeneration system with a complex configuration, and the validity and effectiveness of the method are ascertained.

Description: A robust optimal design method of energy supply systems under uncertain energy demands has been proposed using a mixed- integer linear model for constituent equipment. A robust optimal design problem has been formulated as a three-level min-max- min optimization one by expressing uncertain energy demands by intervals, evaluating the robustness in a performance criterion based on the minimax regret criterion, and considering hierarchical relationships among design variables, uncertain energy demands, and operation variables. Since this problem must be solved by a special algorithm and is too difficult to solve even using a commercial solver, a hierarchical optimization approach has been applied to solve the problem but its application is limited only to small scale toy problems. In this paper, some strategies are introduced into the hierarchical optimization approach to enhance the computation efficiency for the purpose of applying the approach to large scale practical problems. In a case study, the proposed approach is applied to the robust optimal design of a cogeneration system with a complex configuration, and the validity and effectiveness of the method are ascertained.

Description: Dieses Dokument legt Parameter und Formate für die Übertragung sprachbasierter Daten zwischen verschiedenen KI-Ökosystemen fest.

Description: This paper addresses the problem of scheduling vehicles in a public mass transportation system. We show how this problem can be modelled as a special multicommodity flow problem and outline the solution methodology we have developed. Based on polyhedral investigations, we have designed and implemented a branch&cut algorithm and various heuristics with which real vehicle scheduling problems of truely large scale can be solved to optimality. We describe some implementation issues and report computational results.

Description: This paper provides the {\em first} detailed description of the architecture of the computing machines Z1 and Z3 designed by Konrad Zuse in Berlin between 1936 to 1941. The necessary information was obtained from a careful evaluation of the patent application filed by Zuse in 1941. Additional insight was gained from a software simulation of the machine's logic. The Z1 was built using purely mechanical components, the Z3 using electromechanical relays. However, both machines shared a common logical structure and the programming model was exactly the same. We argue that both the Z1 and the Z3 possessed features akin to those of modern computers: memory and processor were separate units, the processor could handle floating-point numbers and compute the four basic arithmetical operations as well as the square root of a number. The program was stored on punched tape and was read sequentially. In the last section of this paper we bring the architecture of the Z1 and Z3 into historical perspective by offering a comparison with computing machines built in other countries.

Description: We study the parallelization of the steepest-edge version of the dual simplex algorithm. Three different parallel implementations are examined, each of which is derived from the CPLEX dual simplex implementation. One alternative uses PVM, one general-purpose System V shared-memory constructs, and one the PowerC extension of C on a Silicon Graphics multi-processor. These versions were tested on different parallel platforms, including heterogeneous workstation clusters, Sun S20-502, Silicon Graphics multi-processors, and an IBM SP2. We report on our computational experience.

Description: We present an algorithm for solving stochastic integer programming problems with recourse, based on a dual decomposition scheme and Lagrangian relaxation. The approach can be applied to multi-stage problems with mixed-integer variables in each time stage. %We outline a branch-and-bound algorithm for obtaining primal feasible and %possibly optimal solutions. Numerical experience is presented for some two-stage test problems.

Description: The paper presents the concept of a new type of algorithm for the numerical computation of what the authors call the {\em essential dynamics\/} of molecular systems. Mathematically speaking, such systems are described by Hamiltonian differential equations. In the bulk of applications, individual trajectories are of no specific interest. Rather, time averages of physical observables or relaxation times of conformational changes need to be actually computed. In the language of dynamical systems, such information is contained in the natural invariant measure (infinite relaxation time) or in almost invariant sets ("large" finite relaxation times). The paper suggests the direct computation of these objects via eigenmodes of the associated Frobenius-Perron operator by means of a multilevel subdivision algorithm. The advocated approach is different to both Monte-Carlo techniques on the one hand and long term trajectory simulation on the other hand: in our setup long term trajectories are replaced by short term sub-trajectories, Monte-Carlo techniques are just structurally connected via the underlying Frobenius-Perron theory. Numerical experiments with a first version of our suggested algorithm are included to illustrate certain distinguishing properties. A more advanced version of the algorithm will be presented in a second part of this paper.

Description: The aim of this work is to study the accuracy and stability of the Chebyshev--approximation method as a time--discretization for wavepacket dynamics. For this frequently used discretization we introduce estimates of the approximation and round--off error. These estimates mathematically confirm the stability of the Chebyshev--approximation with respect to round--off errors, especially for very large stepsizes. But the results also disclose threads to the stability due to large spatial dimensions. All theoretical statements are illustrated by numerical simulations of an analytically solvable example, the harmonic quantum oszillator.

Description: We present an integrated time--space adaptive finite element method for solving systems of twodimensional nonlinear parabolic systems in complex geometry. The partial differential system is first discretized in time using a singly linearly implicit Runge--Kutta method of order three. Local time errors for the step size control are defined by an embedding strategy. These errors are used to propose a new time step by a PI controller algorithm. A multilevel finite element method with piecewise linear functions on unstructured triangular meshes is subsequently applied for the discretization in space. The local error estimate of the finite element solution steering the adaptive mesh refinement is obtained solving local problems with quadratic trial functions located essentially at the edges of the triangulation. This two--fold adaptivity successfully ensures an a priori prescribed tolerance of the solution. The devised method is applied to laminar gaseous combustion and to solid--solid alloying reactions. We demonstrate that for such demanding applications the employed error estimation and adaption strategies generate an efficient and versatile algorithm.

Description: \iffalse Recently, Todorov and Wilf independently realized that de Branges' original proof of the Bieberbach and Milin conjectures and the proof that was later given by Weinstein deal with the same special function system that de Branges had introduced in his work. In this article, we present an elementary proof of this statement based on the defining differential equations system rather than the closed representation of de Branges' function system. Our proof does neither use special functions (like Wilf's) nor the residue theorem (like Todorov's) nor the closed representation (like both), but is purely algebraic. On the other hand, by a similar algebraic treatment, the closed representation of de Branges' function system is derived. Our whole contribution can be looked at as the study of properties of the Koebe function. Therefore, in a very elementary manner it is shown that the known proofs of the Bieberbach and Milin conjectures can be understood as a consequence of the Löwner differential equation, plus properties of the Koebe function. \fi In his 1984 proof of the Bieberbach and Milin conjectures de Branges used a positivity result of special functions which follows from an identity about Jacobi polynomial sums that was found by Askey and Gasper in 1973, published in 1976. In 1991 Weinstein presented another proof of the Bieberbach and Milin conjectures, also using a special function system which (by Todorov and Wilf) was realized to be the same as de Branges'. In this article, we show how a variant of the Askey-Gasper identity can be deduced by a straightforward examination of Weinstein's functions which intimately are related with a Löwner chain of the Koebe function, and therefore with univalent functions.

Description: This paper presents a large-scale real-world application of the minimum-cost flow problem, describes some details of a new implementation of the network simplex algorithm, and reports on computational comparisions. The real-world test sets include minimum-cost flow problems that are based on single-depot vehicle scheduling problems and on a Lagrangean relaxation of multiple-depot vehicle scheduling problems. Some of the problems are extremely large with up to 42,000 nodes and 20,000,000 arcs. The standard test problems are generated with NETGEN and include parts of the DIMACS standard problems. Our network simplex code is compared with \mbox{RELAX-IV}, Cost Scaling 2 version 3.4, and CPLEX's network solver NETOPT.

Description: Integrals of optimal values of random optimization problems depending on a finite dimensional parameter are approximated by using empirical distributions instead of the original measure. Under fairly broad conditions, it is proved that uniform convergence of empirical approximations of the right hand sides of the constraints implies uniform convergence of the optimal values in the linear and convex case.

Description: The adaptive Rothe method approaches a time-dependent PDE as an ODE in function space. This ODE is solved {\em virtually} using an adaptive state-of-the-art integrator. The {\em actual} realization of each time-step requires the numerical solution of an elliptic boundary value problem, thus {\em perturbing} the virtual function space method. The admissible size of that perturbation can be computed {\em a priori} and is prescribed as a tolerance to an adaptive multilevel finite element code, which provides each time-step with an individually adapted spatial mesh. In this way, the method avoids the well-known difficulties of the method of lines in higher space dimensions. During the last few years the adaptive Rothe method has been applied successfully to various problems with infinite speed of propagation of information. The present study concerns the adaptive Rothe method for hyperbolic equations in the model situation of the wave equation. All steps of the construction are given in detail and a numerical example (diffraction at a corner) is provided for the 2D wave equation. This example clearly indicates that the adaptive Rothe method is appropriate for problems which can generally benefit from mesh adaptation. This should be even more pronounced in the 3D case because of the strong Huygens' principle.

Description: A numerical method for the treatment of moving discontinuities in the model equations of chemical engineering systems is presented. The derived model describing the effects of condensation and evaporation in a regenerative air to air heat exchanger yields an illustrative example for these so called moving boundary problems. The presented adaptive moving grid method is based on the algorithm {\sc Pdex} for parabolic partial differential equations. It is shown that the method is suited for problems where the arising discontinuities cause low rates of convergence if the equations are solved with a static grid.

Description: Nahezu flächendeckend sind die mathematischen Fachbereiche der BRD zum Jahresende '95 im WWW vertreten. Durch die relative hohe Zahl von Servern entstehen Schwierigkeiten bei der Sichtung der angebotenen Information. Wir besprechen "Harvest" als brauchbares und gebrauchsfähiges Hilfsmittel zur Dokumentation.

Description: Der Report analysiert die Ergebnisse des Projektes ,,Verbesserung des benutzerorientierten Zugriffs auf fachspezifische Online und CD-ROM Datenbanken für Mathematische Institute der Bundesrepublik Deutschland'' der Deutschen Mathematiker-Vereinigung. An dem Projekt, das vom ZIB geleitet und koordiniert worden ist, haben mehr als 50 mathematische Fachbereiche und Forschungsinstitute teilgenommen. Dieses vom damaligen BMFT (einem Teil des jetzigen Bundesministeriums für Bildung, Wissenschaft, Forschung und Technologie) geförderte Projekt hat wesentlich dazu beigetragen, dass fachspezifische Datenbanken heute in den mathematischen Fachbereichen in Deutschland zu den selbstverständlichen Arbeitsmitteln gehören. Darüber hinaus hat das Projekt die Grundlagen für eine moderne elektronische Informations- und Kommunikationsstruktur in den mathematischen Fachbereichen gelegt.

Description: Dieser Report beschreibt ein Konzept zur einheitlichen Bereitstellung von Software in heterogenen Umgebungen. Software kann so kooperativ durch mehrere Beteiligten (z. B. auch über Institutsgrenzen hinweg) angeboten und genutzt werden. Die Konzepte stammen ursprünglich vom Rechenzentrum der Universität Stuttgart (RUS) und wurden im Rahmen eines vom Verein zur Förderung eines Deutschen Forschungsnetzes (DFN) mit Mitteln des BMBF geförderten Projekts zur Berliner Software Distribution (BeSD) weiterentwickelt.

Description: In this thesis we describe a practical problem that we encountered in the on--line optimization of a complex Flexible Manufacturing System. In the considered system a stacker crane has to fulfill all transportation tasks (jobs) in a single aisled automatic storage system. The jobs have to be sequenced in such a way, that the time needed for the unloaded moves is minimized. The modelling of this question leads to the so--called on--line Hamiltonian path problem. We computationally compare several on--line heuristics and derive lower bounds on the value obtained by an optimal on--line strategy by analyzing two off--line Combinatorial Optimization problems: the asymmetric Hamiltonian path problem with precedence constraints, also called sequential ordering problem (SOP), and the asymmetric Hamiltonian path problem with time windows (AHPPTW). We study the SOP and AHPPTW from a polyhedral point of view and derive several new classes of valid inequalities. Based on the polyhedral investigations we develop branch&cut algorithms for both problems and can achieve encouraging results on solving problem instances from real--world examples of the practical application.

Description: Steht uns das Ende des traditionellen wissenschaftlichen Publizierens bevor? Neue Technologien eröffnen neue Chancen zur Bewältigung der Informationsflut und des gleichzeitigen Informationsmangels. Doch der Einsatz von Technik allein reicht nicht aus.

Description: Der Artikel ist die ausgearbeitete und erweiterte Fassung eines eingeladenen Vortrags der Tagung ,,Die unendliche Bibliothek - Digitale Information in Wissenschaft, Verlag und Bibliothek''. Dieses Treffen, eine Veranstaltung des Börsenvereins des Deutschen Buchhandels e.V., der Deutschen Bibliothek und der Bundesvereinigung Deutscher Bibliothkesverbände, fand im Dezember 1995 in Bonn als Beitrag zur der heute aktuellen Debatte unter Wissenschaftlern, Verlegern, Buchhändlern, Bibliothekaren und Politikern statt, wie unser Wissen und unsere Informationen digital transferiert werden können. Der Vortrag stellte das zentrale Problem des heutigen wissenschaftlichen Informationswesens dar, die gleichzeitige Existenz von Informationsflut und Informationsmangel. Nach einer knappen Bestimmung der Veränderung der Kommunikationsstrukturen in den Wissenschaften fragte er nach den essentiellen Veränderungen der Informationsarten, d.h. nach der Natur der kommenden Globalen Digitalen Bibliothek, die als ein über die ganze Welt und auf viele Institutionen verteilter globaler Speicher gesehen wird. Der Vortrag diskutierte zum Schluss die Bedürfnisse und Interessen der Wissenschaften und ihre spezifische Verantwortung beim Übergang in die elektronische Welt. Der Tagungsband ist erschienen beim Harrassowitz Verlag, Wiesbaden, 1996.

Description: The Internet and the new electronic means of information and communication are transforming scientific communication fundamentally. In particular, mathematicians, physicists and other natural scientists intensify, accelerate and extend their communication by the use of the Internet and its tools, from electronic mail up to the World Wide Web. In doing so, they also exchange scientific results of a new kind and quality yet unknown to traditional information providers such as publishers, libraries, and database suppliers (e.g. in the form of current research software, scientific data collections, observations and experimental data, visualizations, animations etc.). They, on the other hand, perceive the new ways, which are passing their own field of activity, as breakdowns of traditional publishing, as it was termed by the Association of Computing Machinery. In addition, scientific libraries find themselves caught in a structural crisis -- not only because of budget restraints. The {\it Deutsche Mathematiker-Vereinigung} (DMV), however, sees the new electronic means as an opportunity to master a crisis of this kind rather than a threat. By discussing concrete models, which may be - in a certain technical sense -- realizable already today, the article gives an introduction into the subject of a {\it Distributed Information- and Communication System for Mathematics}, a project prepared and planned by the DMV for the years 1996 to 1998. In the context of possible realization variants it also deals with questions of costs, resulting load of network connections, and -- showing the beginnings -- the (absolutely essential) solution of problems related to quality, authenticity, archival and intellectual property rights, which arise with the employment of electronic means. Obviously (even if not discussed explicitly) also computing centers, whose tasks and position are also affected by the electronic revolution, have the chance to find a new and forward-looking role in this field - in particular by new forms of cooperation with scientific libraries.

Description: Dieser Bericht beschreibt die Ergebnisse eines Anwendungsprojektes, das parallel zum Aufbau des Berliner Hochgeschwindigkeitsdatennetzes (Berlin Regional Testbed) am ZIB durchgeführt wurde. Es werden allgemeine Werkzeuge und anwendungsspezifische Arbeitsumgebungen zur netzverteilten Visualisierung und Simulation vorgestellt. Die allgemeinen Werkzeuge unterstützen folgende Aufgaben: Kopplung von Simulationen auf (Hochleistungs-)Rechnern an lokale Grafikarbeitsplätze, objektorientierte und verteilte Visualisierung, Remote-Videoaufzeichnung, Bilddatenkompression und digitaler Filmschnitt. Die spezifischen Arbeitsumgebungen wurden für Aufgaben aus den Bereichen Numerische Mathematik, Astrophysik, Strukturforschung, Chemie, Polymerphysik und Strömungsmechanik entwickelt.

Description: In diesem Handbuch werden die Bausteine zum Aufbau einer graphischen Benutzeroberfläche mit {\tt ZGUI} beschrieben. Auf der einen Seite stehen die Tcl/Tk--Prozeduren, die die graphischen Elemente definieren. Die Beschreibung der Anwendung der Prozeduren und der Interaktionen der Elemente bildet den ersten Teil des Handbuches. Auf der anderen Seite stehen die Anforderungen an Anwendungen, die mit einer {\tt ZGUI}--Benutzeroberlfäche gesteuert werden sollen. Hier findet man im Handbuch die Beschreibung der Anwendungsprogrammierschnittstelle (application programming interface, API).

Description: Dieser Aufsatz ist die Ausarbeitung eines Vortrags auf der 4. Jahrestagung der Gesellschaft Information Bildung (GIB) am 10. und 11. Oktober 1996 an der Humboldt-Universität Berlin. Er enthält einen Überblick über die neuesten Entwicklungen in der Informations- und Kommunikationstechnik und beleuchtet deren Auswirkungen auf den Wissenschaftsbetrieb. Er beginnt mit historischen Anmerkungen zur Entstehung der Schrift und zur Speicherung und Übertragung von Information. Er führt, nach einer knappen Diskussion der Defizite in der gegenwärtigen Informationsversorgung und einem kurzen Ausflug in die Geschichte des Internet und des World Wide Web, zu einer Darstellung ausgewählter aktueller Aktivitäten der Wissenschaften im Bereich elektronischer Information, Kommunikation, Dokumentation und Archivierung. Dabei zeigt sich, dass sich der Begriff wissenschaftlicher Information bereits zu wandeln beginnt. Zur traditionellen papiergebundenen Information treten völlig neue Informationsarten hinzu, von Software- und Datensammlungen über multimediale Information bis hin zu Fernübertagungen von wissenschaftlichen Vorträgen und Experimenten. Eine Vielzahl von Links; (URL's bzw. anklickbaren Verweisen) soll diesen Wandel nicht nur belegen, sondern auch das rasche Auffinden wichtiger Dokumente und Quellen im Internet ermöglichen.

Description: {\footnotesize In der vorliegenden Arbeit werden neue Implementierungen des dualen und primalen revidierten Simplex-Algorithmus für die Lösung linearer Programme (LPs) vorgestellt. Dazu werden die Algorithmen mithilfe einer Zeilenbasis dargestellt, aus der über einen Spezialfall die übliche Darstellung mit einer Spaltenbasis folgt. Beide Darstellungen sind über die Dualität eng miteinander verbunden. Ausserdem wird eine theoretische Untersuchung der numerischen Stabilität von Simplex-Algorithmen durchgeführt, und es werden verschiedene Möglichkeiten der Stabilisierung diskutiert. Beide Darstellungen der Basis werden in den Implementierungen algorithmisch ausgenutzt, wobei der Einsatz der Zeilenbasis für LPs mit mehr Nebenbedingungen als Variablen Geschwindigkeitsvorteile bringt. Darüberhinaus werden weitere Beschleunigung gegenüber anderen state-of-the-art Implentierungen erzielt, und zwar durch den Einsatz eines Phase-1 LPs, das eine grösstmögliche Übereinstimmung mit dem Ausgangs-LPs aufweist, durch eine dynamische Anpassung der Faktorisierungsfrequenz für die Basis-Matrix und durch die Optimierung der Lösung linearer Gleichungssysteme für besonders dünnbesetzte Matrizen und Vektoren. Es wurden drei Implementierungen vorgenommen. Die erste läuft sequentiell auf einem PC oder einer Workstation. Ihre hohe numerische Stabilität und Effizienz durch die Integration der oben genannten Konzepte machen sie zu einem zuverlässigen Hilfsmittel für den täglichen Einsatz z.B.~in Schnittebenenverfahren zur Lösung ganzzahliger Programme. Als Programmiersprache wurde C++ verwendet, und es wurde ein objektorientierter Software-Entwurf zugrundegelegt. Dieser leistet eine hohe Flexibilität und Anpassbarkeit z.B.~für die Integration benutzerdefinierter Pricing-Strategien. Bei den anderen beiden Implentierungen handelt es sich um parallele Versionen für Parallelrechner mit gemeinsamem und für solche mit verteiltem Speicher. Dabei wird der objektorientierte Entwurf so genutzt, dass lediglich die zusätzlichen Aufgaben für die Parallelisierung (Synchronisation, Kommunikation und Verteilung der Arbeit) implementiert werden, während alle Algorithmen von der sequentiellen Implementierung geerbt werden. Die Parallelisierung setzt an vier Punkten an. Der erste und einfachste ist die parallele Berechnung eines Matrix-Vektor-Produktes. Als zweites wurden beim Pricing und Quotiententest parallele Suchalgorithmen eingesetzt. Weiter werden beim steepest-edge Pricing zwei lineare Gleichungssysteme nebenläufig gelöst. Schliesslich wird ein paralleles Block-Pivoting verwendet, bei dem Gleichungssysteme mehrerer aufeinanderfolgender Iterationen gleichzeitig gelöst werden. Ob und welche der Parallelisierungs-Konzepte eine Beschleunigung bewirken, ist problemabhängig. Es gelingt z.B.~mit 32 Prozessoren eine Beschleunigung um mehr als einen Faktor 16 zu erzielen. Schliesslich wird die parallele Lösung dünnbesetzter linearer Gleichungssysteme mit unsymmetrischen Matrizen untersucht und eine Implementierung für den Cray T3D vorgenommen. Sie enthält ein neues Verfahren des Lastausgleichs, das keinen zusätzlichen Aufwand verursacht. Die Implementierung erzielt vergleichsweise günstige Laufzeiten.}

Description: We present parallel formulations of the well established extrapolation algorithms EULSIM and LIMEX and its implementation on a distributed memory architecture. The discretization of partial differential equations by the method of lines yields large banded systems, which can be efficiently solved in parallel only by iterative methods. Polynomial preconditioning with a Neumann series expansion combined with an overlapping domain decomposition appears as a very efficient, robust and highly scalable preconditioner for different iterative solvers. A further advantage of this preconditioner is that all computation can be restricted to the overlap region as long as the subdomain problems are solved exactly. With this approach the iterative algorithms operate on very short vectors, the length of the vectors depends only on the number of gridpoints in the overlap region and the number of processors, but not on the size of the linear system. As the most reliable and fast iterative methods based on this preconditioning scheme appeared GMRES or FOM and BICGSTAB. To further reduce the number of iterations in GMRES or FOM we can reuse the Krylov-spaces constructed in preceeding extrapolation steps. The implementation of the method within the program LIMEX results in a highly parallel and scalable program for solving differential algebraic problems getting an almost linear speedup up to 64 processors even for medium size problems. Results are presented for a difficult application from chemical engineering simulating the formation of aerosols in industrial gas exhaust purification.