Library

Description: Im Rahmen ihrer Strategie zur Langzeitarchivierung forscht die Deutsche Kinemathek in einer Kooperation mit dem Zuse-Institut Berlin (ZIB) an der digitalen Langzeitarchivierung von AV-Materialien. Ausgangspunkt des Projektes sind die enormen Dateigrößen und die heterogenen Dateiformate, die einem Werk und einer Fassung zugeordnet werden müssen. Die Verwendung von persistenten Identifikatoren stellt den Lösungsansatz dar.

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, this review extends to the corresponding partitioning problems.

Description: We present an optimization model which is capable of routing and ordering trains on a microscopic level under a moving block regime. Based on a general timetabling definition (GTTP) that allows the plug in of arbitrarily detailed methods to compute running and headway times, we describe a layered graph approach using velocity expansion, and develop a mixed integer linear programming formulation. Finally, we present promising results for a German corridor scenario with mixed traffic, indicating that applying branch-and-cut to our model is able to solve reasonably sized instances with up to hundred trains to optimality.

Description: We propose a new mixed integer programming based heuristic for computing new benchmark primal solutions for instances of the PESPlib. The PESPlib is a collection of instances for the Periodic Event Scheduling Problem (PESP), comprising periodic timetabling problems inspired by real-world railway timetabling settings, and attracting several international research teams during the last years. We describe two strategies to merge a set of good periodic timetables. These make use of the instance structure and minimum weight cycle bases, finally leading to restricted mixed integer programming formulations with tighter variable bounds. Implementing this timetable merging approach in a concurrent solver, we improve the objective values of the best known solutions for the smallest and largest PESPlib instances by 1.7 and 4.3 percent, respectively.

Description: Die Sicherung und längerfristige Archivierung persönlich relevanter Dokumente und Dateien, in der Fachliteratur als Personal Digital Archiving (PDA) bezeichnet, ist eine für Privatpersonen zunehmend wichtiger werdende Aufgabe. Praktische Anleitungen und weiterführende Hinweise zur Umsetzung dieser Aufgabe gibt die auf unterschiedliche Nutzer:innenperspektiven ausgerichtete Webseite meinDigitalesArchiv.de, die seit 2020 von der nestor-AG PDA bereitgestellt wird. Mit den Informationen dieser Webseite können und sollten Bibliotheken und andere Einrichtungen, die Informationskompetenz vermitteln, Privatpersonen für die Sicherung ihrer persönlichen digitalen Daten sensibilisieren und schulen. Mit der Umsetzung dieser Aufgabe können Öffentliche wie Wissenschaftliche Bibliotheken zur Sicherung auch gesamtgesellschaftlich relevanter Erinnerungsbausteine beitragen.

Description: 二次割当問題は線形緩和が弱いことが知られ，強化のため多様な緩和手法が考案されているが，その一つである二重非負値計画緩和（ DNN 緩和）及びその解法として近年研究が進んでいるニュートン・ブラケット法を紹介し，それらに基づく分枝限定法の実装及び数値実験結果について報告する．

Description: The Periodic Event Scheduling Problem (PESP) is the standard mathematical tool for optimizing periodic timetabling problems in public transport. A solution to PESP consists of three parts: a periodic timetable, a periodic tension, and integer periodic offset values. While the space of periodic tension has received much attention in the past, we explore geometric properties of the other two components, establishing novel connections between periodic timetabling and discrete geometry. Firstly, we study the space of feasible periodic timetables, and decompose it into polytropes, i.e., polytopes that are convex both classically and in the sense of tropical geometry. We then study this decomposition and use it to outline a new heuristic for PESP, based on the tropical neighbourhood of the polytropes. Secondly, we recognize that the space of fractional cycle offsets is in fact a zonotope. We relate its zonotopal tilings back to the hyperrectangle of fractional periodic tensions and to the tropical neighbourhood of the periodic timetable space. To conclude we also use this new understanding to give tight lower bounds on the minimum width of an integral cycle basis.

Description: Optimizing the transient control of gas networks is a highly challenging task. The corresponding model incorporates the combinatorial complexity of determining the settings for the many active elements as well as the non-linear and non-convex nature of the physical and technical principles of gas transport. In this paper, we present the latest improvements of our ongoing work to solve this problem for real-world, large-scale problem instances: By adjusting our mixed-integer non-linear programming model regarding the gas compression capabilities in the network, we reflect the technical limits of the underlying units more accurately while maintaining a similar overall model size. In addition, we introduce a new algorithmic approach that is based on splitting the complexity of the problem by first finding assignments for discrete variables and then determining the continuous variables as locally optimal solution of the corresponding non-linear program. For the first task, we design multiple different heuristics based on concepts for general time-expanded optimization problems that find solutions by solving a sequence of sub-problems defined on reduced time horizons. To demonstrate the competitiveness of our approach, we test our algorithm on particularly challenging historic demand scenarios. The results show that high-quality solutions are obtained reliably within short solving times, making the algorithm well-suited to be applied at the core of time-critical industrial applications.

Description: Public transportation networks are typically operated with a periodic timetable. The periodic event scheduling problem (PESP) is the standard mathematical modeling tool for periodic timetabling. PESP is a computationally very challenging problem: For example, solving the instances of the benchmarking library PESPlib to optimality seems out of reach. Since PESP can be solved in linear time on trees, and the treewidth is a rather small graph parameter in the networks of the PESPlib, it is a natural question to ask whether there are polynomial-time algorithms for input networks of bounded treewidth, or even better, fixed-parameter tractable algorithms. 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. Moreover, we show W[1]-hardness of the general feasibility problem with respect to treewidth, which means that we can most likely only accomplish pseudo-polynomial-time algorithms on input networks with bounded tree- or branchwidth. We present two such algorithms based on dynamic programming. 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: Cut selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP.

Description: Secure energy transport is considered as highly relevant for the basic infrastructure of nowadays society and economy. To satisfy increasing demands and to handle more diverse transport situations, operators of energy networks regularly expand the capacity of their network by building new network elements, known as the expansion planning problem. A key constraint function in expansion planning problems is a nonlinear and nonconvex potential loss function. In order to improve the algorithmic performance of state-of-the-art MINLP solvers, this paper presents an algebraic description for the convex envelope of this function. Through a thorough computational study, we show that this tighter relaxation tremendously improves the performance of the MINLP solver SCIP on a large test set of practically relevant instances for the expansion planning problem. In particular, the results show that our achievements lead to an improvement of the solver performance for a development version by up to 58%.

Description: It is well known as the Kelvin-Helmholtz instability (KHI) that an interface of tangential velocity discontinuity is necessarily unstable, regardless of the velocity difference's strength. However, the KHI is suppressed for shallow water flows if the Froude number, defined by the ratio of the velocity difference to the gravity wave's speed, is sufficiently large. In this investigation, we examine the effect of the depth difference of two fluid layers on the KHI. The depth difference enhances instability. Given the Froude number in the instability range, the growth rate sensitively depends on the depth ratio and increases monotonically with the depth ratio difference from unity. The critical value of the Froude number for stabilization varies with the depth ratio and attains the minimum value √8 for equal depth. This behavior is verified by asymptotic analysis.

Description: The European energy system has been through a fundamental transformation since the Paris Agreement to reduce greenhouse gas emissions. The transition involves several energy-generating and consuming sectors emphasizing sector coupling. The increase in the share of renewable energy sources has revealed the need for flexibility in the electri city grid. Thus, holistic planning of pathways towards decarbonized energy systems also involves assessing the gas infrastructure to provide such a flexibility and support for the security of supply. In this paper, we propose a workflow to investigate such optimal energy transition pathways considering sector coupling. This workflow involves an integrated operational analysis of the electricity market, its transmission grid, and the gas grid in high spatio-temporal resolution. In a case study on a pan-European scale between 2020-2050, we show that carbon neutrality can be reached within feasible additional costs and in time. However, the manifestation of the potential pathways strongly depends on political and technological constraints. Sector coupling acts as an enabler of cross-border cooperation to achieve both, decarbonization and security of supply.

Description: Biological armors derive their mechanical integrity in part from their geometric architectures, often involving tessellations: individual structural elements tiled together to form surface shells. The carapace of boxfish, for example, is comprised of mineralized polygonal plates, called scutes, arranged in a complex geometric pattern and nearly completely encasing the body. In contrast to artificial armors, the boxfish exoskeleton grows with the fish; the relationship between the tessellation and the gross structure of the armor is therefore critical to sustained protection throughout growth. To clarify whether or how the boxfish tessellation is maintained or altered with age, we quantify architectural aspects of the tessellated carapace of the longhorn cowfish Lactoria cornuta through ontogeny (across nearly an order of magnitude in standard length) and in a high-throughput fashion, using high-resolution microCT data and segmentation algorithms to characterize the hundreds of scutes that cover each individual. We show that carapace growth is canalized with little variability across individuals: rather than continually adding scutes to enlarge the carapace surface, the number of scutes is surprisingly constant, with scutes increasing in volume, thickness, and especially width with age. As cowfish and their scutes grow, scutes become comparatively thinner, with the scutes at the edges (weak points in a boxy architecture) being some of the thickest and most reinforced in younger animals and thinning most slowly across ontogeny. In contrast, smaller scutes with more variable curvature were found in the limited areas of more complex topology (e.g. around fin insertions, mouth, and anus). Measurements of Gaussian and mean curvature illustrate that cowfish are essentially tessellated boxes throughout life: predominantly zero curvature surfaces comprised of mostly flat scutes, and with scutes with sharp bends used sparingly to form box edges. Since growth of a curved, tiled surface with a fixed number of tiles would require tile restructuring to accommodate the surface’s changing radius of curvature, our results therefore illustrate a previously unappreciated advantage of the odd boxfish morphology: by having predominantly flat surfaces, it is the box-like body form that in fact permits a relatively straightforward growth system of this tessellated architecture (i.e. where material is added to scute edges). Our characterization of the ontogeny and maintenance of the carapace tessellation provides insights into the potentially conflicting mechanical, geometric and developmental constraints of this species, but also perspectives into natural strategies for constructing mutable tiled architectures.

Description: The electric conductivity of cardiac tissue determines excitation propagation and is important for quantifying ischemia and scar tissue and for building personalized models. Estimating conductivity distributions from endocardial mapping data is a challenging inverse problem due to the computational complexity of the monodomain equation, which describes the cardiac excitation. For computing a maximum posterior estimate, we investigate different optimization approaches based on adjoint gradient computation: steepest descent, limited memory BFGS, and recursive multilevel trust region methods, which are using mesh hierarchies or heterogeneous model hierarchies. We compare overall performance, asymptotic convergence rate, and pre-asymptotic progress on selected examples in order to assess the benefit of our multifidelity acceleration.

Description: Tai256c is the largest unsolved quadratic assignment problem (QAP) instance in QAPLIB; a 1.48% gap remains between the best known feasible objective value and lower bound of the unknown optimal value. This paper shows that the instance can be converted into a 256 dimensional binary quadratic optimization problem (BQOP) with a single cardinality constraint which requires the sum of the binary variables to be 92.The converted BQOP is much simpler than the original QAP tai256c and it also inherits some of the symmetry properties. However, it is still very difficult to solve. We present an efficient branch and bound method for improving the lower bound effectively. A new lower bound with 1.36% gap is also provided.

Description: The combination of Monte Carlo methods and deep learning has recently led to efficient algorithms for solving partial differential equations (PDEs) in high dimensions. Related learning problems are often stated as variational formulations based on associated stochastic differential equations (SDEs), which allow the minimization of corresponding losses using gradient-based optimization methods. In respective numerical implementations it is therefore crucial to rely on adequate gradient estimators that exhibit low variance in order to reach convergence accurately and swiftly. In this article, we rigorously investigate corresponding numerical aspects that appear in the context of linear Kolmogorov PDEs. In particular, we systematically compare existing deep learning approaches and provide theoretical explanations for their performances. Subsequently, we suggest novel methods that can be shown to be more robust both theoretically and numerically, leading to substantial performance improvements.

Description: We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs) such as recently developed diffusion probabilistic models. In particular, we derive a Hamilton-Jacobi-Bellman equation that governs the evolution of the log-densities of the underlying SDE marginals. This perspective allows to transfer methods from optimal control theory to generative modeling. First, we show that the evidence lower bound is a direct consequence of the well-known verification theorem from control theory. Further, we develop a novel diffusion-based method for sampling from unnormalized densities -- a problem frequently occurring in statistics and computational sciences.

Description: This study investigates the progress made in LP and MILP solver performance during the last two decades by comparing the solver software from the beginning of the millennium with the codes available today. On average, we found out that for solving LP/MILP, computer hardware got about 20 times faster, and the algorithms improved by a factor of about nine for LP and around 50 for MILP, which gives a total speed-up of about 180 and 1,000 times, respectively. However, these numbers have a very high variance and they considerably underestimate the progress made on the algorithmic side: many problem instances can nowadays be solved within seconds, which the old codes are not able to solve within any reasonable time.

Description: We study two related problems concerning the number of monochromatic cliques in two-colorings of the complete graph that go back to questions of Erdős. Most notably, we improve the 25-year-old upper bounds of Thomason on the Ramsey multiplicity of K4 and K5 and we settle the minimum number of independent sets of size 4 in graphs with clique number at most 4. Motivated by the elusiveness of the symmetric Ramsey multiplicity problem, we also introduce an off-diagonal variant and obtain tight results when counting monochromatic K4 or K5 in only one of the colors and triangles in the other. The extremal constructions for each problem turn out to be blow-ups of a finite graph and were found through search heuristics. They are complemented by lower bounds and stability results established using Flag Algebras, resulting in a fully computer-assisted approach. More broadly, these problems lead us to the study of the region of possible pairs of clique and independent set densities that can be realized as the limit of some sequence of graphs.

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: Periodic timetabling is a central aspect of both the long-term organization and the day-to-day operations of a public transportation system. The Periodic Event Scheduling Problem (PESP), the combinatorial optimization problem that forms the mathematical basis of periodic timetabling, is an extremely hard problem, for which optimal solutions are hardly ever found in practice. The most prominent solving strategies today are based on mixed-integer programming, and there is a concurrent PESP solver employing a wide range of heuristics [Borndörfer et al., 2020]. We present tropical neighborhood search (tns), a novel PESP heuristic. The method is based on the relations between periodic timetabling and tropical geometry [Bortoletto et al., 2022]. We implement tns into the concurrent solver, and test it on instances of the benchmarking library PESPlib. The inclusion of tns turns out to be quite beneficial to the solver: tns is able to escape local optima for the modulo network simplex algorithm, and the overall share of improvement coming from tns is substantial compared to the other methods available in the solver. Finally, we provide better primal bounds for five PESPlib instances.

Description: OASIcs, Volume 106, ATMOS 2022, Complete Volume

Description: Extracting information about dynamical systems from models learned off simulation data has become an increasingly important research topic in the natural and engineering sciences. Modeling the Koopman operator semigroup has played a central role in this context. As the approximation quality of any such model critically depends on the basis set, recent work has focused on deriving data-efficient representations of the Koopman operator in low-rank tensor formats, enabling the use of powerful model classes while avoiding over-fitting. On the other hand, detailed information about the system at hand can be extracted from models for the infinitesimal generator, also called Kolmogorov backward operator for stochastic differential equations. In this work, we present a data-driven method to efficiently approximate the generator using the tensor train (TT) format. The centerpiece of the method is a TT representation of the tensor of generator evaluations at all data sites. We analyze consistency and complexity of the method, present extensions to practically relevant settings, and demonstrate its applicability to benchmark numerical examples.

Description: Finding connected subgraphs of maximum weight subject to additional constraints on the subgraphs is a common (sub)problem in many applications. In this paper, we study the Maximum Weight Connected Subgraph Problem with a given root node and a lower and upper capacity constraint on the chosen subgraph. In addition, the nodes of the input graph are colored blue and red, and the chosen subgraph is required to be balanced regarding its cumulated blue and red weight. This problem arises as an essential subproblem in district planning applications. We show that the problem is NP-hard and give an integer programming formulation. By exploiting the capacity and balancing condition, we develop a powerful reduction technique that is able to significantly shrink the problem size. In addition, we propose a method to strengthen the LP relaxation of our formulation by identifying conflict pairs, i.e., nodes that cannot be both part of a chosen subgraph. Our computational study confirms the positive impact of the new preprocessing technique and of the proposed conflict cuts.

Description: We consider autocovariance operators of a stationary stochastic process on a Polish space that is embedded into a reproducing kernel Hilbert space. We investigate how empirical estimates of these operators converge along realizations of the process under various conditions. In particular, we examine ergodic and strongly mixing processes and obtain several asymptotic results as well as finite sample error bounds. We provide applications of our theory in terms of consistency results for kernel PCA with dependent data and the conditional mean embedding of transition probabilities. Finally, we use our approach to examine the nonparametric estimation of Markov transition operators and highlight how our theory can give a consistency analysis for a large family of spectral analysis methods including kernel-based dynamic mode decomposition.

Description: This work addresses the problem of determining the number of components from sequential spectroscopic data analyzed by non-negative matrix factorization without separability assumption (SepFree NMF). These data are stored in a matrix M of dimension “measured times” versus “measured wavenumbers” and can be decomposed to obtain the spectral fingerprints of the states and their evolution over time. SepFree NMF assumes a memoryless (Markovian) process to underline the dynamics and decomposes M so that M=WH, with W representing the components’ fingerprints and H their kinetics. However, the rank of this decomposition (i.e., the number of physical states in the process) has to be guessed from pre-existing knowledge on the observed process. We propose a measure for determining the number of components with the computation of the minimal memory effect resulting from the decomposition; by quantifying how much the obtained factorization is deviating from the Markovian property, we are able to score factorizations of a different number of components. In this way, we estimate the number of different entities which contribute to the observed system, and we can extract kinetic information without knowing the characteristic spectra of the single components. This manuscript provides the mathematical background as well as an analysis of computer generated and experimental sequentially measured Raman spectra.

Description: We consider the line planning problem in public transport in the Parametric City, an idealized model that captures typical scenarios by a (small) number of parameters. The Parametric City is rotation symmetric, but optimal line plans are not always symmetric. This raises the question to quantify the symmetry gap between the best symmetric and the overall best solution. For our analysis, we formulate the line planning problem as a mixed integer linear program, that can be solved in polynomial time if the solutions are forced to be symmetric. The symmetry gap is provably small when a specific Parametric City parameter is fixed, and we give an approximation algorithm for line planning in the Parametric City in this case. While the symmetry gap can be arbitrarily large in general, we show that symmetric line plans are a good choice in most practical situations.

Description: In this paper, we consider the eigenvalue PDE problem of the infinitesimal generators of metastable diffusion processes. We propose a numerical algorithm based on training artificial neural networks for solving the leading eigenvalues and eigenfunctions of such high-dimensional eigenvalue problem. The algorithm is useful in understanding the dynamical behaviors of metastable processes on large timescales. We demonstrate the capability of our algorithm on a high-dimensional model problem, and on the simple molecular system alanine dipeptide.

Description: We propose new Markov Chain Monte Carlo algorithms to sample probability distributions on submanifolds, which generalize previous methods by allowing the use of set-valued maps in the proposal step of the MCMC algorithms. The motivation for this generalization is that the numerical solvers used to project proposed moves to the submanifold of interest may find several solutions. We show that the new algorithms indeed sample the target probability measure correctly, thanks to some carefully enforced reversibility property. We demonstrate the interest of the new MCMC algorithms on illustrative numerical examples.

Description: As a result of the legislation for gas markets introduced by the European Union in 2005, separate independent companies have to conduct the transport and trading of natural gas. The current gas market of Germany, which has a market value of more than 54 billion USD, consists of Transmission System Operators (TSO), network users, and traders. Traders can nominate a certain amount of gas anytime and anywhere in the network. Such unrestricted access for the traders, on the other hand, increase the uncertainty in the gas supply management. Some customers’ behaviors may cause abrupt structural changes in gas flow time series. In particular, it is a challenging task for the TSO operators to predict gas nominations 6 to 10 h-ahead. In our study, we aim to investigate the regime changes in time series of nominations to predict the 6 to 10 h-ahead of gas nominations.

Description: Der Kooperative Bibliotheksverbund Berlin-Brandenburg wird heute 25 Jahre alt. Seit dem 1. April 1997 entwickelt der KOBV neue Dienstleistungen für Nutzende und Bibliotheken, baut Informationsinfrastrukturen in Berlin und Brandenburg aus, vernetzt Bibliotheken aus der Region und informiert über aktuelle Themen. Im Sondernewsletter geben uns aktuelle und ehemalige KOBV-Mitarbeitende/Mitglieder Antworten auf Fragen zur Entstehung und Weiterentwicklung des Verbundes. Lesen und feiern Sie mit uns zusammen!

Description: Mit DeepGreen wurde eine Infrastruktur aufgebaut und etabliert, die Zeitschriftenartikel von wissenschaftlichen Verlagen abholt und berechtigten Bibliotheken zur Veröffentlichung in ihren Repositorien sendet. DeepGreen unterstützt Bibliotheken als Dienstleister für Hochschulen, außeruniversitäre Einrichtungen und die dort tätigen Wissenschaftler*innen, Publikationen auf Open-Access-Repositorien frei zugänglich zu machen und fördert das Zusammenspiel von wissenschaftlichen Einrichtungen und Verlagen. DeepGreen wurde von Januar 2016 bis Juni 2021 von der Deutschen Forschungsgemeinschaft gefördert und wird nun vom Kooperativen Bibliotheksverbund Berlin-Brandenburg, von der Bayerischen Staatsbibliothek und von der Universitätsbibliothek Erlangen-Nürnberg in arbeitsteiliger Eigenleistung für zwei Jahre weiterbetrieben. Der vorliegende Beitrag beleuchtet vielfältige Aspekte bei der Realisierung von DeepGreen und geht auf die Perspektiven dieser zentralen Open-Access-Infrastruktur für deutsche Wissenschaftseinrichtungen ein.

Description: DeepGreen wurde vom 01.08.2018 bis zum 30.06.2021 in einer zweiten Projektphase von der Deutschen Forschungsgemeinschaft (DFG) gefördert. DeepGreen unterstützt Bibliotheken als Dienstleister für Hochschulen, außeruniversitäre Forschungseinrichtungen und die dort tätigen Wissenschaftler:innen dabei, Publikationen auf Open-Access-Repositorien frei zugänglich zu machen und fördert das Zusammenspiel von wissenschaftlichen Einrichtungen und Verlagen. An der zweiten Projektphase waren der Kooperative Bibliotheksverbund Berlin-Brandenburg, die Bayerische Staatsbibliothek, der Bibliotheksverbund Bayern, die Universitätsbibliotheken der Friedrich-Alexander-Universität Erlangen-Nürnberg und der Technischen Universität Berlin und das Helmholtz Open Science Office beteiligt. In dem Projekt wurde erfolgreich eine technische und organisatorische Lösung zur automatisierten Verteilung von Artikeldaten wissenschaftlicher Verlage an institutionelle und fachliche Repositorien entwickelt. In der zweiten Projektphase lag der Fokus auf der Erprobung der Datendrehscheibe in der Praxis und der Ausweitung auf weitere Datenabnehmer und weitere Verlage. Im Anschluss an die DFG-geförderte Projektlaufzeit ist DeepGreen in einen zweijährigen Pilotbetrieb übergegangen. Ziel des Pilotbetriebs ist es, den Übergang in einen bundesweiten Real-Betrieb vorzubereiten.

Description: During the apparition of comet 67P/Churyumov-Gerasimenko (67P/C-G) solar irradiation causes varying rates for sublimation of volatile species from the cometary nucleus. Because sublimation processes take place close to the cometary surface, the relative abundance of volatiles in the coma and the ice composition are related to each other. To quantify this relation we assume a model for the expansion of a collisionless gas from the surface into the surrounding space. We use an inverse model approach to relate the in situ measurements of gas densities from the two Rosetta instruments COPS (COmet Pressure Sensor) and DFMS (Double Focusing Mass Spectrometer) at the positions of the spacecraft to the locations of surface gas emissions during the Rosetta mission 2014-2016. We assume the temporally integrated gas emissions to be representative for the ice composition close to the surface. Our analysis shows characteristic differences in the ice compositions between both hemispheres of 67P/C-G. In particular CO2 ice has a reduced abundance on the northern hemisphere. In contrast to the hemispherical differences, the two lobes do not show significant differences in terms of their ice composition.

Description: The Rosetta mission to comet 67P/C-G provided a detailed view of the near nucleus environment of an active Jupiter family comet. The continuous monitoring of the gas pressure with the ROSINA experiment at the location of the Rosetta spacecraft in combination with the images of the dust environment acquired by the OSIRIS cameras allows one to test different hypotheses about the origin of the dust and gas emissions. In addition the orbital elements and the rotation axis and spin rate of the nucleus are affected by the gas release.

Description: The Moon as our nearest celestial object is one of the most important bodies for space resource exploration and planetary science. However, knowledge of the physical properties of the lunar regolith is required for the exploitation of lunar resources and for understanding the Moon's geologic history. This knowledge comes mainly from Apollo in-situ experiments and returned samples, but the global distribution of these properties is still poorly understood. Remote sensing measurements offer the opportunity to derive properties of unsampled areas with the help of models. In our study, a microphysical thermal model for the lunar regolith was developed and the simulated surface temperatures were compared with thermal emission measurements from the Diviner radiometer on board the Lunar Reconnaissance Orbiter (LRO) to derive regolith properties. This work expands upon previous investigations of lunar regolith properties using Diviner data, by more directly simulating physical properties such as particle size and porosity.

Description: Recently developed Concentric Tube Continuum Robots (CTCRs) are widely exploited in, for example in minimally invasive surgeries which involve navigating inside narrow body cavities close to sensitive regions. These CTCRs can be controlled by extending and rotating the tubes in order to reach a target point or perform some task. The robot must deviate as little as possible from this narrow space and avoid damaging neighbouring tissue. We consider \emph{open-loop} optimal control of CTCRs parameterized over pseudo-time, primarily aiming at minimizing the robot's working volume during its motion. External loads acting on the system like tip loads or contact with tissues are not considered here. We also discussed the inclusion of tip's orientation in the optimal framework to perform some tasks. We recall a quaternion-based formulation of the robot configuration, discuss discretization, develop optimization objectives addressing different criteria, and investigate their impact on robot path planning for several numerical examples. This optimal framework can be applied to any backbone based continuum robots.

Description: Image segmentation is an active area of research for more than 30 years. Traditional image segmentation algorithms are problem-specific and limited in scope. On the other hand, machine learning offers an alternative paradigm where predefined features are combined into different classifiers, providing pixel-level classification and segmentation. However, machine learning only can not address the question as to which features are appropriate for a certain classification problem. This paper presents a project supported in part by the International Neuroinformatics Coordination Facility through the Google Summer of code. The project resulted in an automated image segmentation and classification platform, called Active Segmentation for ImageJ (AS/IJ). The platform integrates a set of filters computing differential geometrical invariants and combines them with machine learning approaches.

Description: While energy-intensive industries like the steel industry plan to switch to renewable energy sources, other industries, such as the cement industry, have to rely on carbon capture storage and utilization technologies to reduce the inevitable carbon dioxide (CO2) emissions of their production processes. In this context, we investigate the problem of finding optimal pipeline diameters from a discrete set of diameters for a tree-shaped network transporting captured CO2 from multiple sources to a single sink. The general problem of optimizing arc capacities in potential-based fluid networks is a challenging mixed-integer nonlinear program. Additionally, the behaviour of CO2 is highly sensitive and nonlinear regarding temperature and pressure changes. We propose an iterative algorithm splitting the problem into two parts: a) the pipe-sizing problem under a fixed supply scenario and temperature distribution and b) the thermophysical modelling including mixing effects, the Joule-Thomson effect, and heat exchange with the surrounding environment. We show the effectiveness of our approach by applying our algorithm to a real-world network planning problem for a CO2 network in Western Germany.

Description: Agent-based epidemiological models have been applied widely successfully during the SARS-CoV-2 pandemic and assisted policymakers in assessing the effectiveness of intervention strategies. The computational complexity of agent-based models is still challenging, and therefore it is important to utilize modern multi-core systems as good as possible. In this paper, we are presenting our work on parallelizing the epidemiological simulation model MATSim Episim. Episim combines a large-scale person-centric human mobility model with a mechanistic model of infection and a person-centric disease progression model. In general, the parallelization of agent-based models with an inherent sequential structure — in the case of epidemiological models, the temporal order of the individual movements of the agents — is challenging. Especially when the underlying social network is irregular and dynamic, they require frequent communication between the processing elements. In Episim, however, we were able to take advantage of the fact that people are not contagious on the same day they become infected, and therefore immediate health synchronization is not required. By parallelizing some of the most computationally intensive submodels, we are now able to run MATSim Episim simulations up to eight times faster than the serial version. This makes it feasible to increase the number of agents, e.g. to run simulations for the whole of Germany instead of just Berlin as before.

Description: Im Mai 2009 wurde Wolfram|Alpha gestartet, ein Service, der seinen Namen von seinem Entwickler, dem britischen Mathematiker Stephen Wolfram, ableitet. Dem Benutzer soll nicht nur eine Liste von Webseiten als Ergebnis auf Anfragen geliefert werden, sondern Antworten auf konkrete Fragen geben. In diesem Report soll gezeigt werden, warum sichWolframjAlpha von Suchmaschinen abgrenzt und was die Berechnung von Antworten auf natürlichsprachliche Fragen möglich machen kann.

Description: Wolfram|Alpha was started in May 2009 and it's a service whose name derives from the british mathematician Stephen wolfram. As a result for a request the user is not just supported with a list of websites but with answers for concrete questions. In this report it will be shown why Wolfram|Alpha seperates from search engines and moreover what makes the computation of answers for natural language queries possible.

Description: We consider an optimal control problem from hyperthermia treatment planning and its barrier regularization. We derive basic results, which lay the groundwork for the computation of optimal solutions via an interior point path-following method. Further, we report on a numerical implementation of such a method and its performance at an example problem.

Description: Optical technologies are ubiquitously used in hi-tech devices. As a common feature of such devices one finds structures with dimensions in the order of the wavelength of the used light. To design and produce such devices, the wave nature of light must be taken into account. Accordingly, robust simulation tools are required which are based on rigorously solving Maxwell's equations, the governing equations of light propagation within macroscopic media. This thesis contributes to the modeling and the numerical computation of light scattering problems: Light scattering problems are typically posed on the entire space. The Perfectly-Matched -Layer method (PML) is widely used to restrict the simulation problem onto a bounded computational domain. We propose an adaptive PML method which exhibits a good convergence even for critical problems where standard PML implementations fail. Besides the computation of the near field, that is the electromagnetic field within the computational domain, it is of major interest to evaluate the electromagnetic field in the exterior domain and to compute the far field. So far, this was numerically only possible for simple geometries such as homogeneous exterior domains or layered media. To deal with more complicated devices, for example with waveguide inhomogeneities, we develop an evaluation formula based on the PML solution which allows for an exterior domain field evaluation in a half space above the device. Finally, we generalize the PML method to problems with multiply structured exterior domains. The term “multiply structured exterior domain” is defined in this thesis and means that the exterior domain exhibits several half-infinite structures. Mathematically, this gives rise to various complications. For example, no analytical solutions to Maxwell's equations for standard light sources are available in the exterior domain, which are needed to describe the incoming field in a light scattering problem. To tackle this we propose a new light scattering problem formulation which fits well into the PML method framework and which may be regarded as an extension of classical contributions by Sommerfeld, Wiener and Hopf. An exterior domain evaluation formula for multiply structured exterior domains with an extended illumination is derived as well.

Description: We introduce the coolest path problem, which is a mixture of two well-known problems from distinct mathematical fields. One of them is the shortest path problem from combinatorial optimization. The other is the heat conduction problem from the field of partial differential equations. Together, they make up a control problem, where some geometrical object traverses a digraph in an optimal way, with constraints on intermediate or the final state. We discuss some properties of the problem and present numerical solution techniques. We demonstrate that the problem can be formulated as a linear mixed-integer program. Numerical solutions can thus be achieved within one hour for instances with up to 70 nodes in the graph.

Description: Given a general mixed integer program (MIP), we automatically detect block structures in the constraint matrix together with the coupling by capacity constraints arising from multi-commodity-flow formulations. We identify the underlying graph and generate cutting planes based on cuts in the detected network. Our implementation adds a separator to the branch-and-cut libraries of SCIP and CPLEX. We make use of the complemented mixed integer rounding framework (cMIR) but provide a special purpose aggregation heuristic that exploits the network structure. Our separation scheme speeds-up the computation for a large set of MIPs coming from network design problems by a factor of two on average.

Description: Executing applications in the Grid often requires access to multiple geographically distributed resources. In a Grid environment, these resources belong to different administrative domains, each employing its own scheduling policy. That is, at which time an activity (e.g., compute job, data transfer) is started, is decided by the resource's local management system. In such an environment, the coordinated execution of distributed applications requires guarantees on the quality of service (QoS) of the needed resources. Reserving resources in advance is an accepted means to obtain QoS guarantees from a single provider. The challenge, however, is to coordinate advance reservations of multiple resources. This work presents a system architecture and mechanisms to coordinate multiple advance reservations -- called co-reservations -- for delivering QoS guarantees to complex applications. We formally define the co-reservation problem as an optimization problem. The presented model supports three dimensions of freedom: the start time, the duration and the service level of a reservation. Requests and resources are described in a simple language. After matching the static properties and requirements of either side in a mapping, the reservation mechanism probes information about the future status of the resources. The versatile design of the probing step allows the efficient processing of requests, but also lets the resources express their preferences among the myriads of reservation candidates. Next, the best mapping is found through an implementation of the formal co-reservation model. Then, the mapping has to be secured, i.e., resources need to be allocated to a co-reservation candidate with all-or-nothing semantics. We study several goal-driven sequential and concurrent allocation mechanisms and define schemes for handling allocation failures. Finally, we introduce the concept of virtual resources for seamlessly embedding co-reservations into Grid resource management.

Description: Die Ausführung von Anwendungen erfordert oft mehrere, geographisch verteilte Ressourcen. In Grid-Umgebungen gehören diese Ressourcen zu verschiedenen administrativen Organisationen, wobei jede ihre eigene Schedulingregeln verwendet. Das bedeutet, zu welcher Zeit eine Aktivität gestartet wird (z.B. ein Rechenjob), wird vom lokalen Ressourcenmanagementsystem entschieden. Die koordinierte Ausführung von verteilten Anwendungen erfordert Dienstgütegarantien für die benötigten Ressourcen. Das Reservieren von Ressourcen im Voraus ist ein Mittel, um Dienstgütegarantien von einem einzelnen Ressourcenanbieter zu erhalten. Die Herausforderung in dieser Arbeit ist, Vorausreservierungen von mehreren Ressourcen zu koordinieren. Es wird ein System für die Koordinierung mehrerer Vorausreservierungen -- Co-Reservierungen genannt -- für die Bereitstellung von Dienstgütegarantien vorgestellt. Wir definieren das Co-Reservierungsproblem als Optimierungsproblem. Das vorgestellte Modell unterstützt drei Freiheitsgrade: die Startzeit, die Dauer und die Dienstgüte einer Reservierung. Anfragen und Ressourcen werden in einer einfachen Sprache beschrieben. Nachdem statische Eigenschaften und Anforderungen beider Seiten überprüft wurden, ermittelt der Reservierungsmechanismus Informationen über den zukünftigen Zustand der Ressourcen. Dieser Schritt ist so allgemein gehalten, daß er sowohl ein effizientes Bearbeiten der Anfragen erlaubt als auch den Ressourcen ermöglicht ihre Präferenzen auszudrücken. Im Anschluss wird die optimale Zuweisung von Anfragen zu Ressourcen ermittelt. Im letzten Schritt muss diese Zuweisung umgesetzt werden, d.h., entweder alle oder keine Ressource wird allokiert. Es werden mehrere sequentielle und parallele Allokationsverfahren vorgestellt sowie deren Auswirkung auf verschiedene Metriken untersucht. Die Einbettung von Co-Reservierungen in das Grid-Ressourcenmanagement wird anhand des Konzeptes der virtuellen Ressource dargestellt.

Description: Vorbemerkung Beim Schreiben dieses Artikels, der auf Veränderungen der Kommunikations- und Publikationstechniken und ihre Bedeutung hinweist, ist uns mehr als je zuvor bewusst geworden, wie beschränkt das Medium Papier ist. Es gibt z. B. keine Hyperlinks, durch die man unmittelbar das Erwähnte erleben oder überprüfen kann. Ein schneller Wechsel vom Wort zum Bild, zum Ton oder Video ist nicht möglich. Wer will schon lange URLs abtippen und Medienbrüche erleiden? Wir haben uns daher entschlossen, eine textidentische Version dieses Artikels mit allen URLs – sie liegt Ihnen hier vor – elektronisch anzubieten und in der für die "Gegenworte" (BBAW) gekürzten Fassung nur durch [URL] anzudeuten, dass der Leser an dieser Stelle einfach in der elektronischen Version einen Klick ins Internet machen sollte. Und damit sind wir bereits mitten im Thema.

Description: In this paper we revisit the a priori turbulent flame speed tabulation (TFST) technique for a given parameter space within the region of flamelet combustion-regimes. It can be used as a subgrid-scale (SGS) model in Large Eddy Simulation (LES). In a first step, stationary laminar flamelets are computed and stored over the progress variable following the ideas of flamelet generated manifolds (FGM). In a second step, the incompressible one-dimensional Navier-Stokes equations supplemented by the equation for the progress variable are solved on a grid that resolves all turbulent scales. Additionally, turbulent transport is implemented via the linear eddy model (LEM). The turbulent flame structures are solved until a statistically stationary mean value of the turbulent flame speed has been reached. The results are stored in a table that could be used by large scale premixed combustion models, e.g. front tracking schemes. First results are compared quantitatively with direct numerical simulations (DNS) taken from literature. Then it is illustrated in one example how the new method could help to fix constants in algebraic models for turbulent flame speeds. Further it is shown how the technique can be extended to incorporate turbulent strain effects. Finally we investigate the effect of the use of detailed and tabulated chemistry under unsteady conditions.

Description: Pseudo-Boolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudo-Boolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we investigate the individual strengths of these approaches and compare their computational performance. Furthermore, we integrate these techniques into a branch-and-cut-and-propagate framework, resulting in an efficient nonlinear pseudo-Boolean solver.

Description: The Steiner connectivity problem is a generalization of the Steiner tree problem. It consists in finding a minimum cost set of simple paths to connect a subset of nodes in an undirected graph. We show that polyhedral and algorithmic results on the Steiner tree problem carry over to the Steiner connectivity problem, namely, the Steiner cut and the Steiner partition inequalities, as well as the associated polynomial time separation algorithms, can be generalized. Similar to the Steiner tree case, a directed formulation, which is stronger than the natural undirected one, plays a central role.

Description: Zwischen dem Bibliotheksverbund Bayern (BVB) und dem Kooperativen Bibliotheksverbund Berlin-Brandenburg (KOBV) besteht seit Ende 2007 eine Strategische Allianz, die auf zwei Säulen beruht: einer langfristigen Entwicklungspartnerschaft einerseits und der Kooperation im Dienstleistungsbereich mit der Integration der Verbundkataloge andererseits. Ende 2008 wurde das erste Entwicklungsprojekt "Literaturverwaltungsprogramme" abgeschlossen, dessen Ergebnisse in dieser Handreichung in Form von Handlungsempfehlungen für Bibliotheken vorgestellt werden. Ziel des Projekts war es, den Datenaustausch zwischen den Bibliotheks- und Verbundkatalogen des BVB und KOBV und gängigen Literaturverwaltungsprogrammen zu optimieren. Neben Handlungsempfehlungen für die Implementierung neuer Exportschnittstellen und die Verbesserung bestehender Exportmöglichkeiten werden Hinweise auf verbesserte Nutzerführung gegeben. Die Empfehlungen beziehen sich vorwiegend auf den Datenaustausch zwischen den Bibliothekssystemen Aleph 500, MetaLib und WebOPAC/InfoGuide und den Literaturverwaltungsprogrammen Citavi, EndNote, RefWorks und Zotero.

Description: Every day, millions of people are transported by buses, trains, and airplanes in Germany. Public transit (PT) is of major importance for the quality of life of individuals as well as the productivity of entire regions. Quality and efficiency of PT systems depend on the political framework (state-run, market oriented) and the suitability of the infrastructure (railway tracks, airport locations), the existing level of service (timetable, flight schedule), the use of adequate technologies (information, control, and booking systems), and the best possible deployment of equipment and resources (energy, vehicles, crews). The decision, planning, and optimization problems arising in this context are often gigantic and “scream” for mathematical support because of their complexity. This article sketches the state and the relevance of mathematics in planning and operating public transit, describes today’s challenges, and suggests a number of innovative actions. The current contribution of mathematics to public transit is — depending on the transportation mode — of varying depth. Air traffic is already well supported by mathematics. Bus traffic made significant advances in recent years, while rail traffic still bears significant opportunities for improvements. In all areas of public transit, the existing potentials are far from being exhausted. For some PT problems, such as vehicle and crew scheduling in bus and air traffic, excellent mathematical tools are not only available, but used in many places. In other areas, such as rolling stock rostering in rail traffic, the performance of the existing mathematical algorithms is not yet sufficient. Some topics are essentially untouched from a mathematical point of view; e.g., there are (except for air traffic) no network design or fare planning models of practical relevance. PT infrastructure construction is essentially devoid of mathematics, even though enormous capital investments are made in this area. These problems lead to questions that can only be tackled by engineers, economists, politicians, and mathematicians in a joint effort. Among other things, the authors propose to investigate two specific topics, which can be addressed at short notice, are of fundamental importance not only for the area of traffic planning, should lead to a significant improvement in the collaboration of all involved parties, and, if successful, will be of real value for companies and customers: • discrete optimal control: real-time re-planning of traffic systems in case of disruptions, • model integration: service design in bus and rail traffic. Work on these topics in interdisciplinary research projects could be funded by the German ministry of research and education (BMBF), the German ministry of economics (BMWi), or the German science foundation (DFG).

Description: The steel mill slab design problem from the CSPLib is a binpacking problem that is motivated by an application of the steel industry and that has been widely studied in the constraint programming community. Recently, several people proposed new models and methods to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called multiple knapsack problem with color constraints, originated from the same industrial problem, were discussed in the integer programming community. In particular, a simple integer programming for this problem has been given by Forrest et al. [3]. The aim of this paper is to bring these different studies together. Moreover, we adopt the model of [3] for the steel mill slab problem. Using a state of the art integer program solver, this model is capable to solve all instances of the steel mill slab library, mostly in less than one second, to optimality. We improved, thereby, the solution value of 76 instances.

Description: Nowadays most data networks use shortest path protocols such as OSPF or IS-IS to route traffic. Given administrative routing lengths for the links of a network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. One of the most fundamental problems in planning shortest path networks is to decide whether a given set of routing paths forms a valid routing and, if this is not the case, to find a small subset of the given paths that cannot be shortest paths simultaneously for any routing lengths. In this paper we show that it is NP-hard to approximate the size of the smallest shortest path conflict by a factor less than 7/6.

Description: The Vehicle Positioning Problem (VPP) consists of the assignment of vehicles (buses, trams or trains) of a public transport or railway company to parking positions in a depot and to timetabled trips. Such companies have many different types of vehicles, and each trip can be performed only by vehicles of some of these types. These assignments are non-trivial due to the topology of depots. The parking positions are organized in tracks, which work as one- or two-sided stacks or queues. If a required type of vehicle is not available in the front of any track, shunting movements must be performed in order to change vehicles' positions, which is undesirable and should be avoided. In this text we present integer linear and non-linear programming formulations for some versions of the problem and compare them from a theoretical and a computational point of view.

Description: The understanding of geometric structures and dynamical properties of molecular conformations gives insight into molecular long-term behavior. The identification of metastable conformations together with their life times and transition patterns is the intention of conformation dynamics. Conformation dynamics is a multi-scale approach that leads to a reduced description of the dynamical system in terms of a stochastic transition probability matrix. The present thesis deals with the error analysis of computed matrices and the resulting matrix functions. Since conformational membership vectors, as they are computed by the Robust Perron Cluster Analysis (PCCA+), form an invariant subspace of the transition matrix, subspace-based error estimators are of particular interest. The decomposition of the state space into basis functions and the approximation of integrals by Monte-Carlo quadrature give rise to row-wise correlated random matrices, for which stochastic norms are computed. Together with an appropriate statistical model for the distribution of matrix rows, this allows for the calculation of error bounds and error distributions of the invariant subspace and other variables of interest. Equilibration of errors among the basis functions can be achieved by enhanced sampling in regions where the trajectories are mixing slowly. Hierarchical refinement of such basis functions systematically improves the clustering into metastable conformations by reducing the error in the corresponding invariant subspace. These techniques allow for an evaluation of simulation results and pave the way for the analysis of larger molecules. Moreover, the extension of PCCA+ to non-reversible Markov chains, verified by the corresponding perturbation theory, and the modification of the objective function for the case of soft membership vectors represent a further generalization of the clustering method, thus continuing the development from PCCA over PCCA+ to PCCA++. The methods developed in this thesis are useful for but not limited to conformation dynamics. In fact, they are applicable to a broader class of problems which combine domain decomposition with Monte-Carlo quadrature. Possible application areas may include the chemical master equation or quantum dynamical systems.

Description: Das Verständnis von geometrischen Strukturen und dynamischen Eigenschaften molekularer Konformationen ist essentiell für die Vorhersage des Langzeitverhaltens von Molekülen. Die Identifikation metastabiler Konformationen sowie die Bestimmung von Übergangswahrscheinlichkeiten und Haltezeiten sind Bestandteil der Konformationdynamik. Dabei handelt es sich um eine Mehrskalenmethode, die auf eine reduzierte Beschreibung des Systems mittels einer stochastischen Übergangsmatrix führt. In der vorliegenden Dissertation wurde untersucht, wie man die Genauigkeit der Matrizen sowie der daraus berechneten Größen quantifizieren kann. Im Mittelpunkt stehen dabei Fehlerschätzer für den invarianten Unterraum, da die rechten Eigenvektoren als Grundlage der Robusten Perron Cluster Analyse (PCCA+) zur Identifizierung der metastabilen Konformationen dienen. Die Zerlegung des Zustandsraumes in Basisfunktionen sowie die Approximation der Matrixeinträge mittels Monte-Carlo-Quadratur führen zu zeilenweise korrelierten Zufallsmatrizen. Mit Hilfe einer stochastischen Norm sowie einem geeigneten statistischen Modell für die Verteilung der Matrixzeilen können u.a. Fehlerschranken und -verteilungen für den invarianten Unterraum brechnet werden. Eine Equilibrierung des Fehlers zwischen den Basisfunktionen kann durch erweitertes Sampling in solchen Regionen erreicht werden, in denen die Trajektorien nur langsam mischen.Eine hierarchische Zerlegung dieser Basisfunktionen verbessert systematisch die Zerlegung in metastabile Konformationen, indem sie den Fehler im invarianten Unterraum reduziert. Diese Techniken gestatten eine Evaluierung der Simulationsergebnisse und ebnen den Weg zur Behandlung komplexerer Moleküle. Desweiteren wurden Verallgemeinerungen der PCCA+ untersucht. Die Erweiterung der PCCA+ auf nicht-reversible Markov-Ketten sowie die Modifizierung der Zielfunktion für den Fall der weichen Clusterung setzen die Entwicklung von der PCCA über PCCA+ zu PCCA++ fort. Somit können neue Anwendungsfelder für dieses Cluster-Verfahren erschlossen werden. Die Methoden wurden zwar in Rahmen der Konformationsdynamik entwickelt, jedoch lassen sie sich auf eine weite Problemklasse anwenden, in der Gebietszerlegungsverfahren mit Monte-Carlo-Quadratur kombiniert werden. Mögliche Anwendungsgebiete umfassen die chemische Master-Gleichung oder quantenchemische Systeme.

Description: We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A.~Cayley in 1845. We prove integrability (understood as $4d$-consistency) of a nonlinear difference equation defined by the $2 \times 2 \times 2$ - hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this hypothesis already fails in the case of the $2\times 2\times 2\times 2$ - hyperdeterminant.

Description: A world-wide used program for the simulation of fire-induced flows is the Fire Dynamics Simulator (FDS) which originally was developed for a purely serial execution on single-processor computing systems. Due to steadily increasing problem sizes and accuracy requirements as well as restrictions in storage capacity and computing power on single-processor systems, the efficient simulation of the considered fire scenarios can only be achieved on modern high-performance systems based on multi-processor architectures. The transition to those systems requires the elaborate parallelization of the underlying numerical methods which must guarantee the same result for a given problem as the corresponding serial execution. Unfortunately, one fundamental serial serial solver of FDS, the pressure solver, only possesses a low degree of inherent parallelizm. Its current parallelization may cause additional numerical errors, casually leading to significant losses of accuracy or even numerical instabilities. In order to ensure that the parallelization errors are limited by the leading error of the numerical scheme such that second order convergence for the whole method can be acchieved, optimized parallelization concepts must be designed. With respect to these considerations this articles gives an overview of the current parallel pressure solver as well as the problems related to it and presents an alternative method, SCARC, to overcome the existing complicacies. Part I explains the theory, concept and implementation of this new strategy, whereas Part II describes a series of validation and verification tests to proof its correctness.

Description: Because CFD programs, like FDS, generally consist of a large number of different components representing the variety of participating numerical algorithms and chemical / physical processes, it is nearly impossible to verify such codes in their entirety, for example with comparisons of fire tests. Instead, a careful verification and validation with respect to the underlying mathematical conditions and applied numerical schemes is indispensable. In particular, error cancelations between single program components can only be detected by such detailed component-level tests. In part I of this article series a conceptual deficiency of the FDS program package with regard to multi-mesh computations was illustrated and an alternative domain decomposition strategy FDS-ScaRC was introduced. In this second part we will present the structure of a comprehensive test concept and the needs for a more mathematically and numerically orientated test procedure that is much more suited for a reliable evaluation than only a simple visual comparison of the numerical results with experimental fire tests. After a general introduction of our test concept we will demonstrate the high potential of the new FDS-\scarc{} technique compared to the FDS-FFT technique which is used in the FDS program package as yet. Based on this concept, we will present a comprehensive set of analytical and numerical test results.

Description: The Vehicle Positioning Problem (VPP) is a classical combinatorial optimization problem in public transport planning. A number of models and approaches have been suggested in the literature, which work for small problems, but not for large ones. We propose in this article a novel set partitioning model and an associated column generation solution approach for the VPP. The model provides a tight linear description of the problem. The pricing problem, and hence the LP relaxation itself, can be solved in polynomial resp. pseudo-polynomial time for some versions of the problems.

Description: Since the initial application of mathematical optimisation methods to mine planning in 1965, the Lerchs-Grossmann algorithm for computing the ultimate pit limit, operations researchers have worked on a variety of challenging problems in the area of open pit mining. This thesis focuses on the open pit mining production scheduling problem: Given the discretisation of an orebody as a block model, determine the sequence in which the blocks should be removed from the pit, over the lifespan of the mine, such that the net present value of the mining operation is maximised. In practise, when some material has been removed from the pit, it must be processed further in order to extract the valuable elements contained therein. If the concentration of valuable elements is not sufficiently high, the material is discarded as waste or stockpiled. Realistically-sized block models can contain hundreds of thousands of blocks. A common approach to render these problem instances computationally tractable is the aggregation of blocks to larger scheduling units. The thrust of this thesis is the investigation of a new mixed-integer programming formulation for the open pit mining production scheduling problem, which allows for processing decisions to be made at block level, while the actual mining schedule is still computed at aggregate level. A drawback of this model in its full form is the large number of additional variables needed to model the processing decisions. One main result of this thesis shows how these processing variables can be aggregated efficiently to reduce the problem size significantly, while practically incurring no loss in net present value. The second focus is on the application of lagrangean relaxation to the resource constraints. Using a result of Möhring et al. (2003) for project scheduling, the lagrangean relaxation can be solved efficiently via minimum cut computations in a weighted digraph. Experiments with a bundle algorithm implementation by Helmberg showed how the lagrangean dual can be solved within a small fraction of the time required by standard linear programming algorithms, while yielding practically the same dual bound. Finally, several problem-specific heuristics are presented together with computational results: two greedy sub-MIP start heuristics and a large neighbourhood search heuristic. A combination of a lagrangean-based start heuristic followed by a large neighbourhood search proved to be effective in generating solutions with objective values within a 0.05% gap of the optimum.

Description: Starting from the conservation laws for mass, momentum and energy together with a three species, bulk microphysic model, a model for the interaction of internal gravity waves and deep convective hot towers is derived by using multiscale asymptotic techniques. From the resulting leading order equations, a closed model is obtained by applying weighted averages to the smallscale hot towers without requiring further closure approximations. The resulting model is an extension of the linear, anelastic equations, into which moisture enters as the area fraction of saturated regions on the microscale with two way coupling between the large and small scale. Moisture reduces the effective stability in the model and defines a potential temperature sourceterm related to the net effect of latent heat release or consumption by microscale up- and downdrafts. The dispersion relation and group velocity of the system is analyzed and moisture is found to have several effects: It reduces energy transport by waves, increases the vertical wavenumber but decreases the slope at which wave packets travel and it introduces a lower horizontal cutoff wavenumber, below which modes turn into evanescent. Further, moisture can cause critical layers. Numerical examples for steadystate and timedependent mountain waves are shown and the effects of moisture on these waves are investigated.

Description: In dieser Arbeit wird ein neuer Ansatz zur Modellierung von thermal signifikanten Gefäßsträngen im Hyperthermie-Kontext betrachtet. Ausgehend von einer Konvektions-Diffusions-Gleichung wird durch Reskalierung des Massenflussterms eine Reduktion des Adergebietes auf eine 1D-Struktur erreicht. Nach numerischen Vorbetrachtungen wird die Grenzgleichung innerhalb einer verallgemeinerten Sobolev-Algebra formuliert. Die Untersuchung der Lösungsfamilie in klassischen Funktionenräumen zeigt, dass deren schwacher Grenzwert die Lösung der korrespondierenden Diffusions-Gleichung ist. Die Diskretisierung einer formalen Grenzgleichung mit Linienstromanteil stellt jedoch eine gute Approximation an die Diskretisierung des ursprünglichen Problems dar, wenn man die lokale Maschenweite an die Gefäßradien koppelt und bei erhöhtem Genauigkeitsbedarf auf ein vollständiges 3D-Modell umschaltet.