TY - GEN A1 - Blanco, Marco A1 - Borndörfer, Ralf A1 - Hoang, Nam-Dung A1 - Kaier, Anton A1 - Maristany de las Casas, Pedro A1 - Schlechte, Thomas A1 - Schlobach, Swen T1 - Cost Projection Methods for the Shortest Path Problem with Crossing Costs N2 - Real world routing problems, e.g., in the airline industry or in public and rail transit, can feature complex non-linear cost functions. An important case are costs for crossing regions, such as countries or fare zones. We introduce the shortest path problem with crossing costs (SPPCC) to address such situations; it generalizes the classical shortest path problem and variants such as the resource constrained shortest path problem and the minimum label path problem. Motivated by an application in flight trajectory optimization with overflight costs, we focus on the case in which the crossing costs of a region depend only on the nodes used to enter or exit it. We propose an exact Two-Layer-Dijkstra Algorithm as well as a novel cost-projection linearization technique that approximates crossing costs by shadow costs on individual arcs, thus reducing the SPPCC to a standard shortest path problem. We evaluate all algorithms’ performance on real-world flight trajectory optimization instances, obtaining very good à posteriori error bounds. T3 - ZIB-Report - 17-48 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64817 SN - 1438-0064 ER - TY - GEN A1 - Berg, Mascha A1 - Plöntzke, Julia A1 - Leonhard-Marek, Sabine A1 - Müller, Kerstin-Elisabeth A1 - Röblitz, Susanna T1 - A dynamic model to simulate potassium balance in dairy cows. N2 - High performing dairy cows require a particular composition of nutritional ingredients, adapted to their individual requirements and depending on their production status. The optimal dimensioning of minerals in the diet, one of them being potassium, is indispensable for the prevention of imbalances. The potassium balance in cows is the result of potassium intake, distribution in the organism, and excretion, it is closely related with the glucose and electrolyte metabolism. In this paper, we present a dynamical model for the potassium balance in lactating and non-lactating dairy cows based on ordinary differential equations. Parameter values are obtained from clinical trial data and from the literature. To verify the consistency of the model, we present simulation outcomes for three different scenarios: potassium balance in (i) non-lactating cows with varying feed intake, (ii) non-lactating cows with varying potassium fraction in the diet, and (iii) lactating cows with varying milk production levels. The results give insights into the short and long term potassium metabolism, providing an important step towards the understanding of the potassium network, the design of prophylactic feed additives, and possible treatment strategies. T3 - ZIB-Report - 17-47 KW - cow, potassium, model, ode Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64756 SN - 1438-0064 ER - TY - GEN A1 - Fischer, Frank A1 - Schlechte, Thomas T1 - Strong Relaxations for the Train Timetabling Problem using Connected Configurations N2 - The task of the train timetabling problem or track allocation problem is to find conflict free schedules for a set of trains with predefined routes in a railway network. Especially for non-periodic instances models based on time expanded networks are often used. Unfortunately, the linear programming relaxation of these models is often extremely weak because these models do not describe combinatorial relations like overtaking possibilities very well. In this paper we extend the model by so called connected configuration subproblems. These subproblems perfectly describe feasible schedules of a small subset of trains (2-3) on consecutive track segments. In a Lagrangian relaxation approach we solve several of these subproblems together in order to produce solutions which consist of combinatorially compatible schedules along the track segments. The computational results on a mostly single track corridor taken from the INFORMS RAS Problem Solving Competition 2012 data indicate that our new solution approach is rather strong. Indeed, for this instance the solution of the Lagrangian relaxation is already integral. T3 - ZIB-Report - 17-46 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64743 SN - 1438-0064 ER - TY - GEN A1 - Gamrath, Gerald A1 - Schubert, Christoph T1 - Measuring the impact of branching rules for mixed-integer programming N2 - Branching rules are an integral component of the branch-and-bound algorithm typically used to solve mixed-integer programs and subject to intense research. Different approaches for branching are typically compared based on the solving time as well as the size of the branch-and-bound tree needed to prove optimality. The latter, however, has some flaws when it comes to sophisticated branching rules that do not only try to take a good branching decision, but have additional side-effects. We propose a new measure for the quality of a branching rule that distinguishes tree size reductions obtained by better branching decisions from those obtained by such side-effects. It is evaluated for common branching rules providing new insights in the importance of strong branching. T3 - ZIB-Report - 17-34 KW - mixed-integer programming KW - branch-and-bound KW - branching rule KW - strong branching Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64722 SN - 1438-0064 ER - TY - GEN A1 - Hammerschmidt, Martin A1 - Weiser, Martin A1 - Santiago, Xavier Garcia A1 - Zschiedrich, Lin A1 - Bodermann, Bernd A1 - Burger, Sven T1 - Quantifying parameter uncertainties in optical scatterometry using Bayesian inversion N2 - We present a Newton-like method to solve inverse problems and to quantify parameter uncertainties. We apply the method to parameter reconstruction in optical scatterometry, where we take into account a priori information and measurement uncertainties using a Bayesian approach. Further, we discuss the influence of numerical accuracy on the reconstruction result. T3 - ZIB-Report - 17-37 KW - computational metrology KW - optical metrology KW - computational lithography KW - nanolithography KW - finite- element methods KW - nanooptics Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64704 SN - 1438-0064 ER - TY - GEN A1 - Rehfeldt, Daniel A1 - Koch, Thorsten T1 - Combining NP-Hard Reduction Techniques and Strong Heuristics in an Exact Algorithm for the Maximum-Weight Connected Subgraph Problem N2 - Borne out of a surprising variety of practical applications, the maximum-weight connected subgraph problem has attracted considerable interest during the past years. This interest has not only led to notable research on theoretical properties, but has also brought about several (exact) solvers-with steadily increasing performance. Continuing along this path, the following article introduces several new algorithms such as reduction techniques and heuristics and describes their integration into an exact solver. The new methods are evaluated with respect to both their theoretical and practical properties. Notably, the new exact framework allows to solve common problem instances from the literature faster than all previous approaches. Moreover, one large-scale benchmark instance from the 11th DIMACS Challenge can be solved for the first time to optimality and the primal-dual gap for two other ones can be significantly reduced. T3 - ZIB-Report - 17-45 KW - maximum-weight connected subgraph Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64699 SN - 1438-0064 ER - TY - GEN A1 - Miltenberger, Matthias A1 - Ralphs, Ted A1 - Steffy, Daniel T1 - Exploring the Numerics of Branch-and-Cut for Mixed Integer Linear Optimization T2 - Operations Research Proceedings 2017 N2 - We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the numerical conditioning of the LP relaxations resulting from the branching and cutting operations can be effectively predicted and whether such predictions can be used to make better algorithmic choices. In a first step towards this goal, we discuss here the numerical behavior of an existing solver in order to determine whether our intuitive understanding of this behavior is correct. T3 - ZIB-Report - 17-43 KW - Mixed Integer Programming KW - Linear Programming KW - Algorithm Analysis Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64645 SN - 1438-0064 ER - TY - GEN A1 - Griewank, Andreas A1 - Hasenfelder, Richard A1 - Radons, Manuel A1 - Lehmann, Lutz A1 - Streubel, Tom T1 - Integrating Lipschitzian Dynamical Systems using Piecewise Algorithmic Differentiation N2 - In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side \(F:R^n \to R^n\) based on a generalization of algorithmic differentiation. When applied to such a problem, the classical trapezoidal rule suffers from a loss of accuracy if the solution trajectory intersects a nondifferentiability of \(F\). The advantage of the proposed generalized trapezoidal rule is threefold: Firstly, we can achieve a higher convergence order than with the classical method. Moreover, the method is energy preserving for piecewise linear Hamiltonian systems. Finally, in analogy to the classical case we derive a third order interpolation polynomial for the numerical trajectory. In the smooth case the generalized rule reduces to the classical one. Hence, it is a proper extension of the classical theory. An error estimator is given and numerical results are presented. T3 - ZIB-Report - 17-44 KW - Automatic Differentiation KW - Lipschitz Continuity KW - Piecewise Linearization KW - Nonsmooth KW - Trapezoidal Rule KW - Energy Preservation KW - Dense Output Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64639 SN - 1438-0064 ER - TY - GEN A1 - Schade, Stanley A1 - Schlechte, Thomas A1 - Witzig, Jakob T1 - Structure-based Decomposition for Pattern-Detection for Railway Timetables N2 - We consider the problem of pattern detection in large scale railway timetables. This problem arises in rolling stock optimization planning in order to identify invariant sections of the timetable for which a cyclic rotation plan is adequate. We propose a dual reduction technique which leads to an decomposition and enumeration method. Computational results for real world instances demonstrate that the method is able to produce optimal solutions as fast as standard MIP solvers. T3 - ZIB-Report - 17-40 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64525 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Perregaard, Michael A1 - Mészáros, Csaba T1 - Four good reasons to use an Interior Point solver within a MIP solver N2 - "Interior point algorithms are a good choice for solving pure LPs or QPs, but when you solve MIPs, all you need is a dual simplex." This is the common conception which disregards that an interior point solution provides some unique structural insight into the problem at hand. In this paper, we will discuss some of the benefits that an interior point solver brings to the solution of difficult MIPs within FICO Xpress. This includes many different components of the MIP solver such as branching variable selection, primal heuristics, preprocessing, and of course the solution of the LP relaxation. T3 - ZIB-Report - 17-42 KW - mixed integer programming KW - interior point algorithm KW - Newton barrier method KW - analytic center Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64599 SN - 1438-0064 ER - TY - GEN A1 - Hennings, Felix T1 - Benefits and Limitations of Simplified Transient Gas Flow Formulations N2 - Although intensively studied in recent years, the optimization of the transient (time-dependent) control of large real-world gas networks is still out of reach for current state-of-the-art approaches. For this reason, we present further simplifications of the commonly used model, which lead to a linear description of the gas flow on pipelines. In an empirical analysis of real-world data, we investigate the properties of the involved quantities and evaluate the errors made by our simplification. T3 - ZIB-Report - 17-39 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64570 SN - 1438-0064 ER - TY - GEN A1 - Streubel, Tom A1 - Strohm, Christian A1 - Trunschke, Philipp A1 - Tischendorf, Caren T1 - Generic Construction and Efficient Evaluation of Network DAEs and Their Derivatives in the Context of Gas Networks N2 - We present a concept that provides an efficient description of differential-algebraic equations (DAEs) describing flow networks which provides the DAE function f and their Jacobians in an automatized way such that the sparsity pattern of the Jacobians is determined before their evaluation and previously determined values of f can be exploited. The user only has to provide the network topology and local function descriptions for each network element. The approach uses automatic differentiation (AD) and is adapted to switching element functions via the abs-normal-form (ANF). T3 - ZIB-Report - 17-41 KW - compressed sparse row format KW - algorithmic differentiation KW - abs-normal form KW - piecewise linear tangent approximation KW - piecewise smooth Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64582 SN - 1438-0064 ER - TY - GEN A1 - Renken, Malte A1 - Ahmadi, Amin A1 - Borndörfer, Ralf A1 - Sahin, Guvenc A1 - Schlechte, Thomas T1 - Demand-Driven Line Planning with Selfish Routing N2 - Bus rapid transit systems in developing and newly industrialized countries are often operated at the limits of passenger capacity. In particular, demand during morning and afternoon peaks is hardly or even not covered with available line plans. In order to develop demand-driven line plans, we use two mathematical models in the form of integer programming problem formulations. While the actual demand data is specified with origin-destination pairs, the arc-based model considers the demand over the arcs derived from the origin-destination demand. In order to test the accuracy of the models in terms of demand satisfaction, we simulate the optimal solutions and compare number of transfers and travel times. We also question the effect of a selfish route choice behavior which in theory results in a Braess-like paradox by increasing the number of transfers when system capacity is increased with additional lines. T3 - ZIB-Report - 17-38 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64547 SN - 1438-0064 ER - TY - GEN A1 - Beckenbach, Isabel T1 - A Hypergraph Network Simplex Algorithm N2 - We describe a network simplex algorithm for the minimum cost flow problem on graph-based hypergraphs which are directed hypergraphs of a particular form occurring in railway rotation planning. The algorithm is based on work of Cambini, Gallo, and Scutellà who developed a hypergraphic generalization of the network simplex algorithm. Their main theoretical result is the characterization of basis matrices. We give a similar characterization for graph-based hypergraphs and show that some operations of the simplex algorithm can be done combinatorially by exploiting the underlying digraph structure. T3 - ZIB-Report - 17-36 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64539 SN - 1438-0064 ER - TY - GEN A1 - Müller, Benjamin A1 - Kuhlmann, Renke A1 - Vigerske, Stefan T1 - On the performance of NLP solvers within global MINLP solvers N2 - Solving mixed-integer nonlinear programs (MINLPs) to global optimality efficiently requires fast solvers for continuous sub-problems. These appear in, e.g., primal heuristics, convex relaxations, and bound tightening methods. Two of the best performing algorithms for these sub-problems are Sequential Quadratic Programming (SQP) and Interior Point Methods. In this paper we study the impact of different SQP and Interior Point implementations on important MINLP solver components that solve a sequence of similar NLPs. We use the constraint integer programming framework SCIP for our computational studies. T3 - ZIB-Report - 17-35 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64504 SN - 1438-0064 ER - TY - GEN A1 - Wolf, Thomas A1 - Amadi, Chimaobi T1 - Rational Solutions of Underdetermined Polynomial Equations N2 - In this paper we report on an application of computer algebra in which mathematical puzzles are generated of a type that had been widely used in mathematics contests by a large number of participants worldwide. The algorithmic aspect of our work provides a method to compute rational solutions of single polynomial equations that are typically large with 10^2 ... 10^5 terms and that are heavily underdetermined. It was possible to obtain this functionality by adding a number of new modules for a new type of splitting of equations to the existing package CRACK that is normally used to solve polynomial algebraic and differential systems of equations. T3 - ZIB-Report - 17-33 KW - underdetermined polynomial systems, rational solutions, computer algebra, recreational mathematics Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64488 SN - 1438-0064 ER - TY - GEN A1 - Sagnol, Guillaume A1 - Blanco, Marco A1 - Sauvage, Thibaut T1 - The Cone of Flow Matrices: Approximation Hierarchies and Applications N2 - Let G be a directed acyclic graph with n arcs, a source s and a sink t. We introduce the cone K of flow matrices, which is a polyhedral cone generated by the matrices $\vec{1}_P\vec{1}_P^T\in\RR^{n\times n}$, where $\vec{1}_P\in\RR^n$ is the incidence vector of the (s,t)-path P. We show that several hard flow (or path) optimization problems, that cannot be solved by using the standard arc-representation of a flow, reduce to a linear optimization problem over $\mathcal{K}$. This cone is intractable: we prove that the membership problem associated to $\mathcal{K}$ is NP-complete. However, the affine hull of this cone admits a nice description, and we give an algorithm which computes in polynomial-time the decomposition of a matrix $X\in \operatorname{span} \mathcal{K}$ as a linear combination of some $\vec{1}_P\vec{1}_P^T$'s. Then, we provide two convergent approximation hierarchies, one of them based on a completely positive representation of~K. We illustrate this approach by computing bounds for the quadratic shortest path problem, as well as a maximum flow problem with pairwise arc-capacities. T3 - ZIB-Report - 17-32 KW - Flows in graphs KW - Approximation Hierarchies KW - Copositive Programming KW - Semidefinite Programming Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64399 SN - 1438-0064 ER - TY - GEN A1 - Quer, Jannes A1 - Lie, Han Cheng T1 - Some connections between importance sampling and enhanced sampling methods in molecular dynamics N2 - Enhanced sampling methods play an important role in molecular dynamics, because they enable the collection of better statistics of rare events that are important in many physical phenomena. We show that many enhanced sampling methods can be viewed as methods for performing importance sampling, by identifying important correspondences between the language of molecular dynamics and the language of probability theory. We illustrate these connections by highlighting the similarities between the rare event simulation method of Hartmann and Schütte (J. Stat. Mech. Theor. Exp., 2012), and the enhanced sampling method of Valsson and Parrinello (Phys. Rev. Lett. 113, 090601). We show that the idea of changing a probability measure is fundamental to both enhanced sampling and importance sampling. T3 - ZIB-Report - 17-30 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64289 SN - 1438-0064 ER - TY - GEN A1 - Winkelmann, Stefanie A1 - Schütte, Christof T1 - Hybrid Models for Chemical Reaction Networks: Multiscale Theory and Application to Gene Regulatory Systems N2 - Well-mixed stochastic chemical kinetics are properly modelled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows to express various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. T3 - ZIB-Report - 17-29 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64264 ER - TY - GEN A1 - Rohr, Ulrich-Peter A1 - Herrmann, Pia A1 - Ilm, Katharina A1 - Zhang, Hai A1 - Lohmann, Sabine A1 - Reiser, Astrid A1 - Muranyi, Andrea A1 - Smith, Janice A1 - Burock, Susen A1 - Osterland, Marc A1 - Leith, Katherine A1 - Singh, Shalini A1 - Brunhoeber, Patrick A1 - Bowermaster, Rebecca A1 - Tie, Jeanne A1 - Christie, Michael A1 - Wong, Hui-Li A1 - Waring, Paul A1 - Shanmugam, Kandavel A1 - Gibbs, Peter A1 - Stein, Ulrike T1 - Prognostic value of MACC1 and proficient mismatch repair status for recurrence risk prediction in stage II colon cancer patients: the BIOGRID studies N2 - Background We assessed the novel MACC1 gene to further stratify stage II colon cancer patients with proficient mismatch repair (pMMR). Patients and methods Four cohorts with 596 patients were analyzed: Charité 1 discovery cohort was assayed for MACC1 mRNA expression and MMR in cryo-preserved tumors. Charité 2 comparison cohort was used to translate MACC1 qRT- PCR analyses to FFPE samples. In the BIOGRID 1 training cohort MACC1 mRNA levels were related to MACC1 protein levels from immunohistochemistry in FFPE sections; also analyzed for MMR. Chemotherapy-naïve pMMR patients were stratified by MACC1 mRNA and protein expression to establish risk groups based on recurrence-free survival (RFS). Risk stratification from BIOGRID 1 was confirmed in the BIOGRID 2 validation cohort. Pooled BIOGRID datasets produced a best effect-size estimate. Results In BIOGRID 1, using qRT-PCR and immunohistochemistry for MACC1 detection, pMMR/MACC1-low patients had a lower recurrence probability versus pMMR/MACC1-high patients (5-year RFS of 92% and 67% versus 100% and 68%, respectively). In BIOGRID 2, longer RFS was confirmed for pMMR/MACC1-low versus pMMR/MACC1-high patients (5-year RFS of 100% versus 90%, respectively). In the pooled dataset, 6.5% of patients were pMMR/MACC1-low with no disease recurrence, resulting in a 17% higher 5-year RFS (95% CI (12.6-21.3%)) versus pMMR/MACC1-high patients (P=0.037). Outcomes were similar for pMMR/MACC1-low and deficient MMR (dMMR) patients (5-year RFS of 100% and 96%, respectively). Conclusions MACC1 expression stratifies colon cancer patients with unfavorable pMMR status. Stage II colon cancer patients with pMMR/MACC1-low tumors have a similar favorable prognosis to those with dMMR with potential implications for the role of adjuvant therapy. T3 - ZIB-Report - 17-28 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64184 SN - 1438-0064 ER - TY - GEN A1 - Beckenbach, Isabel A1 - Peis, Britta A1 - Schaudt, Oliver A1 - Scheidweiler, Robert T1 - A Combinatorial Proof of a König-type Theorem for Unimodular Hypergraphs N2 - We state purely combinatorial proofs for König- and Hall-type theorems for a wide class of combinatorial optimization problems. Our methods rely on relaxations of the matching and vertex cover problem and, moreover, on the strong coloring properties admitted by bipartite graphs and their generalizations. T3 - ZIB-Report - 17-27 KW - Packing KW - Covering KW - Total Unimodularity KW - König's Theorem KW - Factors Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64017 SN - 1438-0064 ER - TY - GEN A1 - Homberg, Ulrike A1 - Baum, Daniel A1 - Prohaska, Steffen A1 - Günster, Jens A1 - Krauß-Schüler, Stefanie T1 - Adapting trabecular structures for 3D printing: an image processing approach based on µCT data N2 - Materials with a trabecular structure notably combine advantages such as lightweight, reasonable strength, and permeability for fluids. This combination of advantages is especially interesting for tissue engineering in trauma surgery and orthopedics. Bone-substituting scaffolds for instance are designed with a trabecular structure in order to allow cell migration for bone ingrowth and vascularization. An emerging and recently very popular technology to produce such complex, porous structures is 3D printing. However, several technological aspects regarding the scaffold architecture, the printable resolution, and the feature size have to be considered when fabricating scaffolds for bone tissue replacement and regeneration. Here, we present a strategy to assess and prepare realistic trabecular structures for 3D printing using image analysis with the aim of preserving the structural elements. We discuss critical conditions of the printing system and present a 3-stage approach to adapt a trabecular structure from $\mu$CT data while incorporating knowledge about the printing system. In the first stage, an image-based extraction of solid and void structures is performed, which results in voxel- and graph-based representations of the extracted structures. These representations not only allow us to quantify geometrical properties such as pore size or strut geometry and length. But, since the graph represents the geometry and the topology of the initial structure, it can be used in the second stage to modify and adjust feature size, volume and sample size in an easy and consistent way. In the final reconstruction stage, the graph is then converted into a voxel representation preserving the topology of the initial structure. This stage generates a model with respect to the printing conditions to ensure a stable and controlled voxel placement during the printing process. T3 - ZIB-Report - 17-26 KW - trabecular structures KW - image-based analysis KW - additive manufacturing KW - printability Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-64004 SN - 1438-0064 ER - TY - GEN A1 - Fischer, Lisa A1 - Götschel, Sebastian A1 - Weiser, Martin T1 - Lossy data compression reduces communication time in hybrid time-parallel integrators N2 - Parallel in time methods for solving initial value problems are a means to increase the parallelism of numerical simulations. Hybrid parareal schemes interleaving the parallel in time iteration with an iterative solution of the individual time steps are among the most efficient methods for general nonlinear problems. Despite the hiding of communication time behind computation, communication has in certain situations a significant impact on the total runtime. Here we present strict, yet no sharp, error bounds for hybrid parareal methods with inexact communication due to lossy data compression, and derive theoretical estimates of the impact of compression on parallel efficiency of the algorithms. These and some computational experiments suggest that compression is a viable method to make hybrid parareal schemes robust with respect to low bandwidth setups. T3 - ZIB-Report - 17-25 KW - parallel-in-time integration KW - hybrid parareal KW - convergence KW - lossy compression KW - MPI Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63961 SN - 1438-0064 ER - TY - GEN A1 - Grimm, Boris A1 - Borndörfer, Ralf A1 - Reuther, Markus A1 - Schade, Stanley A1 - Schlechte, Thomas T1 - A Propagation Approach to Acyclic Rolling Stock Rotation Optimization N2 - The rolling stock, i.e., railway vehicles, are one of the key ingredients of a running railway system. As it is well known, the offer of a railway company to their customers, i.e., the railway timetable, changes from time to time. Typical reasons for that are different timetables associated with different seasons, maintenance periods or holidays. Therefore, the regular lifetime of a timetable is split into (more or less) irregular periods where parts of the timetable are changed. In order to operate a railway timetable most railway companies set up sequences that define the operation of timetabled trips by a single physical railway vehicle called (rolling stock) rotations. Not surprisingly, the individual parts of a timetable also affect the rotations. More precisely, each of the parts brings up an acyclic rolling stock rotation problem with start and end conditions associated with the beginning and ending of the corresponding period. In this paper, we propose a propagation approach to deal with large planning horizons that are composed of many timetables with shorter individual lifetimes. The approach is based on an integer linear programming formulation that propagates rolling stock rotations through the irregular parts of the timetable while taking a large variety of operational requirements into account. This approach is implemented within the rolling stock rotation optimization framework ROTOR used by DB Fernverkehr AG, one of the leading railway operators in Europe. Computational results for real world scenarios are presented to evaluate the approach. T3 - ZIB-Report - 17-24 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63930 SN - 1438-0064 ER - TY - GEN A1 - Lange, Alexander A1 - Schwieger, Robert A1 - Plöntzke, Julia A1 - Schäfer, Stefan A1 - Röblitz, Susanna T1 - Follicular competition: the selection of dominant follicles as a synergistic effect N2 - The estrous cycle of mono-ovulatory species such as cows or humans, is known to show two or more waves of follicular growth and decline between two successive ovulations. Within each wave, there is one dominant follicle escorted by subordinate follicles of varying number. Under the surge of the luteinizing hormone a growing dominant follicle ovulates. Rarely the number of ovulating follicles exceeds one. In the biological literature, the change of hormonal concentrations and individually varying numbers of follicular receptors are made responsible for the selection of exactly one dominant follicle, yet a clear cause has not been identified. In this paper, we suggest a synergistic explanation based on competition, formulated by a parsimoniously defined system of ordinary differential equations (ODEs) that quantifies the time evolution of multiple follicles and their competitive interaction during one wave. Not discriminating between follicles, growth and decline are given by fixed rates. Competition is introduced via a growth-suppressing term, equally supported by all follicles. We prove that the number of dominant follicles is determined exclusively by the ratio of follicular growth and competition. This number turns out to be independent of the number of subordinate follicles. The asymptotic behavior of the corresponding dynamical system is investigated rigorously, where we demonstrate that the omega-limit set only contains fixed points. When also including follicular decline, our ODEs perfectly resemble ultrasound data of bovine follicles. Implications for the involved but not explicitly modeled hormones are discussed. T3 - ZIB-Report - 17-21 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63863 SN - 1438-0064 ER - TY - GEN A1 - Gilg, Brady A1 - Klug, Torsten A1 - Martienssen, Rosemarie A1 - Paat, Joseph A1 - Schlechte, Thomas A1 - Schulz, Christof A1 - Seymen, Sinan A1 - Tesch, Alexander T1 - Conflict-Free Railway Track Assignment at Depots N2 - Managing rolling stock with no passengers aboard is a critical component of railway operations. In particular, one problem is to park the rolling stock on a given set of tracks at the end of a day or service. Depending on the parking assignment, shunting may be required in order for a parked train to depart or for an incoming train to park. Given a collection of tracks M and a collection of trains T with fixed arrival-departure timetable, the train assignment problem (TAP) is to determine the maximum number of trains from T that can be parked on M according to the timetable and without the use of shunting. Hence, efficiently solving the TAP allows to quickly compute feasible parking schedules that do not require further shunting adjustments. In this paper, we present two integer programming models for solving the TAP. To our knowledge, this is the first integrated approach that considers track lengths along with the three most common types of parking tracks. We compare these models on a theoretical level. We also prove that a decision version of the TAP is NP-complete, justifying the use of integer programming techniques. Using stochastic and robust modelling techniques, both models produce parking assignments that are optimized and robust according to random train delays. We conclude with computational results for both models, observing that they perform well on real timetables. T3 - ZIB-Report - 17-23 KW - Depot Planning KW - Railway Track Assignment Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63843 SN - 1438-0064 ER - TY - GEN A1 - Bittracher, Andreas A1 - Koltai, Péter A1 - Klus, Stefan A1 - Banisch, Ralf A1 - Dellnitz, Michael A1 - Schütte, Christof T1 - Transition manifolds of complex metastable systems: Theory and data-driven computation of effective dynamics N2 - We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective dynamics. For answering this question, we aim at finding nonlinear coordinates, called reaction coordinates, such that the projection of the dynamics onto these coordinates preserves the dominant time scales of the dynamics. We show that, based on a specific reducibility property, the existence of good low-dimensional reaction coordinates preserving the dominant time scales is guaranteed. Based on this theoretical framework, we develop and test a novel numerical approach for computing good reaction coordinates. The proposed algorithmic approach is fully local and thus not prone to the curse of dimension with respect to the state space of the dynamics. Hence, it is a promising method for data-based model reduction of complex dynamical systems such as molecular dynamics. T3 - ZIB-Report - 17-22 KW - metastability KW - slow dynamics KW - effective dynamics KW - transition manifold KW - embedding KW - transfer operator KW - reaction coordinate Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63822 SN - 1438-0064 ER - TY - GEN A1 - Weiser, Martin A1 - Erdmann, Bodo A1 - Schenkl, Sebastian A1 - Muggenthaler, Holger A1 - Hubig, Michael A1 - Mall, Gita A1 - Zachow, Stefan T1 - Uncertainty in Temperature-Based Determination of Time of Death N2 - Temperature-based estimation of time of death (ToD) can be per- formed either with the help of simple phenomenological models of corpse cooling or with detailed mechanistic (thermodynamic) heat transfer mod- els. The latter are much more complex, but allow a higher accuracy of ToD estimation as in principle all relevant cooling mechanisms can be taken into account. The potentially higher accuracy depends on the accuracy of tissue and environmental parameters as well as on the geometric resolution. We in- vestigate the impact of parameter variations and geometry representation on the estimated ToD based on a highly detailed 3D corpse model, that has been segmented and geometrically reconstructed from a computed to- mography (CT) data set, differentiating various organs and tissue types. From that we identify the most crucial parameters to measure or estimate, and obtain a local uncertainty quantifcation for the ToD. T3 - ZIB-Report - 17-18 KW - forensic medicine KW - determination of time of death KW - heat transfer equation KW - sensitivity i.r.t. thermal parameters KW - sensitivity i.r.t. geometric resolution Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63818 SN - 1438-0064 ER - TY - GEN A1 - Hammerschmidt, Martin A1 - Döpking, Sandra A1 - Burger, Sven A1 - Matera, Sebastian T1 - Field Heterogeneities and their Impact on Photocatalysis: Combining optical and kinetic Monte Carlo Simulations on the Nanoscale N2 - Gaining insights into the working principles of photocatalysts on an atomic scale is a challenging task. The obviously high complexity of the reaction mechanism involving photo-excited electrons and holes is one reason. Another complicating aspect is that the electromagnetic field, driving photocatalysis, is not homogeneous on a nanoscale level for particle based catalysts as it is influenced by the particle’s shape and size. We present a simple model, inspired by the CO2 reduction on titania anatase, which addresses the impact of these heterogeneities on the photocatalytic kinetics by combining kinetic Monte Carlo with electromagnetic wave simulations. We find that average activity and especially efficiency might differ significantly between different particles. Moreover, we find sizable variation of the catalytic activity on a single facet of a nanocrystal. Besides this quantitative heterogeneity, the coverage situation in general changes laterally on this facet and we observe a concomitant change of the rate-determining steps. This heterogeneity on all levels of photocatalytic activity is masked in experimental studies, where only the spatially averaged activity can be addressed. Microkinetic models based on experimental findings might therefore not represent the true micro- scopic behavior, and mechanistic conclusion drawn from these need to be handled with care. T3 - ZIB-Report - 17-20 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63690 SN - 1438-0064 ER - TY - GEN A1 - Zhang, Wei A1 - Schütte, Christof T1 - Reliable approximation of long relaxation timescales in molecular dynamics N2 - Many interesting rare events in molecular systems like ligand association, protein folding or con- formational changes happen on timescales that often are not accessible by direct numerical simulation. Therefore rare event approximation approaches like interface sampling, Markov state model building or advanced reaction coordinate based free energy estimation have attracted huge attention recently. In this article we analyze the reliability of such approaches: How precise is an estimate of long relaxation timescales of molecular systems resulting from various forms of rare event approximation methods? Our results give a theoretical answer to this question by relating it with the transfer operator approach to molecular dynamics. By doing so they also allow for understanding deep connections between the different approaches. T3 - ZIB-Report - 17-19 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63718 SN - 1438-0064 ER - TY - GEN A1 - Schade, Stanley A1 - Borndörfer, Ralf A1 - Breuer, Matthias A1 - Grimm, Boris A1 - Reuther, Markus A1 - Schlechte, Thomas A1 - Siebeneicher, Patrick T1 - Pattern Detection For Large-Scale Railway Timetables N2 - We consider railway timetables of our industrial partner DB Fernverkehr AG that operates the ICE high speed trains in the long-distance passenger railway network of Germany. Such a timetable covers a whole year with 364 days and, typically, includes more than 45,000 trips. A rolling stock rotation plan is not created for the whole timetable at once. Instead the timetable is divided into regular invariant sections and irregular deviations (e.g. for public holidays). A separate rotation plan with a weekly period can then be provided for each of the different sections of the timetable. We present an algorithmic approach to automatically recognize these sections. Together with the supplementing visualisation of the timetable this method has shown to be very relevant for our industrial partner. T3 - ZIB-Report - 17-17 KW - railway timetables KW - visualization KW - pattern detection Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63390 SN - 1438-0064 ER - TY - GEN A1 - Amrhein, Kilian A1 - Hasler, Tim A1 - Klindt, Marco A1 - Oltmanns, Elias A1 - Peters-Kottig, Wolfgang T1 - Digitale Langzeitarchivierung: Mustervorlage für Übernahmevereinbarungen, Version 2 N2 - Digitale Langzeitarchivierung erfolgt auf Grundlage verbindlicher Regelungen zwischen Langzeitarchiv und Datengeber. Detaillierte organisatorische und technische Bedingungen für Datenübernahmen werden dabei in Absprache zwischen den Kooperationspartnern in einer Übernahmevereinbarung festgehalten. Im Rahmen der Entwicklung des Langzeitarchivs EWIG am Zuse Institute Berlin ist die hier dokumentierte zweite Version der Mustervorlage für Übernahmevereinbarungen entstanden. Das Submission Manifest wurde in aktualisierter Version 1.3 eingefügt, es erfolgten sprachliche Präzisierungen, und die Beispiele möglicher Verzeichnisstrukturen für Transferpakete wurden erneuert. T3 - ZIB-Report - 17-15 KW - digital preservation KW - submission agreement Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63245 SN - 1438-0064 ER - TY - GEN A1 - Aboulhassan, Amal A1 - Sicat, Ronell A1 - Baum, Daniel A1 - Wodo, Olga A1 - Hadwiger, Markus T1 - Comparative Visual Analysis of Structure-Performance Relations in Complex Bulk-Heterojunction Morphologies N2 - The structure of Bulk-Heterojunction (BHJ) materials, the main component of organic photovoltaic solar cells, is very complex, and the relationship between structure and performance is still largely an open question. Overall, there is a wide spectrum of fabrication configurations resulting in different BHJ morphologies and correspondingly different performances. Current state- of-the-art methods for assessing the performance of BHJ morphologies are either based on global quantification of morphological features or simply on visual inspection of the morphology based on experimental imaging. This makes finding optimal BHJ structures very challenging. Moreover, finding the optimal fabrication parameters to get an optimal structure is still an open question. In this paper, we propose a visual analysis framework to help answer these questions through comparative visualization and parameter space exploration for local morphology features. With our approach, we enable scientists to explore multivariate correlations between local features and performance indicators of BHJ morphologies. Our framework is built on shape-based clustering of local cubical regions of the morphology that we call patches. This enables correlating the features of clusters with intuition-based performance indicators computed from geometrical and topological features of charge paths. T3 - ZIB-Report - 17-16 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63239 SN - 1438-0064 ER - TY - GEN A1 - Zhukova, Yulia A1 - Hiepen, Christian A1 - Knaus, Petra A1 - Osterland, Marc A1 - Prohaska, Steffen A1 - Dunlop, John W. C. A1 - Fratzl, Peter A1 - Skorb, Ekaterina V. T1 - The role of titanium surface nanotopography on preosteoblast morphology, adhesion and migration N2 - Surface structuring of titanium-based implants with appropriate nanotopographies can significantly modulate their impact on the biological behavior of cells populating these implants. Implant assisted bone tissue repair and regeneration require functional adhesion and expansion of bone progenitors. The surface nanotopography of implant materials used to support bone healing and its effect on cell behavior, in particular cell adhesion, spreading, expansion, and motility, is still not clearly understood. The aim of this study is to investigate preosteoblast proliferation, adhesion, morphology, and migration on different titanium materials with similar surface chemistry, but distinct nanotopographical features. Sonochemical treatment and anodic oxidation were employed to fabricate disordered – mesoporous titania (TMS), and ordered – titania nanotubular (TNT) topographies respectively. The morphological evaluation revealed a surface dependent shape, thickness, and spreading of cells owing to different adherence behavior. Cells were polygonal-shaped and well-spread on glass and TMS, but displayed an elongated fibroblast-like morphology on TNT surfaces. The cells on glass however, were much flatter than on nanostructured surfaces. Both nanostructured surfaces impaired cell adhesion, but TMS was more favorable for cell growth due to its support of cell attachment and spreading in contrast to TNT. Quantitative wound healing assay in combination with live-cell imaging revealed that cells seeded on TMS surfaces migrated in close proximity to neighboring cells and less directed when compared to the migratory behavior on other surfaces. The results indicate distinctly different cell adhesion and migration on ordered and disordered titania nanotopographies, providing important information that could be used in optimizing titanium-based scaffold design to foster bone tissue growth and repair. T3 - ZIB-Report - 17-06 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-63053 SN - 1438-0064 ER - TY - GEN A1 - Tesch, Alexander T1 - Improved Compact Models for the Resource-Constrained Project Scheduling Problem N2 - In this article, we study compact Mixed-Integer Programming (MIP) models for the Resource-Constrained Project Scheduling Problem (RCPSP). Compared to the classical time-indexed formulation, the size of compact models is strongly polynomial in the number of jobs. In addition to two compact models from the literature, we propose a new compact model. We can show that all three compact models are equivalent by successive linear transformations. For their LP-relaxations, however, we state a full inclusion hierarchy where our new model dominates the previous models in terms of polyhedral strength. Moreover, we reveal a polyhedral relationship to the common time-indexed model. Furthermore, a general class of valid cutting planes for the compact models is introduced and finally all models are evaluated by computational experiments. T3 - ZIB-Report - 16-76 KW - Scheduling Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62891 SN - 1438-0064 ER - TY - GEN A1 - Gupta, Pooja A1 - Gramatke, Annika A1 - Einspanier, Ralf A1 - Schütte, Christof A1 - von Kleist, Max A1 - Sharbati, Jutta T1 - In silicio cytotoxicity assessment on cultured rat intestinal cells deduced from cellular impedance measurements N2 - Early and reliable identification of chemical toxicity is of utmost importance. At the same time, reduction of animal testing is paramount. Therefore, methods that improve the interpretability and usability of in vitro assays are essential. xCELLigence’s real-time cell analyzer (RTCA) provides a novel, fast and cost effective in vitro method to probe compound toxicity. We developed a simple mathematical framework for the qualitative and quantitative assessment of toxicity for RTCA measurements. Compound toxicity, in terms of its 50% inhibitory concentration IC_{50} on cell growth, and parameters related to cell turnover were estimated on cultured IEC-6 cells exposed to 10 chemicals at varying concentrations. Our method estimated IC50 values of 113.05, 7.16, 28.69 and 725.15 μM for the apparently toxic compounds 2-acetylamino-fluorene, aflatoxin B1, benzo-[a]-pyrene and chloramphenicol in the tested cell line, in agreement with literature knowledge. IC_{50} values of all apparent in vivo non-toxic compounds were estimated to be non-toxic by our method. Corresponding estimates from RTCA’s in-built model gave false positive (toxicity) predictions in 5/10 cases. Taken together, our proposed method reduces false positive predictions and reliably identifies chemical toxicity based on impedance measurements. The source code for the developed method including instructions is available at https://git.zib.de/bzfgupta/toxfit/tree/master. T3 - ZIB-Report - 17-08 KW - Real-time cell analyzer KW - Toxicity KW - Mathematical modeling KW - IC_{50} Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62666 SN - 1438-0064 ER - TY - GEN A1 - Freytag, Yvonne T1 - Optimal Experimental Design to Estimate the Time of Death in a Bayesian Context N2 - This thesis is devoted to the interdisciplinary work between mathematicians and forensic experts: the modeling of the human body cooling process after death laying the foundation for the estimation of the time of death. An inverse problem needs to be solved. In this thesis the inverse problem computes the time of death given the measured body temperature and the Forward Model that simulates the body cooling process. The Forward Model is based on the heat equation established by Fourier. This differential equation is numerically solved by the discretization over space by the Finite Element Method and the discretization over time by the Implicit Euler Method. The applications in this thesis demand a fast computation time. A model reduction is achieved by the Proper Orthogonal Decomposition in combination with the Galerkin Method. For reasons of simplification the computations and the measurements are restricted to a cylindrical phantom that is made out of homogeneous polyethylene. The estimate of the time of death is accompanied by an uncertainty. The inverse problem is incorporated by Bayesian inference to interpret the quality of the estimate and the effciency of the experiment. The uncertainty of the estimate of the time of death is minimized by approaching the Optimal Design of the Experiment. An objective function measures the certainty of the data and lays the foundation of the optimization problem. Solving the optimization problem is successfully done by relaxing the complex discrete NP-hard problem and applying a gradient-based method. The results of this thesis clearly show that the design of an experiment has a great in- uence on the outcome of the quality of the estimate. The comparison of the estimate and its properties based on different designs and conditions reveals the effciency of the Design of Experiment in the context of the estimation of the time of death. T3 - ZIB-Report - 17-14 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62475 SN - 1438-0064 ER - TY - GEN A1 - Kaplan, Bernhard A1 - Laufer, Jan A1 - Prohaska, Steffen A1 - Buchmann, Jens T1 - Monte-Carlo-based inversion scheme for 3D quantitative photoacoustic tomography N2 - The goal of quantitative photoacoustic tomography (qPAT) is to recover maps of the chromophore distributions from multiwavelength images of the initial pressure. Model-based inversions that incorporate the physical processes underlying the photoacoustic (PA) signal generation represent a promising approach. Monte-Carlo models of the light transport are computationally expensive, but provide accurate fluence distributions predictions, especially in the ballistic and quasi-ballistic regimes. Here, we focus on the inverse problem of 3D qPAT of blood oxygenation and investigate the application of the Monte-Carlo method in a model-based inversion scheme. A forward model of the light transport based on the MCX simulator and acoustic propagation modeled by the k-Wave toolbox was used to generate a PA image data set acquired in a tissue phantom over a planar detection geometry. The combination of the optical and acoustic models is shown to account for limited-view artifacts. In addition, the errors in the fluence due to, for example, partial volume artifacts and absorbers immediately adjacent to the region of interest are investigated. To accomplish large-scale inversions in 3D, the number of degrees of freedom is reduced by applying image segmentation to the initial pressure distribution to extract a limited number of regions with homogeneous optical parameters. The absorber concentration in the tissue phantom was estimated using a coordinate descent parameter search based on the comparison between measured and modeled PA spectra. The estimated relative concentrations using this approach lie within 5 % compared to the known concentrations. Finally, we discuss the feasibility of this approach to recover the blood oxygenation from experimental data. T3 - ZIB-Report - 17-04 KW - quantitative photoacoustic tomography KW - model-based inversion KW - oxygen saturation KW - chromophore concentration KW - photoacoustic imaging KW - Monte Carlo methods for light transport KW - boundary conditions KW - coordinate search Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62318 SN - 1438-0064 ER - TY - GEN A1 - Ralphs, Ted A1 - Shinano, Yuji A1 - Berthold, Timo A1 - Koch, Thorsten T1 - Parallel Solvers for Mixed Integer Linear Programming N2 - In this article, we introduce parallel mixed integer linear programming (MILP) solvers. MILP solving algorithms have been improved tremendously in the last two decades. Currently, commercial MILP solvers are known as a strong optimization tool. Parallel MILP solver development has started in 1990s. However, since the improvements of solving algorithms have much impact to solve MILP problems than application of parallel computing, there were not many visible successes. With the spread of multi-core CPUs, current state-of-the-art MILP solvers have parallel implementations and researches to apply parallelism in the solving algorithm also getting popular. We summarize current existing parallel MILP solver architectures. T3 - ZIB-Report - 16-74 KW - parallel computing KW - integer programming KW - branch-and-bound KW - supercomputing Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62239 SN - 1438-0064 ER - TY - GEN A1 - Chrapary, Hagen A1 - Dalitz, Wolfgang A1 - Neun, Winfried A1 - Sperber, Wolfram T1 - Design, concepts, and state of the art of the swMATH service N2 - In this paper, the concepts and design for an efficient information service for mathematical software and further mathematical research data are presented. The publication-based approach and the Web-based approach are the main building blocks of the service and will be discussed. Heuristic methods are used for identification, extraction, and ranking of information about software and other mathematical research data. The methods provide not only information about the research data but also link software and mathematical research data to the scientific context. T3 - ZIB-Report - 17-11 KW - software information, software citation, mathematical research data Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62263 SN - 1438-0064 ER - TY - GEN A1 - Baumann, Wolfgang A1 - Hege, Hans-Christian A1 - Schwarz, Uwe A1 - Stüben, Hinnerk T1 - Netzverteilte Visualisierung und Simulation N2 - 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. T3 - ZIB-Report - TR–96–08 Y1 - 1996 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5379 ER - TY - GEN A1 - Maher, Stephen J. A1 - Fischer, Tobias A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schenker, Sebastian A1 - Schwarz, Robert A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Weninger, Dieter A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 4.0 N2 - The SCIP Optimization Suite is a powerful collection of optimization software that consists of the branch-cut-and-price framework and mixed-integer programming solver SCIP, the linear programming solver SoPlex, the modeling language Zimpl, the parallelization framework UG, and the generic branch-cut-and-price solver GCG. Additionally, it features the extensions SCIP-Jack for solving Steiner tree problems, PolySCIP for solving multi-objective problems, and SCIP-SDP for solving mixed-integer semidefinite programs. The SCIP Optimization Suite has been continuously developed and has now reached version 4.0. The goal of this report is to present the recent changes to the collection. We not only describe the theoretical basis, but focus on implementation aspects and their computational consequences. T3 - ZIB-Report - 17-12 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62170 SN - 1438-0064 ER - TY - GEN A1 - Weber, Marcus T1 - Eigenvalues of non-reversible Markov chains – A case study N2 - Finite reversible Markov chains are characterized by a transition matrix P that has real eigenvalues and pi-orthogonal eigenvectors, where pi is the stationary distribution of P. This means, that a transition matrix with complex eigenvalues corresponds to a non-reversible Markov chain. This observation leads to the question, whether the imaginary part of that eigendecomposition corresponds to or indicates the “pattern” of the nonreversibility. This article shows that the direct relation between imaginary parts of eigendecompositions and the non-reversibility of a transition matrix is not given. It is proposed to apply the Schur decomposition of P instead of the eigendecomposition in order to characterize its nonreversibility. T3 - ZIB-Report - 17-13 KW - non-reversible KW - transition matrix KW - detailed balance Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62191 SN - 1438-0064 ER - TY - GEN A1 - Weber, Marcus A1 - Fackeldey, Konstantin A1 - Schütte, Christof T1 - Set-free Markov State Building N2 - Molecular dynamics (MD) simulations face challenging problems since the timescales of interest often are much longer than what is possible to simulate and even if sufficiently long simulation are possible the complex nature of the resulting simulation data makes interpretation difficult. Markov State Models (MSMs) help to overcome these problems by making experimentally relevant timescales accessible via coarse grained representations that also allows for convenient interpretation. However, standard set-based MSMs exhibit some caveats limiting their approximation quality and statistical significance. One of the main caveats results from the fact that typical MD trajectories repeatedly re-cross the boundary between the sets used to build the MSM which causes statistical bias in estimating the transition probabilities between these sets. In this article, we present a set-free approach to MSM building utilizing smooth overlapping ansatz functions instead of sets and an adaptive refinement approach. This kind of meshless discretization helps to overcome the recrossing problem and yields an adaptive refinement procedure that allows to improve the quality of the model while exploring state space and inserting new ansatz functions into the MSM. T3 - ZIB-Report - 17-10 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62167 SN - 1438-0064 ER - TY - GEN A1 - Quer, Jannes A1 - Donati, Luca A1 - Keller, Bettina A1 - Weber, Marcus T1 - An automatic adaptive importance sampling algorithm for molecular dynamics in reaction coordinates N2 - In this article we propose an adaptive importance sampling scheme for dynamical quantities of high dimensional complex systems which are metastable. The main idea of this article is to combine a method coming from Molecular Dynamics Simulation, Metadynamics, with a theorem from stochastic analysis, Girsanov's theorem. The proposed algorithm has two advantages compared to a standard estimator of dynamic quantities: firstly, it is possible to produce estimators with a lower variance and, secondly, we can speed up the sampling. One of the main problems for building importance sampling schemes for metastable systems is to find the metastable region in order to manipulate the potential accordingly. Our method circumvents this problem by using an assimilated version of the Metadynamics algorithm and thus creates a non-equilibrium dynamics which is used to sample the equilibrium quantities. T3 - ZIB-Report - 17-09 KW - Adaptive Importance Sampling KW - Molecular Dynamics KW - Metastability KW - Variance Reduction KW - Non Equilibrium Sampling KW - Metadynamics KW - Girsanov Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62075 SN - 1438-0064 ER - TY - GEN A1 - Tesch, Alexander T1 - A Nearly Exact Propagation Algorithm for Energetic Reasoning in O(n^2 log n) N2 - In constraint programming, energetic reasoning constitutes a powerful start time propagation rule for cumulative scheduling problems (CuSP). In this paper, we first present an improved time interval checking algorithm that is derived from a polyhedral model. In a second step, we extend this algorithm to an energetic reasoning propagation algorithm with complexity O(n^2 log n) where n denotes the number of jobs. The key idea is based on a new sweep line subroutine that efficiently evaluates the relevant time intervals for all jobs. In particular, our algorithm yields at least one possible energetic reasoning propagation for each job. Finally, we show that on the vast number of relevant time intervals our approach yields the maximum possible propagation according to the energetic reasoning rule. T3 - ZIB-Report - 16-25 KW - Cumulative Scheduling KW - Energetic Reasoning KW - Sweep Line Algorithm Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-59332 SN - 1438-0064 ER - TY - GEN A1 - Gleixner, Ambros A1 - Maher, Stephen J. A1 - Müller, Benjamin A1 - Pedroso, João Pedro T1 - Exact Methods for Recursive Circle Packing N2 - Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and the recursive packing of rings into other rings. This problem is known as the Recursive Circle Packing Problem (RCPP). We present the first dedicated method for solving RCPP that provides strong dual bounds based on an exact Dantzig–Wolfe reformulation of a nonconvex mixed-integer nonlinear programming formulation. The key idea of this reformulation is to break symmetry on each recursion level by enumerating one-level packings, i.e., packings of circles into other circles, and by dynamically generating packings of circles into rectangles. We use column generation techniques to design a “price-and-verify” algorithm that solves this reformulation to global optimality. Extensive computational experiments on a large test set show that our method not only computes tight dual bounds, but often produces primal solutions better than those computed by heuristics from the literature. T3 - ZIB-Report - 17-07 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62039 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Hoppmann, Heide A1 - Karbstein, Marika T1 - Umsteigen ohne Warten N2 - Wir stellen einen mathematischen Optimierungsansatz zur Berechnung von periodischen Taktfahrplänen vor, bei dem die Umsteigezeiten unter Berücksichtigung des Passagierverhaltens minimiert werden. Wir untersuchen damit den Einfluss wichtiger Systemparameter und Verhaltensmuster auf die Beförderungsqualität. T3 - ZIB-Report - 17-05 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62006 SN - 1438-0064 ER - TY - GEN A1 - Hiller, Benjamin A1 - Koch, Thorsten A1 - Schewe, Lars A1 - Schwarz, Robert A1 - Schweiger, Jonas T1 - A System to Evaluate Gas Network Capacities: Concepts and Implementation N2 - Since 2005, the gas market in the European Union is liberalized and the trading of natural gas is decoupled from its transport. The transport is done by so-called transmissions system operators or TSOs. The market model established by the European Union views the gas transmission network as a black box, providing shippers (gas traders and consumers) the opportunity to transport gas from any entry to any exit. TSOs are required to offer maximum independent capacities at each entry and exit such that the resulting gas flows can be realized by the network without compromising security of supply. Therefore, evaluating the available transport capacities is extremely important to the TSOs. This paper gives an overview of the toolset for evaluating gas network capacities that has been developed within the ForNe project, a joint research project of seven research partners initiated by Open Grid Europe, Germany's biggest TSO. While most of the relevant mathematics is described in the book "Evaluating Gas Network Capacities", this article sketches the system as a whole, describes some developments that have taken place recently, and gives some details about the current implementation. T3 - ZIB-Report - 17-03 KW - operations research in energy KW - gas network optimization KW - entry-exit model KW - freely allocable capacity KW - large-scale mixed-integer nonlinear programming Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61931 SN - 1438-0064 N1 - A revised and extended version is available as ZIB-Report 18-11. ER - TY - GEN A1 - Baum, Daniel A1 - Lindow, Norbert A1 - Hege, Hans-Christian A1 - Lepper, Verena A1 - Siopi, Tzulia A1 - Kutz, Frank A1 - Mahlow, Kristin A1 - Mahnke, Heinz-Eberhard T1 - Revealing hidden text in rolled and folded papyri N2 - Ancient Egyptian papyri are often folded, rolled up or kept as small packages, sometimes even sealed. Physically unrolling or unfolding these packages might severely damage them. We demonstrate a way to get access to the hidden script without physical unfolding by employing computed tomography and mathematical algorithms for virtual unrolling and unfolding. Our algorithmic approaches are combined with manual interaction. This provides the necessary flexibility to enable the unfolding of even complicated and partly damaged papyrus packages. In addition, it allows us to cope with challenges posed by the structure of ancient papyrus, which is rather irregular, compared to other writing substrates like metallic foils or parchment. Unfolding of packages is done in two stages. In the first stage, we virtually invert the physical folding process step by step until the partially unfolded package is topologically equivalent to a scroll or a papyrus sheet folded only along one fold line. To minimize distortions at this stage, we apply the method of moving least squares. In the second stage, the papyrus is simply flattened, which requires the definition of a medial surface. We have applied our software framework to several papyri. In this work, we present the results of applying our approaches to mockup papyri that were either rolled or folded along perpendicular fold lines. In the case of the folded papyrus, our approach represents the first attempt to address the unfolding of such complicated folds. T3 - ZIB-Report - 17-02 KW - unfolding, papyri, computed tomography Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61826 SN - 1438-0064 ER -