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  • biodegradation
  • 1
    ISSN: 1572-9729
    Keywords: biodegradation ; Burkholderia ; fenitrothion ; mpd gene
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Energy, Environment Protection, Nuclear Power Engineering , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract A short rod shaped, gram-negative bacterium strain Burkholderia sp. FDS-1 was isolated from the sludge of the wastewater treating system of an organophosphorus pesticides manufacturer. The isolate was capable of using fenitrothion as the sole carbon source for its growth. FDS-1 first hydrolyzed fenitrothion to 3-methyl-4-nitrophenol, which was further metabolized to nitrite and methylhydroquinone. The addition of other carbon source and omitting phosphorus source had little effect on the hydrolysis of fenitrothion. The gene encoding the organophosphorus hydrolytic enzyme was cloned and sequenced. The sequence was similar to mpd, a gene previously shown to encode a parathion-methyl-hydrolyzing enzyme in Plesiomonas sp. M6. The inoculation of strain FDS-1 (106 cells g−1) to soil treated with 100 mg fenitrothion emulsion kg−1 resulted in a higher degradation rate than in noninoculated soils regardless of the soil sterilized or nonsterilized. These results highlight the potential of this bacterium to be used in the cleanup of contaminated pesticide waste in the environment.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Biodegradation 17 (2006), S. 207-217 
    ISSN: 1572-9729
    Keywords: biodegradation ; DGGE ; K2Ni(CN)4 soil bacterial populations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Energy, Environment Protection, Nuclear Power Engineering , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Metal cyanides are significant contaminants of many soils found at the site of former industrial activity. In this study we isolated bacteria capable of degrading ferric ferrocyanide and K2Ni(CN)4. One of these bacteria a Rhodococcus spp. was subsequently used to bioaugment a minimal medium broth, spiked with K2Ni(CN)4, containing 1 g of either an uncontaminated topsoil or a former coke works site soil. Degradation of the K2Ni(CN)4 was observed in both soils, however, bioaugmentation did not significantly impact the rate or degree of K2Ni(CN)4 removal. Statistical analysis of denaturing gradient gel electrophoresis profiles showed that the topsoil bacterial community had a higher biodiversity, and its structure was not significantly affected by either K2Ni(CN)4 or bioaugmentation. In contrast, profiles from the coke works site indicated significant changes in the bacterial community in response to these additions. Moreover, in both soils although bioaugmentation did not affect rates of biodegradation the Rhodococcus spp. did become established in the communities in broths containing both top and coke works soil. We conclude that bacterial communities from contaminated soils with low biodiversity are much more readily perturbed through interventions such as contamination events or bioaugmentation treatments and discuss the implications of these findings for bioremediation studies.
    Type of Medium: Electronic Resource
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  • 3
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    Publication Date: 2019-10-24
    Keywords: ddc:000
    Language: German
    Type: annualzib , doc-type:report
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  • 4
    Publication Date: 2014-02-26
    Description: We propose a variant of the control reduced interior point method for the solution of state constrained problems. We show convergence of the corresponding interior point pathfollowing algorithm in function space. Morever, we provide error bounds for the iterates.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 5
    Publication Date: 2014-02-26
    Description: This paper aims at presenting the complex coupled network of the human menstrual cycle to the interested community. Beyond the presently popular smaller models, where important network components arise only as extremely simplified source terms, we add: the GnRH pulse generator in the hypothalamus, receptor binding, and the biosynthesis in the ovaries. Simulation and parameter identification are left to a forthcoming paper.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 6
    Publication Date: 2014-02-26
    Description: This work explores two applications of a classical result on the continuity of Nemyckii operators to optimal control with PDEs. First, we present an alternative approach to the analysis of Newton's method for function space problems involving semi-smooth Nemyckii operators. A concise proof for superlinear convergence is presented, and sharpened bounds on the rate of convergence are derived. Second, we derive second order sufficient conditions for problems, where the underlying PDE has poor regularity properties. We point out that the analytical structure in both topics is essentially the same.
    Keywords: ddc:000
    Language: English
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  • 7
    Publication Date: 2014-02-26
    Description: In this paper, we study the efficiency of Nash equilibria for a sequence of nonatomic routing games. We assume that the games are played consecutively in time in an online fashion: by the time of playing game $i$, future games $i+1,\dots,n$ are not known, and, once players of game $i$ are in equilibrium, their corresponding strategies and costs remain fixed. Given a sequence of games, the cost for the sequence of Nash equilibria is defined as the sum of the cost of each game. We analyze the efficiency of a sequence of Nash equilibria in terms of competitive analysis arising in the online optimization field. Our main result states that the online algorithm $\sl {SeqNash}$ consisting of the sequence of Nash equilibria is $\frac{4n}{2+n}$-competitive for affine linear latency functions. For $n=1$, this result contains the bound on the price of anarchy of $\frac{4}{3}$ for affine linear latency functions of Roughgarden and Tardos [2002] as a special case. Furthermore, we analyze a problem variant with a modified cost function that reflects the total congestion cost, when all games have been played. In this case, we prove an upper bound of $\frac{4n}{2+n}$ on the competitive ratio of $\sl {SeqNash}$. We further prove a lower bound of $\frac{3n-2}{n}$ of $\sl {SeqNash}$ showing that for $n=2$ our upper bound is tight.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 8
    Publication Date: 2016-06-09
    Description: To approximate convolutions which occur in evolution equations with memory terms, a variable-stepsize algorithm is presented for which advancing $N$ steps requires only $O(N\log N)$ operations and $O(\log N)$ active memory, in place of $O(N^2)$ operations and $O(N)$ memory for a direct implementation. A basic feature of the fast algorithm is the reduction, via contour integral representations, to differential equations which are solved numerically with adaptive step sizes. Rather than the kernel itself, its Laplace transform is used in the algorithm. The algorithm is illustrated on three examples: a blow-up example originating from a Schrödinger equation with concentrated nonlinearity, chemical reactions with inhibited diffusion, and viscoelasticity with a fractional order constitutive law.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 9
    Publication Date: 2020-11-13
    Description: This paper deals with MIP-based primal heuristics to be used within a branch-and-cut approach for solving multi-layer telecommunication network design problems. Based on a mixed-integer programming formulation for two network layers, we present three heuristics for solving important subproblems, two of which solve a sub-MIP. On multi-layer planning instances with many parallel logical links, we show the effectiveness of our heuristics in finding good solutions early in the branch-and-cut search tree.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 10
    Publication Date: 2019-05-10
    Description: The dynamics of ventricular fibrillation caused by irregular excitation is simulated in the frame of the monodomain model with an action potential model due to Aliev-Panfilov for a human 3D geometry. The numerical solution of this multiscale reaction-diffusion problem is attacked by algorithms which are fully adaptive in both space and time (code library {\sc Kardos}). The obtained results clearly demonstrate an accurate resolution of the cardiac potential during the excitation and the plateau phases (in the regular cycle) as well as after a reentrant excitation (in the irregular cycle).
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 11
    Publication Date: 2020-12-15
    Description: The topic of this paper are integer programming models in which a subset of 0/1-variables encode a partitioning of a set of objects into disjoint subsets. Such models can be surprisingly hard to solve by branch-and-cut algorithms if the permutation of the subsets of the partition is irrelevant. This kind of symmetry unnecessarily blows up the branch-and-cut tree. We present a general tool, called orbitopal fixing, for enhancing the capabilities of branch-and-cut algorithms in solving this kind of symmetric integer programming models. We devise a linear time algorithm that, applied at each node of the branch-and-cut tree, removes redundant parts of the tree produced by the above mentioned permutations. The method relies on certain polyhedra, called orbitopes, which have been investigated in (Kaibel and Pfetsch (2006)). However, it does not add inequalities to the model, and thus, it does not increase the difficulty of solving the linear programming relaxations. We demonstrate the computational power of orbitopal fixing at the example of a graph partitioning problem motivated from frequency planning in mobile telecommunication networks.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 12
    Publication Date: 2014-11-10
    Description: In this paper, we discuss the relation of unsplittable shortest path routing (USPR) to other routing schemes and study the approximability of three USPR network planning problems. Given a digraph $D=(V,A)$ and a set $K$ of directed commodities, an USPR is a set of flow paths $\Phi_{(s,t)}$, $(s,t)\in K$, such that there exists a metric $\lambda=(\lambda_a)\in \mathbb{Z}^A_+$ with respect to which each $\Phi_{(s,t)}$ is the unique shortest $(s,t)$-path. In the \textsc{Min-Con-USPR} problem, we seek for an USPR that minimizes the maximum congestion over all arcs. We show that this problem is hard to approximate within a factor of $\mathcal{O}(|V|^{1-\epsilon})$, but easily approximable within min$(|A|,|K|)$ in general and within $\mathcal{O}(1)$ if the underlying graph is an undirected cycle or a bidirected ring. We also construct examples where the minimum congestion that can be obtained by USPR is a factor of $\Omega(|V|^2)$ larger than that achievable by unsplittable flow routing or by shortest multi-path routing, and a factor of $\Omega(|V|)$ larger than by unsplittable source-invariant routing. In the CAP-USPR problem, we seek for a minimum cost installation of integer arc capacities that admit an USPR of the given commodities. We prove that this problem is $\mathcal{NP}$-hard to approximate within $2-\epsilon$ (even in the undirected case), and we devise approximation algorithms for various special cases. The fixed charge network design problem \textsc{Cap-USPR}, where the task is to find a minimum cost subgraph of $D$ whose fixed arc capacities admit an USPR of the commodities, is shown to be $\mathcal{NPO}$-complete. All three problems are of great practical interest in the planning of telecommunication networks that are based on shortest path routing protocols. Our results indicate that they are harder than the corresponding unsplittable flow or shortest multi-path routing problems.
    Keywords: ddc:000
    Language: English
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  • 13
    Publication Date: 2014-11-11
    Description: In this paper, we investigate the connection availabilities for the new protection scheme Demand-wise Shared Protection (DSP) and describe an appropriate approach for their computation. The exemplary case study on two realistic network scenarios shows that in most cases the availabilities for DSP are comparable with that for 1+1 path protection and better than in case of shared path protection.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 14
    Publication Date: 2016-06-30
    Description: THESEUS, the ZIB threading environment, is a parallel implementation of a protein threading based on a multi-queued branch-and-bound optimal search algorithm to find the best sequence-to-structure alignment through a library of template structures. THESEUS uses a template core model based on secondary structure definition and a scoring function based on knowledge-based potentials reflecting pairwise interactions and the chemical environment, as well as pseudo energies for homology detection, loop alignment, and secondary structure matching. The threading core is implemented in C++ as a SPMD parallization architecture using MPI for communication. The environment is designed for generic testing of different scoring functions, e.g. different secondary structure prediction terms, different scoring matrices and information derived from multiple sequence alignments. A validaton of the structure prediction results has been done on the basis of standard threading benchmark sets. THESEUS successfully participated in the 6th Critical Assessment of Techniques for Protein Structure Prediction (CASP) 2004.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 15
    Publication Date: 2014-02-26
    Description: We consider a multi-queue multi-server system with $n$ servers (processors) and $m$ queues. At the system there arrives a stationary and ergodic stream of $m$ different types of requests with service requirements which are served according to the following $k$-limited head of the line processor sharing discipline: The first $k$ requests at the head of the $m$ queues are served in processor sharing by the $n$ processors, where each request may receive at most the capacity of one processor. By means of sample path analysis and Loynes' monotonicity method, a stationary and ergodic state process is constructed, and a necessary as well as a sufficient condition for the stability of the $m$ separate queues are given, which are tight within the class of all stationary ergodic inputs. These conditions lead to tight necessary and sufficient conditions for the whole system, also in case of permanent customers, generalizing an earlier result by the authors for the case of $n$=$k$=1.
    Keywords: ddc:000
    Language: English
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  • 16
    Publication Date: 2014-02-26
    Description: In order to compute the thermodynamic weights of the different metastable conformations of a molecule, we want to approximate the molecule's Boltzmann distribution in a reasonable time. This is an essential issue in computational drug design. The energy landscape of active biomolecules is generally very rough with a lot of high barriers and low regions. Many of the algorithms that perform such samplings (e.g. the hybrid Monte Carlo method) have difficulties with such landscapes. They are trapped in low-energy regions for a very long time and cannot overcome high barriers. Moving from one low-energy region to another is a very rare event. For these reasons, the distribution of the generated sampling points converges very slowly against the thermodynamically correct distribution of the molecule. The idea of ConfJump is to use $a~priori$ knowledge of the localization of low-energy regions to enhance the sampling with artificial jumps between these low-energy regions. The artificial jumps are combined with the hybrid Monte Carlo method. This allows the computation of some dynamical properties of the molecule. In ConfJump, the detailed balance condition is satisfied and the mathematically correct molecular distribution is sampled.
    Keywords: ddc:000
    Language: English
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  • 17
    Publication Date: 2020-02-11
    Description: "`Volkssport Sudoku"' titelt der Stern in seiner Ausgabe vom 24. Mai2006. In der Tat traut sich derzeit kaum noch eine Zeitung, ohne Sudoku zu erscheinen. Die Begeisterung am Lösen dieser Zahlenrätsel offenbart eine unvermutete Freude am algorithmischen Arbeiten. Mathematisch kann man Sudokus als lineare diophantische Gleichungssysteme mit Nichtnegativitätsbedingungen formulieren. Solche ganzzahligen linearen Programme sind die wichtigsten Modellierungswerkzeuge in zahlreichen Anwendungsgebieten wie z.B. der Optimierung von Telekommunikations- und Verkehrsnetzen. Moderne Verfahren zur Lösung dieser Optimierungsprobleme sind durch Sudokus allerdings deutlich weniger zu beeindrucken als Zeitungsleser.
    Keywords: ddc:000
    Language: German
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  • 18
    Publication Date: 2020-02-11
    Description: This article surveys mathematical models and methods used for physical PCB layout, i.e., component placement and wire routing. The main concepts are briefly described together with relevant references.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 19
    Publication Date: 2020-12-15
    Description: We study online multicommodity minimum cost routing problems in networks, where commodities have to be routed sequentially. Arcs are equipped with load dependent price functions defining the routing weights. We discuss an online algorithm that routes each commodity by minimizing a convex cost function that depends on the demands that are previously routed. We present a competitive analysis of this algorithm showing that for affine linear price functions this algorithm is $4K/2+K$-competitive, where $K$ is the number of commodities. For the parallel arc case this algorithm is optimal. Without restrictions on the price functions and network, no algorithm is competitive. Finally, we investigate a variant in which the demands have to be routed unsplittably.
    Keywords: ddc:000
    Language: English
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  • 20
    Publication Date: 2021-03-16
    Description: Perfect graphs constitute a well-studied graph class with a rich structure, reflected by many characterizations w.r.t different concepts. Perfect graphs are, e.g., characterized as precisely those graphs $G$ where the stable set polytope STAB$(G)$ coincides with the clique constraint stable set polytope QSTAB$(G)$. For all imperfect graphs STAB$(G) \subset$ QSTAB$(G)$ holds and, therefore, it is natural to measure imperfection in terms of the difference between STAB$(G)$ and QSTAB$(G)$. Several concepts have been developed in this direction, for instance the dilation ratio of STAB$(G)$ and QSTAB$(G)$ which is equivalent to the imperfection ratio imp$(G)$ of $G$. To determine imp$(G)$, both knowledge on the facets of STAB$(G)$ and the extreme points of QSTAB$(G)$ is required. The anti-blocking theory of polyhedra yields all {\em dominating} extreme points of QSTAB$(G)$, provided a complete description of the facets of STAB$(\overline G)$ is known. As this is typically not the case, we extend the result on anti-blocking polyhedra to a {\em complete} characterization of the extreme points of QSTAB$(G)$ by establishing a 1-1 correspondence to the facet-defining subgraphs of $\overline G$. We discuss several consequences, in particular, we give alternative proofs of several famous results.
    Keywords: ddc:000
    Language: English
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  • 21
    Publication Date: 2014-11-10
    Description: We give experimental and theoretical results on the problem of computing the treewidth of a graph by exact exponential time algorithms using exponential space or using only polynomial space. We first report on an implementation of a dynamic programming algorithm for computing the treewidth of a graph with running time $O^\ast(2^n)$. This algorithm is based on the old dynamic programming method introduced by Held and Karp for the {\sc Tra veling Salesman} problem. We use some optimizations that do not affect the worst case running time but improve on the running time on actual instances and can be seen to be practical for small instances. However, our experiments show that the space use d by the algorithm is an important factor to what input sizes the algorithm is effective. For this purpose, we settle the problem of computing treewidth under the restriction that the space used is only polynomial. In this direction we give a simple $O^\ast(4^n)$ al gorithm that requires {\em polynomial} space. We also show that with a more complicated algorithm, using balanced separators, {\sc Treewidth} can be computed in $O^\ast(2.9512^n)$ time and polynomial space.
    Keywords: ddc:000
    Language: English
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  • 22
    Publication Date: 2014-03-10
    Description: The dynamic behavior of molecules can often be described by Markov processes. From computational molecular simulations one can derive transition rates or transition probabilities between subsets of the discretized conformational space. On the basis of this dynamic information, the spatial subsets are combined into a small number of so-called metastable molecular conformations. This is done by clustering methods like the Robust Perron Cluster Analysis (PCCA+). Up to now it is an open question how this coarse graining in space can be transformed to a coarse graining of the Markov chain while preserving the essential dynamic information. In the following article we aim at a consistent coarse graining of transition probabilities or rates on the basis of metastable conformations such that important physical and mathematical relations are preserved. This approach is new because PCCA+ computes molecular conformations as linear combinations of the dominant eigenvectors of the transition matrix which does not hold for other clustering methods.
    Keywords: ddc:000
    Language: English
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  • 23
    Publication Date: 2014-02-26
    Description: Das deutschsprachige Bibliothekswesen verfügt mit den \glqq Regeln für den Schlagwortkatalog \grqq (RSWK) unter Verwendung der \glqq Schlagwortnormdatei \grqq (SWD) über ein Instrumentarium, welches zusammen mit einem \glqq Faceted Browsing \grqq das bisher bestehende Angebot für ein Information Retrieval optimal ergänzen kann. Die Verbindung zwischen Standardvokabular (SWD) und Kettenbildung (RSWK) einerseits und eine nach Facetten-Eigenschaften gegliederte Navigation andererseits unterstützt bestmöglich eine inhaltlich bezogene Recherche. Die Stärken und Schwächen der RSWK/SWD werden erörtert und auch Klassifikationen (DDC und RVK) als mögliche Facetten diskutiert.
    Keywords: ddc:000
    Language: German
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  • 24
    Publication Date: 2016-06-09
    Keywords: ddc:000
    Language: English
    Type: masterthesis , doc-type:masterThesis
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  • 25
    Publication Date: 2022-03-14
    Description: A lot of problems arising in Combinatorial Optimization and Operations Research can be formulated as Mixed Integer Programs (MIP). Although MIP-solving is an NP-hard optimization problem, many practically relevant instances can be solved in reasonable time. In modern MIP-solvers like the branch-cut-and-price-framework SCIP, primal heuristics play a major role in finding and improving feasible solutions at the early steps of the solution process. This helps to reduce the overall computational effort, guides the remaining search process, and proves the feasibility of the MIP model. Furthermore, a heuristic solution with a small gap to optimality often is sufficient in practice. We investigate 16 different heuristics, all of which are available in SCIP. Four of them arise from the literature of the last decade, nine are specific implementations of general heuristic ideas, three have been newly developed. We present an improved version of the feasibility pump heuristic by Fischetti et al., which in experiments produced solutions with only a third of the optimality gap compared to the original version. Furthermore, we introduce two new Large Neighborhood Search (LNS) heuristics. Crossover is an LNS improvement heuristic making use of similarities of diverse MIP solutions to generate new incumbent solutions. RENS is an LNS rounding heuristic which evaluates the space of all possible roundings of a fractional LP-solution. This heuristic makes it possible to determine whether a point can be rounded to an integer solution and which is the best possible rounding. We conclude with a computational comparison of all described heuristics. It points out that a single heuristic on its own has only a slight impact on the overall performance of SCIP, but the combination of all of them reduces the running time by a factor of two compared to a version without any heuristics.
    Keywords: ddc:000
    Language: English
    Type: masterthesis , doc-type:masterThesis
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  • 26
    Publication Date: 2014-02-26
    Description: We present a finite volume method for the solution of the two-dimensional Poisson equation $ \nabla\cdot( \beta( {\mbox{\boldmath $x$}}) \nabla u({\mbox{\boldmath $x$}})) = f(\mbox{\boldmath $x$}) $ with variable, discontinuous coefficients and solution discontinuities on irregular domains. The method uses bilinear ansatz functions on Cartesian grids for the solution $u({\mbox{\boldmath $x$})$ resulting in a compact nine-point stencil. The resulting linear problem has been solved with a standard multigrid solver. Singularities associated with vanishing partial volumes of intersected grid cells or the dual bilinear ansatz itself are removed by a two-step asymptotic approach. The method achieves second order of accuracy in the $L^\infty$ and $L^2$ norm.
    Keywords: ddc:000
    Language: English
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  • 27
    Publication Date: 2014-11-11
    Description: In this article we aim at an efficient sampling of the stationary distribution of dynamical systems in the presence of metastabilities. In the past decade many sophisticated algorithms have been inven ted in this field. We do not want to simply add a further one. We address the problem that one has applied a sampling algorithm for a dynamical system many times. This leads to different samplings which more or less represent the stationary distribution partially very well, but which are still far away from ergodicity or from the global stationary distribution. We will show how these samplings can be joined together in order to get one global sampling of the stationary distribution.
    Keywords: ddc:000
    Language: English
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  • 28
    Publication Date: 2014-02-26
    Description: The concept of jump system, introduced by Buchet and Cunningham (1995), is a set of integer points with a certain exchange property. In this paper, we discuss several linear and convex optimization problems on jump systems and show that these problems can be solved in polynomial time under the assumption that a membership oracle for a jump system is available. We firstly present a polynomial-time implementation of the greedy algorithm for the minimization of a linear function. We then consider the minimization of a separable-convex function on a jump system, and propose the first polynomial-time algorithm for this problem. The algorithm is based on the domain reduction approach developed in Shioura (1998). We finally consider the concept of M-convex functions on constant-parity jump systems which has been recently proposed by Murota (2006). It is shown that the minimization of an M-convex function can be solved in polynomial time by the domain reduction approach.
    Keywords: ddc:000
    Language: English
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  • 29
    Publication Date: 2020-12-15
    Description: We introduce orbitopes as the convex hulls of 0/1-matrices that are lexicographically maximal subject to a group acting on the columns. Special cases are packing and partitioning orbitopes, which arise from restrictions to matrices with at most or exactly one 1-entry in each row, respectively. The goal of investigating these polytopes is to gain insight into ways of breaking certain symmetries in integer programs by adding constraints, e.g., for a well-known formulation of the graph coloring problem. We provide a thorough polyhedral investigation of packing and partitioning orbitopes for the cases in which the group acting on the columns is the cyclic group or the symmetric group. Our main results are complete linear inequality descriptions of these polytopes by facet-defining inequalities. For the cyclic group case, the descriptions turn out to be totally unimodular, while for the symmetric group case, both the description and the proof are more involved. The associated separation problems can be solved in linear time.
    Keywords: ddc:000
    Language: English
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  • 30
    Publication Date: 2014-11-21
    Description: The standard computational methods for computing the optimal value functions of Markov Decision Problems (MDP) require the exploration of the entire state space. This is practically infeasible for applications with huge numbers of states as they arise, e.\,g., from modeling the decisions in online optimization problems by MDPs. Exploiting column generation techniques, we propose and apply an LP-based method to determine an $\varepsilon$-approximation of the optimal value function at a given state by inspecting only states in a small neighborhood. In the context of online optimization problems, we use these methods in order to evaluate the quality of concrete policies with respect to given initial states. Moreover, the tools can also be used to obtain evidence of the impact of single decisions. This way, they can be utilized in the design of policies.
    Keywords: ddc:000
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  • 31
    Publication Date: 2014-11-21
    Description: Wir beschäftigen uns mit dem Problem der Betriebsplanung von Laserschweißrobotern im Karosseriebau. Gegeben ist eine Menge von Schweißnähten, die innerhalb einer Fertigungszelle an einem Karosserieteil gefertigt werden müssen. Die Schweißnähte werden durch mehrere parallel betriebene Roboter bearbeitet. Die Aufgabe besteht darin, für jeden Roboter eine Reihenfolge und eine zeitliche Koordinierung seiner Bewegungen zu finden, so dass alle Schweißnähte innerhalb der Taktzeit der Fertigungszelle bearbeitet werden und so wenig Laserquellen wie möglich eingesetzt werden. Dabei müssen einige Nebenbedingungen berücksichtigt werden. Für dieses spezielle Schweißproblem haben wir eine Formulierung als gemischt-ganzzahliges lineares Programm entwickelt, welches sich für die untersuchten praktischen Fälle sehr schnell lösen lässt.
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    Language: German
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  • 32
    Publication Date: 2021-08-05
    Description: Modern applications of mathematical programming must take into account a multitude of technical details, business demands, and legal requirements. Teaching the mathematical modeling of such issues and their interrelations requires real-world examples that are well beyond the toy sizes that can be tackled with the student editions of most commercial software packages. We present a new tool, which is freely available for academic use including complete source code. It consists of an algebraic modeling language and a linear mixed integer programming solver. The performance and features of the tool are in the range of current state-of-the-art commercial tools, though not in all aspects as good as the best ones. Our tool does allow the execution and analysis of large real-world instances in the classroom and can therefore enhance the teaching of problem solving issues. Teaching experience has been gathered and practical usability was tested in classes at several universities and a two week intensive block course at TU Berlin. The feedback from students and teachers has been very positive.
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  • 33
    Publication Date: 2014-11-21
    Description: The Bottleneck Shortest Path Problem is a basic problem in network optimization. The goal is to determine the limiting capacity of any path between two specified vertices of the network. This is equivalent to determining the unsplittable maximum flow between the two vertices. In this note we analyze the complexity of the problem, its relation to the Shortest Path Problem, and the impact of the underlying machine/computation model.
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  • 34
    Publication Date: 2014-02-26
    Description: We introduce a new and rich class of graph coloring manifolds via the Hom complex construction of Lov\´{a}sz. The class comprises examples of Stiefel manifolds, series of spheres and products of spheres, cubical surfaces, as well as examples of Seifert manifolds. Asymptotically, graph coloring manifolds provide examples of highly connected, highly symmetric manifolds.
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  • 35
    Publication Date: 2014-02-26
    Description: We give coordinate-minimal geometric realizations in general position for 17 of the 20 vertex-minimal triangulations of the orientable surface of genus 3 in the 5x5x5-cube.
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  • 36
    Publication Date: 2014-02-26
    Description: Biochemical interactions are determined by the 3D-structure of the involved components - thus the identification of conformations is a key for many applications in rational drug design. {\sf ConFlow} is a new multilevel approach to conformational analysis with main focus on completeness in investigation of conformational space. In contrast to known conformational analysis, the starting point for design is a space-based description of conformational areas. A tight integration of sampling and analysis leads to an identification of conformational areas simultaneously during sampling. An incremental decomposition of high-dimensional conformational space is used to guide the analysis. A new concept for the description of conformations and their path connected components based on convex hulls and {\em Hypercubes}is developed. The first results of the {\sf ConFlow} application constitute a 'proof of concept' and are further more highly encouraging. In comparison to conventional industrial applications, {\sf ConFlow} achieves higher accuracy and a specified degree of completeness with comparable effort.
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  • 37
    Publication Date: 2014-02-26
    Description: We consider linear inverse problems where the solution is assumed to fulfill some general homogeneous convex constraint. We develop an algorithm that amounts to a projected Landweber iteration and that provides and iterative approach to the solution of this inverse problem. For relatively moderate assumptions on the constraint we can always prove weak convergence of the iterative scheme. In certain cases, i.e. for special families of convex constraints, weak convergence implies norm convergence. The presented approach covers a wide range of problems, e.g. Besov- or BV-restoration for which we present also numerical experiments in the context of image processing.
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  • 38
    Publication Date: 2014-03-10
    Description: Whenever the invariant stationary density of metastable dynamical systems decomposes into almost invariant partial densities, its computation as eigenvector of some transition probability matrix is an ill-conditioned problem. In order to avoid this computational difficulty, we suggest to apply an aggregation/disaggregation method which only addresses wellconditioned sub-problems and thus results in a stable algorithm. In contrast to existing methods, the aggregation step is done via a sampling algorithm which covers only small patches of the sampling space. Finally, the theoretical analysis is illustrated by two biomolecular examples.
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  • 39
    Publication Date: 2016-02-29
    Description: \noindent We give a partial description of the $(s,t)-p$-path polytope of a directed graph $D$ which is the convex hull of the incidence vectors of simple directed $(s,t)$-paths in $D$ of length $p$. First, we point out how the $(s,t)-p$-path polytope is located in the family of path and cycle polyhedra. Next, we give some classes of valid inequalities which are very similar to inequalities which are valid for the $p$-cycle polytope, that is, the convex hull of the incidence vectors of simple cycles of length $p$ in $D$. We give necessary and sufficient conditions for these inequalities to be facet defining. Furthermore, we consider a class of inequalities that has been identifie d to be valid for $(s,t)$-paths of cardinality at most $p$. Finally, we transfer the results to related polytopes, in particular, the undirected counterpart of the $(s,t)-p$-path polytope.
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  • 40
    Publication Date: 2020-11-13
    Description: The numerical integration of dynamical contact problems often leads to instabilities at contact boundaries caused by the non-penetration condition between bodies in contact. Even a recent energy dissipative modification due to Kane et al. (1999), which discretizes the non-penetration constraints implicitly, is not able to circumvent artificial oscillations. For this reason, the present paper suggests a contact stabilization which avoids artificial oscillations at contact interfaces and is also energy dissipative. The key idea of this contact stabilization is an additional $L^2$-projection at contact interfaces, which can easily be added to any existing time integration scheme. In case of a lumped mass matrix, this projection can be carried out completely locally, thus creating only negligible additional numerical cost. For the new scheme, an elementary analysis is given, which is confirmed by numerical findings in an illustrative test example (Hertzian two body contact).
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  • 41
    Publication Date: 2016-06-30
    Keywords: ddc:000
    Language: German
    Type: masterthesis , doc-type:masterThesis
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  • 42
    Publication Date: 2014-02-26
    Description: We discuss different approaches for the enumeration of triangulated surfaces. In particular, we enumerate all triangulated surfaces with 9 and 10 vertices. We also show how geometric realizations of orientable surfaces with few vertices can be obtained by choosing coordinates randomly.
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  • 43
    Publication Date: 2014-02-26
    Description: The concept of L##-convexity is introduced by Fujishige--Murota (2000) as a discrete convexity for functions defined over the integer lattice. The main aim of this note is to understand the difference of the two algorithms for L##-convex function minimization: Murota's steepest descent algorithm (2003) and Kolmogorov's primal algorithm (2005).
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  • 44
    Publication Date: 2014-02-26
    Description: In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal triangulations.
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  • 45
    Publication Date: 2020-02-11
    Description: This paper concerns the problem of operating a landside container exchange area that is serviced by multiple semi-automated rail mounted gantry cranes (RMGs) that are moving on a single bi-directional traveling lane. Such a facility is being built by Patrick Corporation at the Port Botany terminal in Sydney. The gantry cranes are a scarce resource and handle the bulk of container movements. Thus, they require a sophisticated analysis to achieve near optimal utilization. We present a three stage algorithm to manage the container exchange facility, including the scheduling of cranes, the control of associated short-term container stacking, and the allocation of delivery locations for trucks and other container transporters. The key components of our approach are a time scale decomposition, whereby an integer program controls decisions across a long time horizon to produce a balanced plan that is fed to a series of short time scale online subproblems, and a highly efficient space-time divisioning of short term storage areas. A computational evaluation shows that our heuristic can find effective solutions for the planning problem; on real-world data it yields a solution at most~8\% above a lower bound on optimal RMG utilization.
    Keywords: ddc:000
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  • 46
    Publication Date: 2014-02-26
    Description: We describe an algorithm for the enumeration of (candidates of) vertex-transitive combinatorial $d$-manifolds. With an implementation of our algorithm, we determine, up to combinatorial equivalence, all combinatorial manifolds with a vertex-transitive automorphism group on $n\leq 13$ vertices. With the exception of actions of groups of small order, the enumeration is extended to 14 and 15 vertices.
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  • 47
    Publication Date: 2014-02-26
    Description: We give coordinate-minimal geometric realizations in general position of all 865 vertex-minimal triangulations of the orientable surface of genus 2 in the 4x4x4-cube.
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  • 48
    Publication Date: 2014-02-26
    Description: We give a complete enumeration of combinatorial 3-manifolds with 10 vertices: There are precisely 247882 triangulated 3-spheres with 10 vertices as well as 518 vertex-minimal triangulations of the sphere product $S^2 x S^1$ and 615 triangulations of the twisted sphere product $S^2 \underline{x} S^1$. An analysis of the 3-spheres with up to 10 vertices shows that all these spheres are shellable, but that there are 29 vertex-minimal non-shellable 3-balls with 9 vertices.
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  • 49
    Publication Date: 2019-05-10
    Description: Adaptive numerical methods in time and space are introduced and studied for linear poroelastic models in two and three space dimensions. We present equivalent models for linear poroelasticity and choose both the {\em displacement--pressure} and the {\em stress--pressure} formulation for our computations. Their discretizations are provided by means of linearly implicit schemes in time and linear finite elements in space. Our concept of adaptivity opens a way to a fast and reliable simulation of different loading cases defined by corresponding boundary conditions. We present some examples using our code {\sf Kardos} and show that the method works efficiently. In particular, it could be used in the simulation of some bone healing models.
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  • 50
    Publication Date: 2016-06-30
    Description: During the last few years more and more functionalities of RNA have been discovered that were previously thought of being carried out by proteins alone. One of the most striking discoveries was the de tection of microRNAs, a class of noncoding RNAs that play an important role in post-transcriptional gene regulation. Large-scale analyses are needed for the still increasingly growing amount of sequen ce data derived from new experimental technologies. In this paper we present a framework for the detection of the distinctive precursor structure of microRNAS that is based on the well-known Smith-Wat erman algorithm and various filtering steps. We conducted experiments on real genomic data and we found several new putative hits for microRNA precursor structures.
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  • 51
    Publication Date: 2014-02-26
    Description: Wir erleben zu Beginn des aufkommenden Informationszeitalters mit dem Siegeszug von Google und anderen Internet-Technologien einen Wandel im Verhalten von Wissenschaftlern und Studenten, der mit dem Einsatz von {\sl Google Scholar} und {\sl Google Book Search} einen Paradigmenwechsel für Bibliotheken und Informationsversorger gleichkommt. Der Artikel untersucht die technischen Hintergründe für den Erfolg dieser besonderen Art des Information Retrievals: Fulltext Indexing und Citation Ranking als besondere Form des Information Minig. Er diskutiert Stärken und auch Schwächen des Google-Ansatzes. Der Autor stellt sich auch der Frage, unter welchen Bedingungen es möglich ist, ein zu {\sl Google Scholar} und der {\sl Google Book Search} konkurrenzfähiges Retrieval in der Landschaft der Bibliotheken und Bibliotheksverbünde zu entrichten. Die These ist, dass dieses unter Einsatz des {\sl Open Source} Indexierers {\sl Lucene} und des Web-Robots {\sl Nutch} möglich ist. Bibliotheken können durch gezielten Einsatz solcher Internet-Technologien dem Nutzer die Leistungen, welche Google uns mit seinen Tools im {\sl Visible Web} und mit Referenzen auf {\sl Citations} in der Welt der Literatur zur Verfügung stellt, in vergleichbarer Art auch für ihre eigenen durch Lizenzen geschützten digitalen Journale und ihre speziellen lokal verfügbaren Ressourcen, auf die Internet-Suchmaschinen keine Zugriff haben, anbieten. Es besteht die Hoffnung, dass Nutzer dann nicht - wie in einer kürzlichen Studie des OCLC konstatiert - überwiegend im Internet verbleiben, sondern bei ihrer Suche auch den Weg zu den Angeboten der örtlichen Bibliothek attraktiv finden.
    Keywords: ddc:000
    Language: German
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  • 52
    Publication Date: 2014-02-26
    Description: We consider a system where the arrivals form a Poisson process and the required service times of the requests are exponentially distributed. According to the generalized processor sharing discipline, each request in the system receives a fraction of the capacity of one processor which depends on the actual number of requests in the system. We derive systems of ordinary differential equations for the LST and for the moments of the conditional waiting time of a request with given required service time as well as a stable and fast recursive algorithm for the LST of the second moment of the conditional waiting time, which in particular yields the second moment of the unconditional waiting time. Moreover, asymptotically tight upper bounds for the moments of the conditional waiting time are given. The presented numerical results for the first two moments of the sojourn times in the $M/M/m-PS$ system show that the proposed algorithms work well.
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  • 53
    Publication Date: 2022-07-07
    Description: We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer method (PML). To cope with Wood anomalies appearing in periodic structures an adaptive strategy to determine optimal PML parameters is developed. We focus on the application to typical EUV lithography line masks. Light propagation within the multi-layer stack of the EUV mask is treated analytically. This results in a drastic reduction of the computational costs and allows for the simulation of next generation lithography masks on a standard personal computer.
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  • 54
    Publication Date: 2020-03-23
    Description: Die harmonische Integration der Navigation und Suche in lizenzierten Journalen und gleichzeitig in freien digitalen Dokumenten unter einer einheitlichen konsistenten Nutzeroberflache ist eines der ungelösten F&E-Probleme der Fachinformation. Hierfür sollen Elemente des Invisible Web und des Visible Web unter Berücksichtigung offener Standards nahtlos #I miteinander verbunden werden. Dem Projekt liegt ein Modell mit Internet-Index, Metasuche und Open Linking über verteilten heterogenen Speichern #I zu Grunde: Verschiedenste Server, digitale Referenzen in Artikeln und Dokumenten, Links in Datenbanken und auf Bestelldienste sollen unter Berücksichtigung von Standort-, Studien- und Lernbedingungen kooperativ miteinander vernetzt werden. Die Leistungsfähigkeit des Modells soll in Pilotimplementierungen getestet und für eine breite Anwendung vorbereitet werden. Auf dieser Basis soll das Vorhaben Verteilter Zeitschriftenserver der AG der Verbundsysteme in eigenen Teilprojekten kooperativ initiiert werden, das jetzt in das Vorhaben Verteilter Dokumentenserver von vascoda integriert ist.
    Keywords: ddc:000
    Language: German
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  • 55
    Publication Date: 2014-02-26
    Description: The mathematical modeling of a special modular catalytic reactor kit leads to a system of partial differential equation in two space dimensions. As customary, this model contains unconfident physical parameters, which may be adapted to fit experimental data. To solve this nonlinear least squares problem we apply a damped Gauss-Newton method. A method of lines approach is used to evaluate the associated model equations. By an a priori spatial discretization a large DAE system is derived and integrated with an adaptive, linearly-implicit extrapolation method. For sensitivity evaluation we apply an internal numerical differentiation technique, which reuses linear algebra information from the model integration. In order not to interfere the control of the Gauss-Newton iteration these computations are done usually very accurately and, therefore, very costly. To overcome this difficulty, we discuss several accuracy adaptation strategies, e.g., a master-slave mode. Finally, we present some numerical experiments.
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  • 56
    Publication Date: 2020-03-06
    Description: Many real world problems can be mapped onto graphs and solved with well-established efficient algorithms studied in graph theory. One such problem is to find large sets of points satisfying some mutual relationship. This problem can be transformed to the problem of finding all cliques of an undirected graph by mapping each point onto a vertex of the graph and connecting any two vertices by an edge whose corresponding points satisfy our desired relationship. Clique detection has been widely studied and there exist efficient algorithms. In this paper we study a related problem, where all points have a set of binary attributes, each of which is either 0 or 1. This is only a small limitation, since all discrete properties can be mapped onto binary attributes. In our case, we want to find large sets of points not only satisfying some mutual relationship; but, in addition, all points of a set also need to have at least one common attribute with value 1. The problem we described can be mapped onto a set of induced subgraphs, where each subgraph represents a single attribute. For attribute $i$, its associated subgraph contains those vertices corresponding to the points with attribute $i$ set to 1. We introduce the notion of a maximal clique of a family, $\mathcal{G}$, of induced subgraphs of an undirected graph, and show that determining all maximal cliques of $\mathcal{G}$ solves our problem. Furthermore, we present an efficient algorithm to compute all maximal cliques of $\mathcal{G}$. The algorithm we propose is an extension of the widely used Bron-Kerbosch algorithm.
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  • 57
    Publication Date: 2014-02-26
    Description: We present an integer linear programming model for the design of multi-layer telecommunication networks. The formulation integrates hardware, capacity, routing, and grooming decisions in \emph{any} n umber of network layers. Practical hardware restrictions and cost can accurately be taken into account for technologies based on connection-oriented routing protocols.
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  • 58
    Publication Date: 2014-02-26
    Description: We introduce FreeLence, a lossless single-rate connectivity compression algorithm for triangle surface meshes. Based upon a geometry-driven traversal scheme we present two novel and simple concepts: free-valence connectivity encoding and entropy coding based on geometric context. Together these techniques yield significantly smaller rates for connectivity compression than current state of the art approaches - valence-based algorithms and Angle- Analyzer, with an average of $36\%$ improvement over the former and an average of $18\%$ over the latter on benchmark 3D models, combined with the ability to well adapt to the regularity of meshes. We also prove that our algorithm exhibits a smaller worst case entropy for a class of "'well-behaved"' triangle meshes than valence-driven connectivity encoding approaches.
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  • 59
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    Publication Date: 2019-10-24
    Keywords: ddc:000
    Language: German
    Type: annualzib , doc-type:report
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  • 60
    Publication Date: 2020-02-11
    Description: In this article, we present a mathematical model and an algorithm to support one of the central strategic planning decisions of network operators: How to organize a large number of locations into a hierarchical network? We propose a solution approach that is based on mixed-integer programming and Lagrangian relaxation techniques. As major advantage, our approach provides not only solutions but also worst-case quality guarantees. Real-world scenarios with more than 750 locations have been solved within 30 minutes to less than 1\% off optimality.
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  • 61
    Publication Date: 2020-02-11
    Description: This paper is concerned with UMTS radio network design. Our task is to reconfigure antennas and the related cells as to improve network quality. In contrast to second generation GSM networks, \emph{interference} plays a paramount role when designing third generation radio networks. A known compact formulation for assessing the interference characteristics of a radio network as coupling relations between cells based on user snapshots is generalized to statistical average load. This enables us to overcome the notorious difficulties of snapshot-based network optimization approaches. We recall a mixed-integer programming model for the network design problem that is based on user snapshots and contrast it with a new network design model based on the average coupling formulation. Exemplarily focusing on the important problem of optimizing antenna tilts, we give computational results for a fast local search algorithm and the application of a MIP solver to both models. These results demonstrate that our new average-based approaches outperform state-of-the-art snapshot models for UMTS radio network optimization.
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  • 62
    Publication Date: 2021-08-05
    Description: Constraint Programs and Mixed Integer Programs are closely related optimization problems originating from different scientific areas. Today's state-of-the-art algorithms of both fields have several strategies in common, in particular the branch-and-bound process to recursively divide the problem into smaller sub problems. On the other hand, the main techniques to process each sub problem are different, and it was observed that they have complementary strenghts. We propose a programming framework {\sffamily SCIP} that integrates techniques from both fields in order to exploit the strenghts of both, Constraint Programming and Mixed Integer Programming. In contrast to other proposals of recent years to combine both fields, {\sffamily SCIP} does not focus on easy implementation and rapid prototyping, but is tailored towards expert users in need of full, in-depth control and high performance.
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  • 63
    Publication Date: 2018-12-06
    Description: In this paper we describe the semantic analysis of differential equations given in the ubiquitous semi-structured formats MathML and OpenMath. The analysis is integrated in a deployed Web indexing framework. Starting from basic classifications for differential equations the proposed system architecture is amenable to extensions for further reconstruction of mathematical content on the Web. The syntactic analysis of mathematical formulae given in the considered formats must overcome ambiguities that stem from the fact that formula particles may have different encodings, which are in principle completely arbitrary. However, it turns out that the syntactic analysis can be done straightforward given some natural heuristic assumptions.
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  • 64
    Publication Date: 2014-02-26
    Description: A new method for noise removal of arbitrary surfaces meshes is presented which focuses on the preservation and sharpening of non-linear geometric features such as curved surface regions and feature lines. Our method uses a prescribed mean curvature flow (PMC) for simplicial surfaces which is based on three new contributions: 1. the definition and efficient calculation of a discrete shape operator and principal curvature properties on simplicial surfaces that is fully consistent with the well-known discrete mean curvature formula, 2. an anisotropic discrete mean curvature vector that combines the advantages of the mean curvature normal with the special anisotropic behaviour along feature lines of a surface, and 3. an anisotropic prescribed mean curvature flow which converges to surfaces with an estimated mean curvature distribution and with preserved non-linear features. Additionally, the PMC flow prevents boundary shrinkage at constrained and free boundary segments.
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  • 65
    Publication Date: 2019-01-29
    Description: A primal-dual interior point method for optimal control problems with PDE constraints is considered. The algorithm is directly applied to the infinite dimensional problem. Existence and convergence of the central path are analyzed. Numerical results from an inexact continuation method applied to a model problem are shown.
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  • 66
    Publication Date: 2014-02-26
    Description: Die in der Arbeitsgemeinschaft der Verbundsysteme zusammengeschlossenen deutschen Verbundsysteme kooperieren zur Realisierung eines die Länder und Verbundregionen übergreifenden offenen Netzwerkes einer offenen digitalen Bibliothek, dem Verteilten Dokumentenserver (VDS). Wesentliche Bestandteile des VDS sind die in den lokalen Bibliotheken und Verbundsystemen verteilten Dokumentenspeicher. Beim Aufbau des VDS verfolgen die deutschen Verbundsysteme für ihre digitalen Ressourcen, Zeitschriften und Dokumente, folgende Ziele [AGV03]: \begin{itemize} \item{Erhalt und dauerhafte Sicherung einmal erworbener Rechte} \item{Bessere Erschließung und Integration in das eigene Angebot} \item{Nahtlose Navigation in lokalen Zeitschriften- und Dokumentenservern und zwischen digitalen Artikeln und Zeitschriften, Dokumenten und Servern} \item{Dauerhafte Sicherung des Zugriffs und perspektivisch Langzeitverfügbarkeit} \end{itemize} Die Verbundsysteme streben an, die Speicherung, Erschließung und das Angebot ihrer digitalen Materialien in einer nationalen Kooperation durchzuführen. Sie entwickeln und betreiben zu diesem Zweck Portal- und Querschnittstechnologien zur Integration ihrer dezentral gespeicherten digitalen Ressourcen mittels Internet-Technologien.
    Keywords: ddc:000
    Language: German
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  • 67
    Publication Date: 2014-02-26
    Description: In this paper, we present a novel approach to the congestion control and resource allocation problem of elastic and real-time traffic in telecommunication networks. With the concept of utility functions, where each source uses a utility function to evaluate the benefit from achieving a transmission rate, we interpret the resource allocation problem as a global optimization problem. The solution to this problem is characterized by a new fairness criterion, \e{utility proportional fairness}. We argue that it is an application level performance measure, i.e. the utility that should be shared fairly among users. As a result of our analysis, we obtain congestion control laws at links and sources that are globally stable and provide a utility proportional fair resource allocation in equilibrium. We show that a utility proportional fair resource allocation also ensures utility max-min fairness for all users sharing a single path in the network. As a special case of our framework, we incorporate utility max-min fairness for the entire network. To implement our approach, neither per-flow state at the routers nor explicit feedback beside ECN (Explicit Congestion Notification) from the routers to the end-systems is required.
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  • 68
    Publication Date: 2014-02-26
    Description: Wie findet man den optimalen Weg im U-Bahnnetz? Das Problem wird als Graph modelliert und dann eine Breitensuche durchgeführt. Will man Weglängen oder Fahrzeiten mitberücksichtigen, so braucht man den Algorithmus von Dijkstra für gewichtige Graphen. Beim Nachdenken über diese Algorithmen werden auch Fragestellungen der Graphentheorie berührt. In einem zweiten Abschnitt werden methodische Hinweise für den Unterricht in der Sekundarstufe I und II gegeben, insbesondere, wie man Lernende dazu bringen kann, ihre Ideen für Algorithmen präzise zu analysieren und zu Papier zu bringen.
    Keywords: ddc:000
    Language: German
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  • 69
    Publication Date: 2014-02-26
    Description: The problem of clustering data can be formulated as a graph partitioning problem. Spectral methods for obtaining optimal solutions have reveceived a lot of attention recently. We describe Perron Cluster Cluster Analysis (PCCA) and, for the first time, establish a connection to spectral graph partitioning. We show that in our approach a clustering can be efficiently computed using a simple linear map of the eigenvector data. To deal with the prevalent problem of noisy and possibly overlapping data we introduce the min Chi indicator which helps in selecting the number of clusters and confirming the existence of a partition of the data. This gives a non-probabilistic alternative to statistical mixture-models. We close with showing favorable results on the analysis of gene expressi on data for two different cancer types.
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  • 70
    Publication Date: 2014-02-26
    Description: In this paper, we study the conflict-free assignment of wavelengths to lightpaths in an optical network with the opportunity to place wavelength converters. To benchmark heuristics for the problem, we develop integer programming formulations and study their properties. Moreover, we study the computational performance of the column generation algorithm for solving the linear relaxation of the most promising formulation. In many cases, a non-zero lower bound on the number of required converters is generated this way. For several instances, we in fact prove optimality since the lower bound equals the best known solution value.
    Keywords: ddc:000
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  • 71
    Publication Date: 2021-02-01
    Description: Operative planning in gas distribution networks leads to large-scale mixed-integer optimization problems involving a hyperbolic PDE defined on a graph. We consider the NLP obtained under prescribed combinatorial decisions---or as relaxation in a branch and bound framework, addressing in particular the KKT systems arising in primal-dual interior methods. We propose a custom solution algorithm using sparse local projections, based on the KKT systems' structual properties induced by the discretized gas flow equations in combination with the underlying network topology. The numerical efficiency and accuracy of the algorithm are investigated, and detailed computational comparisons with a control space method and with the multifrontal solver MA27 are provided.
    Keywords: ddc:000
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  • 72
    Publication Date: 2021-02-01
    Description: The topic of this paper is minimum cost operative planning of pressurized water supply networks over a finite horizon and under reliable demand forecast. Since this is a very hard problem, it is desirable to employ sophisticated mathematical algorithms, which in turn calls for carefully designed models with suitable properties. The paper develops a nonlinear mixed integer model and a nonlinear programming model with favorable properties for gradient-based optimization methods, based on smooth component models for the network elements. In combination with further nonlinear programming techniques (to be reported elsewhere), practically satisfactory near-optimum solutions even for large networks can be generated in acceptable time using standard optimization software on a PC workstation. Such an optimization system is in operation at Berliner Wasserbetriebe.
    Keywords: ddc:000
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  • 73
    Publication Date: 2014-02-26
    Description: Im Rahmen von Problemstellungen der kombinatorischen Optimierung können Schülerinnen und Schüler lernen, Algorithmen selber zu entwickeln. Gleichzeitig lernen sie dabei moderne Mathematik in ihren Anwendungen kennen und erleben die Mathematik als lebendige Wissenschaft.
    Keywords: ddc:000
    Language: German
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  • 74
    Publication Date: 2020-12-15
    Description: Morse matchings capture the essential structural information of discrete Morse functions. We show that computing optimal Morse matchings is NP-hard and give an integer programming formulation for the problem. Then we present polyhedral results for the corresponding polytope and report on computational results.
    Keywords: ddc:000
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  • 75
    Publication Date: 2014-02-26
    Description: In this paper, we study the minimum converter wavelength assignment problem in optical networks. To benchmark the quality of solutions obtained by heuristics, we derive an integer programming formula tion by generalizing the formulation of Mehrotra and Trick (1996) for the vertex coloring problem. To handle the exponential number of variables, we propose a column generation approach. Computational experiments show that the value of the linear relaxation states a good lower bound and can often prove optimality of the best solution generated heuristically.
    Keywords: ddc:000
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  • 76
    Publication Date: 2014-11-10
    Description: The parameter contraction degeneracy -- the maximum minimum degree over all minors of a graph -- is a treewidth lower bound and was first defined in (Bodlaender, Koster, Wolle, 2004). In experiments it was shown that this lower bound improves upon other treewidth lower bounds. In this note, we examine some relationships between the contraction degeneracy and connected components of a graph, block s of a graph and the genus of a graph. We also look at chordal graphs, and we study an upper bound on the contraction degeneracy and another lower bound for treewidth. A data structure that can be used for algorithms computing the degeneracy and similar parameters, is also described.
    Keywords: ddc:000
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  • 77
    Publication Date: 2014-11-10
    Description: The Maximum Cardinality Search algorithm visits the vertices of a graph in some order, such that at each step, an unvisited vertex that has the largest number of visited neighbors becomes visited. An MCS-ordering of a graph is an ordering of the vertices that can be generated by the Maximum Cardinality Search algorithm. The visited degree of a vertex $v$ in an MCS-ordering is the number of neighbors of $v$ that are before $v$ in the ordering. The visited degree of an MCS-ordering $\psi$ of $G$ is the maximum visited degree over all vertices $v$ in $\psi$. The maximum visited degree over all MCS-orderings of graph $G$ is called its {\em maximum visited degree}. Lucena (2003) showed that the treewidth of a graph $G$ is at least its maximum visited degree. We show that the maximum visited degree is of size $O(\log n)$ for planar graphs, and give examples of planar graphs $G$ with maximum visited degree $k$ with $O(k!)$ vertices, for all $k\in \Bbb{N}$. Given a graph $G$, it is NP-complete to determine if its maximum visited degree is at least $k$, for any fixed $k\geq 7$. Also, this problem does not have a polynomial time approximation algorithm with constant ratio, unless P=NP. Variants of the problem are also shown to be NP-complete. We also propose and experimentally analyses some heuristics for the problem. Several tiebreakers for the MCS algorithm are proposed and evaluated. We also give heuristics that give upper bounds on the value of the maximum visited degree of a graph, which appear to give results close to optimal on many graphs from real life applications.
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  • 78
    Publication Date: 2014-02-26
    Description: A new and time efficient model to evaluate the free energy of solvation has been developed. The solvation free energy is separated into an electrostatic term, a hydrogen bond term, and a rest-term, combining both entropic and van der Waals effects. The electrostatic contribution is evaluated with a simplified boundary element method using the partial charges of the MMFF94 force field. The number of hydrogen bonds and the solvent excluded surface area over the surface atoms are used in a linear model to estimate the non-electrostatic contribution. This model is applied to a set of 213 small and mostly organic molecules, yielding an rmsd of 0.87kcal/mol and a correlation with experimental data of r=0.951. The model is applied as a supplementary component of the free energy of binding to estimate binding constants of protein ligand complexes. The intermolecular interaction energy is evaluated by using the MMFF94 force field.
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  • 79
    Publication Date: 2020-03-06
    Description: In this paper we describe a new algorithm for multiple semi-flexible superpositioning of drug-sized molecules. The algorithm identifies structural similarities of two or more molecules. When comparing a set of molecules on the basis of their three-dimensional structures, one is faced with two main problems. (1) Molecular structures are not fixed but flexible, i.e., a molecule adopts different forms. To address this problem, we consider a set of conformers per molecule. As conformers we use representatives of conformational ensembles, generated by the program ZIBMol. (2) The degree of similarity may vary considerably among the molecules. This problem is addressed by searching for similar substructures present in arbitrary subsets of the given set of molecules. The algorithm requires to preselect a reference molecule. All molecules are compared to this reference molecule. For this pairwise comparison we use a two-step approach. Clique detection on the correspondence graph of the molecular structures is used to generate start transformations, which are then iteratively improved to compute large common substructures. The results of the pairwise comparisons are efficiently merged using binary matching trees. All common substructures that were found, whether they are common to all or only a few molecules, are ranked according to different criteria, such as number of molecules containing the substructure, size of substructure, and geometric fit. For evaluating the geometric fit, we extend a known scoring function by introducing weights which allow to favor potential pharmacophore points. Despite considering the full atomic information for identifying multiple structural similarities, our algorithm is quite fast. Thus it is well suited as an interactive tool for the exploration of structural similarities of drug-sized molecules.
    Keywords: ddc:000
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  • 80
    Publication Date: 2014-02-26
    Description: Molecular dynamics simulations of possible ligands for proteins yield large amounts of data in the form of trajectories which are further processed in order to find metastable conformations. These conformations can then be used for docking between ligand and protein. Around this core computation procedure lots of other data have to be managed. It should also be possible for external users not involved in program development to perform computations. As a paradigm for other fields where a similar constitution of program usage and data processing is found we present a software architecture for data generation, access and management. Requirements for this system include: Ease of use, graphical user interface, persistent storage of data concerning molecules, users, programs, program parameters, metadata, and results. A mere storage in the file system would render a quick overview of data more or less impossible. On the other hand, storing large amounts of binary data in a database doesn't yield any advantage concerning speed of access. Therefore, a hybrid approach combining file system and database is appropriate. The system should be easily extensible by inserting new applications which can be controlled and whose results can be collected and stored. The software system described here consists of different components, the presentation layer (graphical user interface), the business logic, the persistence layer (relational database plus file system), and an interface to the compute cluster (batch system for parallel processing). We will discuss the alternatives and take a closer look at the components.
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  • 81
    Publication Date: 2020-03-09
    Description: We propose an approach for transforming the sampling of a molecular conformation distribution into an analytical model based on Hidden Markov Models. The model describes the sampled shape density as a mixture of multivariate unimodal densities. Thus, it delivers an interpretation of the sampled density as a set of typical shapes that appear with different probabilities and are characterized by their geometry, their variability and transition probabilities between the shapes. The gained model is used to identify atom groups of constant shape that are connected by metastable torsion angles. Based on this description an alignment for the original sampling is computed. As it takes into account the different shapes contained in the sampled set, this alignment allows to compute reasonable average shapes and meaningful shape density plots. Furthermore, it enables us to visualize typical conformations.
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  • 82
    Publication Date: 2020-02-11
    Description: We present publicly available data sets related to research on wireless networks. The scenarios contain a wide range of data and are detailed in all aspects. To our knowledge, this is the most realistic, comprehensive, and detailed \emph{public} data collection on mobile networking. We indicate example uses of this data collection in applications related tu UMTS.
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  • 83
    Publication Date: 2020-12-15
    Description: The \emph{line planning problem} is one of the fundamental problems in strategic planning of public and rail transport. It consists of finding lines and corresponding frequencies in a public transport network such that a given travel demand can be satisfied. There are (at least) two objectives. The transport company wishes to minimize its operating cost; the passengers request short travel times. We propose two new multi-commodity flow models for line planning. Their main features, in comparison to existing models, are that the passenger paths can be freely routed and that the lines are generated dynamically.
    Keywords: ddc:000
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  • 84
    Publication Date: 2014-02-26
    Description: The aim of this paper is to give a survey of the known results concerning centrally symmetric polytopes, spheres, and manifolds. We further enumerate nearly neighborly centrally symmetric spheres and centrally symmetric products of spheres with dihedral or cyclic symmetry on few vertices, and we present an infinite series of vertex-transitive nearly neighborly centrally symmetric 3-spheres.
    Keywords: ddc:000
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  • 85
    Publication Date: 2019-05-10
    Description: We focus on the role of anisotropic elasticity in the simulation of the load distribution in a human mandible due to a lateral bite on the leftmost premolar. Based on experimental evidence, we adopt ``local''" orthotropy of the elastic properties of the bone tissue. Since the trajectories of anisotropic elasticity are not accessible from Computer Tomographic (CT) data, they will be reconstructed from (i) the organ's geometry and (ii) from coherent structures which can be recognized from the spatial distribution of the CT values. A sensitivity analysis comprising various 3D FE simulations reveals the relevance of elastic anisotropy for the load carrying behavior of a human mandible: Comparison of the load distributions in isotropic and anisotropic simulations indicates that anisotropy seems to ``spare''" the mandible from loading. Moreover, a maximum degree of anisotropy leads to kind of an load minimization of the mandible, expressed by a minimum of different norms of local strain, evaluated throughout the organ. Thus, we may suggest that anisotropy is not only relevant, but also in some sense ``optimal''.
    Keywords: ddc:000
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  • 86
    Publication Date: 2019-05-10
    Description: The paper extends affine conjugate Newton methods from convex to nonconvex minimization, with particular emphasis on PDE problems originating from compressible hyperelasticity. Based on well-known schemes from finite dimensional nonlinear optimization, three different algorithmic variants are worked out in a function space setting, which permits an adaptive multilevel finite element implementation. These algorithms are tested on two well-known 3D test problems and a real-life example from surgical operation planning.
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  • 87
    Publication Date: 2014-02-26
    Description: We present formulae for the corner points of the multidimensional Hausdorff and Dale Polytopes and show how these results can be used to improve linear programming models for computing e.\,g.\ moments of exit distribution of diffusion processes. Specifically, we compute the mean exit time of twodimensional Brownian motion from the unit square and the unit triangle, as well as higher moments of the exit time of time space Brownian motion from a triangle.
    Keywords: ddc:000
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  • 88
    Publication Date: 2014-11-10
    Description: Normal graphs are defined in terms of cross-intersecting set families: a graph is normal if it admits a clique cover $\cal Q$ and a stable set cover $\cal S$ s.t.~every clique in $\cal Q$ intersects every stable set in $\cal S$. Normal graphs can be considered as closure of perfect graphs by means of co-normal products (Körner 1973) and graph entropy (Czisz\'ar et al. 1990). Perfect graphs have been recently characterized as those graphs without odd holes and odd antiholes as induced subgraphs (Strong Perfect Graph Theorem, Chudnovsky et al. 2002). Körner and de Simone observed that $C_5$, $C_7$, and $\overline C_7$ are minimal not normal and conjectured, as generalization of the Strong Perfect Graph Theorem, that every $C_5$, $C_7$, $\overline C_7$- free graph is normal (Normal Graph Conjecture, Körner and de Simone 1999). We prove this conjecture for a first class of graphs that generalize both odd holes and odd antiholes, the circulants, by characterizing all the normal circulants.
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  • 89
    Publication Date: 2014-02-26
    Description: It is known that the suspension of a simplicial complex can be realized with only one additional point. Suitable iterations of this construction generate highly symmetric simplicial complexes with a various interesting combinatorial and topological properties. In particular, infinitely many non-PL spheres as well as contactible simplicial complexes with a vertex-transitive group of automorphisms cab be contained in this way.
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  • 90
    Publication Date: 2020-03-10
    Description: This paper presents an automatic approach for segmentation of the liver from computer tomography (CT) images based on a 3D statistical shape model. Segmentation of the liver is an important prerequisite in liver surgery planning. One of the major challenges in building a 3D shape model from a training set of segmented instances of an object is the determination of the correspondence between different surfaces. We propose to use a geometric approach that is based on minimizing the distortion of the correspondence mapping between two different surfaces. For the adaption of the shape model to the image data a profile model based on the grey value appearance of the liver and its surrounding tissues in contrast enhanced CT data was developed. The robustness of this method results from a previous nonlinear diffusion filtering of the image data. Special focus is turned to the quantitative evaluation of the segmentation process. Several different error measures are discussed and implemented in a study involving more than 30 livers.
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  • 91
    Publication Date: 2021-08-05
    Description: Mixed integer programs are commonly solved with linear programming based branch-and-bound algorithms. The success of the algorithm strongly depends on the strategy used to select the variable to branch on. We present a new generalization called {\sl reliability branching} of today's state-of-the-art {\sl strong branching} and {\sl pseudocost branching} strategies for linear programming based branch-and-bound algorithms. After reviewing commonly used branching strategies and performing extensive computational studies we compare different parameter settings and show the superiority of our proposed newstrategy.
    Keywords: ddc:000
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  • 92
    Publication Date: 2020-03-09
    Description: This article proposes a Lagrangean relaxation approach to solve integrated duty and vehicle scheduling problems arising in public transport. The approach is based on the proximal bundle method for the solution of concave decomposable functions, which is adapted for the approximate evaluation of the vehicle and duty scheduling components. The primal and dual information generated by the bundle method is used to guide a branch-and-bound type algorithm. Computational results for large-scale real-world integrated vehicle and duty scheduling problems with up to 1,500 timetabled trips are reported. Compared with the results of a classical sequential approach and with reference solutions, integrated scheduling offers remarkable potentials in savings and drivers' satisfaction.
    Keywords: ddc:000
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  • 93
    Publication Date: 2019-05-10
    Description: Structural mechanics simulation of bony organs is of general medical and biomechanical interest, because of the interdependence of the inner architecture of bone and its functional loading already stated by Wolff in 1892. This work is part of a detailed research project concerning the human mandible. By adaptive finite element techniques, stress/strain profiles occurring in the bony structure under biting were simulated. Estimates of the discretization errors, local grid refinement, and multilevel techniques guarantee the reliability and efficiency of the method. In general, our simulation requires a representation of the organ's geometry, an appropriate material description, and the load case due to teeth, muscle, or joint forces. In this paper, we want to focus on the influence of the masticatory system. Our goal is to capture the physiological situation as far as possible. By means of visualization techniques developed by the group, we are able to extract individual muscle fibres from computed tomography data. By a special algorithm, the fibres are expanded to fanlike (esp. for the musc. temporalis) coherent vector fields similar to the anatomical reality. The activity of the fibres can be adapted according to compartmentalisation of the muscles as measured by electromyological experiments. A refined sensitivity analysis proved remarkable impact of the presented approach on the simulation results.
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  • 94
    Publication Date: 2021-02-01
    Description: Operative planning in gas networks with prescribed binary decisions yields large scale nonlinear programs defined on graphs. We study the structure of the KKT systems arising in interior methods and present a customized direct solution algorithm. Computational results indicate that the algorithm is suitable for optimization in small and medium-sized gas networks.
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  • 95
    Publication Date: 2021-02-05
    Description: Der Kooperative Bibliotheksverbund Berlin-Brandenburg (KOBV) verzichtet auf eine einheitliche zentrale Verbunddatenbank zugunsten einer dezentralen, verteilten Struktur. In dieser Architektur erhält die Art der Indexierung der angesprochenen Online-Kataloge eine besondere Bedeutung. So werden sowohl Bibliotheksmitarbeiter als auch Bibliotheksbenutzer immer wieder mit der Recherche in fremden Katalogen konfrontiert, in denen unterschiedliche Indexierungsverfahren realisiert sein können. Ein abgestimmtes Indexierungskonzept verfolgt zwei grundsätzliche Ziele. Einerseits soll durch eine vereinheitlichte Indexierung die Qualität und Zuverlässigkeit der Rechercheergebnisse in der parallelen Suche in mehreren Katalogen über die KOBV-Suchmaschine erhöht werden. Gleichzeitig soll durch eine vereinheitlichte Indexierung die Akzeptanz von Suchen in entfernten Katalogen prinzipiell gesteigert und damit die Bedingungen für die gegenseitige Übernahme von Titeldaten erleichtert werden. Für die Indexierung muss zunächst die Art und der Umfang der im OPAC aufzubauenden Indices festgelegt werden. Aus Sicht des Nutzers entspricht diese Definition den möglichen Sucheinstiegen. Hat man dann entschieden, welche Indexterme aus welchen Feldern in die jeweiligen Indices einfließen sollen, muss bestimmt werden, nach welchen Regeln die Terme behandelt werden. Hier stellt sich insbesondere das Problem der Sonderzeichen wie Bindestriche, Apostrophe und Punkte oder Ziffern in Zeichenketten. Das vorliegende Konzept entstand in Zusammenarbeit der großen Universitätsbibliotheken in Berlin (der Freien Universität, der Humboldt-Universität, der Technischen Universität, der Universität der Künste) mit der KOBV-Verbundzentrale am ZIB.
    Keywords: ddc:000
    Language: German
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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  • 96
    Publication Date: 2014-02-26
    Description: We investigate a special class of quadratic Hamiltonians on $so(4)$ and $so(3,1)$ and describe Hamiltonians that have additional polynomial integrals. One of the main results is a new integrable case with an integral of sixth degree.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
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  • 97
    Publication Date: 2020-11-16
    Description: We present a graph theoretical model for scheduling trains on a single unidirectional track between two stations. The set of departures of all possible train types at all possible (discrete) points of time is turned into an undirected graph $\Gneu$ by joining two nodes if the corresponding departures are in conflict. This graph $\Gneu$ has no odd antiholes and no $k$-holes for any integer $k\geq 5$. In particular, any finite, node induced subgraph of $\Gneu$ is perfect. For any integer $r\geq 2$ we construct minimal headways for $r$ train types so that the resulting graph $\Gneu$ has $2r$-antiholes and $4$-holes at the same time. Hence, $\Gneu$ is neither a chordal graph nor the complement of a chordal graph, in general. At the end we analyse the maximal cliques in $G$.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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  • 98
    Publication Date: 2021-02-01
    Description: Unnecessarily conservative behavior of standard process control techniques can be avoided by stochastic programming models when the distribution of random disturbances is known. In an earlier study we have investigated such an approach for tank level constraints of a distillation process. Here we address techniques that have accelerated the numerical solution of the large and expensive stochastic programs by a factor of six, and then present a refined optimization model for the same application.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
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  • 99
    Publication Date: 2014-02-26
    Description: We investigate the impact of hop-limited routing paths on the total cost of a telecommunication network. For different survivability settings (dedicated protection, link and path restoration), the optimal network cost without restrictions on the admissible path set is compared to the results obtained with two strategies to impose hop limits on routing paths. In a thorough computational study on optimal solutions for nine real-world based problem instances, we show that hop limits should be avoided if the technology allows it and network cost is a major planning issue. In this case, column generation should be employed to deal with all routing paths. If hop-limits are required, these should be defined for each demand individually and as large as possible.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
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  • 100
    Publication Date: 2020-11-13
    Description: Under high load, the automated dispatching of service vehicles for the German Automobile Association (ADAC) must reoptimize a dispatch for 100--150 vehicles and 400 requests in about ten seconds to near optimality. In the presence of service contractors, this can be achieved by the column generation algorithm ZIBDIP. In metropolitan areas, however, service contractors cannot be dispatched automatically because they may decline. The problem: a model without contractors yields larger optimality gaps within ten seconds. One way-out are simplified reoptimization models. These compute a short-term dispatch containing only some of the requests: unknown future requests will influence future service anyway. The simpler the models the better the gaps, but also the larger the model error. What is more significant: reoptimization gap or reoptimization model error? We answer this question in simulations on real-world ADAC data: only the new model ZIBDIP{\footnotesize dummy} can keep up with ZIBDIP.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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