Bibliothek

Beschreibung: Graphs with circular symmetry, called webs, are relevant w.r.t. describing the stable set polytopes of two larger graph classes, quasi-line graphs and claw-free graphs. Providing a decent linear description of the stable set polytopes of claw-free graphs is a long-standing problem. However, even the problem of finding all facets of stable set polytopes of webs is open. So far, it is only known that stable set polytopes of webs with clique number $\leq 3$ have rank facets only while there are examples with clique number $〉4$ having non-rank facets.

Beschreibung: The bio-heat transfer equation is a macroscopic model for describing the heat transfer in microvascular tissue. In [{\sl Deuflhard, Hochmuth 2002}] the authors applied homogenization techniques to derive the bio-heat transfer equation as asymptotic result of boundary value problems which provide a microscopic description for microvascular tissue. Here those results are generalized to a geometrical setting where the regions of blood are allowed to be connected. Moreover, asymptotic corrector results are derived.

Beschreibung: Stable multi-sets are an evident generalization of the well-known stable sets. As integer programs, they constitute a general structure which allows for a wide applicability of the results. Moreover, the study of stable multi-sets provides new insights to well-known properties of stable sets. In this paper, we continue our investigations started in [{\sl Koster and Zymolka 2002}] and present results of three types: on the relation to other combinatorial problems, on the polyhedral structure of the stable multi-set polytope, and on the computational impact of the polyhedral results. First of all, we embed stable multi-sets in a framework of generalized set packing problems and point out several relations. The second part discusses properties of the stable multi-set polytope. We show that the vertices of the linear relaxation are half integer and have a special structure. Moreover, we strengthen the conditions for cycle inequalities to be facet defining, show that the separation problem for these inequalities is polynomial time solvable, and discuss the impact of chords in cycles. The last result allows to interpret cliques as cycles with many chords. The paper is completed with a computational study to the practical importance of the cycle inequalities. The computations show that the performance of state-of-the-art integer programming solvers can be improved significantly by including these inequalities.

Beschreibung: In this paper, first solutions of the dust moment equations developed in [{\sl Woitke & Helling 2002}] for the description of dust formation and precipitation in brown dwarf and giant gas planet atmospheres are presented. We consider the special case of a static brown dwarf atmosphere, where dust particles continuously nucleate from the gas phase, grow by the accretion of molecules, settle gravitationally and re-evaporate thermally. Applying a kinetic description of the relevant microphysical and chemical processes for TiO$_2$-grains, the model makes predictions about the large-scale stratification of dust in the atmosphere, the depletion of molecules from the gas phase, the supersaturation of the gas in the atmosphere as well as the mean size and the mass fraction of dust grains as function of depth. Our results suggest that the nucleation occu in the upper atmosphere where the gas is cool, strongly depleted, but nevertheless highly supersaturated ($S\!\gg\!1$). These particles settle gravitationally and populate the warmer layers below, where the in-situ formation (nucleation) is ineffective or even not possible. During their descent, the particles grow up to radii $\approx\!0.3\,\mu{\rm m}\,...\,150\,\mu{\rm m}$, depending gas around the cloud base. The particles finally sink into layers which are sufficiently hot to cause their thermal evaporation. Hence, an effective transport mechanism for condensable elements exi considered solid/liquid material. In the stationary case studied here, this downward directed element transport by precipitating dust grains is balanced by an upward directed flux of condensable elements from the deep interior of the star via convective mixing (no dust without mixing). We find a self-regulation mechanism which leads to an approximate phase equilibrium ($S\!\approx\!1$) around the cloud base. The mass fraction of dust present in the atmosphere results be to approximately given by the mass fraction of condensable elements in the gas being mixed up.

Beschreibung: Analysis of phenomena that simultaneously occur on quite different spatial and temporal scales require adaptive, hierarchical schemes to reduce computational and storage demands. For data represented as grid functions, the key are adaptive, hierarchical, time-dependent grids that resolve spatio-temporal details without too much redundancy. Here, so-called AMR grids gain increasing popularity. For visualization and feature identification/tracking, the underlying continuous function has to be faithfully reconstructed by spatial and temporal interpolation. Well designed interpolation methods yield better results and help to reduce the amount of data to be stored. We address the problem of temporal interpolation of AMR grid data, e.g.\ for creation of smooth animations or feature tracking. Intermediate grid hierarchies are generated by merging the cells on all refinement levels that are present in the key frames considered. Utilizing a clustering algorithm a structure of nested grids is induced on the resulting collection of cells. The grid functions are mapped to the intermediate hierarchy, thus allowing application of appropriate interpolation techniques.

Beschreibung: An improved general-purpose technique for the visualization of symmetric positive definite tensor fields of rank two is described. It is based on a splatting technique that is built from tiny transparent glyph primitives which are capable to incorporate the full directional information content of a tensor. The result is an information-rich image that allows to read off the preferred directions in a tensor field at each point of a three-dimensional volume or two-dimensional surface. It is useful for analyzing slices or volumes of a three-dimensional tensor field and can be overlayed with standard volume rendering or color mapping. The application of the rendering technique is demonstrated on general relativistic data and the diffusion tensor field of a human brain.

Beschreibung: Graphs with circular symmetry, called webs, are relevant for describing the stable set polytopes of two larger graph classes, quasi-line graphs [{\sl Giles and Trotter 1981, Oriolo 2001}] and claw-free graphs [{\sl Galluccio and Sassano 1997, Giles and Trotter 1981}]. Providing a decent linear description of the stable set polytopes of claw-free graphs is a long-standing problem [{\sl Grötschel, Lov\'asz, and Schrijver 1988}]. However, even the problem of finding all facets of stable set polytopes of webs is open. So far, it is only known that stable set polytopes of webs with clique number $\leq 3$ have rank facets only [{\sl Dahl 1999, Trotter 1975}] while there are examples with clique number $\geq 4$ having non-rank facets [{\sl e.g. Liebling et al. 2003, Oriolo 2001, P\^echer and Wagler 2003}]. In this paper, we provide a construction for non-rank facets of stable set polytopes of webs. We use this construction to prove, for several fixed values of $\omega$ including all odd values at least 5, that there are only finitely many webs with clique number $\omega$ whose stable set polytopes admit rank facets only.

Beschreibung: We present an algorithm that constructs parametrizations of boundary and interface surfaces automatically. Starting with high-resolution triangulated surfaces describing the computational domains, we iteratively simplify the surfaces yielding a coarse approximation of the boundaries with the same topological type. While simplifying we construct a function that is defined on the coarse surface and whose image is the original surface. This function allows access to the correct shape and surface normals of the original surface as well as to any kind of data defined on it. Such information can be used by geometric multigrid solvers doing adaptive mesh refinement. Our algorithm runs stable on all types of input surfaces, including those that describe domains consisting of several materials. We have used our method with success in different fields and we discuss examples from structural mechanics and biomechanics.

Beschreibung: This article investigates a certain class of combinatorial packing problems and some polyhedral relations between such problems and the set packing problem.

Beschreibung: We construct non-constructible simplicial $d$-spheres with $d+10$ vertices and non-constructible, non-realizable simplicial $d$-balls with $d+9$ vertices for $d\geq 3$.

Beschreibung: We consider the problem of designing a network that employs a non-bifurcated shortest path routing protocol. The network's nodes and the set of potential links are given together with a set of forecasted end-to-end traffic demands. All relevant hardware components installable at links or nodes are considered. The goal is to simultaneously choose the network's topology, to decide which hardware components to install on which links and nodes, and to find appropriate routing weights such that the overall network cost is minimized. In this paper, we present a mathematical optimization model for this problem and an algorithmic solution approach based on a Lagrangian relaxation. Computational results achieved with this approach for several real-world network planning problems are reported.

Beschreibung: We investigate the impact of link and path restoration on the cost of telecommunication networks. The surprising result is the following: the cost of an optimal network configuration is almost independent of the restoration concept if (i) the installation of network elements (ADMs, DXCs, or routers) and interface cards, (ii) link capacities, and (iii) working and restoration routings are simultaneously optimized. We present a mixed-integer programming model which integrates all these decisions. Using a branch-and-cut algorithm (with column generation to deal with all potential routing paths), we solve structurally different real-world problem instances and show that the cost of optimal solutions is almost independent of the used restoration concept. In addition, we optimize spare capacities for given shortest working paths which are predetermined with respect to different link metrics. In comparison to simultaneous optimization of working and restoration routings, it turns out that this approach does not allow to obtain predictably good results.

Beschreibung: In the dial-a-ride-problem (DARP) objects have to be moved between given sources and destinations in a transportation network by means of a server. The goal is to find a shortest transportation for the server. We study the DARP when the underlying transportation network forms a caterpillar. This special case is strongly NP-hard in the worst case. We prove that in a probabilistic setting there exists a polynomial time algorithm which almost surely finds an optimal solution. Moreover, with high probability the optimality of the solution found can be certified efficiently. We also examine the complexity of the DARP in a semi-random setting and in the unweighted case.

Beschreibung: The paper presents a new affine invariant theory on asymptotic mesh independence of Newton's method in nonlinear PDEs. Compared to earlier attempts, the new approach is both much simpler and more natural from the algorithmic point of view. The theory is exemplified at collocation methods for ODE boundary value problems and at finite element methods for elliptic PDE problems.

Beschreibung: In this paper we introduce the notion of smoothed competitive analysis of online algorithms. Smoothed analysis has been proposed by [{\sl Spielman and Teng} STOC 2001] to explain the behaviour of algorithms that work well in practice while performing very poorly from a worst case analysis point of view. We apply this notion to analyze the Multi-Level Feedback (MLF) algorithm to minimize the total flow time on a sequence of jobs released over time when the processing time of a job is only known at time of completion. The initial processing times are integers in the range $[1,2^K]$. We use a partial bit randomization model, where the initial processing times are smoothened by changing the $k$ least significant bits under a quite general class of probability distributions. We show that MLF admits a smoothed competitive ratio of $O(max((2^k/\sigma)^3, (2^k/\sigma)^2 2^K-k))$, where $\sigma$ denotes the standard deviation of the distribution. In particular, we obtain a competitive ratio of $O(2^K-k)$ if $\sigma = \Theta(2^k)$. %The analysis holds for an oblivious as well as for a stronger adaptive %adversary. We also prove an $\Omega(2^{K-k})$ lower bound for any deterministic algorithm that is run on processing times smoothened according to the partial bit randomization model. For various other smoothening models, including the additive symmetric smoothening model used by [{\sl Spielman and Teng}], we give a higher lower bound of $\Omega(2^K)$. A direct consequence of our result is also the first average case analysis of MLF. We show a constant expected ratio of the total flow time of MLF to the optimum under several distributions including the uniform distribution.

Beschreibung: For the general G/G/1 processor sharing (PS) system a sample path result for the sojourn times in a busy period is proved, which yields a relation between the sojourn times under PS and FCFS discipline. In particular, the result provides a formula for the mean sojourn time in G/D/1-PS in terms of the mean sojourn time in the corresponding G/D/1-FCFS, generalizing known results for GI/M/1 and M/GI/1. Extensions of the formula provide the basis for a two-moment approximation of the mean sojourn time in G/GI/1-PS in terms of a related G/D/1-FCFS.

Beschreibung: The paper surveys recent progress in the mathematical modelling and simulation of essential molecular dynamics. Particular emphasis is put on computational drug design wherein time scales of $msec$ up to $min$ play the dominant role. Classical long-term molecular dynamics computations, however, would run into ill-conditioned initial value problems already after time spans of only $psec=10^{-12} sec$. Therefore, in order to obtain results for times of pharmaceutical interest, a combined deterministic-stochastic model is needed. The concept advocated in this paper is the direct identification of metastable conformations together with their life times and their transition patterns. It can be interpreted as a {\em transfer operator} approach corresponding to some underlying hybrid Monte Carlo process, wherein short-term trajectories enter. Once this operator has been discretized, which is a hard problem of its own, a stochastic matrix arises. This matrix is then treated by {\em Perron cluster analysis}, a recently developed cluster analysis method involving the numerical solution of an eigenproblem for a Perron cluster of eigenvalues. In order to avoid the 'curse of dimension', the construction of appropriate boxes for the spatial discretization of the Markov operator requires careful consideration. As a biomolecular example we present a rather recent SARS protease inhibitor.

Beschreibung: The operative planning problem in natural gas distribution networks is addressed. An optimization model focusing on the governing PDE and other nonlinear aspects is presented together with a suitable discretization for transient optimization in large networks by SQP methods. Computational results for a range of related dynamic test problems demonstrate the viability of the approach.

Beschreibung: This article presents a new computational approach to the three-dimensional (3D) modeling of ribonucleic acid (RNA) sequences with unknown spatial structure. The main concept is a mapping of the query sequence onto the 3D structures of a suitable template RNA molecule. This technique called \textit{threading} has originally been developed for the modeling of protein 3D structures. The application to RNA systems bridges the information gap between the growing mass of RNA sequence data and the relatively limited number of available 3D structures. The new RNA threading method is demonstrated on a tRNA model system because sufficient representative 3D structures have experimentally been elucidated and deposited in the public databases. Nevertheless, the method is in principle transferable on all other RNA species. Algorithms are developed that decompose these template structures into their secondary structure elements and gather this information in a specific template database. The best template is chosen with public alignment and secondary structure prediction tools which are integrated in the RNA modeling module. The structural information gathered from the template and the best alignment is combined to establish a comprehensive 3D model of the query sequence. A range of complete tRNA structures has successfully been modeled with the RNA threading method. The prototype module visualizes the models and provides convenient access to the proposed 3D structures. Therefore, the method could give new insight into a variety of RNA systems which in the recent years have become increasingly important as potential new pharmaceutical agents.

Beschreibung: Collection of abstracts of the Korean-German Bilateral Symposium on Scientific Computing, Berlin January 15/16, 2004

Beschreibung: Point-to-Multipoint systems are one kind of radio systems supplying wireless access to voice/data communication networks. Such systems have to be run using a certain frequency spectrum, which typically causes capacity problems. Hence it is, on the one hand, necessary to reuse frequencies but, on the other hand, no interference must be caused thereby. This leads to the bandwidth allocation problem, a special case of so-called chromatic scheduling problems. Both problems are NP-hard, and there exist no polynomial time approximation algorithms with a guaranteed quality. One kind of algorithms which turned out to be successful for many other combinatorial optimization problems uses cutting plane methods. In order to apply such methods, knowledge on the associated polytopes is required. The present paper contributes to this issue, exploring basic properties of chromatic scheduling polytopes and several classes of facet-defining inequalities.

Beschreibung: The UMTS radio network planning problem poses the challenge of designing a cost-effective network that provides users with sufficient coverage and capacity. We describe an optimization model for this problem that is based on comprehensive planning data of the EU project MOMENTUM. We present heuristic mathematical methods for this realistic model, including computational results.

Beschreibung: Relaying -- allowing multiple wireless hops -- is a protocol extension for cellular networks conceived to improve data throughput. Its benefits have only been quantified for small example networks. For assessing its general potential, we define a complex resource allocation\slash{}scheduling problem. Several mathematical models are presented for this problem; while a time-expanded MIP approach turns out intractable, a sophisticated column generation scheme leads to good computational results. We thereby show that for selected cases relaying can increase data throughput by 30\% on the average.

Beschreibung: Finding conflict-free wavelength assignments with a minimum number of required conversions for a routing of the lightpaths is one of the important tasks within the design of all-optical networks. We consider this problem in multi-fiber networks with different types of WDM systems. We give a detailed description of the problem and derive its theoretical complexity. For practical application, we propose several sequential algorithms to compute appropriate wavelength assignments. We also perform computational experiments to evaluate their performance. For the iterative algorithms, we identify characteristic patterns of progression. Two of these algorithms qualify for application in practice.

Beschreibung: A recently developed algorithm allows Rigid Body Docking of ligands to proteins, regardless of the accessibility and location of the binding site. The Docking procedure is divided into three subsequent optimization phases, two of which utilize rigid body dynamics. The last one is applied with the ligand already positioned inside the binding pocket and accounts for full flexibility. Initially, a combination of geometrical and force-field based methods is used as a Coarse Docking strategy, considering only Lennard-Jones interactions between the target and pharmaceutically relevant atoms or functional groups. The protein is subjected to a Hot Spot Analysis, which reveals points of high affinity in the protein environment towards these groups. The hot spots are distributed into different subsets according to their group affiliation. The ligand is described as a complementary point set, consisting of the same subsets. Both sets are matched in $\mathrm{I\!R}^{3}$, by superimposing members of the same subsets. In the first instance, steric inhibition is nearly neglected, preventing the system's trajectory from trapping in local minima and thus from finding false positive solutions. Hence the exact location of the binding site can be determined fast and reliably without any additional information. Subsequently, errors resulting from approximations are minimized via finetuning, this time considering both Lennard-Jones and Coulomb forces. Finally, the potential energy of the whole complex is minimized. In a first evaluation, results are rated by a reduced scoring function considering only noncovalent interaction energies. Exemplary Screening results will be given for specific ligands.

Beschreibung: We suggest a new model for the design of telecommunication networks which integrates decisions about the topology, configuration of the switching hardware, link dimensioning, and protected routing of communication demands. Applying the branch-and-cut-algorithm implemented in our network planning and optimization tool DISCNET, we demonstrate that real-world based network planning instances of such an enhanced model can be solved.

Beschreibung: The problem of clustering data can often be transformed into the problem of finding a hidden block diagonal structure in a stochastic matrix. Deuflhard et al. have proposed an algorithm that state s the number $k$ of clusters and uses the sign structure of $k$ eigenvectors of the stochastic matrix to solve the cluster problem. Recently Weber and Galliat discovered that this system of eigenvectors can easily be transformed into a system of $k$ membership functions or soft characteristic functions describing the clusters. In this article we explain the corresponding cluster algorithm and point out the underlying theory. By means of numerical examples we explain how the grade of membership can be interpreted.

Beschreibung: The KOBV Informationsportal aims to be a universal gateway to the sources of information hosted by the partner libraries from the Berlin-Brandenburg area. Due to the large number of these sources, an intuitive navigation is an essential component of the portal. The navigation-component should preserve the partner libraries? independence and overcome their administrative and technical differences. This paper proposes a collection-level navigation with four dimensions: the sources? subject areas (e.g. the first two levels of DDC), the sources? type (e.g. e-journals, databases, OPACs, etc.), the sources? location (e.g. Berlin, Brandenburg) / the library that hosts that source and the sources? accessing state (e.g. free, restricted, etc.).

Beschreibung: Our main result is that every n-dimensional polytope can be described by at most (2n-1) polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an n-dimensional pointed polyhedral cone we prove the bound 2n-2 and for arbitrary polyhedra we get a constructible representation by 2n polynomial inequalities.

Beschreibung: The NETLIB has now served for 18 years as a repository of LP problem instances. From the beginning to the present day there was some uncertainness about the precise values of the optimal solutions. We implemented a program using exact rational arithmetic to compute proofs for the feasibility and optimality of an LP solution. This paper reports the \emph{exact} optimal objective values for all NETLIB problems.

Beschreibung: Based on the knowledge gained from direct numerical simulations which are only possible in the microscale regime, a concept of driven turbulence is presented which allows to enter the mesoscopic scale regime. Here, dust formation under stochastic hydro- and thermodynamic conditions is studied: constructively superimposed stochastic waves initiate dust formation by the creation of singular nucleation events. It, hence, results a varying mean grain size and dust density in space and time. The newly formed dust changes the thermodynamic behavior from almost isotherm to adiabatic and chemically depletes the gas phase.

Beschreibung: Dust formation {in brown dwarf atmospheres} is studied by utilizing a model for driven turbulence in the mesoscopic scale regime. We apply a pseudo-spectral method where waves are created and superimposed {within} a {limited} wavenumber interval. The turbulent kinetic energy distribution follows the Kolmogoroff spectrum which is assumed to be the most likely value. Such superimposed, stochastic waves may occur in a convectively active environment. They cause nucleation fronts and nucleation events and thereby initiate the dust formation process which { continues until} all condensible material is consumed. Small disturbances {are found to} have a large impact on the dust forming system. An initially dust-hostile region, which may originally be optically thin, becomes optically thick in a patchy way showing considerable variations in the dust properties during the formation process. The dust appears in lanes and curls as a result of the interaction with waves, i.e. turbulence, which form larger and larger structures with time. Aiming on a physical understanding of the variability of brown dwarfs, related to structure formation in substellar atmospheres, we work out first necessary criteria for small-scale closure models to be applied in macroscopic simulations of dust forming astrophysical systems.

Beschreibung: Substellar atmospheres are observed to be irregularly variable for which the formation of dust clouds is the most promising candidate explanation. The atmospheric gas is convectively unstable and, last but not least, colliding convective cells are seen as cause for a turbulent fluid field. Since dust formation depends on the local properties of the fluid, turbulence influences the dust formation process and may even allow the dust formation in an initially dust-hostile gas. A regime-wise investigation of dust forming substellar atmospheric situations reveals that the largest scales are determined by the interplay between gravitational settling and convective replenishment which results in a dust-stratified atmosphere. The regime of small scales is determined by the interaction of turbulent fluctuations. Resulting lane-like and curled dust distributions combine to larger and larger structures. We compile necessary criteria for a subgrid model in the frame of large scale simulations as result of our study on small scale turbulence in dust forming gases.

Beschreibung: The solution of scattering problems described by the Helmholtz equation on unbounded domains is of importance for a wide variety of applications, for example in electromagnetics and acoustics. An implementation of a solver for scattering problems based on the programming language Matlab is introduced. The solver relies on the finite-element-method and on the perfectly-matched-layer-method, which allows for the simulation of scattering problems on complex geometries surrounded by inhomogeneous exterior domains. This report gives a number of detailed examples and can be understood as a user manual to the freely accessible code of the solver HelmPole.

Beschreibung: \noindent The size of data sets produced on remote supercomputer facilities frequently exceeds the processing capabilities of local visualization workstations. This phenomenon increasingly limits scientists when analyzing results of large-scale scientific simulations. That problem gets even more prominent in scientific collaborations, spanning large virtual organizations, working on common shared sets of data distributed in Grid environments. In the visualization community, this problem is addressed by distributing the visualization pipeline. In particular, early stages of the pipeline are executed on resources closer to the initial (remote) locations of the data sets. \noindent This paper presents an efficient technique for placing the first two stages of the visualization pipeline (data access and data filter) onto remote resources. This is realized by exploiting the ``extended retrieve'' feature of GridFTP for flexible, high performance access to very large HDF5 files. We reduce the number of network transactions for filtering operations by utilizing a server side data processing plugin, and hence reduce latency overhead compared to GridFTP partial file access. The paper further describes the application of hierarchical rendering techniques on remote uniform data sets, which make use of the remote data filtering stage.

Beschreibung: Relaying is a protocol extension for cellular wireless computer networks; in order to utilize radio resources more efficiently, several hops are allowed within one cell. This paper investigates the principle potential of relaying by casting transmission scheduling as a mathematical optimization problem, namely, a linear program. We analyze the throughput gains showing that, irrespective of the concrete scheduling algorithm, performance gains of up to 30\% on average for concrete example networks are achievable.

Beschreibung: We call an edge $e$ of a perfect graph $G$ critical if $G-e$ is imperfect and call $e$ anticritical if $G+e$ is imperfect. The present paper surveys several questions in this context. We ask in which perfect graphs critical and anticritical edges occur and how to detect such edges. The main result by [{\sl Wagler, PhD thesis 2000}] shows that a graph does not admit any critical edge if and only if it is Meyniel. The goal is to order the edges resp.~non-edges of certain perfect graphs s.t. deleting resp.~adding all edges in this order yields a sequence of perfect graphs only. Results of [{\sl Hayward 1985}] and [{\sl Spinrad & Sritharan 1995}] show the existence of such edge orders for weakly triangulated graphs; the line-perfect graphs are precisely these graphs where all edge orders are perfect [{\sl Wagler 2001}]. Such edge orders cannot exist for every subclass of perfect graphs that contains critically resp.~anticritically perfect graphs where deleting resp.~adding an arbitrary edge yields an imperfect graph. We present several examples and properties of such graphs, discuss constructions and characterizations from [{\sl Wagler 1999, Wagler PhD thesis 2000}]. An application of the concept of critically and anticritically perfect graphs is a result due to [{\sl Hougardy & Wagler 2002}] showing that perfectness is an elusive graph property.

Beschreibung: Hasenbusch has proposed splitting the pseudo-fermionic action into two parts, in order to speed-up Hybrid Monte Carlo simulations of QCD. We have tested a different splitting, also using clover-improved Wilson fermions. An additional speed-up between 5 and 20\% over the original proposal was achieved in production runs.

Beschreibung: A set of vertices $S\subseteq V$ is called a safe separator for treewidth, if $S$ is a separator of $G$, and the treewidth of $G$ equals the maximum of the treewidth over all connected components $W$ of $G-S$ of the graph, obtained by making $S$ a clique in the subgraph of $G$, induced by $W\cup S$. We show that such safe separators are a very powerful tool for preprocessing graphs when we want to compute their treewidth. We give several sufficient conditions for separators to be safe, allowing such separators, if existing, to be found in polynomial time. In particular, every minimal separator of size one or two is safe, every minimal separator of size three that does not split off a component with only one vertex is safe, and every minimal separator that is an almost clique is safe; an almost clique is a set of vertices $W$ such that there is a $v\in W$ with $W-\{v\}$ a clique. We report on experiments that show significant reductions of instance sizes for graphs from proba! bilistic networks and frequency assignment.

Beschreibung: A primal-dual interior point method for optimal control problems is considered. The algorithm is directly applied to the infinite dimensional problem. Existence and convergence of the central path are analyzed, and linear convergence of a short step pathfollowing method is established.

Beschreibung: We explicitly construct small triangulations for a number of well-known $3$-dimensional manifolds and give a brief outline of some aspects of the underlying theory of $3$-manifolds and its historical development.

Beschreibung: The key to molecular conformation dynamics is the direct identification of metastable conformations, which are almost invariant sets of molecular dynamical systems. Once some reversible Markov operator has been discretized, a generalized symmetric stochastic matrix arises. This matrix can be treated by Perron cluster analysis, a rather recent method involving a Perron cluster eigenproblem. The paper presents an improved Perron cluster analysis algorithm, which is more robust than earlier suggestions. Numerical examples are included.

Beschreibung: In this paper, a new shared protection mechanism for meshed optical networks is presented. Significant network design cost reductions can be achieved in comparison to the well-known 1+1 protection scheme. Demand-wise Shared Protection (DSP) bases on the diversification of demand routings and exploits the network connectivity to restrict the number of backup lightpaths needed to provide the desired level of prorection. Computational experiments approve the benefits of the concept DSP for cost efficient optical network designs.

Beschreibung: The correlation of the inner architecture of bone and its functional loading was already stated by Wolff in 1892. Our objective is to demonstrate this interdependence in the case of the human mandible. For this purpose, stress/strain profiles occuring at a human lateral bite were simulated. Additionally, by a combination of computer graphics modules, a three--dimensional volumetric visualization of bone mineral density could be given. Qualitative correspondences between the density profile of the jaw and the simulated stress/strain profiles could be pointed out. In the long run, this might enable the use of the simulation for diagnosis and prognosis. The solution of the underlying partial differential equations describing linear elastic material behaviour was provided by an adaptive finite element method. Estimates of the discretization errors, local grid refinement, and multilevel techniques guaranteed the reliability and efficiency of the method.

Beschreibung: UMTS is a 3rd generation mobile telecommunication system which enables multi-service and multi-bit rate communication going beyond the possibilities of previous systems. The simulator MoDySim models UMTS in great detail. Characteristics of UMTS such as soft hand-over and the interdependency of load and capacity among neighbouring cells are challenges for the parallelisation of such a system. In this paper we explain how the software was parallelised and present performance results of a UMTS simulation for the city of Berlin.

Beschreibung: We report on a numerical reinvestigation of the Aoki phase in lattice QCD with two flavors of Wilson fermions where the parity-flavor symmetry is spontaneously broken. For this purpose the Hybrid Monte Carlo algorithm was used and an explicit symmetry-breaking source term $h\bar{\psi} i \gamma_{5} \tau^{3}\psi$ was added to the Wilson fermion action. The order parameter $\langle\bar{\psi}i\gamma_{5}\tau^{3}\psi\rangle$ was studied at several values of $(\beta,\kappa,h)$ on lattices of sizes $4^4$ to $12^4$. Our largest lattices can be considered as infintely large allowing to extrapolate to $h=0$. The existence of a parity-flavor-breaking phase can be confirmed at $\beta=4.0$ and $\beta=4.3$ while we find no sign of parity-flavor-breaking at $\beta=4.6$ and $\beta=5.0$.

Beschreibung: In this paper we interpret clustering as a mapping of data into a simplex. If the data itself has simplicial struture this mapping becomes linear. Spectral analysis is an often used tool for clustering data. We will show that corresponding singular vectors or eigenvectors comprise simplicial structure. Therefore they lead to a cluster algorithm, which consists of a simple linear mapping. An example for this kind of algorithms is the Perron cluster analysis (PCCA). We have applied it in practice to identify metastable sets of molecular dynamical systems. In contrast to other algorithms, this kind of approach provides an a priori criterion to determine the number of clusters. In this paper we extend the ideas to more general problems like clustering of bipartite graphs.

Beschreibung: The Web of the future will provide a huge amount of information. We need better ways for dealing with and managing the information. A qualified semantic annotation of the information plays a key role for the Web of the future. This article gives an overview about the efforts of the mathematical community to build up a distributed and open information and communication system for mathematics: the Math-Net. The Math-Net Initiative has developed metadata schemas for some classes of Web resources which are relevant in mathematics. Math-Net Services process this information and enable the user to efficiently search and access the information.

Beschreibung: In this paper we propose a new finite element realization of the Perfectly Matched Layer method (PML-method). Our approach allows to deal with arbitrary shaped polygonal domains and with certain types of inhomogeneous exterior domains. Among the covered inhomogeneities are open waveguide structures playing an essential role in integrated optics. We give a detailed insight to implementation aspects. Numerical examples show exponential convergence behavior to the exact solution with the thickness of the PML sponge layer.

Beschreibung: In molecular dynamics applications there is a growing interest in mixed quantum-classical models. The {\em quantum-classical Liouville equation} (QCL) describes most atoms of the molecular system under consideration by means of classical phase space density but an important, small portion of the system by means of quantum mechanics. The QCL is derived from the full quantum dynamical (QD) description by applying the Wigner transform to the classical part'' of the system only. We discuss the conditions under which the QCL model approximates the full QD evolution of the system. First, analysis of the asymptotic properties of the Wigner transform shows that solving the QCL yields a first order approximation of full quantum dynamics. Second, we discuss the adiabatic limit of the QCL. This discussion shows that the QCL solutions may be interpretated as classical phase space densities, at least near the adiabatic limit. Third, it is demonstrated that the QCL yields good approximations of {\em non-adiabatic quantum effects,} especially near so-called {\em avoided crossings} where most quantum-classical models fail.

Beschreibung: Mean-variance portfolio analysis provided the first quantitative treatment of the tradeoff between profit and risk. We investigate in detail the interplay between objective and constraints in a number of single-period variants, including semi-variance models. Particular emphasis is laid on avoiding the penalization of overperformance. The results are then used as building blocks in the development and theoretical analysis of multi-period models based on scenario trees. A key property is the possibility to remove surplus money in future decisions, yielding approximate downside risk minimization.

Beschreibung: The paper compares computational aspects of four approaches to compute conservation laws of single differential equations or systems of them, ODEs and PDEs. The only restriction, required by two of the four corresponding computer algebra programs, is that each DE has to be solvable for a leading derivative. Extra constraints may be given. Examples of new conservation laws include non-polynomial expressions, an explicit variable dependence and conservation laws involving arbitrary functions. Examples involve the following equations: Ito, Liouville, Burgers, Kadomtsev-Petviashvili, Karney-Sen-Chu-Verheest, Boussinesq, Tzetzeica, Benney.

Beschreibung: Recently, a novel concept for the computation of essential features of the dynamics of Hamiltonian systems (such as molecular dynamics) has been proposed. The realization of this concept had been based on subdivision techniques applied to the Frobenius--Perron operator for the dynamical system. The present paper suggests an alternative but related concept that merges the conceptual advantages of the dynamical systems approach with the appropriate statistical physics framework. This approach allows to define the phrase ``conformation'' in terms of the dynamical behavior of the molecular system and to characterize the dynamical stability of conformations. In a first step, the frequency of conformational changes is characterized in statistical terms leading to the definition of some Markov operator $T$ that describes the corresponding transition probabilities within the canonical ensemble. In a second step, a discretization of $T$ via specific hybrid Monte Carlo techniques is shown to lead to a stochastic matrix $P$. With these theoretical preparations, an identification algorithm for conformations is applicable. It is demonstrated that the discretization of $T$ can be restricted to few essential degrees of freedom so that the combinatorial explosion of discretization boxes is prevented and biomolecular systems can be attacked. Numerical results for the n-pentane molecule and the triribonucleotide adenylyl\emph{(3'-5')}cytidylyl\emph{(3'-5')}cytidin are given and interpreted.

Beschreibung: In KOBV we offer the user an efficient tool for searching regional and worldwide accessible library catalogues (KOBV search engine). Search is performed by a distributed Z39.50 retrieval and an index based quicksearch. Due to the number of catalogues, result sets may contain a significant amount of duplicate records. Therefore we integrate a de-duplication procedure into KOBV search engine. It is part of the distributed search and the KOBV quicksearch as well. Main goals are the presentation of uniform retrieval results, the preservation of retrieval quality and cutting off redundant information. At least we keep an eye on efficiency. De-duplication is fully parametrizable, so that settings can be changed easily on line.

Beschreibung: A cascadic multigrid (CMG) method for elliptic problems with strong material jumps is proposed and analyzed. Non--matching grids at interfaces between subdomains are allowed and treated by mortar elements. The arising saddle point problems are solved by a subspace confined conjugate gradient method as smoother for the CMG. Details of algorithmic realization including adaptivity are elaborated. Numerical results illustrate the efficiency of this CMG algorithm.

Beschreibung: In a large distribution center of Herlitz AG, Berlin, we invesigated the elevator subsystem of the fully automated pallet transportation system. Each elevator may carry one pallet and has to serve eight levels. The goal is to minimize the average resp.\ the maximum flow time. The variants of this elevator control problem have been subject of recent theoretical research and are known as online-dial-a-ride problems. In this paper we investigate several online algorithms for several versions of online-dial-a-ride problems by means of a simulation program, developed on the basis of the simulation library AMSEL. We draw statistics from samples of randomly generated data providing for different load situations. Moreover, we provide preliminary studies with real production data for a system of five elevators connected by a conveyor circuit, as can be found at the Herlitz plant. We show which algorithms are best under certain load situations and which lead to break downs under particular circumstances.

Beschreibung: We present an algebraic multigrid preconditioner which uses only the graphs of system matrices. Some elementary coarsening rules are stated, from which an advancing front algorithm for the selection of coarse grid nodes is derived. This technique can be applied to linear Lagrange-type finite element discretizations; for higher-order elements an extension of the multigrid algorithm is provided. Both two- and three-dimensional second order elliptic problems can be handled. Numerical experiments show that the resulting convergence acceleration is comparable to classical geometric multigrid.

Beschreibung: Flavone and the flavylium ion have been studied at Hartree-Fock, M{\o}ller-Plesset and B3LYP hybrid density functional level to determine the structures and barriers to internal rotation. Both molecules have a high perpendicular barrier about the single bond connecting the phenyl ring with the benzopyrone and benzopyrylium ring, respectively. In contrast to biphenyl both molecules have low coplanar barriers. B3LYP overestimates the perpendicular barrier heights compared to other methods. The dependence of the population and orbital energies on the torsion has been investigated and the structures of both flavonoids have been estimated by means of a reaction field model.

Beschreibung: The function of many important biomolecules is related to their dynamic properties and their ability to switch between different {\em conformations}, which are understood as {\em almost invariant} or {\em metastable} subsets of the positional state space of the system. Recently, the present authors and their coworkers presented a novel algorithmic scheme for the direct numerical determination of such metastable subsets and the transition probability between them. Although being different in most aspects, this method exploits the same basic idea as {\sc Dellnitz} and {\sc Junge} in their approach to almost invariance in discrete dynamical systems: the almost invariant sets are computed via certain eigenvectors of the Markov operators associated with the dynamical behavior. In the present article we analyze the application of this approach to (high--friction) Langevin models describing the dynamical behavior of molecular systems coupled to a heat bath. We will see that this can be related to theoretical results for (symmetric) semigroups of Markov operators going back to {\sc Davies}. We concentrate on a comparison of our approach in respect to random perturbations of dynamical systems.

Beschreibung: An introductory chapter on Groebner bases is given which also includes new results on the detection of Groebner bases for sparse polynomial systems. Algorithms for the computation of invariants and equivariants for finite groups, compact Lie groups and algebraic groups are presented and efficient implementation and time comparision are discussed. This chapter also inlcudes improvements of the computation of Noether normalisation and Stanley decomposition. These results are applied in symmetric bifurcation theory and equivariant dynamics. As preparation of the investigation of the orbit space reduction three methods are compared for solving symmetric polynomial systems exactly. The method of orbit space reduction is improved by using the Cohen-Macaulayness of the invariant ring and nested Noether normalization. Finally this is applied for a case of mode interaction in the Taylor-Couette problem.

Beschreibung: A class of sparse polynomial systems is investigated which is defined by a weighted directed graph and a weighted bipartite graph. They arise in the model of mass action kinetics for chemical reaction systems. In this application the number of real positive solutions within a certain affine subspace is of particular interest. We show that the simplest cases are equivalent to binomial systems while in general the solution structure is highly determined by the properties of the two graphs. First we recall results by Feinberg and give rigorous proofs. Secondly, we explain how the graphs determine the Newton polytopes of the system of sparse polynomials and thus determine the solution structure. The results on positive solutions from real algebraic geometry are applied to this particular situation. Examples illustrate the theoretical results.

Beschreibung: We study the improvement of simulations of QCD with dynamical Wilson fermions by combining the Hybrid Monte Carlo algorithm with parallel tempering. As an indicator for decorrelation we use the topological charge.

Beschreibung: We describe a novel method for continuously transforming two triangulated models of arbitrary topology into each other. Equal global topology for both objects is assumed, extensions for genus changes during metamorphosis are provided. The proposed method addresses the major challenge in 3D metamorphosis, namely specifying the morphing process intuitively, with minimal user interaction and sufficient detail. Corresponding regions and point features are interactively identified. These regions are parametrized automatically and consistently, providing a basis for smooth interpolation. Utilizing suitable 3D interaction techniques a simple and intuitive control over the whole morphing process is offered.

Beschreibung: Our focus is on Maxwell's equations in the low frequency range; two specific applications we aim at are time-stepping schemes for eddy current computations and the stationary double-curl equation for time-harmonic fields. We assume that the computational domain is discretized by triangles or tetrahedrons; for the finite element approximation we choose N\'{e}d\'{e}lec's $H(curl)$-conforming edge elements of the lowest order. For the solution of the arising linear equation systems we devise an algebraic multigrid preconditioner based on a spatial component splitting of the field. Mesh coarsening takes place in an auxiliary subspace, which is constructed with the aid of a nodal vector basis. Within this subspace coarse grids are created by exploiting the matrix graphs. Additionally, we have to cope with the kernel of the $curl$-operator, which comprises a considerable part of the spectral modes on the grid. Fortunately, the kernel modes are accessible via a discrete Helmholtz decomposition of the fields; they are smoothed by additional algebraic multigrid cycles. Numerical experiments are included in order to assess the efficacy of the proposed algorithms.

Beschreibung: Large scale simulations running in metacomputing environments face the problem of efficient file I/O. For efficiency it is desirable to write data locally, distributed across the computing environment, and then to minimize data transfer, i.e.\ reduce remote file access. Both aspects require I/O approaches which differ from existing paradigms. For the data output of distributed simulations, one wants to use fast local parallel I/O for all participating nodes, producing a single distributed logical file, while keeping changes to the simulation code as small as possible. For reading the data file as in postprocessing and file based visualization, one wants to have efficient partial access to remote and distributed files, using a global naming scheme and efficient data caching, and again keeping the changes to the postprocessing code small. However, all available software solutions require the entire data to be staged locally (involving possible data recombination and conversion), or suffer from the performance problems of remote or distributed file systems. In this paper we show how to interface the HDF5 I/O library via its flexible Virtual File Driver layer to the Globus Data Grid. We show, that combining these two toolkits in a suitable way provides us with a new I/O framework, which allows efficient, secure, distributed and parallel file I/O in a metacomputing environment.

Beschreibung: Although the m-ATSP (or multi traveling salesman problem) is well known for its importance in scheduling and vehicle routing, it has, to the best of our knowledge, never been studied polyhedraly, i.e., it has always been transformed to the standard ATSP. This transformation is valid only if the cost of an arc from node $i$ to node $j$ is the same for all machines. In many practical applications this is not the case, machines produce with different speeds and require different (usually sequence dependent) setup times. We present first results of a polyhedral analysis of the m-ATSP in full generality. For this we exploit the tight relation between the subproblem for one machine and the prize collecting traveling salesman problem. We show that, for $m\ge 3$ machines, all facets of the one machine subproblem also define facets of the m-ATSP polytope. In particular the inequalities corresponding to the subtour elimination constraints in the one machine subproblems are facet defining for m-ATSP for $m\ge 2$ and can be separated in polynomial time. Furthermore, they imply the subtour elimination constraints for the ATSP-problem obtained via the standard transformation for identical machines. In addition, we identify a new class of facet defining inequalities of the one machine subproblem, that are also facet defining for m-ATSP for $m\ge 2$. To illustrate the efficacy of the approach we present numerical results for a scheduling problem with non-identical machines, arising in the production of gift wrap at Herlitz PBS AG.

Beschreibung: Due to its many applications in control theory, robust optimization, combinatorial optimization and eigenvalue optimization, semidefinite programming had been in wide spread use even before the development of efficient algorithms brought it into the realm of tractability. Today it is one of the basic modeling and optimization tools along with linear and quadratic programming. Our survey is an introduction to semidefinite programming, its duality and complexity theory, its applications and algorithms.

Beschreibung: Given an affine surjection of polytopes $\pi: P \to Q$, the Generalized Baues Problem asks whether the poset of all proper polyhedral subdivisions of $Q$ which are induced by the map $\pi$ has the homotopy type of a sphere. We extend earlier work of the last two authors on subdivisions of cyclic polytopes to give an affirmative answer to the problem for the natural surjections between cyclic polytopes $\pi: C(n,d') \to C(n,d)$ for all $1 \leq d 〈 d' 〈 n$.

Beschreibung: In 1994, Sturmfels gave a polyhedral version of the Cayley Trick of elimination theory: he established an order-preserving bijection between the posets of \emph{coherent} mixed subdivisions of a Minkowski sum $\mathcal{A}_1+\cdots+\mathcal{A}_r$ of point configurations and of \emph{coherent} polyhedral subdivisions of the associated Cayley embedding $\mathcal{C}(\mathcal{A}_1,\dots,\mathcal{A}_r)$. In this paper we extend this correspondence in a natural way to cover also \emph{non-coherent} subdivisions. As an application, we show that the Cayley Trick combined with results of Santos on subdivisions of Lawrence polytopes provides a new independent proof of the Bohne-Dress Theorem on zonotopal tilings. This application uses a combinatorial characterization of lifting subdivisions, also originally proved by Santos.

Beschreibung: It is well known that the following class of systems of evolution equations \begin{eqnarray} \label{nsgen} \cases{ u_{t}=u_{xx}+F(u,v,u_x,v_x),\cr v_{t}=-v_{xx}+G(u,v,u_x,v_x),\cr} \end{eqnarray} is very rich in integrable cases. The complete classification problem is very difficult. Here we consider only the most interesting (from our opinion) subclass of systems (1). Namely, we consider equations linear in all derivatives of the form \begin{eqnarray} \label{kvazgen} \cases{ u_t = u_{xx} + A_{1}(u,v) u_x + A_{2}(u,v) v_x + A_{0}(u,v)\cr v_t = - v_{xx} + B_{1}(u,v) v_x + B_{2}(u,v) u_x + B_{0}(u,v). \cr} \end{eqnarray} without any restrictions on the functions $A_{i}(u,v), B_{i}(u,v)$.

Beschreibung: In this paper we study algorithms for ``Dial-a-Ride'' transportation problems. In the basic version of the problem we are given transportation jobs between the vertices of a graph and the goal is to find a shortest transportation that serves all the jobs. This problem is known to be NP-hard even on trees. We consider the extension when precedence relations between the jobs with the same source are given. Our results include a polynomial time algorithm on paths and an approximation algorithm on general graphs with a performance of~$9/4$. For trees we improve the performance to~$5/3$.

Beschreibung: In this thesis we study and solve integer programs with block structure, i.\,e., problems that after the removal of certain rows (or columns) of the constraint matrix decompose into independent subproblems. The matrices associated with each subproblem are called blocks and the rows (columns) to be removed linking constraints (columns). Integer programs with block structure come up in a natural way in many real-world applications. The methods that are widely used to tackle integer programs with block structure are decomposition methods. The idea is to decouple the linking constraints (variables) from the problem and treat them at a superordinate level, often called master problem. The resulting residual subordinate problem then decomposes into independent subproblems that often can be solved more efficiently. Decomposition methods now work alternately on the master and subordinate problem and iteratively exchange information to solve the original problem to optimality. In Part I we follow a different approach. We treat the integer programming problem as a whole and keep the linking constraints in the formulation. We consider the associated polyhedra and investigate the polyhedral consequences of the involved linking constraints. The variety and complexity of the new inequalities that come into play is illustrated on three different types of real-world problems. The applications arise in the design of electronic circuits, in telecommunication and production planning. We develop a branch-and-cut algorithm for each of these problems, and our computational results show the benefits and limits of the polyhedral approach to solve these real-world models with block structure. Part II of the thesis deals with general mixed integer programming problems, that is integer programs with no apparent structure in the constraint matrix. We will discuss in Chapter 5 the main ingredients of an LP based branch-and-bound algorithm for the solution of general integer programs. Chapter 6 then asks the question whether general integer programs decompose into certain block structures and investigate whether it is possible to recognize such a structure. The remaining two chapters exploit information about the block structure of an integer program. In Chapter 7 we parallelize parts of the dual simplex algorithm, the method that is commonly used for the solution of the underlying linear programs within a branch-and-cut algorithm. In Chapter 8 we try to detect small blocks in the constraint matrix and to derive new cutting planes that strengthen the integer programming formulation. These inequalities may be associated with the intersection of several knapsack problems. We will see that they significantly improve the quality of the general integer programming solver introduced in Chapter 5.

Beschreibung: A new seasonal energy storage for thermal solar systems has been developed on the basis of an adsorption-desorption process. Design and optimization of this storage will be supported by numerical simulations of heat and mass transfer with KARDOS. This paper focuses on the unsteady heat transfer during the major operating step of energetic discharge of the storage, which is characterized by conductive heat transfer in the fixed bed and a strong heat source caused by the adsorption enthalpy. Results are interpreted concerning the influence of variations in the parameter set. The method of implementation of the differential equation will be shown as well as the post-processing and gridwriting programs.

Beschreibung: In this paper, we analyze algorithms for the online dial-a-ride problem with request sets that fulfill a certain worst-case restriction: roughly speaking, a set of requests for the online dial-a-ride problem is reasonable if the requests that come up in a sufficiently large time period can be served in a time period of at most the same length. This new notion is a stability criterion implying that the system is not overloaded. The new concept is used to analyze the online dial-a-ride problem for the minimization of the maximal resp.\ average flow time. Under reasonable load it is possible to distinguish the performance of two particular algorithms for this problem, which seems to be impossible by means of classical competitive analysis.

Beschreibung: The function of many important biomolecules comes from their dynamic properties and their ability to switch between different {\em conformations}. In a conformation, the large scale geometric structure of the molecule is understood to be conserved, whereas on smaller scales the system may well rotate, oscillate or fluctuate. In a recent article [J. Comp. Phys., 151,1 (1999)], the present author and coworkers demonstrated that (a) conformations can be understood as almost invariant sets of some Markov chain being defined via the Hamiltonian system governing the molecular dynamics and that (b) these sets can efficiently be computed via eigenvectors of the corresponding Markov operator. The persent manuscript reviews the mathematical modelling steps behind the novel concept, includes a rigorous analytical justification of this approach and especially of the numerical details of the algorithm, and illustrates its performance when applied to realistic molecular systems.

Beschreibung: This paper summarizes and discusses various characterizations of perfect graphs and mentions some open problems in this area.

Beschreibung: This monograph has been written to illustrate the interlocking of theory, algorithm, and application in developing solution techniques for complex PDE systems. A deep theoretical understanding is necessary to produce a powerful idea leading to a successful algorithm. Efficient and robust implementation is the key to make the algorithm perform satisfactorily. The extra insight obtained by solving real--life problems brings out the structure of the method more clearly and suggests often ways to improve the numerical algorithm. It is my intention to impart the beauty and complexity found in both the theoretical investigation of the adaptive algorithm proposed here, i.e., the coupling of Rosenbrock methods in time and multilevel finite elements in space, and its realization. I hope that this method will find many more interesting applications.

Beschreibung: Many optimization problems have several equivalent mathematical models. It is often not apparent which of these models is most suitable for practical computation, in particular, when a certain application with a specific range of instance sizes is in focus. Our paper addresses the Asymmetric Travelling Salesman Problem with time windows (ATSP-TW) from such a point of view. The real--world application we aim at is the control of a stacker crane in a warehouse. We have implemented codes based on three alternative integer programming formulations of the ATSP-TW and more than ten heuristics. Computational results for real-world instances with up to 233 nodes are reported, showing that a new model presented in a companion paper outperforms the other two models we considered --- at least for our special application --- and that the heuristics provide acceptable solutions.

Beschreibung: The method of symmetry adapted wavepackets (SAWP) to solve the time-dependent Schrödinger equation for a highly symmetric potential energy surface is introduced. The angular dependence of a quantum-mechanical wavepackets is expanded in spherical harmonics where the number of close-coupled equations for the corresponding radial functions can be efficiently reduced by symmetry adaption of the rotational basis using the SWAP approach. Various techniques to generate symmetry adapted spherical harmonics (SASHs) for the point groups of highest symmetry (octahedral, icosahedral) are discussed. The standard projection operator technique involves the use of Wigner rotation matrices. Two methods to circumvent numerical instabilities occuring for large azimuthal quantum numbers are suggested. The first is based on a numerical scheme which employs Gaussian integrations yielding exact and stable results. The second is a recursive algorithm to generate higher order SASHs accurately and efficiently from lower order ones. The paper gives a complete set of ``seed functions'' generated by projection techniques which can be used obtain SASHs for all irreducible representations of the octahedral and icosahedral point groups recursively.

Beschreibung: The article surveys the development of novel mathematical concepts and algorithmic approaches based thereon in view of their possible applicability to biomolecular design. Both a first deterministic approach, based on the Frobenius-Perron operator corresponding to the flow of the Hamiltonian dynamics, and later stochastic approaches, based on a spatial Markov operator or on Langevin dynamics, can be subsumed under the unified mathematical roof of the transfer operator approach to effective dynamics of molecular systems. The key idea of constructing specific transfer operators especially taylored for the purpose of conformational dynamics appears as the red line throughout the paper. Different steps of the algorithm are exemplified by a trinucleotide molecular system as a small representative of possible RNA drug molecules.

Beschreibung: In this paper we discuss several ways to visualize stationary and non-stationary quantum mechanical systems. We demonstrate an approach for the quantitative interpretation of probability density isovalues which yields a reasonable correlation between isosurfaces for different timesteps. As an intuitive quantity for visualizing the momentum of a quantum system we propose the probability flow density which can be treated by vector field visualization techniques. Finally, we discuss the visualization of non-stationary systems by a sequence of single timestep images.

Beschreibung: One of the important tasks in Data Mining is automated cluster analysis. Self-Organizing Maps (SOMs) introduced by {\sc Kohonen} are, in principle, a powerful tool for this task. Up to now, however, its cluster identification part is still open to personal bias. The present paper suggests a new approach towards automated cluster identification based on a combination of SOMs with an eigenmode analysis that has recently been developed by {\sc Deuflhard et al.} in the context of molecular conformational dynamics. Details of the algorithm are worked out. Numerical examples from Data Mining and Molecular Dynamics are included.

Beschreibung: The photoassociation process shows strong dependence on the temporal duration of the electromagnetic field pulses and their frequencies. This dependence is investigated using quantum mechanical simulations that include all ranges of impact parameters and contributions from bound-to-bound transitions. The photoassociation yield of mercury atoms to produce excimer dimers is enhanced for short (ps) and for ultrashort (fs) pulse durations. Ultrashort laser pulses effectively overlap the entire range of free-to-bound transition, therefore achieving a maximum probability. Short pulses show a maximum in the photoassociation yield when their carrier frequency overlaps a particular free-to-bound spectroscopic resonance. Implications of these calculations on efforts to control bimolecular reactions are discussed.

Beschreibung: For using Data Mining, especially cluster analysis, one needs measures to determine the similarity or distance between data objects. In many application fields the data objects can have different information levels. In this case the widely used euclidean distance is an inappropriate measure. The present paper describes a concept how to use data of different information levels in cluster analysis and suggests an appropriate similarity measure. An example from practice is included, that shows the usefulness of the concept and the measure in combination with {\sc Kohonens} Self-Organizing Map algorithm, a well-known and powerful tool for cluster analysis.

Beschreibung: This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs. Valid inequalities for i) general integer programs, ii) problems with local structure such as knapsack constraints, and iii) problems with 0-1 coefficient matrices, such as set packing, are examined in turn. Finally the use of valid inequalities for classes of problems with structure, such as network design, is explored.

Beschreibung: The improvement of simulations of QCD with dynamical Wilson fermions by combining the Hybrid Monte Carlo algorithm with parallel tempering is studied. As an indicator for decorrelation the topological charge is used.

Beschreibung: This series of lectures has been given to a class of mathematics postdocs at a European summer school on Computational Mathematics Driven by Industrial Applications in Martina Franca, Italy (organized by CIME). It deals with a variety of challenging real life problems selected from clinical cancer therapy, communication technology, polymer production, and pharmaceutical drug design. All of these problems from rather diverse application areas share two common features: (a) they have been modelled by various differential equations -- elliptic, parabolic, or Schrödinger--type partial differential equations, countable ordinary diffential equations, or Hamiltonian systems, (b) their numerical solution has turned out to be real challenge to computational mathematics.

Beschreibung: Semidefinite relaxations of quadratic 0-1 programming or graph partitioning problems are well known to be of high quality. However, solving them by primal-dual interior point methods can take much time even for problems of moderate size. The recent spectral bundle method of Helmberg and Rendl can solve quite efficiently large structured equality-constrained semidefinite programs if the trace of the primal matrix variable is fixed, as happens in many applications. We extend the method so that it can handle inequality constraints without seriously increasing computation time. Encouraging preliminary computational results are reported.

Beschreibung: The C++ standard template library has many useful containers for data. The standard library includes two adpators, queue, and stack. The authors have extended this model along the lines of relational database semantics. Sometimes the analogy is striking, and we will point it out occasionally. An adaptor allows the standard algorithms to be used on a subset or modification of the data without having to copy the data elements into a new container. The authors provide many useful adaptors which can be used together to produce interesting views of data in a container.

Beschreibung: This report describes the development of an experimental service for picture-based document retrieval for the Electronic Visualization Library (EVlib). The EVlib is a digital library for scientific visualization, established at the Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB). The picture-based retrieval service allows users to look for documents by describing the pictures they contain. This query method was developed based on the assumption that (1) pictures often represent relevant parts of the contents of a document, and (2) pictures are often remembered well. A picture-based approach provides a new quality of accessing and exploring scientific literature. Motivation, concepts and realization of our service are outlined. Results of a user test are presented, too. The results indicate that this service can be used for searching and browsing the document collection in principle. On the other hand, problems were detected which can give fruitful hints for future work concerning document and image retrieval.

Beschreibung: In this paper, we generalize the nonlocal discrete transparent boundary condition introduced by Schmidt and Deuflhard {[}Comp. Math. Appl. 29 (1995) 53-76{]} and Schmidt and Yevick {[}J. Comput. Phys. 134 (1997) 96-107{]} to propagation methods based on arbitrary Pad\'e approximations to the two-dimensional one-way Helmholtz equation. Our approach leads to a recursive formula for the coefficients appearing in the nonlocal condition which then yields an unconditionally stable propagation method.

Beschreibung: We present nonlocal discrete transparent boundary conditions for a fourth-order wide-angle approximation of the two-dimensional Helmholtz equation. The boundary conditions are exact in the sense that they supply the same discrete solution on a bounded interior domain as would be obtained by considering the problem on the entire unbounded domain with zero boundary conditions at infinity. The proposed algorithm results in an unconditionally stable propagation method. Numerical examples from optics illustrate the efficiency of our approach.