Library

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

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

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

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

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

Description: Beim Entwurf und Ausbau von Informations- und Kommunikationsnetzwerken m{ü}ssen zahlreiche interdependente Entscheidungen getroffen und gleichzeitig mannigfaltige Bedingungen ber{ü}cksichtigt werden. Die verf{ü}gbaren technischen und organisatorischen Alternativm{ö}glichkeiten sind normalerweise so vielf{ä}ltig und komplex, dass eine manuelle Planung praktisch nicht m{ö}glich ist. In diesem Artikel wird das Potential und die Methodik der mathematischen Optimierung bei der kostenoptimalen Planung von Kommunikationsnetzen vorgestellt. Als Ausgangspunkt wird exemplarisch eine typische praktische Aufgabe, die Struktur- und Konfigurationsplanung mehrstufiger Telekommunikationsnetzwerke, dargestellt. Anschließend werden kurz die wesentlichen Modellierungstechniken und Verfahrensans{ä}tze der mathematischen Optimierung skizziert. Abschließend gehen wir auf die Planung einer ad{ä}quaten Informations- und Kommunikations- Infrastruktur f{ü}r ein dezentrales Energieversorgungsnetz ein.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: Dieser Bericht beschreibt die Erfahrungen und Schlussfolgerungen,die im Rahmen der VDS-Vorstudie bei der Speicherung der vom Friedrich-Althoff-Konsortium lizenzierten Zeitschriften des Kluwer-Verlages gewonnen wurden.

Description: Der KOBV setzt für die endnutzerbasierte Online-Fernleihe den Sisis ZFL-Server (Zentraler Fernleih-Server) ein. Mit dem Einsatz des ZFL-Servers können in den Bibliotheken echte Rationalisierungseffekte erzielt werden: Der Server ist in der Lage, Fernleih-Bestellungen an lokale Systeme zu übergeben, so dass sie im lokalen System automatisch - ohne Eingreifen von Bibliotheksmitarbeitern - weiterverarbeitet werden können. Im KOBV können derzeit Sisis- und Aleph-Lokalsysteme diese Schnittstelle voll bedienen. Andere Bibliothekssysteme im KOBV, die diese Schnittstelle nicht bedienen können, werden mittels eines E-Mail-Verfahrens in die Online-Fernleihe integriert. Die vorliegende Kurzbeschreibung der Online-Fernleihe im KOBV soll - im Gegensatz zur Spezifikation, die möglichst vollständig sein sollte - einen leicht verständlichen Einblick in die Abläufe der Online-Fernleihe vermitteln. Nach einem Überblick über zu erwartende Rationalisierungseffekte ist der Ablauf einer Online-Fernleih-Bestellung - veranschaulicht durch eine Graphik mit dem technischen Aufbau im KOBV - kurz dargestellt. \vspace{6mm} {\it Hinweis:} Die von einer Arbeitsgruppe des KOBV erstellte Spezifikation zur Online-Fernleihe ist als ZIB Report 02-30 auf dem Preprint-Server des ZIB veröffentlicht. Siehe: Monika Kuberek (Red.) {\begin{rawhtml} 〈a href="http://www.zib.de/Publications/Reports/ZR-02-30.pdf"〉 〈i〉 Spezifikation für eine Verbund-Fernleih-Software im KOBV〈/i〉 〈/a〉 \end{rawhtml}}

Description: 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.

Description: Mit der Entwicklung des KOBV-Informationsportals soll den Benutzern in der Region Berlin-Brandenburg ein verbesserter Zugang zu Informationsressourcen geboten werden. Einen wesentlichen Anteil diese Auf der Grundlage der Analyse der Rahmenbedingungen werden Anforderungen an die Zugriffskontrolle im KOBV definiert und Lösungsmöglichkeiten auf der Ebene allgemeiner Modelle diskutiert.

Description: 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.).

Description: 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.

Description: 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.

Description: 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.

Description: Der scharfe Wettbewerb innerhalb der Telekommunikationsbranche zwingt die Netzbetreiber dazu, ihre Investitionen genau zu planen und immer wieder Einsparungsmanahmen durchzuführen. Gleichzeitig ist es jedoch wichtig, die Qualität der angebotenen Dienste zu verbessern, um neue Kunden zu gewinnen und langfristig an sich zu binden. Die mathematische Optimierung bietet sich für viele solcher Aufgabenstellungen als hervorragend geeignetes Planungswerkzeug an. Ziel dieses Artikels ist es, ihre Methodik und ihre Anwendung speziell zur Kosten- und Qualitätsoptimierung in Kommunikationsnetzen vorzustellen. Anhand von vier konkreten Planungsaufgaben aus dem Bereich der Festnetzplanung wird aufgezeigt, wie sich komplexe Zusammenhänge in flexiblen mathematischen Modellen abbilden lassen und welche Verfahren zur automatisierten Bearbeitung der Probleme eingesetzt werden können. Die hier vorgestellten Methoden zeichnen sich insbesondere dadurch aus, dass sie neben hochwertigen Lösungen auch eine Qualittsgarantie liefern, mit der sich die Lsungen fundiert bewerten lassen. Die dokumentierten Ergebnisse aus verschiedenen Industrieprojekten belegen die Eignung und Güte der mathematischen Optimierung für die Praxis.

Description: 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.

Description: 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.

Description: 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.

Description: \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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: Peer-to-Peer (P2P) Systeme werden u.a. zur Verwaltung von großen Datenmengen benutzt, die auf verschiedene Rechner verteilt sind. Benutzern soll damit der Zugriff auf Daten innerhalb des Systems leicht ermöglicht werden. Damit in P2P Systemen die Daten effizient verteilt und gesucht werden können, existieren Distributed Hash Tables. Distributed Hash Tables (DHT) sind eine Methode, um globale Informationen persistent speichern zu können. Der Wertebereich der Hashfunktion, welche die zu veröffentlichenden Einträge auf Werte abbildet, wird in Abschnitte aufgeteilt, die einzelnen Knoten zugeteilt werden. Die meisten DHTs haben aber ein Problem bei der Verteilung der Last. Die verschiedenen DHT Systeme beruhen meist auf einem identischen Ansatz der Lastverteilung. Die Last wird nur mit Hilfe einer Hashfunktion verteilt. Es wird davon ausgegangen, dass diese Funktion die Last gleichmäßig verteilt. Im Rahmen dieser Arbeit wurde ein Verfahren zur Last Verteilung entwickelt, simuliert und implementiert. Bei dem Verfahren wird die Last wie bei der Verteilung von Wärme an die Umgebung abgegeben. Es wird mit existierenden Lastbalancierungsalgorithmen verglichen. Mit diesem neuen Verfahren ist es möglich, Last in DHTs besser zu verteilen ohne große Änderungen an den DHTs vorzunehmen. Es wird gezeigt, wie mit dem Verfahren zusätzlich die Fehlertoleranz des P2P Systems erhöht werden kann.

Description: One of the many uses of Peer-to-Peer (P2P) systems is the administration of large data sets that are distributed across different computers, with the goal of facilitating user access to files within the system. Distributed Hash Tables (DHT) are designed to enable the efficient distribution and search of files, by allowing global information to be persistently stored. The range of values of the hash function (the possible entries in the published hash table) are assigned to individual nodes. Most DHTs, however, have a problem with load distribution. The various DHT systems usually operate by distributing load equally among nodes. Thus the load is distributed using the help of the hash function. One assumes this function distributes the load evenly. In the context of this work a method of distributing load has been developed, simulated and implemented. With this method load is transferred in a fashion analogous to the dissipation of heat into the environment. Comparisons with existing algorithms for load balancing are drawn. With the new procedure it is possible to better distribute load in DHTs without requiring major changes to the DHTs themselves. It is shown that with the procedure the fault tolerance of P2P systems may also be increased.

Description: 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.

Description: 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.

Description: 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.

Description: 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.

Description: 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 $\beta=5.0$.

Description: 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.

Description: 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.

Description: 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.

Description: An edge of a perfect graph $G$ is critical if $G-e$ is imperfect. We would like to decide whether $G - e$ is still {\sl almost perfect} or already {\sl very imperfect}. Via relaxations of the stable set polytope of a graph, we define two superclasses of perfect graphs: rank-perfect and weakly rank-perfect graphs. Membership in those two classes indicates how far an imperfect graph is away from being perfect. We study the cases, when a critical edge is removed from the line graph of a bipartite graph or from the complement of such a graph.

Description: Collection of abstracts of the first SIAM-EMS conference Applied Mathematics in our Changing World'' in Berlin, September 2-6, 2001.

Description: {\sc Zimpl} is a little language to translate the mathematical model of a problem into a linear or (mixed-)integer mathematical program expressed in {\tt lp} or {\tt mps} file format which can be read by a LP or MIP solver.

Description: Im ersten Teil des folgenden Aufsatzes werden allgemeine Überlegungen zur Entwicklung von Bibliotheken hin zu Informationsvermittlungsstellen für sowohl elektronische wie auch gedruckte Medien angestellt. Basierend auf den Ergebnissen der Evaluation digitaler Bibliotheken und Informationsportale in Deutschland wird ein erster Kriterienkatalog für ein Verbund-Informationsportal für den Kooperativen Bibliotheksverbund Berlin-Brandenburg entwickelt. Im Anhang befindet sich der Statusbericht über Informationsportale und digitale Bibliotheken in Deutschland. Dazu wurden sieben digitale Bibliotheken auf Verbundebene und 21 Bibliotheken nach Bundesländern evaluiert.

Description: Given a set of service requests (events), a set of guided servers (units), and a set of unguided service contractors (conts), the vehicle dispatching problem {\sl vdp} is the task to find an assignment of events to units and conts as well as tours for all units starting at their current positions and ending at their home positions (dispatch) such that the total cost of the dispatch is minimized. The cost of a dispatch is the sum of unit costs, cont costs, and event costs. Unit costs consist of driving costs, service costs and overtime costs; cont costs consist of a fixed cost per service; event costs consist of late costs linear in the late time, which occur whenever the service of the event starts later than its deadline. The program \textsf{ZIBDIP} based on dynamic column generation and set partitioning yields solutions on heavy-load real-world instances (215 events, 95 units) in less than a minute that are no worse than 1\% from optimum on state-of-the-art personal computers.

Description: Scenario tree models of stochastic programs arise naturally under standard nonanticipativity assumptions. We demonstrate how tree-sparse programs cover the general case, with \emph{arbitrary} information constraints. Detailed examples and intuitive interpretations illuminate the basic thoughts behind the abstract but elementary construction.

Description: In this paper we present an algorithm that accelerates 3D texture-based volume rendering of large and sparse data sets. A hierarchical data structure (known as AMR tree) consisting of nested uniform grids is employed in order to efficiently encode regions of interest. The hierarchies resulting from this kind of space partitioning yield a good balance between the amount of volume to render and the number of texture bricks -- a prerequisite for fast rendering. Comparing our approach to an octree based algorithm we show that our algorithm increases rendering performance significantly for sparse data. A further advantage is that less parameter tuning is necessary.

Description: Mathematical optimization techniques are on their way to becoming a standard tool in chemical process engineering. While such approaches are usually based on deterministic models, uncertainties such as external disturbances play a significant role in many real-life applications. The present article gives an introduction to practical issues of process operation and to basic mathematical concepts required for the explicit treatment of uncertainties by stochastic optimization.

Description: Uncoupling-coupling Monte Carlo (UCMC) combines uncoupling techniques for finite Markov chains with Markov chain Monte Carlo methodology. UCMC aims at avoiding the typical metastable or trapping behavior of Monte Carlo techniques. From the viewpoint of Monte Carlo, a slowly converging long-time Markov chain is replaced by a limited number of rapidly mixing short-time ones. Therefore, the state space of the chain has to be hierarchically decomposed into its metastable conformations. This is done by means of combining the technique of conformation analysis as recently introduced by the authors, and appropriate annealing strategies. We present a detailed examination of the uncoupling-coupling procedure which uncovers its theoretical background, and illustrates the hierarchical algorithmic approach. Furthermore, application of the UCMC algorithm to the $n$-pentane molecule allows us to discuss the effect of its crucial steps in a typical molecular scenario.

Description: Standard model predictive control for real-time operation of industrial production processes may be inefficient in the presence of substantial uncertainties. To avoid overly conservative disturbance corrections while ensuring safe operation, random influences should be taken into account explicitly. We propose a multistage stochastic programming approach within the model predictive control framework and apply it to a distillation process with a feed tank buffering external sources. A preliminary comparison to a probabilistic constraints approach is given and first computational results for the distillation process are presented.

Description: Dynamic stochastic programs are prototypical for optimization problems with an inherent tree structure inducing characteristic sparsity patterns in the KKT systems of interior methods. We propose an integrated modeling and solution approach for such tree-sparse programs. Three closely related natural formulations are theoretically analyzed from a control-theoretic viewpoint and compared to each other. Associated KKT solution algorithms with linear complexity are developed and comparisons to other interior approaches and related problem formulations are discussed.

Description: We introduce a new problem that was motivated by a (more complicated) problem arising in a robotized assembly enviroment. The bin coloring problem is to pack unit size colored items into bins, such that the maximum number of different colors per bin is minimized. Each bin has size~$B\in\mathbb{N}$. The packing process is subject to the constraint that at any moment in time at most $q\in\mathbb{N}$ bins may be partially filled. Moreover, bins may only be closed if they are filled completely. An online algorithm must pack each item must be packed without knowledge of any future items. We investigate the existence of competitive online algorithms for the online uniform binpacking problem. We show upper bounds for the bin coloring problem. We prove an upper bound of $3q$ - 1 and a lower bound of $2q$ for the competitive ratio of a natural greedy-type algorithm, and show that surprisingly a trivial algorithm which uses only one open bin has a strictly better competitive ratio of $2q$ - 1. Morever, we show that any deterministic algorithm has a competitive ratio $\Omega (q)$ and that randomization does not improve this lower bound even when the adversary is oblivious.

Description: In circuit switching networks call streams are characterized by their mean and peakedness (two-moment method). The $GI/M/C/0$ system is used to model a single link, where the $GI$-stream is determined by fitting moments appropriately. For the moments of the overflow traffic of a $GI/M/C/0$ system there are efficient numerical algorithms available. However, for the moments of the freed carried traffic, defined as the moments of a virtual link of infinite capacity to which the process of calls accepted by the link (carried arrival process) is virtually directed and where the virtual calls get fresh exponential i.i.d.\ holding times, only complex numerical algorithms are available. This is the reason why the concept of the freed carried traffic is not used rigorously. The main result of this paper is an efficient algorithm for computing the moments of the freed carried traffic, in particular an explicit formula for its peakedness. This result offers a unified handling of both overflow and carried traffics in networks. Furthermore, some refined characteristics for the overflow and freed carried streams are derived.

Description: In this work we concentrate on developing methods which determine good lower bounds for set partitioning problems (SPP) in an appropriate amount of time. We found out that it makes sense to use the Lagrangian relaxation method for this task. The Lagrangian relaxed problem of SPP has a simple structure, which leads to algorithms and heuristics, whose total complexity per iteration depends linearly on the number of non-zeros of the problem matrix of SPP. In contrast, other methods like simplex methods or interior point methods have a complexity of higher order. Because the problem matrices of our tested instances are sparse, the linear dependence becomes an advantage for the algorithms and heuristics mentioned above. As a reference for the state-of-the-art we have applied the dual simplex method and the barrier function method, implemented in CPLEX. The methods, which we have developed and compared with those of CPLEX, are SBM, CAM, CCBM, and CBM. SBM is a subgradient bundle method derived from the basic subgradient method, which is a global convergent method for determining the maximum of concave functions. CAM is a coordinate ascent method, where the convex coordinate bundle method CCBM and the coordinate bundle method CBM are derivatives from CAM. We observed that the basic subgradient and the coordinate ascent method are improved if bundling techniques can be used. But the motivation for bundling differs for both approaches. In the former case bundling helps to approximate a minimum norm subgradient, which provides a steepest ascent direction, in order to speed up the performance. In the latter case bundling enables proceeding along directions, which are not restricted on the coordinate directions. By this the performance is accelerated. Among all used techniques stabilization is worth mentioning. Stabilization improves the performance especially at the beginning by avoiding too big steps during the proceeding. This leads to a more stabilized progression. Stabilization was successfully applied to SBM, CAM, CCBM, and CBM. As an overall result we conclude the following: \begin{enumerate} \item CPLEX computes the optimal objective values, whereas SBM and CBM has on average a gap of under $1.5\%$. \item In comparison to CPLEX baropt, SBM, CAM, and CBM the algorithm CCBM has a slow convergence because of the convex combination of ascent coordinate directions. An alternative is to relax the convex combination to a simple sum of the corresponding directions. This idea is realized in CBM. \item If we focus on the running time rather than on optimality then CBM is on average the fastest algorithm. \end{enumerate} Note that methods like SBM or CBM are applied on static SPP instances in order to determine a good lower bound. For solving SPP we need dynamical methods. Due to the complex topic of dynamical methods we will not discuss them, but a certain technique is worth mentioning. It is called column generation. We have indicated that this technique needs good Lagrangian multipliers of the corresponding SPP instances in order to generate further columns (in our case duties), which are added to the current SPP instance. Those multipliers are by-products of methods like our six considered methods. Due to the large number of such generation steps the running time depends on the computation time of these methods. Therefore, CBM fits more to this technique than CPLEX baropt or SBM. To sum it up it can be said that applications such as a duty scheduling can be described as set partitioning problems, whose lower bound can be solved by simplex, interior points, subgradient, or coordinate ascent methods. It turns out that the interior points method CPLEX baropt and the heuristic CBM have good performances. Furthermore, good Lagrangian multipliers, which are by-products of these methods, can be used by techniques like column generation. For this particular technique it also turns out that among our tested algorithms CBM is the most efficient one. In general we can state that real-world applications, which have to solve a large number of Lagrangian relaxed SPP instances can improve their performance by using CBM.

Description: The success of large-scale multi-national projects like the forthcoming analysis of the LHC particle collision data at CERN relies to a great extent on the ability to efficiently utilize computing a management software (Datagrid, Globus, etc.), while the effective integration of computing nodes has been largely neglected up to now. This is the focus of our work. We present a framework for a high-performance cluster that can be used as a reliable computing node in the Grid. We outline the cluster architecture, the management of distributed data and the seamless intergration of the cluster into the Grid environment.

Description: Der Aufsatz ist die ausgearbeitete Fassung eines Vortrages, gehalten am 05.04.2001 auf dem 91. Deutschen Bibliothekartag in Bielefeld. Der Kooperative Bibliotheksverbund Berlin-Brandenburg (KOBV) ist im Rahmen eines wissenschaftlichen Projektes in den Jahren 1997 bis 2000 am Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB) aufgebaut worden. Nachdem das Projekt erfolgreich abgeschlossen ist, wird der KOBV 2001 institutionalisiert. In dem Vortrag hat die Verfasserin einen Überblick über das bisher Erreichte, den derzeitigen Stand und die Perspektiven des neuen Verbundes gegeben. Der KOBV stellt eine neue Art von Bibliotheksverbund dar. Sein technisches Konzept und sein organisatorischer Aufbau basieren auf der {\sl Internetphilosophie}. Den informationstechnischen Kern bildet eine Suchmaschine, die die heterogenen lokalen Bibliothekssysteme miteinander verbindet. Die KOBV-Organisation ist dezentral. Sie wird getragen von der Kooperation der Bibliotheken in Berlin und Brandenburg. Eine kleine Verbundzentrale koordiniert dieses Geflecht vernetzter lokaler Einheiten, vertritt den KOBV nach außen und arbeitet - in Form von Projekten - an seiner Weiterentwicklung. Der Entwicklungsaspekt und die Nutzerorientierung sind zwei wesentliche Komponenten in der Verbundarbeit. Berlin und Brandenburg haben auf engem Raum zahlreiche Bibliotheken mit großen, reichhaltigen Medienbeständen. Mittel- bis langfristig sollen Bibliotheken aller Sparten und Größen in den KOBV integriert werden, seien es wissenschaftliche Universalbibliotheken, universitäre Bibliothekssysteme, Spezialbibliotheken, Behörden- und Parlamentsbibliotheken oder öffentliche Bibliotheken. Auch regionale Bibliotheksverbünde können als Subverbünde am KOBV teilnehmen. Mit der KOBV-Suchmaschine ist eine offene Plattform geschaffen worden, auf der weitere Entwicklungen aufsetzen können. Der Aufbau einer virtuellen Regionalbibliothek mit Bestell- und Lieferkomponenten ist eines der Ziele. Darüber hinaus ist es die Vision, in der Region ein virtuelles {\sl Wissensportal} aufzubauen, das dem Nutzer unter einer Adresse den umfassenden Zugang und die umfassende Bereitstellung von Informationen aller Art bietet.

Description: A new approach to the numerical solution of optimal control problems including control and state constraints is presented. Like hybrid methods, the approach aims at combining the advantages of direct and indirect methods. Unlike hybrid methods, however, our method is directly based on interior-point concepts in function space --- realized via an adaptive multilevel scheme applied to the complementarity formulation and numerical continuation along the central path. Existence of the central path and its continuation towards the solution point is analyzed in some theoretical detail. An adaptive stepsize control with respect to the duality gap parameter is worked out in the framework of affine invariant inexact Newton methods. Finally, the performance of a first version of our new type of algorithm is documented by the successful treatment of the well-known intricate windshear problem.

Description: Das \emph{Committee on Electronic Information and Communication} (CEIC) der \emph{International Mathematical Union} (IMU) hat die Aufgabe, sich über die langfristige Informationsversorgung in der Mathematik Gedanken zu machen und Lösungsvorschläge hierfür zu erarbeiten. Das Kernthema ist natürlich "`Elektronisches Publizieren"'. Dazu gehören auch Copyright-Regelungen. % Sie sind -- % neben einer Andeutung der weiteren CEIC-Pläne -- der Fokus dieses % kurzen Artikels. Er schließt mit einem von der IMU verabschiedeten % Aufruf zu vernünftigem Verhalten bei Copyright-Vereinbarungen. Eine % nachhaltige Befolgung dieses Aufrufs -- verbunden mit weiteren % Aktivitäten -- könnte die (derzeit kaum noch bezahlbare und % dadurch gefährdete) Literaturversorgung nachhaltig zum Positiven % verändern. Mit diesem Artikel beginnt eine kleine Serie von Aufsätzen, in denen ich (in meiner Funktion als eines von elf CEIC-Mitgliedern) die Empfehlungen des CEIC erläutern werde. % Das heutige Thema sind die % CEIC-Vorschläge zum Copyright

Description: By computed tomography data (CT), the individual geometry of the mandible is quite well reproduced, also the separation between cortical and trabecular bone. Using anatomical knowledge about the architecture and the functional potential of the masticatory muscles, realistic situations were approximated. The solution of the underlying partial differential equations describing linear elastic material behaviour is provided by an adaptive finite element method. Estimations of the discretization error, local grid refinement, and multilevel techniques guarantee the reliability and efficiency of the method.

Description: Optimization is the task of finding an optimum solution to a given problem. When the decision variables are discrete we speak of a combinatorial optimization problem. Such a problem is online when decisions have to be made before all data of the problem are known. And we speak of a real-time online problem when online decisions have to be computed within very tight time bounds. This paper surveys the are of combinatorial online and real-time optimization, it discusses, in particular, the concepts with which online and real-time algorithms can be analyzed.

Description: This paper describes a new simulation tool for the prediction of aerosol formation and behavior in gas--liquid contact devices such as absorbers, scrubbers, quench coolers, and condensers as well as multistage gas cleaning processes, respectively. Aerosol formation can impact severely the separation efficiency of gas cleaning processes. Aerosol or fog formation can arise by spontaneous condensation or desublimation in supersaturated gas phases. The rigorous description of the mass and energy transfer between the gas phase, the liquid phase, and the growing aerosol droplets leads to a system of partial differential and algebraic equations. For the solution of these systems we have developed the plant simulation tool AerCoDe. This program bases upon the linearly--implicit Euler discretisation, which in combination with extrapolation permits an adaptive step size and order control. Typical simulation results of a multistage industrial flue gas scrubbing process are presented. It is shown, that experimental data can be confirmed if the number concentration of condensation nuclei as an input parameter is roughly known.

Description: This paper discusses online optimization of real-world transportation systems. We concentrate on transportation problems arising in production and manufacturing processes, in particular in company internal logistics. We describe basic techniques to design online optimization algorithms for such systems, but our main focus is decision support for the planner: which online algorithm is the most appropriate one in a particular setting? We show by means of several examples that traditional methods for the evaluation of online algorithms often do not suffice to judge the strengths and weaknesses of online algorithms. We present modifications of well-known evaluation techniques and some new methods, and we argue that the selection of an online algorithm to be employed in practice should be based on a sound combination of several theoretical and practical evaluation criteria, including simulation.

Description: Wireless communication networks employ radio frequencies to establish communication links. The available radio spectrum is very limited. To meet today's radio communication demand, this resource has to be administered and reused carefully in order to control mutual interference. The reuse can be organized via separation in space, time, or frequency, for example. The problem, therefore, arises to distribute frequencies to links in a ``reasonable manner''. This is the basic form of the frequency assignment problem. What ``reasonable'' means, how to quantify this measure of quality, which technical side constraints to consider cannot be answered in general. The exact specification of this task and its mathematical model depend heavily on the particular application considered. In this paper we discuss this issue with respect to the GSM standard for mobile communication.

Description: This paper is a summary of the Round Table: ``The Impact of Mathematical Research on Industry and Vice Versa'' held at 3ecm in Barcelona on July 11, 2000. The round table started with contributions of the three panelists. Irene Fonseca, the panel chair, opened the discussion by stating six questions addressing the main issues of the round table topic. She presented the panel's answers to these questions, drawing on many examples from her own academic experience. In the following additional presentations, the other two panel members added further points of view based on their personal involvement with industry. The round table ended with a lively discussion with members from the audience. This written summary of the oral presentations follows the structure of the round table indicated above.

Description: This article is about \emph{adaptive column generation techniques} for the solution of duty scheduling problems in public transit. The current optimization status is exploited in an adaptive approach to guide the subroutines for duty generation, LP resolution, and schedule construction toward relevant parts of a large problem. Computational results for three European scenarios are reported.

Description: The recent spectral bundle method allows to compute, within reasonable time, approximate dual solutions of large scale semidefinite quadratic 0-1 programming relaxations. We show that it also generates a sequence of primal approximations that converge to a primal optimal solution. Separating with respect to these approximations gives rise to a cutting plane algorithm that converges to the optimal solution under reasonable assumptions on the separation oracle and the feasible set. We have implemented a practical variant of the cutting plane algorithm for improving semidefinite relaxations of constrained quadratic 0-1 programming problems by odd-cycle inequalities. We also consider separating odd-cycle inequalities with respect to a larger support than given by the cost matrix and present a heuristic for selecting this support. Our preliminary computational results for max-cut instances on toroidal grid graphs and balanced bisection instances indicate that warm start is highly efficient and that enlarging the support may sometimes improve the quality of relaxations considerably.

Description: Der Wissenschaftsrat hat in seiner Juli-Sitzung 2001 \glqq Empfehlungen zur digitalen Informationsversorgung durch Hochschulbibliotheken \grqq verabschiedet. Einige der Vorschläge des Wissenschaftsrates können, falls sie von den angesprochenen Institutionen aufgenommen werden, zu einer nachhaltigen Veränderung der wissenschaftlichen Informationslandschaft führen. In meinem kurzen Kommentar zu diesem Papier möchte ich auf einige dieser Anregungen hinweisen.

Description: Von welcher "Informationsumwelt" träumt jemand, der für seine wissenschaftliche (und sonstige) Arbeit digitale Informationstechnologie intensiv einsetzt? In diesem Artikel beschreibe ich meinen "digitalen Traum". Er ist ganz einfach zu formulieren:"Ich will alles und zwar sofort, jederzeit, "überall" und kostenlos zur Verfügung haben." Ich schildere, was davon heute schon (fast) realisiert ist und was noch fehlt. Ich skizziere einige zentrale Schwierigkeiten der vollständigen Realisierung und skizziere mögliche Lösungen.

Description: Im Rahmen der biomechanischen Simulation knöcherner Organe ist die Frage nach einer befriedigenden Materialbeschreibung nach wie vor ungelöst. Computertomographische Datensätze liefern eine räumliche Verteilung der (Röntgen-)Dichte und ermöglichen damit eine gute Darstellung der individuellen Geometrie. Weiter können die verschiedenen Materialbestandteile des Knochens, Spongiosa und Kortikalis, voneinander getrennt werden. Aber die richtungsabängige Information der Materialanisotropie ist verloren. In dieser Arbeit wird ein Ansatz für eine anisotrope Materialbeschreibung vorgestellt, die es ermöglicht, den Einfluss der individuellen knöchernen Struktur auf das makroskopische Materialverhalten abzuschätzen.

Description: Many phenomena in nature and engineering happen simultaneously on rather diverse spatial and temporal scales, i.e.\ exhibit a multi-scale character. Therefore various hierarchical data structures and numerical schemes have been devised to represent quantitatively such phenomena. A special numerical multilevel technique, associated with a particular hierarchical data structure, is so-called Adaptive Mesh Refinement (AMR). This scheme achieves locally very high spatial and temporal resolutions. Due to its popularity, many scientists are in need of interactive visualization tools for AMR data. In this article we present a 3D texture-based volume rendering algorithm for AMR data, that directly utilizes the hierarchical structure. Thereby interactive rendering even for large data sets is achieved. In particular the problems of interpolation artifacts, opacity corrections, and texture memory limitations are addressed. The algorithm's value in practice is demonstrated with simulation and image data.

Description: By combining techniques of preparation, histology, confocal microscopy, data visualization and data processing, we have created and recently published a standard brain model for drosophila and honey bee brains. This report describes the algorithms and implementation of the corresponding software modules. At the same time it serves as a user's guide for scientist who want to reproduce the results for differerent species or mutants.

Description: Several classes of systems of evolution equations with one or two vector unknowns are considered. We investigate also systems with one vector and one scalar unknown. For these classes all equations having the simplest higher symmetry are listed.

Description: Two traffic streams $\Phi_1$, $\Phi_2$ are offered a link. The calls of $\Phi_i$ require exponential holding times with parameter $\mu$ and are accepted if less than $C_i$ trunks are occupied. Approximating the $\Phi_i$ by appropriate renewal processes meeting their first two moments, defined as the moments of the numbers of calls in virtual links of infinite capacity to which the traffic streams as freed traffics are virtually directed and where the calls get fresh exponential i.i.d.\ holding times with parameter $\mu$, stable recursive algorithms of complexity $O(\max(C_1,C_2))$ are derived for the first two defined as above moments of the individual overflow and freed carried traffics. The results offer a unified handling of both overflow and carried traffics in circuit switching networks with trunk reservation, providing a basis for new two-moment network dimensioning algorithms.

Description: We study the performance of QCD simulations with dynamical Wilson fermions by combining the Hybrid Monte Carlo algorithm with parallel tempering on $10^4$ and $12^4$ lattices. In order to compare tempered with standard simulations, covariance matrices between sub-ensembles have to be formulated and evaluated using the general properties of autocorrelations of the parallel tempering algorithm. We find that rendering the hopping parameter $\kappa$ dynamical does not lead to an essential improvement. We point out possible reasons for this observation and discuss more suitable ways of applying parallel tempering to QCD.

Description: Dem vorliegenden Aufsatz liegt ein Vortrag zugrunde, den die Verfasserin auf der Ersten Gemeinsamen Fachtagung der DBV-Landesverbände Berlin und Brandenburg "Wir machen den Weg frei : Fusionen - Kooperationen in Berlin und Brandenburg" am 17. Oktober 2001 gehalten hat, in der Vortragsreihe "Möglichkeiten und Grenzen von Ausleih- und bibliographischen Verbünden - VÖB Berlin, VÖB Brandenburg, KOBV". Der Kooperative Bibliotheksverbund Berlin-Brandenburg (KOBV) ist angetreten, um auf der Basis neuer Technologien zeitgemäße, nutzerorientierte Dienstleistungen für den Informationsbereich zu entwickeln und die Informationsinfrastruktur in der Region Berlin-Brandenburg neu zu organisieren. Dabei setzt der KOBV insbesondere auf das Internet. Die Verfasserin beschreibt die einzelnen Stufen, in denen die Dienste des KOBV aufgebaut wurden und kontinuierlich weiter ausgebaut werden. Dabei zeigt sie Vorteile auf, die Nutzern und Bibliotheken durch den Verbund entstehen, und lotet gleichzeitig die Grenzen aus, die dem Verbund gesetzt sind.

Description: We report numerical results for SBmethod --- a publically available implementation of the spectral bundle method --- applied to the 7$^{th}$ DIMACS challenge test sets that are semidefinite relaxations of combinatorial optimization problems. The performance of the code is heavily influenced by parameters that control bundle update and eigenvalue computation. Unfortunately, no mathematically sound guidelines for setting them are known. Based on our experience with SBmethod, we propose heuristics for dynamically updating the parameters as well as a heuristc for improving the starting point. These are now the default settings of SBmethod Version 1.1. We compare their performance on the DIMACS instances to our previous best choices for Version 1.0. SBmethod Version 1.1 is also part of the independent DIMACS benchmark by H.~Mittelmann. Based on these results we try to analyze strengths and weaknesses of our approach in comparison to other codes for large scale semidefinite programming.

Description: Many {\cal NP}-hard graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied to find (almost) optimal solutions or lower bounds for diverse optimization problems. To apply a tree decomposition approach, the treewidth of the graph has to be determined, independently of the application at hand. Although for fixed $k$, linear time algorithms exist to solve the decision problem ``treewidth $\leq k$'', their practical use is very limited. The computational tractability of treewidth has been rarely studied so far. In this paper, we compare four heuristics and two lower bounds for instances from applications such as the frequency assignment problem and the vertex coloring problem. Three of the heuristics are based on well-known algorithms to recognize triangulated graphs. The fourth heuristic recursively improves a tree decomposition by the computation of minimal separating vertex sets in subgraphs. Lower bounds can be computed from maximal cliques and the minimum degree of induced subgraphs. A computational analysis shows that the treewidth of several graphs can be identified by these methods. For other graphs, however, more sophisticated techniques are necessary.

Description: The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a network's graph. In this paper, we show that pre-processing can help in finding good triangulations for probabilistic networks, that is, triangulations with a minimal maximum clique size. We provide a set of rules for stepwise reducing a graph, without losing optimality. This reduction allows us to solve the triangulation problem on a smaller graph. From the smaller graph's triangulation, a triangulation of the original graph is obtained by reversing the reduction steps. Our experimental results show that the graphs of some well-known real-life probabilistic networks can be triangulated optimally just by preprocessing; for other networks, huge reductions in their graph's size are obtained.

Description: {\begin{rawhtml} 〈a href="http://dx.doi.org/10.1007/s10479-007-0178-0"〉 Revised Version unter http://dx.doi.org/10.1007/s10479-007-0178-0〈/a〉 \end{rawhtml}} Wireless communication is used in many different situations such as mobile telephony, radio and TV broadcasting, satellite communication, and military operations. In each of these situations a frequency assignment problem arises with application specific characteristics. Researchers have developed different modelling ideas for each of the features of the problem, such as the handling of interference among radio signals, the availability of frequencies, and the optimization criterion. This survey gives an overview of the models and methods that the literature provides on the topic. We present a broad description of the practical settings in which frequency assignment is applied. We also present a classification of the different models and formulations described in the literature, such that the common features of the models are emphasized. The solution methods are divided in two parts. Optimization and lower bounding techniques on the one hand, and heuristic search techniques on the other hand. The literature is classified according to the used methods. Again, we emphasize the common features, used in the different papers. The quality of the solution methods is compared, whenever possible, on publicly available benchmark instances.

Description: Telota ist ein Kunstwort, das für alle Aktivitäten der Berlin-Brandenburgischen Akademie der Wissenschaften steht, die der Förderung von Forschung, Kommunikation und Präsentation durch elektronische Medien dienen. In diesem Artikel werden die Entstehung des Telota-Projektes geschildert und die Ziele diskutiert, die mit diesem Projekt erreicht werden sollen. Es geht darum, moderne Informationstechnik bewusst, geplant und nachhaltig für alle Belange der {\rm BBAW} einzusetzen. Informationstechnische Werkzeuge sollen für die wissenschaftliche Arbeit effizient genutzt werden; die Information nach innen und nach außen soll deutlich verbessert werden; eine bessere Kommunikationsinfrastuktur soll die Zusammenarbeit fördern.

Description: The pole condition is a general concept for the theoretical analysis and the numerical solution of a variety of wave propagation problems. It says that the Laplace transform of the physical solution in radial direction has no poles in the lower complex half-plane. In the present paper we show that for the Helmholtz equation with a radially symmetric potential the pole condition is equivalent to Sommerfeld's radiation condition. Moreover, a new representation formula based on the pole condition is derived and used to prove existence, uniqueness and asymptotic properties of solutions. This lays the foundations of a promising new algorithm to solve time-harmonic scattering problems numerically and provides a new approach for analyzing existing algorithms such as the Perfectly Matched Layer (PML) method and the Bayliss-Gunzburger-Turkel (BGT) algorithm.

Description: In this paper we study the PML method for Helmholtz-type scattering problems with radially symmetric potential. The PML method consists in surrounding the computational domain by a \textbf{P}erfectly \textbf{M}atched sponge \textbf{L}ayer. We prove that the approximate solution obtained by the PML method converges exponentially fast to the true solution in the computational domain as the thickness of the sponge layer tends to infinity. This is a generalization of results by Lassas and Somersalo based on boundary integral eqaution techniques. Here we use techniques based on the pole condition instead. This makes it possible to treat problems without an explicitly known fundamental solution.