Real Computability and Hypercomputation - Ziegler, Martin

Interactive Refinement of a Material Flow Simulation Model by Comparing Multiple Simulation Runs in one 3D Environment - Fischer, Matthias; Laroque, Christoph; Huber, Daniel; Krokowski, Jens; Mueck, Bengt; Kortenjan, Michael; Aufenanger, Mark; Dangelmaier, Wilhelm (European Simulation and Modelling Conference (ESM 2007))
The validation of material flow models as well as the selection of promising strategies for the generation of a successful experiment plan is a time-consuming process. A new approach is presented, which supports the simulation expert in his working process by giving him the opportunity to modify the simulated simulation run and afterwards compare the effects of his modification with the original setting, online and in one user interface, implemented by switching the visualizations between the simulation runs or opening up to 5 parallel 3D windows. The method developed therefore clones existing simulation runs online and allows the navigation within these existing simulation runs. The method has been implemented and is validated by a test model, which describes in detail the new working process of a modeler. New research questions are derived from this work, which will define following working steps.

Ein ganzheitlicher Ansatz zur immersiven 3D-Materialflusssimulation innerhalb der Digitalen Fabrik - Dangelmaier, Wilhelm; Laroque, Christoph; Fischer, Matthias (Augmented & Virtual Reality in der Produktentstehung)

Multiple-Access Relay Channel with Network Coding and Non-Ideal Source-Relay Channels - Woldegebreal, Dereje H.; Karl, Holger (2007 4th International Symposium on Wireless Communication Systems)

Optimizing sleeping intervals in preamble sampling MAC for WSNs - Karl, Holger

Estimating Clustering Indexes in Data Streams - Buriol, Luciana S.; Frahling, Gereon; Leonardi, Stefano; Sohler, Christian (Proceedings of the 15th European Symposium on Algorithms (ESA))
We present random sampling algorithms that with probability at least 1 − δ compute a (1 ±ε)-approximation of the clustering coefficient and of the number of bipartite clique subgraphs of a graph given as an incidence stream of edges. The space used by our algorithm to estimate the clustering coefficient is inversely related to the clustering coefficient of the network itself. The space used by our algorithm to compute the number K 3,3 of bipartite cliques is proportional to the ratio between the number of K 1,3 and K 3,3 in the graph. Since the space complexity depends only on the structure of the input graph and not on the number of nodes, our algorithms scale very well with increasing graph size. Therefore they provide a basic tool to analyze the structure of dense clusters in large graphs and have many applications in the discovery of web communities, the analysis of the structure of large social networks and the probing of frequent patterns in large graphs. We implemented both algorithms and evaluated their performance on networks from different application domains and of different size; The largest instance is a webgraph consisting of more than 135 million nodes and 1 billion edges. Both algorithms compute accurate results in reasonable time on the tested instances.

Interaction of radiation with matter. Part II: Light and electrons - Schindlmayr, Arno (Probing the Nanoworld)

Time-dependent density-functional theory for extended systems - Botti, Silvana; Schindlmayr, Arno; Del Sole, Rodolfo; Reining, Lucia (Reports on Progress in Physics)
For the calculation of neutral excitations, time-dependent density functional theory (TDDFT) is an exact reformulation of the many-body time-dependent Schrödinger equation, based on knowledge of the density instead of the many-body wavefunction. The density can be determined in an efficient scheme by solving one-particle non-interacting Schrödinger equations—the Kohn–Sham equations. The complication of the problem is hidden in the—unknown—time-dependent exchange and correlation potential that appears in the Kohn–Sham equations and for which it is essential to find good approximations. Many approximations have been suggested and tested for finite systems, where even the very simple adiabatic local-density approximation (ALDA) has often proved to be successful. In the case of solids, ALDA fails to reproduce optical absorption spectra, which are instead well described by solving the Bethe–Salpeter equation of many-body perturbation theory (MBPT). On the other hand, ALDA can lead to excellent results for loss functions (at vanishing and finite momentum transfer). In view of this and thanks to recent successful developments of improved linear-response kernels derived from MBPT, TDDFT is today considered a promising alternative to MBPT for the calculation of electronic spectra, even for solids. After reviewing the fundamentals of TDDFT within linear response, we discuss different approaches and a variety of applications to extended systems.

Ab initio study of the half-metal to metal transition in strained magnetite - Friák, Martin; Schindlmayr, Arno; Scheffler, Matthias (New Journal of Physics)
Using density-functional theory, we investigate the stability of the half-metallic ground state of magnetite under different strain conditions. The effects of volume relaxation and internal degrees of freedom are fully taken into account. For hydrostatic compression, planar strain in the (001) plane and uniaxial strain along the [001] direction, we derive quantitative limits beyond which magnetite becomes metallic. As a major new result, we identify the bond length between the octahedrally coordinated iron atoms and their neighbouring oxygen atoms as the main characteristic parameter, and we show that the transition occurs if external strain reduces this interatomic distance from 2.06 Å in equilibrium to below a critical value of 1.99 Å. Based on this criterion, we also argue that planar strain due to epitaxial growth does not lead to a metallic state for magnetite films grown on (111)-oriented substrates.

Quasiparticle calculations for point defects at semiconductor surfaces - Schindlmayr, Arno; Scheffler, Matthias (Theory of Defects in Semiconductors)
We present a quantitative parameter-free method for calculating defect states and charge-transition levels of point defects in semiconductors. It combines the strength of density-functional theory for ground-state total energies with quasiparticle corrections to the excitation spectrum obtained from many-body perturbation theory. The latter is implemented within the G0W0 approximation, in which the electronic self-energy is constructed non-self-consistently from the Green’s function of the underlying Kohn–Sham system. The method is general and applicable to arbitrary bulk or surface defects. As an example we consider anion vacancies at the (110) surfaces of III–V semiconductors. Relative to the Kohn–Sham eigenvalues in the local-density approximation, the quasiparticle corrections open the fundamental band gap and raise the position of defect states inside the gap. As a consequence, the charge-transition levels are also pushed to higher energies, leading to close agreement with the available experimental data.

On Testable Properties in Bounded Degree Graphs - Sohler, Christian; Czumaj, Artur (Proceedings of the 17th ACM-SIAM Symposium on Discrete Algorithms (SODA'07))
We study graph properties which are testable for bounded degree graphs in time independent of the input size. Our goal is to distinguish between graphs having a predetermined graph property and graphs that are far from every graph having that property. It is believed that almost all, even very simple graph properties require a large complexity to be tested for arbitrary (bounded degree) graphs. Therefore in this paper we focus our attention on testing graph properties for special classes of graphs. We call a graph family non-expanding if every graph in this family is not a weak expander (its expansion is O(1/log2 n), where n is the graph size). A graph family is hereditary if it is closed under vertex removal. Similarly, a graph property is hereditary if it is closed under vertex removal. Next, we call a graph property Π to be testable for a graph family F if for every graph G ε F, in time independent of the size of G we can distinguish between the case when G satisfies property Π and when it is far from every graph satisfying property Π. In this paper we prove thatIn the bounded degree graph model, any hereditary property is testable if the input graph belongs to a hereditary and non-expanding family of graphs.As an application, our result implies that, for example, any hereditary property (e.g., k-colorability, H-freeness, etc.) is testable in the bounded degree graph model for planar graphs, graphs with bounded genus, interval graphs, etc. No such results have been known before and prior to our work, in the bounded degree graph model very few graph properties have been known to be testable for any graph classes.

StrSort Algorithms for Geometric Problems - Sohler, Christian; Lammersen, Christiane (Proceedings of the 23rd European Workshop on Computational Geometry (EWCG))
In the StrSort model [2], the input is given as a stream, e.g. a sequence of points, and an algorithm can perform (a) streaming and (b) sorting passes to process the stream. A streaming pass reads the input stream from left to right and writes an output stream, which is the input of the next pass. A sorting pass is a black box operation that sorts a stream according to some partial order. In this paper, we develop algorithms for two basic geometric problems in the StrSort model. At first, we propose a divide-and-conquer algorithm that computes the convex hull of a point set in 2D in O(log2 n) passes using O(1) memory. Then we give a StrSort algorithm to compute a (1+ε)-spanner for a point set in Rd for constant d and constant epsilon that uses O(logd-1 n) passes and O(log n) space. This result implies a (1+ε)-approximation of the Euclidean minimum spanning tree in Rd, for constant d and ε.

Testing Expansion in Bounded-Degree Graphs - Sohler, Christian; Czumaj, Artur (Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS))

Small Space Representations for Metric Min-Sum k-Clustering and their Applications - Sohler, Christian; Czumaj, Artur (Proceedings of the 24th International Symposium on Theoretical Aspects of Computer Science (STACS'07))

Sublinear-time approximation algorithms for clustering via random sampling - Sohler, Christian; Czumaj, Artur (Random Structures & Algorithms)
We present a novel analysis of a random sampling approach for four clustering problems in metric spaces: k-median, k-means, min-sum k-clustering, and balanced k-median. For all these problems, we consider the following simple sampling scheme: select a small sample set of input points uniformly at random and then run some approximation algorithm on this sample set to compute an approximation of the best possible clustering of this set. Our main technical contribution is a significantly strengthened analysis of the approximation guarantee by this scheme for the clustering problems.The main motivation behind our analyses was to design sublinear-time algorithms for clustering problems. Our second contribution is the development of new approximation algorithms for the aforementioned clustering problems. Using our random sampling approach, we obtain for these problems the first time approximation algorithms that have running time independent of the input size, and depending on k and the diameter of the metric space only. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2007A preliminary extended abstract of this work appeared in Proceedings of the 31st Annual International Colloquium on Automata, Languages and Programming (ICALP), pp. 396407, 2004.

A PTAS for k-means clustering based on weak coresets - Sohler, Christian; Monemizahdeh, Morteza; Feldman, Dan (Proceedings of the 23rd annual symposium on computational geometry (SoCG'07))

Efficient kinetic data structures for MaxCut - Sohler, Christian; Czumaj, Artur; Frahling, Gereon (Proceedings of the 19th Canadian Conference on Computational Geometry (CCCG))

Dynamic and redundant data placement - Brinkmann, André; Effert, Sascha; Meyer auf der Heide, Friedhelm; Scheideler, Christian (IEEE International Conference on Distributed Computing Systems (ICDCS))
We present a randomized block-level storage virtualization for arbitrary heterogeneous storage systems that can distribute data in a fair and redundant way and can adapt this distribution in an efficient way as storage devices enter or leave the system. More precisely, our virtualization strategies can distribute a set of data blocks among a set of storage devices of arbitrary non-uniform capacities so that a storage device representing x% of the capacity in the system will get x% of the data (as long as this is in principle possible) and the different copies of each data block are stored so that no two copies of a data block are located in the same device. Achieving these two properties is not easy, and no virtualization strategy has been presented so far that has been formally shown to satisfy fairness and redundancy while being time- and space-eflcient and allowing an efficient adaptation to a changing set of devices.

Von der Mechatronik zur Selbstoptimierung - Frank, Ursula; Gausemeier, Jürgen; Schmidt, Alexander; Zimmer, Detmar (Internationales Forum Mechatronik. Intelligente Systeme und Module)

Using Active Patterns for the Conceptual Design of Self-Optimizing Systems Exemplified by an Air Gap Adjustment System - Gausemeier, Jürgen; Dangelmaier, Wilhelm; Zimmer, Detmar; Schmidt, Alexander; Frank, Ursula; Klöpper, Benjamin (Computers and Information in Engineering Conference, Parts A and B)