TY - JOUR
AU - Ziegler, Martin
ID - 17980
JF - Electronic Notes in Theoretical Computer Science
SN - 1571-0661
TI - Revising Type-2 Computation and Degrees of Discontinuity
ER -
TY - CONF
AB - 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.
AU - Buriol, Luciana S.
AU - Frahling, Gereon
AU - Leonardi, Stefano
AU - Sohler, Christian
ID - 18572
SN - 9783540755197
T2 - Proceedings of the 15th European Symposium on Algorithms (ESA)
TI - Estimating Clustering Indexes in Data Streams
VL - 4698
ER -
TY - JOUR
AB - 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.
AU - Botti, Silvana
AU - Schindlmayr, Arno
AU - Del Sole, Rodolfo
AU - Reining, Lucia
ID - 18589
IS - 3
JF - Reports on Progress in Physics
SN - 0034-4885
TI - Time-dependent density-functional theory for extended systems
VL - 70
ER -
TY - JOUR
AB - 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.
AU - Friák, Martin
AU - Schindlmayr, Arno
AU - Scheffler, Matthias
ID - 18591
IS - 1
JF - New Journal of Physics
SN - 0034-4885
TI - Ab initio study of the half-metal to metal transition in strained magnetite
VL - 9
ER -
TY - GEN
AU - Peckhaus, Volker
ID - 18642
T2 - Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 1110.01009]
TI - Kushner, Boris A., “The Constructive Mathematics of A.A. Markov”, American Mathematical Monthly 113 (2006), 559–566
ER -
TY - GEN
AU - Peckhaus, Volker
ID - 18647
T2 - Zentralblatt für Mathematik und ihre Grenzgebiete [Zbl. 1122.00009]
TI - Visser, Henk, “Transpositions”, in: Johan van Benthem (Hg.), The Age of Alternative Logics. Assessing Philosophy of Logic and Mathematics Today. Based on the Conference on Philosophical Insights into Logic and Mathematics, Nancy, France, September 30–October 4, 2002, Dordrecht: Springer 2006, 75–86
ER -
TY - GEN
AU - Peckhaus, Volker
ID - 18825
T2 - Mathematical Reviews [MR2258016 (2007k:01012)]
TI - Ferreirós, José, “Riemann’s Habilitationsvortrag at the Crossroads of Mathematics, Physics, and Philosophy”, in: The Architecture of Modern Mathematics, Oxford University Press: Oxford 2006, 67–96
ER -
TY - GEN
AU - Kutylowski, Jaroslaw
ID - 18933
TI - Competitive Maintenance of Minimum Spanning Trees under Stochastic Adversaries
ER -
TY - CHAP
AU - Seng, Eva- Maria
ED - Krause, Katharina
ID - 19140
T2 - Geschichte der bildenden Kunst in Deutschland, Bd. 4 Spätgotik und Renaissance
TI - Jörg Held (um 1454-1527), Petrarca-Meister, Vogelschau der Stadt Augsburg
ER -
TY - JOUR
AU - Mahnken, Rolf
AU - Caylak, Ismail
ID - 19114
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
TI - Stabilization of bi‐linear mixed finite elements for tetrahedra with enhanced interpolation using volume and area bubble functions
ER -