Eigenvector localization in the heavy-tailed random conductance model

We generalize our former localization result about the principal Dirichlet eigenvector of the i.i.d. heavy-tailed random conductance Laplacian to the first $k$ eigenvectors. We overcome the complication that the higher eigenvectors have fluctuating signs by invoking the Bauer-Fike theorem to show that the $k$th eigenvector is close to the principal eigenvector of an auxiliary spectral problem.Comment: 14 pages. Generalizes the results of article arXiv:1608.02415 to higher order eigenvectors. For better readability, we have copied the main definition

Canonical fitness model for simple scale-free graphs

We consider a fitness model assumed to generate simple graphs with power-law heavy-tailed degree sequence: P(k) \propto k^{-1-\alpha} with 0 < \alpha < 1, in which the corresponding distributions do not posses a mean. We discuss the situations in which the model is used to produce a multigraph and examine what happens if the multiple edges are merged to a single one and thus a simple graph is built. We give the relation between the (normalized) fitness parameter r and the expected degree \nu of a node and show analytically that it possesses non-trivial intermediate and final asymptotic behaviors. We show that the model produces P(k) \propto k^{-2} for large values of k independent of \alpha. Our analytical findings are confirmed by numerical simulations.Comment: 6 pages, 2 figures; published in Phys. Rev. E. To improve readability, formulas and text were added between Eq. (1) and (2

The fractional p-Laplacian emerging from homogenization of the random conductance model with degenerate ergodic weights and unbounded-range jumps

We study a general class of discrete $p$-Laplace operators in the random conductance model with long-range jumps and ergodic weights. Using a variational formulation of the problem, we show that under the assumption of bounded first moments and a suitable lower moment condition on the weights, the homogenized limit operator is a fractional $p$-Laplace operator. Under strengthened lower moment conditions, we can apply our insights also to the spectral homogenization of the discrete Laplace operator to the continuous fractional Laplace operator

2. GI FG SIDAR Graduierten-Workshop über Reaktive Sicherheit (SPRING)

SPRING ist eine wissenschaftliche Veranstaltung im Bereich der Reaktiven Sicherheit, die Nachwuchswissenschaftlern die Möglichkeit bietet, Ergebnisse eigener Arbeiten zu präsentieren und dabei Kontakte über die eigene Universität hinaus zu knüpfen. Nach der Premiere in Berlin fand Spring in 2007 in Dortmund statt. Die Vorträge deckten ein breites Spektrum ab, von noch laufenden Projekten, die ggf. erstmals einem breiteren Publikum vorgestellt werden, bis zu abgeschlossenen Forschungsarbeiten, die zeitnah auch auf Konferenzen präsentiert wurden bzw.\ werden sollen oder einen Schwerpunkt der eigenen Diplomarbeit oder Dissertation bilden. Die zugehörigen Abstracts sind in diesem technischen Bericht zusammengefaßt und wurden über die Universitätsbibliothek Dortmund elektronisch, zitierfähig und recherchierbar veröffentlicht. In dieser Ausgabe finden sich Beiträge zur den folgenden Themen: Vorfallsbehandlung und Web-Services, Dynamische Umgebungen und Verwundbarkeiten, Anomalie- und Protokollerkennung sowie zu verschiedenen Aspekten der IT-Frühwarnung: Malware-Erkennung und -Analyse, Sensorik und Kooperation

Dynamical localization and eigenstate localization in trap models

The one-dimensional random trap model with a power-law distribution of mean sojourn times exhibits a phenomenon of dynamical localization in the case where diffusion is anomalous: The probability to find two independent walkers at the same site, as given by the participation ratio, stays constant and high in a broad domain of intermediate times. This phenomenon is absent in dimensions two and higher. In finite lattices of all dimensions the participation ratio finally equilibrates to a different final value. We numerically investigate two-particle properties in a random trap model in one and in three dimensions, using a method based on spectral decomposition of the transition rate matrix. The method delivers a very effective computational scheme producing numerically exact results for the averages over thermal histories and initial conditions in a given landscape realization. Only a single averaging procedure over disorder realizations is necessary. The behavior of the participation ratio is compared to other measures of localization, as for example to the states' gyration radius, according to which the dynamically localized states are extended. This means that although the particles are found at the same site with a high probability, the typical distance between them grows. Moreover the final equilibrium state is extended both with respect to its gyration radius and to its Lyapunov exponent. In addition, we show that the phenomenon of dynamical localization is only marginally connected with the spectrum of the transition rate matrix, and is dominated by the properties of its eigenfunctions which differ significantly in dimensions one and three.Comment: 10 pages, 10 figures, submitted to EPJ

Evaluating the design of an audit data pseudonymizer using basic building blocks for anonymity

Using an audit data pseudonymization system as an example, we show how the APES approach for basic anonymity building blocks can be used to informally evaluate the design of a given anonymity system. As a by-product we obtain indications of the usefulness and (in)completeness of the APES building blocks approach

Call for Papers - Detection of Intrusions and Malware and Vulnerability Assessment (DIMVA 2004)

Die Fachgruppe SIDAR (Security - Intrusion Detection and Response) der Gesellschaft für Informatik e.V. beschäftigt sich mit der Erkennung und Beherrschung von Vorfällen der Informationssicherheit und veranstaltet vom 6.-7. Juli 2004 einen Workshop zum Thema Erkennung von Schutzzielverletzungen (Intrusion Detection), Malwarebekämpfung (Malicious Agents) sowie Ermittlung von Verwundbarkeiten (Vulnerability Assessment). Ziel des Workshops ist es, eine Übersicht zum Stand der Technik und Praxis in Industrie, Dienstleistung, Verwaltung und Wissenschaft im deutschsprachigen Raum zu geben. Insbesondere sollen Ergebnisse aus den Bereichen Forschung, Entwicklung und Integration vorgestellt, relevante Anwendungen aufgezeigt sowie neue Technologien und daraus resultierende Produktentwicklungen konzeptionell dargestellt werden. Rechtliche Rahmenbedingungen und wirtschaftliche Faktoren sollen ebenfalls betrachtet werden

Fraud Detection from a Business Perspective: Future Directions and Challenges

This contribution summarizes the state of the art of fraud detection in practice and shows the relations between the technology for fraud detection and intrusion detection. We identify prospective directions for further investigation and imminent challenges