Community-aware network sparsification

Network sparsification aims to reduce the number of edges of a network while maintaining its structural properties; such properties include shortest paths, cuts, spectral measures, or network modularity. Sparsification has multiple applications, such as, speeding up graph-mining algorithms, graph visualization, as well as identifying the important network edges. In this paper we consider a novel formulation of the network-sparsification problem. In addition to the network, we also consider as input a set of communities. The goal is to sparsify the network so as to preserve the network structure with respect to the given communities. We introduce two variants of the community-aware sparsification problem, leading to sparsifiers that satisfy different connectedness community properties. From the technical point of view, we prove hardness results and devise effective approximation algorithms. Our experimental results on a large collection of datasets demonstrate the effectiveness of our algorithms.https://epubs.siam.org/doi/10.1137/1.9781611974973.48Accepted manuscrip

The Lorentz force in atmospheres of CP stars: θ\theta Aurigae

Several dynamical processes may induce considerable electric currents in the atmospheres of magnetic chemically peculiar (CP) stars. The Lorentz force, which results from the interaction between the magnetic field and the induced currents, modifies the atmospheric structure and induces characteristic rotational variability of the hydrogen Balmer lines. To study this phenomena we have initiated a systematic spectroscopic survey of the Balmer lines variation in magnetic CP stars. In this paper we continue presentation of results of the program focusing on the high-resolution spectral observations of A0p star \aur (HD 40312). We have detected a significant variability of the H$\alpha$, H$\beta$, and H$\gamma$ spectral lines during full rotation cycle of the star. This variability is interpreted in the framework of the model atmosphere analysis, which accounts for the Lorentz force effects. Both the inward and outward directed Lorentz forces are considered under the assumption of the axisymmetric dipole or dipole+quadrupole magnetic field configurations. We demonstrate that only the model with the outward directed Lorentz force in the dipole+quadrupole configuration is able to reproduce the observed hydrogen line variation. These results present new strong evidences for the presence of non-zero global electric currents in the atmosphere of an early-type magnetic star.Comment: 10 figure

Darwin-Riemann problems in general relativity

A review is given of recent results about the computation of irrotational Darwin-Riemann configurations in general relativity. Such configurations are expected to represent fairly well the late stages of inspiralling binary neutron stars.Comment: 20 pages, 11 PostScript figures, uses PTPTeX, to appear in the Proceedings of Yukawa International Seminar 99 "Black Holes and Gravitational Waves", edited by T. Nakamura & H. Kodama, Prog. Theor. Phys. Supp

Distributed Dominating Set Approximations beyond Planar Graphs

The Minimum Dominating Set (MDS) problem is one of the most fundamental and challenging problems in distributed computing. While it is well-known that minimum dominating sets cannot be approximated locally on general graphs, over the last years, there has been much progress on computing local approximations on sparse graphs, and in particular planar graphs. In this paper we study distributed and deterministic MDS approximation algorithms for graph classes beyond planar graphs. In particular, we show that existing approximation bounds for planar graphs can be lifted to bounded genus graphs, and present (1) a local constant-time, constant-factor MDS approximation algorithm and (2) a local $\mathcal{O}(\log^*{n})$-time approximation scheme. Our main technical contribution is a new analysis of a slightly modified variant of an existing algorithm by Lenzen et al. Interestingly, unlike existing proofs for planar graphs, our analysis does not rely on direct topological arguments.Comment: arXiv admin note: substantial text overlap with arXiv:1602.0299

Searching for periodic sources with LIGO

We investigate the computational requirements for all-sky, all-frequency searches for gravitational waves from spinning neutron stars, using archived data from interferometric gravitational wave detectors such as LIGO. These sources are expected to be weak, so the optimal strategy involves coherent accumulaton of signal-to-noise using Fourier transforms of long stretches of data (months to years). Earth-motion-induced Doppler shifts, and intrinsic pulsar spindown, will reduce the narrow-band signal-to-noise by spreading power across many frequency bins; therefore, it is necessary to correct for these effects before performing the Fourier transform. The corrections can be implemented by a parametrized model, in which one does a search over a discrete set of parameter values. We define a metric on this parameter space, which can be used to determine the optimal spacing between points in a search; the metric is used to compute the number of independent parameter-space points Np that must be searched, as a function of observation time T. The number Np(T) depends on the maximum gravitational wave frequency and the minimum spindown age tau=f/(df/dt) that the search can detect. The signal-to-noise ratio required, in order to have 99% confidence of a detection, also depends on Np(T). We find that for an all-sky, all-frequency search lasting T=10^7 s, this detection threshhold is at a level of 4 to 5 times h(3/yr), where h(3/yr) is the corresponding 99% confidence threshhold if one knows in advance the pulsar position and spin period.Comment: 18 pages, LaTeX, 12 PostScript figures included using psfig. Submitted to Phys. Rev.

The Lorentz force in atmospheres of CP stars: 56 Arietis

The presence of electric currents in the atmospheres of magnetic chemically peculiar (mCP) stars could bring important theoretical constrains about the nature and evolution of magnetic field in these stars. The Lorentz force, which results from the interaction between the magnetic field and the induced currents, modifies the atmospheric structure and induces characteristic rotational variability of pressure-sensitive spectroscopic features, that can be analysed using phase-resolved spectroscopic observations. In this work we continue the presentation of results of the magnetic pressure studies in mCP stars focusing on the high-resolution spectroscopic observations of Bp star 56Ari. We have detected a significant variability of the Halpha, Hbeta, and Hgamma spectral lines during full rotation cycle of the star. Then these observations are interpreted in the framework of the model atmosphere analysis, which accounts for the Lorentz force effects. We used the LLmodels stellar model atmosphere code for the calculation of the magnetic pressure effects in the atmosphere of 56Ari taking into account realistic chemistry of the star and accurate computations of the microscopic plasma properties. The Synth3 code was employed to simulate phase-resolved variability of Balmer lines. We demonstrate that the model with the outward-directed Lorentz force in the dipole+quadrupole configuration is likely to reproduce the observed hydrogen lines variation. These results present strong evidences for the presence of non-zero global electric currents in the atmosphere of this early-type magnetic star.Comment: Accepted by A&A, 9 pages, 7 figures, 2 table

Hierarchical Models for Independence Structures of Networks

We introduce a new family of network models, called hierarchical network models, that allow us to represent in an explicit manner the stochastic dependence among the dyads (random ties) of the network. In particular, each member of this family can be associated with a graphical model defining conditional independence clauses among the dyads of the network, called the dependency graph. Every network model with dyadic independence assumption can be generalized to construct members of this new family. Using this new framework, we generalize the Erd\"os-R\'enyi and beta-models to create hierarchical Erd\"os-R\'enyi and beta-models. We describe various methods for parameter estimation as well as simulation studies for models with sparse dependency graphs.Comment: 19 pages, 7 figure