Fast Structuring of Radio Networks for Multi-Message Communications

We introduce collision free layerings as a powerful way to structure radio networks. These layerings can replace hard-to-compute BFS-trees in many contexts while having an efficient randomized distributed construction. We demonstrate their versatility by using them to provide near optimal distributed algorithms for several multi-message communication primitives. Designing efficient communication primitives for radio networks has a rich history that began 25 years ago when Bar-Yehuda et al. introduced fast randomized algorithms for broadcasting and for constructing BFS-trees. Their BFS-tree construction time was $O(D \log^2 n)$ rounds, where $D$ is the network diameter and $n$ is the number of nodes. Since then, the complexity of a broadcast has been resolved to be $T_{BC} = \Theta(D \log \frac{n}{D} + \log^2 n)$ rounds. On the other hand, BFS-trees have been used as a crucial building block for many communication primitives and their construction time remained a bottleneck for these primitives. We introduce collision free layerings that can be used in place of BFS-trees and we give a randomized construction of these layerings that runs in nearly broadcast time, that is, w.h.p. in $T_{Lay} = O(D \log \frac{n}{D} + \log^{2+\epsilon} n)$ rounds for any constant $\epsilon>0$. We then use these layerings to obtain: (1) A randomized algorithm for gathering $k$ messages running w.h.p. in $O(T_{Lay} + k)$ rounds. (2) A randomized $k$-message broadcast algorithm running w.h.p. in $O(T_{Lay} + k \log n)$ rounds. These algorithms are optimal up to the small difference in the additive poly-logarithmic term between $T_{BC}$ and $T_{Lay}$. Moreover, they imply the first optimal $O(n \log n)$ round randomized gossip algorithm

Filaments from the galaxy distribution and from the velocity field in the local universe

The cosmic web that characterizes the large-scale structure of the Universe can be quantified by a variety of methods. For example, large redshift surveys can be used in combination with point process algorithms to extract long curvilinear filaments in the galaxy distribution. Alternatively, given a full 3D reconstruction of the velocity field, kinematic techniques can be used to decompose the web into voids, sheets, filaments and knots. In this paper we look at how two such algorithms - the Bisous model and the velocity shear web - compare with each other in the local Universe (within 100 Mpc), finding good agreement. This is both remarkable and comforting, given that the two methods are radically different in ideology and applied to completely independent and different data sets. Unsurprisingly, the methods are in better agreement when applied to unbiased and complete data sets, like cosmological simulations, than when applied to observational samples. We conclude that more observational data is needed to improve on these methods, but that both methods are most likely properly tracing the underlying distribution of matter in the Universe.Comment: 6 Pages, 2 figures, Submitted to MNRAS Letter

Ending the License to Exploit: Administrative Oversight of Consumer Contracts

Current approaches to consumer standard form contracts generally assume that aggrieved consumers can adequately detect and challenge exploitative terms and that vigilant courts can effectively scrutinize them. Some even believe that market forces and reputational constraints can deter firms from incorporating exploitative terms into their form contracts or dissuade them from actually relying on such terms. Criticizing these assumptions, this Article calls for a conceptual shift toward the problem of exploitative consumer contracts. This Article suggests supplementing the current means of addressing exploitation in consumer contracts with a dynamic preventive model of administrative oversight. Specifically, this Article proposes a professional system of public supervision over the content of consumer form contracts. This Article demonstrates how such a mechanism, if shrewdly designed, can cost-effectively tackle the widespread use of unfair, unconscionable, or legally invalid terms. Although not a panacea, the proposed regulatory regime has the promise of shifting the main burden of tackling exploitative boilerplate from the currently feeble and ineffective system of private enforcement to a sophisticated and robust scheme of administrative scrutiny

Interferences in the density of two Bose-Einstein condensates consisting of identical or different atoms

The density of two {\it initially independent} condensates which are allowed to expand and overlap can show interferences as a function of time due to interparticle interaction. Two situations are separately discussed and compared: (1) all atoms are identical and (2) each condensate consists of a different kind of atoms. Illustrative examples are presented.Comment: 12 pages, 3 figure

A kinematic classification of the cosmic web

A new approach for the classification of the cosmic web is presented. In extension of the previous work of Hahn et al. (2007) and Forero-Romero et al. (2009) the new algorithm is based on the analysis of the velocity shear tensor rather than the gravitational tidal tensor. The procedure consists of the construction of the the shear tensor at each (grid) point in space and the evaluation of its three eigenvectors. A given point is classified to be either a void, sheet, filament or a knot according to the number of eigenvalues above a certain threshold, 0, 1, 2, or 3 respectively. The threshold is treated as a free parameter that defines the web. The algorithm has been applied to a dark matter only, high resolution simulation of a box of side-length 64$h^{-1}$Mpc and N = $1024^3$ particles with the framework of the WMAP5/LCDM model. The resulting velocity based cosmic web resolves structures down to <0.1$h^{-1}$Mpc scales, as opposed to the ~1$h^{-1}$Mpc scale of the tidal based web. The under-dense regions are made of extended voids bisected by planar sheets, whose density is also below the mean. The over-dense regions are vastly dominated by the linear filaments and knots. The resolution achieved by the velocity based cosmic web provides a platform for studying the formation of halos and galaxies within the framework of the cosmic web.Comment: 8 pages, 4 Figures, MNRAS Accepted 2012 June 19. Received 2012 May 10; in original form 2011 August 2

Planes of satellite galaxies and the cosmic web

Recent observational studies have demonstrated that the majority of satellite galaxies tend to orbit their hosts on highly flattened, vast, possibly co-rotating planes. Two nearly parallel planes of satellites have been confirmed around the M31 galaxy and around the Centaurus A galaxy, while the Milky Way also sports a plane of satellites. It has been argued that such an alignment of satellites on vast planes is unexpected in the standard ({\Lambda}CDM) model of cosmology if not even in contradiction to its generic predictions. Guided by {\Lambda}CDM numerical simulations, which suggest that satellites are channeled towards hosts along the axis of the slowest collapse as dictated by the ambient velocity shear tensor, we re-examine the planes of local satellites systems within the framework of the local shear tensor derived from the Cosmicflows-2 dataset. The analysis reveals that the Local Group and Centaurus A reside in a filament stretched by the Virgo cluster and compressed by the expansion of the Local Void. Four out of five thin planes of satellite galaxies are indeed closely aligned with the axis of compression induced by the Local Void. Being the less massive system, the moderate misalignment of the Milky Way's satellite plane can likely be ascribed to its greater susceptibility to tidal torques, as suggested by numerical simulations. The alignment of satellite systems in the local universe with the ambient shear field is thus in general agreement with predictions of the {\Lambda}CDM model.Comment: 9 pages, 3 figures, 3 tables. Accepted by MNRAS, 9 June 201

Detection of arbitrarily large dynamic ground motions with a dense high-rate GPS network

We describe the detection of teleseismic surface waves from the 3 November 2002 Mw 7.9 Denali fault earthquake in Alaska with a dense network of 1 Hz GPS stations in southern California, about 3900 km from the event. Relative horizontal displacements with amplitudes in excess of 15 mm and duration of 700 seconds agree with integrated velocities recorded by nearby broadband seismometers with an rms difference of 2–3 mm. The displacements are derived from independent 1 Hz instantaneous positions demonstrating that a GPS network can provide direct measurements of arbitrarily large dynamic and static ground horizontal displacements at periods longer than 1 s and amplitudes above 2 mm, with an inherent precision (signal to noise) that improves indefinitely with amplitude without clipping and in real time. High‐rate, real‐time GPS networks can enhance earthquake detection and seismic risk mitigation and support other applications such as intelligent transportation and civil infrastructure monitoring