Distributed Symmetry Breaking in Hypergraphs

Fundamental local symmetry breaking problems such as Maximal Independent Set (MIS) and coloring have been recognized as important by the community, and studied extensively in (standard) graphs. In particular, fast (i.e., logarithmic run time) randomized algorithms are well-established for MIS and $\Delta +1$-coloring in both the LOCAL and CONGEST distributed computing models. On the other hand, comparatively much less is known on the complexity of distributed symmetry breaking in {\em hypergraphs}. In particular, a key question is whether a fast (randomized) algorithm for MIS exists for hypergraphs. In this paper, we study the distributed complexity of symmetry breaking in hypergraphs by presenting distributed randomized algorithms for a variety of fundamental problems under a natural distributed computing model for hypergraphs. We first show that MIS in hypergraphs (of arbitrary dimension) can be solved in $O(\log^2 n)$ rounds ($n$ is the number of nodes of the hypergraph) in the LOCAL model. We then present a key result of this paper --- an $O(\Delta^{\epsilon}\text{polylog}(n))$-round hypergraph MIS algorithm in the CONGEST model where $\Delta$ is the maximum node degree of the hypergraph and $\epsilon > 0$ is any arbitrarily small constant. To demonstrate the usefulness of hypergraph MIS, we present applications of our hypergraph algorithm to solving problems in (standard) graphs. In particular, the hypergraph MIS yields fast distributed algorithms for the {\em balanced minimal dominating set} problem (left open in Harris et al. [ICALP 2013]) and the {\em minimal connected dominating set problem}. We also present distributed algorithms for coloring, maximal matching, and maximal clique in hypergraphs.Comment: Changes from the previous version: More references adde

Reading the geographies of post-war British film culture through the reception of French film

This paper examines the ways in which British specialist film culture anticipated and received the resumed supply of French films at the end of the Second World War. It finds that in serious film journalism and within the rapidly expanding film society movement, new French cinema was the focus of at least as much British attention as Italian neo-realism – the European cinema more famously associated with the era. The paper posits that a number of factors, including anti-Americanism, combined to position the delayed wartime and immediate post-war French releases as a site of impossible expectations and subsequent interpretative difficulty for British cinephiles. In particular, through a case study of the local mediation of French cinema in the English city of Nottingham, this paper considers the role of published criticism for setting the local viewing frame within the provincial film society movement. By tracing the tensions surrounding the circulation of film prints, information, and opinion relating to these prestigious cultural imports, it becomes possible to gain greater insight into both the range of nationally specific meanings attributed to the imported films and the geographic and cultural inequalities at work within the film culture of the country of reception

Detailed study of BBN implications of neutrino oscillation generated neutrino asymmetries in some four neutrino models

We re-examine the evolution of neutrino asymmetries in several four neutrino models. The first case involves the direct creation of $L_{\nu_e}$ by $\nu_e \leftrightarrow \nu_s$ oscillations. In the second case, we consider the mass hierarchy $m_{\nu_\tau} \gg m_{\nu_\mu}, m_{\nu_e}, m_{\nu_s}$ where $\nu_\tau \leftrightarrow \nu_s$ oscillations generate a large $L_{\nu_\tau}$ and some of this asymmetry is converted into $L_{\nu_e}$ by $\nu_{\tau} \leftrightarrow \nu_{e}$ oscillations. We estimate the implications for BBN for a range of cosmologically interesting $\delta m^2$ values. The present paper improves on previous published work by taking into account the finite repopulation rate and the time dependence of the distortions to the neutrino momentum distributions. The treatment of chemical decoupling is also improved.Comment: Expanded discussion on the sign of the neutrino asymmetr

Phase Coherence and Control of Stored Photonic Information

We report the demonstration of phase coherence and control for the recently developed "light storage" technique. Specifically, we use a pulsed magnetic field to vary the phase of atomic spin excitations which result from the deceleration and storing of a light pulse in warm Rb vapor. We then convert the spin excitations back into light and detect the resultant phase shift in an optical interferometric measurement. The coherent storage of photon states in matter is essential for the practical realization of many basic concepts in quantum information processing.Comment: 5 pages, 3 figures. Submitted to Phys. Rev. Let

The Intrinsic Gluon Component of the Nucleon

Using an intrinsic parton model we estimate the rough shape and size of the intrinsic gluon component of the nucleon, corresponding to an energy scale $Q$ of the order \lqcd. It is nearly as hard in shape as the valence quark, while its size accounts for a quarter of the nucleon momentum. Both are in qualitative agreement with the input leading twist gluon distribution assumed by Gl\"uck, Reya and Vogt at this scale in order to reproduce the observed distributions at Q^2 \gsim 1 GeV$^2$ via perturbative QCD evolution.Comment: Latex file (8 pages

On the sign of the neutrino asymmetry induced by active-sterile neutrino oscillations in the early Universe

We deal with the problem of the final sign of the neutrino asymmetry generated by active-sterile neutrino oscillations in the Early Universe solving the full momentum dependent quantum kinetic equations. We study the parameter region $10^{-2} \stackrel{<}{\sim} |\delta m^2|/eV^2\le 10^3$. For a large range of $\sin^2 2\theta_0$ values the sign of the neutrino asymmetry is fixed and does not oscillate. For values of mixing parameters in the region $10^{-6}\stackrel{<}{\sim}\sin^{2}2\theta_{0}\stackrel{<}{\sim} 3\times 10^{-4} ({\rm eV}^{2}/|\delta m^{2}|)$, the neutrino asymmetry appears to undergo rapid oscillations during the period where the exponential growth occurs. Our numerical results indicate that the oscillations are able to change the neutrino asymmetry sign. The sensitivity of the solutions and in particular of the final sign of lepton number to small changes in the initial conditions depends whether the number of oscillations is high enough. It is however not possible to conclude whether this effect is induced by the presence of a numerical error or is an intrinsic feature. As the amplitude of the statistical fluctuations is much lower than the numerical error, our numerical analysis cannot demonstrate the possibility of a chaotical generation of lepton domains. In any case this possibility is confined to a special region in the space of mixing parameters and it cannot spoil the compatibility of the $\nu_{\mu}\leftrightarrow\nu_{s}$ solution to the neutrino atmospheric data obtained assuming a small mixing of the $\nu_{s}$ with an ${\rm eV}-\tau$ neutrino.Comment: Typo's corrected, accepted for publication in Phys.Rev.

Young people, crime and school exclusion: a case of some surprises

During the 1990s the number of young people being permanently excluded from schools in England and Wales increased dramatically from 2,910 (1990/91) to a peak of 12,700 (1996/97). Coinciding with this rise was a resurgence of the debate centring on lawless and delinquent youth. With the publication of Young People and Crime (Graham and Bowling 1995) and Misspent Youth (Audit Commission 1996) the 'common sense assumption' that exclusion from school inexorably promoted crime received wide support, with the school excludee portrayed as another latter day 'folk devil'. This article explores the link between school exclusion and juvenile crime, and offers some key findings from a research study undertaken with 56 young people who had experience of being excluded from school. Self-report interview questions reveal that whilst 40 of the young people had offended, 90% (36) reported that the onset of their offending commenced prior to their first exclusion. Moreover, 50 (89.2% of the total number of young people in the sample), stated that they were no more likely to offend subsequent to being excluded and 31 (55.4%) stated that they were less likely to offend during their exclusion period. Often, this was because on being excluded, they were 'grounded' by their parents

Higgs-Boson Production Induced by Bottom Quarks

Bottom quark-induced processes are responsible for a large fraction of the LHC discovery potential, in particular for supersymmetric Higgs bosons. Recently, the discrepancy between exclusive and inclusive Higgs boson production rates has been linked to the choice of an appropriate bottom factorization scale. We investigate the process kinematics at hadron colliders and show that it leads to a considerable decrease in the bottom factorization scale. This effect is the missing piece needed to understand the corresponding higher order results. Our results hold generally for charged and for neutral Higgs boson production at the LHC as well as at the Tevatron. The situation is different for single top quark production, where we find no sizeable suppression of the factorization scale. Turning the argument around, we can specify how large the collinear logarithms are, which can be resummed using the bottom parton picture.Comment: 18 page