The Power of Two Choices in Distributed Voting

Distributed voting is a fundamental topic in distributed computing. In pull voting, in each step every vertex chooses a neighbour uniformly at random, and adopts its opinion. The voting is completed when all vertices hold the same opinion. On many graph classes including regular graphs, pull voting requires $\Theta(n)$ expected steps to complete, even if initially there are only two distinct opinions. In this paper we consider a related process which we call two-sample voting: every vertex chooses two random neighbours in each step. If the opinions of these neighbours coincide, then the vertex revises its opinion according to the chosen sample. Otherwise, it keeps its own opinion. We consider the performance of this process in the case where two different opinions reside on vertices of some (arbitrary) sets $A$ and $B$, respectively. Here, $|A| + |B| = n$ is the number of vertices of the graph. We show that there is a constant $K$ such that if the initial imbalance between the two opinions is ?$\nu_0 = (|A| - |B|)/n \geq K \sqrt{(1/d) + (d/n)}$, then with high probability two sample voting completes in a random $d$ regular graph in $O(\log n)$ steps and the initial majority opinion wins. We also show the same performance for any regular graph, if $\nu_0 \geq K \lambda_2$ where $\lambda_2$ is the second largest eigenvalue of the transition matrix. In the graphs we consider, standard pull voting requires $\Omega(n)$ steps, and the minority can still win with probability $|B|/n$.Comment: 22 page

Extracting information from short messages

Much currently transmitted information takes the form of e-mails or SMS text messages and so extracting information from such short messages is increasingly important. The words in a message can be partitioned into the syntactic structure, terms from the domain of discourse and the data being transmitted. This paper describes a light-weight Information Extraction component which uses pattern matching to separate the three aspects: the structure is supplied as a template; domain terms are the metadata of a data source (or their synonyms), and data is extracted as those words matching placeholders in the templates

Effect of organic, low-input and conventional production systems on yield and diseases in winter barley

The effect of organic, low-input and conventional management practices on barley yield and disease incidence was assessed in field trials over two years. Conventional fertility management (based on mineral fertiliser applications) and conventional crop protection (based on chemosynthetic pesticides) significantly increased the yield of winter barley as compared to organic fertility and crop protection regimes. Severity of leaf blotch (Rhynchosporium secalis) was highest under organic fertility and crop protection management and was correlated inversely with yield. For mildew (Erysiphe graminis), an interaction between fertility management and crop protection was detected. Conventional crop protection reduced severity of the disease, only under conventional fertility management. Under organic fertility management, incidence of mildew was low and application of synthetic pesticides in “low input” production systems had no significant effect on disease severity

Quantum Melting of the Charge Density Wave State in 1T-TiSe2

We report a Raman scattering study of low-temperature, pressure-induced melting of the CDW phase of 1T-TiSe2. Our Raman scattering measurements reveal that the collapse of the CDW state occurs in three stages: (i) For P<5 kbar, the pressure dependence of the CDW amplitude mode energies and intensities are indicative of a ``crystalline'' CDW regime; (ii) for 5 < P < 25 kbar, there is a decrease in the CDW amplitude mode energies and intensities with increasing pressure that suggests a regime in which the CDW softens, and may decouple from the lattice; and (iii) for P>25 kbar, the absence of amplitude modes reveals a melted CDW regime.Comment: 5 pages, 4 figure

The Local Group: The Ultimate Deep Field

Near-field cosmology -- using detailed observations of the Local Group and its environs to study wide-ranging questions in galaxy formation and dark matter physics -- has become a mature and rich field over the past decade. There are lingering concerns, however, that the relatively small size of the present-day Local Group ($\sim 2$ Mpc diameter) imposes insurmountable sample-variance uncertainties, limiting its broader utility. We consider the region spanned by the Local Group's progenitors at earlier times and show that it reaches $3' \approx 7$ co-moving Mpc in linear size (a volume of $\approx 350\,{\rm Mpc}^3$) at $z=7$. This size at early cosmic epochs is large enough to be representative in terms of the matter density and counts of dark matter halos with $M_{\rm vir}(z=7) \lesssim 2\times 10^{9}\,M_{\odot}$. The Local Group's stellar fossil record traces the cosmic evolution of galaxies with $10^{3} \lesssim M_{\star}(z=0) / M_{\odot} \lesssim 10^{9}$ (reaching $M_{1500} > -9$ at $z\sim7$) over a region that is comparable to or larger than the Hubble Ultra-Deep Field (HUDF) for the entire history of the Universe. It is highly complementary to the HUDF, as it probes much fainter galaxies but does not contain the intrinsically rarer, brighter sources that are detectable in the HUDF. Archaeological studies in the Local Group also provide the ability to trace the evolution of individual galaxies across time as opposed to evaluating statistical connections between temporally distinct populations. In the JWST era, resolved stellar populations will probe regions larger than the HUDF and any deep JWST fields, further enhancing the value of near-field cosmology.Comment: 6 pages, 5 figures; MNRAS Letters, in pres