Randomized rumour spreading: The effect of the network topology

We consider the popular and well-studied push model, which is used to spread information in a given network with n vertices. Initially, some vertex owns a rumour and passes it to one of its neighbours, which is chosen randomly. In each of the succeeding rounds, every vertex that knows the rumour informs a random neighbour. It has been shown on various network topologies that this algorithm succeeds in spreading the rumour within O(log n) rounds. However, many studies are quite coarse and involve huge constants that do not allow for a direct comparison between different network topologies. In this paper, we analyse the push model on several important families of graphs, and obtain tight runtime estimates. We first show that, for any almost-regular graph on n vertices with small spectral expansion, rumour spreading completes after log2 n + log n+o(log n) rounds with high probability. This is the first result that exhibits a general graph class for which rumour spreading is essentially as fast as on complete graphs. Moreover, for the random graph G(n,p) with p=c log n/n, where c > 1, we determine the runtime of rumour spreading to be log2 n + γ (c)log n with high probability, where γ(c) = clog(c/(c-1)). In particular, this shows that the assumption of almost regularity in our first result is necessary. Finally, for a hypercube on n=2d vertices, the runtime is with high probability at least (1+β) .. (log2 n + log n), where β > 0. This reveals that the push model on hypercubes is slower than on complete graphs, and thus shows that the assumption of small spectral expansion in our first result is also necessary. In addition, our results combined with the upper bound of O(log n) for the hypercube (see [11]) imply that the push model is faster on hypercubes than on a random graph G(n, clog n/n), where c is sufficiently close to 1

A coinductive semantics of the Unlimited Register Machine

We exploit (co)inductive specifications and proofs to approach the evaluation of low-level programs for the Unlimited Register Machine (URM) within the Coq system, a proof assistant based on the Calculus of (Co)Inductive Constructions type theory. Our formalization allows us to certify the implementation of partial functions, thus it can be regarded as a first step towards the development of a workbench for the formal analysis and verification of both converging and diverging computations

Distributional chaos for operators with full scrambled sets

In this article we answer in the negative the question of whether hypercyclicity is sufficient for distributional chaos for a continuous linear operator (we even prove that the mixing property does not suffice). Moreover, we show that an extremal situation is possible: There are (hypercyclic and non-hypercyclic) operators such that the whole space consists, except zero, of distributionally irregular vectors.The research of first and third author was supported by MEC and FEDER, project MTM2010-14909 and by GV, Project PROMETEO/2008/101. The research of second author was supported by the Marie Curie European Reintegration Grant of the European Commission under grant agreement no. PERG08-GA-2010-272297. The financial support of these institutions is hereby gratefully acknowledged. We also want to thank X. Barrachina for pointing out to us a gap in the proof of a previous version of Theorem 3.1.Martínez Jiménez, F.; Oprocha, P.; Peris Manguillot, A. (2013). Distributional chaos for operators with full scrambled sets. Mathematische Zeitschrift. 274(1-2):603-612. https://doi.org/10.1007/s00209-012-1087-8S6036122741-2Banks, J., Brooks, J., Cairns, G., Davis, G., Stacey, P.: On Devaney’s definition of chaos. Am. Math. Monthly 99(4), 332–334 (1992)Barrachina, X., Peris, A.: Distributionally chaotic translation semigroups. J. Differ. Equ. Appl. 18, 751–761 (2012)Beauzamy, B.: Introduction to Operator Theory and Invariant Subspaces. North-Holland, Amsterdam (1988)Bermúdez, T., Bonilla, A., Martínez-Giménez, F., Peris, A.: Li–Yorke and distributionally chaotic operators. J. Math. Anal. Appl. 373, 83–93 (2011)Bayart, F., Matheron, E.: Dynamics of linear operators, vol. 179. Cambridge University Press, London(2009).Costakis, G., Sambarino, M.: Topologically mixing hypercyclic operators. Proc. Am. Math. Soc. 132, 385–389 (2004)Devaney, R.L.: An introduction to chaotic dynamical systems, 2nd edn. Addison-Wesley Studies in Nonlinearity. Addison-Wesley Publishing Company Advanced Book Program. Redwood City (1989)Feldman, N.: Hypercyclicity and supercyclicity for invertible bilateral weighted shifts. Proc. Am. Math. Soc. 131, 479–485 (2003)Grosse-Erdmann, K.-G.: Hypercyclic and chaotic weighted shifts. Studia Math. 139(1), 47–68 (2000)Grosse-Erdmann, K.-G., Peris Manguillot, A.: Linear Chaos. Universitext, Springer, London (2011)Hou, B., Cui, P., Cao, Y.: Chaos for Cowen-Douglas operators. Proc. Am. Math. Soc 138, 929–936 (2010)Hou, B., Tian, G., Shi, L.: Some dynamical properties for linear operators. Ill. J. Math. 53, 857–864 (2009)Li, T.Y., Yorke, J.A.: Period three implies chaos. Am. Math. Monthly 82(10), 985–992 (1975)Martínez-Giménez, F., Oprocha, P., Peris, A.: Distributional chaos for backward shifts. J. Math. Anal. Appl. 351, 607–615 (2009)Müller, V., Peris, A.: A Problem of Beauzamy on Irregular Operators (2011). (Preprint)Oprocha, P.: Distributional chaos revisited. Trans. Am. Math. Soc. 361, 4901–4925 (2009)Oprocha, P.: A quantum harmonic oscillator and strong chaos. J. Phys. A 39(47), 14559–14565 (2006)Schweizer, B., Smítal, J.: Measures of chaos and a spectral decomposition of dynamical systems on the interval. Trans. Am. Math. Soc. 344(2), 737–754 (1994)Wu, X., Zhu, P.: The principal measure of a quantum harmonic oscillator. J. Phys. A 44(505101), 6 (2011

A calculation of the BBB_{B} parameter in the static limit

We calculate the $B_{B}$ parameter, relevant for $\overline{B}^0$ -- $B^0$ mixing, from a lattice gauge theory simulation at $\beta = 6.0$. The bottom quarks are simulated in the static theory, the light quarks with Wilson fermions. Improved smearing functions produced by a variational technique, MOST, are used to reduce statistical errors and minimize excited-state contamination of the ground-state signal. We obtain $B_B(4.33 GeV) = 0.98^{+4}_{-4}$ (statistical) $^{+3}_{-18}$ (systematic) which corresponds to $\widehat{B}_B = 1.40^{+6}_{-6}$ (statistical) $^{+4}_{-26}$ (systematic) for the one-loop renormalization-scheme-independent parameter. The systematic errors include the uncertainty due to alternative (less favored) treatments of the perturbatively-calculated mixing coefficients; this uncertainty is at least as large as residual differences between Wilson-static and clover-static results. Our result agrees with extrapolations of results from relativistic (Wilson) heavy quark simulations.Comment: 39 pages (REVTeX) including 10 figures (PostScript); Final version accepted for publication: Added new section for clarity; Included comparison to recent results by other groups; slight numerical changes; Essential conclusions remain the sam

Electrocatalytic oxidation of methanol on CoNi electrodeposited materials

Cobalt-nickel bimetallic materials electrodeposited on Si/Ti/Ni substrates were evaluated for the oxidation of methanol in alkaline media. CoNi samples were prepared potentiostatically selecting conditions adequate to achieve the desired Co/Ni ratio. All samples were characterized by X-ray fluorescence and cyclic voltammetry to determine their composition and electrochemical behaviour. The electrocatalytical performance of prepared samples was evaluated also by cyclic voltammetry using methanol solutions in alkaline media. Material composition, methanol and NaOH concentration, and temperature were the variables studied. The results indicate that a cobalt excess inhibits the methanol oxidation. In the same way, a significant enhancement of the oxidation current was observed on increasing the NaOH concentration up to 0.5 M, but for higher concentrations the electrocatalytic performance of these materials decreases. With regard to the increase of MeOH concentration or temperature, both variables are related to an improvement of the electrocatalytic performance. Finally, the effect of platinum skin on the CoNi deposits was evaluated, concluding that it favours MeOH oxidation but does not protect the substrate surface from the damage exerted by excessive NaOH concentration

Working the interdisciplinary integration: Assesing a bridge activity between two subjects of Environmental Sciences Degree

[EN] This paper describes how an interdicisciplinar group of teachers implements a bridge-activity between two subjects in 2nd course of Environmental Sciences degree. The main goal is to develop both generic and specific competencies related to interdisciplinary work. Students evaluate if these innovation proposals are adequate to develop these skills and what impact produces in their own learning. As main conclusion, to note that coordination between teachers to interconnect subjects within degrees is a very appropriate intervention to provide students with a comprehensive education and skills, they value these activities very positively.[ES] El presente trabajo describe cómo un grupo interdicisciplinar de docentes implanta una actividad puente entre dos asignaturas del 2º curso de grado de Ciencias Ambientales, con el objetivo de desarrollar competencias tanto genéricas como específicas relacionadas con la interdiciplinariedad. Los alumnos evalúan si estas propuestas de innovación docente son adecuadas para desarrollar dichas competencias y qué impacto producen en su propio aprendizaje. Como conclusión principal, destacar que la coordinación entre docentes y el trabajo para interconectar asignaturas dentro de los grados es un ámbito de intervención muy oportuno para dotar a los estudiantes de una formación en competencias e integral, ya que ellos valoran este tipo de actividades muy positivamente.Sandín Vázquez, M.; Lazo Vitoria, X.; Giménez Baldazo, M.; Rodríguez Martínez, M. (2016). Trabajando la integración interdisciplinar: Evaluación de una actividad puente entre dos asignaturas del Grado en Ciencias Ambientales. REDU. Revista de Docencia Universitaria. 14(1):245-260. doi:10.4995/redu.2016.5907.SWORD24526014

Heavy-Light Meson Decay Constant from QCD Sum Rules in Three-Loop Approximation

In this paper we compute the decay constant of the pseudo-scalar heavy-light mesons in the heavy quark effective theory framework of QCD sum rules. In our analysis we include the recently evaluated three-loop result of order $\alpha_s^2$ for the heavy-light current correlator. The value of the bottom quark mass, which essentially limits the accuracy of the sum rules for $B$ meson, is extracted from the nonrelativistic sum rules for $\Upsilon$ resonances in the next-to-next-to-leading approximation. We find stability of our result with respect to all types of corrections and the specific form of the sum rule which reduces the uncertainty. Our results $f_B=206\pm 20$ MeV and $f_D=195\pm 20$ MeV for the $B$ and $D$ meson decay constants are in impressive agreement with recent lattice calculations.Comment: minor editorial changes, references added, to appear in PR