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21 Sep 2012: 1 Exabyte = 260 bytes 1018 bytes encodes: one day’s worth of data from the new SKA.

4 Sep 2012: This means that if you start with a new deck of cards, freshly unwrapped, and then shuffle once every 5 seconds (night and day), it will take you 1.237 x ... I hope you enjoy question #13 on Example Sheet 1 (which is a new question this year).

15 Aug 2012: The now standard technology of unoriented percolation is notby itself enough to answer such questions, and new ideas are needed.

7 Jun 2012: We emphasize asymptotic properties of product-form distributions and we present some new results on the stability of acknowledgement based random access schemes. ... We outline the results of Mikhailov (1979) and Hajek (1982a) on random access schemes

3 Aug 2012: Here we restrictattention to Brownian motion; the new feature is the effect of the drift function f.

15 Aug 2012: Cohen, E. G. D., New types of diusions in lattice gas cellular automata, Micro-scopic Simulations of Complex Hydrodynamical Phenomena (M. ... 137{152. Stochastic Pin-Ball 99. Cohen, E. G. D. and Wang, F., New results for diusion in Lorentz lattice gas

3 Sep 2012: nonparametric minimax testfor infinite-dimensional null- and alternative hypotheses, and new lower bounds forL 2-adaptive confidence sets. ... theory. See Proposition 1and Theorem 5 below for details. We also present a new lower bound which implies

19 Jan 2012: Academic Press, New York. Mastran DV, Thomas CJ (1973) Decision rules for attacking targets ofopportunity.

15 Aug 2012: Year # small states states with Qi < qi original quota qi new quota Qi. ... 2, 2nd edn,. Wiley, New York, 1971. 3. Grimmett, G. R., Stirzaker, D.

10 Nov 2012: Finally, we present a new strategyfor fitting d13C records with smooth functions andconfidence bands. ... New material from Leg 177 Sites 1088. Figure 5. Assemblage of d13C isotopic records determined from benthic foraminifera.

20 Apr 2012: Collisions of Random Walks. Martin T. Barlow Yuval Peres† Perla Sousi‡. April 10, 2012. Abstract. A recurrent graph G has the infinite collision property if two independent randomwalks on G, started at the same point, collide infinitely often a.s

6 Mar 2012: A main contribution of this article is the development of a new approachto testing problems of the kind (2) based on concentration properties of linear cen-tered kernel-type density estimators,

26 Apr 2012: X. . A new search game on 6 locations. When a player makes a tour in AW he chooses it at random.Might something else be better? ... Consider a new game, in which at each new step (of 3 old steps)each player makes a tour of his

15 Aug 2012: mension, Quantum Information Processing. 1, 345–354, (2002). [3] N. Konno, A new type of limit theorems for. ... University Press, (2001). [6] P. Billingsley, Probability and Measure, 3rd. edn, Wiley, New York, (1995).

6 Sep 2012: O Diekmann SA van Gils SM Verduyn Lunel and H O Walther Delay Equations Functional Complex and Nonlinear Analysis Springer Verlag New York. ... bridge HR Varian Microeconomic Analysis third edition Norton New. York JG Wardrop Some theoretical aspects of

15 Aug 2012: Physics 22 89 .[9] G. R. Grimmett, Percolation Springer, New York .

1 Jun 2012: 24, 25], who called these new basis functions needlets—wasemployed to construct risk-adaptive estimators for f (x), x Sd, by a local needletseries with support concentrated in a neighborhood of ... Recent work inthis field, however, can be interpreted

7 Feb 2012: is about to quit —, we increase the prize tog(y), which becomes the new ‘prevailing prize’. ... is about to quit —, we increase the prize tog(y), which becomes the new ‘prevailing prize’. •

15 Aug 2012: The first. result of this paper is a new comparison inequality, proved using an argument devel-. ... In Section 2 we present the new comparison inequality, and we apply it in Section3.

15 Aug 2012: Mathematics and its Applications, vol. 99, Springer, New York, pp. 1–24.Aizenman, M.

21 Mar 2012: The new drug is untested and has an unknown probability of success θ,which the doctor believes to be uniformly distributed over [0, 1]. ... For example, suppose p = 0.6 and 6 trials with the new drug have givens = f = 3.

15 Aug 2012: This is certainly achieved if the earliest jHjk such sr eachstrikes a new integer of H, i.e., an integer struck by no smaller sr (here and laterwe sometimes use real

15 Aug 2012: R. (1989), Percolation, Springer, New York.7. Grimmett, G. R. (1994), Potts models and random-cluster processes with many-bodyinteractions, Journal of Statistical Physics 75, 67–121.

15 Aug 2012: Stochastic Processes and their Applications 26 (1987), 1–30. 9. Janson, S., New versions of Suen’s correlation inequality, Random Structures and Algorithms.

15 Aug 2012: For example, the critical probability of a percolationprocess cannot increase if new edges are added to the lattice. ... Such monotonicity, when true, is usually easy to prove. Strict monotonicity, onthe other hand, presents new difficulties.

15 Aug 2012: Their solutions require a mixture of new ideas, from analysis, geometry, anddiscrete mathematics.

15 Aug 2012: phase diagram of a modied epidemic model in which new susceptiblesare born at some positive rate. ... M. (1985). Interacting Particle Systems. Springer-Verlag, New York.Menshikov, M. V. (1986).

23 Jul 2012: Thelast model is especially challenging because it is non-ferromagnetic, and thus givesrise to new problems of importance and difficulty. ... There are many new complications and some of the basic questions remainunanswered, at least in part.

15 Aug 2012: solve.• Their solutions require a mixture of new ideas, from analysis, geometry,.

15 Aug 2012: We continue similarly, at each stage picking anew trifurcation tk Λ and a new vertex yk Λ.

15 Aug 2012: Thus, from every pair Ci, Cj ofdistinct components, we obtain new elements F ′ of Fs1 by adding an edge joiningCi to Cj. ... their Applications 59 (1995), 267–275. 13. Janson, S., Luczak, T., Ruciński, A., Random Graphs, Wiley, New York, 2000.14.

15 Aug 2012: N ). We writeg = (gki : 1 i N ) for the associated function given by (2.12)–(2.14)subject to the new ordering, and C = g1(A). ... j1, j1,. , N}, and we construct a continuous increasing function g as abovebut subject to the new ordering.

15 Aug 2012: The principal new technique is aform of Russo's formula for random-cluster models reported by Bezuidenhout, Grimmett, andKesten.

15 Aug 2012: In this new network there are jeB(n)j parallelconnections between @B(n) and @B(n1), each of which has (for n M = M(Z))a resistance exceeding c= logn (by

2 Jul 2012: There has been a great deal of interest and activity in percolation theorysince the two Saint-Flour courses, [76, 111], of 1984 and 1996 reprinted inthis new edition. ... Press, New York, 1990,pp. 167–190. 91. O. Häggström, Uniqueness in

20 Dec 2012: We discuss these conditions in detail in Sections 3.2 and 3.3 respectively andcompare both the original and the new bounds to demonstrate the marked improvement. ... Our improved bounds are based on new versions of Markov’s inequality that hold for

15 Aug 2012: New difficulties arise through the presenceof orientations on the edges of the underlying lattice, and new ideas are neededto overcome these problems. ... 8, Springer, Berlin–Heidelberg–New York, 1987, pp. 13–20. 2. Aizenman, M., Newman, C.

15 Aug 2012: Having constructed tm1,we define tm = tm(X, X) by adding to tm1 a new edge 〈ξim , ξm〉 where 1 im < mand ξm ( X{ξ1, ξ2,. ,

15 Aug 2012: The percolation model contains a maxi-mum of (statistical) independence, and has proved a superb testing ground for new. ... Percolation theory has earned a reputation as a source of hard problems which areeasy to state and whose solutions require new

11 Apr 2012: U. In the latter case, we may remove U together with the previous DV stepto obtain a new admissible Λ-path from 0 to x of shorter length than π , a

15 Aug 2012: Each time we reach a new red vertex, there is astrictly positive probability that this vertex is the root of an ǫ-robust treein future generations. ... Soviet Mathe-matics Doklady 28, 23–26. Grimmett, G. R. (1989). Percolation. Springer-Verlag, New

15 Aug 2012: By(3.13), this process is supercritical. It follows that pc(k) p.(iv) A detailed argument would be long and contain no new ideas, and is thereforeomitted.

15 Aug 2012: families a new collection (Yx : x Zd) of random variables, which constitutes a site. ... another vertex is selected as a new starting point, and the process is iterated.

15 Aug 2012: We augment this graph by adding certainnew edges. Specifically, for distinct u,v Λ, we add a new edge between the pairu, v if either:(a) there exists a path of

15 Aug 2012: At each new point that it encounters, this point is a rw point withprobability prw, and the chance that r new points are not rw points is therefore (1 ... LK1. Now, by Theorem 3.4 and the remarks thereafter, each time thatthe above construction

15 Aug 2012: Thegeometry of the interfaces for this model is notably different from that of a spinmodel since the configurations are indexed by edges rather than by vertices, andthis leads to some new ... Although Dobrushin’s work is a helpfulindicator of the

15 Aug 2012: 6. Proofs of main results. In this section we combine the results derived so far with a new argument in orderto prove Theorems 2.1–2.3 for q 1. ... Inthe case q = 1, this gives new information about the probabilities of large deviationsof Cn.

15 Aug 2012: q} where q 1. We intro-duce this new model in Section 3, where we dub it the Blume–Capel–Potts(BCP) model.

15 Aug 2012: THE RANDOM-CLUSTER MODEL. Geoffrey GrimmettAbstra t. The class of random-cluster models is a unification of a variety of sto-chastic processes of significance for probability and statistical physics, including per-colation, Ising, and Potts models;

15 Aug 2012: The only new complication is that for γF (0) > 1 the branching process.