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21 Sep 2012: The theorem requires no exchangeability or randomguessing conditions. • It holds even when B = 1. • ... B. B. j=1. 1{kŜ(A2j1)}1{kŜ(A2j )},and note that E{Π̃B(k)} = p2k,n/2. Now.

15 Aug 2012: 482]. Theorem 4.1. Assume that ψ(a,b) = 0 and that 0 a′ < a, 0 b′ < b. ... Set. a′ =a. a b, b′ =. b. a b,. so that a′ < a and b′ < b, and a′ b′ = 1.

16 Mar 2012: The fact that a system is controllable iff the matrix [B AB A{n-1}B] is of full rank is sometimes called Kalman's criteria,. ... 0 | | 0 -b 0 -b2 | | 0 0 b 0 | |-b | |-b 0 -b2 0 |. So M4 is of rank 4 iff a and b are different.

6 Sep 2012: Mathematical modelling of the Internet. N. N. NN. B. B. BB. ... A Ephremides and B Hajek Information theory and communicationnetworks an unconsummated union IEEE Transactions on InformationTheory.

3 Aug 2012: We do this byrecursively picking good points ti and removing the Ni balls B((B f)(tj), 2k) that intersectB((B f)(ti), 2k). ... We do this by recursivelypicking good points ti and removing the Ni balls B(B(tj), 2k) that intersect B(B(ti), 2k).

6 Mar 2012: ni=1 p(Xi ) d(p). Pn. i=1 p(Xi ) d(p), B B. ... U (B, B) ran-dom variables, and define, for α < N , the random wavelet series.

21 Sep 2012: B. B. j=1. 1{kŜ(A2j1)}1{kŜ(A2j)},and note that E{Π̃B(k)} = p2k,n/2. Now. 0 1B. ... Roy.Statist. Soc., Ser. B, 68, 49–67. • Zou, H. and Hastie, T.

15 Aug 2012: Letδ : {0, 1, 2,. } R be a given function satisfying b δ(b) b 1 for all b. ... Equal proportions Hill (1911). b(b 1)Major fractions Webster (1832) b 1.

21 Mar 2012: 37. 10.3 Infinite-horizon LQ regulation. 38. 10.4 The [A, B, C] system. ... P(xt1 | Xt, Ut) = P(xt1 | xt, ut). (b) Separable (or decomposible) cost function, (i.e.

20 Apr 2012: R2. B(ζ̃(s′),x. ) ,. where ζ̃ is a standard Brownian motion. ... By Lemma 4.3 we get that if and K K′ are large enough, then the integral of g(z) inside theball B = B(0, (K K′)/2) is larger than

3 Sep 2012: for every n N and some constant M that depends on α,α′, r, B.(B) If s > 2r and Cn is an L 2-adaptive and honest confidence set for ... One shows by a standard bias-variancedecomposition, using j̄n J and ‖K j( f )‖r,2 ‖ f ‖r,2, that for every

15 Aug 2012: In either case, for A, B V , we write A B if there exists an openpath joining some a A to some b B, and we write A if there exists ... 1997), On the number of incipient spanning clusters, Nuclear Physics B 485, 551–.

20 Apr 2012: such that Pa,b(Xm = a0,Ym = b0) > 0 for some m 0. ... Let B(x0,r) = {y : d(x0,y) r} and Y Bt (B := B(x0,r)) be the discrete time simplerandom walk on G killed when it exits B(x0,r)

15 Aug 2012: In particular, E(n1 ) 1/(κn3) as n. (c) There exist absolute positive constants A = A(µ), B = B(µ) such that thetotal-variation distance between T n(α) and the ... if νǫ2 1. We substitute this into (4.7) and minimize over ǫ to obtain that

10 Jan 2012: f : T [0, ),. T. f (x) dx = 1, ‖f ‖s, B}.(2.1). ... uniform random vari-ables on [B, B] and define the random wavelet series.

15 Aug 2012: b) for any finite subset A of Zd,. φΛ,p,q(A $ Λ)! ... Proposition 3.2. For all p1,p2 satisfying 0 < p1 < p2 < 1, there exist strictlypositive numbers a = a(p1,p2) and b = b(p1,p2) such that, for any increasingcylinder event

15 Aug 2012: Let be a congurationsatisfying FA() k. There exists a set B = B of edges such that(a) jBj k,(b) (e) = 0 for e 2 B,(c) the conguration obtained from ... Abraham, D. B. and Newman, C. M. (1991). The wetting transition in a random surface model.

15 Aug 2012: that. µ(A B) µ(A)µ(B) for increasing events A, B. ... and b B ( V ) such that a and bare in the same component of (V, η(ω)).

15 Aug 2012: Giventwo edge sets A, B K, we define their interface I(A, B) to be the set of vertices vsuch that there exist a A, b B with both a and ... b) to skipinstances identified as equivalent to earlier ones, using the index function i of Section6.

15 Aug 2012: Since f1 is continuous and strictly increasing,. µρ(A | U1 = b) = λ(B | f1(U1) = b) = λ(B | U1 = b), b = 0, 1,. ... Comm. Math.Phys. 158, 1–16. [4] Bollobás, B. and Riordan, O. (2006a).

15 Aug 2012: For A,B Zd, we say that A is connected to B if thereexist a A and b B such that a b; in this case, we write A B. ... We saythat A is fully connected to B if, for all b B, there exists a A such that a b;in this case, we write A fc B.

11 Apr 2012: More generally, for A, B Zdwe write A B (and similarly for the other relations) if a b for some a A and b B. ... B Ax,m(n) = {ρi = ri for 1 i < k} Ax,m(n).

15 Aug 2012: the vector p has distribution given by Pp,(b) if p1 p2 then p1 p2. ... Take a = b = pc(T) for some small positive. Then choose largeenough so that a0 > pc(T).

15 Aug 2012: a b‖ = ‖b c‖ = ‖c d‖ = ‖d a‖ = 1},. ... Lemma 6.8 If 0 < s < t < 1, there exist a = a(s, t) > 0 and b = b(s, t) > 0such that.

15 Aug 2012: Let. (a′,b′) = (a,b) ǫ(cos α, sin α). where ǫ is small and positive. ... a small amount only. Take a = b = pc(T) ζ for some small positive ζ.

23 Jul 2012: µ1(σ) =1. Z Pexp. {β. eEδe(σ). }, σ 6. (b) Marginal on. ... b) Let ω be given. We have that. (1.18). eE. {(1 p)δω(e),0 pδω(e),1δe(σ). } =

15 Aug 2012: Wehave that. pb(i1, j1, i2, j2) =. . . pπi2qj2 if (i1, j1) = (1,b),. ... p,q whenever ′.Part (b) may be extended as follows to arbitrary equivalence relations.

15 Aug 2012: Similarly, for A,B V , we writeA B if there exist a A and b B such that a b. ... Let b = b(x,ψ) denote the number of edges ofE of the form 〈x,z〉 with ψz = 1.

15 Aug 2012: There exists astrictly positive constant b = b(L) such that the number of points y of L satisfyingkyk r does not exceed brd. ... if and only if j!n Bj! j! Bj for every open ball B Rd.

15 Aug 2012: For any ω and any finite box B, we denote by ωB the followingconfiguration:. ... and b,where the symmetric function κN = κN,ω,C is given by.

20 Dec 2012: 2τ 1 E|Ŝn=2 Lθ|:. (b) Let N̂CPSSn,τ = {1,. , p}Ŝ. ... If τ { 12 1=B, 12 3=.2B/, 12 2=B,. , 1}, then.

15 Aug 2012: For A, B V , we write AH B if either A B 6= or there exist a A and b B. ... 0 otherwise,. where A B means that there exists a A ( V ) and b B ( V ) such that a and bare in the same component of the random hypergraph (V, η(

15 Aug 2012: the vector p has distribution given by Pp,(b) if p1 p2 then p1 p2. ... Take a = b = pc(T) for some small positive. Then choose largeenough so that a0 > pc(T).