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10 May 2013: Abstract. This paper presents a new approach to modeling end-to-end performance for IP networks. ... Results are presented for an IP backbone network, which highlight how this new model finds the natural operating point for TCP, which depends on route

11 Sep 2013: The transformation maps G to a new graph F(G). We have two sets of results.First, the connective constants of G and F(G) satisfy a simple functional relation, and

23 Nov 2013: In both cases, each thickened portion of w isbackward extendable. so that the old wa becomes the new w0.) Since loop-erasure does notincrease distances along the walk among the vertices

12 Sep 2013: 1987). Tilings and Patterns. Freeman, New York.MR0857454. [8] KENYON, R. (2004). ... Springer, New York.MR0894549. [12] KESTEN, H. (1987). Scaling relations for 2D-percolation.

7 Mar 2013: By Lemma 4.4again, X(ω′) X(ω) is finite, so no new infinite components have beencreated, and thus X(ω′) has strictly fewer that n infinite components.Since the modification

3 Jul 2013: It implies criticality of such values, therebyproviding a new proof of the critical point of inhomogeneous systems. ... A great deal of rigorous mathematics exists for critical site percolation on thetriangular lattice, but surprisingly little for other

21 May 2013: It turns out thatO may be chosen insuch a way that the new graph, denotedG′, is isoradial also. ... The new vertexO is the circumcentreof the three dual vertices of the surrounding hexagon ofG3.

14 Mar 2013: Bernoulli 19(2), 2013, 676–719DOI: 10.3150/11-BEJ412. Cluster detection in networks usingpercolationE RY A R I A S - C A S T RO1 and G E O F F R E Y R. G R I M M E T T2. 1Department of Mathematics, University of California, San Diego, CA 92093-0112