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11 May 2024: D Frankel, M Davies, B Bhushan, Y Kulaberoglu, P Urriola-Munoz, J Bertrand-Michel, MR Pergande, AA Smith, S Preet, TJ Park, M Vendruscolo, KS Rankin, SM Cologna, JR Kumita, N

11 May 2024: PW Mote, TJ Dunkerton, ME McIntyre, EA Ray, PH Haynes, JM Russell. –

17 Jun 2019: Assume p > q. Let Tj = inf{n > 1 : Xn = j} if this is finite, and Tj = otherwise.

17 Jun 2019: for j 6= i. Prove that the random vectors Yj AjX are independent, and thatY (Y T1 ,. ,Y TJ )T has a multivariate normal distribution.[ Hint: Random vectors are independent if

30 Aug 2019: connected to nodes ti and tj with arcs of infinite capacity, and each nodeti is connected to a node s′ with an arc of capacity w wi 1 and w = wn.

17 Jun 2019: Show that if g(s, x) is a real-valued function of realvariables s, x, and Tj are the jump times of (Nt, t > 0) then. ... E[exp. {θ. Nt. j=1. g(Tj, Xj). }]= exp. {λ. t. 0(E(eθg(s,X)) 1)ds. },.

17 Jun 2019: ci Πmj=1 taijj. subject to tj > 0 j = 1,.

30 Aug 2019: Show that for any j > 1there exists there exists a positive real number Tj such that.

17 Jun 2019: Find the probability-generating functions of the random variables Hj and Tj.

19 Jun 2019: dependent toll Tj(yj ), and suppose each user selects a route in an attempt to mini-. ... Tj () so that the equilibrium flow pattern minimizes the average delay in the network.