495 research outputs found
Normed-convergence theory for supercritical branching processes
AbstractA proof is given of the basic normed-convergence theorem for the ordinary supercritical Bienaymé-Galton-Watson process with finite mean. Part of it is adapted to obtain an analogous result for inhomogeneous supercritical processes (i.e. branching processes in varying environment). This is used in part to give a detailed discussion on the normed- convergence behaviour of the ordinary process in the ‘explosive’ case (i.e with infinite mean); and rather pathological limit behaviour is found to obtain
Approaching the Ground State of a Quantum Spin Glass using a Zero-Temperature Quantum Monte Carlo
Here we discuss the annealing behavior of an infinite-range Ising
spin glass in presence of a transverse field using a zero-temperature quantum
Monte Carlo. Within the simulation scheme, we demonstrate that quantum
annealing not only helps finding the ground state of a classical spin glass,
but can also help simulating the ground state of a quantum spin glass, in
particularly, when the transverse field is low, much more efficiently.Comment: 8 pages, 6 fig
Transient behaviour in finite absorbing Markov chains
Thesis (M.Sc.) -- University of Adelaide, Dept. of Mathematics, 196
A note on models using the branching process with immigration stopped at zero
Abstract The Galton-Watson process with immigration which is time-homogeneous but not permitted when the process is in state 0 (so that this state is absorbing) is briefly studied in the subcritical and supercritical cases. Results analogous to those for the ordinary Galton-Watson process are found to hold. Partly-new techniques are required, although known end-results on the standard process with and without immigration are used also. In the subcritical case a new parameter is found to be relevant, replacing to some extent the criticality parameter
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Implementing the Magdalena Ridge Observatory interferometer supervisory system
Random Surfing Without Teleportation
In the standard Random Surfer Model, the teleportation matrix is necessary to
ensure that the final PageRank vector is well-defined. The introduction of this
matrix, however, results in serious problems and imposes fundamental
limitations to the quality of the ranking vectors. In this work, building on
the recently proposed NCDawareRank framework, we exploit the decomposition of
the underlying space into blocks, and we derive easy to check necessary and
sufficient conditions for random surfing without teleportation.Comment: 13 pages. Published in the Volume: "Algorithms, Probability, Networks
and Games, Springer-Verlag, 2015". (The updated version corrects small
typos/errors
Relative entropy under mappings by stochastic matrices
AbstractThe relative g-entropy of two finite, discrete probability distributions x = (x1,…,xn) and y = (y1,…,yn) is defined as Hg(x,y) = Σkxkg (yk/kk - 1), where g:(-1,∞)→R is convex and g(0) = 0. When g(t) = -log(1 + t), then Hg(x,y) = Σkxklog(xk/yk), the usual relative entropy. Let Pn = {x ∈ Rn : σixi = 1, xi > 0 ∀i}. Our major results is that, for any m × n column-stochastic matrix A, the contraction coefficient defined as ηğ(A) = sup{Hg(Ax,Ay)/Hg(x,y) : x,y ∈ Pn, x ≠y} satisfies ηg(A) ⩽1 - α(A), where α(A) = minj,kΣi min(aij, aik) is Dobrushin's coefficient of ergodicity. Consequently, ηg(A) < 1 if and only if A is scrambling. Upper and lower bounds on αg(A) are established. Analogous results hold for Markov chains in continuous time
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