Regenerative tree growth: structural results and convergence

We introduce regenerative tree growth processes as consistent families of random trees with n labelled leaves, n>=1, with a regenerative property at branch points. This framework includes growth processes for exchangeably labelled Markov branching trees, as well as non-exchangeable models such as the alpha-theta model, the alpha-gamma model and all restricted exchangeable models previously studied. Our main structural result is a representation of the growth rule by a sigma-finite dislocation measure kappa on the set of partitions of the natural numbers extending Bertoin's notion of exchangeable dislocation measures from the setting of homogeneous fragmentations. We use this representation to establish necessary and sufficient conditions on the growth rule under which we can apply results by Haas and Miermont for unlabelled and not necessarily consistent trees to establish self-similar random trees and residual mass processes as scaling limits. While previous studies exploited some form of exchangeability, our scaling limit results here only require a regularity condition on the convergence of asymptotic frequencies under kappa, in addition to a regular variation condition.Comment: 23 pages, new title, restructured, presentation improve

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pages 76-7

Validation of a mathematical model for road cycling power

Journal ArticleThis investigation sought to determine if cycling power could be accurately modeled. A mathematical model of cycling power was derived, and values for each model parameter were determined. A bicycle-mounted power measurement system was validated by comparison with a laboratory ergometer

Large N and the Dine-Rajaraman problem

We compute the effective action for scattering of three well-separated extremal brane solutions, in 11d supergravity, with zero p_ transfer and small transverse velocities. Using an interpretation of the conjecture of Maldacena, following Hyun, this can be viewed as the large N limit of the Matrix theory description of three supergraviton scattering at leading order. The result is consistent with the perturbative supergravity calculation.Comment: 10 pages, tex (harvmac