On cluster approximations of cellular automata

In this thesis I examine one commonly used class of methods for the analytic approximation of cellular automata, the so-called local cluster approximations. This class subsumes the well known mean-field and pair approximations, as well as higher order generalizations of these. While a straightforward method known as Bayesian extension exists for constructing cluster approximations of arbitrary order on one-dimensional lattices (and certain other cases), for higher-dimensional systems the construction of approximations beyond the pair level becomes more complicated due to the presence of loops. In this thesis I describe the one-dimensional construction as well as a number of approximations suggested for higher-dimensional lattices, comparing them against a number of consistency criteria that such approximations could be expected to satisfy. I also outline a general variational principle for constructing consistent cluster approximations of arbitrary order with minimal bias, and show that the one-dimensional construction indeed satisfies this principle. Finally, I apply this variational principle to derive a novel consistent expression for symmetric three cell cluster frequencies as estimated from pair frequencies, and use this expression to construct a quantitatively improved pair approximation of the well-known lattice contact process on a hexagonal lattice.

First simultaneous measurement of the top quark mass in the lepton+jets and dilepton channels at CDF

We present a measurement of the mass of the top quark using data corresponding to an integrated luminosity of 1.9fb^-1 of ppbar collisions collected at sqrt{s}=1.96 TeV with the CDF II detector at Fermilab's Tevatron. This is the first measurement of the top quark mass using top-antitop pair candidate events in the lepton + jets and dilepton decay channels simultaneously. We reconstruct two observables in each channel and use a non-parametric kernel density estimation technique to derive two-dimensional probability density functions from simulated signal and background samples. The observables are the top quark mass and the invariant mass of two jets from the W decay in the lepton + jets channel, and the top quark mass and the scalar sum of transverse energy of the event in the dilepton channel. We perform a simultaneous fit for the top quark mass and the jet energy scale, which is constrained in situ by the hadronic W boson mass. Using 332 lepton + jets candidate events and 144 dilepton candidate events, we measure the top quark mass to be mtop=171.9 +/- 1.7 (stat. + JES) +/- 1.1 (syst.) GeV/c^2 = 171.9 +/- 2.0 GeV/c^2.