Correlations, fluctuations and stability of a finite-size network of coupled oscillators

The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e. when the population is not synchronous. This demonstration is facilitated by the construction of a non-equilibrium statistical field theoretic formulation of a generic model of coupled oscillators. This theory is consistent with previous results. In the all-to-all case, the fluctuations in this theory are due completely to finite size corrections, which can be calculated in an expansion in 1/N, where N is the number of oscillators. The N -> infinity limit of this theory is what is traditionally called mean field theory for the Kuramoto model.Comment: 25 pages (2 column), 12 figures, modifications for resubmissio

Direct Measurement of the Top Quark Charge at Hadron Colliders

We consider photon radiation in tbar-t events at the upgraded Fermilab Tevatron and the CERN Large Hadron Collider (LHC) as a tool to measure the electric charge of the top quark. We analyze the contributions of tbar-t-gamma production and radiative top quark decays to p-p, pbar-p -> gamma l^+/- nu bbar-b jj, assuming that both b-quarks are tagged. With 20~fb^{-1} at the Tevatron, the possibility that the ``top quark'' discovered in Run I is actually an exotic charge -4/3 quark can be ruled out at the 95% confidence level. At the LHC, it will be possible to determine the charge of the top quark with an accuracy of about 10%.Comment: Revtex, 24 pages, 2 tables, 9 figure

From Foreign to Familiar Mac and Cheese\u27s Journey to America\u27s Comfort Food

This project explores the evolution of macaroni and cheese through recipes ranging from Thomas Jefferson to Wolfgang Puck. These recipes reveal historical trends that coincide with changes in American society and culture. Specifically the role of macaroni and cheese in soul food, as a mass produced commodity, comfort food, and as an example of American overindulgence

Mean-field equations for stochastic firing-rate neural fields with delays: Derivation and noise-induced transitions

In this manuscript we analyze the collective behavior of mean-field limits of large-scale, spatially extended stochastic neuronal networks with delays. Rigorously, the asymptotic regime of such systems is characterized by a very intricate stochastic delayed integro-differential McKean-Vlasov equation that remain impenetrable, leaving the stochastic collective dynamics of such networks poorly understood. In order to study these macroscopic dynamics, we analyze networks of firing-rate neurons, i.e. with linear intrinsic dynamics and sigmoidal interactions. In that case, we prove that the solution of the mean-field equation is Gaussian, hence characterized by its two first moments, and that these two quantities satisfy a set of coupled delayed integro-differential equations. These equations are similar to usual neural field equations, and incorporate noise levels as a parameter, allowing analysis of noise-induced transitions. We identify through bifurcation analysis several qualitative transitions due to noise in the mean-field limit. In particular, stabilization of spatially homogeneous solutions, synchronized oscillations, bumps, chaotic dynamics, wave or bump splitting are exhibited and arise from static or dynamic Turing-Hopf bifurcations. These surprising phenomena allow further exploring the role of noise in the nervous system.Comment: Updated to the latest version published, and clarified the dependence in space of Brownian motion

Integrating Expository Preaching and Teaching As the Model of Ministry for Pray's Mill Baptist Church

INTEGRATING EXPOSITORY PREACHING AND TEACHING AS THE MODEL OF MINISTRY FOR PRAY'S MILL BAPTIST CHURCH Joshua Shane Buice, D.Min. The Southern Baptist Theological Seminary, 2013 Chair: Dr. Robert A. Vogel This project has one overarching goal that seeks to establish expository preaching as the primary method of Bible teaching for Pray's Mill Baptist Church. This goal transcends the time period of this project and looks into the future of our congregation. The first chapter introduces Pray's Mill Baptist Church and the Douglas County community. Chapter 2 lays out a theological foundation for the goals of the project. Chapter 3 evaluates the strengths and weaknesses of preaching methods and examines training techniques related to biblical hermeneutics. The preaching methods reviewed include topical preaching, doctrinal preaching, allegorical preaching, and expository preaching. The hermeneutical techniques reviewed include evaluating the words, the original human author, contextual interpretation, and the single meaning hermeneutic. Chapter 4 explains the process of the project in the life of Pray's Mill Baptist Church. Chapter 5 is an analysis of the project's results in the life of the church