Embedding Brans-Dicke gravity into electroweak theory

We argue that a version of the four dimensional Brans-Dicke theory can be embedded in the standard flat spacetime electroweak theory. The embedding involves a change of variables that separates the isospin from the hypercharge in the electroweak theory.Comment: 4 pages, no figures; replaced to match published versio

Elastic Energy and Phase Structure in a Continuous Spin Ising Chain with Applications to the Protein Folding Problem

We present a numerical Monte Carlo analysis of a continuos spin Ising chain that can describe the statistical proterties of folded proteins. We find that depending on the value of the Metropolis temperature, the model displays the three known nontrivial phases of polymers: At low temperatures the model is in a collapsed phase, at medium temperatures it is in a random walk phase, and at high temperatures it enters the self-avoiding random walk phase. By investigating the temperature dependence of the specific energy we confirm that the transition between the collapsed phase and the random walk phase is a phase transition, while the random walk phase and self-avoiding random walk phase are separated from each other by a cross-over transition. We also compare the predictions of the model to a phenomenological elastic energy formula, proposed by Huang and Lei to describe folded proteins.Comment: 12 pages, 23 figures, RevTeX 4.

Partially Dual variables in SU(2) Yang-Mills Theory

We propose a reformulation of SU(2) Yang-Mills theory in terms of new variables. These variables are appropriate for describing the theory in its infrared limit, and indicate that it admits knotlike configurations as stable solitons. As a consequence we arrive at a dual picture of the Yang-Mills theory where the short distance limit describes asymptotically free, massless point gluons and the large distance limit describes extended, massive knotlike solitons.Comment: 4 pages, revtex twocolum

Mean-Field Dynamics: Singular Potentials and Rate of Convergence

We consider the time evolution of a system of $N$ identical bosons whose interaction potential is rescaled by $N^{-1}$. We choose the initial wave function to describe a condensate in which all particles are in the same one-particle state. It is well known that in the mean-field limit $N \to \infty$ the quantum $N$-body dynamics is governed by the nonlinear Hartree equation. Using a nonperturbative method, we extend previous results on the mean-field limit in two directions. First, we allow a large class of singular interaction potentials as well as strong, possibly time-dependent external potentials. Second, we derive bounds on the rate of convergence of the quantum $N$-body dynamics to the Hartree dynamics.Comment: Typos correcte

Delocalization and Diffusion Profile for Random Band Matrices

We consider Hermitian and symmetric random band matrices $H = (h_{xy})$ in $d \geq 1$ dimensions. The matrix entries $h_{xy}$, indexed by x,y \in (\bZ/L\bZ)^d, are independent, centred random variables with variances s_{xy} = \E |h_{xy}|^2. We assume that $s_{xy}$ is negligible if $|x-y|$ exceeds the band width $W$. In one dimension we prove that the eigenvectors of $H$ are delocalized if $W\gg L^{4/5}$. We also show that the magnitude of the matrix entries \abs{G_{xy}}^2 of the resolvent $G=G(z)=(H-z)^{-1}$ is self-averaging and we compute \E \abs{G_{xy}}^2. We show that, as $L\to\infty$ and $W\gg L^{4/5}$, the behaviour of \E |G_{xy}|^2 is governed by a diffusion operator whose diffusion constant we compute. Similar results are obtained in higher dimensions

On dimension reduction in Gaussian filters

A priori dimension reduction is a widely adopted technique for reducing the computational complexity of stationary inverse problems. In this setting, the solution of an inverse problem is parameterized by a low-dimensional basis that is often obtained from the truncated Karhunen-Loeve expansion of the prior distribution. For high-dimensional inverse problems equipped with smoothing priors, this technique can lead to drastic reductions in parameter dimension and significant computational savings. In this paper, we extend the concept of a priori dimension reduction to non-stationary inverse problems, in which the goal is to sequentially infer the state of a dynamical system. Our approach proceeds in an offline-online fashion. We first identify a low-dimensional subspace in the state space before solving the inverse problem (the offline phase), using either the method of "snapshots" or regularized covariance estimation. Then this subspace is used to reduce the computational complexity of various filtering algorithms - including the Kalman filter, extended Kalman filter, and ensemble Kalman filter - within a novel subspace-constrained Bayesian prediction-and-update procedure (the online phase). We demonstrate the performance of our new dimension reduction approach on various numerical examples. In some test cases, our approach reduces the dimensionality of the original problem by orders of magnitude and yields up to two orders of magnitude in computational savings

Geographic Information System and tools of spatial analysis in a pneumococcal vaccine trial

Background: The goal of this Geographic Information System (GIS) study was to obtain accurate information on the locations of study subjects, road network and services for research purposes so that the clinical outcomes of interest (e.g., vaccine efficacy, burden of disease, nasopharyngeal colonization and its reduction) could be linked and analyzed at a distance from health centers, hospitals, doctors and other important services. The information on locations can be used to investigate more accurate crowdedness, herd immunity and/or transmission patterns. Method. A randomized, placebo-controlled, double-blind trial of an 11-valent pneumococcal conjugate vaccine (11PCV) was conducted in Bohol Province in central Philippines, from July 2000 to December 2004. We collected the information on the geographic location of the households (N = 13,208) of study subjects. We also collected a total of 1982 locations of health and other services in the six municipalities and a comprehensive GIS data over the road network in the area. Results: We calculated the numbers of other study subjects (vaccine and placebo recipients, respectively) within the neighborhood of each study subject. We calculated distances to different services and identified the subjects sharing the same services (calculated by distance). This article shows how to collect a complete GIS data set for human to human transmitted vaccine study in developing country settings in an efficient and economical way. Conclusions: The collection of geographic locations in intervention trials should become a routine task. The results of public health research may highly depend on spatial relationships among the study subjects and between the study subjects and the environment, both natural and infrastructural.Peer reviewe

On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction

In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles becomes large and the strength of the two-body potential tends to 0 like the inverse of the particle number. Our method is applicable for a class of singular interaction potentials including the Coulomb potential. We prove and state our main result for the Heisenberg-picture dynamics of "observables", thus avoiding the use of coherent states. Our formulation shows that the mean-field limit is a "semi-classical" limit.Comment: Corrected typos and included an elementary proof of the Kato smoothing estimate (Lemma 6.1

Weisskopf-Wigner model for wave packet excitation

We consider a laser induced molecular excitation process as a decay of a single energy state into a continuum. The analytic results based on Weisskopf-Wigner approach and perturbation calculations are compared with numerical wave packet results. We find that the decay model describes the excitation process well within the expected parameter region.Comment: 14 pages, Latex2.09, 9 Postscript figures embedded using psfig, see also http://www.physics.helsinki.fi/~kasuomin