Voter Model Perturbations and Reaction Diffusion Equations

We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \ge 3$. Combining this result with properties of the PDE, some methods arising from a low density super-Brownian limit theorem, and a block construction, we give general, and often asymptotically sharp, conditions for the existence of non-trivial stationary distributions, and for extinction of one type. As applications, we describe the phase diagrams of three systems when the parameters are close to the voter model: (i) a stochastic spatial Lotka-Volterra model of Neuhauser and Pacala, (ii) a model of the evolution of cooperation of Ohtsuki, Hauert, Lieberman, and Nowak, and (iii) a continuous time version of the non-linear voter model of Molofsky, Durrett, Dushoff, Griffeath, and Levin. The first application confirms a conjecture of Cox and Perkins and the second confirms a conjecture of Ohtsuki et al in the context of certain infinite graphs. An important feature of our general results is that they do not require the process to be attractive.Comment: 106 pages, 7 figure

Studies of Helium Based Gas Mixtures Using a Small Cell Drift Chamber

An international collaboration is currently working on the construction and design of an asymmetric B Factory at the Stanford Linear Accelerator Center that will be ready to collect data in 1999. The main physics motivation for such a facility is to test the description and mechanism of CP violation in the Standard Model of particle physics and provide insight into the question of why more matter than antimatter is observed in the universe today. In particular, this experiment will measure CP violation in the decay of B mesons. In the early stages of this effort, the Canadian contingent proposed to build the central tracking chamber for the BaBar detector. Presently, a prototype drift chamber is in operation and studies are being performed to test some of the unique features of drift chamber design dictated by the conditions of the experiment. Using cosmic muons, it is possible to study tracking and pattern recognition in the prototype chamber, and therefore calculate the efficiency and spatial resolution of the prototype chamber cells. These performance features will be used to test whether or not the helium-based gas mixtures proposed for the BaBar drift chamber are a viable alternative to the more traditional argon-based gases

Rare B Decays in Collider Experiments

The recent results on the semileptonic and leptonic rare B decays from the collider experiments are reviewed. Additionally, the recent measurements of lepton flavor violation in {tau} decays are presented

Radiative Penguin Decays at the B Factories

Recent results from the B-Factories on radiative decays such as b {yields} s(d){gamma}, b {yields} s{ell}{ell} and leptonic decay B{sup 0} {yields} {tau}{sup +}{tau}{sup -} are reviewed

Two-dimensional vortex behavior in highly underdoped YBa_2Cu_3O_{6+x} observed by scanning Hall probe microscopy

We report scanning Hall probe microscopy of highly underdoped superconducting YBa_2Cu_3O_{6+x} with T_c ranging from 5 to 15 K which showed distinct flux bundles with less than one superconducting flux quantum (Phi_0) through the sample surface. The sub-Phi_0 features occurred more frequently for lower T_c, were more mobile than conventional vortices, and occurred more readily when the sample was cooled with an in-plane field component. We show that these features are consistent with kinked stacks of pancake vortices.Comment: 11 pages, 8 figures, accepted for publication in Physical Review

Projected implicit Runge-Kutta methods for differential-algebraic boundary value problems

Differential-algebraic boundary value problems arise in the modelling of singular optimal control problems and in parameter estimation for singular systems. A new class of numerical methods for these problems is introduced, and shown to overcome difficulties with previously defined numerical methods. 4 refs., 1 tab

On the influence of the cosmological constant on gravitational lensing in small systems

The cosmological constant Lambda affects gravitational lensing phenomena. The contribution of Lambda to the observable angular positions of multiple images and to their amplification and time delay is here computed through a study in the weak deflection limit of the equations of motion in the Schwarzschild-de Sitter metric. Due to Lambda the unresolved images are slightly demagnified, the radius of the Einstein ring decreases and the time delay increases. The effect is however negligible for near lenses. In the case of null cosmological constant, we provide some updated results on lensing by a Schwarzschild black hole.Comment: 8 pages, 1 figure; v2: extended discussion on the lens equation, references added, results unchanged, in press on PR

Prediction of acute multiple sclerosis relapses by transcription levels of peripheral blood cells

<p>Abstract</p> <p>Background</p> <p>The ability to predict the spatial frequency of relapses in multiple sclerosis (MS) would enable physicians to decide when to intervene more aggressively and to plan clinical trials more accurately.</p> <p>Methods</p> <p>In the current study our objective was to determine if subsets of genes can predict the time to the next acute relapse in patients with MS. Data-mining and predictive modeling tools were utilized to analyze a gene-expression dataset of 94 non-treated patients; 62 patients with definite MS and 32 patients with clinically isolated syndrome (CIS). The dataset included the expression levels of 10,594 genes and annotated sequences corresponding to 22,215 gene-transcripts that appear in the microarray.</p> <p>Results</p> <p>We designed a two stage predictor. The first stage predictor was based on the expression level of 10 genes, and predicted the time to next relapse with a resolution of 500 days (error rate 0.079, p < 0.001). If the predicted relapse was to occur in less than 500 days, a second stage predictor based on an additional different set of 9 genes was used to give a more accurate estimation of the time till the next relapse (in resolution of 50 days). The error rate of the second stage predictor was 2.3 fold lower than the error rate of random predictions (error rate = 0.35, p < 0.001). The predictors were further evaluated and found effective both for untreated MS patients and for MS patients that subsequently received immunomodulatory treatments after the initial testing (the error rate of the first level predictor was < 0.18 with p < 0.001 for all the patient groups).</p> <p>Conclusion</p> <p>We conclude that gene expression analysis is a valuable tool that can be used in clinical practice to predict future MS disease activity. Similar approach can be also useful for dealing with other autoimmune diseases that characterized by relapsing-remitting nature.</p