Diffusion on a hypercubic lattice with pinning potential: exact results for the error-catastrophe problem in biological evolution

In the theoretical biology framework one fundamental problem is the so-called error catastrophe in Darwinian evolution models. We reexamine Eigen's fundamental equations by mapping them into a polymer depinning transition problem in a ``genotype'' space represented by a unitary hypercubic lattice. The exact solution of the model shows that error catastrophe arises as a direct consequence of the equations involved and confirms some previous qualitative results. The physically relevant consequence is that such equations are not adequate to properly describe evolution of complex life on the Earth.Comment: 10 pages in LaTeX. Figures are available from the authors. [email protected] (e-mail address

Electrostatics in wind-blown sand

Wind-blown sand, or "saltation," is an important geological process, and the primary source of atmospheric dust aerosols. Significant discrepancies exist between classical saltation theory and measurements. We show here that these discrepancies can be resolved by the inclusion of sand electrification in a physically based saltation model. Indeed, we find that electric forces enhance the concentration of saltating particles and cause them to travel closer to the surface, in agreement with measurements. Our results thus indicate that sand electrification plays an important role in saltation.Comment: 4 journal pages, 5 figures, and supplementary material. Article is in press at PR

Finding the Center of Mass of a Soft Spring

This article shows how to use calculus to find the center of mass position of a soft cylindrical helical spring that is suspended vertically. The spring is non-uniformly stretched by the action of gravity. A general expression for the vertical position of the center of mass is obtained.Comment: LaTeX, 7 pages, 2 figures. Minor changes to agree with published versio

Order reduction approaches for the algebraic Riccati equation and the LQR problem

We explore order reduction techniques for solving the algebraic Riccati equation (ARE), and investigating the numerical solution of the linear-quadratic regulator problem (LQR). A classical approach is to build a surrogate low dimensional model of the dynamical system, for instance by means of balanced truncation, and then solve the corresponding ARE. Alternatively, iterative methods can be used to directly solve the ARE and use its approximate solution to estimate quantities associated with the LQR. We propose a class of Petrov-Galerkin strategies that simultaneously reduce the dynamical system while approximately solving the ARE by projection. This methodology significantly generalizes a recently developed Galerkin method by using a pair of projection spaces, as it is often done in model order reduction of dynamical systems. Numerical experiments illustrate the advantages of the new class of methods over classical approaches when dealing with large matrices

Muon-spin relaxation measurements on the dimerized spin-1/2 chains NaTiSi2O6 and TiOCl

We report muon spin relaxation (muSR) and magnetic susceptibility investigations of two Ti3+ chain compounds which each exhibit a spin gap at low temperature, NaTiSi2O6 and TiOCl. From these we conclude that the spin gap in NaTiSi2O6 is temperature independent, with a value of 2*Delta=660(50)K, arising from orbital ordering at Too = 210K; the associated structural fluctuations activate the muon spin relaxation rate up to temperatures above 270K. In TiOCl we find thermally activated spin fluctuations corresponding to a spin gap 2*Delta=420(40)K below Tc1=67K. We also compare the methods used to extract the spin gap and the concentration of free spins within the samples from muSR and magnetic susceptibility data.Comment: 4 pages, 3 figure

Axiomatic Bargaining Theory on Opportunity Assignments

This paper discusses issues of axiomatic bargaining problems over opportunity assignments. The fair arbitrator uses the principle of "equal opportunity" for all players to make the recommendation on re- source allocations. A framework in such a context is developed and several classical solutions to standard bargaining problems are reformulated and axiomatically characterized. Working Paper 06-4

Scalable and cost-effective NGS genotyping in the cloud

Background: While next-generation sequencing (NGS) costs have plummeted in recent years, cost and complexity of computation remain substantial barriers to the use of NGS in routine clinical care. The clinical potential of NGS will not be realized until robust and routine whole genome sequencing data can be accurately rendered to medically actionable reports within a time window of hours and at scales of economy in the 10’s of dollars. Results: We take a step towards addressing this challenge, by using COSMOS, a cloud-enabled workflow management system, to develop GenomeKey, an NGS whole genome analysis workflow. COSMOS implements complex workflows making optimal use of high-performance compute clusters. Here we show that the Amazon Web Service (AWS) implementation of GenomeKey via COSMOS provides a fast, scalable, and cost-effective analysis of both public benchmarking and large-scale heterogeneous clinical NGS datasets. Conclusions: Our systematic benchmarking reveals important new insights and considerations to produce clinical turn-around of whole genome analysis optimization and workflow management including strategic batching of individual genomes and efficient cluster resource configuration.Yassine Souilmi, Alex K. Lancaster, Jae-Yoon Jung, Ettore Rizzo, Jared B. Hawkins, Ryan Powles, Saaïd Amzazi, Hassan Ghazal, Peter J. Tonellato and Dennis P. Wal

Weak and strong fillability of higher dimensional contact manifolds

For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of weak fillings and prove that it is indeed weaker (at least in dimension five),while also being obstructed by all known manifestations of "overtwistedness". We also find the first examples of contact manifolds in all dimensions that are not symplectically fillable but also cannot be called overtwisted in any reasonable sense. These depend on a higher-dimensional analogue of Giroux torsion, which we define via the existence in all dimensions of exact symplectic manifolds with disconnected contact boundary.Comment: 68 pages, 5 figures. v2: Some attributions clarified, and other minor edits. v3: exposition improved using referee's comments. Published by Invent. Mat