Monodromy of Cyclic Coverings of the Projective Line

We show that the image of the pure braid group under the monodromy action on the homology of a cyclic covering of degree d of the projective line is an arithmetic group provided the number of branch points is sufficiently large compared to the degree.Comment: 47 pages (to appear in Inventiones Mathematicae

The Asymptotic distribution of circles in the orbits of Kleinian groups

Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on the plane which describes the asymptotic distribution of small circles in P, assuming that either the critical exponent of Gamma is strictly bigger than 1 or P does not contain an infinite bouquet of tangent circles glued at a parabolic fixed point of Gamma. Our construction also works for P invariant under a geometrically infinite group Gamma, provided Gamma admits a finite Bowen-Margulis-Sullivan measure and the Gamma-skinning size of P is finite. Some concrete circle packings to which our result applies include Apollonian circle packings, Sierpinski curves, Schottky dances, etc.Comment: 31 pages, 8 figures. Final version. To appear in Inventiones Mat

A new ghost cell/level set method for moving boundary problems:application to tumor growth

In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth

Genetic Relationships of Crown Rust Resistance, Grain Yield, Test Weight, and Seed Weight in Oat

Integrating selection for agronomic performance and quantitative resistance to crown rust, caused by Puccinia coronata Corda var. avenae W.P. Fraser & Ledingham, in oat (Avena sativa L.) requires an understanding of their genetic relationships. This study was conducted to investigate the genetic relationships of crown rust resistance, grain yield, test weight, and seed weight under both inoculated and fungicide-treated conditions. A Design II mating was performed between 10 oat lines with putative partial resistance to crown rust and nine lines with superior grain yield and grain quality potential. Progenies from this mating were evaluated in both crown rust-inoculated and fungicide-treated plots in four Iowa environments to estimate genetic effects and phenotypic correlations between crown rust resistance and grain yield, seed weight, and test weight under either infection or fungicide-treated conditions. Lines from a random-mated population derived from the same parents were evaluated in three Iowa environments to estimate heritabilities of, and genetic correlations between, these traits. Resistance to crown rust, as measured by area under the disease progress curve (AUDPC), was highly heritable (H = 0.89 on an entry-mean basis), and was favorably correlated with grain yield, seed weight, and test weight measured in crown rust-inoculated plots. AUDPC was unfavorably correlated or uncorrelated with grain yield, test weight, and seed weight measured in fungicide-treated plots. To improve simultaneously crown rust resistance, grain yield, and seed weight under both lower and higher levels of crown rust infection, an optimum selection index can be developed with the genetic parameters estimated in this stud

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities — which are mainly related either to nonlinear convection terms and/or some geometric variability — that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and — in the unsteady case — long-time stability of the reduced model. Moreover, we provide an extensive list of literature references

Design and implementation of a human ECoG simulator for testing brain-machine interfaces

10.1109/NER.2013.6696182International IEEE/EMBS Conference on Neural Engineering, NER1311-131

Simultaneous neural control of simple reaching and grasping with the modular prosthetic limb using intracranial EEG

10.1109/TNSRE.2013.2286955IEEE Transactions on Neural Systems and Rehabilitation Engineering223695-705ITNS