Topological Change in Mean Convex Mean Curvature Flow

Consider the mean curvature flow of an (n+1)-dimensional, compact, mean convex region in Euclidean space (or, if n<7, in a Riemannian manifold). We prove that elements of the m-th homotopy group of the complementary region can die only if there is a shrinking S^k x R^(n-k) singularity for some k less than or equal to m. We also prove that for each m from 1 to n, there is a nonempty open set of compact, mean convex regions K in R^(n+1) with smooth boundary for which the resulting mean curvature flow has a shrinking S^m x R^(n-m) singularity.Comment: 19 pages. This version includes a new section proving that certain kinds of mean curvature flow singularities persist under arbitrary small perturbations of the initial surface. Newest update (Oct 2013) fixes some bibliographic reference

Difference Methods for Boundary Value Problems in Ordinary Differential Equations

A general theory of difference methods for problems of the form Ny ≡ y' - f(t,y) = O, a ≦ t ≦ b, g(y(a),y(b))= 0, is developed. On nonuniform nets, t_0 = a, t_j = t_(j-1) + h_j, 1 ≦ j ≦ J, t_J = b, schemes of the form N_(h)u_j = G_j(u_0,•••,u_J) = 0, 1 ≦ j ≦ J, g(u_0,u_J) = 0 are considered. For linear problems with unique solutions, it is shown that the difference scheme is stable and consistent for the boundary value problem if and only if, upon replacing the boundary conditions by an initial condition, the resulting scheme is stable and consistent for the initial value problem. For isolated solutions of the nonlinear problem, it is shown that the difference scheme has a unique solution converging to the exact solution if (i) the linearized difference equations are stable and consistent for the linearized initial value problem, (ii) the linearized difference operator is Lipschitz continuous, (iii) the nonlinear difference equations are consistent with the nonlinear differential equation. Newton’s method is shown to be valid, with quadratic convergence, for computing the numerical solution

To transduce a zebra finch: interrogating behavioral mechanisms in a model system for speech.

The ability to alter neuronal gene expression, either to affect levels of endogenous molecules or to express exogenous ones, is a powerful tool for linking brain and behavior. Scientists continue to finesse genetic manipulation in mice. Yet mice do not exhibit every behavior of interest. For example, Mus musculus do not readily imitate sounds, a trait known as vocal learning and a feature of speech. In contrast, thousands of bird species exhibit this ability. The circuits and underlying molecular mechanisms appear similar between disparate avian orders and are shared with humans. An advantage of studying vocal learning birds is that the neurons dedicated to this trait are nested within the surrounding brain regions, providing anatomical targets for relating brain and behavior. In songbirds, these nuclei are known as the song control system. Molecular function can be interrogated in non-traditional model organisms by exploiting the ability of viruses to insert genetic material into neurons to drive expression of experimenter-defined genes. To date, the use of viruses in the song control system is limited. Here, we review prior successes and test additional viruses for their capacity to transduce basal ganglia song control neurons. These findings provide a roadmap for troubleshooting the use of viruses in animal champions of fascinating behaviors-nowhere better featured than at the 12th International Congress

The High Energy Behavior of the Forward Scattering Parameters---An Amplitude Analysis Update

Utilizing the most recent experimental data, we reanalyze high energy \pbar p and pp data, using the asymptotic amplitude analysis, under the assumption that we have reached `asymptopia'. This analysis gives strong evidence for a $\log \,(s/s_0)$ dependence at {\em current} energies and {\em not} $\log^2 (s/s_0)$, and also demonstrates that odderons are {\em not} necessary to explain the experimental data.Comment: 7 pages in LaTeX, 4 figures and 5 files, uuencoded in file "sigall.uu

Encapsulation task of the low-cost silicon solar array project. Investigation of test methods, material properties, and processes for solar cell encapsulants

The results of an investigation of solar module encapsulation systems applicable to the Low-Cost Solar Array Project 1986 cost and performance goals are presented. Six basic construction elements were identified and their specific uses in module construction defined. A uniform coating basis was established for each element. The survey results were also useful in revealing price ranges for classes of materials and estimating the cost allocation for each element within the encapsulating cost goal. The six construction elements were considered to be substrates, superstrates, pottants, adhesives, outer covers and back covers

Application of velocity-based gain-scheduling to lateral auto-pilot design for an agile missile

In this paper a modern gain-scheduling methodology is proposed which exploits recently developed velocity-based techniques to resolve many of the deficiencies of classical gain-scheduling approaches (restriction to near equilibrium operation, to slow rate of variation). This is achieved while maintaining continuity with linear methods and providing an open design framework (any linear synthesis approach may be used) which supports divide and conquer design strategies. The application of velocity-based gain-scheduling techniques is demonstrated in application to a demanding, highly nonlinear, missile control design task. Scheduling on instantaneous incidence (a rapidly varying quantity) is well-known to lead to considerable difficulties with classical gain-scheduling methods. It is shown that the methods proposed here can, however, be used to successfully design an effective and robust gain-scheduled controller