Non-global parameter estimation using local ensemble Kalman filtering

We study parameter estimation for non-global parameters in a low-dimensional chaotic model using the local ensemble transform Kalman filter (LETKF). By modifying existing techniques for using observational data to estimate global parameters, we present a methodology whereby spatially-varying parameters can be estimated using observations only within a localized region of space. Taking a low-dimensional nonlinear chaotic conceptual model for atmospheric dynamics as our numerical testbed, we show that this parameter estimation methodology accurately estimates parameters which vary in both space and time, as well as parameters representing physics absent from the model

Notes on Mayfly Nymphs from Northeastern Minnesota Which Key to \u3ci\u3eStenonema Vicarium\u3c/i\u3e (Ephemeroptera: Heptageniidae)

(excerpt) A review of the literature indicates that Stenonema vicarium (Walker) adults have not been collected from northeastern Minnesota. However, mayfly nymphs which key to that species, based on the descriptions in Lewis (1974), have been collected from many streams in the area which are also inhabited by nymphs of the closely related species, Stenonema fuscum (Clemens)

Convergent finite difference methods for one-dimensional fully nonlinear second order partial differential equations

This paper develops a new framework for designing and analyzing convergent finite difference methods for approximating both classical and viscosity solutions of second order fully nonlinear partial differential equations (PDEs) in 1-D. The goal of the paper is to extend the successful framework of monotone, consistent, and stable finite difference methods for first order fully nonlinear Hamilton-Jacobi equations to second order fully nonlinear PDEs such as Monge-Amp\`ere and Bellman type equations. New concepts of consistency, generalized monotonicity, and stability are introduced; among them, the generalized monotonicity and consistency, which are easier to verify in practice, are natural extensions of the corresponding notions of finite difference methods for first order fully nonlinear Hamilton-Jacobi equations. The main component of the proposed framework is the concept of "numerical operator", and the main idea used to design consistent, monotone and stable finite difference methods is the concept of "numerical moment". These two new concepts play the same roles as the "numerical Hamiltonian" and the "numerical viscosity" play in the finite difference framework for first order fully nonlinear Hamilton-Jacobi equations. In the paper, two classes of consistent and monotone finite difference methods are proposed for second order fully nonlinear PDEs. The first class contains Lax-Friedrichs-like methods which also are proved to be stable and the second class contains Godunov-like methods. Numerical results are also presented to gauge the performance of the proposed finite difference methods and to validate the theoretical results of the paper.Comment: 23 pages, 8 figues, 11 table

The integral cohomology rings of some p-groups

We determine the integral cohomology rings of an infinite family of p-groups, for odd primes p, with cyclic derived subgroups. Our method involves embedding the groups in a compact Lie group of dimension one, and was suggested by P H Kropholler and J Huebschmann