Dynamic importance sampling for uniformly recurrent markov chains

Importance sampling is a variance reduction technique for efficient estimation of rare-event probabilities by Monte Carlo. In standard importance sampling schemes, the system is simulated using an a priori fixed change of measure suggested by a large deviation lower bound analysis. Recent work, however, has suggested that such schemes do not work well in many situations. In this paper we consider dynamic importance sampling in the setting of uniformly recurrent Markov chains. By ``dynamic'' we mean that in the course of a single simulation, the change of measure can depend on the outcome of the simulation up till that time. Based on a control-theoretic approach to large deviations, the existence of asymptotically optimal dynamic schemes is demonstrated in great generality. The implementation of the dynamic schemes is carried out with the help of a limiting Bellman equation. Numerical examples are presented to contrast the dynamic and standard schemes.Comment: Published at http://dx.doi.org/10.1214/105051604000001016 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Patterning of the C. elegans 1° vulval lineage by RAS and Wnt pathways

In C. elegans, the descendants of the 1° vulval precursor cell (VPC) establish a fixed spatial pattern of two different cell fates: E-F-F-E. The two inner granddaughters attach to the somatic gonadal anchor cell (AC) and generate four vulF cells, while the two outer granddaughters produce four vulE progeny. zmp-1::GFP, a molecular marker that distinguishes these two fates, is expressed in vulE cells, but not vulF cells. We demonstrate that a short-range AC signal is required to ensure that the pattern of vulE and vulF fates is properly established. In addition, signaling between the inner and outer 1° VPC descendants, as well as intrinsic polarity of the 1° VPC daughters, is involved in the asymmetric divisions of the 1° VPC daughters and the proper orientation of the outcome. Finally, we provide evidence that RAS signaling is used during this new AC signaling event, while the Wnt receptor LIN-17 appears to mediate signaling between the inner and outer 1° VPC descendants

Mars Rover imaging systems and directional filtering

Computer literature searches were carried out at Duke University and NASA Langley Research Center. The purpose is to enhance personal knowledge based on the technical problems of pattern recognition and image understanding which must be solved for the Mars Rover and Sample Return Mission. Intensive study effort of a large collection of relevant literature resulted in a compilation of all important documents in one place. Furthermore, the documents are being classified into: Mars Rover; computer vision (theory); imaging systems; pattern recognition methodologies; and other smart techniques (AI, neural networks, fuzzy logic, etc)