High order recombination and an application to cubature on Wiener space

Particle methods are widely used because they can provide accurate descriptions of evolving measures. Recently it has become clear that by stepping outside the Monte Carlo paradigm these methods can be of higher order with effective and transparent error bounds. A weakness of particle methods (particularly in the higher order case) is the tendency for the number of particles to explode if the process is iterated and accuracy preserved. In this paper we identify a new approach that allows dynamic recombination in such methods and retains the high order accuracy by simplifying the support of the intermediate measures used in the iteration. We describe an algorithm that can be used to simplify the support of a discrete measure and give an application to the cubature on Wiener space method developed by Lyons and Victoir [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460 (2004) 169-198].Comment: Published in at http://dx.doi.org/10.1214/11-AAP786 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Measured limits to contamination of optical surfaces by elastomers in vacuum

We have monitored the reflectivity of mirrors that were exposed to a fluoroelastomer (3M-Fluorel 2176) and a room-temperature vulcanizing silicone rubber (RTV-615) in vacuum. The 95% confidence limit on the decrease of mirror reflectivities was less than 0.35 ppm/week for Fluorel and <0.29 ppm@week for RTV-615

A Functional Approach to FBSDEs and Its Application in Optimal Portfolios

In Liang et al (2009), the current authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability spaces. In this paper the authors continue the study of functional differential equations and demonstrate how such approach can be used to solve FBSDEs. By this approach the equations can be solved in one direction altogether rather than in a forward and backward way. The solutions of FBSDEs are then employed to construct the weak solutions to a class of BSDE systems (not necessarily scalar) with quadratic growth, by a nonlinear version of Girsanov's transformation. As the solving procedure is constructive, the authors not only obtain the existence and uniqueness theorem, but also really work out the solutions to such class of BSDE systems with quadratic growth. Finally an optimal portfolio problem in incomplete markets is solved based on the functional differential equation approach and the nonlinear Girsanov's transformation.Comment: 26 page

Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H>1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration, and the classical Ito stochastic calculus. The existence result is based on the Yamada-Watanabe theorem.Comment: 21 page

A Remote Sensing Evaluation of Forest Resources in Indiana's Coastal Zone Management Area

No abstract availabl

Validation of an expert system intended for research in distributed artificial intelligence

The expert system discussed in this paper is designed to function as a testbed for research on cooperating expert systems. Cooperating expert systems are members of an organization which dictates the manner in which the expert systems will interact when solving a problem. The Blackbox Expert described in this paper has been constructed using the C Language Integrated Production System (CLIPS), C++, and X windowing environment. CLIPS is embedded in a C++ program which provides objects that are used to maintain the state of the Blackbox puzzle. These objects are accessed by CLIPS rules through user-defined functions calls. The performance of the Blackbox Expert is validated by experimentation. A group of people are asked to solve a set of test cases for the Blackbox puzzle. A metric has been devised which evaluates the 'correctness' of a solution proposed for a test case of Blackbox. Using this metric and the solutions proposed by the humans, each person receives a rating for their ability to solve the Blackbox puzzle. The Blackbox Expert solves the same set of test cases and is assigned a rating for its ability. Then the rating obtained by the Blackbox Expert is compared with the ratings of the people, thus establishing the skill level of our expert system

Long-term orbital lifetime predictions

Long-term orbital lifetime predictions are analyzed. Predictions were made for three satellites: the Solar Max Mission (SMM), the Long Duration Exposure Facility (LDEF), and the Pegasus Boiler Plate (BP). A technique is discussed for determining an appropriate ballistic coefficient to use in the lifetime prediction. The orbital decay rate should be monitored regularly. Ballistic coefficient updates should be done whenever there is a significant change in the actual decay rate or in the solar activity prediction

The mid-domain effect: It’s not just about space

Ecologists and biogeographers have long sought to understand how and why diversity varies across space. Up until the late 20th century, the dominant role of environmental gradients and historical processes in driving geographical species richness patterns went largely undisputed. However, almost 20 years ago, Colwell & Hurtt (1994) proposed a radical reappraisal of ecological gradient theory that called into question decades of empirical and theoretical research. That controversial idea was later termed the ‘the mid-domain effect’: the simple proposition that in the absence of environmental gradients, the random placement of species ranges within a bounded domain will give rise to greatest range overlap, and thus richness, at the center of the domain (Colwell & Lees, 2000) (Fig. 1a). The implication of this line of reasoning is that the conventional null model of equal species richness regardless of latitude, elevation or depth should be replaced by one where richness peaks at some midpoint in geographical space. Our intention here is to draw attention to a neglected, yet important manifestation of the mid-domain effect, namely the application of mid-domain models (also referred to as geometric constraint models) to non-spatial domains. If individual species have ranges that exist not just in geographical space but also in environmental factors, such as temperature, rainfall, pH, productivity or disturbance, shouldn’t we also expect mid-domain richness peaks along non-spatial gradients? A mid-domain model applied to non-spatial gradients predicts the maximum potential richness for every value of an environmental factor. As with spatial mid-domain models, realized richness would probably be less, but the limits to richness are still predicted to be hump-shaped. Indeed, hump-shaped relationships emerge with remarkably high frequency across various non-spatial gradients. For instance, two of ecology’s most fundamental, albeit controversial theories – the productivity–diversity relationship and the intermediate disturbance hypothesis – predict mid-domain peaks in species richness. However, the potential of non-spatial mid-domain models has gone largely ignored

Shot Noise in Gravitational-Wave Detectors with Fabry-Perot Arms

Shot-noise-limited sensitivity is calculated for gravitational-wave interferometers with Fabry–Perot arms, similar to those being installed at the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the Italian–French Laser Interferometer Collaboration (VIRGO) facility. This calculation includes the effect of nonstationary shot noise that is due to phase modulation of the light. The resulting formula is experimentally verified by a test interferometer with suspended mirrors in the 40-m arms