Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography

By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty

Three months journeying of a Hawaiian monk seal

Hawaiian monk seals (Monachus schauinslandi) are endemic to the Hawaiian Islands and are the most endangered species of marine mammal that lives entirely within the jurisdiction of the United States. The species numbers around 1300 and has been declining owing, among other things, to poor juvenile survival which is evidently related to poor foraging success. Consequently, data have been collected recently on the foraging habitats, movements, and behaviors of monk seals throughout the Northwestern and main Hawaiian Islands. Our work here is directed to exploring a data set located in a relatively shallow offshore submerged bank (Penguin Bank) in our search of a model for a seal's journey. The work ends by fitting a stochastic differential equation (SDE) that mimics some aspects of the behavior of seals by working with location data collected for one seal. The SDE is found by developing a time varying potential function with two points of attraction. The times of location are irregularly spaced and not close together geographically, leading to some difficulties of interpretation. Synthetic plots generated using the model are employed to assess its reasonableness spatially and temporally. One aspect is that the animal stays mainly southwest of Molokai. The work led to the estimation of the lengths and locations of the seal's foraging trips.Comment: Published in at http://dx.doi.org/10.1214/193940307000000473 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Patterns of Lone Actor Terrorism in the United States

This research explores the differences in geospatial and temporal patterns between lone actor and group-based terrorists in the United States. These include differences in demographics, precursor activities, proximity to the terrorism incidents, and longevity of conducting terrorist activities. Data for this analysis were derived from the American Terrorism Study (ATS). The ATS includes information on federal criminal cases resulting from FBI investigations for “terrorism or terrorism-related activities.” The analysis includes data from 264 prevented or completed terrorism incidents in the United States from 1980-present. These incidents involved 314 indictees charged with over 3,000 federal criminal counts. They were responsible for 1,788 recorded precursor activities that occurred at over 1,100 geocoded addresses

Modal survey of the space shuttle solid rocket motor using multiple input methods

The ability to accurately characterize propellant in a finite element model is a concern of engineers tasked with studying the dynamic response of the Space Shuttle Solid Rocket Motor (SRM). THe uncertainties arising from propellant characterization through specimem testing led to the decision to perform a model survey and model correlation of a single segment of the Shuttle SRM. Multiple input methods were used to excite and define case/propellant modes of both an inert segment and, later, a live propellant segment. These tests were successful at defining highly damped, flexible modes, several pairs of which occured with frequency spacing of less than two percent

Simulations of closed-loop wavefront reconstruction for multiconjugate adaptive optics on giant telescopes

The multi-conjugate adaptive optics (MCAO) systems proposed for future giant telescopes will require new, computationally efficient, concepts for wavefront reconstruction due to their very large number of deformable mirror (DM) actuators and wavefront sensor (WFS) measurements. Preliminary versions of such reconstruction algorithms have recently been developed, and simulations of MCAO systems with 9000 or more DM actuators and 33000 or more WFS measurements are now possible using a single desktop computer. However, the results obtained to date are limited to the case of open-loop wavefront reconstruction, and more work is needed to develop computationally efficient reconstructors for the more realistic case of a closed-loop MCAO system that iteratively measures and corrects time-varying wavefront distortions. In this paper, we describe and investigate two reconstruction concepts for this application. The first approach assumes that knowledge of the DM actuator command vector and the DM-to-WFS influence matrix may be used to convert a closed-loop WFS measurement into an accurate estimate of the corresponding open-loop measurement, so that a standard open-loop wavefront reconstructor may be applied. The second approach is a very coarse (but computationally efficient) approximation to computing the minimum variance wavefront reconstructor for the residual wavefront errors in a closed-loop AO system. Sample simulation results are presented for both concepts with natural guide star (NGS) AO and laser guide star (LGS) MCAO systems on 8- and 32-meter class telescopes. The first approach yields a stable control loop with closed-loop performance comparable to the open-loop estimation accuracy of the classical minimum variance reconstructor. The second approach is unstable when implemented in a type I servo system

Multi-site mean-field theory for cold bosonic atoms in optical lattices

We present a detailed derivation of a multi-site mean-field theory (MSMFT) used to describe the Mott-insulator to superfluid transition of bosonic atoms in optical lattices. The approach is based on partitioning the lattice into small clusters which are decoupled by means of a mean field approximation. This approximation invokes local superfluid order parameters defined for each of the boundary sites of the cluster. The resulting MSMFT grand potential has a non-trivial topology as a function of the various order parameters. An understanding of this topology provides two different criteria for the determination of the Mott insulator superfluid phase boundaries. We apply this formalism to $d$-dimensional hypercubic lattices in one, two and three dimensions, and demonstrate the improvement in the estimation of the phase boundaries when MSMFT is utilized for increasingly larger clusters, with the best quantitative agreement found for $d=3$. The MSMFT is then used to examine a linear dimer chain in which the on-site energies within the dimer have an energy separation of $\Delta$. This system has a complicated phase diagram within the parameter space of the model, with many distinct Mott phases separated by superfluid regions.Comment: 30 pages, 23 figures, accepted for publication in Phys. Rev.

Computationally efficient wavefront reconstructor for simulation of multiconjugate adaptive optics on giant telescopes

Multi-conjugate adaptive optical (MCAO) systems with from 10,000 to 100,000 degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront reconstruction algorithms for these systems is impractical, since the number of calculations required to compute (apply) the reconstruction matrix scales as the cube (square) of the number of AO degrees of freedom. Significant improvements in computational efficiency are possible by exploiting the sparse and/or periodic structure of the deformable mirror influence matrices and the atmospheric turbulence covariance matrices appearing in these calculations. In this paper, we review recent progress in developing an iterative sparse matrix implementation of minimum variance wavefront reconstruction for MCAO. The basic method is preconditioned conjugate gradients, using a multigrid preconditioner incorporating a layer-oriented, iterative smoothing operator. We outline the key elements of this approach, including special considerations for laser guide star (LGS) MCAO systems with tilt-removed LGS wavefront measurements and auxiliary full aperture tip/tilt measurements from natural guide stars. Performance predictions for sample natural guide star (NGS) and LGS MCAO systems on 8 and 16 meter class telescopes are also presented

Using a Modified Purse Seine to Collect and Monitor Estuarine Fishes

We developed a modified purse seine to sample shallow water estuarine habitats and evaluated the efficacy of using this gear as a tool for monitoring estuarine fish populations in Tampa Bay, Florida. The purse seine (183-m long, 5.2 m deep and 50-mm stretch mesh nylon throughout) was easily deployed and retrieved by a 7 m flat-bottomed, bow-driven boat with a hydraulic wench and aluminum pursing davit. Retention rates of pinfish (Lagodon rhomboides) marked and released into 35 net sets averaged 49% (range 9-100%). Retention rates were not significantly influenced by sets over vegetated and unvegetated bottom types, various water depths from 1-3.3m and sets with and without bycatch. We then used the modified purse seine to sample fishes at 550 randomly selected sites in Tampa Bay from January 1997 to December 1998. Sampled habitats ranged from 1.0 to 3.3 m deep and included seagrass beds and non-vegetated sand or mud bottoms. Benthic, demersal, and pelagic fishes were captured, indicating the purse seine effectively sampled the entire water column. A wide size range of fishes was collected including pre-recruitment sizes of several economically important species. The ability of purse seines to fish independent of adjacent shorelines allowed us to sample nearshore waters that included large expanses of sea grass meadow

Parallel Deterministic and Stochastic Global Minimization of Functions with Very Many Minima

The optimization of three problems with high dimensionality and many local minima are investigated under five different optimization algorithms: DIRECT, simulated annealing, Spall’s SPSA algorithm, the KNITRO package, and QNSTOP, a new algorithm developed at Indiana University