Rectangular Full Packed Format for Cholesky's Algorithm: Factorization, Solution and Inversion

We describe a new data format for storing triangular, symmetric, and Hermitian matrices called RFPF (Rectangular Full Packed Format). The standard two dimensional arrays of Fortran and C (also known as full format) that are used to represent triangular and symmetric matrices waste nearly half of the storage space but provide high performance via the use of Level 3 BLAS. Standard packed format arrays fully utilize storage (array space) but provide low performance as there is no Level 3 packed BLAS. We combine the good features of packed and full storage using RFPF to obtain high performance via using Level 3 BLAS as RFPF is a standard full format representation. Also, RFPF requires exactly the same minimal storage as packed format. Each LAPACK full and/or packed triangular, symmetric, and Hermitian routine becomes a single new RFPF routine based on eight possible data layouts of RFPF. This new RFPF routine usually consists of two calls to the corresponding LAPACK full format routine and two calls to Level 3 BLAS routines. This means {\it no} new software is required. As examples, we present LAPACK routines for Cholesky factorization, Cholesky solution and Cholesky inverse computation in RFPF to illustrate this new work and to describe its performance on several commonly used computer platforms. Performance of LAPACK full routines using RFPF versus LAPACK full routines using standard format for both serial and SMP parallel processing is about the same while using half the storage. Performance gains are roughly one to a factor of 43 for serial and one to a factor of 97 for SMP parallel times faster using vendor LAPACK full routines with RFPF than with using vendor and/or reference packed routines

Influence of optical aberrations in an atomic gyroscope

In atom interferometry based on light-induced diffraction, the optical aberrations of the laser beam splitters are a dominant source of noise and systematic effect. In an atomic gyroscope, this effect is dramatically reduced by the use of two atomic sources. But it remains critical while coupled to fluctuations of atomic trajectories, and appears as a main source of noise to the long term stability. Therefore we measure these contributions in our setup, using cold Cesium atoms and stimulated Raman transitions

Late Cenozoic Geomorphic Evolution of the Texas Panhandle and Northeastern New Mexico: Case Studies of Structural Controls of Regional Drainage Development

Salt dissolution has affected parts of the Upper Permian Salado, Seven Rivers, San Andres, Glorieta, and upper Clear Fork Formations beneath the Pecos River Valley in eastern New Mexico and beneath the Canadian River Valley and the Rolling Plains of the Texas Panhandle. Extensive dissolution of the salts of the Salado and Seven Rivers Formations has also occurred beneath the Southern High Plains. The cumulative thickness of salt lost to dissolution exceeds 150 m (500 ft) along the western, northern, and eastern margins of the Palo Duro Basin. Dissolution and subsidence occurred during the deposition of the Tertiary Ogallala Formation, but Ogallala deposition kept pace with subsidence. Following the end of Ogallala deposition in the late Pliocene, surface subsidence resulted in lacustrine basins along trends of relatively rapid dissolution. Preserved lacustrine sediments contain Blancan faunas, confirming minimum late Pliocene ages for the basins. Continued subsidence along trends of relatively rapid dissolution during the late Tertiary and early Quaternary resulted in a series of basins that diverted many of the streams flowing southeasterly across the Southern High Plains. As a result of subsidence, the headwaters of the ancestral Brazos River were diverted during the middle Pleistocene from a southeasterly drainage through the Portales paleovalley to a southerly drainage through the Pecos Valley. The present-day headwaters of the Canadian River are probably a former tributary of the Pecos-Portales-Brazos system that was diverted to the northeast along a subsidence trend caused by dissolution during the late Pliocene or early Quaternary.Bureau of Economic Geolog

The Lookup Technique to Replace Nested-IF Formulas in Spreadsheet Programming

Spreadsheet programmers often implement contingent logic using a nested-IF formula even though this technique is difficult to test and audit and is believed to be risky. We interpret the programming of contingent logic in spreadsheets in the context of traditional computer programming. We investigate the “lookup technique” as an alternative to nested-IF formulas, describe its benefits for testing and auditing, and define its limitations. The lookup technique employs four distinct principles: 1) make logical tests visible; 2) make outcomes visible; 3) make logical structure visible; and 4) replace a multi-function nested-IF formula with a single-function lookup formula. It can be used only for certain simple contingent logic. We describe how the principles can be applied in more complex situations, and suggest avenues for further research

Propagation of Bose-Einstein condensates in a magnetic waveguide

Gaseous Bose-Einstein condensates of 2-3 million atoms were loaded into a microfabricated magnetic trap using optical tweezers. Subsequently, the condensates were released into a magnetic waveguide and propagated 12 mm. Single-mode propagation was observed along homogeneous segments of the waveguide. Inhomogeneities in the guiding potential arose from geometric deformations of the microfabricated wires and caused strong transverse excitations. Such deformations may restrict the waveguide physics that can be explored with propagating condensates.Comment: 5 pages, 4 figure

Geologic Review of Propsed Amarillo Area Site for the Superconducting Super Collider (SSC)

In June 1987, the Texas National Research Laboratory Commission commissioned the Bureau of Economic Geology at The University of Texas at Austin to conduct a review and brief report on the geology of the proposed site for the Superconducting Super Collider (SSC) in the Amarillo area. They also requested a surface geologic map of the site. An informal task force was assembled for this purpose, including Jay A. Raney (Coordinator), Thomas C. Gustavson, and S. Christopher Caran from the Bureau of Economic Geology. This report is accompanied by the geologic map (Plate 1) of the proposed Amarillo area site in the Texas Panhandle.Bureau of Economic Geolog

Electromagnetic Delineation of Saline Ground-Water Plumes in Alluvium and Bedrock Along the Canadian River Between Ute Reservoir and Rana Canyon, New Mexico

Lake Meredith, which supplies water for domestic use to all major Texas cities on the Southern High Plains, exceeds the Texas Water Commission's standards for chloride and sulfate content (300 mg/L) as well as the U.S. Environmental Protection Agency's standard for sodium (250 mg/L). Location of the sources of these solutes is a necessary first step in any remediation effort to reduce the salinity of river waters and ultimately the salinity of Lake Meredith. Initial examination of the conductivity and salinity of Canadian River waters, which supply Lake Meredith, was completed in May 1992. The results of these analyses indicated that saline ground-water discharge areas were concentrated in the river segment between the Ute Reservoir and Rana Canyon, New Mexico, and that ground-water conductivity surveys should be focused along this part of the river. This assessment of the distribution of saline ground-water plumes in alluvium and bedrock along the Canadian River between the Ute Reservoir and Rana Canyon, New Mexico, is an integrated geological and geophysical study that incorporates both the use of extensive ground conductivity measurements and joint measurements. These data are used to identify sites of potential ground-water discharge to the river and to suggest preferred ground-water flow paths.Bureau of Economic Geolog

Quantum-enhanced gyroscopy with rotating anisotropic Bose–Einstein condensates

High-precision gyroscopes are a key component of inertial navigation systems. By considering matter wave gyroscopes that make use of entanglement it should be possible to gain some advantages in terms of sensitivity, size, and resources used over unentangled optical systems. In this paper we consider the details of such a quantum-enhanced atom interferometry scheme based on atoms trapped in a carefully-chosen rotating trap. We consider all the steps: entanglement generation, phase imprinting, and read-out of the signal and show that quantum enhancement should be possible in principle. While the improvement in performance over equivalent unentangled schemes is small, our feasibility study opens the door to further developments and improvements