The Geometry of Niggli Reduction I: The Boundary Polytopes of the Niggli Cone

Correct identification of the Bravais lattice of a crystal is an important step in structure solution. Niggli reduction is a commonly used technique. We investigate the boundary polytopes of the Niggli-reduced cone in the six-dimensional space G6 by algebraic analysis and organized random probing of regions near 1- through 8-fold boundary polytope intersections. We limit consideration of boundary polytopes to those avoiding the mathematically interesting but crystallographically impossible cases of 0 length cell edges. Combinations of boundary polytopes without a valid intersection in the closure of the Niggli cone or with an intersection that would force a cell edge to 0 or without neighboring probe points are eliminated. 216 boundary polytopes are found: 15 5-D boundary polytopes of the full G6 Niggli cone, 53 4-D boundary polytopes resulting from intersections of pairs of the 15 5-D boundary polytopes, 79 3-D boundary polytopes resulting from 2-fold, 3-fold and 4-fold intersections of the 15 5-D boundary polytopes, 55 2-D boundary polytopes resulting from 2-fold, 3-fold, 4-fold and higher intersections of the 15 5-D boundary polytopes, 14 1-D boundary polytopes resulting from 3-fold and higher intersections of the 15 5-D boundary polytopes. All primitive lattice types can be represented as combinations of the 15 5-D boundary polytopes. All non-primitive lattice types can be represented as combinations of the 15 5-D boundary polytopes and of the 7 special-position subspaces of the 5-D boundary polytopes. This study provides a new, simpler and arguably more intuitive basis set for the classification of lattice characters and helps to illuminate some of the complexities in Bravais lattice identification. The classification is intended to help in organizing database searches and in understanding which lattice symmetries are "close" to a given experimentally determined cell

The Geometry of Niggli Reduction II: BGAOL -- Embedding Niggli Reduction

Niggli reduction can be viewed as a series of operations in a six-dimensional space derived from the metric tensor. An implicit embedding of the space of Niggli-reduced cells in a higher dimensional space to facilitate calculation of distances between cells is described. This distance metric is used to create a program, BGAOL, for Bravais lattice determination. Results from BGAOL are compared to the results from other metric-based Bravais lattice determination algorithms

The State of Working America 2006/2007

[Excerpt] Yet, despite this unequivocally beneficial development, many Americans report dissatisfaction with where the economy seems to be headed, and many worry about their own and their children’s well-being. These concerns have led some policy makers and economists to ask: why aren’t people happier about the economy? The question seems reasonable to those who follow the top-line numbers of the economy, such as the growth of the total economy (e.g. gross domestic product), the stock market, or corporate profits. The question is easily answered, however, for those who follow and report on the data that fill the chapters of this book

The State of Working America, 2004/2005

The State of Working America, prepared biennially since 1988 by the Economic Policy Institute, includes a wide variety of data on family incomes, wages, taxes, unemployment, wealth, and poverty--data that enable the authors to closely examine the effect of the economy on the living standards of the American people

Converting three-space matrices to equivalent six-space matrices for Delone scalars in S6.

The transformations from the primitive cells of the centered Bravais lattices to the corresponding centered cells have conventionally been listed as three-by-three matrices that transform three-space lattice vectors. Using those three-by-three matrices when working in the six-dimensional space of lattices represented as Selling scalars as used in Delone (Delaunay) reduction, one could transform to the three-space representation, apply the three-by-three matrices and then back-transform to the six-space representation, but it is much simpler to have the equivalent six-by-six matrices and apply them directly. The general form of the transformation from the three-space matrix to the corresponding matrix operating on Selling scalars (expressed in space S6) is derived, and the particular S6matrices for the centered Delone types are listed. (Note: in his later publications, Boris Delaunay used the Russian version of his surname, Delone.)

An Invertible Seven-Dimensional Dirichlet Cell Characterization of Lattices

Characterization of crystallographic lattices is an important tool in structure solution, crystallographic database searches and clustering of diffraction images in serial crystallography. Characterization of lattices by Niggli-reduced cells (based on the three shortest non-coplanar lattice edge vectors) or by Delaunay-reduced cells (based on four edge vectors summing to zero and all meeting at obtuse or right angles) are commonly used. The Niggli cell derives from Minkowski reduction. The Delaunay cell derives from Selling reduction. All are related to the Wigner-Seitz (or Dirichlet, or Voronoi) cell of the lattice, which consists of the points at least as close to a chosen lattice point than they are to any other lattice point. Starting from a Niggli-reduced cell, the Dirichlet cell is characterized by the planes determined by thirteen lattice half-edges: the midpoints of the three Niggli cell edges, the six Niggli cell face diagonals and the four body-diagonals, but seven of the edge lengths are sufficient: three edge lengths, the three shorter of each pair of face-diagonal lengths and the shortest body-diagonal length, from which the Niggli-reduced cell may be recovered.Comment: 29 pages, 2 figure

The Optimal Projection Equations for Fixed-Order Sampled-Data Dynamic Compensation with Computation Delay

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/57876/1/FixedOrderSampledData.pd

Simulation of Hyperspectral Images

A software package generates simulated hyperspectral imagery for use in validating algorithms that generate estimates of Earth-surface spectral reflectance from hyperspectral images acquired by airborne and spaceborne instruments. This software is based on a direct simulation Monte Carlo approach for modeling three-dimensional atmospheric radiative transport, as well as reflections from surfaces characterized by spatially inhomogeneous bidirectional reflectance distribution functions. In this approach, "ground truth" is accurately known through input specification of surface and atmospheric properties, and it is practical to consider wide variations of these properties. The software can treat both land and ocean surfaces, as well as the effects of finite clouds with surface shadowing. The spectral/spatial data cubes computed by use of this software can serve both as a substitute for, and a supplement to, field validation data

Znaczna poprawa kliniczna u chorego z niewydolnością serca i zespołem obturacyjnego bezdechu sennego po właściwym ustaleniu stałego, dodatniego ciśnienia w drogach oddechowych

Zaburzenia oddychania w czasie snu często towarzyszą niewydolności krążenia i mogą przybierać postać zespołu obturacyjnego i ośrodkowego bezdechu sennego. Użycie aparatów wytwarzających stałe dodatnie ciśnienie w drogach oddechowych (CPAP, continuous positive airway pressure) u chorych na niewydolność krążenia ze współistniejącym zespołem obturacyjnego bezdechu sennego prowadzi do poprawy profilu neuroendokrynnego i polepszenia funkcji serca. Obturacja dróg oddechowych (jak również ciśnienie CPAP konieczne do jej pokonania) u chorego na niewydolność krążenia może podlegać dużym zmianom spowodowanym zmiennym obrzękiem dróg oddechowych. W niniejszej pracy przedstawiono opis pacjenta z niewydolnością krążenia, którego objawy sercowo-naczyniowe znacząco poprawiły się w czasie leczenia współistniejacego zespołu obturacyjnego bezdechu sennego po właściwym ustaleniu ciśnienia przy użyciu aparatu automatycznie dostosowującego dodatnie ciśnienie w drogach oddechowych (AutoPAP). Pneumonol. Alergol. Pol. 2011; 79, 1: 48-51Sleep disordered breathing (SDB) is frequently present in heart failure (HF), and it may take the form of obstructive (OSA) and central (CSA) sleep apnea. The use of continuous positive airway pressure (CPAP) in patients with OSA and HF is associated with an improved neuroendocrine profile and cardiac function. The degree of upper airway obstruction and the airway closing pressure (and the PAP pressure used to relieve it) may all be highly variable in a setting of uncontrolled HF, mostly due to variable airway oedema. We present a case of a man with HF whose cardiac symptoms radically improved after adequate treatment of his OSA with an auto-adjusting PAP device. Pneumonol. Alergol. Pol. 2011; 79, 1: 48-5