Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Case

In blind hyperspectral unmixing (HU), the pure-pixel assumption is well-known to be powerful in enabling simple and effective blind HU solutions. However, the pure-pixel assumption is not always satisfied in an exact sense, especially for scenarios where pixels are heavily mixed. In the no pure-pixel case, a good blind HU approach to consider is the minimum volume enclosing simplex (MVES). Empirical experience has suggested that MVES algorithms can perform well without pure pixels, although it was not totally clear why this is true from a theoretical viewpoint. This paper aims to address the latter issue. We develop an analysis framework wherein the perfect endmember identifiability of MVES is studied under the noiseless case. We prove that MVES is indeed robust against lack of pure pixels, as long as the pixels do not get too heavily mixed and too asymmetrically spread. The theoretical results are verified by numerical simulations

Identification and proposed control of helicopter transmission noise at the source

Helicopter cabin interiors require noise treatment which is expensive and adds weight. The gears inside the main power transmission are major sources of cabin noise. Work conducted by the NASA Lewis Research Center in measuring cabin interior noise and in relating the noise spectrum to the gear vibration of the Army OH-58 helicopter is described. Flight test data indicate that the planetary gear train is a major source of cabin noise and that other low frequency sources are present that could dominate the cabin noise. Companion vibration measurements were made in a transmission test stand, revealing that the single largest contributor to the transmission vibration was the spiral bevel gear mesh. The current understanding of the nature and causes of gear and transmission noise is discussed. It is believed that the kinematical errors of the gear mesh have a strong influence on that noise. The completed NASA/Army sponsored research that applies to transmission noise reduction is summarized. The continuing research program is also reviewed

Lattice Quantum Gravity: Review and Recent Developments

We review the status of different approaches to lattice quantum gravity indicating the successes and problems of each. Recent developments within the dynamical triangulation formulation are then described. Plenary talk at LATTICE 95 July 11-15, Melbourne, Australia.Comment: 12 pages, 8 figure

Automatic tool path generation for numerically controlled machining of sculptured surfaces

This dissertation presents four new tool path generation approaches for numerically controlled machining of sculptured surfaces: TRI\sb-XYINDEX, FINISH, FIVEX\sb-INDEX, FIX\sb-AXIS\sb-INDEX. All of the above systems index the tool across the object surface in the Cartesian space so that evenly distributed tool paths are accomplished. TRI\sb-XYINDEX is a three-axis tool path generation system which uses a surface triangle set (STS) representation of the surface for tool position calculations. Surface edges are detected with local searching algorithms. Quick tool positioning is achieved by selecting candidate elements of polygons. Test results show that TRI\sb-XYINDEX is more efficient when machining surfaces which are relatively flat while the discrete point approach is faster for highly curved surfaces. FINISH was developed for generating three-axis ball-end tool paths for local surface finishing. It was based on the SPS. Given a surface with excess material represented by a set of discrete points, FINISH automatically identifies the undercut areas. Results show that FINISH provides significant improvements in machining efficiency. FIVEX\sb-INDEX is developed for generating five-axis flat-end tool paths. It uses an STS approximation. Contact points on the surface are derived from edge lists obtained from the intersections of vertical cutting planes with the polygon set. The distances between adjacent end points set an initial step-forward increment between surface contact points. To verify tool movements, some intermediate tool positions are interpolated. The key features of FIVEX\sb-INDEX are: (1) a polygon set representing an object which may be composed of multiple surfaces; (2) Surface contact point generation by cutting plane intersection; (3) simple tool incrementing and positioning algorithms; (4) minimal user interaction; (5) user controlled accuracy of resulting tool paths. FIX\sb-AXIS\sb-INDEX is a subsystem of FIVEX\sb-INDEX, generating tool paths for a tool with fixed orientations. Surface contact points are generated similar to FIVEX\sb-INDEX while tool positions are corrected with the highest point technique along the tool axis direction. Linear fitting is applied to output tool positions. FIX\sb-AXIS\sb-INDEX is preferred for machining surfaces curved in one direction, such as ruled surfaces. Test results show that FIX\sb-AXIS\sb-INDEX can serve as a three-axis tool path generation system but a five-axis machine is required to do it. (Abstract shortened by UMI.)

Orbital Magnetism in the Ballistic Regime: Geometrical Effects

We present a general semiclassical theory of the orbital magnetic response of noninteracting electrons confined in two-dimensional potentials. We calculate the magnetic susceptibility of singly-connected and the persistent currents of multiply-connected geometries. We concentrate on the geometric effects by studying confinement by perfect (disorder free) potentials stressing the importance of the underlying classical dynamics. We demonstrate that in a constrained geometry the standard Landau diamagnetic response is always present, but is dominated by finite-size corrections of a quasi-random sign which may be orders of magnitude larger. These corrections are very sensitive to the nature of the classical dynamics. Systems which are integrable at zero magnetic field exhibit larger magnetic response than those which are chaotic. This difference arises from the large oscillations of the density of states in integrable systems due to the existence of families of periodic orbits. The connection between quantum and classical behavior naturally arises from the use of semiclassical expansions. This key tool becomes particularly simple and insightful at finite temperature, where only short classical trajectories need to be kept in the expansion. In addition to the general theory for integrable systems, we analyze in detail a few typical examples of experimental relevance: circles, rings and square billiards. In the latter, extensive numerical calculations are used as a check for the success of the semiclassical analysis. We study the weak-field regime where classical trajectories remain essentially unaffected, the intermediate field regime where we identify new oscillations characteristic for ballistic mesoscopic structures, and the high-field regime where the typical de Haas-van Alphen oscillations exhibit finite-size corrections. We address the comparison with experimental data obtained in high-mobility semiconductor microstructures discussing the differences between individual and ensemble measurements, and the applicability of the present model.Comment: 88 pages, 15 Postscript figures, 3 further figures upon request, to appear in Physics Reports 199