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NASA NTRS1981

A complete X-ray sample of the high latitude sky from HEAO-1 A-2: log N lo S and luminosity functions

An experiment was performed in which a complete X-ray survey of the 8.2 steradians of the sky at galactic latitudes where the absolute value of b is 20 deg down to a limiting sensitivity of 3.1 x ten to the minus 11th power ergs/sq cm sec in the 2-10 keV band. Of the 85 detected sources 17 were identified with galactic objects, 61 were identified with extragalactic objects, and 7 remain unidentified. The log N - log S relation for the non-galactic objects is well fit by the Euclidean relationship. The X-ray spectra of these objects were used to construct log N - log S in physical units. The complete sample of identified sources was used to construct X-ray luminosity functions, using the absolute maximum likelihood method, for clusters galaxies and active galactic nuclei.

Piccinotti, G.↗

NASA NTRS1981

Evolving nucleotide binding surfaces

An analysis is presented of the stability and nature of binding of a nucleotide to several known dehydrogenases. The employed approach includes calculation of hydrophobic stabilization of the binding motif and its intermolecular interaction with the ligand. The evolutionary changes of the binding motif are studied by calculating the Euclidean deviation of the respective dehydrogenases. Attention is given to the possible structural elements involved in the origin of nucleotide recognition by non-coded primordial polypeptides.

Kieber-Emmons, T.↗

NASA NTRS1981

CROP type analysis using Landsat digital data

Classification and statistical sampling techniques for crop type discrimination using Landsat digital data have been developed by the University of California in cooperation with NASA and the California Department of Water Resources. Ratioed bands (MSS 7/5 and 5/4) and a sun-angle corrected Euclidean albedo band were prepared from data for the Sacramento Valley for five different dates. The test area was stratified into general crop groupings based on the particular patterns of irrigation timing for each crop. Data classified within each stratum were used to produce a crop type map. Comparison with ground data indicates that certain crops and crop groups are discernable. Small grains and rice are easily identifiable, as are deciduous fruit varieties as a group. However, it is not feasible to separate various fruit and nut varieties, or separate vegetable crops with these techniques at present.

Brown, C. E.↗

NASA NTRS1983

Applications of the contravariant form of the Navier-Stokes equations

The contravariant Navier-Stokes equations in weak conservation form are well suited to certain fluid flow analysis problems. Three dimensional contravariant momentum equations may be used to obtain Navier-Stokes equations in weak conservation form on a nonplanar two dimensional surface with varying streamsheet thickness. Thus a three dimensional flow can be simulated with two dimensional equations to obtain a quasi-three dimensional solution for viscous flow. When the Navier-Stokes equations on the two dimensional nonplanar surface are transformed to a generalized body fitted mesh coordinate system, the resulting equations are similar to the equations for a body fitted mesh coordinate system on the Euclidean plane. Contravariant momentum components are also useful for analyzing compressible, three dimensional viscous flow through an internal duct by parabolic marching. This type of flow is efficiently analyzed by parabolic marching methods, where the streamwise momentum equation is uncoupled from the two crossflow momentum equations. This can be done, even for ducts with a large amount of turning, if the Navier-Stokes equations are written with contravariant components.

Katsanis, T.↗

NASA NTRS1981

Control of nonlinear time-varying systems

Necessary and sufficient conditions are given for a time-varying nonlinear system of specific form to be transformed into a time-invariant controllable linear system. Since the present work will be in a neighborhood of the origin, it is unnecessary to name specific sets and it is assumed that all assumptions, conditions and results hold in an open set in the appropriate Euclidean space that contains the origin. This theory can be combined with the global inverse function theorems to produce global results.

Hunt, L. R.↗

NASA NTRS1984

A Systolic VLSI Design of a Pipeline Reed-solomon Decoder

A pipeline structure of a transform decoder similar to a systolic array was developed to decode Reed-Solomon (RS) codes. An important ingredient of this design is a modified Euclidean algorithm for computing the error locator polynomial. The computation of inverse field elements is completely avoided in this modification of Euclid's algorithm. The new decoder is regular and simple, and naturally suitable for VLSI implementation.

Shao, H. M.↗

NASA NTRS1984

Modeling concepts for communication of geometric shape data

ANSI5, an abbreviation for Section 5 of the American National Standard under Engineering Drawing and Related Documentation Practices (Committee Y14) on Digital Representation for Communication of Product Definition Data (ANSI Y14.26M-1981), allows encoding of a broad range of geometric shapes to be communicated through digital channels. A brief review of its underlying concepts is presented. The intent of ANSI5 is to devise a unified set of concise language formats for transmission of data pertaining to five types of geometric entities in Euclidean 3 space (E(3)). These are regarded as point like, curve like, surface like, solid like, and a combination of these types. For the first four types, ANSI5 makes a distinction between the geometry and topology. Geometry is a description of the spatial occupancy of the entity, and topology discusses the interconnectedness of the entity's boundary components.

Collins, M. F.↗

NASA NTRS1984

A Simple Algorithm for the Metric Traveling Salesman Problem

An algorithm was designed for a wire list net sort problem. A branch and bound algorithm for the metric traveling salesman problem is presented for this. The algorithm is a best bound first recursive descent where the bound is based on the triangle inequality. The bounded subsets are defined by the relative order of the first K of the N cities (i.e., a K city subtour). When K equals N, the bound is the length of the tour. The algorithm is implemented as a one page subroutine written in the C programming language for the VAX 11/750. Average execution times for randomly selected planar points using the Euclidean metric are 0.01, 0.05, 0.42, and 3.13 seconds for ten, fifteen, twenty, and twenty-five cities, respectively. Maximum execution times for a hundred cases are less than eleven times the averages. The speed of the algorithms is due to an initial ordering algorithm that is a N squared operation. The algorithm also solves the related problem where the tour does not return to the starting city and the starting and/or ending cities may be specified. It is possible to extend the algorithm to solve a nonsymmetric problem satisfying the triangle inequality.

Grimm, M. J.↗

NASA NTRS1982

An evaluation of thematic mapper simulator data for mapping forest cover

Computer-aided analysis techniques applied to Thematic Mapper Simulator (TMS) data were evaluated for the purpose of mapping forest cover types. Classification results obtained using a supervised set of training statistics and various combinations of three and four channel subsets of the seven available TMS channels are compared for the L2 (Minimum Euclidean Distance), GML (Gaussian Maximum Likelihood), and SECHO (Supervised Extraction and Classification of Homogeneous Objects) classification algorithms. SECHO performed significantly better than either of the two per-point classifiers for the untransformed data. Overall classification results of the Karhunen-Loeve transformation increased for the L2 algorithm, but decreased for both the GML and SECHO algorithms.

Dean, M. E.↗

NASA NTRS1982

Advances in information extraction techniques

Sundry recent developments are presented which show some potential for affecting the automatic extraction of information from remotely sensed data. Pattern representations more abstract than Euclidean vector spaces offer some hope of unifying structural and decision theoretical approaches. The estimation of expected classification error rates is becoming more sophisticated and rigorous, but useful finite-sample results for nonparametric distributions appear unobtainable. Focus on computational complexity allows comparison of algorithms, while software engineering techniques reduce the effort necessary to develop and maintain complex image processing systems. Advances in computer systems architecture, commercial database technology, and man-machine communications should be closely monitored by the remote sensing community. A NASA-sponsored recommendation for research directions in mathematical pattern recognition are offered.

Nagy, G.↗

NASA NTRS1983

Analysis of Landsat for monitoring vegetables in New York mucklands

This pilot study assessed the feasibility of relying on Landsat multispectral scanner data for inventorying vegetables grown in mucklands,in variably shaped, variably sized fields. Classification of muckland vegetables using a Euclidean distance classifier and a parallelepiped classifier was performed with reasonable accuracy (generally over 60 percent) based on only one date of Landsat data. Prior canonical and principal component analyses did not improve the classification accuracy but did reduce the dimensionality of the data.

Zhu, M. H.↗

NASA NTRS1985

A Factorization Approach to the Linear Regulator Quadratic Cost Problem

A factorization approach to the linear regulator quadratic cost problem is developed. This approach makes some new connections between optimal control, factorization, Riccati equations and certain Wiener-Hopf operator equations. Applications of the theory to systems describable by evolution equations in Hilbert space and differential delay equations in Euclidean space are presented.

Milman, M. H.↗

NASA NTRS1985

Combined trellis coding with asymmetric MPSK modulation: An MSAT-X report

Traditionally symmetric, multiple phase-shift-keyed (MPSK) signal constellations, i.e., those with uniformly spaced signal points around the circle, have been used for both uncoded and coded systems. Although symmetric MPSK signal constellations are optimum for systems with no coding, the same is not necessarily true for coded systems. This appears to show that by designing the signal constellations to be asymmetric, one can, in many instances, obtain a significant performance improvement over the traditional symmetric MPSK constellations combined with trellis coding. The joint design of n/(n + 1) trellis codes and asymmetric 2 sup n + 1 - point MPSK is considered, which has a unity bandwidth expansion relative to uncoded 2 sup n-point symmetric MPSK. The asymptotic performance gains due to coding and asymmetry are evaluated in terms of the minimum free Euclidean distance free of the trellis. A comparison of the maximum value of this performance measure with the minimum distance d sub min of the uncoded system is an indication of the maximum reduction in required E sub b/N sub O that can be achieved for arbitrarily small system bit-error rates. It is to be emphasized that the introduction of asymmetry into the signal set does not effect the bandwidth of power requirements of the system; hence, the above-mentioned improvements in performance come at little or no cost. MPSK signal sets in coded systems appear in the work of Divsalar.

Simon, M. K.↗

NASA NTRS1985

A cluster analysis method for identification of subpopulations of cells in flow cytometric list-mode arrays

A specialized program was developed for flow cytometric list-mode data using an heirarchical tree method for identifying and enumerating individual subpopulations, the method of principal components for a two-dimensional display of 6-parameter data array, and a standard sorting algorithm for characterizing subpopulations. The program was tested against a published data set subjected to cluster analysis and experimental data sets from controlled flow cytometry experiments using a Coulter Electronics EPICS V Cell Sorter. A version of the program in compiled BASIC is usable on a 16-bit microcomputer with the MS-DOS operating system. It is specialized for 6 parameters and up to 20,000 cells. Its two-dimensional display of Euclidean distances reveals clusters clearly, as does its 1-dimensional display. The identified subpopulations can, in suitable experiments, be related to functional subpopulations of cells.

Li, Z. K.↗

NASA NTRS1985

A new description of combined trellis coding with asymmetric modulation

The combination of rate k/(k+t) trellis codes with digital modulations described by an asymmetric 2 sup k+1-point signal constellation has been recently shown to yield performance improvement over the traditional symmetric constellation combined with the same trellis code. The approach taken is to specify an underlying trellis code and then map the output code symbols into the fixed signal constellation based on a rule called mapping by set partitioning. The latter process is tantamount to assigning signals from the constellation to the trellis code transitions so as to maximize the free Euclidean distance of the code. Recently, a new description of trellis codes has been given that combines the above two steps into one. The ideas introduced are further explored, placing particular emphasis on the optimization of the signal constellation asymmetry. It can be concluded that the trellis-coded amplitude modulation (AM) designs given are very close to being optimum.

Simon, M. K.↗

NASA NTRS1984

On the surface density of X-ray selected BL Lacertae objects

Only a handful of BL Lac objects have been found as a result of systematic optical identification of serendipitous Einstein X-ray sources. By combining the data from two flux-limited complete X-ray surveys (the HEAO 1 A-2 and the Einstein Observatory Medium Sensitivity Survey) the surface density of X-ray emitting BL Lac objects is evaluated as a function of their X-ray flux. It is found that a single power law is not an acceptable representation of the BL Lac objects' X-ray log N-log S. The number-flux relationship is consistent with the Euclidean slope at 'high' flux levels but shows a drastic flattnring below fluxes of the order of 10 to the -12th ergs per sq cm/s. The implications of this result are briefly discussed with respect to the luminosity function, the cosmological evolution, and the X-ray to optical flux ratio in BL Lac objects.

Maccacaro, T.↗

NASA NTRS1985

A VLSI design of a pipeline Reed-Solomon decoder

Shao, H. M.↗

NASA NTRS1985

A remark about pointed bubbles

The polymer expansion is a formal algebraic identity between a partition function and logarithm in statistical physics problems. The expansion gives a systematic method to control the free energy or to establish exponential tree-graph decay of connected correlations. Here, the convergence properties of the polymer expansion are analyzed in connection with three practical examples, including: intersecting bonds in chemical polymer chains; a connected closed hypersurface built from the (d-1)-faces of the d-dimensional unit cubes; and the set of Feynamn diagrams in the perturbation series of the Euclidean field theory partition function Z. The example of connected polymer chains is generalized to apply to other lattice models, including n-state Ising models at high temperature; short range lattice gases at high temperature; and weak coupling lattice field and gauge theories.

Garabedian, P. R.↗