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At least 163 records · Page 9

Squeezed states as representations of symplectic groups

It is shown that the SU(1,1)-like and SU(2)-like two-photon coherent states can be combined to form a O(3,2)-like two-photon state. Since the O(3,2) group has many subgroups, there are also many new interesting new coherent and squeezed two-photon states. Among them is the two-photon sheared state whose symmetry property is like that for the two-dimensional Euclidean group. There are now two-phonon coherent states which may exhibit symmetries not yet observed for photons, including sheared states. Let us note that both SU(1,1) and S(3,2) are isomorphic to the symplectic groups Sp(2) and Sp(4) respectively, and that symplectic transformations consist of rotations and squeeze transformations.

Han, D.↗

Multi-Scale Fractal Analysis of Image Texture and Pattern

Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely independent of scale. Self-similarity is defined as a property of curves or surfaces where each part is indistinguishable from the whole, or where the form of the curve or surface is invariant with respect to scale. An ideal fractal (or monofractal) curve or surface has a constant dimension over all scales, although it may not be an integer value. This is in contrast to Euclidean or topological dimensions, where discrete one, two, and three dimensions describe curves, planes, and volumes. Theoretically, if the digital numbers of a remotely sensed image resemble an ideal fractal surface, then due to the self-similarity property, the fractal dimension of the image will not vary with scale and resolution. However, most geographical phenomena are not strictly self-similar at all scales, but they can often be modeled by a stochastic fractal in which the scaling and self-similarity properties of the fractal have inexact patterns that can be described by statistics. Stochastic fractal sets relax the monofractal self-similarity assumption and measure many scales and resolutions in order to represent the varying form of a phenomenon as a function of local variables across space. In image interpretation, pattern is defined as the overall spatial form of related features, and the repetition of certain forms is a characteristic pattern found in many cultural objects and some natural features. Texture is the visual impression of coarseness or smoothness caused by the variability or uniformity of image tone or color. A potential use of fractals concerns the analysis of image texture. In these situations it is commonly observed that the degree of roughness or inexactness in an image or surface is a function of scale and not of experimental technique. The fractal dimension of remote sensing data could yield quantitative insight on the spatial complexity and information content contained within these data. A software package known as the Image Characterization and Modeling System (ICAMS) was used to explore how fractal dimension is related to surface texture and pattern. The ICAMS software was verified using simulated images of ideal fractal surfaces with specified dimensions. The fractal dimension for areas of homogeneous land cover in the vicinity of Huntsville, Alabama was measured to investigate the relationship between texture and resolution for different land covers.

Emerson, Charles W.↗

Signal Analysis of Helicopter Blade-Vortex-Interaction Acoustic Noise Data

Blade-Vortex-Interaction (BVI) produces annoying high-intensity impulsive noise. NASA Ames collected several sets of BVI noise data during in-flight and wind tunnel tests. The goal of this work is to extract the essential features of the BVI signals from the in-flight data and examine the feasibility of extracting those features from BVI noise recorded inside a large wind tunnel. BVI noise generating mechanisms and BVI radiation patterns an are considered and a simple mathematical-physical model is presented. It allows the construction of simple synthetic BVI events that are comparable to free flight data. The boundary effects of the wind tunnel floor and ceiling are identified and more complex synthetic BVI events are constructed to account for features observed in the wind tunnel data. It is demonstrated that improved recording of BVI events can be attained by changing the geometry of the rotor hub, floor, ceiling and microphone. The Euclidean distance measure is used to align BVI events from each blade and improved BVI signals are obtained by time-domain averaging the aligned data. The differences between BVI events for individual blades are then apparent. Removal of wind tunnel background noise by optimal Wiener-filtering is shown to be effective provided representative noise-only data have been recorded. Elimination of wind tunnel reflections by cepstral and optimal filtering deconvolution is examined. It is seen that the cepstral method is not applicable but that a pragmatic optimal filtering approach gives encouraging results. Recommendations for further work include: altering measurement geometry, real-time data observation and evaluation, examining reflection signals (particularly those from the ceiling) and performing further analysis of expected BVI signals for flight conditions of interest so that microphone placement can be optimized for each condition.

Rogers, James C.↗

The Intensity Distribution of Faint Gamma-Ray Bursts Detected with BATSE

We have recently completed a search of 6 years of archival Burst and Transient Source Experiment (BATSE) data for gamma-ray bursts (GRBS) that were too faint to activate the real-time burst detection system running onboard the spacecraft. These "non-triggered" bursts can be combined with the "triggered" bursts detected onboard to produce a GRB intensity distribution that reaches peak fluxes a factor of approximately 2 lower than could be studied previously. The value of the (V/V(max)) statistic (in Euclidean space) for the bursts we detect is 0.177 +/- 0.006. This surprisingly low value is obtained because we detected very few bursts on the 4.096 s and 8.192 s time scales (where most bursts have their highest signal-to-noise ratio) that were not already detected on the 1.024 s time scale. If allowance is made for a power-law distribution of intrinsic peak luminosities, the extended peak flux distribution is consistent with models in which the redshift distribution of the gamma-ray burst rate approximately traces the star formation history of the Universe. We argue that this class of models is preferred over those in which the burst rate is independent of redshift. These results lend support to the conclusions of previous studies predicting that relatively few faint bursts are waiting to be found below the BATSE onboard detection threshold.

Kommers, Jefferson↗

Leonid's Particle Analyses from Stratospheric Balloon Collection on Xerogel Surfaces

Recovered from a stratospheric balloon above 20 km on 17-18 November 1998, at least eight candidate microparticles were collected and analyzed from low-density silica xerogel collection plates. Capture time at Leonids' storm peak was validated locally along the balloon trajectory by direct video imaging of meteor fluence up to 24/hr above 98% of the Earth's atmosphere. At least one 30 micron particle agrees morphologically to a smooth, unmelted spherule and compares most closely in non-volatile elemental ratios (Mg/Si, Al/Si, and Fe/Si) to compositional data in surface/ocean meteorite collections. A Euclidean tree diagram based on composition makes a most probable identification as a non-porous stratospherically collected particle and a least probable identification as terrestrial matter or an ordinary chondrite. If of extraterrestrial origin, the mineralogical class would be consistent with a stony (S) type of silicate, olivine [(Mg,Fe)2SiO4] and pyroxene [(Mg, Fe)Si!O3)--or oxides, herecynite [(Fe,Mg) Al2O4].

Noever, David↗

Radio Sources in Galaxy Clusters at 28.5 GHz

We present serendipitous observations of radio sources at 28.5 GHz (1 cm), which resulted from our program to image thermal Sunyaev-Zeldovich (SZ) effect in 56 galaxy clusters. In a total area of about 0.8 degrees sq., we find 64 radio sources with fluxes down to - 0.4 mJy (> 4sigma,), and within 250" from the pointing centers. The spectral indices (S varies as v(sup -alpha) of 54 sources with published low frequency flux densities range from -0.6 approximately < alpha and alpha approximately < 2 with a mean of 0.77 +/- 0.06, and a median of 0.84. Extending low frequency surveys of radio sources towards galaxy clusters CL 0016+16, Abell 665, and Abell 2218 to 28.5 GHz, and selecting sources with S(sub l.4GHz) >/= 7 mJy to form an unbiased sample, we find a mean spectral index of 0.71 +/- 0.08 and a median of 0.71. We find 4 to 7 times more sources predicted from a low frequency survey in areas without galaxy clusters. This excess cannot be accounted for by gravitational lensing of a background radio population by cluster potentials, indicating most of the detected sources are associated with galaxy clusters. The differential source count slope, gamma is approximately 1.96 (dN/dS varies as S(exp -gamma)), is flatter than what is expected for a nonevolving Euclidean population (gamma = 2.5). For the cluster Abell 2218, the presence of unsubtracted radio sources with S(sub 28.5GHz) is approximately < 0.5 mJy (- 5 sigma), can only contribute to temperature fluctuations at a level of DeltaT is approximately 10 to 25 microK. The corresponding error due to radio point source contamination in the Hubble constant derived through a combined analysis of 28.5 GHz SZ images and X-ray emission observations ranges from 1% to 6%.

Cooray, Asantha R.↗

Low Density Parity Check Codes Based on Finite Geometries: A Rediscovery and More

Low density parity check (LDPC) codes with iterative decoding based on belief propagation achieve astonishing error performance close to Shannon limit. No algebraic or geometric method for constructing these codes has been reported and they are largely generated by computer search. As a result, encoding of long LDPC codes is in general very complex. This paper presents two classes of high rate LDPC codes whose constructions are based on finite Euclidean and projective geometries, respectively. These classes of codes a.re cyclic and have good constraint parameters and minimum distances. Cyclic structure adows the use of linear feedback shift registers for encoding. These finite geometry LDPC codes achieve very good error performance with either soft-decision iterative decoding based on belief propagation or Gallager's hard-decision bit flipping algorithm. These codes can be punctured or extended to obtain other good LDPC codes. A generalization of these codes is also presented.

Kou, Yu↗

Observations of GRB 990123 by the Compton Gamma Ray Observatory

GRB 990123 was the first burst from which simultaneous optical, X-ray, and gamma-ray emission was detected; its afterglow has been followed by an extensive set of radio, optical, and X-ray observations. We have studied the gamma-ray burst itself as observed by the Compton Gamma Ray Observatory detectors. We find that gamma-ray fluxes are not correlated with the simultaneous optical observations and that the gamma-ray spectra cannot be extrapolated simply to the optical fluxes. The burst is well fitted by the standard four-parameter GRB function, with the exception that excess emission compared with this function is observed below approx. 15 keV during some time intervals. The burst is characterized by the typical hard-to-soft and hardness-intensity correlation spectral evolution patterns. The energy of the peak of the vf (sub v), spectrum, E (sub p), reaches an unusually high value during the first intensity spike, 1470 plus or minus 110 keV, and then falls to approx. 300 keV during the tail of the burst. The high-energy spectrum above approx. 1 MeV is consistent with a power law with a photon index of about -3. By fluence, GRB 990123 is brighter than all but 0.4% of the GRBs observed with BATSE (Burst and Transient Source Experiment), clearly placing it on the -3/2 power-law portion of the intensity distribution. However, the redshift measured for the afterglow is inconsistent with the Euclidean interpretation of the -3/2 power law. Using the redshift value of greater than or equal to 1.61 and assuming isotropic emission, the gamma-ray energy exceeds 10 (exp 54) ergs.

Briggs, M. S.↗

Multiobjective Evolutionary Path Planning via Sugeno-Based Tournament Selection

This paper introduces a new tournament selection algorithm that can be used for evolutionary path planning systems. The fuzzy (Sugeno) tournament selection algorithm (STSA) described in this paper selects candidate paths (CPs) to be parents and undergo reproduction based on: (1) path feasibility, (2) the euclidean distance of a path from the origin to its destination, and (3) the average change in the slope of a path. In this paper, we provide a detailed description of the fuzzy inference system used in the STSA as well as some examples of its usefulness. We then use 12 instances of our STSA to rank a population of CPs based on the above criteria. We also show how the STSA can obviate the need for the development of an explicit (lexicographic multiobjective) evaluation function and use it to develop multiobjective motion paths.

Dozier, Gerry↗

Low Density Parity Check Codes: Bandwidth Efficient Channel Coding

Low Density Parity Check (LDPC) Codes provide near-Shannon Capacity performance for NASA Missions. These codes have high coding rates R=0.82 and 0.875 with moderate code lengths, n=4096 and 8176. Their decoders have inherently parallel structures which allows for high-speed implementation. Two codes based on Euclidean Geometry (EG) were selected for flight ASIC implementation. These codes are cyclic and quasi-cyclic in nature and therefore have a simple encoder structure. This results in power and size benefits. These codes also have a large minimum distance as much as d,,, = 65 giving them powerful error correcting capabilities and error floors less than lo- BER. This paper will present development of the LDPC flight encoder and decoder, its applications and status.

Fong, Wai↗

Comparison of Histograms for Use in Cloud Observation and Modeling

Cloud observation and cloud modeling data can be presented in histograms for each characteristic to be measured. Combining information from single-cloud histograms yields a summary histogram. Summary histograms can be compared to each other to reach conclusions about the behavior of an ensemble of clouds in different places at different times or about the accuracy of a particular cloud model. As in any scientific comparison, it is necessary to decide whether any apparent differences are statistically significant. The usual methods of deciding statistical significance when comparing histograms do not apply in this case because they assume independent data. Thus, a new method is necessary. The proposed method uses the Euclidean distance metric and bootstrapping to calculate the significance level.

Green, Lisa↗

The relationship between perceived length and egocentric location in Muller-Lyer figures with one versus two chevrons

We examined the apparent dissociation of perceived length and perceived position with respect to the Muller-Lyer (M-L) illusion. With the traditional (two-chevron) figure, participants made accurate open-loop pointing responses at the endpoints of the shaft, despite the presence of a strong length illusion. This apparently non-Euclidean outcome replicated that of Mack, Heuer, Villardi, and Chambers (1985) and Gillam and Chambers (1985) and contradicts any theory of the M-L illusion in which mislocalization of shaft endpoints plays a role. However, when one of the chevrons was removed, a constant pointing error occurred in the predicted direction, as well as a strong length illusion. Thus, with one-chevron stimuli, perceived length and location were no longer completely dissociated. We speculated that the presence of two opposing chevrons suppresses the mislocalizing effects of a single chevron, especially for figures with relatively short shafts.

NASA Center ARC↗

ATTITUDE FILTERING ON SO(3)

A new method is presented for the simultaneous estimation of the attitude of a spacecraft and an N-vector of bias parameters. This method uses a probability distribution function defined on the Cartesian product of SO(3), the group of rotation matrices, and the Euclidean space W N .The Fokker-Planck equation propagates the probability distribution function between measurements, and Bayes s formula incorporates measurement update information. This approach avoids all the issues of singular attitude representations or singular covariance matrices encountered in extended Kalman filters. In addition, the filter has a consistent initialization for a completely unknown initial attitude, owing to the fact that SO(3) is a compact space.

Markley, F. Landis↗

Design of Serially Concatenated Trellis Coded Modulation

Serial concatenation of an outer binary convolutional code with an inner TCM code over a multidimensional Euclidean constellation through an interleaver, allows to extend the extremely good performance of turbo codes to the case of high spectral efficiency.

Serial Concatenated trellis code↗

Bounded-Angle Iterative Decoding of LDPC Codes

Bounded-angle iterative decoding is a modified version of conventional iterative decoding, conceived as a means of reducing undetected-error rates for short low-density parity-check (LDPC) codes. For a given code, bounded-angle iterative decoding can be implemented by means of a simple modification of the decoder algorithm, without redesigning the code. Bounded-angle iterative decoding is based on a representation of received words and code words as vectors in an n-dimensional Euclidean space (where n is an integer).

Dolinar, Samuel↗

Monitoring by Use of Clusters of Sensor-Data Vectors

The inductive monitoring system (IMS) is a system of computer hardware and software for automated monitoring of the performance, operational condition, physical integrity, and other aspects of the health of a complex engineering system (e.g., an industrial process line or a spacecraft). The input to the IMS consists of streams of digitized readings from sensors in the monitored system. The IMS determines the type and amount of any deviation of the monitored system from a nominal or normal ( healthy ) condition on the basis of a comparison between (1) vectors constructed from the incoming sensor data and (2) corresponding vectors in a database of nominal or normal behavior. The term inductive reflects the use of a process reminiscent of traditional mathematical induction to learn about normal operation and build the nominal-condition database. The IMS offers two major advantages over prior computational monitoring systems: The computational burden of the IMS is significantly smaller, and there is no need for abnormal-condition sensor data for training the IMS to recognize abnormal conditions. The figure schematically depicts the relationships among the computational processes effected by the IMS. Training sensor data are gathered during normal operation of the monitored system, detailed computational simulation of operation of the monitored system, or both. The training data are formed into vectors that are used to generate the database. The vectors in the database are clustered into regions that represent normal or nominal operation. Once the database has been generated, the IMS compares the vectors of incoming sensor data with vectors representative of the clusters. The monitored system is deemed to be operating normally or abnormally, depending on whether the vector of incoming sensor data is or is not, respectively, sufficiently close to one of the clusters. For this purpose, a distance between two vectors is calculated by a suitable metric (e.g., Euclidean distance) and "sufficiently close" signifies lying at a distance less than a specified threshold value. It must be emphasized that although the IMS is intended to detect off-nominal or abnormal performance or health, it is not necessarily capable of performing a thorough or detailed diagnosis. Limited diagnostic information may be available under some circumstances. For example, the distance of a vector of incoming sensor data from the nearest cluster could serve as an indication of the severity of a malfunction. The identity of the nearest cluster may be a clue as to the identity of the malfunctioning component or subsystem. It is possible to decrease the IMS computation time by use of a combination of cluster-indexing and -retrieval methods. For example, in one method, the distances between each cluster and two or more reference vectors can be used for the purpose of indexing and retrieval. The clusters are sorted into a list according to these distance values, typically in ascending order of distance. When a set of input data arrives and is to be tested, the data are first arranged as an ordered set (that is, a vector). The distances from the input vector to the reference points are computed. The search of clusters from the list can then be limited to those clusters lying within a certain distance range from the input vector; the computation time is reduced by not searching the clusters at a greater distance.

Iverson, David L.↗

Optimal Codes for the Burst Erasure Channel

Deep space communications over noisy channels lead to certain packets that are not decodable. These packets leave gaps, or bursts of erasures, in the data stream. Burst erasure correcting codes overcome this problem. These are forward erasure correcting codes that allow one to recover the missing gaps of data. Much of the recent work on this topic concentrated on Low-Density Parity-Check (LDPC) codes. These are more complicated to encode and decode than Single Parity Check (SPC) codes or Reed-Solomon (RS) codes, and so far have not been able to achieve the theoretical limit for burst erasure protection. A block interleaved maximum distance separable (MDS) code (e.g., an SPC or RS code) offers near-optimal burst erasure protection, in the sense that no other scheme of equal total transmission length and code rate could improve the guaranteed correctible burst erasure length by more than one symbol. The optimality does not depend on the length of the code, i.e., a short MDS code block interleaved to a given length would perform as well as a longer MDS code interleaved to the same overall length. As a result, this approach offers lower decoding complexity with better burst erasure protection compared to other recent designs for the burst erasure channel (e.g., LDPC codes). A limitation of the design is its lack of robustness to channels that have impairments other than burst erasures (e.g., additive white Gaussian noise), making its application best suited for correcting data erasures in layers above the physical layer. The efficiency of a burst erasure code is the length of its burst erasure correction capability divided by the theoretical upper limit on this length. The inefficiency is one minus the efficiency. The illustration compares the inefficiency of interleaved RS codes to Quasi-Cyclic (QC) LDPC codes, Euclidean Geometry (EG) LDPC codes, extended Irregular Repeat Accumulate (eIRA) codes, array codes, and random LDPC codes previously proposed for burst erasure protection. As can be seen, the simple interleaved RS codes have substantially lower inefficiency over a wide range of transmission lengths.

Hamkins, Jon↗

Serial turbo trellis coded modulation using a serially concatenated coder

Serial concatenated trellis coded modulation (SCTCM) includes an outer coder, an interleaver, a recursive inner coder and a mapping element. The outer coder receives data to be coded and produces outer coded data. The interleaver permutes the outer coded data to produce interleaved data. The recursive inner coder codes the interleaved data to produce inner coded data. The mapping element maps the inner coded data to a symbol. The recursive inner coder has a structure which facilitates iterative decoding of the symbols at a decoder system. The recursive inner coder and the mapping element are selected to maximize the effective free Euclidean distance of a trellis coded modulator formed from the recursive inner coder and the mapping element. The decoder system includes a demodulation unit, an inner SISO (soft-input soft-output) decoder, a deinterleaver, an outer SISO decoder, and an interleaver.

Divsalar, Dariush↗