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On Holo-Hilbert Spectral Analysis: A Full Informational Spectral Representation for Nonlinear and Non-Stationary Data

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert-Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time- frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and nonstationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities.

Huang, Norden E.↗

Over-Expression, Purification and Crystallization of Human Dihydrolipoamide Dehydrogenase

Dehydrolipoamide dehydrogenase (E3; dihydrolipoan-tide:NAD+ oxidoreductase, EC 1.8.1.4) is a common catalytic component found in pyruvate dehydrogenase complex, alpha-ketoglutarate dehydrogenase complex, and branched-chain cc-keto acid dehydrogenase complex. E3 is also a component (referred to as L protein) of the glycine cleavage system in bacterial metabolism (2). Active E3 forms a homodimer with four distinctive subdomain structures (FAD binding, NAD+ binding, central and interface domains) with non-covalently but tightly bound FAD in the holoenzyme. Deduced amino acids from cloned full-length human E3 gene showed a total of 509 amino acids with a leader sequence (N-terminal 35 amino acids) that is excised (mature form) during transportation of expressed E3 into mitochondria membrane. So far, three-dimensional structure of human E3 has not been reported. Our effort to achieve the elucidation of the X-ray crystal structure of human E3 will be presented. Recombinant pPROEX-1 expression vector (from GIBCO BRL Life Technologies) having the human E3 gene without leader sequence was constructed by Polymerase Chain Reaction (PCR) and subsequent ligation, and cloned in E.coli XL1-Blue by transformation. Since pPROEX-1 vector has an internal His-tag (six histidine peptide) located at the upstream region of a multicloning site, one-step affinity purification of E3 using nickelnitriloacetic acid (Ni-NTA) agarose resin, which has a strong affinity to His-tag, was feasible. Also a seven-amino-acid spacer peptide and a recombinant tobacco etch virus protease recognition site (seven amino acids peptide) found between His-tag and first amino acid of expressed E3 facilitated the cleavage of His-tag from E3 after the affinity purification. By IPTG induction, ca. 15 mg of human E3 (mature form) was obtained from 1L LB culture with overnight incubation at 25C. Over 98% of purity of E3 from one-step Ni-NTA agarose affinity purification was confirmed by SDS-PAGE analysis. For crystallization, E3 samples were prepared with and without His-tag. To minimize the aggregation of E3, apo- and holo- forms of E3s were tested, as well as a mutated E3. Dynamic light scattering measurements revealed that the E3 preparations without His-tag and substrate are highly monodispersive with regard to homodimers. Consequent crystallization trials of this E3 preparation led to single crystals of E3 grown by the vapor diffusion method. Crystals were obtained within a few days from solution containing poly (ethylene glycol) monomethyl ether 5000 as a precipitant. Autoindexing and integration of the X-ray diffraction data showed that E3 crystals belong to an orthorhombic system with unit cell parameters a-- 123. 1, b= 165.3 and c=214.3A. Further optimization of protein preparation and crystallization experiments for the structural determination will be discussed.

Hong, Y. S.↗

Horizontal Wind Measurements using the HARLIE Holographic Lidar

We report the results of three campaigns in which the horizontal wind vector at cloud altitudes was measured using the holographic, conical-scan lidar HARLIE in its nadir-viewing mode. Measurements were made during the HOLO-1 and -2 tests in Utah and New Hampshire in March and June 1999, respectively, and at the DoE-ARM site in Oklahoma in September/October 2000. A novel algorithm facilitates the wind vector analysis of the HARLIE data. Observed wind velocity and direction were compared with radiosonde records and with other data obtained from video cloud imagery and independent lidar ranging. The results demonstrate good agreement between HARLIE data and the results of other methods. The conically scanning holographic lidar opens up new possibilities for obtaining the vertical profile of horizontal winds.

Wilkerson, Thomas↗

Large Aperture Scanning Lidar Based on Holographic Optical Elements

Lidar remote sensing instruments can make a significant contribution to satisfying many of the required measurements of atmospheric and surface parameters for future spaceborne platforms, including topographic altimeters, atmospheric profiles of, wind, humidity, temperature, trace molecules, aerosols, and clouds. It is highly desirable to have wide measurement swaths for rapid coverage rather than just the narrow ribbon of data that is obtained with a nadir only observation. For most applications global coverage is required, and for wind measurements scanning or pointing is required in order to retrieve the full 3-D wind vector from multiple line-of-sight Doppler measurements. Conventional lidar receivers make up a substantial portion of the instrument's size and weight. Wide angle scanning typically requires a large scanning mirror in front of the receiver telescope, or pointing the entire telescope and aft optics assembly, Either of these methods entails the use of large bearings, motors, gearing and their associated electronics. Spaceborne instruments also need reaction wheels to counter the torque applied to the spacecraft by these motions. NASA has developed simplified conical scanning telescopes using Holographic Optical Elements (HOEs) to reduce the size, mass, angular momentum, and cost of scanning lidar systems. NASA has developed two operating lidar systems based on 40 cm diameter HOEs. The first such system, named Prototype Holographic Atmospheric Scanner for Environmental Remote Sensing (PHASERS) was a joint development between NASA Goddard Space Flight Center (GSFC) and the University of Maryland College Park. PHASERS is based on a reflection HOE for use at the doubled Nd:YAG laser wavelength of 532 nm and has recently undergone a number of design changes in a collaborative effort between GSFC and Saint Anselm College in New Hampshire. The next step was to develop IR transmission HOEs for use with the Nd:YAG fundamental in the Holographic Airborne Rotating Lidar Instrument Experiment (HARLIE). The HOE spins like a compact disk in a large ring ball bearing. In an aircraft the HOE faces down, looking out through a window at an angle of 45 degrees off-nadir. The HOE diffracts 85% of the incident 532 nm light into a 160 micron spot at a focal length of 1 meter. HARLIE is a field deployable lidar measuring aerosol, cloud, and boundary layer backscatter for atmospheric research. It has flown several times and is also used from a ground-based trailer in an upward-looking mode. The HOE generates a 45 degree conical scan pattern by rotating at speeds up to 30 rpm. Like PHASERS, the HOE in HARLIE serves both as the laser collimating lens as well as the receiver telescope primary optic. The telescope is coupled to the receiver package via fiber optic. The transmitter is a diode pumped Nd:YAG laser operating at 1064 nm, delivering 1 mJ pulses at a 5 KHz rep-rate. The receiver has a 200 microradian field-of-view and a 0.5 nm optical bandpass. The photon counting data system utilizes a single Geiger-mode silicon avalanche photodiode detector, This new technology has also presented us with new data visualization challenges as well as new measurement techniques. The backscatter data obtained from a stationary (i.e. ground-based) scanning HOE lidar is on the surface of a cone, which when viewed over many consecutive scans can reveal atmospheric motions on this surface over time as the atmosphere advects over the site. In a moving platform such as an airplane or satellite, the data from consecutive scans cover different areas under the flight path, revealing atmospheric structure in 3-dimensions. An example of a visualization of HARLIE ground-based data is presented, showing aerosol backscatter on a 90 degree conical surface generated from one 360 degree scan of the lidar during the HOLO-1 field campaign on the afternoon of 10 March 1999. Higher backscatter levels are rendered as lighter signal against a dark background. Breaking Kelvin-Helmholtz waves are evident on the north side of the scan at an altitude of 10-11 km. Time series of successive scans made at regular intervals render unique views of atmospheric motions, from which vertical profiles of atmospheric wind vectors can be obtained using a unique data analysis approach. Wind vectors obtained from the lidar were compared with co-located radiosonde wind profiles during an intensive operating period in September-October 2000 at the Atmospheric Radiation Measurement Program's Southern Great Plains Central Facility.

Schwemmer, Geary K.↗