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NASA NTRS2005

Application of the Hilbert-Huang Transform to Financial Data

A paper discusses the application of the Hilbert-Huang transform (HHT) method to time-series financial-market data. The method was described, variously without and with the HHT name, in several prior NASA Tech Briefs articles and supporting documents. To recapitulate: The method is especially suitable for analyzing time-series data that represent nonstationary and nonlinear phenomena including physical phenomena and, in the present case, financial-market processes. The method involves the empirical mode decomposition (EMD), in which a complicated signal is decomposed into a finite number of functions, called "intrinsic mode functions" (IMFs), that admit well-behaved Hilbert transforms. The HHT consists of the combination of EMD and Hilbert spectral analysis. The local energies and the instantaneous frequencies derived from the IMFs through Hilbert transforms can be used to construct an energy-frequency-time distribution, denoted a Hilbert spectrum. The instant paper begins with a discussion of prior approaches to quantification of market volatility, summarizes the HHT method, then describes the application of the method in performing time-frequency analysis of mortgage-market data from the years 1972 through 2000. Filtering by use of the EMD is shown to be useful for quantifying market volatility.

Huang, Norden↗

NASA NTRS2003

Acoustical Applications of the HHT Method

A document discusses applications of a method based on the Huang-Hilbert transform (HHT). The method was described, without the HHT name, in Analyzing Time Series Using EMD and Hilbert Spectra (GSC-13817), NASA Tech Briefs, Vol. 24, No. 10 (October 2000), page 63. To recapitulate: The method is especially suitable for analyzing time-series data that represent nonstationary and nonlinear physical phenomena. The method involves the empirical mode decomposition (EMD), in which a complicated signal is decomposed into a finite number of functions, called intrinsic mode functions (IMFs), that admit well-behaved Hilbert transforms. The HHT consists of the combination of EMD and Hilbert spectral analysis.

Huang, Norden E.↗

NASA NTRS2017

A Space-Based Observational Strategy for Characterizing the First Stars and Galaxies Using the Redshifted 21cm Global Spectrum

The redshifted 21 cm monopole is expected to be a powerful probe of the epoch of the first stars and galaxies(10 less than z less than 35). The global 21 cm signal is sensitive to the thermal and ionization state of hydrogen gas and thusprovides a tracer of sources of energetic photonsprimarily hot stars and accreting black holeswhich ionize andheat the high redshift intergalactic medium (IGM). This paper presents a strategy for observations of the globalspectrum with a realizable instrument placed in a low-altitude lunar orbit, performing night-time 40120 MHzspectral observations, while on the farside to avoid terrestrial radio frequency interference, ionospheric corruption,and solar radio emissions. The frequency structure, uniformity over large scales, and unpolarized state of theredshifted 21 cm spectrum are distinct from the spectrally featureless, spatially varying, and polarized emissionfrom the bright foregrounds. This allows a clean separation between the primordial signal and foregrounds. Forsignal extraction, we model the foreground, instrument, and 21 cm spectrum with eigenmodes calculated viaSingular Value Decomposition analyses. Using a Markov Chain Monte Carlo algorithm to explore the parameterspace defined by the coefficients associated with these modes, we illustrate how the spectrum can be measured andhow astrophysical parameters (e.g., IGM properties, first star characteristics) can be constrained in the presence offoregrounds using the Dark Ages Radio Explorer (DARE).

Burns, Jack O.↗

DOE OSTI2020

Many‐body response of benzene at monolayer MoS 2 : Van der Waals interactions and spectral broadening

Abstract Models of surface enhancement of molecular electronic response properties are challenging for two reasons: (a) molecule‐surface interactions require a simultaneous solution of the molecular and the surface dynamic response (a daunting task), and (b) when solving for the electronic structure of the combined molecule + surface system, it is not trivial to single out the particular physical effects responsible for enhancement. To tackle this problem, in this work, we apply a formally exact decomposition of the system's response function into subsystem contributions by using subsystem density functional theory (DFT), which grants access to dynamic polarizabilities and optical spectra. In order to access information about the interactions between the subsystems, we extend a previously developed subsystem‐based adiabatic connection fluctuation‐dissipation theorem of DFT to separate the additive from the nonadditive correlation energy and identify the nonadditive correlation as the van der Waals interactions. As an example, we choose benzene adsorbed on monolayer MoS 2 . We isolate the contributions to benzene's dynamic response arising from the interaction with the surface, and for the first time, we evaluate the enhancements to the effectiveness of C 6 coefficients as a function of benzene‐MoS 2 distance and adsorption site. We also quantify the spectral broadening of the benzene's electronic excited states due to their interaction with the surface. We find that the broadening has a similar decay law with the molecule‐surface distance as the leading van der Waals interactions (ie, R −6 ) and that the surface enhancement of dispersion interactions between benzene molecules is less than 5% but is still large enough (0.5 kcal/mol) to likely play a role in the prediction of interface morphologies.

Umerbekova, Alina↗

NASA NTRS1988

Nonconforming mortar element methods: Application to spectral discretizations

Spectral element methods are p-type weighted residual techniques for partial differential equations that combine the generality of finite element methods with the accuracy of spectral methods. Presented here is a new nonconforming discretization which greatly improves the flexibility of the spectral element approach as regards automatic mesh generation and non-propagating local mesh refinement. The method is based on the introduction of an auxiliary mortar trace space, and constitutes a new approach to discretization-driven domain decomposition characterized by a clean decoupling of the local, structure-preserving residual evaluations and the transmission of boundary and continuity conditions. The flexibility of the mortar method is illustrated by several nonconforming adaptive Navier-Stokes calculations in complex geometry.

Maday, Yvon↗

NASA NTRS1989

Direct simulation of compressible turbulence

Several direct simulations of 3-D homogeneous, compressible turbulence are presented with emphasis on the differences with incompressible turbulent simulations. A fully spectral collocation algorithm, periodic in all directions coupled with a 3rd order Runge-Kutta time discretization scheme is sufficient to produce well-resolved flows at Taylor Reynolds numbers below 40 on grids of 128x128x128. A Helmholtz decomposition of velocity is useful to differentiate between the purely compressible effects and those effects solely due to vorticity production. In the context of homogeneous flows, this decomposition in unique. Time-dependent energy and dissipation spectra of the compressible and solenoidal velocity components indicate the presence of localized small scale structures. These structures are strongly a function of the initial conditions. Researchers concentrate on a regime characterized by very small fluctuating Mach numbers Ma (on the order of 0.03) and density and temperature fluctuations much greater than sq Ma. This leads to a state in which more than 70 percent of the kinetic energy is contained in the so-called compressible component of the velocity. Furthermore, these conditions lead to the formation of curved weak shocks (or shocklets) which travel at approximately the sound speed across the physical domain. Various terms in the vorticity and divergence of velocity production equations are plotted versus time to gain some understanding of how small scales are actually formed. Possible links with Burger turbulence are examined. To visualize better the dynamics of the flow, new graphic visualization techniques have been developed. The 3-D structure of the shocks are visualized with the help of volume rendering algorithms developed in-house. A combination of stereographic projection and animation greatly increase the number of visual cues necessary to properly interpret the complex flow.

Zang, T. A.↗

NASA NTRS1978

Closure of a kinetic model of plasma in strong turbulence by relaxation

A Fokker-Planck kinetic equation for a turbulent plasma is derived by a repeated cascade decomposition. Calculation of the propagator and the kinetic equation determine the transport coefficients (diffusivity and turbulent viscosity) by means of a closure based on a relaxation procedure governing the approach to equilibrium. The k to the minus third power spectral law is obtained, which governs the coupling between the velocity and the electrostatic field fluctuations.

Tchen, C. M.↗

NASA NTRS1991

Partitioning of unstructured problems for parallel processing

Many large-scale computational problems are based on unstructured computational domains. Primary examples are unstructured grid calculations based on finite volume methods in computational fluid dynamics, or structural analysis problems based on finite element approximations. The question of how to distribute such unstructured computational domains over a large number of processors in a MIMD machine with distributed memory is addressed. A graph theoretical framework for these problems is established. Based on this framework three decomposition algorithms are introduced. In particular a new decomposition algorithm is discussed, which is based on the computation of an eigenvector of the Laplacian matrix associated with the graph. Numerical comparisons on large-scale two- and three-dimensional problems demonstrate the superiority of the new spectral bisection algorithm.

Simon, H. D.↗

DOE OSTI2023

Uncovering acoustic signatures of pore formation in laser powder bed fusion

Abstract We present a machine learning workflow to discover signatures in acoustic measurements that can be utilized to create a low-dimensional model to accurately predict the location of keyhole pores formed during additive manufacturing processes. Acoustic measurements were sampled at 100 kHz during single-layer laser powder bed fusion (LPBF) experiments, and spatio-temporal registration of pore locations was obtained from post-build radiography. Power spectral density (PSD) estimates of the acoustic data were then decomposed using non-negative matrix factorization with custom $$\varvec{k}$$ k -means clustering (NMF $$\varvec{k}$$ k ) to learn the underlying spectral patterns associated with pore formation. NMF $$\varvec{k}$$ k returned a library of basis signals and matching coefficients to blindly construct a feature space based on the PSD estimates in an optimized fashion. Moreover, the NMF $$\varvec{k}$$ k decomposition led to the development of computationally inexpensive machine learning models which are capable of quickly and accurately identifying pore formation with classification accuracy of supervised and unsupervised label learning greater than 95% and 90%, respectively. The intrinsic data compression of NMF k , the relatively light computational cost of the machine learning workflow, and the high classification accuracy makes the proposed workflow an attractive candidate for edge computing toward in-situ keyhole pore prediction in LPBF.

36 MATERIALS SCIENCE↗

DOE OSTI2025

BCARS Simulated Phantom Dataset for Evaluation of Processing Pipelines

Broadband coherent anti-Stokes Raman scattering (BCARS) microscopy is a powerful label-free biological imaging technique, but the raw signal requires careful processing. The vibrationally resonant (Raman) fingerprint signal is usually small compared with instrumental noise sources and the nonresonant background (NRB) inherent in the BCARS signal. Fortunately, the NRB exhibits a systematic phase relationship with the coherent Raman response, acting as a heterodyne amplifier for the weak fingerprint signal. Due to this heterodyne effect, the Raman response can be recovered quantitatively and invariantly across different instruments, provided the NRB shape is known. Even with heterodyne amplification, the amplitudes of fingerprint signal components are often comparable to system noise. Singular value decomposition (SVD), which utilizes spatial information, is often employed for additional noise filtering. Consequently, finding optimal processing parameters to properly distinguish the NRB and Raman responses and suppress noise in the complex BCARS signal requires a reference system that realistically represents the spectral and spatial properties of BCARS signals obtained from biological samples. We present a digital tissue phantom that meets these criteria as a tool for testing candidate signal processing pipelines. The digital phantom is generated with simulated hyperspectral Raman images having system-specific noise and background characteristics. Here, we analyze phantom datasets with differing background and signal-to-noise conditions to evaluate their impact on the performance of multiple signal processing pipelines. Specifically, we investigate the application of a Butterworth filter-based routine to directly estimate the NRB from the BCARS signal. Additionally, we evaluate a Lorentzian wavelet transform as an alternative to the Hilbert transform for extracting the Raman spectrum from the BCARS signal. While we demonstrate this phantom for BCARS, it can be used for any spectroscopic Raman imaging approach.

Dixon, Jessica Z. [Georgia Institute of Technology↗

NASA NTRS2000

Evaluation of the Use of Second Generation Wavelets in the Coherent Vortex Simulation Approach

The objective of this study is to investigate the use of the second generation bi-orthogonal wavelet transform for the field decomposition in the Coherent Vortex Simulation of turbulent flows. The performances of the bi-orthogonal second generation wavelet transform and the orthogonal wavelet transform using Daubechies wavelets with the same number of vanishing moments are compared in a priori tests using a spectral direct numerical simulation (DNS) database of isotropic turbulence fields: 256(exp 3) and 512(exp 3) DNS of forced homogeneous turbulence (Re(sub lambda) = 168) and 256(exp 3) and 512(exp 3) DNS of decaying homogeneous turbulence (Re(sub lambda) = 55). It is found that bi-orthogonal second generation wavelets can be used for coherent vortex extraction. The results of a priori tests indicate that second generation wavelets have better compression and the residual field is closer to Gaussian. However, it was found that the use of second generation wavelets results in an integral length scale for the incoherent part that is larger than that derived from orthogonal wavelets. A way of dealing with this difficulty is suggested.

Goldstein, D. E.↗

NASA NTRS2004

Simultaneous Multiwavelength Monitoring of 3C66A

The radio-selected BL Lac object 3C66A was the target of an intensive multiwavelength campaign from Sept. 2003 through Feb. 2004. It was monitored by the Whole Earth Blazar Telescope (WEBT) collaboration, in tandem with 20 X-ray monitoring observations by the Rossi X-Ray Timing Explorer (RXTE), VHE gamma-ray observations by STACEE and VERITAS, and long-term monitoring at radio frequencies. In addition. 9 observations using the VLBA are being carried out during the campaign and throughout the year 2004 to follow possible structural changes of the source. 21 pointings with RXTE during the period Sept. 15 - Dec. 27, 2003. All collected data have been fully analyzed, and first results have already been published at the 8th HEAD Meeting in New Orleans, LA, in Sept. 2004, and will also be presented at the 205th AAS Meeting in San Diego, CA, in Jan. 2005. A first Journal paper, to be submitted to the Astrophysical Journal, is currently in preparation, and we plan to have it ready for submission in January 2005. A gradual brightening of the source over the course of the campaign was observed at all optical frequencies, culminating in a very bright flare at the end of January 2004. Optical light curves indicate intraday microvariability on time scales down to about 1.3 hours. No significant color-magnitude correlation for the entire data set was evident, but there is a slight indication of a gradual spectral softening in the optical over the entire duration of multi-day outbursts (in both the rising and decaying phase). The X-ray spectrum is consistent with a power-law with a photon spectral index of approx. 2.1, indicating that the RXTE energy band might be located right at the intersection of the synchrotron and the high-energy emission components. No significant flux or spectral variability at X-ray energies was detected, though there seems to be a trend of very modest brightening in tandem with the optical flux. The first 4 VLBA epochs indicate a rather smooth jet with only very moderate internal structure. After decomposition in Gaussian components, evidence for superluminal motion (11.0+/-4.7/h c) was found in only one out of 6 jet components. The radial radio brightness profile suggests a magnetic field decay infinity/r and, thus, a predominantly perpendicular magnetic field orientation.

Boettcher, M.↗

NASA NTRS1992

Measuring dry plant residues in grasslands: A case study using AVIRIS

Grasslands, savannah, and hardwood rangelands are critical ecosystems and sensitive to disturbance. Approximately 20 percent of the Earth's surface are grasslands and represent 3 million ha. in California alone. Developing a methodology for estimating disturbance and the effects of cumulative impacts on grasslands and rangelands is needed to effectively monitor these ecosystems. Estimating the dry biomass residue remaining on rangelands at the end of the growing season provides a basis for evaluating the effectiveness of land management practices. The residual biomass is indicative of the grazing pressure and provides a measure of the system capacity for nutrient cycling since it represents the maximum organic matter available for decomposition, and finally, provides a measure of the erosion potential for the ecosystem. Remote sensing presents a possible method for measuring dry residue. However, current satellites have had limited application due to the coarse spatial scales (relative to the patch dynamics) and insensitivity of the spectral coverage to resolve dry plant material. Several hypotheses for measuring the biochemical constituents of dry plant material, particularly cellulose and lignin, using high spectral resolution sensors were proposed. The use of Airborne Visible/Infrared Imaging Spectrometers (AVIRIS) to measure dry plant residues over an oak savannah on the eastern slopes of the Coast Range in central California was investigated and it was asked what spatial and spectral resolutions are needed to quantitatively measure dry plant biomass in this ecosystem.

Fitzgerald, Michael↗

NASA NTRS1978

Synchronized flash photolysis and pulse deposition in matrix isolation experiments

An apparatus is described which permits flash photolysis of a pulse-deposited gas mixture in a matrix isolation experiment. This technique obviates the limitations of in situ photolysis imposed by the cage effect and by secondary photolysis. The matrix is deposited in pulses at 30-s intervals and photolyzed sequentially by four synchronized flashlamps approximately 1 ms before the pulse strikes the cold surface. Pulsed deposition maintains adequate isolation and causes line narrowing, which enhances spectral sensitivity. The efficacy of flash photolysis combined with pulsed deposition for producing and trapping transient species was demonstrated by infrated detection of CF3 (from photolysis of CF3I/Ar mixtures) and of ClCO (from photolysis of Cl2/CO/Ar mixtures). The apparatus was used to study the photolytic decomposition of gaseous tricarbonylironcyclobutadiene, C4H4Fe(CO)3. The results indicate that the primary photolytic step is not elimination of C4H4, as suggested earlier, but rather of CO.

Allamandola, Louis J.↗

DOE OSTI2024

Nonperturbative random matrix model of N = 2 JT supergravity

It is shown how to nonperturbatively define a random matrix model that captures key physics of N = 2 Jackiw-Teitelboim supergravity, going well beyond the perturbative topological expansion defined recently by Turiaci and Witten. A decomposition into an infinite family of certain multicritical models is derived, leading to the definition of a nonlinear ordinary differential equation from which the physics may be computed. Bogomol’nyi-Prasad-Sommerfield (BPS) states are naturally described by the model. The nonperturbative completions of the spectral densities for non-BPS multiplets are readily extracted. Published by the American Physical Society 2024

Johnson, Clifford V. (ORCID:0000000189645830)↗

DOE OSTI2025

Intrinsic Kinetics of Polyethylene Terephthalate Pyrolysis via Micropyrolysis and Multivariate Chromatographic Analysis

This study provides an in-depth investigation of the primary decomposition of polyethylene terephthalate (PET) via pyrolysis, employing an experimental-analytic workflow that integrates design of experiments (DoE), micropyrolysis coupled with comprehensive two-dimensional gas chromatography (GC×GC), and multivariate data analysis to verify intrinsic kinetic conditions and elucidate evolving product distributions for mapping key reaction pathways. Peaks that could not be identified using commercial spectral libraries were assigned using Mass Frontier simulations, enabling the identification of divinyl terephthalate, ethyl vinyl terephthalate, and 2-(benzoyloxy)ethyl vinyl terephthalate. A polar×polar (non-orthogonal) column set tailored for the detection of carboxylic acids enhanced the quantification of benzoic acid, 4-vinylbenzoic acid, 4-ethylbenzoic acid, and methylbenzoic acid by up to 6-fold relative to an orthogonal column combination (non-polar×mid-polar). Moreover, pyrolysis variables were systematically evaluated using a Box- Behnken design (BBD), encompassing pyrolysis temperature (500−600 °C), sample weight (50−150 μg), and carrier gas flow rate (100−300 mL min −1 ). Among these, pyrolysis temperature was the only statistically significant factor influencing product yields, ranging from 58.78 to 84.26 wt %. In contrast, neither the sample weight nor the carrier gas flow rate had a significant effect on product yields within the evaluated experimental space. At 600 °C, the major pyrolysis products were benzoic acid (up to 20.20 ± 1.46 wt %) and CO 2 (up to 21.28 ± 1.46 wt %), which can be produced through decarboxylation reactions. These findings underscore the critical importance of selecting appropriate analytical columns for the accurate quantification of heteroatomcontaining products such as carboxylic acids, which may otherwise be underestimated or undetected due to their reactivity with the stationary phase of non-polar and mid-polar columns, as well as other GC components. They also highlight the importance of selecting pyrolysis conditions for investigating the primary decomposition of PET under an isothermal kinetically limited regime.

aromatic compounds↗

NASA NTRS1991

Vegetation Biochemistry: What Can Imaging Spectrometry Tell Us About Canopies?

Changes in ecosystem processes such as productivity and decomposition may be expressed in the canopy foliar chemistry resulting from altered carbon allocation patterns, metabolic processes and nutrient availability. Understanding carbon balance on land over large regions requires quantitative determination of leaf constituents such as lignin and total nitrogen from remote sensing imaging systems. Results from spectral reflectance measurements of stacked leaves in the laboratory show that spectrum matching techniques are applicable to the derivation of the equivalent liquid water thickness in plants as well as to the extraction of dry leaf matter reflectance spectra from spectra of green leaves. The residual spectra derived by subtracting water spectra from the spectra of green leaves shows a feature at 1.72 micrometers that can be related to the lignin content of the leaves. Oak leaves have a deeper residual absorption feature than do cotton leaves which is consistent with their relative lignin content. Similar results are achieved when deriving the residuals from images taken over areas of grass and pine trees. Imaging spectrometry provides promise in developing images of various foliar biochemical constituents.

Goetz, Alexander F. H.↗

DOE OSTI2026

Efficient simulation of optical spectra via machine learning and physical decomposition of environmental effects

Simulations of optical spectra can provide key insights to aid experimental interpretation of electronic excitation phenomena. For chromophores in the condensed phase, these spectra, which incorporate the coupling between electronic excitation and molecular and solvent nuclear motions, can be simulated using excitation energies obtained from molecular dynamics simulations of the chromophore and solvent. Here, we present a hybrid scheme that exploits machine learning and physically informed spectral densities to show that as few as 25 ground and excited state energetic gradient calculations can be used to construct models that accurately predict environment-influenced vibronic coupling in optical spectra. We demonstrate our approach for the green fluorescent protein chromophore in water and the cresyl violet chromophore in methanol. We show that our hybrid approach, employing a machine learning model for the high-frequency spectral density and an ab initio parameterized Debye spectral density for the low-frequency, results in a systematic improvement of the optical absorption lineshape, leading to a simple machine learning scheme that can be used for the simulation of spectral densities and optical spectra.

Snider, Andrew [Univ. of California, Merced, CA (U↗