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DOE OSTI2025

The effective number of parameters in kernel density estimation

We devise a new formula for measuring the effective degrees of freedom (EDoF) in kernel density estimation (KDE). Starting from the orthogonal polynomial sequence (OPS) expansion for the ratio of the empirical to the oracle density, we show how convolution with the kernel leads to a new OPS with respect to which one may express the resulting KDE. The expansion coefficients of the two OPS systems can then be related via a kernel sensitivity matrix, which leads to a natural oracle definition of EDoF through the trace operator. Asymptotic properties of the (empirical) plug-in EDoF are worked out through influence functions, and connections with other empirical EDoFs are established. Minimization of Kullback-Leibler divergence is investigated as an alternative to integrated squared error based bandwidth selection rules, yielding a new normal scale rule. The methodology, which arises from a proper oracle formulation and is not restricted to convolution kernels, suggests the possibility of a new bandwidth selection rule based on an information criterion such as AIC.

bandwidth selection↗

NASA NTRS2005

On the Hilbert-Huang Transform Theoretical Developments

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as linearity, of being stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposition data, the HHT allows spectrum analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a near orthogonal adaptive basis, a basis that is derived from the data. The IMFs can be further analyzed for spectrum interpretation by the classical Hilbert Transform. A new engineering spectrum analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications post additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs near orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the developments of new HHT processing options, such as real-time and 2-D processing using Field Programmable Array (FPGA) computational resources, enhanced HHT synthesis, and broaden the scope of HHT applications for signal processing.

Kizhner, Semion↗

NASA NTRS2006

On Certain Theoretical Developments Underlying the Hilbert-Huang Transform

One of the main traditional tools used in scientific and engineering data spectral analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as being linear and stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectral analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposed data, the HHT allows spectral analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real-value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a nearly orthogonal derived from the data (adaptive) basis. The IMFs can be further analyzed for spectrum content by using the classical Hilbert Transform. A new engineering spectral analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications pose additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs nearly orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the development of new HHT processing options, such as real-time and 2-D processing using Field Programmable Gate Array (FPGA) computational resources,

Kizhner, Semion↗

DOE OSTI2021

Two‐Dimensional (2D) or Quasi‐2D Superstructures from DNA‐Coated Colloidal Particles

Abstract This contribution describes the synthesis of colloidal di‐patch particles functionalized with DNA on the patches and their assembly into colloidal superstructures via cooperative depletion and DNA‐mediated interactions. The assembly into flower‐like Kagome, brick‐wall like monolayer, orthogonal packed single or double layers, wrinkled monolayer, and colloidal honeycomb superstructures can be controlled by tuning the particles’ patch sizes and assembly conditions. Based on these experimental results, we generate an empirical phase diagram. The principles revealed by the phase diagram provide guidance in the design of two‐dimensional (2D) materials with desired superstructures. Our strategy might be translatable to the assembly of three‐dimensional (3D) colloidal structures.

Liu, Mingzhu↗

DOE OSTI2021

Two‐Dimensional (2D) or Quasi‐2D Superstructures from DNA‐Coated Colloidal Particles

Liu, Mingzhu↗

DOE OSTI2026

Conjugation-based genome engineering enables rapid prototyping and bioproduction in non-model bacteria

Abstract Non-model bacteria offer unique metabolic capabilities for sustainable bioproduction, yet their limited genetic accessibility hinders systematic strain development. Here we present conjugation-based serine recombinase-assisted genome engineering (cSAGE), a broad-host-range platform that enables predictable, iterative genomic integration in transformation-resistant bacteria. cSAGE combines conjugative DNA delivery, standardized low-copy vectors, orthogonal recombinases, and modular genetic parts to support rapid pathway assembly and cross-host benchmarking. Using purple nonsulfur bacteria as a testbed, we integrate promoter engineering, multi-payload genome modification, and genome-scale metabolic modeling to empirically evaluate host-dependent pathway performance. Applying this workflow, we identify strain-specific differences in photosynthetic conversion of lignin-derived p -coumarate to the thermoplastic precursor p -vinylphenol. By enabling genome engineering and functional comparison across diverse bacteria using a single plasmid system, cSAGE provides a general framework for non-model strain prototyping and biotransformation discovery.

Guzman, Michael S. [Department of Chemical Enginee↗

NASA NTRS1977

An empirical model for ocean radar backscatter and its application in inversion routine to eliminate wind speed and direction effects

Several regression models were tested to explain the wind direction dependence of the 1975 JONSWAP (Joint North Sea Wave Project) scatterometer data. The models consider the radar backscatter as a harmonic function of wind direction. The constant term accounts for the major effect of wind speed and the sinusoidal terms for the effects of direction. The fundamental accounts for the difference in upwind and downwind returns, while the second harmonic explains the upwind-crosswind difference. It is shown that a second harmonic model appears to adequately explain the angular variation. A simple inversion technique, which uses two orthogonal scattering measurements, is also described which eliminates the effect of wind speed and direction. Vertical polarization was shown to be more effective in determining both wind speed and direction than horizontal polarization.

Dome, G. J.↗

DOE OSTI2021

Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

German, Péter (ORCID:0000000307285283)↗

DOE OSTI2022

Skew-Symmetric adjacency matrices for clustering directed graphs

Graph clustering methods often critically rely on the symmetry of graph matrices. Developing analogous methods for digraphs often proves more challenging, because digraph matrices are typically asymmetric and not orthogonally diagonalizable. However, researchers have recently proposed several complex-valued Hermitian digraph matrices. In particular, one such representation has been utilized as an input to an algorithm for finding imbalanced cuts. In this work, we establish an algebraic relationship between this matrix and an associated real-valued matrix. We show using this real-valued matrix for imbalanced cut-finding algorithms is not only sufficient but advantageous. Our algorithm uses less memory and asymptotically less computation while provably preserving solution quality. We also show our method can be easily implemented using standing computational building blocks, possesses better numerical properties, and loans itself to a natural interpretation via an objective function relaxation argument. We empirically demonstrate these advantages on real world data sets and show how our algorithm can uncover meaningful cluster structure.

Hayashi, Koby↗

NASA NTRS2000

Non-Tidal Non-Seasonal Oceanic Mass Redistribution Estimated from the TOPEX/Poseidon Observation

Topex/Poseidon altimetry data are used to estimate the non-tidal mass redistribution as a function of space-time. The goal is to study the contribution of ocean circulations in the geodynamic effects including Earth's rotational and gravitational variations. We examine the non-seasonal anomalies at monthly sampling rate over the T/P span of eight years, concentrating especially on interannual variabilities. Since the sea-surface height data obtained from altimetry is the combined effect of steric change (primarily thermal effect) and the mass flux, and because the former has zero contribution to the geodynamic effects, one needs to do a so-called steric correction by removing from the altimetry data the steric contributions. We achieve it using multiyear monthly sea-surface temperature maps, together with monthly "climatology" for mixed-layer depth maps for mean-months of the year. We analyze both sets of the altimetry data and the steric correction data using the empirical orthogonal function/principal component analysis (in which we take care of issues associated with the area-weighting and non-zero mean), and examine the most important modes, either globally or regionally. In particular, the ENSO in the tropical Pacific/Indian Oceans exhibits the most prominent pattern. The net mass transport after the steric correction can then be compared with: (1) ocean general circulation model outputs for the same period of time (such as from POCM-4B); (2) non-atmospheric Earth rotation variations obtained from space geodesy data and atmospheric angular momentum data; (3) non-atmospheric low-degree gravitational variations from satellite-laser-ranging observations and global atmospheric data.

Chao, Benjamin F.↗

NASA NTRSDate not supplied

Mapping Aerosol Lidar Ratios Over Ocean for CALIPSO Using Modis AOD-Constrained Retrievals and A Global Aerosol Model

The CALIPSO aerosol algorithms currently assign one lidar ratio value for each of the seven tropospheric aerosol types. In a future data products release, the CALIPSO project aims to improve these algorithms by developing regional and seasonal lidar ratio climatologies. In this study, aerosol lidar ratios are inferred through Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) backscatter profiles constrained by collocated aerosol optical depth from Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) datasets. The analysis is subsampled for only those profiles that are cloud-free and contain one aerosol type (based on CALIOP feature classification). In addition, the CALIOP profiles are collocated with aerosol volume fractions simulated by the Goddard Chemistry Aerosol Radiation and Transport (GOCART) model. In this talk, the twelve-year (2006-2017) mean spatial distributions of inferred aerosol lidar ratios for CALIOP-classified marine aerosols and the corresponding modeled sea salt volume fractions (SSVF) will be shown. Model-assisted climatological lidar ratio maps on a seasonal scale will also be presented, developed from the empirical relationship found between the modeled SSVF and lidar ratios. A comparison with past studies will be provided as well as results of a sensitivity study regarding the variability of retrieved lidar ratios as a function of horizontal averaging resolution. While the majority of this talk will focus on lidar ratios for CALIOP-classified marine aerosols, preliminary results will be shown for other aerosol types over ocean, such as dust and elevated smoke.

Travis Toth↗