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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

The fractional Fourier transform and applications

This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

Bailey, David H.↗
NASA NTRS2005

Quantitative Electron Probe Microanalysis: State of the Art

Quantitative electron-probe microanalysis (EPMA) has improved due to better instrument design and X-ray correction methods. Design improvement of the electron column and X-ray spectrometer has resulted in measurement precision that exceeds analytical accuracy. Wavelength-dispersive spectrometer (WDS) have layered-dispersive diffraction crystals with improved light-element sensitivity. Newer energy-dispersive spectrometers (EDS) have Si-drift detector elements, thin window designs, and digital processing electronics with X-ray throughput approaching that of WDS Systems. Using these systems, digital X-ray mapping coupled with spectrum imaging is a powerful compositional mapping tool. Improvements in analytical accuracy are due to better X-ray correction algorithms, mass absorption coefficient data sets,and analysis method for complex geometries. ZAF algorithms have ban superceded by Phi(pz) algorithms that better model the depth distribution of primary X-ray production. Complex thin film and particle geometries are treated using Phi(pz) algorithms, end results agree well with Monte Carlo simulations. For geological materials, X-ray absorption dominates the corretions end depends on the accuracy of mass absorption coefficient (MAC) data sets. However, few MACs have been experimentally measured, and the use of fitted coefficients continues due to general success of the analytical technique. A polynomial formulation of the Bence-Albec alpha-factor technique, calibrated using Phi(pz) algorithms, is used to critically evaluate accuracy issues and can be also be used for high 2% relative and is limited by measurement precision for ideal cases, but for many elements the analytical accuracy is unproven. The EPMA technique has improved to the point where it is frequently used instead of the petrogaphic microscope for reconnaissance work. Examples of stagnant research areas are: WDS detector design characterization of calibration standards, and the need for more complete treatment of the continuum X-ray fluorescence correction.

Carpernter, P. K.↗
NASA NTRS1984

On the impact of communication complexity in the design of parallel numerical algorithms

This paper describes two models of the cost of data movement in parallel numerical algorithms. One model is a generalization of an approach due to Hockney, and is suitable for shared memory multiprocessors where each processor has vector capabilities. The other model is applicable to highly parallel nonshared memory MIMD systems. In the second model, algorithm performance is characterized in terms of the communication network design. Techniques used in VLSI complexity theory are also brought in, and algorithm independent upper bounds on system performance are derived for several problems that are important to scientific computation.

Gannon, D.↗
NASA NTRS1984

On the impact of communication complexity on the design of parallel numerical algorithms

This paper describes two models of the cost of data movement in parallel numerical alorithms. One model is a generalization of an approach due to Hockney, and is suitable for shared memory multiprocessors where each processor has vector capabilities. The other model is applicable to highly parallel nonshared memory MIMD systems. In this second model, algorithm performance is characterized in terms of the communication network design. Techniques used in VLSI complexity theory are also brought in, and algorithm-independent upper bounds on system performance are derived for several problems that are important to scientific computation.

Gannon, D. B.↗
NASA NTRS2004

Serial-Turbo-Trellis-Coded Modulation with Rate-1 Inner Code

Serially concatenated turbo codes have been proposed to satisfy requirements for low bit- and word-error rates and for low (in comparison with related previous codes) complexity of coding and decoding algorithms and thus low complexity of coding and decoding circuitry. These codes are applicable to such high-level modulations as octonary phase-shift keying (8PSK) and 16-state quadrature amplitude modulation (16QAM); the signal product obtained by applying one of these codes to one of these modulations is denoted, generally, as serially concatenated trellis-coded modulation (SCTCM). These codes could be particularly beneficial for communication systems that must be designed and operated subject to limitations on bandwidth and power. Some background information is prerequisite to a meaningful summary of this development. Trellis-coded modulation (TCM) is now a well-established technique in digital communications. A turbo code combines binary component codes (which typically include trellis codes) with interleaving. A turbo code of the type that has been studied prior to this development is composed of parallel concatenated convolutional codes (PCCCs) implemented by two or more constituent systematic encoders joined through one or more interleavers. The input information bits feed the first encoder and, after having been scrambled by the interleaver, enter the second encoder. A code word of a parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders. The suboptimal iterative decoding structure for such a code is modular, and consists of a set of concatenated decoding modules one for each constituent code connected through an interleaver identical to the one in the encoder side. Each decoder performs weighted soft decoding of the input sequence. PCCCs yield very large coding gains at the cost of a reduction in the data rate and/or an increase in bandwidth.

Divsalar, Dariush↗
NASA NTRS1993

Adaptive fuzzy system for 3-D vision

An adaptive fuzzy system using the concept of the Adaptive Resonance Theory (ART) type neural network architecture and incorporating fuzzy c-means (FCM) system equations for reclassification of cluster centers was developed. The Adaptive Fuzzy Leader Clustering (AFLC) architecture is a hybrid neural-fuzzy system which learns on-line in a stable and efficient manner. The system uses a control structure similar to that found in the Adaptive Resonance Theory (ART-1) network to identify the cluster centers initially. The initial classification of an input takes place in a two stage process; a simple competitive stage and a distance metric comparison stage. The cluster prototypes are then incrementally updated by relocating the centroid positions from Fuzzy c-Means (FCM) system equations for the centroids and the membership values. The operational characteristics of AFLC and the critical parameters involved in its operation are discussed. The performance of the AFLC algorithm is presented through application of the algorithm to the Anderson Iris data, and laser-luminescent fingerprint image data. The AFLC algorithm successfully classifies features extracted from real data, discrete or continuous, indicating the potential strength of this new clustering algorithm in analyzing complex data sets. The hybrid neuro-fuzzy AFLC algorithm will enhance analysis of a number of difficult recognition and control problems involved with Tethered Satellite Systems and on-orbit space shuttle attitude controller.

Mitra, Sunanda↗
NASA NTRS2016

Performance Analysis of a Hardware Implemented Complex Signal Kurtosis Radio-Frequency Interference Detector

Radio-frequency interference (RFI) is a known problem for passive remote sensing as evidenced in the L-band radiometers SMOS, Aquarius and more recently, SMAP. Various algorithms have been developed and implemented on SMAP to improve science measurements. This was achieved by the use of a digital microwave radiometer. RFI mitigation becomes more challenging for microwave radiometers operating at higher frequencies in shared allocations. At higher frequencies larger bandwidths are also desirable for lower measurement noise further adding to processing challenges. This work focuses on finding improved RFI mitigation techniques that will be effective at additional frequencies and at higher bandwidths. To aid the development and testing of applicable detection and mitigation techniques, a wide-band RFI algorithm testing environment has been developed using the Reconfigurable Open Architecture Computing Hardware System (ROACH) built by the Collaboration for Astronomy Signal Processing and Electronics Research (CASPER) Group. The testing environment also consists of various test equipment used to reproduce typical signals that a radiometer may see including those with and without RFI. The testing environment permits quick evaluations of RFI mitigation algorithms as well as show that they are implementable in hardware. The algorithm implemented is a complex signal kurtosis detector which was modeled and simulated. The complex signal kurtosis detector showed improved performance over the real kurtosis detector under certain conditions. The real kurtosis is implemented on SMAP at 24 MHz bandwidth. The complex signal kurtosis algorithm was then implemented in hardware at 200 MHz bandwidth using the ROACH. In this work, performance of the complex signal kurtosis and the real signal kurtosis are compared. Performance evaluations and comparisons in both simulation as well as experimental hardware implementations were done with the use of receiver operating characteristic (ROC) curves. The complex kurtosis algorithm has the potential to reduce data rate due to onboard processing in addition to improving RFI detection performance.

microwaves↗
NASA NTRS1985

An efficient algorithm for estimating noise covariances in distributed systems

An efficient computational algorithm for estimating the noise covariance matrices of large linear discrete stochatic-dynamic systems is presented. Such systems arise typically by discretizing distributed-parameter systems, and their size renders computational efficiency a major consideration. The proposed adaptive filtering algorithm is based on the ideas of Belanger, and is algebraically equivalent to his algorithm. The earlier algorithm, however, has computational complexity proportional to p to the 6th, where p is the number of observations of the system state, while the new algorithm has complexity proportional to only p-cubed. Further, the formulation of noise covariance estimation as a secondary filter, analogous to state estimation as a primary filter, suggests several generalizations of the earlier algorithm. The performance of the proposed algorithm is demonstrated for a distributed system arising in numerical weather prediction.

Dee, D. P.↗
NASA NTRS2004

Random Matrix Approach to Quantum Adiabatic Evolution Algorithms

We analyze the power of quantum adiabatic evolution algorithms (Q-QA) for solving random NP-hard optimization problems within a theoretical framework based on the random matrix theory (RMT). We present two types of the driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that the failure mechanism of the QAA is due to the interaction of the ground state with the "cloud" formed by all the excited states, confirming that in the driven RMT models. the Landau-Zener mechanism of dissipation is not important. We show that the QAEA has a finite probability of success in a certain range of parameters. implying the polynomial complexity of the algorithm. The second model corresponds to the standard QAEA with the problem Hamiltonian taken from the Gaussian Unitary RMT ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. However, the driven RMT model always leads to the exponential complexity of the algorithm due to the presence of the long-range intertemporal correlations of the eigenvalues. Our results indicate that the weakness of effective transitions is the leading effect that can make the Markovian type QAEA successful.

Boulatov, Alexei↗
DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Design of automata theory of cubical complexes with applications to diagnosis and algorithmic description

The following problems are considered: (1) methods for development of logic design together with algorithms, so that it is possible to compute a test for any failure in the logic design, if such a test exists, and developing algorithms and heuristics for the purpose of minimizing the computation for tests; and (2) a method of design of logic for ultra LSI (large scale integration). It was discovered that the so-called quantum calculus can be extended to render it possible: (1) to describe the functional behavior of a mechanism component by component, and (2) to compute tests for failures, in the mechanism, using the diagnosis algorithm. The development of an algorithm for the multioutput two-level minimization problem is presented and the program MIN 360 was written for this algorithm. The program has options of mode (exact minimum or various approximations), cost function, cost bound, etc., providing flexibility.

Roth, J. P.↗
NASA NTRS1972

Design of automata theory of cubical complexes with applications to diagnosis and algorithmic description

Methods for development of logic design together with algorithms for failure testing, a method for design of logic for ultra-large-scale integration, extension of quantum calculus to describe the functional behavior of a mechanism component-by-component and to computer tests for failures in the mechanism using the diagnosis algorithm, and the development of an algorithm for the multi-output 2-level minimization problem are discussed.

Roth, J. P.↗
NASA NTRS1989

Bunch-Kaufman factorization for real symmetric indefinite banded matrices

The Bunch-Kaufman algorithm for factoring symmetric indefinite matrices was rejected for banded matrices because it destroys the banded structure of the matrix. Herein, it is shown that for a subclass of real symmetric matrices which arise in solving the generalized eigenvalue problem using Lanczos's method, the Bunch-Kaufman algorithm does not result in major destruction of the bandwidth. Space time complexities of the algorithm are given and used to show that the Bunch-Kaufman algorithm is a significant improvement over LU factorization.

Jones, Mark T.↗
DOE OSTI2025

Open-Source and FAIR Research Software for Proteomics

Scientific discovery relies on innovative software as much as experimental methods, especially in proteomics, where computational tools are essential for mass spectrometer setup, data analysis, and interpretation. Since the introduction of SEQUEST, proteomics software has grown into a complex ecosystem of algorithms, predictive models, and workflows, but the field faces challenges, including the increasing complexity of mass spectrometry data, limited reproducibility due to proprietary software, and difficulties integrating with other omics disciplines. Closed-source, platform-specific tools exacerbate these issues by restricting innovation, creating inefficiencies, and imposing hidden costs on the community. Open-source software (OSS), aligned with the FAIR Principles (Findable, Accessible, Interoperable, Reusable), offers a solution by promoting transparency, reproducibility, and community-driven development, which fosters collaboration and continuous improvement. In this manuscript, we explore the role of OSS in computational proteomics, its alignment with FAIR principles, and its potential to address challenges related to licensing, distribution, and standardization. Drawing on lessons from other omics fields, we present a vision for a future where OSS and FAIR principles underpin a transparent, accessible, and innovative proteomics community.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

FPT Algorithm for Two-Dimensional Cyclic Convolutions

Fast-polynomial-transform (FPT) algorithm computes two-dimensional cyclic convolution of two-dimensional arrays of complex numbers. New algorithm uses cyclic polynomial convolutions of same length. Algorithm regular, modular, and expandable.

Truong, Trieu-Kie↗
NASA NTRS1989

A unifying framework for rigid multibody dynamics and serial and parallel computational issues

A unifying framework for various formulations of the dynamics of open-chain rigid multibody systems is discussed. Their suitability for serial and parallel processing is assessed. The framework is based on the derivation of intrinsic, i.e., coordinate-free, equations of the algorithms which provides a suitable abstraction and permits a distinction to be made between the computational redundancy in the intrinsic and extrinsic equations. A set of spatial notation is used which allows the derivation of the various algorithms in a common setting and thus clarifies the relationships among them. The three classes of algorithms viz., O(n), O(n exp 2) and O(n exp 3) or the solution of the dynamics problem are investigated. Researchers begin with the derivation of O(n exp 3) algorithms based on the explicit computation of the mass matrix and it provides insight into the underlying basis of the O(n) algorithms. From a computational perspective, the optimal choice of a coordinate frame for the projection of the intrinsic equations is discussed and the serial computational complexity of the different algorithms is evaluated. The three classes of algorithms are also analyzed for suitability for parallel processing. It is shown that the problem belongs to the class of N C and the time and processor bounds are of O(log2/2(n)) and O(n exp 4), respectively. However, the algorithm that achieves the above bounds is not stable. Researchers show that the fastest stable parallel algorithm achieves a computational complexity of O(n) with O(n exp 4), respectively. However, the algorithm that achieves the above bounds is not stable. Researchers show that the fastest stable parallel algorithm achieves a computational complexity of O(n) with O(n exp 2) processors, and results from the parallelization of the O(n exp 3) serial algorithm.

Fijany, Amir↗