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NASA NTRS2001

Crystallization of bFGF-DNA Aptamer Complexes Using a Sparse Matrix Designed for Protein-Nucleic Acid Complexes

The Sparse Matrix approach for obtaining lead crystallization conditions has proven to be very fruitful for the crystallization of proteins and nucleic acids. Here we report a Sparse Matrix developed specifically for the crystallization of protein-DNA complexes. This method is rapid and economical, typically requiring 2.5 mg of complex to test 48 conditions. The method was originally developed to crystallize basic fibroblast growth factor (bFGF) complexed with DNA sequences identified through in vitro selection, or SELEX, methods. Two DNA aptamers that bind with approximately nanomolar affinity and inhibit the angiogenic properties of bFGF were selected for co-crystallization. The Sparse Matrix produced lead crystallization conditions for both bFGF-DNA complexes.

Cannone, Jaime J.↗

NASA NTRS2004

Electromagnetic Formation Flight (EMFF) for Sparse Aperture Arrays

Traditional methods of actuating spacecraft in sparse aperture arrays use propellant as a reaction mass. For formation flying systems, propellant becomes a critical consumable which can be quickly exhausted while maintaining relative orientation. Additional problems posed by propellant include optical contamination, plume impingement, thermal emission, and vibration excitation. For these missions where control of relative degrees of freedom is important, we consider using a system of electromagnets, in concert with reaction wheels, to replace the consumables. Electromagnetic Formation Flight sparse apertures, powered by solar energy, are designed differently from traditional propulsion systems, which are based on V. This paper investigates the design of sparse apertures both inside and outside the Earth's gravity field.

Kwon, Daniel W.↗

NASA NTRS2010

Directivity of a Sparse Array in the Presence of Atmospheric-Induced Phase Fluctuations for Deep Space Communications

Widely distributed (sparse) ground-based arrays have been utilized for decades in the radio science community for imaging celestial objects, but have only recently become an option for deep space communications applications with the advent of the proposed Next Generation Deep Space Network (DSN) array. But whereas in astronomical imaging, observations (receive-mode only) are made on the order of minutes to hours and atmospheric-induced aberrations can be mostly corrected for in post-processing, communications applications require transmit capabilities and real-time corrections over time scales as short as fractions of a second. This presents an unavoidable problem with the use of sparse arrays for deep space communications at Ka-band which has yet to be successfully resolved, particularly for uplink arraying. In this paper, an analysis of the performance of a sparse antenna array, in terms of its directivity, is performed to derive a closed form solution to the expected array loss in the presence of atmospheric-induced phase fluctuations. The theoretical derivation for array directivity degradation is validated with interferometric measurements for a two-element array taken at Goldstone, California. With the validity of the model established, an arbitrary 27-element array geometry is defined at Goldstone, California, to ascertain its performance in the presence of phase fluctuations. It is concluded that a combination of compact array geometry and atmospheric compensation is necessary to ensure high levels of availability.

Nessel, James A.↗

NASA NTRSDate not supplied

Sparse Linear Algebra Toolkit for Computational Aerodynamics

Finding solutions to sparse linear systems of equations is an essential step in Computational Engineering applications of interest to NASA. Linear systems of equations are composed and solved in almost every computational engineering application. The characteristics of linear systems vary greatly from one application to another. Accordingly, there are a wide variety of methods for the solution of linear systems of equations. The operations and methods prepared by the authors are focused on linear systems of interest to NASA, primarily those associated with Computational Fluid Dynamics (CFD), Aeroelasticity, and Aeroacoustics. The Sparse Linear Algebra Toolkit (SLAT) is a coordinated collection of software featuring operations, methods, and data structures that are useful when solving sparse linear systems of equations on modern computer architectures. The implemented operations and methods are designed and tuned for parallelism in shared memory, in distributed memory, and across the hybrid combination of distributed-shared memory. The toolkit includes novel methods and implementations for modern architectures and facilitates development of new approaches for meeting NASA’s evolving computational engineering challenges using evolving computer architectures that are not available in vendor libraries. In this paper, significant features and interfaces within SLAT are presented and verified for simulations performed with NASA’s CFD solver, FUN3D. The runtime and scaling performance of the Generalized Minimum Residual (GMRES) method implemented in SLAT is analyzed for the linear subproblems within the solution of turbulent Navier-Stokes equations employed in the simulation of high-lift configurations. Prior to this work, the SPARSKIT GMRES implementation was the only Krylov subspace method available within FUN3D. A strong scaling study shows the SLAT GMRES implementation facilitates accurate Reynolds-averaged Navier-Stokes CFD solutions between 15% and 56% faster than the SPARSKIT GMRES implementation.

Stephen L Wood↗

NASA NTRS2021

Infrared Imaging using Sparse Microresonator Arrays and Compressed Sensing

In this work, we present an uncooled infrared (IR) thermal imager featuring a sparse array of resonant pixels that can be monolithically integrated with the readout electronics for long-term operation in high-temperature environments. Each of the detector pixels is made of an IR-sensitive GaN microresonator developed to be operated at up to 500 0C. The pixels are employed in sparse array configuration to allow for routing the signal carrying traces and to ease the routing from pixel to circuit, as well as to reduce the power consumption at the expense of moderate post-processing time and increased complexity to recover the image. Three 128 by 128 sparse resonator arrays with the array densities of 10%, 25% and 37.5% are designed, and used in conjunction with the Compressed Sensing (CS) method to reconstruct complex test images from highly incomplete data. Capabilities and performance metrics of the recovery technique are explored.

Rais-Zadeh, Mina↗

NASA NTRS2021

Thermal Infrared Detector Sparse Array for NASA Planetary Applications

In this work, we present an uncooled infrared (IR) thermal imager featuring a sparse array of resonant pixels that can be monolithically integrated with the readout electronics for long-term operation in hightemperature environments. Each of the detector pixels is made of an IR-sensitive GaN microresonator developed to be operated at up to 500 0C. The pixels are employed in sparse array configuration to allow for routing the signal carrying traces and to ease the routing from pixel to circuit, as well as to reduce the power consumption. A 128´128 sparse resonator array with the array density of 37.5% is designed and used in conjunction with the Compressed Sensing method to reconstruct complex test images from highly incomplete data. Capabilities and performance metrics of the recovery technique are explored.

Rais-Zadeh, Mina↗

NASA NTRSDate not supplied

Applicability of Loads Estimation Techniques Using Sparse Acceleration Sensor Data to Spacecraft Structural Health Monitoring

The use of structural health monitoring systems on spacecraft structures can play a crucial role in ensuring the safety, reliability, and longevity of the structure by gathering and analyzing onboard sensor data. Of specific importance is monitoring for excessive loading at critical interfaces as any off-nominal structural excitations experienced by spacecraft structures can cause early unpredicted high structural life consumption or damage. The availability and cost of flight-certified sensors along with the size of spacecraft structures and allowable payload mass drives the need for a method to estimate loads using sparsely-located sensors. Numerous approaches such as physics-based, statistical learning, and physics-enhanced statistical learning algorithms have gained popularity among structural prognostics applications. However, developing noise-robust prediction models to assess loads and structural life predictions from a sparse multi-sensor data acquisition system can be a challenging task. This paper discusses the evaluation of physics-based versus machine-learning algorithms for predicting loads and structural life at mission critical locations on the spacecraft structure using a finite element loads analysis with the application of simulated noise and noise reduction techniques. To estimate the loads from accelerations, the physics-based algorithm leverages a loads transformation matrix from a Craig-Bampton reduced finite element model. A System Equivalent Reduction Expansion Process (SEREP) and a pseudo-inverse approach are considered to expand from the onboard sensor degrees of freedom to the Craig-Bampton model degrees of freedom. The machine learning algorithm provides a data driven solution/mapping of the sensor accelerations to the loads at the mission critical locations using a high dimensionality analysis. Although these strategies produce comparable loads prediction without noise, the limitations of these strategies with incorporating simulated noise and noise reduction techniques with low signal to noise ratio signals are evaluated. The study demonstrates the immense potential of statistical learning algorithms for sparse structural prognostic models and enhancing signal denoising techniques. These findings also highlight the need for noise-resilient prognostic models and low-noise data acquisition systems onboard spacecraft structures.

Spacecraft Structural Health Monitoring↗

NASA NTRS1995

A General Purpose Sparse Matrix Parallel Solvers Package

A general purpose solver package for constructing and solving a range of sparse linear systems arising from discretization of PDEs on unstructured meshes is developed. Once the sparse symmetric complex matrix is constructed, it can be solved by either a preconditioned bi-conjugate gradient solver, a two-stage Cholesky LDLT factorization solver, or a hybrid solver combining the above two methods.

solver sparse matrix solvers package PDE↗

NASA NTRS1995

A General Purpose Sparse Matrix Parallel Solvers Package

solver sparse matrix solvers package PDE↗

NASA NTRS1970

Sorting and ordering sparse linear systems

Transformations of sparse linear systems by row-column permutations are considered and various algorithms are constructed to transform arbitrary symmetric positive definite sparse matrices, as well as matrices in band form, doubly bordered band form, and doubly bordered block diagonal form.

Tewarson, R. P.↗

NASA NTRS1972

Objective sea level pressure analysis for sparse data areas

A computer procedure was used to analyze the pressure distribution over the North Pacific Ocean for eleven synoptic times in February, 1967. Independent knowledge of the central pressures of lows is shown to reduce the analysis errors for very sparse data coverage. The application of planned remote sensing of sea-level wind speeds is shown to make a significant contribution to the quality of the analysis especially in the high gradient mid-latitudes and for sparse coverage of conventional observations (such as over Southern Hemisphere oceans). Uniform distribution of the available observations of sea-level pressure and wind velocity yields results far superior to those derived from a random distribution. A generalization of the results indicates that the average lower limit for analysis errors is between 2 and 2.5 mb based on the perfect specification of the magnitude of the sea-level pressure gradient from a known verification analysis. A less than perfect specification will derive from wind-pressure relationships applied to satellite observed wind speeds.

Druyan, L. M.↗

NASA NTRS1973

Objective sea-level pressure analysis for data-sparse areas.

A computer procedure, described in an earlier study, uses the wind speed field near the ocean surface in combination with a small number of observations of pressure and wind velocity to specify the maritime sea-level pressure field. An improved version was used to analyze the pressure distribution over the North Pacific Ocean for eleven synoptic times in February 1967. Independent knowledge of the central pressures of lows is shown to reduce the analysis errors for very sparse data coverage. The application of planned remote sensing of sea-level wind speeds is shown to make a significant contribution to the quality of the analysis especially in the high gradient midlatitudes and for sparse coverage of conventional observations (such as over Southern Hemisphere oceans). Uniform distribution of the available observations of sea-level pressure and wind velocity yields results far superior to those derived from a random distribution.

Druyan, L. M.↗

NASA NTRS1975

Sparse matrix techniques applied to modal analysis of multi-section duct liners

A simplified procedure is presented for analysis of ducts with discretely nonuniform properties. The analysis uses basis functions as the generalized coordinates. The duct eigenfunctions are approximated by finite series of these functions. The emphasis is on solution of the resulting large sparse set of linear equations. Characteristics of sparse matrix algorithms are outlined and some criteria for application are established. Analogies with structural methods are used to illustrate variations which can increase efficiency in generating values for design optimization routines. The effects of basis function selection, number of eigenfunctions and identification and ordering of equations on the sparsity and solution stability are included.

Arnold, W. R.↗

NASA NTRS1982

Out-of-Core Solutions of Complex Sparse Linear Equations

ETCLIB is library of subroutines for obtaining out-of-core solutions of complex sparse linear equations. Routines apply to dense and sparse matrices too large to be stored in core. Useful for solving any set of linear equations, but particularly useful in cases where coefficient matrix has no special properties that guarantee convergence with any of interative processes. The only assumption made is that coefficient matrix is not singular.

Yip, E. L.↗

NASA NTRS1985

Iterative solution of large, sparse linear systems on a static data flow architecture - Performance studies

The applicability of static data flow architectures to the iterative solution of sparse linear systems of equations is investigated. An analytic performance model of a static data flow computation is developed. This model includes both spatial parallelism, concurrent execution in multiple PE's, and pipelining, the streaming of data from array memories through the PE's. The performance model is used to analyze a row partitioned iterative algorithm for solving sparse linear systems of algebraic equations. Based on this analysis, design parameters for the static data flow architecture as a function of matrix sparsity and dimension are proposed.

Reed, D. A.↗

NASA NTRS1985

Parallel, iterative solution of sparse linear systems - Models and architectures

Solving large, sparse, linear systems of equations is a fundamental problem in large scale scientific and engineering computation. A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. A data transfer model predicting both the probability that data must be transferred between two tasks and the amount of data to be transferred is presented. This model is used to derive an execution time model for predicting parallel execution time and an optimal number of tasks given the dimension and sparsity of the coefficient matrix and the costs of computation, synchronization, and communication. The suitability of different parallel architectures for solving randomly sparse linear systems is discussed. Based on the complexity of task scheduling, one parallel architecture, based on a broadcast bus, is presented and analyzed.

Reed, D. A.↗

NASA NTRS1987

Solution of the two-dimensional Navier-Stokes equations using sparse matrix solvers

The use of direct sparse matrix solvers in the solution of the Navier-Stokes equations is investigated. The Yale Sparse Matrix Package and its implementation in the solution algorithm is described. The streamfunction-vorticity form of the Navier-Stokes equations are discretized and linearized and the resulting system of equations are solved using this package. Several viscous flow problems are investigated, including flow in a cavity and flow around a NACA0012 airfoil. Massively separated flow around a sine wave airfoil is investigated and high Reynolds number solutions are obtained. A solution of the unsteady flow around a Joukowski airfoil at high angle of attack is presented.

Bender, Erich E.↗

NASA NTRS1988

Data traffic reduction schemes for sparse Cholesky factorizations

Load distribution schemes are presented which minimize the total data traffic in the Cholesky factorization of dense and sparse, symmetric, positive definite matrices on multiprocessor systems with local and shared memory. The total data traffic in factoring an n x n sparse, symmetric, positive definite matrix representing an n-vertex regular 2-D grid graph using n (sup alpha), alpha is equal to or less than 1, processors are shown to be O(n(sup 1 + alpha/2)). It is O(n(sup 3/2)), when n (sup alpha), alpha is equal to or greater than 1, processors are used. Under the conditions of uniform load distribution, these results are shown to be asymptotically optimal. The schemes allow efficient use of up to O(n) processors before the total data traffic reaches the maximum value of O(n(sup 3/2)). The partitioning employed within the scheme, allows a better utilization of the data accessed from shared memory than those of previously published methods.

Naik, Vijay K.↗