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At least 343 records · Page 19

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DOE OSTI2024

Shorter function summaries for finite state machine-based high consequence systems using logic synthesis and tautologies (Final Report LDRD 24-1302)

Computer programs are often viewed as collections of functions – each function has parameters (inputs) and computes a return value, and each has potential side effects that modify program state (outputs). In this research, a Sandia symbolic execution tool designed to support “human-in-the-loop” analysis was modified to automatically create “function summaries,” and a new tool, “diaboolical,” was created to support enhancing readability of the summary using a novel approach to bit-vector simplification that leverages logic synthesis and tautologies. For this effort, students at Auburn University created several finite state machines (FSMs) to serve as exemplars for high-consequence systems. Function summaries for each of the machines were obtained, and then portions of the summaries were simplified using both diaboolical and the simplification procedure of a popular SMT solver. A comparison of the results shows that diaboolical can often produce smaller function summaries, with expression length improvements over the unsimplified function summaries ranging from 0% to 90% for diaboolical and 0% to 65% for the SMT solver, though diaboolical had a significantly greater cost in time. Diaboolical was evaluated against a collection of “arbitrary” C-code as well as FSM exemplars, and for both datasets it achieved an approximately 10% improvement in expression length compared to simplifications that could be obtained using existing techniques. Function summaries can assist assurance efforts that evaluate existing systems and their executable code. A smaller function summary is likely easier for humans to understand and could thus increase the ability and efficacy of assurance practices centered around the analysis of executable artifacts.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nev- ertheless, the majority of these studies examine how well deep neural networks can model functions with uniform regularities. In this paper, we explore a different angle: how deep neural networks can adapt to varying degrees of smoothness in functions and nonuni- form data distributions across different locations and scales. More precisely, we focus on a broad class of functions defined by nonlinear tree-based approximation methods. This class encompasses a range of function types, such as functions with uniform regularities and discontinuous functions. We develop nonparametric approximation and estimation theories for this class using deep ReLU networks. Our results show that deep neural networks are adaptive to the nonuniform smoothness of functions and nonuniform data distributions at different locations and scales. We apply our results to several function classes, and derive the corresponding approximation and generalization errors. The validity of our results is demonstrated through numerical experiments.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1979

On one-dimensional stretching functions for finite-difference calculations

The class of one-dimensional stretching functions used in finite-difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One is an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two-sided stretching function, for which the arbitrary slopes at the two ends of the one-dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent.

Vinokur, M.↗

NASA NTRS1983

On one-dimensional stretching functions for finite-difference calculations

The class of one-dimensional stretching functions used in finite-difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two-sided stretching function, for which the arbitrary slopes at the two ends of the one-dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent. Previously announced in STAR as N80-25055

Vinokur, M.↗

NASA NTRS1986

Surface infrastructure functions, requirements and subsystems for a manned Mars mission

Planning and development for a permanently manned scientific outpost on Mars requires an in-depth understanding and analysis of the functions the outpost is expected to perform. The optimum configuration that accomplishes these functions then arises during the trade studies process. In a project this complex, it becomes necessary to use a formal methodology to document the design and planning process. The method chosen for this study is called top-down functional decomposition. This method is used to determine the functions that are needed to accomplish the overall mission, then determine what requirements and systems are needed to do each of the functions. This method facilitates automation of the trades and options process. In the example, this was done with an off-the shelf software package called TK! olver. The basic functions that a permanently manned outpost on Mars must accomplish are: (1) Establish the Life Critical Systems; (2) Support Planetary Sciences and Exploration; and (3) Develop and Maintain Long-term Support Functions, including those systems needed towards self-sufficiency. The top-down functional decomposition methology, combined with standard spread sheet software, offers a powerful tool to quickly assess various design trades and analyze options. As the specific subsystems, and the relational rule algorithms are further refined, it will be possible to very accurately determine the implications of continually evolving mission requirements.

Kyle Fairchild↗

NASA NTRS1989

An indirect method for numerical optimization using the Kreisselmeir-Steinhauser function

A technique is described for converting a constrained optimization problem into an unconstrained problem. The technique transforms one of more objective functions into reduced objective functions, which are analogous to goal constraints used in the goal programming method. These reduced objective functions are appended to the set of constraints and an envelope of the entire function set is computed using the Kreisselmeir-Steinhauser function. This envelope function is then searched for an unconstrained minimum. The technique may be categorized as a SUMT algorithm. Advantages of this approach are the use of unconstrained optimization methods to find a constrained minimum without the draw down factor typical of penalty function methods, and that the technique may be started from the feasible or infeasible design space. In multiobjective applications, the approach has the advantage of locating a compromise minimum design without the need to optimize for each individual objective function separately.

Wrenn, Gregory A.↗

NASA NTRS1988

Space station functional relationships analysis

A systems engineering process is developed to assist Space Station designers to understand the underlying operational system of the facility so that it can be physically arranged and configured to support crew productivity. The study analyzes the operational system proposed for the Space Station in terms of mission functions, crew activities, and functional relationships in order to develop a quantitative model for evaluation of interior layouts, configuration, and traffic analysis for any Station configuration. Development of the model involved identification of crew functions, required support equipment, criteria of assessing functional relationships, and tools for analyzing functional relationship matrices, as well as analyses of crew transition frequency, sequential dependencies, support equipment requirements, potential for noise interference, need for privacy, and overall compatability of functions. The model can be used for analyzing crew functions for the Initial Operating Capability of the Station and for detecting relationships among these functions. Note: This process (FRA) was used during Phase B design studies to test optional layouts of the Space Station habitat module. The process is now being automated as a computer model for use in layout testing of the Space Station laboratory modules during Phase C.

Tullis, Thomas S.↗

NASA NTRS1990

Three-dimensional potential flows from functions of a 3D complex variable

Potential, or ideal, flow velocities can be found from the gradient of an harmonic function. An ordinary complex valued analytic function can be written as the sum of two real valued functions, both of which are harmonic. Thus, 2D complex valued functions serve as a source of functions that describe two-dimensional potential flows. However, this use of complex variables has been limited to two-dimensions. Recently, a new system of three-dimensional complex variables has been developed at the NASA Ames Research Center. As a step toward application of this theory to the analysis of 3D potential flow, several functions of a three-dimensional complex variable have been investigated. The results for two such functions, the 3D exponential and 3D logarithm, are presented in this paper. Potential flows found from these functions are investigated. Important characteristics of these flows fields are noted.

Kelly, Patrick↗

NASA NTRS1992

Description of the SSF PMAD dc testbed control system data acquisition function

A functional description of the various levels of the SSF power management and distribution dc test-bed control system architecture is presented, and the data acquisition function and the status of its implementation are described. The data requirements for the test-bed control system are dictated by the functionality being implemented at each level of the architecture. The test-bed control system hierarchy data acquisition function is distributed among its various levels. Fast-acting control functions that require time critical data are implemented at the lowest level. These functions require periodic data sampling to assure safe system operation and performance. Slower response control functions are implemented at the higher levels and require data to be reported at least every second. The present data acquisition function meets the requirements for a hierarchical and distributed power management and control system.

Baez, Anastacio N.↗

NASA NTRS1955

On the Kernel function of the integral equation relating the lift and downwash distributions of oscillating finite wings in subsonic flow

This report treats the Kernel function of an integral equation that relates a known prescribed downwash distribution to an unknown lift distribution for a harmonically oscillating finite wing in compressible subsonic flow. The Kernel function is reduced to a form that can be accurately evaluated by separating the Kernel function into two parts: a part in which the singularities are isolated and analytically expressed and a nonsingular part which may be tabulated. The form of the Kernel function for the sonic case (Mach number 1) is treated separately. In addition, results for the special cases of Mach number of 0 (incompressible case) and frequency of 0 (steady case) are given. The derivation of the integral equation which involves this Kernel function is reproduced as an appendix. Another appendix gives the reduction of the form of the Kernel function obtained herein for the three-dimensional case to a known result of Possio for two-dimensional flow. A third appendix contains some remarks on the evaluation of the Kernel function, and a fourth appendix presents an alternate form of expression for the Kernel function.

Watkins, Charles E↗

NASA NTRS1993

ERS-1 and Seasat scatterometer measurements of ocean winds: Model functions and the directional distribution of short waves

Calculation of accurate vector winds from scatterometers requires knowledge of the relationship between backscatter cross-section and the geophysical variable of interest. As the detailed dynamics of wind generation of centimetric waves and radar-sea surface scattering at moderate incidence angles are not well known, empirical scatterometer model functions relating backscatter to winds must be developed. Less well appreciated is the fact that, given an accurate model function and some knowledge of the dominant scattering mechanisms, significant information on the amplitudes and directional distributions of centimetric roughness elements on the sea surface can be inferred. accurate scatterometer model functions can thus be used to investigate wind generation of short waves under realistic conditions. The present investigation involves developing an empirical model function for the C-band (5.3 GHz) ERS-1 scatterometer and comparing Ku-band model functions with the C-band model to infer information on the two-dimensional spectrum of centimetric roughness elements in the ocean. The C-band model function development is based on collocations of global backscatter measurements with operational surface analyses produced by meteorological agencies. Strengths and limitations of the method are discussed, and the resulting model function is validated in part through comparison with the actual distributions of backscatter cross-section triplets. Details of the directional modulation as well as the wind speed sensitivity at C-band are investigated. Analysis of persistent outliers in the data is used to infer the magnitudes of non-wind effects (such as atmospheric stratification, swell, etc.). The ERS-1 C-band instrument and the Seasat Ku-band (14.6 GHz) scatterometer both imaged waves of approximately 3.4 cm wavelength assuming that Bragg scattering is the dominant mechanism. Comparisons of the C-band and Ku-band model functions are used both to test the validity of the postulated Bragg mechanism and to investigate the directional distribution of the imaged waves under a variety of conditions where Bragg scatter is dominant.

Freilich, Michael H.↗

NASA NTRS1994

Evaluation of current tropospheric mapping functions by Deep Space Network very long baseline interferometry

To compare the validity of current algorithms that map zenith tropospheric delay to arbitrary elevation angles, 10 different tropospheric mapping functions are used to analyze the current data base of Deep Space Network Mark 3 intercontinental very long baseline interferometric (VLBI) data. This analysis serves as a stringent test because of the high proportion of low-elevation observations necessitated by the extremely long baselines. Postfit delay and delay-rate residuals are examined, as well as the scatter of baseline lengths about the time-linear model that characterizes tectonic motion. Among the functions that utilize surface meteorological data as input parameters, the Lanyi 1984 mapping shows the best performance both for residuals and baselines, through the 1985 Davis function is statistically nearly identical. The next best performance is shown by the recent function of Niell, which is based on an examination of global atmospheric characteristics as a function of season and uses no weather data at the time of the measurements. The Niell function shows a slight improvement in residuals relative to Lanyi, but also an increase in baseline scatter that is significant for the California-Spain baseline. Two variants of the Chao mapping function, as well as the Chao tables used with the interpolation algorithm employed in the Orbit Determination Program software, show substandard behavior for both VLBI residuals and baseline scatter. The length of the California-Australia baseline (10,600 km) in the VLBI solution can vary by as much as 5 to 10 cm for the 10 mapping functions.

Sovers, O. J.↗

NASA NTRS1994

The luminosity function at the end of the main sequence: Results of a deep, large-area, CCD survey for cool dwarfs

The luminosity function at the end of the main sequence is determined from V, R, and I data taken by the charge coupled devices (CCD)/Transit Instrument, a dedicated telescope surveying an 8.25 min wide strip of sky centered at delta = +28 deg, thus sampling Galactic latitudes of +90 deg down to -35 deg. A selection of 133 objects chosen via R - I and V - I colors has been observed spectroscopically at the 4.5 m Multiple Mirror Telescope to assess contributions by giants and subdwarfs and to verify that the reddest targets are objects of extremely late spectral class. Eighteen dwarfs of type M6 or later have been discovered, with the latest being of type M8.5. Data used for the determination of the luminosity function cover 27.3 sq. deg down to a completeness limit of R = 19.0. This luminosity function, computed at V, I, and bolometric magnitudes, shows an increase at the lowest luminosities, corresponding to spectral types later than M6- an effect suggested in earlier work by Reid & Gilmore and Legget & Hawkins. When the luminosity function is segregated into north Galactic and south Galactic portions, it is found that the upturn at faint magnitudes exists only in the southern sample. In fact, no dwarfs with M(sub I) is greater than or equal to 12.0 are found within the limiting volume of the 19.4 sq deg northern sample, in stark contrast to the smaller 7.9 sq deg area at southerly latitudes where seven such dwarfs are found. This fact, combined with the fact that the Sun is located approximately 10-40 pc north of the midplane, suggests that the latest dwarfs are part of a young population with a scale height much smaller than the 350 pc value generally adopted for other M dwarfs. These objects comprise a young population either because the lower metallicities prevelant at earlier epochs inhibited the formation of late M dwarfs or because the older counterparts of this population have cooled beyond current detection limits. The latter scenario would hold if these late-type M dwarfs are substellar. The luminosity function data together with an empirical derivation of the mass-luminosity relation (from Henry & McCarthy) are used to compute a mass function independent of theory. This mass function increases toward the end of the main sequence, but the observed density of M dwarfs is still insufficient to account for the missing mass. If the increases seen in the luminosity and mass functions are indicative of a large, unseen, substellar population, brown dwarfs may yet add significantly to the mass of the Galaxy.

Kirkpatrick, J. Davy↗

NASA NTRS1994

An optical study of the faint end of the stellar luminosity function

We implement a new method by which to study the faint end of the field star luminosity function. The method relies on deep, multicolor photometry of fields projected against highly obscured, nearby molecular clouds. The clouds act as nearby opaque screens and delimit a well-defined survey volume which is in principle free of the problem of distinguishing nearby, intrinsically faint dwarf stars from more distant red giants. This study is based upon deep photographic and CCD photometry at optical (V, R, I) bandpasses toward the most highly obscured portions of the Taurus and Ophiuchus molecular clouds. The total volume delimited by the clouds is approximately 200 cu pc. Within this region our survey is complete for all stars brighter than M(sub V) = 16-17 mag; at R and I, the survey is complete down to the lowest mass stars capable of sustaining core hydrogen burning. We estimate the faint end of the field star luminosity function for the composite Taurus and Ophiuchus foreground sample and find that it resembles the local luminosity function down to M(sub V) approx. 16. At still fainter magnitudes we find more stars than do photometric parallex studies of the polar regions. This difference widens dramatically if even the simplest correction for incompleteness is applied to our data. We therefore tentatively conclude that the luminosity function rises beyond M(sub V) approx. 16; even if we discard our attempts to correct for incompleteness in the faintest magnitude bins, the luminosity function at least remains flat for the lowest mass stars. Our provisional finding that the luminosity function rises beyond its well-known peak at M(sub V) approx. 12-13, implies that the initial mass function (IMF) probably rises beyond the turnover point associated with this peak. Even if our most conservative estimate for the faint end of the luminosity function is used-in which no corrections are made for incompleteness-the IMF must at least remain flat down to the edge of the hydrogen-burning main sequence.

Jarrett, T. H.↗

NASA NTRS1995

The point spread function of the soft X-ray telescope aboard Yohkoh

The point spread function of the SXT telescope aboard Yohkoh has been measured in flight configuration in three different X-ray lines at White Sands Missile Range. We have fitted these data with an elliptical generalization of the Moffat function. Our fitting method consists of chi squared minimization in Fourier space, especially designed for matching of sharply peaked functions. We find excellent fits with a reduced chi squared of order unity or less for single exposure point spread functions over most of the CCD. Near the edges of the CCD the fits are less accurate due to vignetting. From fitting results with summation of multiple exposures we find a systematic error in the fitting function of the order of 3% near the peak of the point spread function, which is close to the photon noise for typical SXT images in orbit. We find that the full width to half maximum and fitting parameters vary significantly with CCD location. However, we also find that point spread functions measured at the same location are consistent to one another within the limit determined by photon noise. A 'best' analytical fit to the PSF as function of position on the CCD is derived for use in SXT image enhancemnent routines. As an aside result we have found that SXT can determine the location of point sources to about a quarter of a 2.54 arc sec pixel.

Martens, Petrus C.↗

NASA NTRS1996

Functional performance of pyrovalves

Following several flight and ground test failures of spacecraft systems using single-shot, 'normally closed' pyrotechnically actuated valves (pyrovalves), a Government/Industry cooperative program was initiated to assess the functional performance of five qualified designs. The goal of the program was to provide information on functional performance of pyrovalves to allow users the opportunity to improve procurement requirements. Specific objectives included the demonstration of performance test methods, the seating; these gases/particles entered the fluid path of measurement of 'blowby' (the passage of gases from the pyrotechnic energy source around the activating piston into the valve's fluid path), and the quantification of functional margins for each design. Experiments were conducted at NASA's Langley Research Center on several units for each of the five valve designs. The test methods used for this program measured the forces and energies required to actuate the valves, as well as the energies and the pressures (where possible) delivered by the pyrotechnic sources. Functional performance ranged widely among the designs. Blowby cannot be prevented by o-ring seals; metal-to-metal seals were effective. Functional margin was determined by dividing the energy delivered by the pyrotechnic sources in excess to that required to accomplish the function by the energy required for that function. Two of the five designs had inadequate functional margins with the pyrotechnic cartridges evaluated.

Bement, Laurence J.↗

NASA NTRS2002

Functional Groups Based on Leaf Physiology: Are they Spatially and Temporally Robust?

The functional grouping hypothesis, which suggests that complexity in function can be simplified by grouping species with similar responses, was tested in the Florida scrub habitat. Functional groups were identified based on how species in fire maintained FL scrub function in terms of carbon, water and nitrogen dynamics. The suite of physiologic parameters measured to determine function included both instantaneous gas exchange measurements obtained from photosynthetic light response curves and integrated measures of function. Using cluster analysis, five distinct physiologically-based functional groups were identified. Using non-parametric multivariate analyses, it was determined that these five groupings were not altered by plot differences or by the three different management regimes; prescribed burn, mechanically treated and burn, and fire-suppressed. The physiological groupings also remained robust between the two years 1999 and 2000. In order for these groupings to be of use for scaling ecosystem processes, there needs to be an easy-to-measure morphological indicator of function. Life form classifications were able to depict the physiological groupings more adequately than either specific leaf area or leaf thickness. THe ability of life forms to depict the groupings was improved by separating the parasitic Ximenia americana from the shrub category.

Foster, Tammy E.↗

NASA NTRS2004

DNA in a Tunnel: A Comfy Spot for Recognition - or -The Structure of BsoBI Complexed with DNA. What can we Learn about Function via Structure Determination and how can this be Applied to Bone or Muscle Biology?

The structure and function of a biologically active molecule are related. To understand its function, it is necessary (but not always sufficient) to know the structure of the molecule. There are many ways of relating the molecular function with the structure. Mutation analysis can identify pertinent amino acids of an enzyme, or alternatively structure comparison of the of two similar molecules with different function may lead to understanding which parts are responsible for a functional aspect, or a series of "structural cartoons" - enzyme structure, enzyme plus substrate, enzyme with transition state analog, and enzyme with product - may give insight in the function of a molecule. As an example we will discuss the structure and function of the restriction enzyme BsoBI from Bacillus stearothemzophilus in complex with its cognate DNA. The enzyme forms a unique complex with DNA in that it completely encircles the DNA. The structure reveals the enzyme-DNA contacts, how the DNA is distorted compared with the canonical forms, and elegantly shows how two distinct DNA sequences can be recognized with the same efficiency. Based on the structure we may also propose a hypothesis how the enzymatic mechanism works. The knowledge gained thru studies such as this one can be used to alter the function by changing the molecular structure. Usually this is done by design of inhibitors specifically active against and fitting into an active site of the enzyme of choice. In the case of BsoBI one of the objectives of the study was to alter the enzyme specificity. In bone biology there are many candidates available for molecular study in order to explain, alter, or (temporarily) suspend activity. For example, the understanding of a pathway that negatively regulates bone formation may be a good target for drug design to stimulate bone formation and have good potential as the basis for new countermeasures against bone loss. In principle the same approach may aid muscle atrophy, radiation damage, immune response changes and other risks identified for long-duration Space travel.

vanderWoerd, Mark↗