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NASA NTRS1973

A unified development of several techniques for the representation of random vectors and data sets

Linear vector space theory is used to develop a general representation of a set of data vectors or random vectors by linear combinations of orthonormal vectors such that the mean squared error of the representation is minimized. The orthonormal vectors are shown to be the eigenvectors of an operator. The general representation is applied to several specific problems involving the use of the Karhunen-Loeve expansion, principal component analysis, and empirical orthogonal functions; and the common properties of these representations are developed.

Bundick, W. T.↗

NASA NTRS1972

On the mapping associated with the complex representation of functions and processes.

The mapping between function spaces that is implied by the representation of a real 'bandpass' function by a complex 'low-pass' function is explicitly accepted. The discussion is extended to the representation of stationary random processes where the mapping is between spaces of random processes. This approach clarifies the nature of the complex representation, especially in the case of random processes and, in addition, derives the properties of the complex representation.-

Harger, R. O.↗

NASA NTRS1988

State variable representations in digital control systems with MA-prefiltered measurements

This paper derives three discrete state variable representations for a continuous-time plant driven by a zero-order hold with a combination of instantaneous measurements and measurements prefiltered by a multiinput/multioutput moving average (MA) process. These representations allow the control system engineer to model plants of this type accurately in a form which permits him to use standard techniques to design digital feedback controllers for them. An example is presented which illustrates how to obtain the coefficient matrices in each representation. Guidelines are presented for choosing the best representation to use for any given plant of this type.

Polites, Michael E.↗

NASA NTRS1988

A representational framework and user-interface for an image understanding workstation

Problems in image understanding involve a wide variety of data (e.g., image arrays, edge maps, 3-D shape models) and processes or algorithms (e.g., convolution, feature extraction, rendering). The underlying structure of an Image Understanding Workstation designed to support mulitple levels and types of representations for both data and processes is described, also the user-interface. The Image Understanding Workstation consists of two parts: the Image Understanding (IU) Framework, and the user-interface. The IU Framework is the set of data and process representations. It includes multiple levels of representation for data such as images (2-D), sketches (2-D), surfaces (2 1/2 D), and models (3-D). The representation scheme for processes characterizes their inputs, outputs, and parameters. Data and processes may reside on different classes of machines. The user-interface to the IU Workstation gives the user convenient access for creating, manipulating, transforming, and displaying image data. The user-interface follows the structure of the IU Framework and gives the user control over multiple types of data and processes. Both the IU Framework and user-interface are implemented on a LISP machine.

Schroeder, Joyce D.↗

NASA NTRS1989

From primal sketches to the recovery of intensity and reflectance representations

A local change in intensity (edge) is a characteristic that is preserved when an image is filtered through a bandpass filter. Primal sketch representations of images, using the bandpass-filtered data, have become a common process since Marr proposed his model for early human vision. Here, researchers move beyond the primal sketch extraction to the recovery of intensity and reflectance representations using only the bandpass-filtered data. Assessing the response of an ideal step edge to the Laplacian of Gaussian (NAb/A squared G) filter, they found that the resulting filtered data preserves the original change of intensity that created the edge in addition to the edge location. Using the filtered data, they can construct the primal sketches and recover the original (relative) intensity levels between the boundaries. It was found that the result of filtering an ideal step edge with the Intensity-Dependent Spatial Summation (IDS) filter preserves the actual intensity on both sides of the edge, in addition to the edge location. The IDS filter also preserves the reflectance ratio at the edge location. Therefore, one can recover the intensity levels between the edge boundaries as well as the (relative) reflectance representation. The recovery of the reflectance representation is of special interest as it erases shadowing degradations and other dependencies on temporal illumination. This method offers a new approach to low-level vision processing as well as to high data-compression coding. High compression can be gained by transmitting only the information associated with the edge location (edge primitives) that is necessary for the recovery

Alter-Gartenberg, Rachel↗

NASA NTRS1990

Process and representation in graphical displays

How people comprehend graphics is examined. Graphical comprehension involves the cognitive representation of information from a graphic display and the processing strategies that people apply to answer questions about graphics. Research on representation has examined both the features present in a graphic display and the cognitive representation of the graphic. The key features include the physical components of a graph, the relation between the figure and its axes, and the information in the graph. Tests of people's memory for graphs indicate that both the physical and informational aspect of a graph are important in the cognitive representation of a graph. However, the physical (or perceptual) features overshadow the information to a large degree. Processing strategies also involve a perception-information distinction. In order to answer simple questions (e.g., determining the value of a variable, comparing several variables, and determining the mean of a set of variables), people switch between two information processing strategies: (1) an arithmetic, look-up strategy in which they use a graph much like a table, looking up values and performing arithmetic calculations; and (2) a perceptual strategy in which they use the spatial characteristics of the graph to make comparisons and estimations. The user's choice of strategies depends on the task and the characteristics of the graph. A theory of graphic comprehension is presented.

Gillan, Douglas J.↗

NASA NTRS1989

Precedence relationship representations of mechanical assembly sequences

Two types of precedence relationship representations for mechanical assembly sequences are presented: precedence relationships between the establishment of one connection between two parts and the establishment of another connection, and precedence relationships between the establishment of one connection and states of the assembly process. Precedence relationship representations have the advantage of being very compact. The problem with these representations was how to guarantee their correctness and completeness. Two theorems are presented each of which leads to the generation of one type of precedence relationship representation guaranteeing its correctness and completeness for a class of assemblies.

Homendemello, L. S.↗

NASA NTRS1990

On-board ephemeris representation for Topex/Poseidon

The Topex/Poseidon satellite requires real-time on-board knowledge of the satellite and TDRS ephemeris for attitude determination and control and High-Gain Antenna (HGA) pointing. The ephemeris representation concept for the MMS (Multimission Modular Spacecraft) satellites has shown that compressing the predicted ephemeris in a Fourier Power Series (FPS) before uplinking in conjunction with the On-Board Computer (OBC) ephemeris reconstruction algorithms is an efficient technique for ephemeris representation. As an MMS-based satellite, Topex/Poseidon has inherited the Landsat ephemeris representation concept including a daily FPS upload. This paper presents the Topex/Poseidon concept, analysis, and results including the conclusion that the ephemeris representation duration could be extended to 10 days or more and convenient weekly uploading is adopted without an increase in OBC memory requirements.

Salama, Ahmed H.↗

NASA NTRS1994

A rapid-pressure correlation representation consistent with the Taylor-Proudman theorem materially-frame-indifferent in the 2D limit

A nonlinear representation for the rapid-pressure correlation appearing in the Reynolds stress equations, consistent with the Taylor-Proudman theorem, is presented. The representation insures that the modeled second-order equations are frame-invariant with respect to rotation when the flow is two-dimensional in planes perpendicular to the axis of rotation. The representation satisfies realizability in a new way: a special ansatz is used to obtain analytically, the values of coefficients valid away from the realizability limit: the model coefficients are functions of the state of the turbulence that are valid for all states of the mechanical turbulence attaining their constant limiting values only when the limit state is achieved. Utilization of all the mathematical constraints are not enough to specify all the coefficients in the model. The unspecified coefficients appear as free parameters which are used to insure that the representation is asymptotically consistent with the known equilibrium states of a homogeneous sheared turbulence. This is done by insuring that the modeled evolution equations have the same fixed points as those obtained from computer and laboratory experiments for the homogeneous shear. Results of computations of the homogeneous shear, with and without rotation, and with stabilizing and destabilizing curvature, are shown. Results are consistently better, in a wide class of flows which the model not been calibrated, than those obtained with other nonlinear models.

Ristorcelli, J. R.↗

NASA NTRS1990

Implementation of a frame-based representation in CLIPS

Knowledge representation is one of the major concerns in expert systems. The representation of domain-specific knowledge should agree with the nature of the domain entities and their use in the real world. For example, architectural applications deal with objects and entities such as spaces, walls, and windows. A natural way of representing these architectural entities is provided by frames. This research explores the potential of using the expert system shell CLIPS, developed by NASA, to implement a frame-based representation that can accommodate architectural knowledge. These frames are similar but quite different from the 'template' construct in version 4.3 of CLIPS. Templates support only the grouping of related information and the assignment of default values to template fields. In addition to these features frames provide other capabilities including definition of classes, inheritance between classes and subclasses, relation of objects of different classes with 'has-a', association of methods (demons) of different types (standard and user-defined) to fields (slots), and creation of new fields at run-time. This frame-based representation is implemented completely in CLIPS. No change to the source code is necessary.

Assal, Hisham↗

NASA NTRS2004

Improving Evolvability through Generative Representations

One of the main limitations of computer automated design systems is the representation used for encoding designs. Using computer programs as an analogy, representations can be thought of as having the properties of combination, control-flow and abstraction. Generative representations are those which have the ability to reuse elements in an encoding through either iteration, a form of control-flow, or abstraction. Here we argue that generative representations improve the evolvability of designs by capturing design dependencies in a way that makes them easier to change, and we support this with examples from two design substrates.

Hornby, Gregory S.↗

NASA NTRS2008

A Data Type for Efficient Representation of Other Data Types

A self-organizing, monomorphic data type denoted a sequence has been conceived to address certain concerns that arise in programming parallel computers. A sequence in the present sense can be regarded abstractly as a vector, set, bag, queue, or other construct. Heretofore, in programming a parallel computer, it has been necessary for the programmer to state explicitly, at the outset, what parts of the program and the underlying data structures must be represented in parallel form. Not only is this requirement not optimal from the perspective of implementation; it entails an additional requirement that the programmer have intimate understanding of the underlying parallel structure. The present sequence data type overcomes both the implementation and parallel structure obstacles. In so doing, the sequence data type provides unified means by which the programmer can represent a data structure for natural and automatic decomposition to a parallel computing architecture. Sequences exhibit the behavioral and structural characteristics of vectors, but the underlying representations are automatically synthesized from combinations of programmers advice and execution use metrics. Sequences can vary bidirectionally between sparseness and density, making them excellent choices for many kinds of algorithms. The novelty and benefit of this behavior lies in the fact that it can relieve programmers of the details of implementations. The creation of a sequence enables decoupling of a conceptual representation from an implementation. The underlying representation of a sequence is a hybrid of representations composed of vectors, linked lists, connected blocks, and hash tables. The internal structure of a sequence can automatically change from time to time on the basis of how it is being used. Those portions of a sequence where elements have not been added or removed can be as efficient as vectors. As elements are inserted and removed in a given portion, then different methods are utilized to provide both an access and memory strategy that is optimized for that portion and the use to which it is put.

James, Mark↗

NASA NTRS2011

Monthly Representations of Mid-Tropospheric Carbon Dioxide from the Atmospheric Infrared Sounder

The Atmospheric Infrared Sounder (AIRS) on NASA's Earth Observing System Aqua spacecraft was launched in May of 2002 and acquires hyperspectral infrared spectra used to generate a wide range of atmospheric products including temperature, water vapor, and trace gas species including carbon dioxide. Here we present monthly representations of global concentrations of mid-tropospheric carbon dioxide produced from 8 years of data obtained by AIRS between the years of 2003 and 2010. We define them as "representations" rather than "climatologies" to reflect that the files are produced over a relatively short time period and represent summaries of the Level 3 data. Finally, they have not yet been independently validated. The representations have a horizontal resolution of 2.0 deg x 2.5 deg (Latitude x Longitude) and faithfully reproduce the original 8 years of monthly L3 CO2 concentrations with a standard deviation of 1.48 ppm and less than 2% outliers. The representations are intended for use in studies of the global general circulation of CO2 and identification of anomalies in CO2 typically associated with atmospheric transport. The seasonal variability and trend found in the AIRS CO2 data are discussed.

Carbon Dioxide↗

NASA NTRS2022

Improved representation of agricultural land use and crop management for large-scale hydrological impact simulation in Africa using SWAT+

To date, most regional and global hydrological models either ignore the representation of cropland or consider crop cultivation in a simplistic way or in abstract terms without any management practices. Yet, the water balance of cultivated areas is strongly influenced by applied management practices (e.g. planting, irrigation, fertilization, and harvesting). The SWAT+ (Soil and Water Assessment Tool) model represents agricultural land by default in a generic way, where the start of the cropping season is driven by accumulated heat units. However, this approach does not work for tropical and subtropical regions such as sub-Saharan Africa, where crop growth dynamics are mainly controlled by rainfall rather than temperature. In this study, we present an approach on how to incorporate crop phenology using decision tables and global datasets of rainfed and irrigated croplands with the associated cropping calendar and fertilizer applications in a regional SWAT+ model for northeastern Africa. We evaluate the influence of the crop phenology representation on simulations of leaf area index (LAI) and evapotranspiration (ET) using LAI remote sensing data from Copernicus Global Land Service (CGLS) and WaPOR (Water Productivity through Open access of Remotely sensed derived data) ET data, respectively. Results show that a representation of crop phenology using global datasets leads to improved temporal patterns of LAI and ET simulations, especially for regions with a single cropping cycle. However, for regions with multiple cropping seasons, global phenology datasets need to be complemented with local data or remote sensing data to capture additional cropping seasons. In addition, the improvement of the cropping season also helps to improve soil erosion estimates, as the timing of crop cover controls erosion rates in the model. With more realistic growing seasons, soil erosion is largely reduced for most agricultural hydrologic response units (HRUs), which can be considered as a move towards substantial improvements over previous estimates. We conclude that regional and global hydrological models can benefit from improved representations of crop phenology and the associated management practices. Future work regarding the incorporation of multiple cropping seasons in global phenology data is needed to better represent cropping cycles in areas where they occur using regional to global hydrological models.

crop phenology↗

NASA NTRS1972

Geopotential representation with sampling functions.

Satellite-to-ocean altitudes measured to meter accuracy eventually can yield a geoid representation with significant short-wavelength structure over ocean areas. To cope conveniently with this expected detail, one suggested analytical technique would represent the geopotential or the geoid as an expansion in sampling functions that are linear combinations of spherical harmonics. Each of the sampling functions makes its principal contribution to the geopotential in a single geographical region. For a representation truncated after degree N, there are (N + 1) squared such functions associated with a like number of points distributed nearly regularly on the globe. The features of this geopotential representation can be illustrated by considering the case N = 22, for which an expansion in sampling functions can be produced that is equivalent to the geopotential of the 1969 Smithsonian standard earth.

Lundquist, C. A.↗

NASA NTRS1974

A representation of Jacchia's thermospheric models in spherical harmonic functions

The Jacchia models are represented in terms of spherical harmonic functions. This representation has the advantage of ease of comparison with other global theoretical and empirical models that use this mathematical form. Furthermore, it is analytic, continuous, and has continuous derivatives all over the globe. The representation of the exospheric temperatures shows clearly the amplitudes of the various periodic terms and uses relatively few constants. An example of a similar representation for the total mass density at a particular height and level of solar activity is given as well.

Blum, P.↗

NASA NTRS1975

Use of the Wigner representation in scattering problems

The basic equations of quantum scattering were translated into the Wigner representation, putting quantum mechanics in the form of a stochastic process in phase space, with real valued probability distributions and source functions. The interpretative picture associated with this representation is developed and stressed and results used in applications published elsewhere are derived. The form of the integral equation for scattering as well as its multiple scattering expansion in this representation are derived. Quantum corrections to classical propagators are briefly discussed. The basic approximation used in the Monte-Carlo method is derived in a fashion which allows for future refinement and which includes bound state production. Finally, as a simple illustration of some of the formalism, scattering is treated by a bound two body problem. Simple expressions for single and double scattering contributions to total and differential cross-sections as well as for all necessary shadow corrections are obtained.

Bemler, E. A.↗

NASA NTRS1974

Integral representation of field variables for the finite element solution of viscous flow problems

The kinematics aspects of compressible and incompressible viscous flow problems are recasted into an integral representation for the velocity vector. For the incompressible flow problem, the kinetics aspect is similarly recasted into an integral representation. The result is a system of integral equations ideally suited for the finite element method. The integral representations are shown to permit the confinement of the computation field to the region of nonnegligible vorticity and dilatation which, for the incompressible flow, is identified with the viscous region. This drastic reduction in computation field results in a superior solution speed which is further improved by the use of a flowfield segmentation technique. The new approach is further shown to remove the difficulties associated with previous methods in specifying the far field and extraneous boundary conditions.

Wu, J. C.↗