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The computer algebra language MACSYMA enables the programmer to include symbolic physical units in computer calculations, and features automatic detection of dimensionally-inhomogeneous formulas and conversion of inconsistent units in a dimensionally homogeneous formula. Some examples illustrate these features.
Three symbol-lock detectors proposed as alternatives in advanced receivers processing non-return-to-zero binary data signals. Two perform operations similar to those of older square-law and absolute-value types. However, integrals computed during nonoverlapping symbol periods and, therefore, only one integrator needed in each such detector. Proposed detectors simpler, but performances worse because noises in overlapping samples correlated, whereas noises in nonoverlapping samples not correlated. Third detector is signal-power-estimator type. Signal integrated during successive half symbol cycles, and therefore only one integrator needed. Half-cycle integrals multiplied to eliminate effect of symbol polarity, and products accumulated during M-cycle observation period to smooth out estimate of signal power. If estimated signal power exceeds threshold, delta, then lock declared.
The theoretical and practical connections between connectionist schemes such as neural-network computers and traditional symbolic processing architectures involving a high degree of parallelism are explored, reviewing the results of recent investigations. Topics addressed include data flow, data structure, and control flow; conventional pointers; associative addressing; hashing and reduced representations; the problem of binding values to variables; and levels of parallelism. It is concluded that connectionism is more closely related to traditional computer science and technology than is generally admitted; more cooperation between followers of the two approaches is recommended.
This paper puts forth an architecture for implementing a loop for advanced data structure of arrays in CLIPS. An attempt is made to use multi-field variables in such an architecture to process a set of data during the decision making cycle. Also, current limitations on the expert system shells are discussed in brief in this paper. The resulting architecture is designed to circumvent the current limitations set by the expert system shell and also by the operating environment. Such advanced data structures are needed for tightly coupling symbolic and numeric computation modules.
Computer simulated noise performance of the symbol synchronizer loop (SSL) in the Block 5 receiver is compared with the theoretical noise performance. Good agreement is seen at the higher loop SNR's (SNR(sub L)'s), with gradual degradation as the SNR(sub L) is decreased. For the different cases simulated, cycle slipping is observed (within the simulation time of 10(exp 4) seconds) at SNR(sub L)'s below different thresholds, ranging from 6 to 8.5 dB, comparable to that of a classical phase-locked loop. An important point, however, is that to achieve the desired loop SNR above the seemingly low threshold to avoid cycle slipping, a large data-to-loop-noise power ratio, P(sub D)/(N(sub 0)B(sub L)), is necessary (at least 13 dB larger than the desired SNR(sub L) in the optimum case and larger otherwise). This is due to the large squaring loss (greater than or equal to 13 dB) inherent in the SSL. For the special case of symbol rates approximately equaling the loop update rate, a more accurate equivalent model accounting for an extra loop update period delay (characteristic of the SSL phase detector design) is derived. This model results in a more accurate estimation of the noise-equivalent bandwidth of the loop.
Digital computer-aided circuit sensitivity analysis using symbols, with example of band pass filter analysis
The power spectral density of the output symbol sequence of a convolutional encoder is computed for two different input symbol stream source models, namely, an NRZ signaling format and a first order Markov source. In the former, the two signaling states of the binary waveform are not necessarily assumed to occur with equal probability. The effects of alternate symbol inversion on this spectrum are also considered. The mathematical results are illustrated with many examples corresponding to optimal performance codes.
The power spectral density of the output symbol sequence of a convolutional encoder is computed for two different input symbol stream source models, namely, an NRZ signaling format and a first-order Markov source. The effects of alternate symbol inversion on this spectrum are also considered. The mathematical results are illustrated with many examples corresponding to optimal performance codes. It is demonstrated that only for the case of a purely random input source (e.g., NRZ data with equiprobable symbols) and a particular class of codes is the output spectrum identical to the input spectrum except for a frequency scaling (expansion) by the reciprocal of the code rate.
Data compression via block-adaptive Huffman coding is considered. The compressor consecutively processes blocks of N data symbols, estimates source statistics by computing the relative frequencies of each source symbol in the block, and then synthesizes a Huffman code based on these estimates. In order to let the decompressor know which Huffman code is being used, the compressor must begin the transmission of each compressed block with a short preamble or header file. This file is an encoding of the list n = (n(sub 1), n(sub 2)....,n(sub m)), where n(sub i) is the length of the Hufffman codeword associated with the ith source symbol. A simple method of doing this encoding is to individually encode each n(sub i) into a fixed-length binary word of length log(sub 2)l, where l is an a priori upper bound on the codeword length. This method produces a maximum preamble length of mlog(sub 2)l bits. The object is to show that, in most cases, no substantially shorter header of any kind is possible.
The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.
Flow charts, symbol dictionaries, and computer program listings for guidance and control launch and abort simulation for spacecraft are presented.
The problem of incorporating visual input into robot systems is described. The photochemistry of the stratosphere, particularly possible permutations of the ozone layer, is discussed. Photoelectrochemical properties of metal thio-hypodiphosphates are investigated. Extreme eigenvalues are computed by the Lancqos approach. The rotational Raman spectra of the molecular atmosphere is studied. A computer operated mathematical symbolic manipulation system is described. Preparation of polycrystalline semiconductor electrodes of tungsten and molybdenum dichalcogenides is received.
A program which was written to simulate Real Time Minimal-Byte-Error Probability (RTMBEP) decoding of full unit-memory (FUM) convolutional codes on a 3-bit quantized AWGN channel is described. This program was used to compute the symbol-error probability of FUM codes and to determine the signal to noise (SNR) required to achieve a bit error rate (BER) of 10 to the minus 6th power for corresponding concatenated systems. A (6,6/30) FUM code, 6-bit Reed-Solomon code combination was found to achieve the required BER at a SNR of 1.886 dB. The RTMBEP algorithm was then modified for decoding partial unit-memory (PUM) convolutional codes. A simulation program was also written to simulate the symbol-error probability of these codes.
A majority of the current expert systems focus on the symbolic-oriented logic and inference mechanisms of artificial intelligence (AI). Common rule-based systems employ empirical associations and are not well suited to deal with problems often arising in engineering. Described is a prototype expert system which combines both symbolic and numeric computing. The expert system's configuration is presented and its application to a spacecraft attitude control problem is discussed.
Various papers on advances in fluid dynamics are presented. Individual topics addressed include: nonunique solutions of the Euler equations; numerical solution of the biharmonic equation using a spectral multigrid method; finite-volume shape and placement for efficiency, accuracy, and physics; NND schemes and their application to numerical simulation of complex plume flow problems; symbolic analysis and computational algorithm construction; and velocity and mass flux distribution measurements of spherical glass beads in air flow in a 90-deg vertical-to-horizontal bend. Also discussed are: hyperbolic solution adaptive mesh generation; progress and future directions in CFD; numerical simulation of shock focusing; microbubble formation and splitting in a turbulent boundary layer for turbulence reduction; numerical study of spherical Taylor-Couette flow, trajectories of vortex lines beneath a free surface or above a plane; and a mathematical model for response of the coronary circulation to high sustained gravitational force fields.
Approach to solution of nonlinear ordinary differential equations involves transfer functions based on recently-introduced Laplace-Borel and Fourier-Borel transforms. Main theorem gives transform of response of nonlinear system as Cauchy product of transfer function and transform of input function of system, together with memory effects. Used to determine responses of electrical circuits containing variable inductances or resistances. Also possibility of doing all noncommutative algebra on computers in such symbolic programming languages as Macsyma, Reduce, PL1, or Lisp. Process of solution organized and possibly simplified by algebraic manipulations reducing integrals in solutions to known or tabulated forms.
This paper describes the analysis of a rulebase for fault diagnosis, isolation, and recovery for NASA's Manned Maneuvering Unit (MMU). The MMU is used by a human astronaut to move around a spacecraft in space. In order to provide maneuverability, there are several thrusters oriented in various directions, and hand-controlled devices for useful groups of them. The rulebase describes some error detection procedures, and corrective actions that can be applied in a few cases. The approach taken in this paper is to treat rulebases as symbolic objects and compute correctness and 'reasonableness' criteria that use the statistical distribution of various syntactic structures within the rulebase. The criteria should identify awkward situations, and otherwise signal anomalies that may be errors. The rulebase analysis agorithms are derived from mathematical and computational criteria that implement certain principles developed for rulebase evaluation. The principles are Consistency, Completeness, Irredundancy, Connectivity, and finally, Distribution. Several errors were detected in the delivered rulebase. Some of these errors were easily fixed. Some errors could not be fixed with the available information. A geometric model of the thruster arrangement is needed to show how to correct certain other distribution nomalies that are in fact errors. The investigations reported here were partially supported by The Aerospace Corporation's Sponsored Research Program.
A report presents a slightly different perspective of the subject matter of Fusing Symbolic and Numerical Diagnostic Computations (NPO-42512), which appears elsewhere in this issue of NASA Tech Briefs. Briefly, the subject matter is the X-2000 Anomaly Detection Language, which is a developmental computing language for fusing two diagnostic computer programs one implementing a numerical analysis method, the other implementing a symbolic analysis method into a unified event-based decision analysis software system for real-time detection of events. In the case of the cited companion NASA Tech Briefs article, the contemplated events that one seeks to detect would be primarily failures or other changes that could adversely affect the safety or success of a spacecraft mission. In the case of the instant report, the events to be detected could also include natural phenomena that could be of scientific interest. Hence, the use of X- 2000 Anomaly Detection Language could contribute to a capability for automated, coordinated use of multiple sensors and sensor-output-data-processing hardware and software to effect opportunistic collection and analysis of scientific data.