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Self-decoding FET-hybrid or integrated-circuit tree configuration uses minimum number of components and can be sequenced by clock or computer. Redundancy features can readily be incorporated into tree configuration; as tree grows in size and more sensors are included, percentage of parts that will affect given percentage of sensors steadily decreases.
Development documentation programs are considered. A document tree is defined as the syntactic representation of a document when it is divided into subdivisions such as chapters and sections; a developmental tree is also defined as a tree of information obtained during the course of the development of the computer program. A developmental subtree is emphasized and described. A printed subprogram is also included.
Tree codes are known to be capable of performing arbitrarily close to the rate-distortion function for any memoryless source and single-letter fidelity criterion. Tree coding and tree search strategies are investigated for the discrete-time memoryless Gaussian source encoded for a signal-power-to-mean-squared-error ratio of about 30 dB (about 5 binary digits per source output). Also, a theoretical lower bound on average search effort is derived. Two code search strategies (the Viterbi algorithm and the stack algorithm) were simulated in assembly language on a large digital computer. After suitable modifications, both strategies yielded encoding with a signal-to-distortion ratio about 1 dB below the limit set by the rate-distortion function. Although this performance is better than that of any previously known instrumentable scheme, it unfortunately requires search computation of the order of 100,000 machine cycles per source output encoded.
A class of multistage decision tree classifiers is proposed and studied relative to the classification of multispectral remotely sensed data. The decision tree classifiers are shown to have the potential for improving both the classification accuracy and the computation efficiency. Dimensionality in pattern recognition is discussed and two theorems on the lower bound of logic computation for multiclass classification are derived. The automatic or optimization approach is emphasized. Experimental results on real data are reported, which clearly demonstrate the usefulness of decision tree classifiers.
A new classifier has been developed for the computerized analysis of remote sensor data. The decision tree classifier is essentially a maximum likelihood classifier using multistage decision logic. It is characterized by the fact that an unknown sample can be classified into a class using one or several decision functions in a successive manner. The classifier is applied to the analysis of data sensed by Landsat-1 over Kenosha Pass, Colorado. The classifier is illustrated by a tree diagram which for processing purposes is encoded as a string of symbols such that there is a unique one-to-one relationship between string and decision tree.
The classification of large dimensional data sets arising from the merging of remote sensing data with more traditional forms of ancillary data is considered. Decision tree classification, a popular approach to the problem, is characterized by the property that samples are subjected to a sequence of decision rules before they are assigned to a unique class. An automated technique for effective decision tree design which relies only on apriori statistics is presented. This procedure utilizes a set of two dimensional canonical transforms and Bayes table look-up decision rules. An optimal design at each node is derived based on the associated decision table. A procedure for computing the global probability of correct classfication is also provided. An example is given in which class statistics obtained from an actual LANDSAT scene are used as input to the program. The resulting decision tree design has an associated probability of correct classification of .76 compared to the theoretically optimum .79 probability of correct classification associated with a full dimensional Bayes classifier. Recommendations for future research are included.
Detection and disease damage assessment of citrus tree losses in a Florida citrus grove were made by establishing a registration (grove site location) coordinate system, developing a damage assessment system, and testing sequential aerial color infrared (ACIR) photography at the scale of 1 in. = 333 ft (2.5 cm = 100 m) during the winter, spring, and summer seasons of 1978 and spring of 1979. Spring photography was the easiest to photo interpret, showed the greatest differences between healthy and diseased trees, and had the least shadow and background interference for photo interpretation. Trees showing slight disease damage were detected in ACIR before they were found in ground surveys.
Attenuation due to single trees is experimentally investigated using UHF transmissions at 869 MHz between a remotely piloted aircraft and a ground receiver system located in a stationary vehicle. Single trees of each tree type in full foliage were found to attenuate from 10-20 dB, with an average median value of about 12 dB. Attenuation coefficients associated with path lengths through the foliage may on average be about 1 dB/m, with maximum values closer to 2 dB/m.
The inverse and forward dynamics problems for a set of rigid bodies connected by hinges to form a topological tree are solved by using recursive techniques from linear filtering and smoothing theory. An inward filtering sequence computes a set of constraint moments and forces. This is followed by an outward sequence to determine a corresponding set of angular and linear accelerations. An inward sequence begins at the tips of all of the terminal bodies of the tree and proceeds inwardly through all of the branches until it reaches the root. Similarly, an outward sequence begins at the root and propagates to all of the tree branches until it reaches the tips of the terminal bodies. The paper also provides an approach to evaluate recursively the composite multibody system inertia matrix and its inverse.
Spaceborne computing systems must provide reliable, continuous operation for extended periods. Due to weight, power, and volume constraints, these systems must manage resources very effectively. A fault diagnosis algorithm is described which enables fast and flexible diagnoses in the dynamic distributed computing environments planned for future space missions. The algorithm uses a knowledge base that is easily changed and updated to reflect current system status. Augmented fault trees represented in an object-oriented form provide deep system knowledge that is easy to access and revise as a system changes. Given such a fault tree, a set of failure events that have occurred, and a set of failure events that have not occurred, this diagnosis system uses forward and backward chaining to propagate causal and temporal information about other failure events in the system being diagnosed. Once the system has established temporal and causal constraints, it reasons backward from heuristically selected failure events to find a set of basic failure events which are a likely cause of the occurrence of the top failure event in the fault tree. The diagnosis system has been implemented in common LISP using Flavors.
The performance of parallel combinatorial OR-tree searches is analytically evaluated. This performance depends on the complexity of the problem to be solved, the error allowance function, the dominance relation, and the search strategies. The exact performance may be difficult to predict due to the nondeterminism and anomalies of parallelism. The authors derive the performance bounds of parallel OR-tree searches with respect to the best-first, depth-first, and breadth-first strategies, and verify these bounds by simulation. They show that a near-linear speedup can be achieved with respect to a large number of processors for parallel OR-tree searches. Using the bounds developed, the authors derive sufficient conditions for assuring that parallelism will not degrade performance and necessary conditions for allowing parallelism to have a speedup greater than the ratio of the numbers of processors. These bounds and conditions provide the theoretical foundation for determining the number of processors required to assure a near-linear speedup.
The acoustical back scattering from a simple scale model of a tree has been experimentally measured. The model consisted of a trunk and six limbs, each with 4 branches; no foliage or twigs were included. The data from the anechoic chamber measurements were then mathematically combined to construct the effective back scattering from groups of trees. Also, initial measurements have been conducted out-of-doors on a single tree in an open field in order to characterize its acoustic scattering as a function of azimuth angle. These measurements were performed in the spring, prior to leaf development. The data support a statistical model of forest scattering; the scattered signal spectrum is highly irregular but with a remarkable general resemblance to the incident signal spectrum. Also, the scattered signal's spectra showed little dependence upon scattering angle.
Some recent work is reviewed which relates families of trees to symbolic algorithms for the exact computation of series which approximate solutions of ordinary differential equations. It turns out that the vector space whose basis is the set of finite, rooted trees carries a natural multiplication related to the composition of differential operators, making the space of trees an algebra. This algebraic structure can be exploited to yield a variety of algorithms for manipulating vector fields and the series and algebras they generate.
It is described how Minimum Description Length (MDL) can be applied to the problem of DNA and protein evolutionary tree reconstruction. If there is a set of mutations that transform a common ancestor into a set of the known sequences, and this description is shorter than the information to encode the known sequences directly, then strong evidence for an evolutionary relationship has been found. A heuristic algorithm is described that searches for the simplest tree (smallest MDL) that finds close to optimal trees on the test data. Various ways of extending the MDL theory to more complex evolutionary relationships are discussed.
One of the frequently cited shortcomings of fault-tree models, their inability to model so-called sequence dependencies, is discussed. Several sources of such sequence dependencies are discussed, and new fault-tree gates to capture this behavior are defined. These complex behaviors can be included in present fault-tree models because they utilize a Markov solution. The utility of the new gates is demonstrated by presenting several models of the fault-tolerant parallel processor, which include both hot and cold spares.
The lack of accurate extensive geometric data on tree canopies has retarded development and validation of radiative transfer models. A stratified sampling method was devised to measure the three-dimensional geometry of 16 walnut trees which had received irrigation treatments of either 100 or 33 per cent of evapotranspirational (ET) demand for the previous two years. Graphic reconstructions of the three-dimensional geometry were verified by 58 independent measurements. The distributions of stem- and leaf-size classes, lengths, and angle classes were determined and used to calculate leaf area index (LAI), stem area, and biomass. Reduced irrigation trees have lower biomass of stems, leaves and fruit, lower LAI, steeper leaf angles and altered biomass allocation to large stems. These data can be used in ecological models that link canopy processes with remotely sensed measurements.
Algorithms for learning classification trees have had successes in artificial intelligence and statistics over many years. How a tree learning algorithm can be derived from Bayesian decision theory is outlined. This introduces Bayesian techniques for splitting, smoothing, and tree averaging. The splitting rule turns out to be similar to Quinlan's information gain splitting rule, while smoothing and averaging replace pruning. Comparative experiments with reimplementations of a minimum encoding approach, Quinlan's C4 and Breiman et al. Cart show the full Bayesian algorithm is consistently as good, or more accurate than these other approaches though at a computational price.
It is noted that current approaches used to assess the dependability of complex systems such as Space Station Freedom and the Air Traffic Control System are incapable of handling the size and complexity of these highly integrated designs. A novel technique for modeling such systems which is built upon current techniques in Markov theory and combinatorial analysis is described. It enables the development of a hierarchical representation of system behavior which is more flexible than either technique alone. A solution strategy which is based on an object-oriented approach to model representation and evaluation is discussed. The technique is virtually transparent to the user since the fault tree models can be built graphically and the objects defined automatically. The tree modularization procedure allows the two model types, Markov and combinatoric, to coexist and does not require that the entire fault tree be translated to a Markov chain for evaluation. This effectively reduces the size of the Markov chain required and enables solutions with less truncation, making analysis of longer mission times possible. Using the fault-tolerant parallel processor as an example, a model is built and solved for a specific mission scenario and the solution approach is illustrated in detail.