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Necessary conditions of optimality for control problems with state variable inequality constraints, using separating hyperplane theorem
A fluoroscopic tomography system capable of synthesizing body sections at a number of levels within the body has been developed. The synthesized body sections may lie either in a range of planes parallel to, tilted with respect to, skewed with respect to, or both tilted and skewed with respect to the plane of motion of the X-ray tube target. In addition, body sections can be presented which are contoured to the patient's anatomy. That is to say, they may even encompass such complex surfaces as a quadratic hyperplane. In addition, tomograms of organs in motion can be imaged.
A model for the Landsat multispectral scanner data, representing a generalization of the commonly used Gaussian model, has been formulated and analyzed. The model hypothesizes that the data for different crop types essentially lie on distinct hyperplanes in the feature space. Tests of this model reveal that: (1) the agricultural data from any single acquisition (i.e., four-channel) of Landsat are essentially two dimensional, regardless of the crop type; and (2) the data from different sites and different stages of crop development all lie on planes which are parallel. These findings have significant implications for data display, classification, feature extraction, and signature extension.
A generalized four channel hyperplane to discriminate water from nonwater was developed using LANDSAT-3 multispectral scaner (MSS) scenes and matching same/next day color infrared aerial photography. The MSS scenes varied in sun elevation angle from 40 to 58 deg. The 28 matching air photo frames contained over 1400 water bodies larger than one surface acre. A preliminary water discriminant, was used to screen the data and eliminate from further consideration all pixels distant from water in MSS spectral space. A linear discriminant was iteratively fitted to the labelled pixels. This discriminant correctly classified 98.7% of the water pixels and 98.6% of the nonwater pixels. The discriminant detected 91.3% of the 414 water bodies over 10 acres in surface area, and misclassified as water 36 groups of contiguous nonwater pixels.
A generalized four-channel hyperplane to discriminate water from non-water was developed using LANDSAT-3 multispectral scanner (MSS) scences and matching same/next-day color infrared aerial photography. The MSS scenes over upstate New York, eastern Washington, Montana and Louisiana taken between May and October 1978 varied in Sun elevation angle from 40 to 58 degrees. The 28 matching air photo frames selected for analysis contained over 1400 water bodies larger than one surface acre. A preliminary water discriminant was used to screen the data and eliminate from further consideration all pixels distant from water in MSS spectral space. Approximately 1300 pixels, half of them non-edge water pixels and half non-water pixels spectrally close to water, were labelled. A linear discriminant was iteratively fitted to the labelled pixels, giving more weight to those pixels that were difficult to discriminate. This discriminant correctly classified 98.7 percent of the water pixels and 98.6 percent of the non-water pixels.
A new method of automatic generation of concurrent programs which constructs arrays defined by sets of recursive equations is described. It is assumed that the time of computation of an array element is a linear combination of its indices, and integer programming is used to seek a succession of hyperplanes along which array elements can be computed concurrently. The method can be used to schedule equations involving variable length dependency vectors and mutually recursive arrays. Portions of the work reported here have been implemented in the PS automatic program generation system.
A pattern recognition system was developed that successfully recognizes simulated spectra of five different types of transportation noise sources. The system generates hyperplanes during a training stage to separate the classes and correctly classify unknown patterns in classification mode. A feature selector in the system reduces a large number of features to a smaller optimal set, maximizing performance and minimizing computation.
The objective is to demonstrate discrete extremum methods of structural analysis as a tool for structural system reliability evaluation. Specifically, linear and multiobjective linear programming models for analysis of rigid plastic frames under proportional and multiparametric loadings, respectively, are considered. Kinematic and static approaches for analysis form a primal-dual pair in each of these models and have a polyhedral format. Duality relations link extreme points and hyperplanes of these polyhedra and lead naturally to dual methods for system reliability evaluation.
A new derivation is presented for the bounds on the size of a multilayer neural network to exactly implement an arbitrary training set; namely, the training set can be implemented with zero error with two layers and with the number of the hidden-layer neurons equal to no.1 is greater than p - 1. The derivation does not require the separation of the input space by particular hyperplanes, as in previous derivations. The weights for the hidden layer can be chosen almost arbitrarily, and the weights for the output layer can be found by solving no.1 + 1 linear equations. The method presented exactly solves (M), the multilayer neural network training problem, for any arbitrary training set.
The common data format (CDF) is described in terms of its support applications for the database management of visualization systems. The CDF is a self-describing data abstraction technique for the storage and manipulation of multidimensional data that are based on block structures. The discipline-independent approach is designed to manage, manipulate, archive, display, and analyze data, and can be applied to heterogeneous equipment communicating different data structures over networks. An improved CDF version incorporates a hyperplane access allowing random aggregate access to subdimensional blocks within a multidimensional variable. The visualization pipeline is also discussed, which controls the flow of data and permits the visualization of different classes of data representation techniques. The system is found to accommodate a large variety of scientific data structures and large disk-based data sets.
Described here is sparse distributed memory (SDM) as a neural-net associative memory. It is characterized by two weight matrices and by a large internal dimension - the number of hidden units is much larger than the number of input or output units. The first matrix, A, is fixed and possibly random, and the second matrix, C, is modifiable. The SDM is compared and contrasted to (1) computer memory, (2) correlation-matrix memory, (3) feet-forward artificial neural network, (4) cortex of the cerebellum, (5) Marr and Albus models of the cerebellum, and (6) Albus' cerebellar model arithmetic computer (CMAC). Several variations of the basic SDM design are discussed: the selected-coordinate and hyperplane designs of Jaeckel, the pseudorandom associative neural memory of Hassoun, and SDM with real-valued input variables by Prager and Fallside. SDM research conducted mainly at the Research Institute for Advanced Computer Science (RIACS) in 1986-1991 is highlighted.
A method was developed to plan feasible and obstacle-avoiding paths for two spatial robots working cooperatively in a known static environment. Cooperating spatial robots as referred to herein are robots which work in 6D task space while simultaneously grasping and manipulating a common, rigid payload. The approach is configuration space (c-space) based and performs selective rather than exhaustive c-space mapping. No expensive precomputations are required. A novel, divide-and-conquer type of heuristic is used to guide the selective mapping process. The heuristic does not involve any robot, environment, or task specific assumptions. A technique was also developed which enables solution of the cooperating redundant robot path planning problem without requiring the use of inverse kinematics for a redundant robot. The path planning strategy involves first attempting to traverse along the configuration space vector from the start point towards the goal point. If an unsafe region is encountered, an intermediate via point is identified by conducting a systematic search in the hyperplane orthogonal to and bisecting the unsafe region of the vector. This process is repeatedly applied until a solution to the global path planning problem is obtained. The basic concept behind this strategy is that better local decisions at the beginning of the trouble region may be made if a possible way around the 'center' of the trouble region is known. Thus, rather than attempting paths which look promising locally (at the beginning of a trouble region) but which may not yield overall results, the heuristic attempts local strategies that appear promising for circumventing the unsafe region.
We examine the problem of retrieving three-dimensional lightning locations from radio frequency Time-Of-Arrival (TOA) measurements. Arbitrary antenna locations are considered. By judiciously differencing measurements that are related to the location of the antennas and their excitation times, the problem is converted from the initial spherical nonlinear form to a system of linear equations. In the linear formalism, the source location and time-of-occurrence is viewed geometrically as an intersection of hyperplanes in the four-dimensional Minkowski space (x,y,z,t). The linear equations are solved to obtain explicit analytic expressions for the location and time variables. Retrieval errors are not interpreted with conventional Geometrical Dilution of Precision (GDOP) arguments as discussed by Holmes and Reedy (1951), but with more recent inversion analyses considered by Twomey (1977). Measurement errors are propagated analytically so that the specific effect of these errors on the solution is clarified. The sensitivity of the solution on the number of antennas used, antenna network geometry, source position, and measurement differencing schemes are discussed in terms of the eigenvalues of the linear system.