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Vector analysis of electrocardiogram data to detect changes in human myocardium bioelectric activity due to hypoxia
Characteristic vector analysis applied to inflection ratio spectra is a new approach to analyzing spectral data. The technique applied to remote data collected with the multichannel ocean color sensor (MOCS), a passive sensor, simultaneously maps the distribution of two different phytopigments, chlorophyll alpha and phycoerythrin, the ocean. The data set presented is from a series of warm core ring missions conducted during 1982. The data compare favorably with a theoretical model and with data collected on the same mission by an active sensor, the airborne oceanographic lidar (AOL).
Characteristic vector analysis is being used to extract spectral signatures of suspended matter in the ocean from remote ocean color data collected with MOCS (Multichannel Ocean Color Sensor), a multispectral scanner. Spectral signatures appear to be obtainable either directly from characteristic vectors or through a transformation of these eigenvectors. Quantification of the suspended matter associated with each resulting signature seems feasible using associated coefficients generated by the technique. This paper presents eigenvectors associated with algae, 'sediment', acid waste, sewage sludge, and oil. The results suggest an efficient method of transmitting from satellites multispectral data of pollution in our oceans.
Lunar samples represent a heterogeneous assemblage of rocks with complex inter-relationships that are difficult to decipher using standard petrogenetic approaches. These inter-relationships reflect several distinct petrogenetic trends as well as thermomechanical mixing of distinct components. Additional complications arise from the unequal quality of chemical analyses and from the fact that many samples (e.g., breccia clasts) are too small to be representative of the system from which they derived. Polytopic vector analysis (PVA) is a multi-variate procedure used as a tool for exploratory data analysis. PVA allows the analyst to classify samples and clarifies relationships among heterogenous samples with complex petrogenetic histories. It differs from orthogonal factor analysis in that it uses non-orthogonal multivariate sample vectors to extract sample endmember compositions. The output from a Q-mode (sample based) factor analysis is the initial step in PVA. The Q-mode analysis, using criteria established by Miesch and Klovan and Miesch, is used to determine the number of endmembers in the data system. The second step involves determination of endmembers and mixing proportions with all output expressed in the same geochemical variable as the input. The composition of endmembers is derived by analysis of the variability of the data set. Endmembers need not be present in the data set, nor is it necessary for their composition to be known a priori. A set of any endmembers defines a 'polytope' or classification figure (triangle for a three component system, tetrahedron for a four component system, a 'five-tope' in four dimensions for five component system, et cetera).
A specialized single-axis, five-beam three-component laser velocimeter was constructed and used to study the flow field in a juncture. The juncture was defined by a blunt leading edged vertical splitter plate and a sharp leading edged horizontal plate. The investigations were conducted in the Low Turbulence Pressure Tunnel at a Mach number of 0.1 and a Reynolds number of 2.2 x 10 to the 6th per meter over the model. The three-component velocity flow field in the juncture was measured, Reynolds stresses calculated, and the velocity vector analysis performed.
A specialized single-axis, five-beam three-component laser velocimeter was constructed and used to study the flow field in a juncture. The juncture was defined by a blunt leading, edged vertical splitter plate and a sharp leading edged horizontal plate. The investigations were conducted in the Low Turbulence Pressure Tunnel at a Mach number of 0.1 and a Reynolds number of 2.2 x 10(exp 6) per meter over the model. The three-component velocity flow field in the juncture was measured, Reynolds stresses calculated and the velocity vector analysis performed.
The Hilbert space L2(omega) of vector functions is studied. A breakdown of L2(omega) into orthogonal subspaces is discussed and the properties of the operators for projection onto these subspaces are investigated from the standpoint of preserving the differential properties of the vectors being projected. Finally, the properties of the operators are examined.
An extension of the time vector technique for determining stability and control derivatives from flight data is formulated. The technique provides for explicit determination of derivatives by means of simultaneous analysis of two maneuvers which differ by a dependent control input. The control derivatives for the dependent input are also explicitly determined. This extended technique is preferable to the application of the time vector method to single maneuvers in that no estimates of derivatives are required. An example illustrating the application of the technique is given.
A MACSYMA program is described which performs symbolic vector algebra and vector calculus. The program can combine and simplify symbolic expressions including dot products and cross products, together with the gradient, divergence, curl, and Laplacian operators. The distribution of these operators over sums or products is under user control, as are various other expansions, including expansion into components in any specific orthogonal coordinate system. There is also a capability for deriving the scalar or vector potential of a vector field. Examples include derivation of the partial differential equations describing fluid flow and magnetohydrodynamics, for 12 different classic orthogonal curvilinear coordinate systems.
Various 12-lead ECG criteria have been established to detect right ventricular hypertrophy as a marker of pulmonary hypertension (PH). While some criteria offer good specificity they lack sensitivity because of a low prevalence of positive findings in the PH population. We hypothesized that three-dimensional equivalent dipole (ED) model could serve as a better detection tool of PH. We enrolled: 1) 17 patients (12 female, 5 male, mean age 57 years, range 19-79 years) with echocardiographically detected PH (systolic pulmonary arterial pressure greater than 35 mmHg) and no significant left ventricular disease; and 2) 19 healthy controls (7 female, 12 male, mean age 44, range 31-53 years) with no known heart disease. In each subject we recorded a 5-minute high-resolution 12-lead conventional ECG and constructed principal signals using singular value decomposition. Assuming a standard thorax dimension of an adult person with homogenous and isotropic distribution of thorax conductance, we determined moving equivalent dipoles (ED), characterized by the 3D location in the thorax, dipolar strength and the spatial orientation, in time intervals of 5 ms. We used the sum of all ED vectors in the second half of the QRS complex to derive the amplitude of the right-sided ED vector (RV), if the orientation of ED was to the right side of the thorax, and in the first half the QRS to derive the amplitude of the left-sided vector (LV), if the orientation was leftward. Finally, the parameter RV/LV ratio was determined over an average of 256 complexes. The groups differed in age and gender to some extent. There was a non-significant trend toward higher RV in patients with PH (438 units 284) than in controls (280 plus or minus 140) (p = 0.066) but the overlap was such that RV alone was not a good predictor of PH. On the other hand, the RV/LV ratio was a better predictor of PH, with 11/17 (64.7%) of PH patients but only in 1/19 (5.3%) control subjects having RV/LV ratio greater than or equal to 0.70 (p less than 0.001). The use of ED for evaluating PH shows good specificity at a reasonable sensitivity. The results are limited due to the small study groups and differences in age and gender, but further investigations are warranted, including of ED's diagnostic accuracy for PH versus that of other proposed ECG and VCG criteria.
Report presents two general methods for reducing mathematical complexities of state equations of robot-arm dynamics. Robot arms contain both rotary and linear joints. Both methods start with homogenous coordinates and Lagrangian formulation of mechanics briefly summarized in report. First method uses matrix-analysis techniques; second, vector-analysis techniques. Vector-analysis method includes new differential-vector representation of centripetal and Coriolis forces.
Analysis of integration error in lunar orbit trajectory program and effect of selenopotential parameters on solution vector
Boundary element analysis (BEA) can be characterized as a numerical technique that generally shifts the computational burden in the analysis toward numerical integration and the solution of nonsymmetric and either dense or blocked sparse systems of algebraic equations. Researchers have explored the concept that the fundamental characteristics of BEA can be exploited to generate effective implementations on vector and parallel computers. In this paper, the results of some of these investigations are discussed. The performance of overall algorithms for BEA on vector supercomputers, massively data parallel single instruction multiple data (SIMD), and relatively fine grained distributed memory multiple instruction multiple data (MIMD) computer systems is described. Some general trends and conclusions are discussed, along with indications of future developments that may prove fruitful in this regard.
This is a request for a second renewal (3d year of funding) of a research project on the topic of multiresolution and explicit methods for vector field analysis and visualization. In this report, we describe the progress made on this research project during the second year and give a statement of the planned research for the third year. There are two aspects to this research project. The first is concerned with the development of techniques for computing tangent curves for use in visualizing flow fields. The second aspect of the research project is concerned with the development of multiresolution methods for curvilinear grids and their use as tools for visualization, analysis and archiving of flow data. We report on our work on the development of numerical methods for tangent curve computation first.
Spectral signatures of suspended matter in the ocean are being extracted through characteristic vector analysis of remote ocean color data collected with MOCS (Multichannel Ocean Color Sensor). Spectral signatures appear to be obtainable through analyses of 'linear' clusters that appear on scatter diagrams associated with eigenvectors. Signatures associated with acid waste, sewage sludge, oil, and algae are presented. The application of vector analysis to two acid waste dumps overflown two years apart is examined in some detail. The relationships between eigenvectors and spectral signatures for these examples are analyzed. These cases demonstrate the value of characteristic vector analysis in remotely identifying pollutants in the ocean and in determining the consistency of their spectral signatures.
Multivariate analysis was used to determine the joint distribution of the four variables represented by the components of the wind vector at an initial time and after a specified elapsed time is hypothesized to be quadravariate normal; the fourteen statistics of this distribution, calculated from 15 years of twice-daily rawinsonde data are presented by monthly reference periods for each month from 0 to 27 km. The hypotheses that the wind component changes with respect to time is univariate normal, that the joint distribution of wind component change with respect to time is univariate normal, that the joint distribution of wind component changes is bivariate normal, and that the modulus of vector wind change is Rayleigh are tested by comparison with observed distributions. Statistics of the conditional bivariate normal distributions of vector wind at a future time given the vector wind at an initial time are derived. Wind changes over time periods from 1 to 5 hours, calculated from Jimsphere data, are presented. Extension of the theoretical prediction (based on rawinsonde data) of wind component change standard deviation to time periods of 1 to 5 hours falls (with a few exceptions) within the 95 percentile confidence band of the population estimate obtained from the Jimsphere sample data. The joint distributions of wind change components, conditional wind components, and 1 km vector wind shear change components are illustrated by probability ellipses at the 95 percentile level.
A statistical analysis of the temporal variability of wind vectors at 1 km altitude intervals from 0 to 27 km altitude taken from a 10-year data sample of twice-daily rawinsode wind measurements over Vandenberg Air Force Base, California is presented.
In this paper, we review the history of the dyadic as developed by Gibbs. This mathematical construct appeared in the second part of Gibbs's pamphlet on vector analysis (published in 1884), and it represented the first known development of a Cartesian theory of tensors. Gibbs made extensive use of the dyadic to express his theory of linear vector functions, that is, functions that acted on vectors and mapped them to new vectors. The dyadic proved to be a capable vehicle in Gibbs's hands, and his theory for dyadics (which we would now call second-order Cartesian tensors) was relatively advanced. The theory detailed notions such as the decomposition of vectors and conditions under which a tensor would have an inverse. While Gibbs's theory for linear operators expressed by dyadics was robust, it did not seem to garner the attention that the more conventional vector analysis (published in the first half of his pamphlet in 1881) did. Perhaps in part because of the general unfamiliarity with the dyadic, two distinct and conflicting definitions of the gradient of a vector field have arisen in the literature. The details of these differences in notation, possible reasons for the difference, and a potential resolution are proposed.