Analysis Of Orientation Data Research Articles

Introduction of JD 19: Nutation

Due to both precise time measurements and precise geodetic positioning methods (like Very Long Baseline Interferometry (VLBI), Lunar Laser Ranging (LLR), Satellite Laser Ranging (SLR) and Global Positioning System (GPS)), the position of the instantaneous axis of the Earth’s rotation in space is measured with a precision better than a tenth of milliarcsecond. Simultaneously the amplitudes of the nutations of the Celestial Ephemeris Pole (CEP) deduced from the observations, i.e. the periodic motions in space of the CEP due to the luni-solar attraction or to other planetary attractions, have also been improved. However, these observed nutation amplitudes differ with respect to the computated ones based on an elliptical, uniformly rotating and deformable Earth responding to the lunar and solar attractions, as adopted by the IAU in 1980. The first session on “Observations and data reduction” dealt with Earth’s orientation observations and data analysis for deriving precession and nutations, as well as the associated residuals with respect to the adopted precession constant and nutation series. Comparisons between the different results have been presented including in-phase and out-of-phase components of the prograde and retrograde nutations or of nutations in longitude and in obliquity (see Session 1 of our JD: Newhall et al., McCarthy and Luzum, Herring, and Session 2: Gross). These differences “observed - adopted” nutations achieve several milliarcseconds and exhibit periodic as well as secular characteristics.

On the statistical analysis of orientation data

The statistical analysis of data in the form of orientations is a relatively new discipline and results from the literature on this subject are not yet widely known outside the statistics community. This paper provides an introduction to and the key references for statistical methods for analysing orientation data. More specifically, the problem of estimating an unknown orientation is considered and results on the precision of such an estimated orientation are described. The calculation of average orientation and dispersion parameters for a sample of orientations is also considered. Finally, procedures for generating and testing for random orientations are described. The methodology is illustrated with crystal orientation data obtained from the analysis of electron back-scattering patterns.

The collection and analysis of discontinuity orientation data for engineering design, with examples : S.D. Priest, Comprehensive rock engineering. Vol. 3, ed J.A. Hudson, (Pergamon), 1993, pp 167–192

The collection and analysis of discontinuity orientation data for engineering design, with examples : S.D. Priest, Comprehensive rock engineering. Vol. 3, ed J.A. Hudson, (Pergamon), 1993, pp 167–192

Statistical Analysis of Single Grain Orientation Data Generated from Model Textures

Statistical Analysis of Single Grain Orientation Data Generated from Model Textures

A30 Computerized and centralized participant entry in large-scale, multi-centered clinical trials

Since a neural network (NN) approach has been shown to be applicable to the problem of Higgs boson detection at LHC [I. Iashvili, A. Kharchilava, CMS TN-1996/100; M. Mjahed, Nucl. Phys. B 140 (2005) 799], we study the use of NNs in the problem of tagging b jets in pp→bb¯HSUSY, HSUSY→ττ in the Compact Muons Solenoid experiment [F. Hakl, et al., Nucl. Instr. and Meth. A 502 (2003) 489; S. Lehti, CMS NOTE-2001/019; G. Segneri, F. Palla, CMS NOTE-2002/046]. B tagging is an important tool for separating the Higgs events with associated b jets from the Drell–Yan background Z,γ*→ττ, for which the associated jets are mostly light quark and gluon jets.We teach multi-layer perceptrons (MLPs) available in the object oriented implementation of data analysis framework ROOT [ROOT—An Object Oriented Data Analysis Framework, in: Proceedings of the AIHENP’96 Workshop, Lausanne, September 1996, Nucl. Instr. and Meth. A 389 (1997) 81]. The following learning methods are evaluated: steepest descent algorithm, (BFGS) Broyden–Fletcher–Goldfarb–Shanno algorithm, and variants of conjugate gradients. The ROOT code generation feature of standalone C++ classifiers is utilized.We compare the b tagging performance of MLPs with another ROOT based feed forward NN tool NeuNet [J.P. Ernenwein, NeuNet software for ROOT], which uses a common back-propagation learning method. In addition, we demonstrate the use of the self-organizing map program package (SOM_PAK) and the learning vector quantization program package (LVQ_PAK) [T. Kohonen, et al., SOM_PAK: the self-organizing map program package, Technical Report A31; T. Kohonen, et al., LVQ_PAK: the learning vector quantization program package, Technical Report A30, Laboratory of Computer and Information Science, Helsinki University of Technology, FIN-02150 Espoo, Finland, 1996] in the b tagging problem.

The analysis of three-dimensional orientation data

For many observed orientation patterns of three-dimensional geological data no statistical tests are available that define the probability with which a measured sample represents the parent population. Consequently, there is no accepted definition of an appropriate sample size and patterns can only be compared qualitatively by visual inspection. Empirical solutions to these problems are proposed and applied to quartz c-axis orientation patterns. An estimate of the distribution of orientations in a parent population is provided by an orientation diagram prepared by contouring a measured sample represented on the surface of a sphere using a counting circle 100/n% of the area of the projected hemisphere, where n is the sample size. Contouring the sample as it is accumulated allows identification of the sample size beyond which there is no significant change in the measured pattern. Data from similar-sized samples of computer-simulated random patterns provide outside estimates of the likely differences between the measured sample and the parent population. Pairs of patterns are compared using the mean absolute difference between the matrices used to prepare the contoured diagrams. A measure of their similarity is provided by the magnitude of this difference as a function of the departure of the two patterns from randomness, as indicated by the amount of empty space present. Characterization of the traditionally recognized types of quartz c-axis orientation patterns, using the parameters of the orientation patterns or their normalized eigenvectors, is successful only with point maximum, partial girdle, girdle, and random orientation patterns.

Discussion of the Paper by Vardi and Lee

Discussion of the Paper by Vardi and Lee

Fuzzy objective functions applied to the analysis of discontinuity orientation data : Harrison, J P Proc ISRM Symposium: Eurock'92, Chester, 14–17 September 1992P25–30. Publ London: Thomas Telford, 1992

Fuzzy objective functions applied to the analysis of discontinuity orientation data : Harrison, J P Proc ISRM Symposium: Eurock'92, Chester, 14–17 September 1992P25–30. Publ London: Thomas Telford, 1992

Towards statistics of crystal orientations in quantitative texture anaylsis

By the application of Rodrigues parameters, crystal orientations are represented as points on the unit semi-hypersphere S4+ ⊃ \bb R4 or equivalently on the projective hyperplane H3 ⊃ \bb R4. For the statistical analysis of orientation data, probability models on S4+ ≡ H3 are required. Among different hyperspherical analogs of the normal distribution in Euclidean space, corresponding to various of its characterizations, the Bingham model distribution is characterized as the hyperspherical analog for statistical purposes. Maximum-likelihood estimates of its parameter matrices and single-sample significance tests of uniformity and rotational symmetry are presented. In terms of probability theory and stochastic processes, the hyperspherical Brownian-diffusion distribution is the analog of the normal distribution in Euclidean space. An orientation distribution derived by Savelova [Ind. Lab. (USSR), (1984), 50, 468–474] and erroneously related to a central-limit-type theorem for rotations by Matthies, Muller & Vinel [Textures Microstruct. (1988), 10, 77–96], with the Brownian-diffusion distribution on S4+ ≡ H3, recalls the fact that no simple analog of the central limit theorem in Euclidean space exists for arbitrary spaces and manifolds, e.g. for SP, SP+, SO(p), p ≥ 2. Therefore, interpretations of preferred orientations in terms of mechanisms of texture development related to an imaginary simple analog of the central limit theorem would generally be misleading. Individual crystal-orientation measurements may initially require different nonparametric methods of analysis. As a counterpart of pole-to-orientation density inversion of diffraction data, hyperspherical kernel orientation density estimation is suggested for individual orientation measurements. With the application of non-negative kernels, the estimated orientation density is always non-negative. The critical smoothing parameter of this method is determined on information-theoretical grounds. For patterns of preferred orientation too complex to be sufficiently approximated by the parametric Bingham model distribution, a clustering of individual orientation measurements into disjunct classes is suggested that relates similarity of orientations to multimodality of the estimated orientation density; each class of orientations may then be individually analyzed by parametric methods.

Quickplot: A microcomputer-based program for processing of orientation data

QuickPlot is an interactive, MS-DOS based computer program which allows plotting, contouring, rotation, and statistical analysis of orientation data. Output of stereographic equal-area projections, modified Flinn, and triangular fabric diagrams may be saved as PIC-format graphics files, which can be printed readily, plotted, or incorporated into widely used graphics software to edit or combine diagrams.

定向性方位データの統計学的解析法

定向性方位データの統計学的解析法

Statistical analysis of animal orientation data

A general method is presented for analysis of animal orientation data in which one or more directional components occur. A probability model that includes 10 possible unimodal and bimodal description of orientation behaviour is defined. Statistical methods, based on likelihood inference, are then used to determine (1) the description most appropriate for a given data set and (2) measures of uncertainty for all model parameters. In contrast with earlier techniques that require an experimenter to choose subjectively among possible models, the approach described here treats all models within a single framework that provides objective criteria for model selection. For illustration, the method is applied to four data sets collected from orientation tests on juvenile sockeye salmon, Oncorhynchus nerka. Numerical and graphical analyses indicate that the theory proposed here has practical value for using animal orientation data to test biological hypotheses.

The broken axis approach — a new way to analyze bi-directional circular data

A new technique is demonstrated that allows detection of bi-directional asymmetric modes in circular data. The method makes it possible to search for and find the best possible description of data sets that are distributed on a circle. It was primarily developed for analysis of avian orientation data, but it is equally well suited for circular data in general. Critical levels of statistically significant deviations from uniformity, according to analyses by the new technique, are provided.

The problem of movelength and turn definition in analysis of orientation data

This study examines the analysis of arthropod orientation data. Three problems are discussed: (1) dealing with time as it applies to spatial data, (2) determining the appropriate movelength to be used in collecting and in analyzing data, and (3) defining a turn, to discriminate between "gait noise" and course changes. The main objective is to determine the solution to defining the most appropriate movelength for comparisons between variables and between species. The technique described here for selecting the appropriate movelength that has relevance to both the locomotory rate of the animal and its body length, reduces variation resulting from lateral translational movements, prevents the use of movelengths that lead to artifactual or unrealistic turning values per move, and permits comparisons of species and individuals under various stimulus conditions.

An Iterative Approach to Two-Dimensional Laplacian Smoothing with Application to Image Restoration

Abstract Smoothing methods are increasingly important in modern graphically oriented data analysis. There are several fast and reliable univariate cross-validated smoothing algorithms, but comparable methods are not available in higher dimensions. This article develops an iterative approach to two-dimensional Laplacian spline smoothing based on tensor-product cubic B splines. Estimating equations are developed and solved iteratively using two-line symmetric successive over relaxation with conjugate gradient acceleration. An asymptotic approximation for the generalized cross-validation score is described. The resulting algorithm is naturally suited to two-dimensional scatterplot smoothing but has potential value for image restoration as well. This is illustrated on a multicolor image example. Along with an image restoration an uncertainty assessment based on the entropy of the marginal posterior pixel value distribution is produced. This analysis particularly highlights the statistical uncertainty in resol...

Smoothing and extrapolation of crustal stress orientation measurements

The theory and mechanics of a statistical smoothing algorithm for estimating stress fields based on observed data are described. Incorporated into the algorithm are tunable parameters which allow the user to adjust the smoothness and fidelity of the fitted stress field. In addition, the user has the option of using robustness weights, or to weight the predicted stress field by assigning quality ranks to each data point. Fitted stress fields can be displayed as either a gridded map (axes of maximum, or minimum, horizontal stress are shown as short bars located at each point in an evenly spaced grid), or as a stress trajectory map. Examples of predicted stress fields for southern California and western Canada, based on borehole elongation data, are displayed as stress trajectory maps. A predicted paleostress field for the Spanish Peaks intrusion complex in Colorado, based on vertical dike orientations, is displayed as a gridded map. The smoothing algorithm is not limited to the analysis of stress orientation data. Any data consisting of a set of undirected lines measured at discrete locations are appropriate for input; possible candidates include strain data, mineral or intersection lineations, and lineaments.

Stimulus control of eye orientations: Shaping S+ only versus shaping S- only

Abstract To determine how stimulus control of eye orientation was established and how that process affected learning, an analysis of normal preschool children's eye orientations and pointing responses to each of two simultaneously presented stimuli (S+ and S-) was conducted. Using a probe design to test for acquisition, each subject was trained on two tasks. In one task, S+ (selections of this stimulus produced reinforcement) was held constant at the final criterion level while S- (selections of this stimulus never produced reinforcement) was manipulated using stimulus shaping procedures. The second task was programmed with the opposite method (S+ shaped while S- held constant). Results showed that more pointing response errors, more occurences of eye orientations, and longer durations of eye orientations characterized conditions where S+ was held constant and S- was shaped. The individual analysis of the eye orientation data indicated that differences in eye orientation to stimuli under the two programs were largely due to relatively higher frequency of orientation to the S- stimulus under program condtions that shaped S- and held S+ constant.

Spatial analysis of two-dimensional orientation data

A frequently encountered problem in structural geology is the analysis and interpretation of directional data with a geographical distribution. Such data may arise, for example, as samples of fracture strikes collected at a number of locations (rocky outcrops, road cuttings, etc.), trends of geological structures mapped in underground mines where they are exposed in the tunnel roof, or as lineaments annotated on aerial or satellite photographs. From such data, it is of interest to determine the structural domains in the area, that is, to partition the area into subareas of homogeneous structural pattern. This paper presents a method for performing such an analysis, and applies it to a data set collected from an underground coal mine.

Comments on “Two Statistics for the Analysis of Orientation Data in Geography”

Comments on “Two Statistics for the Analysis of Orientation Data in Geography”

TWO STATISTICS FOR THE ANALYSIS OF ORIENTATION DATA IN GEOGRAPHY

Two versions of the An statistic of Ajne and Stephens are introduced, explained, interpreted and evaluated. These statistics possess important advantages over those currently used by geographers for the analysis of orientation data. They are invariant with respect to the point of origin of measurements, do not assume a circular-normal distribution and are not limited by sample size. Used in conjunction, they allow the significance of direction as well as orientation to be determined.