Tyler shape depth

In many problems from multivariate analysis, the parameter of interest is a shape matrix, that is, a normalized version of the corresponding scatter or dispersion matrix. In this paper, we propose a depth concept for shape matrices that involves data points only through their directions from the center of the distribution. We use the terminology Tyler shape depth since the resulting estimator of shape, namely the deepest shape matrix, is the median-based counterpart of the M-estimator of shape of Tyler (1987). Beyond estimation, shape depth, like its Tyler antecedent, also allows hypothesis testing on shape. Its main benefit, however, lies in the ranking of shape matrices it provides, whose practical relevance is illustrated in principal component analysis and in shape-based outlier detection. We study the invariance, quasi-concavity and continuity properties of Tyler shape depth, the topological and boundedness properties of the corresponding depth regions, existence of a deepest shape matrix and prove Fisher consistency in the elliptical case. Finally, we derive a Glivenko-Cantelli-type result and establish almost sure consistency of the deepest shape matrix estimator.Comment: 28 pages, 5 figure

Shape analysis based on depth-ordering

In this paper we propose a new method for shape analysis based on the ordering of shapes using band-depth. We use this band-depth to non-parametrically define a global depth for a shape with respect to a reference population, typically consisting of normal control subjects. This allows us to globally quantify differences with respect to “normality”. Using the depth-ordering of shapes also allows the detection of localized shape differences by using α-central values of shapes. We propose permutation tests to statistically assess global and local shape differences. We further determine the directionality of shape differences (local inflation versus deflation). The method is evaluated on a synthetically generated striatum dataset, and applied to detect shape differences in the hippocampus between subjects with first-episode schizophrenia and normal controls

View subspaces for indexing and retrieval of 3D models

View-based indexing schemes for 3D object retrieval are gaining popularity since they provide good retrieval results. These schemes are coherent with the theory that humans recognize objects based on their 2D appearances. The viewbased techniques also allow users to search with various queries such as binary images, range images and even 2D sketches. The previous view-based techniques use classical 2D shape descriptors such as Fourier invariants, Zernike moments, Scale Invariant Feature Transform-based local features and 2D Digital Fourier Transform coefficients. These methods describe each object independent of others. In this work, we explore data driven subspace models, such as Principal Component Analysis, Independent Component Analysis and Nonnegative Matrix Factorization to describe the shape information of the views. We treat the depth images obtained from various points of the view sphere as 2D intensity images and train a subspace to extract the inherent structure of the views within a database. We also show the benefit of categorizing shapes according to their eigenvalue spread. Both the shape categorization and data-driven feature set conjectures are tested on the PSB database and compared with the competitor view-based 3D shape retrieval algorithmsComment: Three-Dimensional Image Processing (3DIP) and Applications (Proceedings Volume) Proceedings of SPIE Volume: 7526 Editor(s): Atilla M. Baskurt ISBN: 9780819479198 Date: 2 February 201

What Determines the Depth of BALs? Keck HIRES Observations of BALQSO 1603+300

We find that the depth and shape of the broad absorption lines (BALs) in BALQSO 1603+3002 are determined largely by the fraction of the emitting source which is covered by the BAL flow. In addition, the observed depth of the BALs is poorly correlated with their real optical depth. The implication of this result is that abundance studies based on direct extraction of column densities from the depth of the absorption troughs are unreliable. Our conclusion is based on analysis of unblended absorption features of two lines from the same ion (in this case the Si IV doublet), which allows unambiguous separation of covering factor and optical depth effects. The complex morphology of the covering factor as a function of velocity suggests that the BALs are produced by several physically separated outflows. The covering factor is ion dependent in both depth and velocity width. We also find evidence that in BALQSO 1603+3002 the flow does not cover the broad emission line region.Comment: 13 pages, 2 figures, accepted for publication in Ap

Technique for Magnetic Susceptibility Determination in the High Doped Semiconductors by Electron Spin Resonance

Method for determining the magnetic susceptibility in the high doped semiconductors is considered. A procedure that is based on double integration of the positive part of the derivative of the absorption line having a Dyson shape and takes into account the depth of the skin layer is described. Analysis is made for the example of arsenic doped germanium samples at a rather high concentration corresponding to the insulator metal phase transition.Comment: Pages 13, figures 9, references 1

Repeated patterns in tree genetic programming

We extend our analysis of repetitive patterns found in genetic programming genomes to tree based GP. As in linear GP, repetitive patterns are present in large numbers. Size fair crossover limits bloat in automatic programming, preventing the evolution of recurring motifs. We examine these complex properties in detail: e.g. using depth v. size Catalan binary tree shape plots, subgraph and subtree matching, information entropy, syntactic and semantic fitness correlations and diffuse introns. We relate this emergent phenomenon to considerations about building blocks in GP and how GP works

Analysis of a quantum memory for photons based on controlled reversible inhomogeneous broadening

We present a detailed analysis of a quantum memory for photons based on controlled and reversible inhomogeneous broadening (CRIB). The explicit solution of the equations of motion is obtained in the weak excitation regime, making it possible to gain insight into the dependence of the memory efficiency on the optical depth, and on the width and shape of the atomic spectral distributions. We also study a simplified memory protocol which does not require any optical control fields.Comment: 9 pages, 4 figures (Accepted for publication in Phys. Rev. A

Microlensing By a Prolate All-Macho Halo

It is widely believed that dark matter halos are flattened, that is closer to oblate than prolate. The evidence cited is based largely on observations of galaxies which do not look anything like our own and on numerical simulations which use ad hoc initial conditions. Given what we believe to be a ``reasonable doubt'' concerning the shape of dark Galactic halo we calculate the optical depth and event rate for microlensing of stars in the LMC assuming a wide range of models that include both prolate and oblate halos. We find, in agreement with previous analysis, that the optical depth for a spherical (E0) halo and for an oblate (E6) halo are roughly the same, essentially because two competing effects cancel approximately. However the optical depth for an E6 prolate halo is reduced by ~35%. This means that an all-Macho prolate halo with reasonable parameters for the Galaxy is consistent with the published microlensing event rate.Comment: 7 pages (24K), LaTeX; 2 Postscript figure