Characterization of the subdifferential of some matrix norms

AbstractA characterization is given of the subdifferential of matrix norms from two classes, orthogonally invariant norms and operator (or subordinate) norms. Specific results are derived for some special cases

Modelling Outliers and Missing Values in traffic Count Data Using the ARIMA Model.

This paper considers the application of the methodology to traffic count time series in which both missing values and outliers are present. Intervention analysis and detection using large residuals are shown to he reasonably effective but possible problems that result from non- stationarity in the data are identified. It is shown that despite considerable variabilty in the types of series the model selected from the ARIMA family is surprisingly homogeneous

About the Algebraic Solutions of Smallest Enclosing Cylinders Problems

Given n points in Euclidean space E^d, we propose an algebraic algorithm to compute the best fitting (d-1)-cylinder. This algorithm computes the unknown direction of the axis of the cylinder. The location of the axis and the radius of the cylinder are deduced analytically from this direction. Special attention is paid to the case d=3 when n=4 and n=5. For the former, the minimal radius enclosing cylinder is computed algebrically from constrained minimization of a quartic form of the unknown direction of the axis. For the latter, an analytical condition of existence of the circumscribed cylinder is given, and the algorithm reduces to find the zeroes of an one unknown polynomial of degree at most 6. In both cases, the other parameters of the cylinder are deduced analytically. The minimal radius enclosing cylinder is computed analytically for the regular tetrahedron and for a trigonal bipyramids family with a symmetry axis of order 3.Comment: 13 pages, 0 figure; revised version submitted to publication (previous version is a copy of the original one of 2010

Dark matter halos and the anisotropy of ultra-high energy cosmic rays

Several explanations for the existence of Ultra High Energy Cosmic Rays invoke the idea that they originate from the decay of massive particles created in the reheating following inflation. It has been suggested that the decay products can explain the observed isotropic flux of cosmic rays. We have calculated the anisotropy expected for various models of the dark matter distribution and find that at present data are too sparse above $4 \times 10^{19}$ eV to discriminate between different models. However we show that with data from three years of operation of the southern section of the Pierre Auger Observatory significant progress in testing the proposals will be made.Comment: 21 pages, 6 figures (ps), Astroparticle Physics (accepted for publication

Convex recovery of a structured signal from independent random linear measurements

This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with recent results for standard Gaussian measurements, but the argument applies to a much wider class of measurement ensembles. To demonstrate the power of this approach, the paper presents a short analysis of phase retrieval by trace-norm minimization. The key technical tool is a framework, due to Mendelson and coauthors, for bounding a nonnegative empirical process.Comment: 18 pages, 1 figure. To appear in "Sampling Theory, a Renaissance." v2: minor corrections. v3: updated citations and increased emphasis on Mendelson's contribution

DCE-MRI biomarkers of tumour heterogeneity predict CRC liver metastasis shrinkage following bevacizumab and FOLFOX-6

Background: There is limited evidence that imaging biomarkers can predict subsequent response to therapy. Such prognostic and/or predictive biomarkers would facilitate development of personalised medicine. We hypothesised that pre-treatment measurement of the heterogeneity of tumour vascular enhancement could predict clinical outcome following combination anti-angiogenic and cytotoxic chemotherapy in colorectal cancer (CRC) liver metastases. Methods: Ten patients with 26 CRC liver metastases had two dynamic contrast-enhanced MRI (DCE-MRI) examinations before starting first-line bevacizumab and FOLFOX-6. Pre-treatment biomarkers of tumour microvasculature were computed and a regression analysis was performed against the post-treatment change in tumour volume after five cycles of therapy. The ability of the resulting linear model to predict tumour shrinkage was evaluated using leave-one-out validation. Robustness to inter-visit variation was investigated using data from a second baseline scan. Results: In all, 86% of the variance in post-treatment tumour shrinkage was explained by the median extravascular extracellular volume (ve), tumour enhancing fraction (EF), and microvascular uniformity (assessed with the fractal measure box dimension, d0) (R2=0.86, P<0.00005). Other variables, including baseline volume were not statistically significant. Median prediction error was 12%. Equivalent results were obtained from the second scan. Conclusion: Traditional image analyses may over-simplify tumour biology. Measuring microvascular heterogeneity may yield important prognostic and/or predictive biomarkers

3DTV: Capture, transmission, and display of 3D video

[No abstract available

Orbiting Resonances and Bound States in Molecular Scattering

A family of orbiting resonances in molecular scattering is globally described by using a single pole moving in the complex angular momentum plane. The extrapolation of this pole at negative energies gives the location of the bound states. Then a single pole trajectory, that connects a rotational band of bound states and orbiting resonances, is obtained. These complex angular momentum singularities are derived through a geometrical theory of the orbiting. The downward crossing of the phase-shifts through pi/2, due to the repulsive region of the molecular potential, is estimated by using a simple hard-core model. Some remarks about the difference between diffracted rays and orbiting are also given.Comment: 18 pages, 3 figures, to appear in Physical Review