Proton, helium, and electron spectra during the large solar particle events of October-November 2003

The extraordinary period from late October through early November 2003 was marked by more than 40 coronal mass ejections (CME), eight X-class flares, and five large solar energetic particle (SEP) events. Using data from instruments on the ACE, SAMPEX, and GOES-11 spacecraft, the fluences of H, He, O, and electrons have been measured in these five events over the energy interval from ∼0.1 to >100 MeV/nucleon for the ions and ∼0.04 to 8 MeV for electrons. The H, He, and O spectra are found to resemble double power laws, with a break in the spectral index between ∼5 and ∼50 MeV/nucleon which appears to depend on the charge-to-mass ratio of the species. Possible interpretations of the relative location of the H and He breaks are discussed. The electron spectra can also be characterized by double power laws, but incomplete energy coverage prevents an exact determination of where and how the spectra steepen. The proton and electron fluences in the 28 October 2003 SEP event are comparable to the largest observed during the previous solar maximum, and within a factor of 2 or 3 of the largest SEP events observed during the last 50 years. The 2-week period covered by these observations accounted for ∼20% of the high-energy solar-particle fluence over the years from 1997 to 2003. By integrating over the energy spectra, the total energy content of energetic protons, He, and electrons in the interplanetary medium can be estimated. After correcting for the location of the events, it is found that the kinetic energy in energetic particles amounts to a significant fraction of the estimated CME kinetic energy, implying that shock acceleration must be relatively efficient in these events

The robustness of objective fabric pilling evaluation method

Previously, we proposed a new method to identify fabric pilling and objectively measure fabric pilling intensity based on the two-dimensional dual-tree complex wavelet reconstruction and neural network classification. Here we further evaluate the robustness of the method. Our results indicate that the pilling identification method is robust to significant variation in the brightness and contrast of the image, rotation of the image, and 2 i (i is an integer) times dilation of the image. The pilling feature vector developed to characterize the pilling intensity is robust to brightness change but is sensitive to large rotations of the image. As long as all fabric images are adjusted to have the same contrast level and the sample is illuminated from the same direction, the pilling feature vectors are comparable and can be used to classify the pilling intensity.<br /

`Iconoclastic', Categorical Quantum Gravity

This is a two-part, `2-in-1' paper. In Part I, the introductory talk at `Glafka--2004: Iconoclastic Approaches to Quantum Gravity' international theoretical physics conference is presented in paper form (without references). In Part II, the more technical talk, originally titled ``Abstract Differential Geometric Excursion to Classical and Quantum Gravity'', is presented in paper form (with citations). The two parts are closely entwined, as Part I makes general motivating remarks for Part II.Comment: 34 pages, in paper form 2 talks given at ``Glafka--2004: Iconoclastic Approaches to Quantum Gravity'' international theoretical physics conference, Athens, Greece (summer 2004

On Some Problems in Discrete Wavelet Analysis of Bivariate Spectra with an Application to Business Cycle Synchronization in the Euro Zone

The paper considers some of the problems emerging from discrete wavelet analysis of popular bivariate spectral quantities like the coherence and phase spectra and the frequency-dependent time delay. The approach taken here, introduced by Whitcher and Craigmile (2004), is based on the maximal overlap discrete Hilbert wavelet transform (MODHWT). Firstly, we point at a deficiency in the implementation of the MODHWT and suggest using a modified implementation scheme resembling the one applied in the context of the dual-tree complex wavelet transform of Kingsbury (see Selesnick et al., 2005). Secondly, via a broad set of simulation experiments we examine small and large sample properties of two wavelet estimators of the scale-dependent time delay. The estimators are: the wavelet cross-correlator and the wavelet phase angle-based estimator. Our results provide some practical guidelines for empirical examination of short- and medium-term lead-lag relations for octave frequency bands. Besides, we show how the MODHWT-based wavelet quantities can serve to approximate the Fourier bivariate spectra and discuss certain issues connected with building confidence intervals for them. The discrete wavelet analysis of coherence and phase angle is illustrated with a scale-dependent examination of business cycle synchronization between 11 euro zone member countries. The study is supplemented with wavelet analysis of variance and covariance of the euro zone business cycles. The empirical examination underlines good localization properties and high computational efficiency of the wavelet transformations applied, and provides new arguments in favour of the endogeneity hypothesis of the optimum currency area criteria as well as a wavelet evidence on dating the Great Moderation in the euro zone

Sparsity-inducing Nonconvex Nonseparable Regularization for Convex Image Processing

A popular strategy for determining solutions to linear least-squares problems relies on using sparsity-promoting regularizers and is widely exploited in image processing applications such as, e.g., image denoising, deblurring and inpainting. It is well known that, in general, non-convex regularizers hold the potential for promoting sparsity more effectively than convex regularizers such as, e.g., those involving the $ell_1$ norm. To avoid the intrinsic difficulties related to non-convex optimization, the Convex Non-Convex (CNC) strategy has been proposed, which allows the use of non-convex regularization while maintaining convexity of the total objective function. In this paper, a new CNC variational model is proposed, based on a more general parametric non-convex non-separable regularizer. The proposed model is applicable to a greater variety of image processing problems than prior CNC methods. We derive the convexity conditions and related theoretical properties of the presented CNC model, and we analyze existence and uniqueness of its solutions. A primal-dual forward-backward splitting algorithm is proposed for solving the related saddle-point problem. The convergence of the algorithm is demonstrated theoretically and validated empirically. Several numerical experiments are presented which prove the effectiveness of the proposed approach