A measure of statistical complexity based on predictive information

We introduce an information theoretic measure of statistical structure, called 'binding information', for sets of random variables, and compare it with several previously proposed measures including excess entropy, Bialek et al.'s predictive information, and the multi-information. We derive some of the properties of the binding information, particularly in relation to the multi-information, and show that, for finite sets of binary random variables, the processes which maximises binding information are the 'parity' processes. Finally we discuss some of the implications this has for the use of the binding information as a measure of complexity.Comment: 4 pages, 3 figure

Radiation Rates for Low Z Impurities in Edge Plasmas

The role of impurity radiation in the reduction of heat loads on divertor plates in present experiments such as DIII-D, JET, JT-60, ASDEX, and Alcator C-Mod, and in planned experiments such as ITER and TPX places a new degree of importance on the accuracy of impurity radiation emission rates for electron temperatures below 250 eV for ITER and below 150 eV for present experiments. We have calculated the radiated power loss using a collisional radiative model for Be, B, C, Ne and Ar using a multiple configuration interaction model which includes density dependent effects, as well as a very detailed treatment of the energy levels and meta-stable levels. The "collisional radiative" effects are very important for Be at temperatures below 10 eV. The same effects are present for higher Z impurities, but not as strongly. For some of the lower Z elements, the new rates are about a factor of two lower than those from a widely used, simpler average-ion package (ADPAK) developed for high Z ions and for higher temperatures. Following the approach of Lengyel for the case where electron heat conduction is the dominant mechanism for heat transport along field lines, our analysis indicates that significant enhancements of the radiation losses above collisional radiative model rates due to such effects as rapid recycling and charge exchange recombination will be necessary for impurity radiation to reduce the peak heat loads on divertor plates for high heat flux experiments such as ITER.Comment: Preprint for the 11th PSI meeting, gzipped postscript with 11 figures, 14 page

Calculations of Energy Losses due to Atomic Processes in Tokamaks with Applications to the ITER Divertor

Reduction of the peak heat loads on the plasma facing components is essential for the success of the next generation of high fusion power tokamaks such as the International Thermonuclear Experimental Reactor (ITER) 1 . Many present concepts for accomplishing this involve the use of atomic processes to transfer the heat from the plasma to the main chamber and divertor chamber walls and much of the experimental and theoretical physics research in the fusion program is directed toward this issue. The results of these experiments and calculations are the result of a complex interplay of many processes. In order to identify the key features of these experiments and calculations and the relative role of the primary atomic processes, simple quasi-analytic models and the latest atomic physics rate coefficients and cross sections have been used to assess the relative roles of central radiation losses through bremsstrahlung, impurity radiation losses from the plasma edge, charge exchange and hydrogen radiation losses from the scrape-off layer and divertor plasma and impurity radiation losses from the divertor plasma. This anaysis indicates that bremsstrahlung from the plasma center and impurity radiation from the plasma edge and divertor plasma can each play a significant role in reducing the power to the divertor plates, and identifies many of the factors which determine the relative role of each process. For instance, for radiation losses in the divertor to be large enough to radiate the power in the divertor for high power experiments, a neutral fraction of 10-3 to 10-2 and an impurity recycling rate of netrecycle of ~ 10^16 s m^-3 will be required in the divertor.Comment: Preprint for the 1994 APSDPP meeting, uuencoded and gzipped postscript with 22 figures, 40 pages

Blind Wavelet-Based Image Watermarking

In this chapter, the watermarking technique is blind; blind watermarking does not need any of the original images or any information about it to recover watermark. In this technique the watermark is inserted into the high frequencies. Three-level wavelet transform is applied to the image, and the size of the watermark is equal to the size of the detailed sub-band. Significant coefficients are used to embed the watermark. The proposed technique depends on quantization. The proposed watermarking technique generates images with less degradation

A measure of statistical complexity based on predictive information with application to finite spin systems

NOTICE: this is the author’s version of a work that was accepted for publication in 'Physical Letters A'. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in PHYSICAL LETTERS A, 376 (4): 275-281, JAN 2012. DOI:10.1016/j.physleta.2011.10.066

Constructive function approximation: theory and practice

In this paper we study the theoretical limits of finite constructive convex approximations of a given function in a Hilbert space using elements taken from a reduced subset. We also investigate the trade-off between the global error and the partial error during the iterations of the solution. These results are then specialized to constructive function approximation using sigmoidal neural networks. The emphasis then shifts to the implementation issues associated with the problem of achieving given approximation errors when using a finite number of nodes and a finite data set for training

New extreme-point robust stability results for discrete-time polynomials

This paper provides some new extreme-point robust-stability results for discrete-time polynomials with special uncertainties in the coefficient space. The proofs, obtained using the barycentric coordinates, are simple and the results specialize to existing robust-stability results