A Variational Calculation of TE and TM Cutoff Wavenumbers in Circular Eccentric Guides by Conformal Mapping

The cutoff wavenumbers of higher order modes in circular eccentric guides are computed with the variational analysis combined with a conformal mapping. A conformal mapping is applied to the variational formulation, and the variational equation is solved by the finite-element method. Numerical results for TE and TM cutoff wavenumbers are presented for different distances between the centers and ratio of the radii. Comparisons with numerical results found in the literature validate the presented method

Invariant density for a class of initial distributions under quadratic mapping

For the discrete-time quadratic map xt+1=4xt(1-xt) the evolution equation for a class of non-uniform initial densities is obtained. It is shown that in the t to infinity limit all of them approach the invariant density for the map.

Spectral clustering independent component analysis for tissue classification from brain MRI

A spectral angle based feature extraction method, Spectral Clustering Independent Component Analysis (SC-ICA), is proposed in this work to improve the brain tissue classification from Magnetic Resonance Images (MRI). SC-ICA provides equal priority to global and local features; thereby it tries to resolve the inefficiency of conventional approaches in abnormal tissue extraction. First, input multispectral MRI is divided into different clusters by a spectral distance based clustering. Then, Independent Component Analysis (ICA) is applied on the clustered data, in conjunction with Support Vector Machines (SVM) for brain tissue analysis. Normal and abnormal datasets, consisting of real and synthetic T1-weighted, T2-weighted and proton density/fluid-attenuated inversion recovery images, were used to evaluate the performance of the new method. Comparative analysis with ICA based SVM and other conventional classifiers established the stability and efficiency of SC-ICA based classification, especially in reproduction of small abnormalities. Clinical abnormal case analysis demonstrated it through the highest Tanimoto Index/accuracy values, 0.75/98.8%, observed against ICA based SVM results, 0.17/96.1%, for reproduced lesions. Experimental results recommend the proposed method as a promising approach in clinical and pathological studies of brain diseases