Inverse Nodal Problem for a Conformable Fractional Diffusion Operator

In this paper, a diffusion operator including conformable fractional derivatives of order {\alpha} ({\alpha} in (0,1)) is considered. The asymptotics of the eigenvalues, eigenfunctions and nodal points of the operator are obtained. Furthermore, an effective procedure for solving the inverse nodal problem is given

Two Practical Methods for Coronal Intensity Determination

Determining the relative brightness of the solar corona is one of the most critical stages in solar eclipse studies. For this purpose, images taken with different exposures and polarization angles in white-light observations are used. The composite image of each polarization angle is produced by combining the images of different exposures. With the help of the intensity calibration function of these images, the relative intensity of the corona can be calculated. The total brightness of the solar corona is calculated using Stokes parameters obtained from intensity values of three polarization angles. In this study, two methods are presented: the first is used to obtain the intensity calibration function of the photographic material using calibration images, and the second is used to calculate the combined intensity values of images taken with different polarization angles.Comment: 15 pages, including 13 figures and 5 tables, accepted for publication in Solar Physic

Expectation Propagation for Approximate Inference: Free Probability Framework

We study asymptotic properties of expectation propagation (EP) -- a method for approximate inference originally developed in the field of machine learning. Applied to generalized linear models, EP iteratively computes a multivariate Gaussian approximation to the exact posterior distribution. The computational complexity of the repeated update of covariance matrices severely limits the application of EP to large problem sizes. In this study, we present a rigorous analysis by means of free probability theory that allows us to overcome this computational bottleneck if specific data matrices in the problem fulfill certain properties of asymptotic freeness. We demonstrate the relevance of our approach on the gene selection problem of a microarray dataset.Comment: Both authors are co-first authors. The main body of this paper is accepted for publication in the proceedings of the 2018 IEEE International Symposium on Information Theory (ISIT

Can the Capability Approach be Evaluated within the Frame of Mainstream Economics? A Methodological Analysis

The aim of this article is to examine the capability approach of Amartya Sen and mainstream economic theory in terms of their epistemological, methodological and philosophical/cultural aspects. The reason for undertaking this analysis is the belief that Sen’s capability approach, contrary to some economists’ claim, is uncongenial to mainstream economic views on epistemology and methodology (not on ontologically). However, while some social scientists regard that Sen, on the whole, is a mainstream economist, his own approach strongly criticizes both the theory and practice of mainstream economics.Amartya Sen, Mainstream economics, Methodological individualism.