Independent component analysis (ICA) is a cornerstone of modern data analysis. Its goal is to recover a latent random vector S with independent components from samples of X = AS where A is an unknown mixing matrix. Critically, all existing methods for ICA rely on and exploit strongly the assumption that S is not Gaussian as otherwise A becomes unidentifiable. In this paper, we show that in fact...

In this paper, weak approximations of multi-dimensional stochastic differential equations with discontinuous drift coefficients are considered. Here as the approximated process, the Euler-Maruyama approximation of SDEs with approximated drift coefficients is used, and we provide a rate of weak convergence of them. Finally we present a rate of weak convergence of the Euler-Maruyama approximation...

This paper establishes the impact of topological and graphical properties on the comprehension of Euler diagrams. To-date, various studies have examined the impact of individual properties of Euler diagrams, such as curve shape and orientation. This has allowed us to establish guides for using these properties such as ‘draw Euler diagrams with circles’ and ‘draw Euler diagrams without regard to...

introduction: from maturity to menopause, women are worried about pregnancy. abstinence from sex or use of pregnancy prevention methods are choices for them. as abstinence is impossible, the only remaining choice is use of pregnancy prevention methods. effective control of pregnancy is really essential for the health of mother and infant and also control of unplanned increase in population. reg...

We explore the performance and advantages/disadvantages of using unconditionally stable explicit super time-stepping (STS) algorithms versus implicit schemes with Krylov solvers for integrating parabolic operators in thermodynamic MHD models of the solar corona. Specifically, we compare the second-order Runge-Kutta Legendre (RKL2) STS method with the implicit backward Euler scheme computed usin...

We determine the expected curvature polynomial of random real projec-tive varieties given as the zero set of independent random polynomials with Gaussian distribution, whose distribution is invariant under the action of the orthogonal group. In particular, the expected Euler characteristic of such random real projective varieties is found. This considerably extends previously known results on t...

It is shown that very small time steps are required to correctly reproduce the synchronization properties of large networks of integrate-and-re neurons when the diierential system describing their dynamics is integrated with the standard Euler or second order Runge-Kutta algorithms. The reason for that behavior is analyzed and a simple improvement of these algorithms is proposed.

We present and analyse two implicit methods for Ito stochastic differential equations (SDEs) with Poisson-driven jumps. The first method, SSBE, is a split-step extension of the backward Euler method. The second method, CSSBE, arises from the introduction of a compensated, martingale, form of the Poisson process. We show that both methods are amenable to rigorous analysis when a one-sided Lipsch...

We determine the expected curvature polynomial of random real projec-tive varieties given as the zero set of independent random polynomials with Gaussian distribution, whose distribution is invariant under the action of the orthogonal group. In particular, the expected Euler characteristic of such random real projective varieties is found. This considerably extends previously known results on t...

We deal with monotone inclusion problems of the form 0 ∈ Ax+Dx+NC(x) in real Hilbert spaces, where A is a maximally monotone operator, D a cocoercive operator and C the nonempty set of zeros of another cocoercive operator. We propose a forwardbackward penalty algorithm for solving this problem which extends the one proposed by H. Attouch, M.-O. Czarnecki and J. Peypouquet in [3]. The condition ...