In this paper we prove the symmetry result for solutions of nonlinear elliptic Neumann boundary value problems by using the Alexandrov's method of reflection and maximum principle, on the unit ball in the n-dimensional Euclidean space with n ≥3

The present paper combines nonlinear shrinkage with the Multivariate Generalized Hyperbolic (MGHyp) distribution to account for heavy tails in estimating the first and second moments in high dimensions. An Expectation-Maximization (EM) algorithm is developed that is fast, stable, and applicable...

We document two robust features of the cross-sectional distribution of usual weekly hours and hourly wages. First, usual weekly hours are heavily concentrated around 40 hours, while at the same time a substantial share of total hours come from individuals who work more than 50 hours. Second,...

Over recent decades, various USA government regulations and incentives, at both federal and state levels, encourage the development of green energy sources and the reduction of CO 2 emissions. In this paper, we investigate the degree of persistency of shocks to CO 2 per capita series in 50...

Complex systems derive sophisticated behavioural dynamics by connecting individual component dynamics via a complex network. The resilience of complex systems is a critical ability to regain desirable behaviour after perturbations. In the past years our understanding of large-scale networked...

Solving non-linear parabolic partial differential equations (PDEs) in high dimension becomes an interest for its curse of dimensionality problem. Recently, a deep learning method associated with a backward stochastic differential equation (deep-BSDE) to solve the PDEs draws intensive discussions...