We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in$R$^{3}away from the nuclei.

Macrophages play an important role in the inflammatory responses involved with spinal cord injury (SCI). We have previously demonstrated that infiltrated bone marrow-derived macrophages (BMDMs) engulf myelin debris, forming myelin-laden macrophages (mye-M). These mye-M promote disease progression through their pro-inflammatory phenotype, enhanced neurotoxicity, and impaired phagocytic capacity for apoptotic cells. We thus hypothesize that the excessive accumulation of mye-M is the root of secondary injury, and that targeting mye-M represents an efficient strategy to improve the local inflammatory microenvironment in injured spinal cords and to further motor neuron function recovery. In this study, we administer murine embryonic stem cell conditioned media (ESC-M) as a cell-free stem cell based therapy to treat a mouse model of SCI. We showed that BMDMs, but not microglial cells, engulf myelin debris generated at the injury site. Phagocytosis of myelin debris leads to the formation of mye-M in the injured spinal cord, which are surrounded by activated microglia cells. These mye-M are pro-inflammatory and lose the normal macrophage phagocytic capacity for apoptotic cells. We therefore focus on how to trigger lipid efflux from mye-M and thus restore their function. Using ESC-M as an immune modulating treatment for inflammatory damage after SCI, we rescued mye-M function and improved functional locomotor recovery. ESC-M treatment on mye-M resulted in improved exocytosis of internalized lipids and a normal capacity for apoptotic cell phagocytosis. Furthermore, when ESC-M was administered

We study an efficient dynamic blind source separation algorithm of convolutive sound mixtures based on updating statistical information in the frequency domain, and minimizing the support of time domain demixing filters by a weighted least square method. The permutation and scaling indeterminacies of separation, and concatenations of signals in adjacent time frames are resolved with optimization of l 1 l norm on cross-correlation coefficients at multiple time lags. The algorithm is a direct method without iterations, and is adaptive to the environment. Computations on recorded benchmark mixtures of speech and music signals show excellent performance. The method in general separates a foreground source from a background of sounds as often encountered in realistic situations.

We revisit the homogenization problem for the Poisson equation in periodically perforated domains with zero Neumann data at the boundary of the holes and prescribed Dirichlet data at the outer boundary. It is known that, if the periodicity of the holes goes to zero but their volume fraction remains fixed and positive, the limit problem is a Dirichlet boundary value problem posed in the domain without the holes, and the effective diffusion coefficients are non-trivially modified; if that volume fraction goes to zero instead, i.e. the holes are dilute, the effective operator remains the Laplacian (that is, unmodified). Our main results contain the study of a "continuity" in those effective models with respect to the volume fraction of the holes and some new convergence rates for homogenization in the dilute setting. Our method explores the classical two-scale expansion ansatz and relies on asymptotic analysis of the rescaled cell problems using layer potential theory.

In this paper, we show that general homogeneous manifolds G/P satisfy Conjecture O of Galkin, Golyshev and Iritani which `underlies' Gamma conjectures I and II of them. Our main tools are the quantum Chevalley formula for G/P and a theory on nonnegative matrices including Perron-Frobenius theorem.