Unstable and Stable Galaxy Models

To determine the stability and instability of a given steady galaxy configuration is one of the fundamental problems in the Vlasov theory for galaxy dynamics. In this article, we study the stability of isotropic spherical symmetric galaxy models $f_{0}(E)$, for which the distribution function $f_{0}$ depends on the particle energy $E$ only. In the first part of the article, we derive the first sufficient criterion for linear instability of $f_{0}(E):$ $f_{0}(E)$ is linearly unstable if the second-order operator $$A_{0}\equiv-\Delta+4\pi\int f_{0}^{\prime}(E)\{I-\mathcal{P}\}dv$$ has a negative direction, where $\mathcal{P}$ is the projection onto the function space $\{g(E,L)\},$ $L$ being the angular momentum [see the explicit formula (\ref{A0-radial})]. In the second part of the article, we prove that for the important King model, the corresponding $A_{0}$ is positive definite. Such a positivity leads to the nonlinear stability of the King model under all spherically symmetric perturbations.Comment: to appear in Comm. Math. Phy

Unstable Galaxy Models

The dynamics of collisionless galaxy can be described by the Vlasov-Poisson system. By the Jean's theorem, all the spherically symmetric steady galaxy models are given by a distribution of {\Phi}(E,L), where E is the particle energy and L the angular momentum. In a celebrated Doremus-Feix-Baumann Theorem, the galaxy model {\Phi}(E,L) is stable if the distribution {\Phi} is monotonically decreasing with respect to the particle energy E. On the other hand, the stability of {\Phi}(E,L) remains largely open otherwise. Based on a recent abstract instability criterion of Guo-Lin, we constuct examples of unstable galaxy models of f(E,L) and f(E) in which f fails to be monotone in E

Utilization of Different Anti-Viral Mechanisms By Mammalian Embryonic Stem Cells and Differentiated Cells

Embryonic stem cells (ESCs) have received tremendous attention because of their potential applications in regenerative medicine. Over the past two decades, intensive research has not only led to the generation of various types of cells from ESCs that can be potentially used for the treatment of human diseases but also led to the formation of new concepts and breakthroughs that have significantly impacted our understanding of basic cell biology and developmental biology. Recent studies have revealed that ESCs and other types of pluripotent cells do not have a functional interferon (IFN)-based anti-viral mechanism, challenging the idea that the IFN system is developed as the central component of anti-viral innate immunity in all types of cells in vertebrates. This finding also provided important insight into a question that has been uncertain for a long time: whether or not the RNA interference (RNAi) anti-viral mechanism operates in mammalian cells. An emerging paradigm is that mammals may have adapted distinct anti-viral mechanisms at different stages of organismal development; the IFN-based system is mainly used by differentiated somatic cells, while the RNAi anti-viral mechanism may be used in ESCs. This paper discusses the molecular basis and biological implications for mammals to have different anti-viral mechanisms during development

Transient Inhibition of Cell Proliferation does not Compromise Self-Renewal of Mouse Embryonic Stem Cells

Embryonic stem cells (ESCs) have unlimited capacity for self-renewal and can differentiate into various cell types when induced. They also have an unusual cell cycle control mechanism driven by constitutively active cyclin dependent kinases (Cdks). In mouse ESCs (mESCs). It is proposed that the rapid cell proliferation could be a necessary part of mechanisms that maintain mESC self-renewal and pluripotency, but this hypothesis is not in line with the finding in human ESCs (hESCs) that the length of the cell cycle is similar to differentiated cells. Therefore, whether rapid cell proliferation is essential for the maintenance of mESC state remains unclear. We provide insight into this uncertainty through chemical intervention of mESC cell cycle. We report here that inhibition of Cdks with olomoucine II can dramatically slow down cell proliferation of mESCs with concurrent down-regulation of cyclin A, B and E, and the activation of the Rb pathway. However, mESCs display can recover upon the removal of olomoucine II and are able to resume normal cell proliferation without losing self-renewal and pluripotency, as demonstrated by the expression of ESC markers, colony formation, embryoid body formation, and induced differentiation. We provide a mechanistic explanation for these observations by demonstrating that Oct4 and Nanog, two major transcription factors that play critical roles in the maintenance of ESC properties, are up-regulated via de novo protein synthesis when the cells are exposed to olomoucine II. Together, our data suggest that short-term inhibition of cell proliferation does not compromise the basic properties of mESCs. (C) 2012 Elsevier Inc. All rights reserved

On determination of the geometric cosmological constant from the OPERA experiment of superluminal neutrinos

The recent OPERA experiment of superluminal neutrinos has deep consequences in cosmology. In cosmology a fundamental constant is the cosmological constant. From observations one can estimate the effective cosmological constant $\Lambda_{eff}$ which is the sum of the quantum zero point energy $\Lambda_{dark energy}$ and the geometric cosmological constant $\Lambda$. The OPERA experiment can be applied to determine the geometric cosmological constant $\Lambda$. It is the first time to distinguish the contributions of $\Lambda$ and $\Lambda_{dark energy}$ from each other by experiment. The determination is based on an explanation of the OPERA experiment in the framework of Special Relativity with de Sitter space-time symmetry.Comment: 7 pages, no figure