Schwarzschild-de Sitter Metric and Inertial Beltrami Coordinates

Under consideration of coordinate conditions, we get the Schwarzschild-Beltrami-de Sitter (S-BdS) metric solution of the Einstein field equations with a cosmological constant $\Lambda$. A brief review to the de Sitter invariant special relativity (dS-SR), and de Sitter general relativity (dS-GR, or GR with a $\Lambda$) is presented. The Beltrami metric $B_{\mu\nu}$ provides inertial reference frame for the dS-spacetime. By examining the Schwarzschild-de Sitter (S-dS) metric $g_{\mu\nu}^{(M)}$ existed in literatures since 1918, we find that the existed S-dS metric $g_{\mu\nu}^{(M)}$ describes some mixing effects of gravity and inertial-force, instead of a pure gravity effect arisen from "solar mass" $M$ in dS-GR. In this paper, we solve the vacuum Einstein equation of dS-GR, with the requirement of gravity-free metric $g_{\mu\nu}^{(M)}|_{M\rightarrow 0}=B_{\mu\nu}$. In this way we find S-BdS solution of dS-GR, written in inertial Beltrami coordinates. This is a new form of S-dS metric. Its physical meaning and possible applications are discussed.Comment: 16 pages, 1 figur

Identifying Functional Mechanisms of Gene and Protein Regulatory Networks in Response to a Broader Range of Environmental Stresses

Cellular responses to sudden environmental stresses or physiological changes provide living organisms with the opportunity for final survival and further development. Therefore, it is an important topic to understand protective mechanisms against environmental stresses from the viewpoint of gene and protein networks. We propose two coupled nonlinear stochastic dynamic models to reconstruct stress-activated gene and protein regulatory networks via microarray data in response to environmental stresses. According to the reconstructed gene/protein networks, some possible mutual interactions, feedforward and feedback loops are found for accelerating response and filtering noises in these signaling pathways. A bow-tie core network is also identified to coordinate mutual interactions and feedforward loops, feedback inhibitions, feedback activations, and cross talks to cope efficiently with a broader range of environmental stresses with limited proteins and pathways