Unconstrained Hamiltonian formulation of General Relativity with thermo-elastic sources

A new formulation of the Hamiltonian dynamics of the gravitational field interacting with(non-dissipative) thermo-elastic matter is discussed. It is based on a gauge condition which allows us to encode the six degrees of freedom of the ``gravity + matter''-system (two gravitational and four thermo-mechanical ones), together with their conjugate momenta, in the Riemannian metric q_{ij} and its conjugate ADM momentum P^{ij}. These variables are not subject to constraints. We prove that the Hamiltonian of this system is equal to the total matter entropy. It generates uniquely the dynamics once expressed as a function of the canonical variables. Any function U obtained in this way must fulfil a system of three, first order, partial differential equations of the Hamilton-Jacobi type in the variables (q_{ij},P^{ij}). These equations are universal and do not depend upon the properties of the material: its equation of state enters only as a boundary condition. The well posedness of this problem is proved. Finally, we prove that for vanishing matter density, the value of U goes to infinity almost everywhere and remains bounded only on the vacuum constraints. Therefore the constrained, vacuum Hamiltonian (zero on constraints and infinity elsewhere) can be obtained as the limit of a ``deep potential well'' corresponding to non-vanishing matter. This unconstrained description of Hamiltonian General Relativity can be useful in numerical calculations as well as in the canonical approach to Quantum Gravity.Comment: 29 pages, TeX forma

Genome of the marsupial Monodelphis domestica reveals innovation in non-coding sequences

We report a high-quality draft of the genome sequence of the grey, short-tailed opossum (Monodelphis domestica). As the first metatherian (\u27marsupial\u27) species to be sequenced, the opossum provides a unique perspective on the organization and evolution of mammalian genomes. Distinctive features of the opossum chromosomes provide support for recent theories about genome evolution and function, including a strong influence of biased gene conversion on nucleotide sequence composition, and a relationship between chromosomal characteristics and X chromosome inactivation. Comparison of opossum and eutherian genomes also reveals a sharp difference in evolutionary innovation between protein-coding and non-coding functional elements. True innovation in protein-coding genes seems to be relatively rare, with lineage-specific differences being largely due to diversification and rapid turnover in gene families involved in environmental interactions. In contrast, about 20% of eutherian conserved non-coding elements (CNEs) are recent inventions that postdate the divergence of Eutheria and Metatheria. A substantial proportion of these eutherian-specific CNEs arose from sequence inserted by transposable elements, pointing to transposons as a major creative force in the evolution of mammalian gene regulation. ©2007 Nature Publishing Group