Extended Palatini action for general relativity and the natural emergence of the cosmological constant

In the Palatini action of general relativity the connection and the metric are treated as independent dynamical variables. Instead of assuming a relation between these quantities, the desired relation between them is derived through the Euler-Lagrange equations of the Palatini action. In this manuscript we construct an extended Palatini action, where we do not assume any a priori relationship between the connection, the covariant metric tensor, and the contravariant metric tensor. Instead we treat these three quantities as independent dynamical variables. We show that this action reproduces the standard Einstein field equations depending on a single metric tensor. We further show that in this formulation the cosmological constant has an additional theoretical significance. Normally the cosmological constant is added to the Einstein field equations for the purpose of having general relativity be consistent with cosmological observations. In the formulation presented here, the nonvanishing cosmological constant also ensures the self-consistency of the theory.Comment: in the revised version the original scalar matter action is replaced with a general matter actio

Quantitative bounds on convergence of time-inhomogeneous Markov chains

Convergence rates of Markov chains have been widely studied in recent years. In particular, quantitative bounds on convergence rates have been studied in various forms by Meyn and Tweedie [Ann. Appl. Probab. 4 (1994) 981-1101], Rosenthal [J. Amer. Statist. Assoc. 90 (1995) 558-566], Roberts and Tweedie [Stochastic Process. Appl. 80 (1999) 211-229], Jones and Hobert [Statist. Sci. 16 (2001) 312-334] and Fort [Ph.D. thesis (2001) Univ. Paris VI]. In this paper, we extend a result of Rosenthal [J. Amer. Statist. Assoc. 90 (1995) 558-566] that concerns quantitative convergence rates for time-homogeneous Markov chains. Our extension allows us to consider f-total variation distance (instead of total variation) and time-inhomogeneous Markov chains. We apply our results to simulated annealing.Comment: Published at http://dx.doi.org/10.1214/105051604000000620 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Laminar flow analysis of plane disk slinger seal

Flow and temperature field analysis of a plane disk slinger sea

Integrating genomics and phylogenetics in understanding the history of Trichinella species

In 2004, funding was received by Washington University’s Genome Sequencing Center through NHGRI, to completely sequence several nematode genomes as part of a holistic effort to advance our understanding of the human genome and evolution within the Metazoa. Trichinella spiralis was among this group of worms because of its strategic location at the base of the phylum Nematoda, and the belief that extant species represented an ancient divergent event that occurred as early as the Paleozoic. At the same time, a concerted effort was put forth to solidify the phylogeny of extant species of Trichinella based upon molecular analyses of a multi-gene system to understand the history of the genus and thereby enhance utilization of the forthcoming sequence data. Since the inception of this research, several findings have emerged: (1) the size of T. spiralis genome estimated by flow cytometry (71.3 Mb) is substantially smaller than originally predicted (270 Mb); (2) to date, a subset of the total of 3,534,683 sequences have been assembled into a 59.3 Mb unique sequence; (3) 19% of the assembled sequence is comprised of repetitive elements; and (4) sequence data are predicated upon extant T. spiralis which probably diverged as little as 20 million years ago. Thus, the utility of the T. spiralis genome as representative of an archaic species must be tempered with the knowledge that encapsulated and non-encapsulated clades probably separated during the mid-Miocene as temperate ecosystems changed

Fabrication of titanium multi-wall Thermal Protection System (TPS) test panel arrays

Several arrays were designed and tested. Tests included vibrational and acoustical tests, radiant heating tests, and thermal conductivity tests. A feasible manufacturing technique was established for producing the protection system panels