On the representation theory of the Bondi-Metzner-Sachs group and its variants in three space-time dimensions

The original Bondi-Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian radiating 4-dim space-times. As such, B is the best candidate for the universal symmetry group of General Relativity (G.R.). In 1973, with this motivation, P. J. McCarthy classified all relativistic B-invariant-systems in terms of strongly continuous irreducible unitary repesentations (IRS) of B. Here we introduce the analogue B(2,1) of the BMS group B in 3 space-time dimensions. B(2,1) itself admits thirty-four analogues both real in all signatures and in complex space-times. In order to find the IRS of both B(2,1) and its analogues we need to extend Wigner-Mackey's theory of induced representations. The necessary extension is described and is reduced to the solution of three problems. These problems are solved in the case where B(2,1) and its analogues are equipped with the Hilbert topology. The extended theory is necessary in order to construct the IRS of both B and its analogues in any number d of space-time dimensions, d is greater or equal to 3, and also in order to construct the IRS of their supersymmetric counterparts. We use the extended theory to obtain the necessary data in order to construct the IRS of B(2,1): The main results of the representation theory are: The IRS are induced from little groups which are compact. The finite little groups are cyclic groups of even order. The inducing construction is exhaustive notwithstanding the fact that B(2,1) is not locally compact in the employed Hilbert topology.Comment: 39 page

The best constant for centered Hardy-Littlewood maximal inequality

We find the exact value of the best possible constant $C$ for the weak type $(1,1)$ inequality for the one dimensional centered Hardy-Littlewood maximal operator. We prove that $C$ is the largest root of the quadratic equation $12C^{2}-22C+5=0$ thus obtaining $C=1.5675208...$. This is the first time the best constant for one of the fundamental inequalities satisfied by a centered maximal operator is precisely evaluated.Comment: 42 pages, published versio

Local lower norm estimates for dyadic maximal operators and related Bellman functions

We provide lower $L^q$ and weak $L^p$-bounds for the localized dyadic maximal operator on $R^n$, when the local $L^1$ and the local $L^p$ norm of the function are given. We actually do that in the more general context of homo- geneous tree-like families in probability spaces.Comment: 9 page

Inferring the high velocity of landslides in Valles Marineris on Mars from morphological analysis

The flow characteristics and velocities of three landslides in Valles Marineris on Mars are investigated using detailed morphological analyses of high-resolution images and dynamical calculations based on the run-up and curvature of the landslide deposits. The morphologies of the landslides are described, especially concerning those characteristics that can provide information on the dynamics and velocity. The long runout and estimated high velocities, often exceeding 100 m/s, confirm a low basal friction experienced by these landslides. Because subaqueous landslides on Earth exhibit reduced friction, we explore the scenario of sub-lacustrine failures, but find little support to this hypothesis. The environmental conditions that better explain the low friction and the presence of longitudinal furrows suggest an aerial environment with a basal soft and naturally lubricating medium on which friction diminished gradually; in this perspective, ice is the most promising candidate

The Mitochondrial Myopathy, Encephalopathy, Lactic Acidosis, and Stroke-like Episode Syndrome-associated Human Mitochondrial tRNALeu(UUR) Mutation Causes Aminoacylation Deficiency and Concomitant Reduced Association of mRNA with Ribosomes

The pathogenetic mechanism of the mitochondrial tRNALeu(UUR) A3243G transition associated with the mitochondrial myopathy, encephalopathy, lactic acidosis, and stroke-like episodes (MELAS) syndrome has been investigated in transmitochondrial cell lines constructed by transfer of mutant mitochondrial DNA (mtDNA)-carrying mitochondria from three genetically unrelated MELAS patients or of isogenic wild-type mtDNA-carrying organelles into human mtDNA-less cells. An in vivo footprinting analysis of the mtDNA segment within the tRNALeu(UUR) gene that binds the transcription termination factor failed to reveal any difference in occupancy of sites or qualitative interaction with the protein between mutant and wild-type mtDNAs. Cell lines nearly homoplasmic for the mutation exhibited a strong (70-75%) reduction in the level of aminoacylated tRNALeu(UUR) and a decrease in mitochondrial protein synthesis rate. The latter, however, did not show any significant correlation between synthesis defect of the individual polypeptides and number or proportion of UUR codons in their mRNAs, suggesting that another step, other than elongation, may be affected. Sedimentation analysis in sucrose gradient showed a reduction in size of the mitochondrial polysomes, while the distribution of the two rRNA components and of the mRNAs revealed decreased association of mRNA with ribosomes and, in the most affected cell line, pronounced degradation of the mRNA associated with slowly sedimenting structures. Therefore, several lines of evidence indicate that the protein synthesis defect in A3243G MELAS mutation-carrying cells is mainly due to a reduced association of mRNA with ribosomes, possibly as a consequence of the tRNALeu(UUR) aminoacylation defect

A new species in the major malaria vector complex sheds light on reticulated species evolution

Complexes of closely related species provide key insights into the rapid and independent evolution of adaptive traits. Here, we described and studied Anopheles fontenillei sp.n., a new species in the Anopheles gambiae complex that we recently discovered in the forested areas of Gabon, Central Africa. Our analysis placed the new taxon in the phylogenetic tree of the An. gambiae complex, revealing important introgression events with other members of the complex. Particularly, we detected recent introgression, with Anopheles gambiae and Anopheles coluzzii, of genes directly involved in vectorial capacity. Moreover, genome analysis of the new species allowed us to clarify the evolutionary history of the 3La inversion. Overall, An. fontenillei sp.n. analysis improved our understanding of the relationship between species within the An. gambiae complex, and provided insight into the evolution of vectorial capacity traits that are relevant for the successful control of malaria in Africa

Optimal designs for a class of nonlinear regression models

For a broad class of nonlinear regression models we investigate the local E- and c-optimal design problem. It is demonstrated that in many cases the optimal designs with respect to these optimality criteria are supported at the Chebyshev points, which are the local extrema of the equi-oscillating best approximation of the function f_0\equiv 0 by a normalized linear combination of the regression functions in the corresponding linearized model. The class of models includes rational, logistic and exponential models and for the rational regression models the E- and c-optimal design problem is solved explicitly in many cases.Comment: Published at http://dx.doi.org/10.1214/009053604000000382 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org