A Holder Continuous Nowhere Improvable Function with Derivative Singular Distribution

We present a class of functions $\mathcal{K}$ in $C^0(\R)$ which is variant of the Knopp class of nowhere differentiable functions. We derive estimates which establish \mathcal{K} \sub C^{0,\al}(\R) for 0<\al<1 but no $K \in \mathcal{K}$ is pointwise anywhere improvable to C^{0,\be} for any \be>\al. In particular, all $K$'s are nowhere differentiable with derivatives singular distributions. $\mathcal{K}$ furnishes explicit realizations of the functional analytic result of Berezhnoi. Recently, the author and simulteously others laid the foundations of Vector-Valued Calculus of Variations in $L^\infty$ (Katzourakis), of $L^\infty$-Extremal Quasiconformal maps (Capogna and Raich, Katzourakis) and of Optimal Lipschitz Extensions of maps (Sheffield and Smart). The "Euler-Lagrange PDE" of Calculus of Variations in $L^\infty$ is the nonlinear nondivergence form Aronsson PDE with as special case the $\infty$-Laplacian. Using $\mathcal{K}$, we construct singular solutions for these PDEs. In the scalar case, we partially answered the open $C^1$ regularity problem of Viscosity Solutions to Aronsson's PDE (Katzourakis). In the vector case, the solutions can not be rigorously interpreted by existing PDE theories and justify our new theory of Contact solutions for fully nonlinear systems (Katzourakis). Validity of arguments of our new theory and failure of classical approaches both rely on the properties of $\mathcal{K}$.Comment: 5 figures, accepted to SeMA Journal (2012), to appea

Hairs on the cosmological horizon

We investigate the possibility of having hairs on the cosmological horizon. The cosmological horizon shares similar properties of black hole horizons in the aspect of having hairs on the horizons. For those theories admitting haired black hole solutions, the nontrivial matter fields may reach and extend beyond the cosmological horizon. For Q-stars and boson stars, the matter fields cannot reach the cosmological horizon. The no short hair conjecture keeps valid, despite the asymptotic behavior (de Sitter or anti-de Sitter) of black hole solutions. We prove the no scalar hair theorem for anti-de Sitter black holes. Using the Bekenstein's identity method, we also prove the no scalar hair theorem for the de Sitter space and de Sitter black holes if the scalar potential is convex.Comment: Revtex, no figures, 16 page

Defects in Friction Stir Welding of Steel

Defects associated with friction stir welding of two steel grades including DH36 and EH46 were investigated. Different welding parameters including tool rotational and tool traverse (linear) speeds were applied to understand their effect on weld seam defects including microcracks and voids formation. SEM images and infinite focus microscopy were employed to identify the defects types. Two new defects associated with the friction stir welding process are introduced in this work. The first defect identified in this work is a microcrack found between the plunge and the steady state region and attributed to the traverse moving of the tool with unsuitable speed from the plunge-dwell to the steady state stage. The tool traverse speed has recommended to travel 20 mm more with accelerated velocity range of 0.1 from the maximum traverse speed until reaching the steady state. The maximum recommended traverse speed in the steady state was also suggested to be less than 400 mm/min in order to avoid the lack in material flow. The second type of defect observed in this work was microcracks inside the stirred zone caused by elemental precipitations of TiN. The precipitates of TiN were attributed to the high tool rotational speed which caused the peak temperature to exceed 1200 °C at the top of the stirred zone and based on previous work. The limit of tool rotational speed was recommended to be maintained in the range of 200-500 RPM based on the mechanical experiments on the FSW samples

Properties of a Yeast Cytochrome P-450-Containing Enzyme System which Catalyzes the Hydroxylation of Fatty Acids, Alkanes, and Drugs

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65977/1/j.1432-1033.1973.tb02948.x.pd

Control of Alzheimer's Amyloid Beta Toxicity by the High Molecular Weight Immunophilin FKBP52 and Copper Homeostasis in Drosophila

FK506 binding proteins (FKBPs), also called immunophilins, are prolyl-isomerases (PPIases) that participate in a wide variety of cellular functions including hormone signaling and protein folding. Recent studies indicate that proteins that contain PPIase activity can also alter the processing of Alzheimer's Amyloid Precursor Protein (APP). Originally identified in hematopoietic cells, FKBP52 is much more abundantly expressed in neurons, including the hippocampus, frontal cortex, and basal ganglia. Given the fact that the high molecular weight immunophilin FKBP52 is highly expressed in CNS regions susceptible to Alzheimer's, we investigated its role in Aβ toxicity. Towards this goal, we generated Aβ transgenic Drosophila that harbor gain of function or loss of function mutations of FKBP52. FKBP52 overexpression reduced the toxicity of Aβ and increased lifespan in Aβ flies, whereas loss of function of FKBP52 exacerbated these Aβ phenotypes. Interestingly, the Aβ pathology was enhanced by mutations in the copper transporters Atox1, which interacts with FKBP52, and Ctr1A and was suppressed in FKBP52 mutant flies raised on a copper chelator diet. Using mammalian cultures, we show that FKBP52 (−/−) cells have increased intracellular copper and higher levels of Aβ. This effect is reversed by reconstitution of FKBP52. Finally, we also found that FKBP52 formed stable complexes with APP through its FK506 interacting domain. Taken together, these studies identify a novel role for FKBP52 in modulating toxicity of Aβ peptides

Human and mouse essentiality screens as a resource for disease gene discovery.

The identification of causal variants in sequencing studies remains a considerable challenge that can be partially addressed by new gene-specific knowledge. Here, we integrate measures of how essential a gene is to supporting life, as inferred from viability and phenotyping screens performed on knockout mice by the International Mouse Phenotyping Consortium and essentiality screens carried out on human cell lines. We propose a cross-species gene classification across the Full Spectrum of Intolerance to Loss-of-function (FUSIL) and demonstrate that genes in five mutually exclusive FUSIL categories have differing biological properties. Most notably, Mendelian disease genes, particularly those associated with developmental disorders, are highly overrepresented among genes non-essential for cell survival but required for organism development. After screening developmental disorder cases from three independent disease sequencing consortia, we identify potentially pathogenic variants in genes not previously associated with rare diseases. We therefore propose FUSIL as an efficient approach for disease gene discovery

A large scale hearing loss screen reveals an extensive unexplored genetic landscape for auditory dysfunction

The developmental and physiological complexity of the auditory system is likely reflected in the underlying set of genes involved in auditory function. In humans, over 150 non-syndromic loci have been identified, and there are more than 400 human genetic syndromes with a hearing loss component. Over 100 non-syndromic hearing loss genes have been identified in mouse and human, but we remain ignorant of the full extent of the genetic landscape involved in auditory dysfunction. As part of the International Mouse Phenotyping Consortium, we undertook a hearing loss screen in a cohort of 3006 mouse knockout strains. In total, we identify 67 candidate hearing loss genes. We detect known hearing loss genes, but the vast majority, 52, of the candidate genes were novel. Our analysis reveals a large and unexplored genetic landscape involved with auditory function.The full extent of the genetic basis for hearing impairment is unknown. Here, as part of the International Mouse Phenotyping Consortium, the authors perform a hearing loss screen in 3006 mouse knockout strains and identify 52 new candidate genes for genetic hearing loss.PMC563879