A Carleman type theorem for proper holomorphic embeddings

In 1927, Carleman showed that a continuous, complex-valued function on the real line can be approximated in the Whitney topology by an entire function restricted to the real line. In this paper, we prove a similar result for proper holomorphic embeddings. Namely, we show that a proper \cC^r embedding of the real line into \C^n can be approximated in the strong \cC^r topology by a proper holomorphic embedding of \C into \C^n

On the canonical degrees of curves in varieties of general type

A widely believed conjecture predicts that curves of bounded geometric genus lying on a variety of general type form a bounded family. One may even ask whether the canonical degree of a curve $C$ in a variety of general type is bounded from above by some expression $a\chi(C)+b$, where $a$ and $b$ are positive constants, with the possible exceptions corresponding to curves lying in a strict closed subset (depending on $a$ and $b$). A theorem of Miyaoka proves this for smooth curves in minimal surfaces, with $a>3/2$. A conjecture of Vojta claims in essence that any constant $a>1$ is possible provided one restricts oneself to curves of bounded gonality. We show by explicit examples coming from the theory of Shimura varieties that in general, the constant $a$ has to be at least equal to the dimension of the ambient variety. We also prove the desired inequality in the case of compact Shimura varieties.Comment: 10 pages, to appear in Geometric and Functional Analysi

Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio

A mathematical model of melt lake development on an ice shelf

The accumulation of surface meltwater on ice shelves can lead to the formation of melt lakes. Melt lakes have been implicated in ice shelf collapse; Antarctica's Larsen B Ice Shelf was observed to have a large amount of surface melt lakes present preceding its collapse in 2002. Such collapse can affect ocean circulation and temperature, cause habitat loss and contribute to sea level rise through the acceleration of tributary glaciers. We present a mathematical model of a surface melt lake on an idealised ice shelf. The model incorporates a calculation of the ice shelf surface energy balance, heat transfer through the firn, the production and percolation of meltwater into the firn, the formation of ice lenses and the development and refreezing of surface melt lakes. The model is applied to the Larsen C Ice Shelf, where melt lakes have been observed. This region has warmed several times the global average over the last century and the Larsen C firn layer could become saturated with meltwater by the end of the century. When forced with weather station data, our model produces surface melting, meltwater accumulation, and melt lake development consistent with observations. We examine the sensitivity of lake formation to uncertain parameters, and provide evidence of the importance of processes such as lateral meltwater transport. We conclude that melt lakes impact surface melt and firn density and warrant inclusion in dynamic-thermodynamic models of ice shelf evolution within climate models, of which our model could form the basis for the thermodynamic component

Maintenance of complex I and its supercomplexes by NDUF-11 is essential for mitochondrial structure, function and health

Mitochondrial supercomplexes form around a conserved core of monomeric complex I and dimeric complex III; wherein a subunit of the former, NDUFA11, is conspicuously situated at the interface. We identified nduf-11 (B0491.5) as encoding the Caenorhabditis elegans homologue of NDUFA11. Animals homozygous for a CRISPR-Cas9-generated knockout allele of nduf-11 arrested at the second larval (L2) development stage. Reducing (but not eliminating) expression using RNAi allowed development to adulthood, enabling characterisation of the consequences: destabilisation of complex I and its supercomplexes and perturbation of respiratory function. The loss of NADH dehydrogenase activity was compensated by enhanced complex II activity, with the potential for detrimental reactive oxygen species (ROS) production. Cryo-electron tomography highlighted aberrant morphology of cristae and widening of both cristae junctions and the intermembrane space. The requirement of NDUF-11 for balanced respiration, mitochondrial morphology and development presumably arises due to its involvement in complex I and supercomplex maintenance. This highlights the importance of respiratory complex integrity for health and the potential for its perturbation to cause mitochondrial disease. This article has an associated First Person interview with Amber Knapp-Wilson, joint first author of the paper

Maintenance of complex I and its supercomplexes by NDUF-11 is essential for mitochondrial structure, function and health

Mitochondrial supercomplexes form around a conserved core of monomeric complex I and dimeric complex III; wherein a subunit of the former, NDUFA11, is conspicuously situated at the interface. We identified nduf-11 (B0491.5) as encoding the Caenorhabditis elegans homologue of NDUFA11. Animals homozygous for a CRISPR-Cas9-generated knockout allele of nduf-11 arrested at the second larval (L2) development stage. Reducing (but not eliminating) expression using RNAi allowed development to adulthood, enabling characterisation of the consequences: destabilisation of complex I and its supercomplexes and perturbation of respiratory function. The loss of NADH dehydrogenase activity was compensated by enhanced complex II activity, with the potential for detrimental reactive oxygen species (ROS) production. Cryo-electron tomography highlighted aberrant morphology of cristae and widening of both cristae junctions and the intermembrane space. The requirement of NDUF-11 for balanced respiration, mitochondrial morphology and development presumably arises due to its involvement in complex I and supercomplex maintenance. This highlights the importance of respiratory complex integrity for health and the potential for its perturbation to cause mitochondrial disease. This article has an associated First Person interview with Amber Knapp-Wilson, joint first author of the paper

An embedding of ℂ in ℂ 2 with hyperbolic complement

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46249/1/208_2005_Article_BF01445264.pd