Martin boundary of a reflected random walk on a half-space

The complete representation of the Martin compactification for reflected random walks on a half-space $\Z^d\times\N$ is obtained. It is shown that the full Martin compactification is in general not homeomorphic to the ``radial'' compactification obtained by Ney and Spitzer for the homogeneous random walks in $\Z^d$ : convergence of a sequence of points $z_n\in\Z^{d-1}\times\N$ to a point of on the Martin boundary does not imply convergence of the sequence $z_n/|z_n|$ on the unit sphere $S^d$. Our approach relies on the large deviation properties of the scaled processes and uses Pascal's method combined with the ratio limit theorem. The existence of non-radial limits is related to non-linear optimal large deviation trajectories.Comment: 42 pages, preprint, CNRS UMR 808

Whole-genome sequencing and the clinician: a tale of two cities.

Clinicians are faced with unprecedented opportunities to identify the genetic aetiologies of hitherto molecularly uncharacterised conditions via the use of high-throughput sequencing. Access to genomic technology and resultant data is no longer limited to clinicians, geneticists and bioinformaticians, however; ongoing commercialisation gives patients themselves ever greater access to sequencing services. We report an increasingly common medical scenario by describing two neuromuscular patients-a mother and adult son-whose consumer access to whole-genome sequencing affected their diagnostic journey

Simultaneous TE Analysis of 19 Heliconiine Butterflies Yields Novel Insights into Rapid TE-Based Genome Diversification and Multiple SINE Births and Deaths

Transposable elements (TEs) play major roles in the evolution of genome structure and function. However, because of their repetitive nature, they are difficult to annotate and discovering the specific roles they may play in a lineage can be a daunting task. Heliconiine butterflies are models for the study of multiple evolutionary processes including phenotype evolution and hybridization. We attempted to determine how TEs may play a role in the diversification of genomes within this clade by performing a detailed examination of TE content and accumulation in 19 species whose genomes were recently sequenced. We found that TE content has diverged substantially and rapidly in the time since several subclades shared a common ancestor with each lineage harboring a unique TE repertoire. Several novel SINE lineages have been established that are restricted to a subset of species. Furthermore, the previously described SINE, Metulj, appears to have gone extinct in two subclades while expanding to significant numbers in others. This diversity in TE content and activity has the potential to impact how heliconiine butterflies continue to evolve and diverge

Growing old, yet staying young: The role of telomeres in bats' exceptional longevity

Understanding aging is a grand challenge in biology. Exceptionally long-lived animals have mechanisms that underpin extreme longevity. Telomeres are protective nucleotide repeats on chromosome tips that shorten with cell division, potentially limiting life span. Bats are the longest-lived mammals for their size, but it is unknown whether their telomeres shorten. Using >60 years of cumulative mark-recapture field data, we show that telomeres shorten with age inRhinolophus ferrumequinumandMiniopterus schreibersii, but not in the bat genus with greatest longevity,Myotis. As in humans, telomerase is not expressed inMyotis myotisblood or fibroblasts. Selection tests on telomere maintenance genes show thatATMandSETX, which repair and prevent DNA damage, potentially mediate telomere dynamics inMyotisbats. Twenty-one telomere maintenance genes are differentially expressed inMyotis, of which 14 are enriched for DNA repair, and 5 for alternative telomere-lengthening mechanisms. We demonstrate how telomeres, telomerase, and DNA repair genes have contributed to the evolution of exceptional longevity inMyotisbats, advancing our understanding of healthy aging

Voluntary exercise can strengthen the circadian system in aged mice

Consistent daily rhythms are important to healthy aging according to studies linking disrupted circadian rhythms with negative health impacts. We studied the effects of age and exercise on baseline circadian rhythms and on the circadian system's ability to respond to the perturbation induced by an 8 h advance of the light:dark (LD) cycle as a test of the system's robustness. Mice (male, mPer2luc/C57BL/6) were studied at one of two ages: 3.5 months (n = 39) and >18 months (n = 72). We examined activity records of these mice under entrained and shifted conditions as well as mPER2::LUC measures ex vivo to assess circadian function in the suprachiasmatic nuclei (SCN) and important target organs. Age was associated with reduced running wheel use, fragmentation of activity, and slowed resetting in both behavioral and molecular measures. Furthermore, we observed that for aged mice, the presence of a running wheel altered the amplitude of the spontaneous firing rate rhythm in the SCN in vitro. Following a shift of the LD cycle, both young and aged mice showed a change in rhythmicity properties of the mPER2::LUC oscillation of the SCN in vitro, and aged mice exhibited longer lasting internal desynchrony. Access to a running wheel alleviated some age-related changes in the circadian system. In an additional experiment, we replicated the effect of the running wheel, comparing behavioral and in vitro results from aged mice housed with or without a running wheel (>21 months, n = 8 per group, all examined 4 days after the shift). The impact of voluntary exercise on circadian rhythm properties in an aged animal is a novel finding and has implications for the health of older people living with environmentally induced circadian disruption

A Relativistic Type Ibc Supernova Without a Detected Gamma-ray Burst

Long duration gamma-ray bursts (GRBs) mark the explosive death of some massive stars and are a rare sub-class of Type Ibc supernovae (SNe Ibc). They are distinguished by the production of an energetic and collimated relativistic outflow powered by a central engine (an accreting black hole or neutron star). Observationally, this outflow is manifested in the pulse of gamma-rays and a long-lived radio afterglow. To date, central engine-driven SNe have been discovered exclusively through their gamma-ray emission, yet it is expected that a larger population goes undetected due to limited satellite sensitivity or beaming of the collimated emission away from our line-of-sight. In this framework, the recovery of undetected GRBs may be possible through radio searches for SNe Ibc with relativistic outflows. Here we report the discovery of luminous radio emission from the seemingly ordinary Type Ibc SN 2009bb, which requires a substantial relativistic outflow powered by a central engine. The lack of a coincident GRB makes SN 2009bb the first engine-driven SN discovered without a detected gamma-ray signal. A comparison with our extensive radio survey of SNe Ibc reveals that the fraction harboring central engines is low, ~1 percent, measured independently from, but consistent with, the inferred rate of nearby GRBs. Our study demonstrates that upcoming optical and radio surveys will soon rival gamma-ray satellites in pinpointing the nearest engine-driven SNe. A similar result for a different supernova is reported independently.Comment: To appear in Nature on Jan 28 2010. Embargoed for discussion in the press until 13:00 US Eastern Time on Jan 27 (Accepted version, 27 pages, Manuscript and Suppl. Info.

Interacting Supernovae: Types IIn and Ibn

Supernovae (SNe) that show evidence of strong shock interaction between their ejecta and pre-existing, slower circumstellar material (CSM) constitute an interesting, diverse, and still poorly understood category of explosive transients. The chief reason that they are extremely interesting is because they tell us that in a subset of stellar deaths, the progenitor star may become wildly unstable in the years, decades, or centuries before explosion. This is something that has not been included in standard stellar evolution models, but may significantly change the end product and yield of that evolution, and complicates our attempts to map SNe to their progenitors. Another reason they are interesting is because CSM interaction is an efficient engine for making bright transients, allowing super-luminous transients to arise from normal SN explosion energies, and allowing transients of normal SN luminosities to arise from sub-energetic explosions or low radioactivity yield. CSM interaction shrouds the fast ejecta in bright shock emission, obscuring our normal view of the underlying explosion, and the radiation hydrodynamics of the interaction is challenging to model. The CSM interaction may also be highly non-spherical, perhaps linked to binary interaction in the progenitor system. In some cases, these complications make it difficult to definitively tell the difference between a core-collapse or thermonuclear explosion, or to discern between a non-terminal eruption, failed SN, or weak SN. Efforts to uncover the physical parameters of individual events and connections to possible progenitor stars make this a rapidly evolving topic that continues to challenge paradigms of stellar evolution.Comment: Final draft of a chapter in the "SN Handbook". Accepted. 25 pages, 3 fig