Trapping in the random conductance model

We consider random walks on $\Z^d$ among nearest-neighbor random conductances which are i.i.d., positive, bounded uniformly from above but whose support extends all the way to zero. Our focus is on the detailed properties of the paths of the random walk conditioned to return back to the starting point at time $2n$. We show that in the situations when the heat kernel exhibits subdiffusive decay --- which is known to occur in dimensions $d\ge4$ --- the walk gets trapped for a time of order $n$ in a small spatial region. This shows that the strategy used earlier to infer subdiffusive lower bounds on the heat kernel in specific examples is in fact dominant. In addition, we settle a conjecture concerning the worst possible subdiffusive decay in four dimensions.Comment: 21 pages, version to appear in J. Statist. Phy

The Age of the Oldest Stars in the Local Galactic Disk From Hipparcos Parallaxes of G and K Subgiants

We review the history of the discovery of field subgiant stars and their importance in the age dating of the Galactic disk. We use the cataloged data from the Hipparcos satellite in this latter capacity. Based on Hipparcos parallaxes accurate to 10% or better, the absolute magnitude of the lower envelope of the nearly horizontal subgiant sequence for field stars in the H-R diagram for B-V colors between 0.85 and 1.05 is measured to be M_V = 4.03 +/- 0.06. The age of the field stars in the solar neighborhood is found to be 7.9 +/- 0.7 Gyr by fitting the theoretical isochrones for [Fe/H] = +0.37 to the lower envelope of the Hipparcos subgiants. The same grid of isochrones yields ages, in turn, of 4.0 +/- 0.2 Gyr, 6.2 +/- 0.5 Gyr, and 7.5 to 10 Gyr for the old Galactic clusters M67, NGC188, and NGC6791. The ages of both the Galactic disk in the solar neighborhood and of NGC6791 are, nevertheless, likely between 3 and 5 Gyr younger than the oldest halo globular clusters, which have ages of 13.5 Gyr. The most significant results are (1) the supermetallicity of the oldest local disk stars, and (2) the large age difference between the most metal-poor component of the halo and the thick and thin disk in the solar neighborhood. These facts are undoubtedly related and pose again the problem of the proper scenario for the timing of events in the formation of the halo and the Galactic disk in the solar neighborhood. [Abstract Abridged]Comment: 44 pages, 12 Figures; accepted for publication in PASP; high resolution versions of Figures 1, 2, 6 and 9 available at http://bubba.ucdavis.edu/~lubin/Sandage

Horizontal Branch evolution, metallicity and sdB stars

Context. Abundance anomalies have been observed in field sdB stars and in nearly all Horizontal Branch (HB) stars of globular clusters with Teff > 11 000K whatever be the cluster metallicity. Aims. The aim is to determine the abundance variations to be expected in sdB stars and in HB stars of metallicities Z \geq 0.0001 and what observed abundances teach us about hydrodynamical processes competing with atomic diffusion. Methods. Complete stellar evolution models, including the effects of atomic diffusion and radiative acceleration, have been computed from the zero age main-sequence for metallicities of Z0 = 0.0001, 0.001, 0.004 and 0.02. On the HB the masses were selected to cover the Teff interval from 7000 to 37000K. Some 60 evolutionary HB models were calculated. The calculations of surface abundance anomalies during the horizontal branch depend on one parameter, the surface mixed mass. Results. For sdB stars with Teff 11 000K in all observed clusters, independent of metallicity, it was found that most observed abundance anomalies (even up to ~ x 200) were compatible, within error bars, with expected abundances. A mixed mass of ~1.E-7 M\odot was determined by comparison with observations. Conclusions. Observations of globular cluster HB stars with Teff > 11 000K and of sdB stars with Teff < 37 000K suggest that most observed abundance anomalies can be explained by element separation driven by radiative acceleration occuring at a mass fraction of ~1.E-7 M\odot. Mass loss or turbulence appear to limit the separation between 1.E-7 M\odot and the surface.Comment: Accepted for publication by A&

Cardiac expression of the cystic fibrosis transmembrane conductance regulator involves novel Exon 1 usage to produce a unique amino-terminal protein

Cystic fibrosis is caused by mutations in the cystic fibrosis transmembrane conductance regulator (CFTR) gene, which encodes a chloride channel present in many cells. In cardiomyocytes, we report that multiple exon 1 usage and alternative splicing produces four CFTR transcripts, with different 5'-untranslated regions, CFTRTRAD-139, CFTR-1C/-1A, CFTR-1C, and CFTR-1B. CFTR transcripts containing the novel upstream exons (exons -1C, -1B, and -1A) represent more than 90% of cardiac expressed CFTR mRNA. Regulation of cardiac CFTR expression, in response to developmental and pathological stimuli, is exclusively due to the modulation of CFTR-1C and CFTR-1C/-1A expression. Upstream open reading frames have been identified in the 5'-untranslated regions of all CFTR transcripts that, in conjunction with adjacent stem-loop structures, modulate the efficiency of translation initiation at the AUG codon of the main CFTR coding region in CFTRTRAD-139 and CFTR-1C/-1A transcripts. Exon(-1A), only present in CFTR-1C/-1A transcripts, encodes an AUG codon that is in-frame with the main CFTR open reading frame, the efficient translation of which produces a novel CFTR protein isoform with a curtailed amino terminus. As the expression of this CFTR transcript parallels the spatial and temporal distribution of the cAMP-activated whole-cell current density in normal and diseased hearts, we suggest that CFTR-1C/-1A provides the molecular basis for the cardiac cAMP-activated chloride channel. Our findings provide further insight into the complex nature of in vivo CFTR expression, to which multiple mRNA transcripts, protein isoforms, and post-transcriptional regulatory mechanisms are now added

Visuo-spatial cognition in Williams syndrome: Reviewing and accounting for the strengths and weaknesses in performance

Individuals with Williams syndrome typically show relatively poor visuo-spatial abilities in comparison to stronger verbal skills. However, individuals' level of performance is not consistent across all visuo-spatial tasks. The studies assessing visuo-spatial functioning in Williams syndrome are critically reviewed, in order to provide a clear pattern of the relative difficulty of these tasks. This prompts a possible explanation of the variability in performance seen which focuses on the processing demands of some of these tasks. Individuals with Williams syndrome show an atypical processing style on tests of construction, which does not affect tests of perception

Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States

The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects that channel noise can have on neural dynamics are generally studied using numerical simulations of stochastic models. Algorithms based on discrete Markov Chains (MC) seem to be the most reliable and trustworthy, but even optimized algorithms come with a non-negligible computational cost. Diffusion Approximation (DA) methods use Stochastic Differential Equations (SDE) to approximate the behavior of a number of MCs, considerably speeding up simulation times. However, model comparisons have suggested that DA methods did not lead to the same results as in MC modeling in terms of channel noise statistics and effects on excitability. Recently, it was shown that the difference arose because MCs were modeled with coupled activation subunits, while the DA was modeled using uncoupled activation subunits. Implementations of DA with coupled subunits, in the context of a specific kinetic scheme, yielded similar results to MC. However, it remained unclear how to generalize these implementations to different kinetic schemes, or whether they were faster than MC algorithms. Additionally, a steady state approximation was used for the stochastic terms, which, as we show here, can introduce significant inaccuracies. We derived the SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable - allowing an easy and efficient DA implementation. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods.Comment: 32 text pages, 10 figures, 1 supplementary text + figur

Position of the Third Na+ Site in the Aspartate Transporter GltPh and the Human Glutamate Transporter, EAAT1

Glutamate transport via the human excitatory amino acid transporters is coupled to the co-transport of three Na+ ions, one H+ and the counter-transport of one K+ ion. Transport by an archaeal homologue of the human glutamate transporters, GltPh, whose three dimensional structure is known is also coupled to three Na+ ions but only two Na+ ion binding sites have been observed in the crystal structure of GltPh. In order to fully utilize the GltPh structure in functional studies of the human glutamate transporters, it is essential to understand the transport mechanism of GltPh and accurately determine the number and location of Na+ ions coupled to transport. Several sites have been proposed for the binding of a third Na+ ion from electrostatic calculations and molecular dynamics simulations. In this study, we have performed detailed free energy simulations for GltPh and reveal a new site for the third Na+ ion involving the side chains of Threonine 92, Serine 93, Asparagine 310, Aspartate 312, and the backbone of Tyrosine 89. We have also studied the transport properties of alanine mutants of the coordinating residues Threonine 92 and Serine 93 in GltPh, and the corresponding residues in a human glutamate transporter, EAAT1. The mutant transporters have reduced affinity for Na+ compared to their wild type counterparts. These results confirm that Threonine 92 and Serine 93 are involved in the coordination of the third Na+ ion in GltPh and EAAT1

AmFm and lithium gap stars: Stellar evolution models with mass loss

A thorough study of the effects of mass loss on internal and surface abundances of A and F stars is carried out in order to constrain mass loss rates for these stars, as well as further elucidate some of the processes which compete with atomic diffusion. Self-consistent stellar evolution models of 1.3 to 2.5 M_sun stars including atomic diffusion and radiative accelerations for all species within the OPAL opacity database were computed with mass loss and compared to observations as well as previous calculations with turbulent mixing. Models with unseparated mass loss rates between 5 x 10^-14 and 10^-13 M_sun/yr reproduce observations for many cluster AmFm stars as well as Sirius A and o Leonis. These models also explain cool Fm stars, but not the Hyades lithium gap. Like turbulent mixing, these mass loss rates reduce surface abundance anomalies; however, their effects are very different with respect to internal abundances. For most of the main sequence lifetime of an A or F star, surface abundances in the presence of such mass loss depend on separation which takes place between log(Delta M/M_star)= -6 and -5. The current observational constraints do not allow us to conclude that mass loss is to be preferred over turbulent mixing (induced by rotation or otherwise) in order to explain the AmFm phenomenon. Internal concentration variations which could be detectable through asteroseismic tests should provide further information. If atomic diffusion coupled with mass loss are to explain the Hyades Li gap, the wind would need to be separated.Comment: 27 pages, 25 figures, accepted for publication in A&