Three routes to the exact asymptotics for the one-dimensional quantum walk

We demonstrate an alternative method for calculating the asymptotic behaviour of the discrete one-coin quantum walk on the infinite line, via the Jacobi polynomials that arise in the path integral representation. This is significantly easier to use than the Darboux method. It also provides a single integral representation for the wavefunction that works over the full range of positions, $n,$ including throughout the transitional range where the behaviour changes from oscillatory to exponential. Previous analyses of this system have run into difficulties in the transitional range, because the approximations on which they were based break down here. The fact that there are two different kinds of approach to this problem (Path Integral vs. Schr\"{o}dinger wave mechanics) is ultimately a manifestation of the equivalence between the path-integral formulation of quantum mechanics and the original formulation developed in the 1920s. We discuss how and why our approach is related to the two methods that have already been used to analyse these systems.Comment: 25 pages, AMS preprint format, 4 figures as encapsulated postscript. Replaced because there were sign errors in equations (80) & (85) and Lemma 2 of the journal version (v3

The degree of alignment between circumbinary disks and their binary hosts

Funding: I.C. was supported by NASA through the NASA Hubble Fellowship grant HST-HF2-51405.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555.All four circumbinary (CB) protoplanetary disks orbiting short-period (P < 20 days) double-lined spectroscopic binaries (SB2s)—a group that includes UZ Tau E, for which we present new Atacama Large Millimeter/Submillimeter Array data—exhibit sky-plane inclinations idisk that match, to within a few degrees, the sky-plane inclinations i⋆ of their stellar hosts. Although for these systems the true mutual inclinations θ between disk and binary cannot be directly measured because relative nodal angles are unknown, the near coincidence of i disk and i⋆ suggests that θ is small for these most compact of systems. We confirm this hypothesis using a hierarchical Bayesian analysis, showing that 68% of CB disks around short-period SB2s have θ < 3.°0. Near coplanarity of CB disks implies near coplanarity of CB planets discovered by Kepler, which in turn implies that the occurrence rate of close-in CB planets is similar to that around single stars. By contrast, at longer periods ranging from 30 to 105 days (where the nodal degeneracy can be broken via, e.g., binary astrometry), CB disks exhibit a wide range of mutual inclinations, from coplanar to polar. Many of these long-period binaries are eccentric, as their component stars are too far separated to be tidally circularized. We discuss how theories of binary formation and disk-binary gravitational interactions can accommodate all these observations.Publisher PDFPeer reviewe

Hierarchical Star Formation in Nearby LEGUS Galaxies

Hierarchical structure in ultraviolet images of 12 late-type LEGUS galaxies is studied by determining the numbers and fluxes of nested regions as a function of size from ~1 to ~200 pc, and the number as a function of flux. Two starburst dwarfs, NGC 1705 and NGC 5253, have steeper number-size and flux-size distributions than the others, indicating high fractions of the projected areas filled with star formation. Nine subregions in 7 galaxies have similarly steep number-size slopes, even when the whole galaxies have shallower slopes. The results suggest that hierarchically structured star-forming regions several hundred parsecs or larger represent common unit structures. Small galaxies dominated by only a few of these units tend to be starbursts. The self-similarity of young stellar structures down to parsec scales suggests that star clusters form in the densest parts of a turbulent medium that also forms loose stellar groupings on larger scales. The presence of super star clusters in two of our starburst dwarfs would follow from the observed structure if cloud and stellar subregions more readily coalesce when self-gravity in the unit cell contributes more to the total gravitational potential.Comment: 9 pages, 4 figures, accepted for ApJ

Complex exon-intron marking by histone modifications is not determined solely by nucleosome distribution

It has recently been shown that nucleosome distribution, histone modifications and RNA polymerase II (Pol II) occupancy show preferential association with exons (“exon-intron marking”), linking chromatin structure and function to co-transcriptional splicing in a variety of eukaryotes. Previous ChIP-sequencing studies suggested that these marking patterns reflect the nucleosomal landscape. By analyzing ChIP-chip datasets across the human genome in three cell types, we have found that this marking system is far more complex than previously observed. We show here that a range of histone modifications and Pol II are preferentially associated with exons. However, there is noticeable cell-type specificity in the degree of exon marking by histone modifications and, surprisingly, this is also reflected in some histone modifications patterns showing biases towards introns. Exon-intron marking is laid down in the absence of transcription on silent genes, with some marking biases changing or becoming reversed for genes expressed at different levels. Furthermore, the relationship of this marking system with splicing is not simple, with only some histone modifications reflecting exon usage/inclusion, while others mirror patterns of exon exclusion. By examining nucleosomal distributions in all three cell types, we demonstrate that these histone modification patterns cannot solely be accounted for by differences in nucleosome levels between exons and introns. In addition, because of inherent differences between ChIP-chip array and ChIP-sequencing approaches, these platforms report different nucleosome distribution patterns across the human genome. Our findings confound existing views and point to active cellular mechanisms which dynamically regulate histone modification levels and account for exon-intron marking. We believe that these histone modification patterns provide links between chromatin accessibility, Pol II movement and co-transcriptional splicing

The Initial Mass Function and Disk Frequency of the Rho Ophiuchi Cloud: An Extinction-Limited Sample

We have completed an optical spectroscopic survey of an unbiased, extinction-limited sample of candidate young stars covering 1.3 square degrees of the Rho Ophiuchi star forming region. While infrared, X-ray, and optical surveys of the cloud have identified many young stellar objects (YSOs), these surveys are biased towards particular stages of stellar evolution and are not optimal for studies of the disk frequency and initial mass function.We have obtained over 300 optical spectra to help identify 135 association members based on the presence of H-alpha in emission, lithium absorption, X-ray emission, a mid-infrared excess, a common proper motion, reflection nebulosity, and/or extinction considerations. Spectral types along with R and I band photometry were used to derive effective temperatures and bolometric luminosities for association members to compare with theoretical tracks and isochrones for pre-main-sequence stars. An average age of 3.1 Myr is derived for this population which is intermediate between that of objects embedded in the cloud core of Rho Ophiuchi and low mass stars in the Upper Scorpius subgroup. Consistent with this age we find a circumstellar disk frequency of 27% plus or minus 5%. We also constructed an initial mass function for an extinction-limited sample of 123 YSOs (A_v less than or equal to 8 mag), which is consistent with the field star initial mass function for YSOs with masses > 0.2 M_sun. There may be a deficit of brown dwarfs but this result relies on completeness corrections and requires confirmation.Comment: 46 pages, 7 figures, 4 table

Evanescence in Coined Quantum Walks

In this paper we complete the analysis begun by two of the authors in a previous work on the discrete quantum walk on the line [J. Phys. A 36:8775-8795 (2003) quant-ph/0303105 ]. We obtain uniformly convergent asymptotics for the "exponential decay'' regions at the leading edges of the main peaks in the Schr{\"o}dinger (or wave-mechanics) picture. This calculation required us to generalise the method of stationary phase and we describe this extension in some detail, including self-contained proofs of all the technical lemmas required. We also rigorously establish the exact Feynman equivalence between the path-integral and wave-mechanics representations for this system using some techniques from the theory of special functions. Taken together with the previous work, we can now prove every theorem by both routes.Comment: 32 pages AMS LaTeX, 5 figures in .eps format. Rewritten in response to referee comments, including some additional references. v3: typos fixed in equations (131), (133) and (134). v5: published versio

No Major Change in vCJD Agent Strain after Secondary Transmission via Blood Transfusion

The identification of transmission of variant Creutzfeldt-Jakob disease (vCJD) by blood transfusion has prompted investigation to establish whether there has been any alteration in the vCJD agent following this route of secondary transmission. Any increase in virulence or host adaptation would require a reassessment of the risk analyses relating to the possibility of a significant secondary outbreak of vCJD. Since there are likely to be carriers of the vCJD agent in the general population, there is a potential for further infection by routes such as blood transfusion or contaminated surgical instruments.We inoculated both wild-type and transgenic mice with material from the first case of transfusion associated vCJD infection.The strain transmission properties of blood transfusion associated vCJD infection show remarkable similarities to the strain of vCJD associated with transmission from bovine spongiform encephalopathy (BSE).Although it has been hypothesized that adaptation of the BSE agent through secondary passage in humans may result in a greater risk of onward transmission due to an increased virulence of the agent for humans, our data presented here in two murine models suggest no significant alterations to transmission efficiency of the agent following human-to-human transmission of vCJD

Longer fixation duration while viewing face images

The spatio-temporal properties of saccadic eye movements can be influenced by the cognitive demand and the characteristics of the observed scene. Probably due to its crucial role in social communication, it is argued that face perception may involve different cognitive processes compared with non-face object or scene perception. In this study, we investigated whether and how face and natural scene images can influence the patterns of visuomotor activity. We recorded monkeys’ saccadic eye movements as they freely viewed monkey face and natural scene images. The face and natural scene images attracted similar number of fixations, but viewing of faces was accompanied by longer fixations compared with natural scenes. These longer fixations were dependent on the context of facial features. The duration of fixations directed at facial contours decreased when the face images were scrambled, and increased at the later stage of normal face viewing. The results suggest that face and natural scene images can generate different patterns of visuomotor activity. The extra fixation duration on faces may be correlated with the detailed analysis of facial features

Polydnavirus genomes reflect their dual roles as mutualists and pathogens

AbstractSymbionts often exhibit significant reductions in genome complexity while pathogens often exhibit increased complexity through acquisition and diversification of virulence determinants. A few organisms have evolved complex life cycles in which they interact as symbionts with one host and pathogens with another. How the predicted and opposing influences of symbiosis and pathogenesis affect genome evolution in such instances, however, is unclear. The Polydnaviridae is a family of double-stranded (ds) DNA viruses associated with parasitoid wasps that parasitize other insects. Polydnaviruses (PDVs) only replicate in wasps but infect and cause severe disease in parasitized hosts. This disease is essential for survival of the parasitoid's offspring. Thus, a true mutualism exists between PDVs and wasps as viral transmission depends on parasitoid survival and parasitoid survival depends on viral infection of the wasp's host. To investigate how life cycle and ancestry affect PDVs, we compared the genomes of Campoletis sonorensis ichnovirus (CsIV) and Microplitis demolitor bracovirus (MdBV). CsIV and MdBV have no direct common ancestor, yet their encapsidated genomes share several features including segmentation, diversification of virulence genes into families, and the absence of genes required for replication. In contrast, CsIV and MdBV share few genes expressed in parasitized hosts. We conclude that the similar organizational features of PDV genomes reflect their shared life cycle but that PDVs associated with ichneumonid and braconid wasps have likely evolved different strategies to cause disease in the wasp's host and promote parasitoid survival