A pp-adic Approach to the Weil Representation of Discriminant Forms Arising from Even Lattices

Suppose that $M$ is an even lattice with dual $M^{*}$ and level $N$. Then the group $Mp_{2}(\mathbb{Z})$, which is the unique non-trivial double cover of $SL_{2}(\mathbb{Z})$, admits a representation $\rho_{M}$, called the Weil representation, on the space $\mathbb{C}[M^{*}/M]$. The main aim of this paper is to show how the formulae for the $\rho_{M}$-action of a general element of $Mp_{2}(\mathbb{Z})$ can be obtained by a direct evaluation which does not depend on ``external objects'' such as theta functions. We decompose the Weil representation $\rho_{M}$ into $p$-parts, in which each $p$-part can be seen as subspace of the Schwartz functions on the $p$-adic vector space $M_{\mathbb{Q}_{p}}$. Then we consider the Weil representation of $Mp_{2}(\mathbb{Q}_{p})$ on the space of Schwartz functions on $M_{\mathbb{Q}_{p}}$, and see that restricting to $Mp_{2}(\mathbb{Z})$ just gives the $p$-part of $\rho_{M}$ again. The operators attained by the Weil representation are not always those appearing in the formulae from 1964, but are rather their multiples by certain roots of unity. For this, one has to find which pair of elements, lying over a matrix in $SL_{2}(\mathbb{Q}_{p})$, belong to the metaplectic double cover. Some other properties are also investigated.Comment: 29 pages, shortened a lo

Pneumonia care and the nursing home: a qualitative descriptive study of resident and family member perspectives

BACKGROUND: Nursing home residents are frequently sent to hospital for diagnostic tests or to receive acute health care services. These transfers are both costly and for some, associated with increased risks. Although improved technology allows long-term care facilities to deliver more complex health care on site, if this is to become a trend then residents and family members must see the value of such care. This qualitative study examined resident and family member perspectives on in situ care for pneumonia. METHODS: A qualitative descriptive study design was used. Participants were residents and family members of residents treated for pneumonia drawn from a larger randomized controlled trial of a clinical pathway to manage nursing home-acquired pneumonia on-site. A total of 14 in-depth interviews were conducted. Interview data were analyzed using the editing style, described by Miller and Crabtree, to identify key themes. RESULTS: Both residents and family members preferred that pneumonia be treated in the nursing home, where possible. They both felt that caring and attention are key aspects of care which are more easily accessible in the nursing home setting. However, residents felt that staff or doctors should make the decision whether to hospitalize them, whereas family members wanted to be consulted or involved in the decision-making process. CONCLUSION: These findings suggest that interventions to reduce hospitalization of nursing home residents with pneumonia are consistent with resident and family member preferences

3T3 Cell Lines Stably Expressing Pax6 or Pax6(5a) – A New Tool Used for Identification of Common and Isoform Specific Target Genes

Pax6 and Pax6(5a) are two isoforms of the evolutionary conserved Pax6 gene often co-expressed in specific stochiometric relationship in the brain and the eye during development. The Pax6(5a) protein differs from Pax6 by having a 14 amino acid insert in the paired domain, causing the two proteins to have different DNA binding specificities. Difference in functions during development is proven by the fact that mutations in the 14 amino acid insertion for Pax6(5a) give a slightly different eye phenotype than the one described for Pax6. Whereas quite many Pax6 target genes have been published during the last years, few Pax6(5a) specific target genes have been reported on. However, target genes identified by Pax6 knockout studies can probably be Pax6(5a) targets as well, since this isoform also will be affected by the knockout. In order to identify new Pax6 target genes, and to try to distinguish between genes regulated by Pax6 and Pax6(5a), we generated FlpIn-3T3 cell lines stably expressing Pax6 or Pax6(5a). RNA was harvested from these cell lines and used in gene expression microarrays where we identified a number of genes differentially regulated by Pax6 and Pax6(5a). A majority of these were associated with the extracellular region. By qPCR we verified that Ncam1, Ngef, Sphk1, Dkk3 and Crtap are Pax6(5a) specific target genes, while Tgfbi, Vegfa, EphB2, Klk8 and Edn1 were confirmed as Pax6 specific target genes. Nbl1, Ngfb and seven genes encoding different glycosyl transferases appeared to be regulated by both. Direct binding to the promoters of Crtap, Ctgf, Edn1, Dkk3, Pdgfb and Ngef was verified by ChIP. Furthermore, a change in morphology of the stably transfected Pax6 and Pax6(5a) cells was observed, and the Pax6 expressing cells were shown to have increased proliferation and migration capacities

Multi-messenger observations of a binary neutron star merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ~1.7 s with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of 40+8-8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 Mo. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ~40 Mpc) less than 11 hours after the merger by the One- Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ~9 and ~16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta

Efficient Subtractive Cloning of Genes Activated by Lipopolysaccharide and Interferon γ in Primary-Cultured Cortical Cells of Newborn Mice.

Innate immune responses play a central role in neuroprotection and neurotoxicity during inflammatory processes that are triggered by pathogen-associated molecular pattern-exhibiting agents such as bacterial lipopolysaccharide (LPS) and that are modulated by inflammatory cytokines such as interferon γ (IFNγ). Recent findings describing the unexpected complexity of mammalian genomes and transcriptomes have stimulated further identification of novel transcripts involved in specific physiological and pathological processes, such as the neural innate immune response that alters the expression of many genes. We developed a system for efficient subtractive cloning that employs both sense and antisense cRNA drivers, and coupled it with in-house cDNA microarray analysis. This system enabled effective direct cloning of differentially expressed transcripts, from a small amount (0.5 µg) of total RNA. We applied this system to isolation of genes activated by LPS and IFNγ in primary-cultured cortical cells that were derived from newborn mice, to investigate the mechanisms involved in neuroprotection and neurotoxicity in maternal/perinatal infections that cause various brain injuries including periventricular leukomalacia. A number of genes involved in the immune and inflammatory response were identified, showing that neonatal neuronal/glial cells are highly responsive to LPS and IFNγ. Subsequent RNA blot analysis revealed that the identified genes were activated by LPS and IFNγ in a cooperative or distinctive manner, thereby supporting the notion that these bacterial and cellular inflammatory mediators can affect the brain through direct but complicated pathways. We also identified several novel clones of apparently non-coding RNAs that potentially harbor various regulatory functions. Characterization of the presently identified genes will give insights into mechanisms and interventions not only for perinatal infection-induced brain damage, but also for many other innate immunity-related brain disorders

Silicate mineralogy at the surface of Mercury

NASA’s MESSENGER spacecraft has revealed geochemical diversity across Mercury’s volcanic crust. Near-infrared to ultraviolet spectra and images have provided evidence for the Fe2+-poor nature of silicate minerals, magnesium sulfide minerals in hollows and a darkening component attributed to graphite, but existing spectral data is insufficient to build a mineralogical map for the planet. Here we investigate the mineralogical variability of silicates in Mercury’s crust using crystallization experiments on magmas with compositions and under reducing conditions expected for Mercury. We find a common crystallization sequence consisting of olivine, plagioclase, pyroxenes and tridymite for all magmas tested. Depending on the cooling rate, we suggest that lavas on Mercury are either fully crystallized or made of a glassy matrix with phenocrysts. Combining the experimental results with geochemical mapping, we can identify several mineralogical provinces: the Northern Volcanic Plains and Smooth Plains, dominated by plagioclase, the High-Mg province, strongly dominated by forsterite, and the Intermediate Plains, comprised of forsterite, plagioclase and enstatite. This implies a temporal evolution of the mineralogy from the oldest lavas, dominated by mafic minerals, to the youngest lavas, dominated by plagioclase, consistent with progressive shallowing and decreasing degree of mantle melting over time