A solution to the Al-Salam--Chihara moment problem

We study the $q$-hypergeometric difference operator $L$ on a particular Hilbert space. In this setting $L$ can be considered as an extension of the Jacobi operator for $q^{-1}$-Al-Salam--Chihara polynomials. Spectral analysis leads to unitarity and an explicit inverse of a $q$-analog of the Jacobi function transform. As a consequence a solution of the Al-Salam--Chihara indeterminate moment problem is obtained.Comment: 22 page

Evolution of Skull and Mandible Shape in Cats (Carnivora: Felidae)

The felid family consists of two major subgroups, the sabretoothed and the feline cats, to which all extant species belong, and are the most anatomically derived of all carnivores for predation on large prey with a precision killing bite. There has been much controversy and uncertainty about why the skulls and mandibles of sabretoothed and feline cats evolved to become so anatomically divergent, but previous models have focused on single characters and no unifying hypothesis of evolutionary shape changes has been formulated. Here I show that the shape of the skull and mandible in derived sabrecats occupy entirely different positions within overall morphospace from feline cats, and that the evolution of skull and mandible shape has followed very different paths in the two subgroups. When normalised for body-size differences, evolution of bite forces differ markedly in the two groups, and are much lower in derived sabrecats, and they show a significant relationship with size and cranial shape, whereas no such relationship is present in feline cats. Evolution of skull and mandible shape in modern cats has been governed by the need for uniform powerful biting irrespective of body size, whereas in sabrecats, shape evolution was governed by selective pressures for efficient predation with hypertrophied upper canines at high gape angles, and bite forces were secondary and became progressively weaker during sabrecat evolution. The current study emphasises combinations of new techniques for morphological shape analysis and biomechanical studies to formulate evolutionary hypotheses for difficult groups

Mutations in FKBP10 can cause a severe form of isolated Osteogenesis imperfecta

<p>Abstract</p> <p>Background</p> <p>Mutations in the <it>FKBP10 </it>gene were first described in patients with Osteogenesis imperfecta type III. Two follow up reports found <it>FKBP10 </it>mutations to be associated with Bruck syndrome type 1, a rare disorder characterized by congenital contractures and bone fragility. This raised the question if the patients in the first report indeed had isolated Osteogenesis imperfecta or if Bruck syndrome would have been the better diagnosis.</p> <p>Methods</p> <p>The patients described here are affected by severe autosomal recessive Osteogenesis imperfecta without contractures.</p> <p>Results</p> <p>Homozygosity mapping identified <it>FKBP10 </it>as a candidate gene, and sequencing revealed a base pair exchange that causes a C-terminal premature stop codon in this gene.</p> <p>Conclusions</p> <p>Our study demonstrates that <it>FKBP10 </it>mutations not only cause Bruck syndrome or Osteogenesis imperfecta type III but can result in a severe type of isolated Osteogenesis imperfecta type IV with prenatal onset. Furthermore, it adds dentinogenesis imperfecta to the spectrum of clinical symptoms associated with <it>FKBP10 </it>mutations.</p

The Making of a Monster: Postnatal Ontogenetic Changes in Craniomandibular Shape in the Great Sabercat Smilodon

Derived sabercats had craniomandibular morphologies that in many respects were highly different from those of extant felids, and this has often been interpreted functionally as adaptations for predation at extreme gape angles with hypertrophied upper canines. It is unknown how much of this was a result of intraspecific postnatal ontogeny, since juveniles of sabercats are rare and no quantitative study has been made of craniomandibular ontogeny. Postnatal ontogenetic craniomandibular shape changes in two morphologically derived sabercats, Smilodon fatalis and S. populator, were analysed using geometric morphometrics and compared to three species of extant pantherines, the jaguar, tiger, and Sunda clouded leopard. Ontogenetic shape changes in Smilodon usually involved the same areas of the cranium and mandible as in extant pantherines, and large-scale modularization was similar, suggesting that such may have been the case for all felids, since it followed the same trends previously observed in other mammals. However, in other respects Smilodon differed from extant pantherines. Their crania underwent much greater and more localised ontogenetic shape changes than did the mandibles, whereas crania and mandibles of extant pantherines underwent smaller, fewer and less localised shape changes. Ontogenetic shape changes in the two species of Smilodon are largely similar, but differences are also present, notably those which may be tied to the presence of larger upper canines in S. populator. Several of the specialized cranial characters differentiating adult Smilodon from extant felids in a functional context, which are usually regarded as evolutionary adaptations for achieving high gape angles, are ontogenetic, and in several instances ontogeny appears to recapitulate phylogeny to some extent. No such ontogenetic evolutionary adaptive changes were found in the extant pantherines. Evolution in morphologically derived sabercats involved greater cranial ontogenetic changes than among extant felids, resulting in greatly modified adult craniomandibular morphologies

Stochastic Gravity: Theory and Applications

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hol

A Novel Mutation in LEPRE1 That Eliminates Only the KDEL ER- Retrieval Sequence Causes Non-Lethal Osteogenesis Imperfecta

Prolyl 3-hydroxylase 1 (P3H1), encoded by the LEPRE1 gene, forms a molecular complex with cartilage-associated protein (CRTAP) and cyclophilin B (encoded by PPIB) in the endoplasmic reticulum (ER). This complex is responsible for one step in collagen post-translational modification, the prolyl 3-hydroxylation of specific proline residues, specifically α1(I) Pro986. P3H1 provides the enzymatic activity of the complex and has a Lys-Asp-Glu-Leu (KDEL) ER-retrieval sequence at the carboxyl terminus. Loss of function mutations in LEPRE1 lead to the Pro986 residue remaining unmodified and lead to slow folding and excessive helical post-translational modification of type I collagen, which is seen in both dominant and recessive osteogenesis imperfecta (OI). Here, we present the case of siblings with non-lethal OI due to novel compound heterozygous mutations in LEPRE1 (c.484delG and c.2155dupC). The results of RNA analysis and real-time PCR suggest that mRNA with c.2155dupC escapes from nonsense-mediated RNA decay. Without the KDEL ER- retrieval sequence, the product of the c.2155dupC variant cannot be retained in the ER. This is the first report of a mutation in LEPRE1 that eliminates only the KDEL ER-retrieval sequence, whereas other functional domains remain intact. Our study shows, for the first time, that the KDEL ER- retrieval sequence is essential for P3H1 functionality and that a defect in KDEL is sufficient for disease onset

Precise measurement of the W-boson mass with the CDF II detector

We have measured the W-boson mass MW using data corresponding to 2.2/fb of integrated luminosity collected in proton-antiproton collisions at 1.96 TeV with the CDF II detector at the Fermilab Tevatron collider. Samples consisting of 470126 W->enu candidates and 624708 W->munu candidates yield the measurement MW = 80387 +- 12 (stat) +- 15 (syst) = 80387 +- 19 MeV. This is the most precise measurement of the W-boson mass to date and significantly exceeds the precision of all previous measurements combined

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

X-ray emission from the Sombrero galaxy: discrete sources

We present a study of discrete X-ray sources in and around the bulge-dominated, massive Sa galaxy, Sombrero (M104), based on new and archival Chandra observations with a total exposure of ~200 ks. With a detection limit of L_X = 1E37 erg/s and a field of view covering a galactocentric radius of ~30 kpc (11.5 arcminute), 383 sources are detected. Cross-correlation with Spitler et al.'s catalogue of Sombrero globular clusters (GCs) identified from HST/ACS observations reveals 41 X-rays sources in GCs, presumably low-mass X-ray binaries (LMXBs). We quantify the differential luminosity functions (LFs) for both the detected GC and field LMXBs, whose power-low indices (~1.1 for the GC-LF and ~1.6 for field-LF) are consistent with previous studies for elliptical galaxies. With precise sky positions of the GCs without a detected X-ray source, we further quantify, through a fluctuation analysis, the GC LF at fainter luminosities down to 1E35 erg/s. The derived index rules out a faint-end slope flatter than 1.1 at a 2 sigma significance, contrary to recent findings in several elliptical galaxies and the bulge of M31. On the other hand, the 2-6 keV unresolved emission places a tight constraint on the field LF, implying a flattened index of ~1.0 below 1E37 erg/s. We also detect 101 sources in the halo of Sombrero. The presence of these sources cannot be interpreted as galactic LMXBs whose spatial distribution empirically follows the starlight. Their number is also higher than the expected number of cosmic AGNs (52+/-11 [1 sigma]) whose surface density is constrained by deep X-ray surveys. We suggest that either the cosmic X-ray background is unusually high in the direction of Sombrero, or a distinct population of X-ray sources is present in the halo of Sombrero.Comment: 11 figures, 5 tables, ApJ in pres