Bounds for Rankin--Selberg integrals and quantum unique ergodicity for powerful levels

43 pages; various minor corrections (many thanks to the referee) and improvements in clarity and exposition. To appear in JAMS43 pages; various minor corrections (many thanks to the referee) and improvements in clarity and exposition. To appear in JAMSLet f be a classical holomorphic newform of level q and even weight k. We show that the pushforward to the full level modular curve of the mass of f equidistributes as qk -> infinity. This generalizes known results in the case that q is squarefree. We obtain a power savings in the rate of equidistribution as q becomes sufficiently "powerful" (far away from being squarefree), and in particular in the "depth aspect" as q traverses the powers of a fixed prime. We compare the difficulty of such equidistribution problems to that of corresponding subconvexity problems by deriving explicit extensions of Watson's formula to certain triple product integrals involving forms of non-squarefree level. By a theorem of Ichino and a lemma of Michel--Venkatesh, this amounts to a detailed study of Rankin--Selberg integrals int|f|^2 E attached to newforms f of arbitrary level and Eisenstein series E of full level. We find that the local factors of such integrals participate in many amusing analogies with global L-functions. For instance, we observe that the mass equidistribution conjecture with a power savings in the depth aspect is equivalent to the union of a global subconvexity bound and what we call a "local subconvexity bound"; a consequence of our local calculations is what we call a "local Lindelof hypothesis"

Some analytic aspects of automorphic forms on GL(2) of minimal type

27 pagesLet $\pi$ be a cuspidal automorphic representation of $PGL_2(\mathbb{A}_\mathbb{Q})$ of arithmetic conductor $C$ and archimedean parameter $T$, and let $\phi$ be an $L^2$-normalized automorphic form in the space of $\pi$. The sup-norm problem asks for bounds on $\| \phi \|_\infty$ in terms of $C$ and $T$. The quantum unique ergodicity (QUE) problem concerns the limiting behavior of the $L^2$-mass $|\phi|^2 (g) \, d g$ of $\phi$. All previous work on these problems in the conductor-aspect has focused on the case that $\phi$ is a newform. In this work, we study these problems for a class of automorphic forms that are not newforms. Precisely, we assume that for each prime divisor $p$ of $C$, the local component $\pi_p$ is supercuspidal (and satisfies some additional technical hypotheses), and consider automorphic forms $\phi$ for which the local components $\phi_p \in \pi_p$ are "minimal" vectors. Such vectors may be understood as non-archimedean analogues of lowest weight vectors in holomorphic discrete series representations of $PGL_2(\mathbb{R})$. For automorphic forms as above, we prove a sup-norm bound that is sharper than what is known in the newform case. In particular, if $\pi_\infty$ is a holomorphic discrete series of lowest weight $k$, we obtain the optimal bound $C^{1/8 -\epsilon} k^{1/4 - \epsilon} \ll_{\epsilon} |\phi|_\infty \ll_{\epsilon} C^{1/8 + \epsilon} k^{1/4+\epsilon}$. We prove also that these forms give analytic test vectors for the QUE period, thereby demonstrating the equivalence between the strong QUE and the subconvexity problems for this class of vectors. This finding contrasts the known failure of this equivalence for newforms of powerful level

Aerosol characteristics during winter fog at Agra, North India

Simultaneous measurements on physical, chemical and optical properties of aerosols over a tropical semi-arid location, Agra in north India, were undertaken during December 2004. The average concentration of total suspended particulates (TSP) increased by about 1.4 times during intense foggy/hazy days. Concentrations of SO4 2-, NO3 -, NH4 + and Black Carbon (BC) aerosols increased by 4, 2, 3.5 and 1.7 times, respectively during that period. Aerosols were acidic during intense foggy/hazy days but the fog water showed alkaline nature, mainly due to the neutralizing capacity of NH4 aerosols. Trajectory analyses showed that air masses were predominantly from NW direction, which might be responsible for transport of BC from distant and surrounding local sources. Diurnal variation of BC on all days showed a morning and an evening peak that were related to domestic cooking and vehicular emissions, apart from boundary layer changes. OPAC (Optical properties of aerosols and clouds) model was used to compute the optical properties of aerosols. Both OPAC-derived and observed aerosol optical depth (AOD) values showed spectral variation with high loadings in the short wavelengths (<1 μm). AOD value at 0.5 μm wavelength was significantly high during intense foggy/hazy days (1.22) than during clear sky or less foggy/hazy days (0.63). OPAC-derived Single scattering albedo (SSA) was 0.84 during the observational period, indicating significant contribution of absorbing aerosols. However, the BC mass fraction to TSP increased by only 1 during intense foggy/hazy days and thereby did not show any impact on SSA during that period. A large increase was observed in the shortwave (SW) atmospheric (ATM) forcing during intense foggy/hazy days (+75.8 W/m2) than that during clear sky or less foggy/hazy days (+38 W/m2), mainly due to increase in absorbing aerosols. Whereas SW forcing at surface (SUF) increased from -40 W/m2 during clear sky or less foggy/hazy days to -76 W/m2 during intense foggy/hazy days, mainly due to the scattering aerosols like SO4 2-

The contribution of genetic variants to disease depends on the ruler

Our understanding of the genetic basis of disease has evolved from descriptions of overall heritability or familiality to the identification of large numbers of risk loci. One can quantify the impact of such loci on disease using a plethora of measures, which can guide future research decisions. However, different measures can attribute varying degrees of importance to a variant. In this Analysis, we consider and contrast the most commonly used measures-specifically, the heritability of disease liability, approximate heritability, sibling recurrence risk, overall genetic variance using a logarithmic relative risk scale, the area under the receiver-operating curve for risk prediction and the population attributable fraction-and give guidelines for their use that should be explicitly considered when assessing the contribution of genetic variants to disease

A transient homotypic interaction model for the influenza A virus NS1 protein effector domain

Influenza A virus NS1 protein is a multifunctional virulence factor consisting of an RNA binding domain (RBD), a short linker, an effector domain (ED), and a C-terminal 'tail'. Although poorly understood, NS1 multimerization may autoregulate its actions. While RBD dimerization seems functionally conserved, two possible apo ED dimers have been proposed (helix-helix and strand-strand). Here, we analyze all available RBD, ED, and full-length NS1 structures, including four novel crystal structures obtained using EDs from divergent human and avian viruses, as well as two forms of a monomeric ED mutant. The data reveal the helix-helix interface as the only strictly conserved ED homodimeric contact. Furthermore, a mutant NS1 unable to form the helix-helix dimer is compromised in its ability to bind dsRNA efficiently, implying that ED multimerization influences RBD activity. Our bioinformatical work also suggests that the helix-helix interface is variable and transient, thereby allowing two ED monomers to twist relative to one another and possibly separate. In this regard, we found a mAb that recognizes NS1 via a residue completely buried within the ED helix-helix interface, and which may help highlight potential different conformational populations of NS1 (putatively termed 'helix-closed' and 'helix-open') in virus-infected cells. 'Helix-closed' conformations appear to enhance dsRNA binding, and 'helix-open' conformations allow otherwise inaccessible interactions with host factors. Our data support a new model of NS1 regulation in which the RBD remains dimeric throughout infection, while the ED switches between several quaternary states in order to expand its functional space. Such a concept may be applicable to other small multifunctional proteins

ANCA vasculitis induction management during the COVID-19 pandemic

As the severe acute respiratory syndrome coronavirus 2 pandemic evolved and became a global health threat, the safety of immunosuppression in antineutrophil cytoplasmic antibody-associated vasculitis (AAV) became of utmost important for clinicians and patients. Although timely initiation of immunosuppressive therapy is critical to quell the acute inflammation and prevent AAV-associated mortality and morbidity, concerns for increased susceptibility to Coronavirus Disease 2019 (COVID-19), delayed viral clearance, and decreased humoral response to infection led to speculation about modification in induction therapy practices may be deployed by physicians caring for patients with AAV. This international retrospective cohort study investigated the influence of the COVID-19 pandemic on AAV induction therapy and patient outcomes in different parts of the world by studying differences in treatment regimens in the United States, United Kingdom, and Europe

Chinese and white Canadian satisfaction and compliance with physicians

BACKGROUND: Patient satisfaction has become an important indicator of primary care and healthcare system performance. Ethnic disparities in patient satisfaction and compliance with physician care have been studied in several countries. However, this issue has not received significant attention in Canada. The unique characteristics of the Canadian healthcare system and ethnic population make it worthwhile to examine this issue in this population. Therefore, we conducted a survey among Chinese and Whites in a Canadian city to determine their reported satisfaction, and perceptions of physicians. METHODS: The survey was conducted in English, Mandarin and Cantonese in 2005 among Chinese and White Canadians, 18 years of age or older, who had visited at least one physician in Canada. RESULTS: We analyzed 746 Chinese and 711 Whites in the general practitioner (GP) visit group and 485 Chinese and 637 Whites in the specialist visit group. A lower proportion of Chinese compared to Whites reported that they were very satisfied or satisfied with GP (73.7% vs. 92.8%) and specialist care (75.5% vs. 85.6%) and the differences between the two groups remained after adjustment for demographic variables and chronic conditions (risk adjusted OR: 0.70, 95%CI: 0.42–1.18 for the GP visit group and OR: 0.77, 95%CI: 0.48–1.23 for the specialist visit group). A similar proportion of Chinese and Whites reported that they always followed a physician's advice (59.4% vs. 59.6% for the GP visit group and 67.2% vs. 62.8% for the specialist visit group). Non-English speaking Chinese and recent arrivals in Canada were less likely to be satisfied with GPs than Chinese born in Canada [risk adjusted OR: 0.5, 95%CI: 0.3–0.9, 0.2 and 0.1–0.7, respectively]. CONCLUSION: Chinese Canadians reported lower satisfaction with physicians and perceived physicians slightly more negatively than White Canadians. Particularly, Chinese with limited English and short length of stay in Canada were less satisfied than Canadian born Chinese

Implications of Advancing Paternal Age: Does It Affect Offspring School Performance?

Average paternal age is increasing in many high income countries, but the implications of this demographic shift for child health and welfare are poorly understood. There is equivocal evidence that children of older fathers are at increased risk of neurodevelopmental disorders and reduced IQ. We therefore report here on the relationship between paternal age and a composite indicator of scholastic achievement during adolescence, i.e. compulsory school leaving grades, among recent birth cohorts in Stockholm County where delayed paternity is notably common. We performed a record-linkage study comprising all individuals in Stockholm County who finished 9 years of compulsory school from 2000 through 2007 (n = 155,875). Data on school leaving grades and parental characteristics were retrieved from administrative and health service registers and analyzed using multiple linear regression. Advancing paternal age at birth was not associated with a decrease in school leaving grades in adolescent offspring. After adjustment for year of graduation, maternal age and parental education, country of birth and parental mental health service use, offspring of fathers aged 50 years or older had on average 0.3 (95% CI −3.8, 4.4) points higher grades than those of fathers aged 30–34 years. In conclusion, advancing paternal age is not associated with poorer school performance in adolescence. Adverse effects of delayed paternity on offspring cognitive function, if any, may be counterbalanced by other potential advantages for children born to older fathers

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