Twisting eigensystems of Drinfeld Hecke eigenforms by characters

We address some questions posed by Goss related to the modularity of Drinfeld modules of rank 1 defined over the field of rational functions in one variable with coefficients in a finite field. For each positive characteristic valued Dirichlet character, we introduce certain projection operators on spaces of Drinfeld modular forms with character of a given weight and type such that when applied to a Hecke eigenform return a Hecke eigenform whose eigensystem has been twisted by the given Dirichlet character. Unlike the classical case, however, the effect on Goss' $u$-expansions for these eigenforms --- and even on Petrov's $A$-expansions --- is more complicated than a simple twisting of the $u-$ (or $A-$) expansion coefficients by the given character. We also introduce Eisenstein series with character for irreducible levels $\mathfrak{p}$ and show that they and their Fricke transforms are Hecke eigenforms with a new type of $A$-expansion and $A$-expansion in the sense of Petrov, respectively. We prove congruences between certain cuspforms in Petrov's special family and the Eisenstein series and their Fricke transforms introduced here, and we show that in each weight there are as many linearly independent Eisenstein series with character as there are cusps for $\Gamma_1(\mathfrak{p})$.Comment: Research funded by the Alexander von Humboldt Foundatio

The Legendre determinant form for Drinfeld modules in arbitrary rank

For each positive integer $r$, we construct a nowhere-vanishing, single-cuspidal Drinfeld modular form for \GL_r(\FF_q[\theta]), necessarily of least possible weight, via determinants using rigid analytic trivializations of the universal Drinfeld module of rank $r$ and deformations of vectorial Eisenstein series. Along the way, we deduce that the cycle class map from de Rham cohomology to Betti cohomology is an isomorphism for Drinfeld modules of all ranks over \FF_q[\theta].Comment: 14 page

Explicit Formulae for LL-values in Positive Characteristic

We focus on the generating series for the rational special values of Pellarin's $L$-series in $1 \leq s \leq 2(q-1)$ indeterminates, and using interpolation polynomials we prove a closed form formula relating this generating series to the Carlitz exponential, the Anderson-Thakur function, and the Anderson generating functions for the Carlitz module. We draw several corollaries, including explicit formulae and recursive relations for Pellarin's $L$-series in the same range of $s$, and divisibility results on the numerators of the Bernoulli-Carlitz numbers by monic irreducibles of degrees one and two.Comment: Some helpful clarifications in the introduction. Final edit, as appears online in Math.

On certain generating functions in positive characteristic

We present new methods for the study of a class of generating functions introduced by the second author which carry some formal similarities with the Hurwitz zeta function. We prove functional identities which establish an explicit connection with certain deformations of the Carlitz logarithm introduced by M. Papanikolas and involve the Anderson-Thakur function and the Carlitz exponential function. They collect certain functional identities in families for a new class of L-functions introduced by the first author. This paper also deals with specializations at roots of unity of these generating functions, producing a link with Gauss-Thakur sums.Comment: 18 pages. Refereed versio

Out-of-hospital cardiac arrest survival in international airports

Background  The highest achievable survival rate following out-of-hospital cardiac arrest is unknown. Data from airports serving international destinations (international airports) provide the opportunity to evaluate the success of pre-hospital resuscitation in a relatively controlled but real-life environment.  Methods  This retrospective cohort study included all cases of out-of-hospital cardiac arrest at international airports with resuscitation attempted between January 1st, 2013 and December 31st, 2015. Crude incidence, patient, event characteristics and survival to hospital discharge/survival to 30 days (survival) were calculated. Mixed effect logistic regression analyses were performed to identify predictors of survival. Variability in survival between airports/countries was quantified using the median odds ratio.  Results  There were 800 cases identified, with an average of 40 per airport. Incidence was 0.024/100,000 passengers per year. Percentage survival for all patients was 32%, and 58% for patients with an initial shockable heart rhythm.  In adjusted analyses, initial shockable heart rhythm was the strongest predictor of survival (odds ratio, 36.7; 95% confidence interval [CI], 15.5 to 87.0). In the bystander-witnessed subgroup, delivery of a defibrillation shock by a bystander was a strong predictor of survival (odds ratio 4.8; 95% CI, 3.0 to 7.8). Grouping of cases was significant at country level and survival varied between countries.  Conclusions  In international airports, there was 32% of patients survived an out-of-hospital cardiac arrest, substantially more than in the general population. Our analysis suggested similarity between airports within countries, but differences between countries. Systematic data collection and reporting is essential to ensure international airports continually maximise activities to increase survival

Am I overweight? A longitudinal study on parental and peers weight-related perceptions on dietary behaviors and weight status among adolescents

Objective: An investigation of the interplay between various types of adolescents’ perceptions of weight status in predicting adolescents’ nutrition behavior and their body mass was conducted. In particular, it was hypothesized that the relationship between parental and peers’ perceptions of their own weight status (reported by adolescents) and objectively measured weight status of adolescents would be mediated by three types of adolescents’ weight status perceptions (adolescents’ own weight perceptions, parental perceptions of adolescents’ weight status perceived by participants, and peers’ perceptions of adolescents’ weight status perceived by participants) and by adolescents’ nutrition behaviors. Design: Data were collected twice, with a 13-month follow-up. Participants (N = 1096) were aged 14–20, with BMI ranging from 16.20 to 41.21. Multiple mediation analysis with two sequential mediators was applied. Main outcome measures: At the baseline adolescents completed the questionnaire assessing their nutrition behaviors and weight status perceptions. Weight and height were measured objectively at baseline and follow-up. Results: Two types of weight perceptions (adolescents’ own weight status perceptions, peers’ perceptions of adolescents’ weight status reported by participants), and adolescents’ nutrition behaviors mediated the relationship between the others’ own weight perceptions and adolescents’ weight status. No indirect effects of others’ own weight perceptions on adolescents’ weight status through parental perceptions were found. Conclusion: Adolescents’ nutrition behaviors and body weight status depend on what they think about their own weight status and what they think of their peers’ perceptions, but do not depend on what adolescents think of their parents’ perceptions

First-Hand Experience and Second-Hand Information: Changing Trust across Three Levels of Government

Little is known about how different sources of information drive citizen trust in government. To address that gap this article compares disaster evacuees to observers, noting how trust differs as attention to media coverage increases. First-hand experience supplies information to update trust through biological and personal processes and performance assessments, while secondary sources provide information about other people's experiences, filtered through lenses that take an active role in crafting information. These two types of information have varying effects depending on the level of government being trusted. Using surveys administered a year after Hurricane Katrina, I find that Katrina evacuees have the highest trust in federal government, until they start paying attention to media coverage, and that attention to coverage has the most dramatic effect on these evacuees compared to all other groups. I also find that increasing attention to second-hand information corresponds with higher trust in local officials, and that this effect decreases as the level of government increases. It appears media coverage creates a comparison in the mind of hurricane evacuees, causing them to update their performance assessments based on comparing their own experience to that which they observe, thereby updating their political trust