On modular signs

We consider some questions related to the signs of Hecke eigenvalues or Fourier coefficients of classical modular forms. One problem is to determine to what extent those signs, for suitable sets of primes, determine uniquely the modular form, and we give both individual and statistical results. The second problem, which has been considered by a number of authors, is to determine the size, in terms of the conductor and weight, of the first sign-change of Hecke eigenvalues. Here we improve significantly the recent estimate of Iwaniec, Kohnen and Sengupta.Comment: 23 pages, 1 figure; new version with new coauthor and strong improvements of two of the two main results

Search for methylamine in high mass hot cores

We aim to detect methylamine, CH$_{3}$NH$_{2}$, in a variety of hot cores and use it as a test for the importance of photon-induced chemistry in ice mantles and mobility of radicals. Specifically, CH$_3$NH$_2$ cannot be formed from atom addition to CO whereas other NH$_2$-containing molecules such as formamide, NH$_2$CHO, can. Submillimeter spectra of several massive hot core regions were taken with the James Clerk Maxwell Telescope. Abundances are determined with the rotational diagram method where possible. Methylamine is not detected, giving upper limit column densities between 1.9 $-$ 6.4 $\times$ 10$^{16}$ cm$^{-2}$ for source sizes corresponding to the 100 K envelope radius. Combined with previously obtained JCMT data analyzed in the same way, abundance ratios of CH$_{3}$NH$_{2}$, NH$_{2}$CHO and CH$_{3}$CN with respect to each other and to CH$_{3}$OH are determined. These ratios are compared with Sagittarius B2 observations, where all species are detected, and to hot core models. The observed ratios suggest that both methylamine and formamide are overproduced by up to an order of magnitude in hot core models. Acetonitrile is however underproduced. The proposed chemical schemes leading to these molecules are discussed and reactions that need further laboratory studies are identified. The upper limits obtained in this paper can be used to guide future observations, especially with ALMA.Comment: 14 pages, 5 figures, accepted for publication in A&

Sum of Two Squares - Pair Correlation and Distribution in Short Intervals

In this work we show that based on a conjecture for the pair correlation of integers representable as sums of two squares, which was first suggested by Connors and Keating and reformulated here, the second moment of the distribution of the number of representable integers in short intervals is consistent with a Poissonian distribution, where "short" means of length comparable to the mean spacing between sums of two squares. In addition we present a method for producing such conjectures through calculations in prime power residue rings and describe how these conjectures, as well as the above stated result, may by generalized to other binary quadratic forms. While producing these pair correlation conjectures we arrive at a surprising result regarding Mertens' formula for primes in arithmetic progressions, and in order to test the validity of the conjectures, we present numericalz computations which support our approach.Comment: 3 figure

Supporting parent-child conversations in a history museum

BACKGROUND: Museums can serve as rich resources for families to learn about the social world through engagement with exhibits and parent-child conversation about exhibits. AIMS: This study examined ways of engaging parents and child about two related exhibits at a cultural and history museum. Sample participants consisted of families visiting the Animal Antics and the Gone Potty exhibits at the British Museum. METHODS: Whilst visiting two exhibits at the British Museum, 30 families were assigned to use a backpack of activities, 13 were assigned to a booklet of activities, and 15 were assigned to visit the exhibits without props (control condition). RESULTS: Compared to the families in the control condition, the interventions increased the amount of time parents and children engaged together with the exhibit. Additionally, recordings of the conversations revealed that adults asked more questions related to the exhibits when assigned to the two intervention conditions compared to the control group. Children engaged in more historical talk when using the booklets than in the other two conditions. CONCLUSIONS: The findings suggest that providing support with either booklets or activities for children at exhibits may prove beneficial to parent-child conversations and engagement with museum exhibits

Identification and Removal of Noise Modes in Kepler Photometry

We present the Transiting Exoearth Robust Reduction Algorithm (TERRA) --- a novel framework for identifying and removing instrumental noise in Kepler photometry. We identify instrumental noise modes by finding common trends in a large ensemble of light curves drawn from the entire Kepler field of view. Strategically, these noise modes can be optimized to reveal transits having a specified range of timescales. For Kepler target stars of low photometric noise, TERRA produces ensemble-calibrated photometry having 33 ppm RMS scatter in 12-hour bins, rendering individual transits of earth-size planets around sun-like stars detectable as ~3 sigma signals.Comment: 18 pages, 7 figures, submitted to PAS

Generalization of the effective Wiener-Ikehara theorem

International audienceWe consider the classical Wiener–Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform. In this generality, we prove the otherwise known asymptotic evaluation of the transformed function, when the usual conditions of the Wiener-Ikehara theorem hold. However, our version also provides an effective error term, not known thus far in this generality. The crux of the proof is a proper asymptotic variation of the lemmas of Ganelius and Tenenbaum, also constructed for the sake of an effective version of the Wiener–Ikehara theorem

The Effect of Symmetrical, Hand-held Load Carriage on Thoracic Rotation during Gait: An Observational Study

Title: The Effect of Symmetrical, Hand-held Load Carriage on Thoracic Rotation during Gait: An Observational Study Authors: Danny J. McMillian, PT, DSc, OCS, CSCS ; Robert C. Bennett, SPT ; Claire E. Tenenbaum, SPT ; Daniel C. Winnwalker, SPT Affiliation: Physical Therapy Program, University of Puget Sound Purpose: During unloaded ambulation arm, trunk and leg motion produces reciprocal, anti-phase rotation between the pelvis and thoracic spine. Anti-phase rotation allows for efficient, stable gait patterns and promotes balanced segmental forces. Research demonstrates that several common factors cause in-phase thoracic spine and pelvic rotation resulting in decreased gait efficiency. Factors include load carriage, slow gait velocity, and locomotor pathologies that promote protective spinal stabilization such as low back pain and pregnancy-related pelvic girdle pain. Since painful spinal and pelvic conditions are frequently treated with physical therapy interventions that promote stabilization, clinicians should be cognizant of the degree to which such exercises may alter normal gait mechanics.A previous, as yet unpublished study from our lab has shown that gait mechanics transition from anti-phase to in-phase rotation with as little as 5% of an individual’s body weight carried as a asymmetrical hand-held load. The purpose of the current study was to establish if altered gait kinematics, specifically thoracic spinal rotation relative to the pelvis, occurs with symmetrical hand-held loads. Subjects: Adult volunteers, 18-30 years old, with no gait or health complications. Materials & Methods: Each subject walked at a cadence of 100 beats per minute for a distance of 48 feet and repeated seven different conditions three times in randomized order. The conditions were: 1) no load, 2) holding an empty canvas bag in each hand, 3) holding 2% of body weight (BW), 4) holding 4% BW, 5) holding 6% BW, 6) holding 8% BW, and 7) holding 10% BW. Each percentage of BW was carried bilaterally and subjects were blinded to conditions 2-7. Ten Bonita cameras recorded each condition at 120 hertz, and gait kinematics were analyzed with VICON Nexus 1.8.4 motion analysis system. In order to compare the average thoracic rotation relative to the pelvis for each condition a repeated measures ANOVA with Bonferroni adjustment was performed with alpha value p\u3c0.05. Results: Compared to condition 1 (unloaded walking), condition 2-7 demonstrated significant decrease in rotational angles of the thoracic spine relative to the pelvis (p\u3c0.001). Furthermore, condition 2 demonstrated a significant decrease in thoracic rotation as compared to conditions 5 (p\u3c0.004) and 7 (p\u3c0.034). Conclusion: Thoracic spine rotation decreases when walking with unloaded bags in each hand. Diminished rotation was likely due to decreasing arm swing. Consistent with the effects of muscular stabilization, increased load generally decreased rotation further. Clinical Relevance: This information is clinically applicable when working with individuals who have some degree of in-phase gait kinematics and need rehabilitation in order to return to activities that necessitate gait with hand-held loads. In these cases, clinicians should consider first reestablishing optimal transverse plane kinematics, then incorporating only the minimally necessary amount of hand-held load

The accuracy of drainage network delineation as a function of environmental factors: A case study in Central and Northern Sweden

Drainage networks delineated from Digital Elevation Models (DEMs), are the basis for the modelling of geomorphological and hydrological processes, biogeochemical cycling, and water resources management. Besides providing effective models of water flows, automatically extracted drainage networks based on topography can diverge from reality to varying degrees. The variability of such disagreement within catchments has rarely been examined as a function of the heterogeneity of land cover, soil type, and slope in the catchment of interest. This research gap might not only substantially limit our knowledge of the uncertainty of hydrological prediction, but can also cause problems for users attempting to use the data at a local scale. Using 1:100000 scale land cover maps, Quaternary deposits maps, and 2 m resolution DEMs, it is found that the accuracy of delineated drainage networks tends to be lower in areas with denser vegetation, lower hydraulic conductivity, and higher erodibility. The findings of this study could serve as a guide for the more thoughtful usage of delineated drainage networks in environmental planning, and in the uncertainty analysis of hydrological and biochemical predictions. Therefore, this study makes a first attempt at filling the knowledge gap described above