The Sign of Fourier Coefficients of Half-Integral Weight Cusp Forms

From a result of Waldspurger, it is known that the normalized Fourier coefficients $a(m)$ of a half-integral weight holomorphic cusp eigenform \f are, up to a finite set of factors, one of $\pm \sqrt{L(1/2, f, \chi_m)}$ when $m$ is square-free and $f$ is the integral weight cusp form related to \f by the Shimura correspondence. In this paper we address a question posed by Kohnen: which square root is $a(m)$? In particular, if we look at the set of $a(m)$ with $m$ square-free, do these Fourier coefficients change sign infinitely often? By partially analytically continuing a related Dirichlet series, we are able to show that this is so

Brain connectivity inversely scales with developmental temperature in Drosophila

Variability of synapse numbers and partners despite identical genes reveals the limits of genetic determinism. Here, we use developmental temperature as a non-genetic perturbation to study variability of brain wiring and behavior in Drosophila. Unexpectedly, slower development at lower temperatures increases axo-dendritic branching, synapse numbers, and non-canonical synaptic partnerships of various neurons, while maintaining robust ratios of canonical synapses. Using R7 photoreceptors as a model, we show that changing the relative availability of synaptic partners using a DIPγ mutant that ablates R7’s preferred partner leads to temperature-dependent recruitment of non-canonical partners to reach normal synapse numbers. Hence, R7 synaptic specificity is not absolute but based on the relative availability of postsynaptic partners and presynaptic control of synapse numbers. Behaviorally, movement precision is temperature robust, while movement activity is optimized for the developmentally encountered temperature. These findings suggest genetically encoded relative and scalable synapse formation to develop functional, but not identical, brains and behaviors

Measuring Recoiling Nucleons From the Nucleus with the Future Electron Ion Collider

Short range correlated nucleon-nucleon (NN) pairs are an important part of the nuclear ground state. They are typically studied by scattering an electron from one nucleon in the pair and detecting its spectator correlated partner (“spectator-nucleon tagging”). The Electron Ion Collider (EIC) should be able to detect these nucleons, since they are boosted to high momentum in the laboratory frame by the momentum of the ion beam. To determine the feasibility of these studies with the planned EIC detector configuration, we have simulated quasielastic scattering for two electron and ion beam energy configurations: 5 GeV e− and 41 GeV/A ions, and 10 GeV e− and 110 GeV/A ions. We show that the knocked-out and recoiling nucleons can be detected over a wide range of initial nucleon momenta. We also show that these measurements can achieve much larger momentum transfers than current fixed target experiments. By detecting both low and high initial-momentum nucleons, the planned EIC has the potential to provide the data that should allow scientists to definitively show if the European Muon Collaboration effect and short-range correlation are connected, and to improve our understanding of color transparency

Systematic functional analysis of rab GTPases reveals limits of neuronal robustness to environmental challenges in flies

Rab GTPases are molecular switches that regulate membrane trafficking in all cells. Neurons have particular demands on membrane trafficking and express numerous Rab GTPases of unknown function. Here, we report the generation and characterization of molecularly defined null mutants for all 26 rab genes in Drosophila. In flies, all rab genes are expressed in the nervous system where at least half exhibit particularly high levels compared to other tissues. Surprisingly, loss of any of these 13 nervous system-enriched Rabs yielded viable and fertile flies without obvious morphological defects. However, all 13 mutants differentially affected development when challenged with different temperatures, or neuronal function when challenged with continuous stimulation. We identified a synaptic maintenance defect following continuous stimulation for six mutants, including an autophagy-independent role of rab26. The complete mutant collection generated in this study provides a basis for further comprehensive studies of Rab GTPases during development and function in vivo

Observation of Large Missing-Momentum \u3cb\u3e(e, e\u27 p)\u3c/b\u3e Cross-Section Scaling and the Onset of Correlated-Pair Dominance in Nuclei

We report the measurement of B scaling in (e,e′p) cross-section ratios off nuclei relative to deuterium at large missing momentum of 350 ≤ Pmiss ≤ 600 MeV/c. The observed scaling extends over a kinematic range of 0.7 ≤ B ≤ 1.8, which is significantly wider than 1.4 ≤ B ≤ 1.8 previously observed for inclusive (e,e′) cross-section ratios. The B-integrated cross-section ratios become constant (i.e., scale) beginning at pmiss ≈ kF, the nuclear Fermi momentum. Comparing with theoretical calculations we find good agreement with generalized contact formalism calculations for high missing momentum (\u3e375 MeV /c), suggesting the observed scaling results from interacting with nucleons in short-range correlated (SRC) pairs. For low missing momenta, mean-field calculations show good agreement with the data for pmiss \u3c kF, and suggest a potential non-negligible contribution to the measured cross-section ratios from scattering off single, uncorrelated, nucleons up to pmiss ≈ 350 MeV /c. Therefore, SRCs become dominant in nuclei at pmiss ≈ 350 MeV /c, well above the nuclear Fermi Surface of kF ≈ 250 MeV/c

Seizure prediction : ready for a new era

Acknowledgements: The authors acknowledge colleagues in the international seizure prediction group for valuable discussions. L.K. acknowledges funding support from the National Health and Medical Research Council (APP1130468) and the James S. McDonnell Foundation (220020419) and acknowledges the contribution of Dean R. Freestone at the University of Melbourne, Australia, to the creation of Fig. 3.Peer reviewedPostprin