Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

ENIGMA and global neuroscience: A decade of large-scale studies of the brain in health and disease across more than 40 countries

This review summarizes the last decade of work by the ENIGMA (Enhancing NeuroImaging Genetics through Meta Analysis) Consortium, a global alliance of over 1400 scientists across 43 countries, studying the human brain in health and disease. Building on large-scale genetic studies that discovered the first robustly replicated genetic loci associated with brain metrics, ENIGMA has diversified into over 50 working groups (WGs), pooling worldwide data and expertise to answer fundamental questions in neuroscience, psychiatry, neurology, and genetics. Most ENIGMA WGs focus on specific psychiatric and neurological conditions, other WGs study normal variation due to sex and gender differences, or development and aging; still other WGs develop methodological pipelines and tools to facilitate harmonized analyses of "big data" (i.e., genetic and epigenetic data, multimodal MRI, and electroencephalography data). These international efforts have yielded the largest neuroimaging studies to date in schizophrenia, bipolar disorder, major depressive disorder, post-traumatic stress disorder, substance use disorders, obsessive-compulsive disorder, attention-deficit/hyperactivity disorder, autism spectrum disorders, epilepsy, and 22q11.2 deletion syndrome. More recent ENIGMA WGs have formed to study anxiety disorders, suicidal thoughts and behavior, sleep and insomnia, eating disorders, irritability, brain injury, antisocial personality and conduct disorder, and dissociative identity disorder. Here, we summarize the first decade of ENIGMA's activities and ongoing projects, and describe the successes and challenges encountered along the way. We highlight the advantages of collaborative large-scale coordinated data analyses for testing reproducibility and robustness of findings, offering the opportunity to identify brain systems involved in clinical syndromes across diverse samples and associated genetic, environmental, demographic, cognitive, and psychosocial factors

A Study of Exclusive Charmless Semileptonic B Decays and Extraction of |V_{ub}| at CLEO

We have studied semileptonic B decay to the exclusive charmless states pi, rho/omega, eta and eta' using the full 15.5 fb^-1 CLEO Upsilon(4S) sample, with measurements performed in subregions of phase space to minimize dependence on a priori knowledge of the form factors involved. We find total branching fractions B(B^0 -> pi^-l^+nu) = (1.37 +- 0.15_stat +- 0.11_sys) x 10^-4 and B(B^0 -> rho^- l^+ nu) = (2.93 +- 0.37_stat +- 0.37_sys) x 10^-4. We find evidence for B^+ -> eta' l^+ nu, with B(B^+ -> eta' l^+ nu) = (2.66 +- 0.80_stat +- 0.56_sys) x 10^-4 and 1.20 x 10^-4 eta' l^+ nu) < 4.46 x 10^-4 (90% CL). We also limit B(B^+ -> eta l^+ nu) < 1.01 x 10^-4 (90% CL). By combining our B -> pi l nu information with unquenched lattice calculations, we find |V_ub| = (3.6 +- 0.4 +- 0.2 +0.6 -0.4) x 10^-3, where the errors are statistical, experimental systematic, and theoretical systematic, respectively.Comment: 35 pages, 15 figures; revise

Resonant Structure of τ→3ππ0ντ\tau\to 3\pi\pi^{0}\nu_{\tau} and τ→ωπντ\tau\to \omega\pi\nu_{\tau} Decays

The resonant structure of the four pion final state in the decay $\tau \to 3\pi\pi^0\nu_\tau$ is analyzed using 4.27 million $\tau^+\tau^-$ pairs collected by the CLEO II experiment. We search for second class currents in the decay $\tau \to \omega\pi\nu_\tau$ using spin-parity analysis and establish an upper limit on the non-vector current contribution. The mass and width of the $\rho'$ resonance are extracted from a fit to the $\tau \to \omega\pi\nu_\tau$ spectral function. A partial wave analysis of the resonant structure of the $\tau \to 3\pi\pi^0\nu_\tau$ decay is performed; the spectral decomposition of the four pion system is dominated by the $\omega\pi$ and $a_1 \pi$ final states.Comment: 34 pages postscript, also available through http://w4.lns.cornell.edu/public/CLN

Search for Lepton-Flavor-Violating Decays of B Mesons

We have searched a sample of 9.6 million BB-bar events for the lepton-flavor-violating decays B --> h e^{+-} mu^{-+}, B^+ --> h^- e^+ e^+, B^+ --> h^- e^+ mu^+, and B^+ --> h^- mu^+ mu^+, where h is pi, K, rho, and K*(892), a total of sixteen modes. We find no evidence for these decays, and place 90% confidence level upper limits on their branching fractions that range from 1.0 to 8.3 X 10^{-6}.Comment: 8 pages postscript, also available through http://w4.lns.cornell.edu/public/CLNS, PRD R

Determination of the Michel Parameters and the tau Neutrino Helicity in tau Decay

Using the CLEO II detector at the $e^+e^-$ storage ring CESR, we have determined the Michel parameters $\rho$, $\xi$, and $\delta$ in $\tau^\mp \to l^\mp\nu\bar{\nu}$ decay as well as the tau neutrino helicity parameter $h_{\nu_\tau}$ in $\tau^\mp \to \pi^\mp\pi^0\nu$ decay. From a data sample of $3.02\times 10^6$ tau pairs produced at $\sqrt{s}=10.6 GeV$, using events of the topology $e^+e^- \to \tau^+\tau^- \to (l^\pm\nu\bar{\nu}) (\pi^\mp\pi^0\nu)$ and $e^+e^- \to \tau^+\tau^- \to (\pi^\pm\pi^0\bar{\nu}) (\pi^\mp\pi^0\nu)$, and the determined sign of $h_{\nu_\tau}$, the combined result of the three samples is: $\rho = 0.747\pm 0.010\pm 0.006$, $\xi = 1.007\pm 0.040\pm 0.015$, $\xi\delta = 0.745\pm 0.026\pm 0.009$, and $h_{\nu_\tau} = -0.995\pm 0.010\pm 0.003$. The results are in agreement with the Standard Model V-A interaction.Comment: 18 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Measurement of the Branching Ratios for the Decays of Ds+→ηπ+,η′π+,ηρ+D_{s}^{+}\to \eta\pi^{+}, \eta^{'}\pi^{+}, \eta\rho^{+}, and eta′ρ+eta^{'}\rho^{+}

Using a data sample with integrated luminosity of about 3.9 fb^{-1} collected in e+ e- annihilation with the CLEO-II detector at the Cornell Electron Storage Ring, we have measured the branching ratios for the decay modes Ds -> (eta, eta') pi and Ds -> (eta, eta') rho relative to Ds -> phi pi. These decay modes are among the most common hadronic decays of the Ds's and can be related by factorization to the semileptonic decays Ds -> (eta,eta') l nu. The results obtained are compared with previous CLEO results and with the branching ratios measured for the related semileptonic decays. We also report results on the Cabibbo-suppressed decays of the D+ to the same final states.Comment: 18 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Search for Exclusive Charmless Hadronic B Decays

We have searched for two-body charmless hadronic decays of $B$ mesons. Final states include $\pi\pi$, $K \pi$, and $KK$ with both charged and neutral kaons and pions; $\pi\rho$, $K \rho$, and $K^*\pi$; and $K\phi$, $K^*\phi$, and $\phi\phi$. The data used in this analysis consist of 2.6~million $B\bar{B}$~pairs produced at the $\Upsilon(4S)$ taken with the CLEO-II detector at the Cornell Electron Storage Ring (CESR). We measure the branching fraction of the sum of $B^0 \rightarrow \pi^+\pi^-$ and $B^0 \rightarrow K^+\pi^-$ to be $(1.8^{+0.6+0.2}_{-0.5-0.3}\pm0.2) \times 10^{-5}$. In addition, we place upper limits on individual branching fractions in the range from $10^{-4}$ to $10^{-6}$.Comment: 33 page LATEX file, uses REVTEX and psfig, 14 figures in a separate uuencoded postscript file, postscript version also available through http://w4.lns.cornell.edu/public/CLN

Tau Neutrino Helicity from h±h^{\pm} Energy Correlations

We report a measurement of the magnitude of the tau neutrino helicity from tau-pair events taken with the CLEO detector at the CESR electron-positron storage ring. Events in which each tau undergoes the decay tau -> h nu, with h a charged pion or kaon, are analyzed for energy correlations between the daughter hadrons, yielding |xi| = 2*|h_nu| = 1.03 +/- 0.06 +/- 0.04, with the first error statistical and the second systematic.Comment: 11 pages, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Limit on the Two-Photon Production of the Glueball Candidate fJ(2220)f_{J}(2220) at CLEO

We use the CLEO detector at the Cornell electron-positron storage ring, CESR, to search for the two-photon production of the glueball candidate f_J(2220) in its decay to K_s K_s. We present a restrictive upper limit on the product of the two-photon partial width and the K_s K_s branching fraction. We use this limit to calculate a lower limit on the stickiness, which is a measure of the two-gluon coupling relative to the two-photon coupling. This limit on stickiness indicates that the f_J(2220) has substantial glueball content.Comment: 9 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN