The Bivariate Normal Copula

We collect well known and less known facts about the bivariate normal distribution and translate them into copula language. In addition, we prove a very general formula for the bivariate normal copula, we compute Gini's gamma, and we provide improved bounds and approximations on the diagonal.Comment: 24 page

An Italian foreign policy of religious engagement: challenges and prospects

A new awareness of the role of religion in international relations has started to inform concrete policy discussions in several Western Ministries of Foreign Affairs under the heading of ‘religious engagement’ in foreign policy. Italy is no exception, but as the country which hosts the Holy See, it represents a special case. As the approach to religion found in the historical record of Italian foreign policy shows, Italy has a comparative advantage and could well develop a unique model of religious engagement by strengthening the central structures involved in religious matters and foreign policy, as well as by using the vast network of Rome-based religious non-state actors as a forum of consultation and policy advice

Charge Delocalization in Self-Assembled Mixed-Valence Aromatic Cation Radicals

The spontaneous assembly of aromatic cation radicals (D+•) with their neutral counterpart (D) affords dimer cation radicals (D2+•). The intermolecular dimeric cation radicals are readily characterized by the appearance of an intervalence charge-resonance transition in the NIR region of their electronic spectra and by ESR spectroscopy. The X-ray crystal structure analysis and DFT calculations of a representative dimer cation radical (i.e., the octamethylbiphenylene dimer cation radical) have established that a hole (or single positive charge) is completely delocalized over both aromatic moieties. The energetics and the geometrical considerations for the formation of dimer cation radicals is deliberated with the aid of a series of cyclophane-like bichromophoric donors with drastically varied interplanar angles between the cofacially arranged aryl moieties. X-ray crystallography of a number of mixed-valence cation radicals derived from monochromophoric benzenoid donors established that they generally assemble in 1D stacks in the solid state. However, the use of polychromophoric intervalence cation radicals, where a single charge is effectively delocalized among all of the chromophores, can lead to higher-order assemblies with potential applications in long-range charge transport. As a proof of concept, we show that a single charge in the cation radical of a triptycene derivative is evenly distributed on all three benzenoid rings and this triptycene cation radical forms a 2D electronically coupled assembly, as established by X-ray crystallography

Measurement of the Proton and Deuteron Spin Structure Functions g2 and Asymmetry A2

We have measured the spin structure functions g2p and g2d and the virtual photon asymmetries A2p and A2d over the kinematic range 0.02 < x < 0.8 and 1.0 < Q^2 < 30(GeV/c)^2 by scattering 38.8 GeV longitudinally polarized electrons from transversely polarized NH3 and 6LiD targets.The absolute value of A2 is significantly smaller than the sqrt{R} positivity limit over the measured range, while g2 is consistent with the twist-2 Wandzura-Wilczek calculation. We obtain results for the twist-3 reduced matrix elements d2p, d2d and d2n. The Burkhardt-Cottingham sum rule integral - int(g2(x)dx) is reported for the range 0.02 < x < 0.8.Comment: 12 pages, 4 figures, 1 tabl

Observation of Parity Nonconservation in Moller Scattering

We report a measurement of the parity-violating asymmetry in fixed target electron-electron (Moller) scattering: A_PV = -175 +/- 30 (stat.) +/- 20 (syst.) parts per billion. This first direct observation of parity nonconservation in Moller scattering leads to a measurement of the electron's weak charge at low energy Q^e_W = -0.053 +/- 0.011. This is consistent with the Standard Model expectation at the current level of precision: sin^2\theta_W(M_Z)_MSbar = 0.2293 +/- 0.0024 (stat.) +/- 0.0016 (syst.) +/- 0.0006 (theory).Comment: Version 3 is the same as version 2. These versions contain minor text changes from referee comments and a change in the extracted value of Q^e_W and sin^2\theta_W due to a change in the theoretical calculation of the bremsstrahulung correction (ref. 16

Single-Cell Analysis of Ploidy and Centrosomes Underscores the Peculiarity of Normal Hepatocytes

Polyploidization is the most well recognized feature of the liver. Yet, a quantitative and behavioral analysis of centrosomes and DNA content in normal hepatocytes has been limited by the technical challenges of methods available. By using a novel approach employing FISH for chromosomes 18, X and Y we provide, for the first time, a detailed analysis of DNA copies during physiological development in the liver at single cell level. We demonstrate that aneuploidy and unbalanced DNA content in binucleated hepatocytes are common features in normal adult liver. Despite the common belief that hepatocytes contain 1, 2 or no more than 4 centrosomes, our double staining for centrosome associated proteins reveals extranumerary centrosomes in a high percentage of cells as early as 15 days of age. We show that in murine liver the period between 15 days and 1.5 months marks the transition from a prevalence of mononucleated cells to up to 75% of binucleated cells. Our data demonstrate that this timing correlates with a switch in centrosomes number. At 15 days the expected 1 or 2 centrosomes converge with several hepatocytes that contain 3 centrosomes; at 1.5 months the percentage of cells with 3 centrosomes decreases concomitantly with the increase of cells with more than 4 centrosomes. Our analysis shows that the extranumerary centrosomes emerge in concomitance with the process of binucleation and polyploidization and maintain α-tubulin nucleation activity. Finally, by integrating interphase FISH and immunofluorescent approaches, we detected an imbalance between centrosome number and DNA content in liver cells that deviates from the equilibrium expected in normal cells. We speculate that these unique features are relevant to the peculiar biological function of liver cells which are continuously challenged by stress, a condition that could predispose to genomic instability

Measurement of the Proton and Deuteron Spin Structure Function g_1 in the Resonance Region

We have measured the proton and deuteron spin structure functions g_1^p and g_1^d in the region of the nucleon resonances for W^2 < 5 GeV^2 and $Q^2\simeq 0.5$ and $Q^2\simeq 1.2$ GeV^2 by inelastically scattering 9.7 GeV polarized electrons off polarized $^{15}NH_3$ and $^{15}ND_3$ targets. We observe significant structure in g_1^p in the resonance region. We have used the present results, together with the deep-inelastic data at higher W^2, to extract $\Gamma(Q^2)\equiv\int_0^1 g_1(x,Q^2) dx$. This is the first information on the low-Q^2 evolution of Gamma toward the Gerasimov-Drell-Hearn limit at Q^2 = 0.Comment: 7 pages, 2 figure

Measurements of the Q2Q^2-Dependence of the Proton and Neutron Spin Structure Functions g1p and g1n

The structure functions g1p and g1n have been measured over the range 0.014 < x < 0.9 and 1 < Q2 < 40 GeV2 using deep-inelastic scattering of 48 GeV longitudinally polarized electrons from polarized protons and deuterons. We find that the Q2 dependence of g1p (g1n) at fixed x is very similar to that of the spin-averaged structure function F1p (F1n). From a NLO QCD fit to all available data we find $\Gamma_1^p - \Gamma_1^n =0.176 \pm 0.003 \pm 0.007$ at Q2=5 GeV2, in agreement with the Bjorken sum rule prediction of 0.182 \pm 0.005.Comment: 17 pages, 3 figures. Submitted to Physics Letters