Bayesian inference with an adaptive proposal density for GARCH models

We perform the Bayesian inference of a GARCH model by the Metropolis-Hastings algorithm with an adaptive proposal density. The adaptive proposal density is assumed to be the Student's t-distribution and the distribution parameters are evaluated by using the data sampled during the simulation. We apply the method for the QGARCH model which is one of asymmetric GARCH models and make empirical studies for for Nikkei 225, DAX and Hang indexes. We find that autocorrelation times from our method are very small, thus the method is very efficient for generating uncorrelated Monte Carlo data. The results from the QGARCH model show that all the three indexes show the leverage effect, i.e. the volatility is high after negative observations

Precision Measurement of the n-3He Incoherent Scattering Length Using Neutron Interferometry

We report the first measurement of the low-energy neutron-$^3$He incoherent scattering length using neutron interferometry: $b_i' = (-2.512\pm 0.012{statistical}\pm0.014{systematic})$ fm. This is in good agreement with a recent calculation using the AV18+3N potential. The neutron-$^3$He scattering lengths are important for testing and developing nuclear potential models that include three nucleon forces, effective field theories for few-body nuclear systems, and neutron scattering measurements of quantum excitations in liquid helium. This work demonstrates the first use of a polarized nuclear target in a neutron interferometer.Comment: 4 figure

Detection of a dense clump in a filament interacting with W51e2

In the framework of the Herschel/PRISMAS Guaranteed Time Key Program, the line of sight to the distant ultracompact HII region W51e2 has been observed using several selected molecular species. Most of the detected absorption features are not associated with the background high-mass star-forming region and probe the diffuse matter along the line of sight. We present here the detection of an additional narrow absorption feature at ~70 km/s in the observed spectra of HDO, NH3 and C3. The 70 km/s feature is not uniquely identifiable with the dynamic components (the main cloud and the large-scale foreground filament) so-far identified toward this region. The narrow absorption feature is similar to the one found toward low-mass protostars, which is characteristic of the presence of a cold external envelope. The far-infrared spectroscopic data were combined with existing ground-based observations of 12CO, 13CO, CCH, CN, and C3H2 to characterize the 70 km/s component. Using a non-LTE analysis of multiple transitions of NH3 and CN, we estimated the density (n(H2) (1-5)x10^5 cm^-3) and temperature (10-30 K) for this narrow feature. We used a gas-grain warm-up based chemical model with physical parameters derived from the NH3 data to explain the observed abundances of the different chemical species. We propose that the 70 km/s narrow feature arises in a dense and cold clump that probably is undergoing collapse to form a low-mass protostar, formed on the trailing side of the high-velocity filament, which is thought to be interacting with the W51 main cloud. While the fortuitous coincidence of the dense clump along the line of sight with the continuum-bright W51e2 compact HII region has contributed to its non-detection in the continuum images, this same attribute makes it an appropriate source for absorption studies and in particular for ice studies of star-forming regions.Comment: Accepted for publication in A&

Neutron interferometric measurement of the scattering length difference between the triplet and singlet states of n-3^3He

We report a determination of the n-$^3$He scattering length difference $\Delta b^{\prime} = b_{1}^{\prime}-b_{0}^{\prime} =$ ($-5.411$ $\pm$ $0.031$ (statistical) $\pm$ $0.039$ (systematic)) fm between the triplet and singlet states using a neutron interferometer. This revises our previous result $\Delta b^{\prime} =$ (-5.610 $\pm$ $0.027$ (statistical) $\pm$ $0.032$ (systematic) fm obtained using the same technique in 2008. This revision is due to a re-analysis of the 2008 experiment that includes a more robust treatment of the phase shift caused by magnetic field gradients near the $^3$He cell. Furthermore, we more than doubled our original data set from 2008 by acquiring six months of additional data in 2013. Both the new data set and a re-analysis of the older data are in good agreement. Scattering lengths of low Z isotopes are valued for use in few-body nuclear effective field theories, provide important tests of modern nuclear potential models and in the case of $^3$He aid in the interpretation of neutron scattering from quantum liquids. The difference $\Delta b^{\prime}$ was determined by measuring the relative phase shift between two incident neutron polarizations caused by the spin-dependent interaction with a polarized $^3$He target. The target $^3$He gas was sealed inside a small, flat windowed glass cell that was placed in one beam path of the interferometer. The relaxation of $^3$He polarization was monitored continuously with neutron transmission measurements. The neutron polarization and spin flipper efficiency were determined separately using $^3$He analyzers and two different polarimetry analysis methods. A summary of the measured scattering lengths for n-$^3$He with a comparison to nucleon interaction models is given

Proton-3^{3}He elastic scattering at low energies

We present new accurate measurements of the differential cross section $\sigma(\theta)$ and the proton analyzing power $A_{y}$ for proton-$^{3}$He elastic scattering at various energies. A supersonic gas jet target has been employed to obtain these low energy cross section measurements. The $\sigma(\theta)$ distributions have been measured at $E_{p}$ = 0.99, 1.59, 2.24, 3.11, and 4.02 MeV. Full angular distributions of $A_{y}$ have been measured at $E_{p}$ = 1.60, 2.25, 3.13, and 4.05 MeV. This set of high-precision data is compared to four-body variational calculations employing realistic nucleon-nucleon (NN) and three-nucleon (3N) interactions. For the unpolarized cross section the agreement between the theoretical calculation and data is good when a $3N$ potential is used. The comparison between the calculated and measured proton analyzing powers reveals discrepancies of approximately 50% at the maximum of each distribution. This is analogous to the existing ``$A_{y}$ Puzzle'' known for the past 20 years in nucleon-deuteron elastic scattering.Comment: 22 pages, 9 figures, to be published in Physical Review C, corrected reference 4

ISO observation of molecular hydrogen and fine-structure lines in the photodissociation region IC 63

We wish to constrain the main physical properties of the photodissociation region (PDR) IC 63. We present the results of a survey for the lowest pure-rotational lines of H_2 with the Short Wavelength Spectrometer and for the major fine-structure cooling lines of O i at 63 and 145 μm and C ii at 157.7 μm with the Long Wavelength Spectrometer on board the Infrared Space Observatory (ISO) in the high-density PDR IC 63. The observations are compared with available photochemical models based on optical absorption and/or millimetre emission line data with and without enhanced H_2 formation rate on grain surfaces. The cloud density n_H is constrained by the fine-structure lines. The models include both collisional excitation and ultraviolet (UV) pumping of the H_2 ro-vibrational levels. Molecular pure-rotational lines up to S(5) are detected. The inferred column density of warm H_2 at 106 ± 11 K is (5.9 ± 1.8)^(+0.9)_(−0.7) × 10^(21) cm^(−2), while that of the hot component at 685 ± 68 K is (1.2 ± 0.4) × 10^(19) cm^(−2). Fine-structure lines are also detected in the far-infrared spectrum of IC 63. The fine-structure lines constrain the density of the PDR to be (1–5) × 10^3 cm^(−3). The impinging UV field on the PDR is enhanced by a factor of 10^3 compared to the mean interstellar field and is consistent with direct measurements in the UV. PDR models that include an enhanced H2 formation at high dust temperature give higher H_2 intensities than models without enhancement. However, the predicted intensities are still lower than the observed intensities

Exact correlation functions of the BCS model in the canonical ensemble

We evaluate correlation functions of the BCS model for finite number of particles. The integrability of the Hamiltonian relates it with the Gaudin algebra ${\cal G}[sl(2)]$. Therefore, a theorem that Sklyanin proved for the Gaudin model, can be applied. Several diagonal and off-diagonal correlators are calculated. The finite size scaling behavior of the pairing correlation function is studied.Comment: 4 pages revtex; 2 figures .eps. Revised version to be published in Phys. Rev. Let