Commuting difference operators arising from the elliptic C_2^{(1)}-face model

We study a pair of commuting difference operators arising from the elliptic C_2^{(1)}-face model. The operators, whose coefficients are expressed in terms of the Jacobi's elliptic theta function, act on the space of meromorphic functions on the weight space of the C_2 type simple Lie algebra. We show that the space of functions spanned by the level one characters of the affine Lie algebra sp(4,C) is invariant under the action of the difference operators.Comment: latex2e file, 19 pages, no figures; added reference

Eisenhart Lift of 22--Dimensional Mechanics

The Eisenhart lift is a variant of geometrization of classical mechanics with $d$ degrees of freedom in which the equations of motion are embedded into the geodesic equations of a Brinkmann-type metric defined on $(d+2)$-dimensional spacetime of Lorentzian signature. In this work, the Eisenhart lift of $2$-dimensional mechanics on curved background is studied. The corresponding $4$-dimensional metric is governed by two scalar functions which are just the conformal factor and the potential of the original dynamical system. We derive a conformal symmetry and a corresponding quadratic integral, associated with the Eisenhart lift. The energy--momentum tensor is constructed which, along with the metric, provides a solution to the Einstein equations. Uplifts of $2$-dimensional superintegrable models are discussed with a particular emphasis on the issue of hidden symmetries. It is shown that for the $2$-dimensional Darboux--Koenigs metrics, only type I can result in Eisenhart lifts which satisfy the weak energy condition. However, some physically viable metrics with hidden symmetries are presented.Comment: 20 page

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

The Distance to the Galactic Center Derived From Infrared Photometry of Bulge Red Clump Stars

On the basis of the near infrared observations of bulge red clump stars near the Galactic center, we have determined the galactocentric distance to be R_0 = 7.52 +- 0.10 (stat) +- 0.35 (sys) kpc. We observed the red clump stars at |l| < 1.0 deg and 0.7 deg < |b| < 1.0 deg with the IRSF 1.4 m telescope and the SIRIUS camera in the H and Ks bands. After extinction and population corrections, we obtained (m - M)_0 = 14.38 +- 0.03 (stat) +- 0.10 (sys). The statistical error is dominated by the uncertainty of the intrinsic local red clump stars' luminosity. The systematic error is estimated to be +- 0.10 including uncertainties in extinction and population correction, zero-point of photometry, and the fitting of the luminosity function of the red clump stars. Our result, R_0 = 7.52 kpc, is in excellent agreement with the distance determined geometrically with the star orbiting the massive black hole in the Galactic center. The recent result based on the spatial distribution of globular clusters is also consistent with our result. In addition, our study exhibits that the distance determination to the Galactic center with the red clump stars, even if the error of the population correction is taken into account, can achieve an uncertainty of about 5%, which is almost the same level as that in recent geometrical determinations.Comment: 14 pages, 4 figures, accepted by Ap

Similarity reduction of the modified Yajima-Oikawa equation

We study a similarity reduction of the modified Yajima-Oikawa hierarchy. The hierarchy is associated with a non-standard Heisenberg subalgebra in the affine Lie algebra of type A_2^{(1)}. The system of equations for self-similar solutions is presented as a Hamiltonian system of degree of freedom two, and admits a group of B\"acklund transformations isomorphic to the affine Weyl group of type A_2^{(1)}. We show that the system is equivalent to a two-parameter family of the fifth Painlev\'e equation.Comment: latex2e file, 18 pages, no figures; (v2)Introduction is modified. Some typos are correcte

Model-based registration for pneumothorax deformation analysis using intraoperative cone-beam CT images

[2020 42nd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), 20-24 July 2020, Montreal, QC, Canada]Because the lung deforms during surgery because of pneumothorax, it is important to be able to track the location of a tumor. Deformation of the whole lung can be estimated using intraoperative cone-beam CT (CBCT) images. In this study, we used deformable mesh registration methods for paired CBCT images in the inflated and deflated states, and analyzed their deformation. We proposed a deformable mesh registration framework for deformations of partial organ shapes involving large deformation and rotation. Experimental results showed that the proposed methods reduced errors in point-to-point correspondence. As a result of registration using surgical clips placed on the lung surface during imaging, it was confirmed that an average error of 3.9 mm occurred in eight cases. The result of analysis showed that both tissue rotation and contraction had large effects on displacement

Numerical study of O(a) improved Wilson quark action on anisotropic lattice

The $O(a)$ improved Wilson quark action on the anisotropic lattice is investigated. We carry out numerical simulations in the quenched approximation at three values of lattice spacing ($a_{\sigma}^{-1}=1$--2 GeV) with the anisotropy $\xi=a_{\sigma}/a_{\tau}=4$, where $a_{\sigma}$ and $a_{\tau}$ are the spatial and the temporal lattice spacings, respectively. The bare anisotropy $\gamma_F$ in the quark field action is numerically tuned by the dispersion relation of mesons so that the renormalized fermionic anisotropy coincides with that of gauge field. This calibration of bare anisotropy is performed to the level of 1 % statistical accuracy in the quark mass region below the charm quark mass. The systematic uncertainty in the calibration is estimated by comparing the results from different types of dispersion relations, which results in 3 % on our coarsest lattice and tends to vanish in the continuum limit. In the chiral limit, there is an additional systematic uncertainty of 1 % from the chiral extrapolation. Taking the central value $\gamma_F=\gamma_F^*$ from the result of the calibration, we compute the light hadron spectrum. Our hadron spectrum is consistent with the result by UKQCD Collaboration on the isotropic lattice. We also study the response of the hadron spectrum to the change of anisotropic parameter, $\gamma_F \to \gamma_F^* + \delta\gamma_F$. We find that the change of $\gamma_F$ by 2 % induces a change of 1 % in the spectrum for physical quark masses. Thus the systematic uncertainty on the anisotropic lattice, as well as the statistical one, is under control.Comment: 27 pages, 25 eps figures, LaTe

Self-Consistent MHD Modeling of a Coronal Mass Ejection, Coronal Dimming, and a Giant Cusp-Shaped Arcade Formation

We performed magnetohydrodynamic simulation of coronal mass ejections (CMEs) and associated giant arcade formations, and the results suggested new interpretations of observations of CMEs. We performed two cases of the simulation: with and without heat conduction. Comparing between the results of the two cases, we found that reconnection rate in the conductive case is a little higher than that in the adiabatic case and the temperature of the loop top is consistent with the theoretical value predicted by the Yokoyama-Shibata scaling law. The dynamical properties such as velocity and magnetic fields are similar in the two cases, whereas thermal properties such as temperature and density are very different.In both cases, slow shocks associated with magnetic reconnectionpropagate from the reconnection region along the magnetic field lines around the flux rope, and the shock fronts form spiral patterns. Just outside the slow shocks, the plasma density decreased a great deal. The soft X-ray images synthesized from the numerical results are compared with the soft X-ray images of a giant arcade observed with the Soft X-ray Telescope aboard {\it Yohkoh}, it is confirmed that the effect of heat conduction is significant for the detailed comparison between simulation and observation. The comparison between synthesized and observed soft X-ray images provides new interpretations of various features associated with CMEs and giant arcades.Comment: 39 pages, 18 figures. Accepted for publication in the Astrophysical Journal. The PDF file with high resplution figures can be downloaded from http://www.kwasan.kyoto-u.ac.jp/~shiota/study/ApJ62426.preprint.pdf