Refinement Type Inference via Horn Constraint Optimization

We propose a novel method for inferring refinement types of higher-order functional programs. The main advantage of the proposed method is that it can infer maximally preferred (i.e., Pareto optimal) refinement types with respect to a user-specified preference order. The flexible optimization of refinement types enabled by the proposed method paves the way for interesting applications, such as inferring most-general characterization of inputs for which a given program satisfies (or violates) a given safety (or termination) property. Our method reduces such a type optimization problem to a Horn constraint optimization problem by using a new refinement type system that can flexibly reason about non-determinism in programs. Our method then solves the constraint optimization problem by repeatedly improving a current solution until convergence via template-based invariant generation. We have implemented a prototype inference system based on our method, and obtained promising results in preliminary experiments.Comment: 19 page

The chaotic behavior of the black hole system GRS 1915+105

A modified non-linear time series analysis technique, which computes the correlation dimension $D_2$, is used to analyze the X-ray light curves of the black hole system GRS 1915+105 in all twelve temporal classes. For four of these temporal classes $D_2$ saturates to $\approx 4-5$ which indicates that the underlying dynamical mechanism is a low dimensional chaotic system. Of the other eight classes, three show stochastic behavior while five show deviation from randomness. The light curves for four classes which depict chaotic behavior have the smallest ratio of the expected Poisson noise to the variability ($< 0.05$) while those for the three classes which depict stochastic behavior is the highest ($> 0.2$). This suggests that the temporal behavior of the black hole system is governed by a low dimensional chaotic system, whose nature is detectable only when the Poisson fluctuations are much smaller than the variability.Comment: Accepted for publication in Astrophysical Journa

Oscillations of rapidly rotating relativistic stars

Non-axisymmetric oscillations of rapidly rotating relativistic stars are studied using the Cowling approximation. The oscillation spectra have been estimated by Fourier transforming the evolution equations describing the perturbations. This is the first study of its kind and provides information on the effect of fast rotation on the oscillation spectra while it offers the possibility in studying the complete problem by including spacetime perturbations. Our study includes both axisymmetric and non-axisymmetric perturbations and provides limits for the onset of the secular bar mode rotational instability. We also present approximate formulae for the dependence of the oscillation spectrum from rotation. The results suggest that it is possible to extract the relativistic star's parameters from the observed gravitational wave spectrum.Comment: this article will be published in Physical Review

On the possible existence of short-period g-mode instabilities powered by nuclear burning shells in post-AGB H-deficient (PG1159-type) stars

We present a pulsational stability analysis of hot post-AGB H-deficient pre-white dwarf stars with active He-burning shells. The stellar models employed are state-of-the-art equilibrium structures representative of PG1159 stars derived from the complete evolution of the progenitor stars. On the basis of fully nonadiabatic pulsation computations, we confirmed theoretical evidence for the existence of a separate PG1159 instability strip in the $\log T_{\rm eff} - \log g$ diagram characterized by short-period $g$-modes excited by the $\epsilon$-mechanism. This instability strip partially overlaps the already known GW Vir instability strip of intermediate/long period $g$-modes destabilized by the classical $\kappa$-mechanism acting on the partial ionization of C and/or O in the envelope of PG1159 stars. We found that PG1159 stars characterized by thick He-rich envelopes and located inside this overlapping region could exhibit both short and intermediate/long periods simultaneously. we study the particular case of VV 47, a pulsating planetary nebula nucleus that has been reported to exhibit a series of unusually short pulsation periods. We found that the long periods exhibited by VV 47 can be readily explained by the classical $\kappa$-mechanism, while the observed short-period branch below $\approx 300$ s could correspond to modes triggered by the He-burning shell through the $\epsilon$-mechanism, although more observational work is needed to confirm the reality of these short-period modes. Were the existence of short-period $g$-modes in this star convincingly confirmed by future observations, VV 47 could be the first known pulsating star in which both the $\kappa$-mechanism and the $\epsilon$-mechanism of mode driving are simultaneously operating.Comment: 9 pages, 5 figures, 2 tables. To be published in The Astrophysical Journa

Radiative Transfer Effects in He I Emission Lines

We consider the effect of optical depth of the 2 ^{3}S level on the nebular recombination spectrum of He I for a spherically symmetric nebula with no systematic velocity gradients. These calculations, using many improvements in atomic data, can be used in place of the earlier calculations of Robbins. We give representative Case B line fluxes for UV, optical, and IR emission lines over a range of physical conditions: T=5000-20000 K, n_{e}=1-10^{8} cm^{-3}, and tau_{3889}=0-100. A FORTRAN program for calculating emissivities for all lines arising from quantum levels with n < 11 is also available from the authors. We present a special set of fitting formulae for the physical conditions relevant to low metallicity extragalactic H II regions: T=12,000-20,000 K, n_{e}=1-300 cm^{-3}, and tau_{3889} < 2.0. For this range of physical conditions, the Case B line fluxes of the bright optical lines 4471 A, 5876 A, and 6678 A, are changed less than 1%, in agreement with previous studies. However, the 7065 A corrections are much smaller than those calculated by Izotov & Thuan based on the earlier calculations by Robbins. This means that the 7065 A line is a better density diagnostic than previously thought. Two corrections to the fitting functions calculated in our previous work are also given.Comment: To be published in 10 April 2002 ApJ; relevant code available at ftp://wisp.physics.wisc.edu/pub/benjamin/Heliu

Inclusion of turbulence in solar modeling

The general consensus is that in order to reproduce the observed solar p-mode oscillation frequencies, turbulence should be included in solar models. However, until now there has not been any well-tested efficient method to incorporate turbulence into solar modeling. We present here two methods to include turbulence in solar modeling within the framework of the mixing length theory, using the turbulent velocity obtained from numerical simulations of the highly superadiabatic layer of the sun at three stages of its evolution. The first approach is to include the turbulent pressure alone, and the second is to include both the turbulent pressure and the turbulent kinetic energy. The latter is achieved by introducing two variables: the turbulent kinetic energy per unit mass, and the effective ratio of specific heats due to the turbulent perturbation. These are treated as additions to the standard thermodynamic coordinates (e.g. pressure and temperature). We investigate the effects of both treatments of turbulence on the structure variables, the adiabatic sound speed, the structure of the highly superadiabatic layer, and the p-mode frequencies. We find that the second method reproduces the SAL structure obtained in 3D simulations, and produces a p-mode frequency correction an order of magnitude better than the first method.Comment: 10 pages, 12 figure

Asteroseismic Theory of Rapidly Oscillating Ap Stars

This paper reviews some of the important advances made over the last decade concerning theory of roAp stars.Comment: 9 pages, 5 figure

Hemodynamic Assessment of Celiaco-mesenteric Anastomosis in Patients with Pancreaticoduodenal Artery Aneurysm Concomitant with Celiac Artery Occlusion using Flow-sensitive Four-dimensional Magnetic Resonance Imaging

ObjectivesMany pancreaticoduodenal artery (PDA) aneurysms are associated with celiac artery (CA) stenosis. The pathogenesis of PDA aneurysm may be associated with hemodynamic changes due to CA stenosis/occlusion. The aim of this study was to assess the hemodynamic changes of celiaco-mesenteric anastomosis in patients with PDA aneurysms concomitant with CA occlusion using four-dimensional flow-sensitive magnetic resonance imaging (4D-Flow).Methods4D-Flow was performed preoperatively on five patients. Seven age- and sex-matched individuals were used as controls. Hemodynamic parameters such as flow volume and maximum flow velocity in PDAs, gastroduodenal arteries, common hepatic arteries, and superior mesenteric arteries were compared between both groups. Wall shear stress (WSS) and oscillatory shear index (OSI) were mapped in both groups.ResultsIn the patient group, 4D-Flow identified retrograde flow of both gastroduodenal arteries and common hepatic arteries. Heterogeneous distribution patterns of both WSS and OSI were identified across the entire PDA in the patient group. OSI mapping showed multiple regions with extremely high OSI values (OSI > 0.3) in all patients. All PDA aneurysms, which were surgically resected, were atherosclerotic.Conclusions4D-Flow identified hemodynamic changes in celiaco-mesenteric arteries in patients with PDA aneurysms with concomitant CA occlusion. These hemodynamic changes may be associated with PDA aneurysm formation

A novel type of proximity focusing RICH counter with multiple refractive index aerogel radiator

A proximity focusing ring imaging Cherenkov detector, with the radiator consisting of two or more aerogel layers of different refractive indices, has been tested in 1-4 GeV/c pion beams at KEK. Essentially, a multiple refractive index aerogel radiator allows for an increase in Cherenkov photon yield on account of the increase in overall radiator thickness, while avoiding the simultaneous degradation in single photon angular resolution associated with the increased uncertainty of the emission point. With the refractive index of consecutive layers suitably increasing in the downstream direction, one may achieve overlapping of the Cherenkov rings from a single charged particle. In the opposite case of decreasing refractive index, one may obtain well separated rings. In the former combination an approximately 40% increase in photon yield is accompanied with just a minor degradation in single photon angular resolution. The impact of this improvement on the pion/kaon separation at the upgraded Belle detector is discussed.Comment: submitted to Nucl. Instr. Meth.