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

Numerical simulations of the kappa-mechanism with convection

A strong coupling between convection and pulsations is known to play a major role in the disappearance of unstable modes close to the red edge of the classical Cepheid instability strip. As mean-field models of time-dependent convection rely on weakly-constrained parameters, we tackle this problem by the means of 2-D Direct Numerical Simulations (DNS) of kappa-mechanism with convection. Using a linear stability analysis, we first determine the physical conditions favourable to the kappa-mechanism to occur inside a purely-radiative layer. Both the instability strips and the nonlinear saturation of unstable modes are then confirmed by the corresponding DNS. We next present the new simulations with convection, where a convective zone and the driving region overlap. The coupling between the convective motions and acoustic modes is then addressed by using projections onto an acoustic subspace.Comment: 5 pages, 6 figures, accepted for publication in Astrophysics and Space Science, HELAS workshop (Rome june 2009

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.

Magnetic Connectivity between Active Regions 10987, 10988, and 10989 by Means of Nonlinear Force-Free Field Extrapolation

Extrapolation codes for modelling the magnetic field in the corona in cartesian geometry do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, \textit{e.g.}, a single active region. We apply a method for nonlinear force-free coronal magnetic field modelling of photospheric vector magnetograms in spherical geometry which allows us to study the connectivity between multi-active regions. We use vector magnetograph data from the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS)/Vector Spectromagnetograph(VSM) to model the coronal magnetic field, where we study three neighbouring magnetically connected active regions (ARs: 10987, 10988, 10989) observed on 28, 29, and 30 March 2008, respectively. We compare the magnetic field topologies and the magnetic energy densities and study the connectivities between the active regions(ARs). We have studied the time evolution of magnetic field over the period of three days and found no major changes in topologies as there was no major eruption event. From this study we have concluded that active regions are much more connected magnetically than the electric current.Comment: Solar Physic

A test of time-dependent theories of stellar convection

Context: In Cepheids close to the red edge of the classical instability strip, a coupling occurs between the acoustic oscillations and the convective motions close to the surface.The best topical models that account for this coupling rely on 1-D time-dependent convection (TDC) formulations. However, their intrinsic weakness comes from the large number of unconstrained free parameters entering in the description of turbulent convection. Aims: We compare two widely used TDC models with the first two-dimensional nonlinear direct numerical simulations (DNS) of the convection-pulsation coupling in which the acoustic oscillations are self-sustained by the kappa-mechanism. Methods: The free parameters appearing in the Stellingwerf and Kuhfuss TDC recipes are constrained using a chi2-test with the time-dependent convective flux that evolves in nonlinear simulations of highly-compressible convection with kappa-mechanism. Results: This work emphasises some inherent limits of TDC models, that is, the temporal variability and non-universality of their free parameters. More importantly, within these limits, Stellingwerf's formalism is found to give better spatial and temporal agreements with the nonlinear simulation than Kuhfuss's one. It may therefore be preferred in 1-D TDC hydrocodes or stellar evolution codes.Comment: 7 pages, 5 figures, 2 tables, accepted for publication in A&

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

Nonlinear force-free modelling: influence of inaccuracies in the measured magnetic vector

Context: Solar magnetic fields are regularly extrapolated into the corona starting from photospheric magnetic measurements that can suffer from significant uncertainties. Aims: Here we study how inaccuracies introduced into the maps of the photospheric magnetic vector from the inversion of ideal and noisy Stokes parameters influence the extrapolation of nonlinear force-free magnetic fields. Methods: We compute nonlinear force-free magnetic fields based on simulated vector magnetograms, which have been produced by the inversion of Stokes profiles, computed froma 3-D radiation MHD simulation snapshot. These extrapolations are compared with extrapolations starting directly from the field in the MHD simulations, which is our reference. We investigate how line formation and instrumental effects such as noise, limited spatial resolution and the effect of employing a filter instrument influence the resulting magnetic field structure. The comparison is done qualitatively by visual inspection of the magnetic field distribution and quantitatively by different metrics. Results: The reconstructed field is most accurate if ideal Stokes data are inverted and becomes less accurate if instrumental effects and noise are included. The results demonstrate that the non-linear force-free field extrapolation method tested here is relatively insensitive to the effects of noise in measured polarization spectra at levels consistent with present-day instruments. Conclusions heading: Our results show that we can reconstruct the coronal magnetic field as a nonlinear force-free field from realistic photospheric measurements with an accuracy of a few percent, at least in the absence of sunspots.Comment: A&A, accepted, 9 Pages, 4 Figure

Convective quenching of stellar pulsations

Context: we study the convection-pulsation coupling that occurs in cold Cepheids close to the red edge of the classical instability strip. In these stars, the surface convective zone is supposed to stabilise the radial oscillations excited by the kappa-mechanism. Aims: we study the influence of the convective motions onto the amplitude and the nonlinear saturation of acoustic modes excited by kappa-mechanism. We are interested in determining the physical conditions needed to lead to a quenching of oscillations by convection. Methods: we compute two-dimensional nonlinear simulations (DNS) of the convection-pulsation coupling, in which the oscillations are sustained by a continuous physical process: the kappa-mechanism. Thanks to both a frequential analysis and a projection of the physical fields onto an acoustic subspace, we study how the convective motions affect the unstable radial oscillations. Results: depending on the initial physical conditions, two main behaviours are obtained: (i) either the unstable fundamental acoustic mode has a large amplitude, carries the bulk of the kinetic energy and shows a nonlinear saturation similar to the purely radiative case; (ii) or the convective motions affect significantly the mode amplitude that remains very weak. In this second case, convection is quenching the acoustic oscillations. We interpret these discrepancies in terms of the difference in density contrast: larger stratification leads to smaller convective plumes that do not affect much the purely radial modes, while large-scale vortices may quench the oscillations.Comment: 15 pages, 17 figures, 3 tables, accepted for publication in A&