An approximation scheme for quasi-stationary distributions of killed diffusions

In this paper we study the asymptotic behavior of the normalized weighted empirical occupation measures of a diffusion process on a compact manifold which is killed at a smooth rate and then regenerated at a random location, distributed according to the weighted empirical occupation measure. We show that the weighted occupation measures almost surely comprise an asymptotic pseudo-trajectory for a certain deterministic measure-valued semiflow, after suitably rescaling the time, and that with probability one they converge to the quasi-stationary distribution of the killed diffusion. These results provide theoretical justification for a scalable quasi-stationary Monte Carlo method for sampling from Bayesian posterior distributions.Comment: v2: revised version, 29 pages, 1 figur

Theoretical properties of quasi-stationary Monte Carlo methods

This paper gives foundational results for the application of quasi-stationarity to Monte Carlo inference problems. We prove natural sufficient conditions for the quasi-limiting distribution of a killed diffusion to coincide with a target density of interest. We also quantify the rate of convergence to quasi-stationarity by relating the killed diffusion to an appropriate Langevin diffusion. As an example, we consider in detail a killed Ornstein--Uhlenbeck process with Gaussian quasi-stationary distribution.Comment: 27 pages, 1 figure. Final version of accepted paper. Minor typos correcte

Rotational and Vibrational Dynamics of Interstitial Molecular Hydrogen

The calculation of the hindered roton-phonon energy levels of a hydrogen molecule in a confining potential with different symmetries is systematized for the case when the rotational angular momentum $J$ is a good quantum number. One goal of this program is to interpret the energy-resolved neutron time of flight spectrum previously obtained for H$_{2}$C$_{60}$. This spectrum gives direct information on the energy level spectrum of H$_2$ molecules confined to the octahedral interstitial sites of solid C$_{60}$. We treat this problem of coupled translational and orientational degrees of freedom a) by construction of an effective Hamiltonian to describe the splitting of the manifold of states characterized by a given value of $J$ and having a fixed total number of phonon excitations, b) by numerical solutions of the coupled translation-rotation problem on a discrete mesh of points in position space, and c) by a group theoretical symmetry analysis. Results obtained from these three different approaches are mutually consistent. The results of our calculations explain several hitherto uninterpreted aspects of the experimental observations, but show that a truly satisfactory orientational potential for the interaction of an H$_2$ molecule with a surrounding array of C atoms has not yet been developed.Comment: 53 pages, 9 figures, to appear in Phys. Rev B (in press). Phys. Rev. B (in press

Synchronization of coupled neural oscillators with heterogeneous delays

We investigate the effects of heterogeneous delays in the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types of synchronized oscillations of variable period. We analyze this synchronization based on the interplay of the different time delays and support the numerical results by analytical findings. In addition, we elaborate on bursting-like dynamics with two competing timescales on the basis of the autocorrelation function.Comment: 18 pages, 14 figure

Similarities and differences between biliary sludge and microlithiasis: Their clinical and pathophysiological significances

The terms biliary sludge and cholesterol microlithiasis (hereafter referred to as microlithiasis) were originated from different diagnostic techniques and may represent different stages of cholesterol gallstone disease. Although the pathogenesis of biliary sludge and microlithiasis may be similar, microlithiasis could be preceded by biliary sludge, followed by persistent precipitation and aggregation of solid cholesterol crystals, and eventually, gallstone formation. Many clinical conditions are clearly associated with the formation of biliary sludge and microlithiasis, including total parenteral nutrition, rapid weight loss, pregnancy, organ transplantation, administration of certain medications, and a variety of acute and chronic illnesses. Numerous studies have demonstrated complete resolution of biliary sludge in approximately 40% of patients, a cyclic pattern of disappearing and reappearing in about 40%, and progression to gallstones in nearly 20%. Although only a minority of patients with ultrasonographic demonstration of biliary sludge develop gallstones, it is still a matter of controversy whether microlithiasis could eventually evolve to cholesterol gallstones. Biliary sludge and microlithiasis are asymptomatic in the vast majority of patients; however, they can cause biliary colic, acute cholecystitis, and acute pancreatitis. Biliary sludge and microlithiasis are most often diagnosed ultrasonographically and bile microscopy is considered the gold standard for their diagnosis. Specific measures to prevent the development of biliary sludge are not practical or cost-effective in the general population. Laparoscopic cholecystectomy offers the most definitive therapy on biliary sludge. Endoscopic sphincterotomy or surgical intervention is effective for microlithiasis-induced pancreatitis. Ursodeoxycholic acid can effectively prevent the recurrence of solid cholesterol crystals and significantly reduce the risk of recurrent pancreatitis. Keywords: Biliary sludge, Cholesterol microlithiasis, Acute cholecystitis, Acute pancreatitis, Biliary colic, Cholesterol monohydrate crystals, Lithogenic bil

Label Transfer from APOGEE to LAMOST: Precise Stellar Parameters for 450,000 LAMOST Giants

In this era of large-scale stellar spectroscopic surveys, measurements of stellar attributes ("labels," i.e. parameters and abundances) must be made precise and consistent across surveys. Here, we demonstrate that this can be achieved by a data-driven approach to spectral modeling. With The Cannon, we transfer information from the APOGEE survey to determine precise Teff, log g, [Fe/H], and [$\alpha$/M] from the spectra of 450,000 LAMOST giants. The Cannon fits a predictive model for LAMOST spectra using 9952 stars observed in common between the two surveys, taking five labels from APOGEE DR12 as ground truth: Teff, log g, [Fe/H], [\alpha/M], and K-band extinction $A_k$. The model is then used to infer Teff, log g, [Fe/H], and [$\alpha$/M] for 454,180 giants, 20% of the LAMOST DR2 stellar sample. These are the first [$\alpha$/M] values for the full set of LAMOST giants, and the largest catalog of [$\alpha$/M] for giant stars to date. Furthermore, these labels are by construction on the APOGEE label scale; for spectra with S/N > 50, cross-validation of the model yields typical uncertainties of 70K in Teff, 0.1 in log g, 0.1 in [Fe/H], and 0.04 in [$\alpha$/M], values comparable to the broadly stated, conservative APOGEE DR12 uncertainties. Thus, by using "label transfer" to tie low-resolution (LAMOST R $\sim$ 1800) spectra to the label scale of a much higher-resolution (APOGEE R $\sim$ 22,500) survey, we substantially reduce the inconsistencies between labels measured by the individual survey pipelines. This demonstrates that label transfer with The Cannon can successfully bring different surveys onto the same physical scale.Comment: 27 pages, 14 figures. Accepted by ApJ on 16 Dec 2016, implementing suggestions from the referee reports. Associated code available at https://github.com/annayqho/TheCanno

Liquid-like thermal conduction in a crystalline solid

A solid conducts heat through both transverse and longitudinal acoustic phonons, but a liquid employs only longitudinal vibrations. Here, we report that the crystalline solid AgCrSe2 has liquid-like thermal conduction. In this compound, Ag atoms exhibit a dynamic duality that they are exclusively involved in intense low-lying transverse acoustic phonons while they also undergo local fluctuations inherent in an order-to-disorder transition occurring at 450 K. As a consequence of this extreme disorder-phonon coupling, transverse acoustic phonons become damped as approaching the transition temperature, above which they are not defined anymore because their lifetime is shorter than the relaxation time of local fluctuations. Nevertheless, the damped longitudinal acoustic phonon survives for thermal transport. This microscopic insight might reshape the fundamental idea on thermal transport properties of matter and facilitates the optimization of thermoelectrics.Comment: four figures, supplemental informatio

Missing Iron Problem and Type Ia Supernova Enrichment of Hot Gas in Galactic Spheroids

Type Ia supernovae (Ia SNe) provide a rich source of iron for hot gas in galactic stellar spheroids. However, the expected super-solar iron abundance of the hot gas is not observed. Instead, X-ray observations often show decreasing iron abundance toward galactic central regions, where the Ia SN enrichment is expected to be the highest. We examine the cause of this missing iron problem by studying the enrichment process and its effect on X-ray abundance measurements of the hot gas. The evolution of Ia SN iron ejecta is simulated in the context of galaxy-wide hot gas outflows, in both supersonic and subsonic cases, as may be expected for hot gas in galactic bulges or elliptical galaxies of intermediate masses. SN reverse-shock heated iron ejecta is typically found to have a very high temperature and low density, hence producing little X-ray emission. Such hot ejecta, driven by its large buoyancy, can quickly reach a substantially higher outward velocity than the ambient medium, which is dominated by mass loss from evolved stars. The ejecta is gradually and dynamically mixed with the medium at large galactic radii. The ejecta is also slowly diluted and cooled by {\sl insitu} mass injection from evolved stars. These processes together naturally result in the observed positive gradient in the average radial iron abundance distribution of the hot gas, even if mass-weighted. This trend is in addition to the X-ray measurement bias that tends to underestimate the iron abundance for the hot gas with a temperature distribution.Comment: 18 pages, 9 figures, MNRAS in pres