12,474 research outputs found
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 is a good quantum number. One
goal of this program is to interpret the energy-resolved neutron time of flight
spectrum previously obtained for HC. This spectrum gives direct
information on the energy level spectrum of H molecules confined to the
octahedral interstitial sites of solid C. 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 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 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 [/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 . The model is then
used to infer Teff, log g, [Fe/H], and [/M] for 454,180 giants, 20% of
the LAMOST DR2 stellar sample. These are the first [/M] values for the
full set of LAMOST giants, and the largest catalog of [/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
[/M], values comparable to the broadly stated, conservative APOGEE DR12
uncertainties. Thus, by using "label transfer" to tie low-resolution (LAMOST R
1800) spectra to the label scale of a much higher-resolution (APOGEE R
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
- …