Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations

We construct a new framework for accelerating Markov chain Monte Carlo in posterior sampling problems where standard methods are limited by the computational cost of the likelihood, or of numerical models embedded therein. Our approach introduces local approximations of these models into the Metropolis-Hastings kernel, borrowing ideas from deterministic approximation theory, optimization, and experimental design. Previous efforts at integrating approximate models into inference typically sacrifice either the sampler's exactness or efficiency; our work seeks to address these limitations by exploiting useful convergence characteristics of local approximations. We prove the ergodicity of our approximate Markov chain, showing that it samples asymptotically from the \emph{exact} posterior distribution of interest. We describe variations of the algorithm that employ either local polynomial approximations or local Gaussian process regressors. Our theoretical results reinforce the key observation underlying this paper: when the likelihood has some \emph{local} regularity, the number of model evaluations per MCMC step can be greatly reduced without biasing the Monte Carlo average. Numerical experiments demonstrate multiple order-of-magnitude reductions in the number of forward model evaluations used in representative ODE and PDE inference problems, with both synthetic and real data.Comment: A major update of the theory and example

Metal-Poor Stars Observed with the Magellan Telescope. III. New Extremely and Ultra Metal-Poor Stars from SDSS/SEGUE and Insights on the Formation of Ultra Metal-Poor Stars

We report the discovery of one extremely metal-poor (EMP; [Fe/H]<-3) and one ultra metal-poor (UMP; [Fe/H]<-4) star selected from the SDSS/SEGUE survey. These stars were identified as EMP candidates based on their medium-resolution (R~2,000) spectra, and were followed-up with high-resolution (R~35,000) spectroscopy with the Magellan-Clay Telescope. Their derived chemical abundances exhibit good agreement with those of stars with similar metallicities. We also provide new insights on the formation of the UMP stars, based on comparison with a new set of theoretical models of supernovae nucleosynthesis. The models were matched with 20 UMP stars found in the literature, together with one of the program stars (SDSS J1204+1201), with [Fe/H]=-4.34. From fitting their abundances, we find that the supernovae progenitors, for stars where carbon and nitrogen are measured, had masses ranging from 20.5 M_sun to 28 M_sun and explosion energies from 0.3 to 0.9x10^51 erg. These results are highly sensitive to the carbon and nitrogen abundance determinations, which is one of the main drivers for future high-resolution follow-up of UMP candidates. In addition, we are able to reproduce the different CNO abundance patterns found in UMP stars with a single progenitor type, by varying its mass and explosion energy.Comment: 15 pages, 12 figures; accepted for publication in Ap

EMG and its possible use in the treatment of vertical imbalance

EMG recordings were measured on the frontalis muscle of nine subjects, two of which were controls. Prism was then placed before the subject\u27s left eye and changes in EMG were recorded. We found substantial changes in only three subjects. The other subjects showed no significant trends with the placement or removal of prisms

Effectiveness of a Proposed System Design on Academic Management of Kampala International University: Design, Development and Implementation

This study aimed at answering questions concerning the significant effect of the proposed system design on the academic management of KIU in terms of supportability, reliability, maintainability and availability. Using a quasi-experimental design on a total sample of 750 respondents (i.e. the Users, Academic Staff and Students) and t-sample test, the study revealed that there was a significant effect by the proposed design on the academic management system. The study thus recommends that all stakeholders should be trained to interact and use it which will save a lot of time for the students, academic staff and university branches in processing academic data. Key Words: Proposed Academic management System, Supportability, Reliability, availability, Maintainabilit

Relative Riemann-Zariski spaces

In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described either as projective limits of schemes in the category of locally ringed spaces or as certain spaces of valuations. We apply these spaces to prove the following two new results: a strong version of stable modification theorem for relative curves; a decomposition theorem which asserts that any separated morphism between quasi-compact and quasi-separated schemes factors as a composition of an affine morphism and a proper morphism. (In particular, we obtain a new proof of Nagata's compactification theorem.)Comment: 30 pages, the final version, to appear in Israel J. of Mat

A New Family of High-Current Cyclotrons for Isotope Production

We have developed a new family of compact cyclotrons designed to accelerate record-high currents of ions with charge-to-mass of 1/2. We have detailed engineering designs for a 5 mA H2+ cyclotron (delivering 10 mA of protons) and are extending this concept to 5 mA of deuterons (D+). The innovations enabling the high currents are: 1) bunching with an RFQ that enables efficient capture and 2) space-charge-mitigated stable bunch formation established in the first few turns. These developments can be applied to cyclotron from 5 to around 60 MeV/amu. A 20 MeV/amu deuteron cyclotron would be effective for 225Ac production via (n,2n) with fast neutrons generated by deuteron breakup in beryllium.Comment: 22 pages, 9 figures, paper to be submitted to the Journal of Radioanalytical and Nuclear Chemistry, as part of the Proceedings of the 11th International Conference on Isotopes, held in Saskatoon, Canada, July 202

Alignment and preliminary outcomes of an ELT-size instrument to a very large telescope: LINC-NIRVANA at LBT

LINC-NIRVANA (LN) is a high resolution, near infrared imager that uses a multiple field-of-view, layer-oriented, multi-conjugate AO system, consisting of four multi-pyramid wavefront sensors (two for each arm of the Large Binocular Telescope, each conjugated to a different altitude). The system employs up to 40 star probes, looking at up to 20 natural guide stars simultaneously. Its final goal is to perform Fizeau interferometric imaging, thereby achieving ELT-like spatial resolution (22.8 m baseline resolution). For this reason, LN is also equipped with a fringe tracker, a beam combiner and a NIR science camera, for a total of more than 250 optical components and an overall size of approximately 6x4x4.5 meters. This paper describes the tradeoffs evaluated in order to achieve the alignment of the system to the telescope. We note that LN is comparable in size to planned ELT instrumentation. The impact of such alignment strategies will be compared and the selected procedure, where the LBT telescope is, in fact, aligned to the instrument, will be described. Furthermore, results coming from early night-time commissioning of the system will be presented.Comment: 8 pages, 6 pages, AO4ELT5 Proceedings, 201

The structural properties of the multi-layer graphene/4H-SiC(000-1) system as determined by Surface X-ray Diffraction

We present a structural analysis of the multi-layer graphene-4HSiC(000-1}) system using Surface X-Ray Reflectivity. We show for the first time that graphene films grown on the C-terminated (000-1}) surface have a graphene-substrate bond length that is very short (0.162nm). The measured distance rules out a weak Van der Waals interaction to the substrate and instead indicates a strong bond between the first graphene layer and the bulk as predicted by ab-initio calculations. The measurements also indicate that multi-layer graphene grows in a near turbostratic mode on this surface. This result may explain the lack of a broken graphene symmetry inferred from conduction measurements on this system [C. Berger et al., Science 312, 1191 (2006)].Comment: 9 pages with 6 figure