New, efficient, and accurate high order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions

We construct new, efficient, and accurate high-order finite differencing operators which satisfy summation by parts. Since these operators are not uniquely defined, we consider several optimization criteria: minimizing the bandwidth, the truncation error on the boundary points, the spectral radius, or a combination of these. We examine in detail a set of operators that are up to tenth order accurate in the interior, and we surprisingly find that a combination of these optimizations can improve the operators' spectral radius and accuracy by orders of magnitude in certain cases. We also construct high-order dissipation operators that are compatible with these new finite difference operators and which are semi-definite with respect to the appropriate summation by parts scalar product. We test the stability and accuracy of these new difference and dissipation operators by evolving a three-dimensional scalar wave equation on a spherical domain consisting of seven blocks, each discretized with a structured grid, and connected through penalty boundary conditions.Comment: 16 pages, 9 figures. The files with the coefficients for the derivative and dissipation operators can be accessed by downloading the source code for the document. The files are located in the "coeffs" subdirector

Globally Optimal Crowdsourcing Quality Management

We study crowdsourcing quality management, that is, given worker responses to a set of tasks, our goal is to jointly estimate the true answers for the tasks, as well as the quality of the workers. Prior work on this problem relies primarily on applying Expectation-Maximization (EM) on the underlying maximum likelihood problem to estimate true answers as well as worker quality. Unfortunately, EM only provides a locally optimal solution rather than a globally optimal one. Other solutions to the problem (that do not leverage EM) fail to provide global optimality guarantees as well. In this paper, we focus on filtering, where tasks require the evaluation of a yes/no predicate, and rating, where tasks elicit integer scores from a finite domain. We design algorithms for finding the global optimal estimates of correct task answers and worker quality for the underlying maximum likelihood problem, and characterize the complexity of these algorithms. Our algorithms conceptually consider all mappings from tasks to true answers (typically a very large number), leveraging two key ideas to reduce, by several orders of magnitude, the number of mappings under consideration, while preserving optimality. We also demonstrate that these algorithms often find more accurate estimates than EM-based algorithms. This paper makes an important contribution towards understanding the inherent complexity of globally optimal crowdsourcing quality management

Nonstatistical dynamics on potentials exhibiting reaction path bifurcations and valley-ridge inflection points

We study reaction dynamics on a model potential energy surface exhibiting post-transition state bifurcation in the vicinity of a valley ridge inflection point. We compute fractional yields of products reached after the VRI region is traversed, both with and without dissipation. It is found that apparently minor variations in the potential lead to significant changes in the reaction dynamics. Moreover, when dissipative effects are incorporated, the product ratio depends in a complicated and highly non-monotonic fashion on the dissipation parameter. Dynamics in the vicinity of the VRI point itself play essentially no role in determining the product ratio, except in the highly dissipative regime.Comment: 33 pages, 10 figures, corrected the author name in reference [6

Accessing and assessing lunar resources with PROSPECT

PROSPECT is a package in development by ESA to assess the in-situ resource potential of lunar regolith. PROSPECT will: obtain sub-surface regolith samples, extract volatiles, identify chemical species, quantify abundances, and characterize isotopes

ALMA Observations of the Young Substellar Binary System 2M1207

We present ALMA observations of the 2M1207 system, a young binary made of a brown dwarf with a planetary-mass companion at a projected separation of about 40 au. We detect emission from dust continuum at 0.89 mm and from the $J = 3 - 2$ rotational transition of CO from a very compact disk around the young brown dwarf. The small radius found for this brown dwarf disk may be due to truncation from the tidal interaction with the planetary-mass companion. Under the assumption of optically thin dust emission, we estimated a dust mass of 0.1 $M_{\oplus}$ for the 2M1207A disk, and a 3$\sigma$ upper limit of $\sim 1~M_{\rm{Moon}}$ for dust surrounding 2M1207b, which is the tightest upper limit obtained so far for the mass of dust particles surrounding a young planetary-mass companion. We discuss the impact of this and other non-detections of young planetary-mass companions for models of planet formation, which predict the presence of circum-planetary material surrounding these objects.Comment: 10 pages, 6 figures, accepted for publication in A

An automated method for the determination of deoxyribonuclease activity as exemplified by fractionation of the components of the medicament Varidase®

The activity of most deoxyribonuclease enzymes can be monitored by measuring the change in absorbance at 260 nm which accompanies the breakdown of the double-stranded structure of native DNA. An automated method for determining deoxyribonuclease activity, based on such an absorbance change, which can overcome problems of inhibition arising from the presence of inorganic cations, is described. Variations in inorganic cation concentration is a particular problem when measuring the activity of chromatographic fractions eluted via a salt gradient. A comparison is made between the automated and a manual method for the assay of deoxyribonuclease active constituents, of the medicament ‘Varidase’, eluted from a Cellex-D (Bio-Rad Laboratories Ltd) anionic exchange resin using a 0.05-1.0 M sodium chloride gradient