STARC: Structured Annotations for Reading Comprehension

We present STARC (Structured Annotations for Reading Comprehension), a new annotation framework for assessing reading comprehension with multiple choice questions. Our framework introduces a principled structure for the answer choices and ties them to textual span annotations. The framework is implemented in OneStopQA, a new high-quality dataset for evaluation and analysis of reading comprehension in English. We use this dataset to demonstrate that STARC can be leveraged for a key new application for the development of SAT-like reading comprehension materials: automatic annotation quality probing via span ablation experiments. We further show that it enables in-depth analyses and comparisons between machine and human reading comprehension behavior, including error distributions and guessing ability. Our experiments also reveal that the standard multiple choice dataset in NLP, RACE, is limited in its ability to measure reading comprehension. 47% of its questions can be guessed by machines without accessing the passage, and 18% are unanimously judged by humans as not having a unique correct answer. OneStopQA provides an alternative test set for reading comprehension which alleviates these shortcomings and has a substantially higher human ceiling performance.Comment: ACL 2020. OneStopQA dataset, STARC guidelines and human experiments data are available at https://github.com/berzak/onestop-q

Feeding selectivity of brown trout (Salmo trutta) in Loch Ness, Scotland

The aim of this study was to compare statistically the zooplankton assemblage ingested by brown trout (Salmo trutta) in Loch Ness with that of the zooplankton in the water column. This would allow the examination of the apparent paradox that very few copepods appear to be consumed by trout at a time of year when they are numerous and readily available as food. The investigation was limited to the crustacean zooplankters, since the Rotifera are generally so small that they are only of interest to fish in the first few days of life. 25 trout were obtained from anglers, and the stomach contents of non-"ferox" animals analysed. Samples of pelagic zooplankton were obtained approximately monthly from 30-m vertical net-hauls (mesh size 100 km). It is concluded that the variation in dietary composition with trout wet weight indicates an ontogenetic habitat shift producing spatial separation of young and older individuals

Supersymmetry and Schr\"odinger-type operators with distributional matrix-valued potentials

Building on work on Miura's transformation by Kappeler, Perry, Shubin, and Topalov, we develop a detailed spectral theoretic treatment of Schr\"odinger operators with matrix-valued potentials, with special emphasis on distributional potential coefficients. Our principal method relies on a supersymmetric (factorization) formalism underlying Miura's transformation, which intimately connects the triple of operators $(D, H_1, H_2)$ of the form [D= (0 & A^*, A & 0) \text{in} L^2(\mathbb{R})^{2m} \text{and} H_1 = A^* A, H_2 = A A^* \text{in} L^2(\mathbb{R})^m.] Here $A= I_m (d/dx) + \phi$ in $L^2(\mathbb{R})^m$, with a matrix-valued coefficient $\phi = \phi^* \in L^1_{\text{loc}}(\mathbb{R})^{m \times m}$, $m \in \mathbb{N}$, thus explicitly permitting distributional potential coefficients $V_j$ in $H_j$, $j=1,2$, where [H_j = - I_m \frac{d^2}{dx^2} + V_j(x), \quad V_j(x) = \phi(x)^2 + (-1)^{j} \phi'(x), j=1,2.] Upon developing Weyl--Titchmarsh theory for these generalized Schr\"odinger operators $H_j$, with (possibly, distributional) matrix-valued potentials $V_j$, we provide some spectral theoretic applications, including a derivation of the corresponding spectral representations for $H_j$, $j=1,2$. Finally, we derive a local Borg--Marchenko uniqueness theorem for $H_j$, $j=1,2$, by employing the underlying supersymmetric structure and reducing it to the known local Borg--Marchenko uniqueness theorem for $D$.Comment: 36 page

Inverse Spectral Theory for Sturm-Liouville Operators with Distributional Potentials

We discuss inverse spectral theory for singular differential operators on arbitrary intervals $(a,b) \subseteq \mathbb{R}$ associated with rather general differential expressions of the type $$\tau f = \frac{1}{r} \left(- \big(p[f' + s f]\big)' + s p[f' + s f] + qf\right),$$ where the coefficients $p$, $q$, $r$, $s$ are Lebesgue measurable on $(a,b)$ with $p^{-1}$, $q$, $r$, $s \in L^1_{\text{loc}}((a,b); dx)$ and real-valued with $p\not=0$ and $r>0$ a.e.\ on $(a,b)$. In particular, we explicitly permit certain distributional potential coefficients. The inverse spectral theory results derived in this paper include those implied by the spectral measure, by two-spectra and three-spectra, as well as local Borg-Marchenko-type inverse spectral results. The special cases of Schr\"odinger operators with distributional potentials and Sturm--Liouville operators in impedance form are isolated, in particular.Comment: 29 page

Run Time Approximation of Non-blocking Service Rates for Streaming Systems

Stream processing is a compute paradigm that promises safe and efficient parallelism. Modern big-data problems are often well suited for stream processing's throughput-oriented nature. Realization of efficient stream processing requires monitoring and optimization of multiple communications links. Most techniques to optimize these links use queueing network models or network flow models, which require some idea of the actual execution rate of each independent compute kernel within the system. What we want to know is how fast can each kernel process data independent of other communicating kernels. This is known as the "service rate" of the kernel within the queueing literature. Current approaches to divining service rates are static. Modern workloads, however, are often dynamic. Shared cloud systems also present applications with highly dynamic execution environments (multiple users, hardware migration, etc.). It is therefore desirable to continuously re-tune an application during run time (online) in response to changing conditions. Our approach enables online service rate monitoring under most conditions, obviating the need for reliance on steady state predictions for what are probably non-steady state phenomena. First, some of the difficulties associated with online service rate determination are examined. Second, the algorithm to approximate the online non-blocking service rate is described. Lastly, the algorithm is implemented within the open source RaftLib framework for validation using a simple microbenchmark as well as two full streaming applications.Comment: technical repor

Spontaneous decay of periodic magnetostatic equilibria

In order to understand the conditions which lead a highly magnetized, relativistic plasma to become unstable, and in such cases how the plasma evolves, we study a prototypical class of magnetostatic equilibria where the magnetic field satisfies $\nabla \times\mathbf B = \alpha \mathbf B$, where $\alpha$ is spatially uniform, on a periodic domain. Using numerical solutions we show that generic examples of such equilibria are unstable to ideal modes (including incompressible ones) which are marked by exponential growth in the linear phase. We characterize the unstable mode, showing how it can be understood in terms of merging magnetic and current structures, and explicitly demonstrate its instability using the energy principle. Following the nonlinear evolution of these solutions, we find that they rapidly develop regions with relativistic velocities and electric fields of comparable magnitude to the magnetic field, liberating magnetic energy on dynamical timescales and eventually settling into a configuration with the largest allowable wavelength. These properties make such solutions a promising setting for exploring the mechanisms behind extreme cosmic sources of gamma rays.Comment: 5 pages, 4 figures + 6 pages supplemental material; revised to match version accepted by PRL; for associated movies see http://youtu.be/EPY_yx7H3_Q and http://youtu.be/Umww9oh08C

The influence of process gas type on the enamel surface condition of a high power diode laser generated single-stage ceramic tile grout seal

Almost all laser materials processing operations require the simultaneous use of an process or assist gas. This paper examines the use of O2, Ar, N2 and He as process gasses during the firing of a vitreous enamel to form a single-stage ceramic tile grout seal with a high power diode laser (HPDL) and the effects thereof on the surface condition of the glaze. The findings revealed marked differences in the surface condition of the HPDL generated enamel glaze depending upon the process gas used. The use of O2 as the process gas was seen to result in glazes with far fewer microcracks and porosities than those generated with any of the other three gasses, particularly He. Such differences were found to be due to the ability of the smaller O2 gas molecules to dissolve molecularly into the open structure of the HPDL generated enamel glaze and also, the inherent reactiveness of O2 which consequently effects exothermic reactions when it is used as a process gas. Both occurrences were seen, in turn, to affect the cooling rate and therefore the tendency of the molten glaze to generate microcracks when cooled

Inverse Spectral Problems for Schr\"odinger-Type Operators with Distributional Matrix-Valued Potentials

The principal purpose of this note is to provide a reconstruction procedure for distributional matrix-valued potential coefficients of Schr\"odinger-type operators on a half-line from the underlying Weyl-Titchmarsh function.Comment: 14 pages. arXiv admin note: text overlap with arXiv:1206.496