Test vectors for Rankin-Selberg LL-functions

We study the local zeta integrals attached to a pair of generic representations $(\pi,\tau)$ of $GL_n\times GL_m$, $n>m$, over a $p$-adic field. Through a process of unipotent averaging we produce a pair of corresponding Whittaker functions whose zeta integral is non-zero, and we express this integral in terms of the Langlands parameters of $\pi$ and $\tau$. In many cases, these Whittaker functions also serve as a test vector for the associated Rankin-Selberg (local) $L$-function.Comment: arXiv admin note: text overlap with arXiv:1804.0772

Another look at the relative importance of sectors and regions in determining property returns

This paper re-examines the relative importance of sector and regional effects in determining property returns. Using the largest property database currently available in the world, we decompose the returns on individual properties into a national effect, common to all properties, and a number of sector and regional factors. However, unlike previous studies, we categorise the individual property data into an ever-increasing number of property-types and regions, from a simple 3-by-3 classification, up to a 10 by 63 sector/region classification. In this way we can test the impact that a finer classification has on the sector and regional effects. We confirm the earlier findings of previous studies that sector-specific effects have a greater influence on property returns than regional effects. We also find that the impact of the sector effect is robust across different classifications of sectors and regions. Nonetheless, the more refined sector and regional partitions uncover some interesting sector and regional differences, which were obscured in previous studies. All of which has important implications for property portfolio construction and analysis

An Evaluation of Size-Resolved Cloud Microphysics Scheme Numerics for Use with Radar Observations. Part I: Collision-Coalescence

This study evaluates some available schemes designed to solve the stochastic collection equation (SCE) for collision-coalescence of hydrometeors using a size-resolved (bin) microphysics approach, and documents their numerical properties within the framework of a box model. Comparing three widely used SCE schemes, we find that all converge to almost identical solutions at sufficiently fine mass grids. However, one scheme converges far slower than the other two and shows pronounced numerical diffusion at the large-drop tail of the size distribution. One of the remaining two schemes is recommended on the basis that it is well-converged on a relatively coarse mass grid, stable for large time steps, strictly mass-conservative, and computationally efficient. To examine the effects of SCE scheme choice on simulating clouds and precipitation, two of the three schemes are compared in large-eddy simulations of a drizzling stratocumulus field. A forward simulator that produces Doppler spectra from the large-eddy simulation results is used to compare the model output directly with radar observations. The scheme with pronounced numerical diffusion predicts excessively large mean Doppler velocities and overly broad and negatively skewed spectra compared with observations, consistent with numerical diffusion demonstrated in the box model. Statistics obtained using the recommended scheme are closer to observations, but notable differences remain, indicating that factors other than SCE scheme accuracy are limiting simulation fidelity

Ventricular tachycardia associated with lacosamide co-medication in drug-resistant epilepsy.

We report a case of sustained ventricular tachycardia following the initiation of lacosamide as adjunctive epilepsy treatment. A 49-year-old male with intractable frontal lobe seizures experienced severe ventricular tachycardia following the addition of 400 mg lacosamide to his existing regimen of carbamazepine, lamotrigine, clonazepam, and valproate. The tachycardia occurred during a cardiac stress test; stress tests prior to initiation of lacosamide were normal. Conduction defects, including QRS prolongation, persisted during hospitalization until lacosamide was discontinued. The patient had no prior history of cardiac arrhythmia but did possess cardiac risk factors, including hypertension, hypercholesterolemia, and low heart rate variability. This case represents one part of a growing body of literature suggesting a link between arrhythmia and use of lacosamide, which enhances slow inactivation of sodium channels in both the brain and the heart. We believe further study may be necessary to assess the safety of lacosamide in epilepsy patients with cardiac risk factors

Applying Graph Theory to Examine the Dynamics of Student Discussions in Small-Group Learning.

Group work in science, technology, engineering, and mathematics courses is an effective means of improving student outcomes, and many different factors can influence the dynamics of student discussions and, ultimately, the success of collaboration. The substance and dynamics of group discussions are commonly examined using qualitative methods such as discourse analysis. To complement existing work in the literature, we developed a quantitative methodology that uses graph theory to map the progression of talk-turns of discussions within a group. We observed groups of students working with peer facilitators to solve problems in biological sciences, with three iterations of data collection and two major refinements of graph theory calculations. Results include general behaviors based on the turns in which different individuals talk and graph theory parameters to quantify group characteristics. To demonstrate the potential utility of the methodology, we present case studies with distinct patterns: a centralized group in which the peer facilitator behaves like an authority figure, a decentralized group in which most students talk their fair share of turns, and a larger group with subgroups that have implications for equity, diversity, and inclusion. Together, these results demonstrate that our adaptation of graph theory is a viable quantitative methodology to examine group discussions

Electronic Quantum Monte Carlo Calculations of Atomic Forces, Vibrations, and Anharmonicities

Atomic forces are calculated for first-row monohydrides and carbon monoxide within electronic quantum Monte Carlo (QMC). Accurate and efficient forces are achieved by using an improved method for moving variational parameters in variational QMC. Newton's method with singular value decomposition (SVD) is combined with steepest descent (SD) updates along directions rejected by the SVD, after initial SD steps. Dissociation energies in variational and diffusion QMC agree well with experiment. The atomic forces agree quantitatively with potential energy surfaces, demonstrating the accuracy of this force procedure. The harmonic vibrational frequencies and anharmonicity constants, derived from the QMC energies and atomic forces, also agree well with experimental values.Comment: 6 pages, 2 figures; updated conten