Moments of Askey-Wilson polynomials

New formulas for the nth moment of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and staircase tableaux. A related positivity theorem is given and another one is conjectured.Comment: 23 page

Reconciling Reconciliation: Differing Conceptions of the Supreme Court of Canada and the Canadian Truth and Reconciliation Commission

This paper considers the concept of reconciliation as it is utilized in two fora: the Supreme Court of Canada (the Court) and the Truth and Reconciliation Commission on the legacy of the “Indian residential schools” (TRC). The concept’s development in the Court’s jurisprudence, as compared to the scholarly literature of transitional justice, warrants careful consideration. The Court has used the term in decisions seeking to balance assertions of Indigenous sovereignty in the context of Canadian colonialism. However, this concept of reconciliation is quite different from that which has entered Canadian discourse from the TRC. The author suggests that the vision of reconciliation enunciated by the TRC as a mutual process to be engaged in by Indigenous and non-Indigenous peoples alike would be a more just conception to adopt

Survivor Assistance through Technology Transfer in Tanzania

This article describes how cutting-edge technology is being developed and disseminated in landmine-affected countries. Focusing particularly on the Tanzania Training Center for Orthopedic Technologists, the authors examine how a process of appropriate, resource-effective casting is being advanced and then shared through training workshops. Improved technology and its successful transfer are vital to better assisting landmine survivors, a goal the Center for International Rehabilitation is working to achieve

XWalk: Random Walk Based Candidate Retrieval for Product Search

In e-commerce, head queries account for the vast majority of gross merchandise sales and improvements to head queries are highly impactful to the business. While most supervised approaches to search perform better in head queries vs. tail queries, we propose a method that further improves head query performance dramatically. We propose XWalk, a random-walk based graph approach to candidate retrieval for product search that borrows from recommendation system techniques. XWalk is highly efficient to train and inference in a large-scale high traffic e-commerce setting, and shows substantial improvements in head query performance over state-of-the-art neural retreivers. Ensembling XWalk with a neural and/or lexical retriever combines the best of both worlds and the resulting retrieval system outperforms all other methods in both offline relevance-based evaluation and in online A/B tests

Ultrafast spectroscopy of propagating coherent acoustic phonons in GaN/InGaN heterostructures

We show that large amplitude, coherent acoustic phonon wavepackets can be generated and detected in In$_x$Ga$_{1-x}$N/GaN epilayers and heterostructures in femtosecond pump-probe differential reflectivity experiments. The amplitude of the coherent phonon increases with increasing Indium fraction $x$ and unlike other coherent phonon oscillations, both \textit{amplitude} and \textit{period} are strong functions of the laser probe energy. The amplitude of the oscillation is substantially and almost instantaneously reduced when the wavepacket reaches a GaN-sapphire interface below the surface indicating that the phonon wavepackets are useful for imaging below the surface. A theoretical model is proposed which fits the experiments well and helps to deduce the strength of the phonon wavepackets. Our model shows that localized coherent phonon wavepackets are generated by the femtosecond pump laser in the epilayer near the surface. The wavepackets then propagate through a GaN layer changing the local index of refraction, primarily through the Franz-Keldysh effect, and as a result, modulate the reflectivity of the probe beam. Our model correctly predicts the experimental dependence on probe-wavelength as well as epilayer thickness.Comment: 11 pages, 14 figure

Chirality-Selective Excitation of Coherent Phonons in Carbon Nanotubes

Using pre-designed trains of femtosecond optical pulses, we have selectively excited coherent phonons of the radial breathing mode of specific-chirality single-walled carbon nanotubes within an ensemble sample. By analyzing the initial phase of the phonon oscillations, we prove that the tube diameter initially increases in response to ultrafast photoexcitation. Furthermore, from excitation profiles, we demonstrate that an excitonic absorption peak of carbon nanotubes periodically oscillates as a function of time when the tube diameter undergoes radial breathing mode oscillations.Comment: 4 pages, 4 figure

The Combinatorics of Associated Laguerre Polynomials

The explicit double sum for the associated Laguerre polynomials is derived combinatorially. The moments are described using certain statistics on permutations and permutation tableaux. Another derivation of the double sum is provided using only the moment generating function