Fast Mesh Refinement in Pseudospectral Optimal Control

Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy --- simply increase the order $N$ of the Lagrange interpolating polynomial and the mathematics of convergence automates the distribution of the grid points. Unfortunately, as $N$ increases, the condition number of the resulting linear algebra increases as $N^2$; hence, spectral efficiency and accuracy are lost in practice. In this paper, we advance Birkhoff interpolation concepts over an arbitrary grid to generate well-conditioned PS optimal control discretizations. We show that the condition number increases only as $\sqrt{N}$ in general, but is independent of $N$ for the special case of one of the boundary points being fixed. Hence, spectral accuracy and efficiency are maintained as $N$ increases. The effectiveness of the resulting fast mesh refinement strategy is demonstrated by using \underline{polynomials of over a thousandth order} to solve a low-thrust, long-duration orbit transfer problem.Comment: 27 pages, 12 figures, JGCD April 201

Enrichment exercises in spelling for grades two, three, and four

Thesis (Ed.M.)--Boston Universit

A simple model to study phylogeographies and speciation patterns in space

In this working paper, we present a simple theoretical framework based on network theory to study how speciation, the process by which new species appear, shapes spatial patterns of diversity. We show that this framework can be expanded to account for different types of networks and interactions, and incorporates different modes of speciation.Comment: 4 pages, 1 figure, 34 reference

Time-trends and treatment gaps in the antithrombotic management of patients with atrial fibrillation after percutaneous coronary intervention: Insights from the CHUM AF-STENT Registry.

BACKGROUND: The management of atrial fibrillation and flutter (AF) patients undergoing percutaneous coronary intervention (PCI) has undergone a rapid recent evolution. In 2016, the Canadian Cardiovascular Society (CCS) published expert recommendations to help guide clinicians in balancing bleeding and thrombotic risks in these patients. HYPOTHESIS: Antithrombotic regimen prescriptions for AF patients undergoing PCI evolved after the publication of the 2016 CCS AF guidelines. METHODS: A prospective cohort of AF patients undergoing PCI with placement of a coronary stent from a single tertiary academic center was analyzed for the recommended antithrombotic regimen at discharge. Prescribing behavior was compared between three time periods (Cohort A [2010-2011]; Cohort B [2014-2015]; Cohort C [2017]) using the χ2 test. In addition, antithrombotic management in Cohorts B and C were compared to guideline-recommended therapy. RESULTS: A total of 459 patients with AF undergoing PCI were identified. Clinical and procedural characteristics were similar between cohorts, with the exception of an increase in drug-eluting stent (DES) use over time (P < .01). Overall, the rate of oral anticoagulation (OAC) increased over time (P < .01), associated with an increase in nonvitamin K OAC prescription (P < .01) and a concomitant decrease in vitamin K antagonist prescription (P < .01). Despite this, the overall rate of anticoagulation remains below what would be predicted with perfect guideline compliance (75% vs 94%, P < .01). CONCLUSION: There has been a dramatic shift in clinical practice for AF patients requiring PCI, with increases in prescription of OAC even in the context of an increase in the use of DES. However, room for further practice optimization still exists

Separation and identification of dominant mechanisms in double photoionization

Double photoionization by a single photon is often discussed in terms of two contributing mechanisms, {\it knock-out} (two-step-one) and {\it shake-off} with the latter being a pure quantum effect. It is shown that a quasi-classical description of knock-out and a simple quantum calculation of shake-off provides a clear separation of the mechanisms and facilitates their calculation considerably. The relevance of each mechanism at different photon energies is quantified for helium. Photoionization ratios, integral and singly differential cross sections obtained by us are in excellent agreement with benchmark experimental data and recent theoretical results.Comment: 4 pages, 5 figure

Dynamic MAIT cell response with progressively enhanced innateness during acute HIV-1 infection.

Mucosa-associated invariant T (MAIT) cell loss in chronic HIV-1 infection is a significant insult to antimicrobial immune defenses. Here we investigate the response of MAIT cells during acute HIV-1 infection utilizing the RV217 cohort with paired longitudinal pre- and post-infection samples. MAIT cells are activated and expand in blood and mucosa coincident with peak HIV-1 viremia, in a manner associated with emerging microbial translocation. This is followed by a phase with elevated function as viral replication is controlled to a set-point level, and later by their functional decline at the onset of chronic infection. Interestingly, enhanced innate-like pathways and characteristics develop progressively in MAIT cells during infection, in parallel with TCR repertoire alterations. These findings delineate the dynamic MAIT cell response to acute HIV-1 infection, and show how the MAIT compartment initially responds and expands with enhanced function, followed by progressive reprogramming away from TCR-dependent antibacterial responses towards innate-like functionality

Multiphoton detachment of electrons from negative ions

A simple analytical solution for the problem of multiphoton detachment from negative ions by a linearly polarized laser field is found. It is valid in the wide range of intensities and frequencies of the field, from the perturbation theory to the tunneling regime, and is applicable to the excess-photon as well as near-threshold detachment. Practically, the formulae are valid when the number of photons is greater than two. They produce the total detachment rates, relative intensities of the excess-photon peaks, and photoelectron angular distributions for the hydrogen and halogen negative ions, in agreement with those obtained in other, more numerically involved calculations in both perturbative and non-perturbative regimes. Our approach explains the extreme sensitivity of the multiphoton detachment probability to the asymptotic behaviour of the bound-state wave function. Rapid oscillations in the angular dependence of the $n$-photon detachment probability are shown to arise due to interference of the two classical trajectories which lead to the same final state after the electron emerges at the opposite sides of the atom when the field is close to maximal.Comment: 27 pages, Latex, and PostScript figures fig1.ps, fig2.ps, fig3.ps, accepted for publication in Phys. Rev.

A Parallel Autonomy Research Platform

We present the development of a full-scale “parallel autonomy” research platform including software and hardware. In the parallel autonomy paradigm, the control of the vehicle is shared; the human is still in control of the vehicle, but the autonomy system is always running in the background to prevent accidents. Our holistic approach includes: (1) a driveby-wire conversion method only based on reverse engineering, (2) mounting of relatively inexpensive sensors onto the vehicle, (3) implementation of a localization and mapping system, (4) obstacle detection and (5) a shared controller as well as (6) integration with an advanced autonomy simulation system (Drake) for rapid development and testing. The system can operate in three modes: (a) manual driving, (b) full autonomy, where the system is in complete control of the vehicle and (c) parallel autonomy, where the shared controller is implemented. We present results from extensive testing of a full-scale vehicle on closed tracks that demonstrate these capabilities