Teaching Linear Algebra in a Mechanized Mathematical Environment

This paper outlines our ideas on how to teach linear algebra in a mechanized mathematical environment, and discusses some of our reasons for thinking that this is a better way to teach linear algebra than the ``old fashioned way''. We discuss some technological tools such as Maple, Matlab, Python, and Jupyter Notebooks, and some choices of topics that are especially suited to teaching with these tools. The discussion is informed by our experience over the past thirty or more years teaching at various levels, especially at the University of Western Ontario.Comment: 16 pages, 2 figure

Multispectral imaging of organ viability during uterine transplantation surgery in rabbits and sheep

Uterine transplantation surgery (UTx) has been proposed as a treatment for permanent absolute uterine factor infertility (AUFI) in the case of the congenital absence or surgical removal of the uterus. Successful surgical attachment of the organ and its associated vasculature is essential for the organ’s reperfusion and long-term viability. Spectral imaging techniques have demonstrated the potential for the measurement of hemodynamics in medical applications. These involve the measurement of reflectance spectra by acquiring images of the tissue in different wavebands. Measures of tissue constituents at each pixel can then be extracted from these spectra through modeling of the light–tissue interaction. A multispectral imaging (MSI) laparoscope was used in sheep and rabbit UTx models to study short- and long-term changes in oxygen saturation following surgery. The whole organ was imaged in the donor and recipient animals in parallel with point measurements from a pulse oximeter. Imaging results confirmed the re-establishment of adequate perfusion in the transplanted organ after surgery. Cornual oxygenation trends measured with MSI are consistent with pulse oximeter readings, showing decreased StO2 immediately after anastomosis of the blood vessels. Long-term results show recovery of StO2 to preoperative levels

New Constraints on the Complex Mass Substructure in Abell 1689 from Gravitational Flexion

In a recent publication, the flexion aperture mass statistic was found to provide a robust and effective method by which substructure in galaxy clusters might be mapped. Moreover, we suggested that the masses and mass profile of structures might be constrained using this method. In this paper, we apply the flexion aperture mass technique to HST ACS images of Abell 1689. We demonstrate that the flexion aperture mass statistic is sensitive to small-scale structures in the central region of the cluster. While the central potential is not constrained by our method, due largely to missing data in the central 0.5$^\prime$ of the cluster, we are able to place constraints on the masses and mass profiles of prominent substructures. We identify 4 separate mass peaks, and use the peak aperture mass signal and zero signal radius in each case to constrain the masses and mass profiles of these substructures. The three most massive peaks exhibit complex small-scale structure, and the masses indicated by the flexion aperture mass statistic suggest that these three peaks represent the dominant substructure component of the cluster ($\sim 7\times 10^{14}h^{-1}M_\odot$). Their complex structure indicates that the cluster -- far from being relaxed -- may have recently undergone a merger. The smaller, subsidiary peak is located coincident with a group of galaxies within the cluster, with mass $\sim 1\times10^{14}h^{-1}M_\odot$. These results are in excellent agreement with previous substructure studies of this cluster.Comment: 18 pages, 10 figures, MNRAS accepted (7 Dec 2010

The Newtonian limit of spacetimes for accelerated particles and black holes

Solutions of vacuum Einstein's field equations describing uniformly accelerated particles or black holes belong to the class of boost-rotation symmetric spacetimes. They are the only explicit solutions known which represent moving finite objects. Their Newtonian limit is analyzed using the Ehlers frame theory. Generic spacetimes with axial and boost symmetries are first studied from the Newtonian perspective. The results are then illustrated by specific examples such as C-metric, Bonnor-Swaminarayan solutions, self-accelerating "dipole particles", and generalized boost-rotation symmetric solutions describing freely falling particles in an external field. In contrast to some previous discussions, our results are physically plausible in the sense that the Newtonian limit corresponds to the fields of classical point masses accelerated uniformly in classical mechanics. This corroborates the physical significance of the boost-rotation symmetric spacetimes

Gangrenous cholecystitis in an asymptomatic patient found during an elective laparoscopic cholecystectomy: a case report

<p>Abstract</p> <p>Introduction</p> <p>Gangrenous cholecystitis is a severe complication of acute cholecystitis. We present an unusual case of gangrenous cholecystitis which was totally asymptomatic, with normal pre-operative parameters, and was discovered incidentally during a laparoscopic cholecystectomy. We have not found any similar cases in the published literature.</p> <p>Case presentation</p> <p>A 79-year-old British Caucasian man presented initially with acute cholecystitis which responded to conservative management. After six weeks he was asymptomatic and had normal blood parameters. An elective laparoscopic cholecystectomy was performed and our patient was found to have a totally gangrenous gall bladder.</p> <p>Conclusion</p> <p>It is important to keep a high index of suspicion for the diagnosis of gangrenous cholecystitis in order to avoid potentially serious complications.</p

Elastic deformation of a fluid membrane upon colloid binding

When a colloidal particle adheres to a fluid membrane, it induces elastic deformations in the membrane which oppose its own binding. The structural and energetic aspects of this balance are theoretically studied within the framework of a Helfrich Hamiltonian. Based on the full nonlinear shape equations for the membrane profile, a line of continuous binding transitions and a second line of discontinuous envelopment transitions are found, which meet at an unusual triple point. The regime of low tension is studied analytically using a small gradient expansion, while in the limit of large tension scaling arguments are derived which quantify the asymptotic behavior of phase boundary, degree of wrapping, and energy barrier. The maturation of animal viruses by budding is discussed as a biological example of such colloid-membrane interaction events.Comment: 14 pages, 9 figures, REVTeX style, follow-up on cond-mat/021242

(Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap

We reconsider in some detail a construction allowing (Borel) convergence of an alternative perturbative expansion, for specific physical quantities of asymptotically free models. The usual perturbative expansions (with an explicit mass dependence) are transmuted into expansions in 1/F, where $F \sim 1/g(m)$ for $m \gg \Lambda$ while $F \sim (m/\Lambda)^\alpha$ for m \lsim \Lambda, $\Lambda$ being the basic scale and $\alpha$ given by renormalization group coefficients. (Borel) convergence holds in a range of $F$ which corresponds to reach unambiguously the strong coupling infrared regime near $m\to 0$, which can define certain "non-perturbative" quantities, such as the mass gap, from a resummation of this alternative expansion. Convergence properties can be further improved, when combined with $\delta$ expansion (variationally improved perturbation) methods. We illustrate these results by re-evaluating, from purely perturbative informations, the O(N) Gross-Neveu model mass gap, known for arbitrary $N$ from exact S matrix results. Comparing different levels of approximations that can be defined within our framework, we find reasonable agreement with the exact result.Comment: 33 pp., RevTeX4, 6 eps figures. Minor typos, notation and wording corrections, 2 references added. To appear in Phys. Rev.