38,004 research outputs found

    It\u27s Fun, But Is It Science? Goals and Strategies in a Problem-Based Learning Course

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    All students at Hampshire College must complete a science requirement in which they demonstrate their understanding of how science is done, examine the work of science in larger contexts, and communicate their ideas effectively. Human Biology: Selected Topics in Medicine is one of 18-20 freshman seminars designed to move students toward completing this requirement. Students work in cooperative groups of 4-6 people to solve actual medical cases about which they receive information progressively. Students assign themselves homework tasks to bring information back for group deliberation. The goal is for case teams to work cooperatively to develop a differential diagnosis and recommend treatment. Students write detailed individual final case reports. Changes observed in student work over six years of developing this course include: increased motivation to pursue work in depth, more effective participation on case teams, increase in critical examination of evidence, and more fully developed arguments in final written reports. As part of a larger study of eighteen introductory science courses in two institutions, several types of pre- and post-course assessments were used to evaluate how teaching approaches might have influenced students’ attitudes about science, their ability to learn science, and their understanding of how scientific knowledge is developed [1]. Preliminary results from interviews and Likert-scale measures suggest improvements in the development of some students’ views of epistemology and in the importance of cooperative group work in facilitating that development

    Regularity Theory and Superalgebraic Solvers for Wire Antenna Problems

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    We consider the problem of evaluating the current distribution J(z)J(z) that is induced on a straight wire antenna by a time-harmonic incident electromagnetic field. The scope of this paper is twofold. One of its main contributions is a regularity proof for a straight wire occupying the interval [−1,1][-1,1]. In particular, for a smooth time-harmonic incident field this theorem implies that J(z)=I(z)/1−z2J(z) = I(z)/\sqrt{1-z^2}, where I(z)I(z) is an infinitely differentiable function—the previous state of the art in this regard placed II in the Sobolev space W1,pW^{1,p}, p>1p>1. The second focus of this work is on numerics: we present three superalgebraically convergent algorithms for the solution of wire problems, two based on HallĂ©n's integral equation and one based on the Pocklington integrodifferential equation. Both our proof and our algorithms are based on two main elements: (1) a new decomposition of the kernel of the form G(z)=F1(z)ln⁡ ⁣∣z∣+F2(z)G(z) = F_1(z) \ln\! |z| + F_2(z), where F1(z)F_1(z) and F2(z)F_2(z) are analytic functions on the real line; and (2) removal of the end-point square root singularities by means of a coordinate transformation. The HallĂ©n- and Pocklington-based algorithms we propose converge superalgebraically: faster than O(N−m)\mathcal{O}(N^{-m}) and O(M−m)\mathcal{O}(M^{-m}) for any positive integer mm, where NN and MM are the numbers of unknowns and the number of integration points required for construction of the discretized operator, respectively. In previous studies, at most the leading-order contribution to the logarithmic singular term was extracted from the kernel and treated analytically, the higher-order singular derivatives were left untreated, and the resulting integration methods for the kernel exhibit O(M−3)\mathcal{O}(M^{-3}) convergence at best. A rather comprehensive set of tests we consider shows that, in many cases, to achieve a given accuracy, the numbers NN of unknowns required by our codes are up to a factor of five times smaller than those required by the best solvers previously available; the required number MM of integration points, in turn, can be several orders of magnitude smaller than those required in previous methods. In particular, four-digit solutions were found in computational times of the order of four seconds and, in most cases, of the order of a fraction of a second on a contemporary personal computer; much higher accuracies result in very small additional computing times

    The minimal model for the Batalin-Vilkovisky operad

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    The purpose of this paper is to explain and to generalize, in a homotopical way, the result of Barannikov-Kontsevich and Manin which states that the underlying homology groups of some Batalin-Vilkovisky algebras carry a Frobenius manifold structure. To this extent, we first make the minimal model for the operad encoding BV-algebras explicit. Then we prove a homotopy transfer theorem for the associated notion of homotopy BV-algebra. The final result provides an extension of the action of the homology of the Deligne-Mumford-Knudsen moduli space of genus 0 curves on the homology of some BV-algebras to an action via higher homotopical operations organized by the cohomology of the open moduli space of genus zero curves. Applications in Poisson geometry and Lie algebra cohomology and to the Mirror Symmetry conjecture are given.Comment: New section added containing applications to Poisson geometry, Lie algebra cohomology and to the Mirror Symmetry conjecture. [36 pages, 4 figures

    Dixmier traces on noncompact isospectral deformations

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    We extend the isospectral deformations of Connes, Landi and Dubois-Violette to the case of Riemannian spin manifolds carrying a proper action of the noncompact abelian group RlR^l. Under deformation by a torus action, a standard formula relates Dixmier traces of measurable operators to integrals of functions on the manifold. We show that this relation persists for actions of RlR^l, under mild restrictions on the geometry of the manifold which guarantee the Dixmier traceability of those operators.Comment: 30 pages, no figures; several minor improvements, to appear in J. Funct. Ana

    The Microstructure of the Bond Market in the 20th Century

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    Bonds are traded in OTC markets, where opacity and fragmentation imply large transaction costs for retail investors. Is there something special about bonds, in contrast to stocks, that precludes trading in transparent, limit-order markets? Historical experience suggests this is not the case. Before WWII, there was an active market in corporate and municipal bonds on the NYSE. Activity dropped dramatically, in the late 1920s for municipals and in the mid 1940s for corporate, as trading migrated to the OTC market. This migration occurred simultaneously with an increase in the role of institutional investors, which fare better than retail investors in OTC market. Based on current and historical high frequency data, we find that, for retail investors, trading costs in municipal bonds were half as large in 1926-1927 as they are now. The difference in transactions costs is likely to reflect the difference in market structures.

    Quasi-particle dephasing time in disordered d-wave superconductors

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    We evaluate the low-temperature cutoff for quantum interference 1/tf induced in a d-wave superconductor by the diffusion enhanced quasiparticle interactions in the presence of disorder. We carry out our analysis in the framework of the non-linear sigma-model which allows a direct calculation of 1/tf, as the mass of the transverse modes of the theory. Only the triplet amplitude in the particle-hole channel and the Cooper amplitude with is pairing symmetry contribute to 1/tf. We discuss the possible relevance of our results to the present disagreement between thermal transport data in cuprates and the localization theory for d-wave quasiparticles

    Communications system evolutionary scenarios for Martian SEI support

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    In the Space Exploration Initiative (SEI) mission scenarios, expanding human presence is the primary driver for high data rate Mars-Earth communications. To support an expanding human presence, the data rate requirement will be gradual, following the phased implementation over time of the evolving SEI mission. Similarly, the growth and evolution of the space communications infrastructure to serve this requirement will also be gradual to efficiently exploit the useful life of the installed communications infrastructure and to ensure backward compatibility with long-term users. In work conducted over the past year, a number of alternatives for supporting high data rate Mars-Earth communications have been analyzed with respect to their compatibility with gradual evolution of the space communications infrastructure. The alternatives include RF, millimeter wave (MMW), and optical implementations, and incorporate both surface and space-based relay terminals in the Mars and Earth regions. Each alternative is evaluated with respect to its ability to efficiently meet a projected growth in data rate over time, its technology readiness, and its capability to satisfy the key conditions and constraints imposed by evolutionary transition. As a result of this analysis, a set of attractive alternative communications architectures have been identified and described, and a road map is developed that illustrates the most rational and beneficial evolutionary paths for the communications infrastructure
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