1,741 research outputs found

    Spin structures on loop spaces that characterize string manifolds

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    Classically, a spin structure on the loop space of a manifold is a lift of the structure group of the looped frame bundle from the loop group to its universal central extension. Heuristically, the loop space of a manifold is spin if and only if the manifold itself is a string manifold, against which it is well-known that only the if-part is true in general. In this article we develop a new version of spin structures on loop spaces that exists if and only if the manifold is string, as desired. This new version consists of a classical spin structure plus a certain fusion product related to loops of frames in the manifold. We use the lifting gerbe theory of Carey-Murray, recent results of Stolz-Teichner on loop spaces, and some own results about string geometry and Brylinski-McLaughlin transgression.Comment: 30 pages. v2 comes with some minor corrections and improvement

    Spatial hazard models: limitations and applications

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    The paper develops an important spatial extension of longitudinal models. Longitudinal models capture variations in the timing of events. Recently, they have also been applied to variations in the spacing of events, using distance as a mathematical equivalent of time. Spatial relationships are, however, characterized by two-dimensionality, and distance alone is therefore insufficient for the assessment of their variations. The methodological extension defines spacing and spatial relationships via two dimensions and develops the associated mathematical and statistical apparatus using joint probability density functions of movement along both axes. The proposed extension will be applied to an empirical example, using data on spatio-temporal fertility patterns in Italy over the last three decades.

    The Professional Artist as Public School Educator: A Research Report of the Chicago Arts Partnerships in Education

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    Over the past eight years, the Chicago Arts Partnerships in Education (CAPE) has undergone an extensive regimen of program research and evaluation, utilizing both staff members and external consultants to collect, analyze, and interpret information on program effectiveness. This information has been used to shape and strengthen the partnership program each year in response to the needs of students, teachers and teaching artists as well as to changing political and cultural pressures within the Chicago Public School System. In addition,the documentation and publication of insights and lessons learned through arts integration experiences in the schools has contributed significantly to the wider body of research in the field of arts education.During the early years of the program, evaluation efforts focused on general descriptions of the program goals and objectives along with initial impacts on student life.Positive trends were identified in terms of administrative and faculty attitudes and increased involvement in thearts partnerships, due mainly to student interest. More recently, a closer, more detailed analysis of CAPE's growing influence on student learning, teaching practice and school climate has highlighted the value of quality, arts integrated instruction, including evidence of positive effects on standardized math and reading test scores.Last year, our research turned to program sustainability, partly in light of reduced funding, as well as to the assimilation of new partnership schools and an increasing organizational focus on the professional development of participating teachers and artists. In the vast majority of cases, CAPE partnerships have evolved through trials and successes to bring lasting effects on administrators, teachers, and students.Through these studies, it is increasingly apparent that the participation of well-trained teaching artists is a valuable, and in some cases vital, addition to the general education of youth. The presence and artistic know-how brought to the classroom by these talented, dedicated professionals can, and is, having notable, sustainable influence on whole school improvement through transforming the daily learning experiences of educators and students alike. Not only does the presence of a quality arts program enliven a school atmosphere and promote the advancement of artistic skills and aesthetic knowledge, but a closer look at rigorous arts integrated activities in the classroom is revealing important insights into the cognitive benefits of arts education. Not only can artfully constructed lessons that authentically bridge the arts and academic content domains assist in the acquisition of artistic understanding, but they can enhance learning across the academic curriculum and, perhaps more importantly, the underlying thinking curriculu

    Connections on non-abelian Gerbes and their Holonomy

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    We introduce an axiomatic framework for the parallel transport of connections on gerbes. It incorporates parallel transport along curves and along surfaces, and is formulated in terms of gluing axioms and smoothness conditions. The smoothness conditions are imposed with respect to a strict Lie 2-group, which plays the role of a band, or structure 2-group. Upon choosing certain examples of Lie 2-groups, our axiomatic framework reproduces in a systematical way several known concepts of gerbes with connection: non-abelian differential cocycles, Breen-Messing gerbes, abelian and non-abelian bundle gerbes. These relationships convey a well-defined notion of surface holonomy from our axiomatic framework to each of these concrete models. Till now, holonomy was only known for abelian gerbes; our approach reproduces that known concept and extends it to non-abelian gerbes. Several new features of surface holonomy are exposed under its extension to non-abelian gerbes; for example, it carries an action of the mapping class group of the surface.Comment: 57 pages. v1 is preliminary. v2 is completely rewritten, former Sections 1 and 2 have been moved into a separate paper (arxiv:1303.4663), and the discussion of non-abelian surface holonomy has been improved and extended. v3 is the final and published version with a few minor correction

    THE EMERGENCE OF A KNOWLEDGE AGGLOMERATION: A SPATIO-TEMPORAL ANALYSIS OF INTELLECTUAL CAPITAL IN INDIANA

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    U.S. States and communities increasingly compete for intellectual power so as to thrive toward an economically vibrant setting that spurs the entrepreneurial spirit and attracts businesses and industries from around the world. As a recent report by the U.S. census reveals, 17 U.S. States have gained such intellectual power through the net inmigration of young, single and college educated persons. The State of Indiana is among the remaining thirty-three States that have a negative net balance, even ranking among the bottom ten in their ability to attract this highly valued population segment. In fact, for every young, single, college educated inmigrant, Indiana loses nearly two to other states. However, an analysis at the state-level hides important small-scale variations. This paper therefore investigates the processes leading to changes in the spatial distribution of knowledge workers across Indiana counties, with emphases on in-situ change, retention, intra- and interstate migration. The analysis shows that these demographic changes at the county level in fact reveal a less bleak picture than the state-wide aggregate figures suggest, and uncover remarkable peaks in the landscape of intellectual capital that can serve as a catalyst for attracting intellectual capital from outside the State.

    Arts for All School Arts Survey: Measuring Quality, Access and Equity in Arts Education

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    As part of its goal to make quality, sequential arts education a reality in all public K-12 classrooms in Los Angeles County, Arts for All connects school districts with effective tools and resources to improve arts learning. The Arts for All School Arts Survey: Measuring Quality, Access and Equity in Arts Education is the most recent of these tools to be introduced. It was developed to measure access to and quality of arts instruction at the school site level as well as to develop a system for collecting and reporting the data. The results are useful to schools and school districts to find out what is working, what's not working, and to point the way toward improvement. But the results can also provide a picture of what's happening across a region. The following summary describes how the survey was built and its first test in five school districts encompassing 100 schools. As a result of this test, some refinements will be made in the survey, but the survey's strength and utility have been proven. Los Angeles County now has a means of objectively measuring quality and access to arts education and making the results easily accessible

    Fusion of implementers for spinors on the circle

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    We consider the space of odd spinors on the circle, and a decomposition into spinors supported on either the top or on the bottom half of the circle. If an operator preserves this decomposition, and acts on the bottom half in the same way as a second operator acts on the top half, then the fusion of both operators is a third operator acting on the top half like the first, and on the bottom half like the second. Fusion restricts to the Banach Lie group of restricted orthogonal operators, which supports a central extension of implementers on a Fock space. In this article, we construct a lift of fusion to this central extension. Our construction uses Tomita-Takesaki theory for the Clifford-von Neumann algebras of the decomposed space of spinors. Our motivation is to obtain an operator-algebraic model for the basic central extension of the loop group of the spin group, on which the fusion of implementers induces a fusion product in the sense considered in the context of transgression and string geometry. In upcoming work we will use this model to construct a fusion product on a spinor bundle on the loop space of a string manifold, completing a construction proposed by Stolz and Teichner.Comment: 49 page
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