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  • Articles  (4)
  • Low Dimensional Geometry and Topology Special Feature  (3)
  • Spatial Cyberinfrastructure  (1)
  • National Academy of Sciences  (4)
  • American Society of Hematology
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  • 2010-2014  (4)
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  • 2011  (4)
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  • 1
    Publication Date: 2011-05-18
    Description: Heegaard Floer theory is a kind of topological quantum field theory (TQFT), assigning graded groups to closed, connected, oriented 3-manifolds and group homomorphisms to smooth, oriented four-dimensional cobordisms. Bordered Heegaard Floer homology is an extension of Heegaard Floer homology to 3-manifolds with boundary, with extended-TQFT-type gluing properties. In this survey, we explain the formal structure and construction of bordered Floer homology and sketch how it can be used to compute some aspects of Heegaard Floer theory.
    Keywords: Low Dimensional Geometry and Topology Special Feature
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
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  • 2
    Publication Date: 2011-05-18
    Description: Surface diagrams are a new way to specify any smooth closed orientable 4-manifold by an orientable surface decorated with simple closed curves. These curves are cyclically indexed, and each curve has a unique transverse intersection with the next. The aim of this paper is to announce a uniqueness theorem for these objects (within a fixed homotopy class) that turns out to be similar to the Reidemeister-Singer theorem for Heegaard splittings of 3-manifolds.
    Keywords: Low Dimensional Geometry and Topology Special Feature
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
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  • 3
    Publication Date: 2011-05-18
    Description: We discuss generic smooth maps from smooth manifolds to smooth surfaces, which we call “Morse 2-functions,” and homotopies between such maps. The two central issues are to keep the fibers connected, in which case the Morse 2-function is “fiber-connected,” and to avoid local extrema over one-dimensional submanifolds of the range, in which case the Morse 2-function is “indefinite.” This is foundational work for the long-range goal of defining smooth invariants from Morse 2-functions using tools analogous to classical Morse homology and Cerf theory.
    Keywords: Low Dimensional Geometry and Topology Special Feature
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
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  • 4
    Publication Date: 2011-04-06
    Description: Cyberinfrastructure integrates advanced computer, information, and communication technologies to empower computation-based and data-driven scientific practice and improve the synthesis and analysis of scientific data in a collaborative and shared fashion. As such, it now represents a paradigm shift in scientific research that has facilitated easy access to computational utilities and streamlined collaboration across distance and disciplines, thereby enabling scientific breakthroughs to be reached more quickly and efficiently. Spatial cyberinfrastructure seeks to resolve longstanding complex problems of handling and analyzing massive and heterogeneous spatial datasets as well as the necessity and benefits of sharing spatial data flexibly and securely. This article provides an overview and potential future directions of spatial cyberinfrastructure. The remaining four articles of the special feature are introduced and situated in the context of providing empirical examples of how spatial cyberinfrastructure is extending and enhancing scientific practice for improved synthesis and analysis of both physical and social science data. The primary focus of the articles is spatial analyses using distributed and high-performance computing, sensor networks, and other advanced information technology capabilities to transform massive spatial datasets into insights and knowledge.
    Keywords: Spatial Cyberinfrastructure
    Print ISSN: 0027-8424
    Electronic ISSN: 1091-6490
    Topics: Biology , Medicine , Natural Sciences in General
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