118,966 research outputs found
Dimension-independent simplification and refinement of Morse complexes
No full textAscending and descending Morse complexes, determined by a scalar field f defined over a manifold M, induce a subdivision of M into regions associated with critical points of f, and compactly represent the topology of M. We define two simplification operators on Morse complexes, which work in arbitrary dimensions, and we define their inverse refinement operators. We describe how simplification and refinement operators affect Morse complexes on M, and we show that these operators form a complete set of atomic operators to create and update Morse complexes on M. Thus, any operator that modifies Morse complexes on M can be expressed as a suitable sequence of the atomic simplification and refinement operators we have defined. The simplification and refinement operators also provide a suitable basis for the construction of a multi-resolution representation of Morse complexes
Dimension-Independent Simplification and Multi-Resolution Representation of Morse Complexes
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Building Morphological Representations for 2D and 3D Scalar Fields
No full textAscending and descending Morse complexes, defined by the critical points and integral lines of a scalar field f defined on a manifold domain D, induce a subdivision of D into regions of uniform gradient flow, and thus provide a compact description of the morphology of f on D. We propose a dimension-independent representation for the ascending and descending Morse complexes, and we describe a data structure which assumes a discrete representation of the field as a simplicial mesh, that we call the incidence-based data structure. We present algorithms for building such data structure for 2D and 3D scalar fields, which make use of a watershed approach to compute the cells of the Morse decompositions
Topological modifications and hierarchical representation of cell complexes in arbitrary dimensions
No full textWe propose a set of atomic modeling operators for simplifying and refining cell complexes in arbitrarydimensions. Such operators either preserve the homology of the cell complex, or they modify it in a con-trolled way. We show that such operators form a minimally complete basis for updating cell complexes,and we compare them with various operators previously proposed in the literature. Based on the newoperators, we define a hierarchical model for cell complexes, that we call aHierarchical Cell Complex(HCC), and we discuss its properties. AnHCCimplicitly encodes a virtually continuous set of complexesobtained from the original complex through the application of our operators. Then, we describe theimplementation of a version of theHCCbased on the subset of the proposed modeling operators whichpreserve homology. We apply the homology-preservingHCCto enhance the efficiency in extractinghomology generators at different resolutions. To this aim, we propose an algorithm which computeshomology generators on the coarsest representation of the original complex, and uses the hierarchicalmodel to propagate them to complexes at any intermediate resolution, and we prove its correctness.Finally, we present experimental results showing the efficiency and effectiveness of the proposedapproac
Comics aren't just for fun anymore: the practical use of comics by TESOL professionals
No full textThesis (M.A.)--University of Wisconsin-River Falls, 2013. ii + 173 leaves. Includes bibliographical references (leaves 155-173).Comics, in the form of comic strips, comic books, and single panel cartoons are ubiquitous in classroom materials for teaching English to speakers of other languages (TESOL). While comics material is widely accepted as a teaching aid in TESOL, there is relatively little research into why comics are popular as a teaching instrument and how the effectiveness of comics can be maximized in TESOL. This thesis is designed to bridge the gap between conventional wisdom on the use of comics in ESL/EFL instruction and research related to visual aids in learning and language acquisition. The hidden science behind comics use in TESOL is examined to reveal the nature of comics, the psychological impact of the medium on learners, the qualities that make some comics more educational than others, and the most empirically sound ways to use comics in education. The definition of the comics medium itself is explored; characterizations of comics created by TESOL professionals, comic scholars, and psychologists are indexed and analyzed. This definition is followed by a look at the current role of comics in society at large, the teaching community in general, and TESOL specifically. From there, this paper explores the psycholinguistic concepts of construction of meaning and the language faculty. Through an analysis of the evolution of language, art history, and the psychology of perception, comics are revealed to be an innate form of human communication that originated in pre-literate ancient times; this medium continues to be a powerful form of non-verbal communication to this day. Next, educational theories particularly relevant to comics use in TESOL are examined, with a focus Allan Pavio's Dual Coding theory of learning and Stephen Krashen's Input and Affective Filter Hypotheses. Each major section of this thesis contains a subsection of case studies from TESOL fieldwork, followed by an index of the things teachers should know and do to use the information in the section effectively
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