4,303 research outputs found

    Locally continuously perfect groups of homeomorphisms

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    The notion of a locally continuously perfect group is introduced and studied. This notion generalizes locally smoothly perfect groups introduced by Haller and Teichmann. Next, we prove that the path connected identity component of the group of all homeomorphisms of a manifold is locally continuously perfect. The case of equivariant homeomorphism group and other examples are also considered.Comment: 14 page

    On the unification of geodetic leveling datums using satellite altimetry

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    Techniques are described for determining the height of Mean Sea Level (MSL) at coastal sites from satellite altimetry. Such information is of value in the adjustment of continental leveling networks. Numerical results are obtained from the 1977 GEOS-3 altimetry data bank at Goddard Space Flight Center using the Bermuda calibration of the altimeter. Estimates are made of the heights of MSL at the leveling datums for Australia and a hypothetical Galveston datum for central North America. The results obtained are in reasonable agreement with oceanographic estimates obtained by extrapolation. It is concluded that all gravity data in the Australian bank AUSGAD 76 and in the Rapp data file for central North America refer to the GEOS-3 altimeter geoid for 1976.0 with uncertainties which do not exceed + or - 0.1 mGal

    Decision-level adaptation in motion perception

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    Prolonged exposure to visual stimuli causes a bias in observers’ responses to subsequent stimuli. Such adaptation-induced biases are usually explained in terms of changes in the relative activity of sensory neurons in the visual system which respond selectively to the properties of visual stimuli. However, the bias could also be due to a shift in the observer’s criterion for selecting one response rather than the alternative; adaptation at the decision level of processing rather than the sensory level. We investigated whether adaptation to implied motion is best attributed to sensory-level or decision-level bias. Three experiments sought to isolate decision factors by changing the nature of the participants’ task while keeping the sensory stimulus unchanged. Results showed that adaptation-induced bias in reported stimulus direction only occurred when the participant’s task involved a directional judgement, and disappeared when adaptation was measured using a non-directional task (reporting where motion was present in the display, regardless of its direction). We conclude that adaptation to implied motion is due to decision-level bias, and that a propensity towards such biases may be widespread in sensory decision-makin

    Aperiodic invariant continua for surface homeomorphisms

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    We prove that if a homeomorphism of a closed orientable surface S has no wandering points and leaves invariant a compact, connected set K which contains no periodic points, then either K=S and S is a torus, or KK is the intersection of a decreasing sequence of annuli. A version for non-orientable surfaces is given.Comment: 8 pages, to appear in Mathematische Zeitschrif

    How fMRI Can Inform Cognitive Theories

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    How can functional magnetic resonance imaging (fMRI) advance cognitive theory? Some have argued that fMRI can do little beyond localizing brain regions that carry out certain cognitive functions (and may not even be able to do that). However, in this article, we argue that fMRI can inform theories of cognition by helping to answer at least four distinct kinds of questions. Which mental functions are performed in brain regions specialized for just that function (and which are performed in more general-purpose brain machinery)? When fMRI markers of a particular Mental Process X are found, is Mental Process X engaged when people perform Task Y? How distinct are the representations of different stimulus classes? Do specific pairs of tasks engage common or distinct processing mechanisms? Thus, fMRI data can be used to address theoretical debates that have nothing to do with where in the brain a particular process is carried out
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