434 research outputs found

    The divine sympathy: an essay on kenotic Christology

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    Information Foraging for Perceptual Decisions

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    We tested an information foraging framework to characterize the mechanisms that drive active (visual) sampling behavior in decision problems that involve multiple sources of information. Experiments 1 through 3 involved participants making an absolute judgment about the direction of motion of a single random dot motion pattern. In Experiment 4, participants made a relative comparison between 2 motion patterns that could only be sampled sequentially. Our results show that: (a) Information (about noisy motion information) grows to an asymptotic level that depends on the quality of the information source; (b) The limited growth is attributable to unequal weighting of the incoming sensory evidence, with early samples being weighted more heavily; (c) Little information is lost once a new source of information is being sampled; and (d) The point at which the observer switches from 1 source to another is governed by online monitoring of his or her degree of (un)certainty about the sampled source. These findings demonstrate that the sampling strategy in perceptual decision-making is under some direct control by ongoing cognitive processing. More specifically, participants are able to track a measure of (un)certainty and use this information to guide their sampling behavior

    Cohomology of skew-holomorphic Lie algebroids

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    We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.Comment: 16 pages. v2: Final version to be published in Theor. Math. Phys. (incorporates only very minor changes

    Modular classes of Poisson-Nijenhuis Lie algebroids

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    The modular vector field of a Poisson-Nijenhuis Lie algebroid AA is defined and we prove that, in case of non-degeneracy, this vector field defines a hierarchy of bi-Hamiltonian AA-vector fields. This hierarchy covers an integrable hierarchy on the base manifold, which may not have a Poisson-Nijenhuis structure.Comment: To appear in Letters in Mathematical Physic

    On localization in holomorphic equivariant cohomology

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    We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.Comment: 16 pages. Completely rewritten, new title. v3: Minor changes in the exposition. v4: final version to appear in Centr. Eur. J. Mat

    Formal Hecke algebras and algebraic oriented cohomology theories

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    In the present paper we generalize the construction of the nil Hecke ring of Kostant-Kumar to the context of an arbitrary algebraic oriented cohomology theory of Levine-Morel and Panin-Smirnov, e.g. to Chow groups, Grothendieck's K_0, connective K-theory, elliptic cohomology, and algebraic cobordism. The resulting object, which we call a formal (affine) Demazure algebra, is parameterized by a one-dimensional commutative formal group law and has the following important property: specialization to the additive and multiplicative periodic formal group laws yields completions of the nil Hecke and the 0-Hecke rings respectively. We also introduce a deformed version of the formal (affine) Demazure algebra, which we call a formal (affine) Hecke algebra. We show that the specialization of the formal (affine) Hecke algebra to the additive and multiplicative periodic formal group laws gives completions of the degenerate (affine) Hecke algebra and the usual (affine) Hecke algebra respectively. We show that all formal affine Demazure algebras (and all formal affine Hecke algebras) become isomorphic over certain coefficient rings, proving an analogue of a result of Lusztig.Comment: 28 pages. v2: Some results strengthened and references added. v3: Minor corrections, section numbering changed to match published version. v4: Sign errors in Proposition 6.8(d) corrected. This version incorporates an erratum to the published versio

    Integral Grothendieck-Riemann-Roch theorem

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    We show that, in characteristic zero, the obvious integral version of the Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the Todd and Chern characters is true (without having to divide the Chow groups by their torsion subgroups). The proof introduces an alternative to Grothendieck's strategy: we use resolution of singularities and the weak factorization theorem for birational maps.Comment: 24 page

    Weak splittings of quotients of Drinfeld and Heisenberg doubles

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    We investigate the fine structure of the simplectic foliations of Poisson homogeneous spaces. Two general results are proved for weak splittings of surjective Poisson submersions from Heisenberg and Drinfeld doubles. The implications of these results are that the torus orbits of symplectic leaves of the quotients can be explicitly realized as Poisson-Dirac submanifolds of the torus orbits of the doubles. The results have a wide range of applications to many families of real and complex Poisson structures on flag varieties. Their torus orbits of leaves recover important families of varieties such as the open Richardson varieties.Comment: 20 pages, AMS Late

    Support varieties for selfinjective algebras

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    Support varieties for any finite dimensional algebra over a field were introduced by Snashall-Solberg using graded subalgebras of the Hochschild cohomology. We mainly study these varieties for selfinjective algebras under appropriate finite generation hypotheses. Then many of the standard results from the theory of support varieties for finite groups generalize to this situation. In particular, the complexity of the module equals the dimension of its corresponding variety, all closed homogeneous varieties occur as the variety of some module, the variety of an indecomposable module is connected, periodic modules are lines and for symmetric algebras a generalization of Webb's theorem is true
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