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Orientation Maps in V1 and Non-Euclidean Geometry
In the primary visual cortex, the processing of information uses the distribution of orientations in the visual input: neurons react to some orientations in the stimulus more than to others. In manyExpand
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How tempered representations of a semisimple Lie group contract to its Cartan motion group
George W. Mackey suggested in 1975 that there should be analogies between the irreducible unitary representations of a noncompact semisimple Lie group G and those of its Cartan motion group − theExpand
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Monochromaticity of Orientation Maps in V1 Implies Minimum Variance for Hypercolumn Size
In the primary visual cortex of many mammals, the processing of sensory information involves recognizing stimuli orientations. The repartition of preferred orientations of neurons in some areas isExpand
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Appreciation to Journal of Mathematical Imaging and Vision Reviewers
Représentations de groupes de Lie et fonctionnement géométrique du cerveau
Cette these etudie deux problemes independants ou l’analyse harmonique non-commutative, theorie des representations de groupes de Lie, joue un role. Le premier probleme a ete suggere par lesExpand
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On the analogy between real reductive groups and Cartan motion groups: A proof of the Connes-Kasparov isomorphism
Abstract Alain Connes and Nigel Higson pointed out in the 1990s that the Connes-Kasparov “conjecture” for the K-theory of reduced group C ⁎ -algebras seemed, in the case of reductive Lie groups, toExpand
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Invariant Gaussian Fields on Homogeneous Spaces : Explicit Constructions and Geometric Measure of the Zero-set
This paper is concerned with the properties of Gaussian random fields defined on a riemannian homogeneous space, under the assumption that the probability distribution be invariant under the isometryExpand
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Un effet de moiré sur les espaces symétriques de type non-compact
Nous montrons que sur un espace symetrique X de type non compact, de meme que l'interference constructive d'ondes d'Helgason dont les directions de propagation balaient le "bord" de X fournit sesExpand
A Mackey-Analogy based Proof of the Connes-Kasparov Isomorphism for Real Reductive Groups
We give a new representation-theory based proof of the Connes-Kasparov conjecture for the K-theory of reduced C*-algebras of real reductive Lie groups. Our main tool is a natural correspondenceExpand
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Continuity of the Mackey-Higson bijection
When $G$ is a real reductive group and $G_0$ is its Cartan motion group, the Mackey-Higson bijection is a natural one-to-one correspondence between all irreducible tempered representations of $G$ andExpand
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