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193
A functional limit theorem for the profile of search trees
 Annals of Applied Probability
, 2008
"... We study the profile Xn,k of random search trees including binary search trees and mary search trees. Our main result is a functional limit theorem of the normalized profile Xn,k/EXn,k for k =⌊α log n ⌋ in a certain range of α. A central feature of the proof is the use of the contraction method to ..."
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Cited by 21 (11 self)
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We study the profile Xn,k of random search trees including binary search trees and mary search trees. Our main result is a functional limit theorem of the normalized profile Xn,k/EXn,k for k =⌊α log n ⌋ in a certain range of α. A central feature of the proof is the use of the contraction method to prove convergence in distribution of certain random analytic functions in a complex domain. This is based on a general theorem concerning the contraction method for random variables in an infinitedimensional Hilbert space. As part of the proof, we show that the Zolotarev metric is complete for a Hilbert space. 1. Introduction. Search
The Intrinsic Structure of Optic Flow Incorporating Measurement Duality
 International Journal of Computer Vision
, 1997
"... The purpose of this report 1 is to define optic flow for scalar and density images without using a priori knowledge other than its defining conservation principle, and to incorporate measurement duality, notably the scalespace paradigm. It is argued that the design of optic flow based applicati ..."
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Cited by 20 (13 self)
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The purpose of this report 1 is to define optic flow for scalar and density images without using a priori knowledge other than its defining conservation principle, and to incorporate measurement duality, notably the scalespace paradigm. It is argued that the design of optic flow based applications may benefit from a manifest separation between factual image structure on the one hand, and goalspecific details and hypotheses about image flow formation on the other. The approach is based on a physical symmetry principle known as gauge invariance. Dataindependent models can be incorporated by means of admissible gauge conditions, each of which may single out a distinct solution, but all of which must be compatible with the evidence supported by the image data. The theory is illustrated by examples and verified by simulations, and performance is compared to several techniques reported in the literature. 1 Introduction The conventional "spacetime" representation of a movie as...
Extension of conformal nets and superselection structure
, 2008
"... Starting with a conformal Quantum Field Theory on the real line, we show that the Haag dual net is still conformal with respect to a new representation of the Möbius group. We infer from this that every conformal net is normal and conormal, namely the local von Neumann algebra associated with an int ..."
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Cited by 18 (14 self)
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Starting with a conformal Quantum Field Theory on the real line, we show that the Haag dual net is still conformal with respect to a new representation of the Möbius group. We infer from this that every conformal net is normal and conormal, namely the local von Neumann algebra associated with an interval coincides with its double relative commutant inside the local von Neumann algebra associated with any larger interval. The net and the dual net give together rise to an infinite dimensional symmetry group, of which we study a class of positive energy irreducible representations. We mention how superselsection sectors extend to the dual net and we illustrate by examples how, in general, this process generates solitonic sectors. We describe the free theories associated with the lowest weight n representations of PSL(2, R), showing that they violate 3regularity for n> 2. When n ≥ 2, we obtain examples of non Möbiuscovariant sectors of a 3regular (non 4regular) net.
The Fuzzy Supersphere
, 1998
"... We introduce the fuzzy supersphere as sequence of finitedimensional, noncommutative Z2graded algebras tending in a suitable limit to a dense subalgebra of the Z2graded algebra of H1functions on the (22)dimensional supersphere. Noncommutative analogues of the body map (to the (fuzzy) sphere) ..."
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Cited by 18 (2 self)
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We introduce the fuzzy supersphere as sequence of finitedimensional, noncommutative Z2graded algebras tending in a suitable limit to a dense subalgebra of the Z2graded algebra of H1functions on the (22)dimensional supersphere. Noncommutative analogues of the body map (to the (fuzzy) sphere) and the superdeRham complex are introduced. In particular we reproduce the equality of the superdeRham cohomology of the supersphere and the ordinary deRham cohomology of its body on the "fuzzy level".
On the wave equation with a large rough potential
, 2003
"... Abstract. We prove an optimal dispersive L ∞ decay estimate for a three dimensional wave equation perturbed with a large non smooth potential belonging to a particular Kato class. The proof is based on a spectral representation of the solution and suitable resolvent estimates for the perturbed opera ..."
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Cited by 18 (0 self)
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Abstract. We prove an optimal dispersive L ∞ decay estimate for a three dimensional wave equation perturbed with a large non smooth potential belonging to a particular Kato class. The proof is based on a spectral representation of the solution and suitable resolvent estimates for the perturbed operator. 1.
PSEUDORATIONAL INPUT/OUTPUT MAPS AND THEIR REALIZATIONS: A FRACTIONAL REPRESENTATION APPROACH TO INFINITEDIMENSIONAL SYSTEMS
, 1988
"... This paper studies matrix fractional representation for impulse responses of a certain class of infinitedimensional linear systems which contains, in particular, delaydifferential systems. Such impulse responses are called pseudorational in this paper. This fractional representation is effectivel ..."
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Cited by 14 (9 self)
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This paper studies matrix fractional representation for impulse responses of a certain class of infinitedimensional linear systems which contains, in particular, delaydifferential systems. Such impulse responses are called pseudorational in this paper. This fractional representation is effectively used to derive concrete function space models from the abstract shift realizations. Given a fractional representation Q P, a standard observable realization, analogous to Fuhrmann realizations for finitedimensional systems, is associated to it. A new notion of coprimeness called approximate left coprimeness is introduced, and it is shown that the standard observable realization associated to the representation Ql, p is canonical if and only if Q and P are approximately left coprime. Some examples are discussed to illustrate the relationships among various coprimeness concepts that have appeared in the literature.
On a generalized ConnesHochschildKostantRosenberg theorem
 Adv. Math
, 2006
"... Abstract. The central result here is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild homology is identified with the space of differential fo ..."
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Cited by 14 (3 self)
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Abstract. The central result here is an explicit computation of the Hochschild and cyclic homologies of a natural smooth subalgebra of stable continuous trace algebras having smooth manifolds X as their spectrum. More precisely, the Hochschild homology is identified with the space of differential forms on X, and the periodic cyclic homology with the twisted de Rham cohomology of X, thereby generalizing some fundamental results of Connes and HochschildKostantRosenberg. The ConnesChern character is also identified here with the twisted Chern character. 1.
Commutative geometries are spin manifolds
 Rev. Math. Phys
"... In [1], Connes presented axioms governing noncommutative geometry. He went on to claim that when specialised to the commutative case, these axioms recover spin or spin c geometry depending on whether the geometry is “real ” or not. We attempt to flesh out the details of Connes ’ ideas. As an illustr ..."
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Cited by 13 (1 self)
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In [1], Connes presented axioms governing noncommutative geometry. He went on to claim that when specialised to the commutative case, these axioms recover spin or spin c geometry depending on whether the geometry is “real ” or not. We attempt to flesh out the details of Connes ’ ideas. As an illustration we present a proof of his claim, partly extending the validity of the result to pseudoRiemannian spin manifolds. Throughout we are as explicit and elementary as possible. 1
The Spectrum of Weakly Coupled Map Lattices
, 1997
"... We consider weakly coupled analytic expanding circle maps on the lattice Z d (for d ≥ 1), with small coupling strength ɛ and coupling between two sites decaying exponentially with the distance. We study the spectrum of the associated (PerronFrobenius) transfer operators. We give a Fréchet space on ..."
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Cited by 12 (1 self)
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We consider weakly coupled analytic expanding circle maps on the lattice Z d (for d ≥ 1), with small coupling strength ɛ and coupling between two sites decaying exponentially with the distance. We study the spectrum of the associated (PerronFrobenius) transfer operators. We give a Fréchet space on which the operator associated to the full system has a simple eigenvalue at 1 (corresponding to the SRB measure µɛ previously obtained by Bricmont–Kupiainen [BK1]) and the rest of the spectrum, except maybe for continuous spectrum, is inside a disc of radius smaller than one. For d = 1 we also construct Banach spaces of densities with respect to µɛ on which perturbation theory, applied to the difference of fixed high iterates of the normalised coupled and uncoupled transfer operators, yields localisation of the full spectrum of the coupled operator (i.e., the first spectral gap and beyond). As a sideeffect, we show that the whole spectra of the truncated coupled transfer operators (on bounded analytic functions) are O(ɛ)close to the truncated uncoupled spectra, uniformly in the spatial size. Our method uses polymer expansions and also gives the exponential decay of timecorrelations for a larger class of observables than those considered in [BK1].
Reachability of a Class of InfiniteDimensional Linear . . .
, 1989
"... This paper studies the question of quasi(approximate) reachability of the standard observable realizations of pseudorational impulse responses introduced by the author. The framework places the current theory of retarded and neutral delaydifferential systems into a unified input/output framework. ..."
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Cited by 12 (10 self)
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This paper studies the question of quasi(approximate) reachability of the standard observable realizations of pseudorational impulse responses introduced by the author. The framework places the current theory of retarded and neutral delaydifferential systems into a unified input/output framework. Several necessary and sufficient conditions for quasiteachability are derived. In particular, new criteria for quasiteachability and eigenfunction completeness are obtained for general delaydifferential systems with no restriction on the type of delays. Furthermore, as a byproduct, the theory leads to necessary and sufficient conditions for approximate left coprimeness of matrices with distribution entries. Examples are discussed to illustrate the theory.