Results 11  20
of
145
Nuclear and Trace Ideals in Tensored *Categories
, 1998
"... We generalize the notion of nuclear maps from functional analysis by defining nuclear ideals in tensored categories. The motivation for this study came from attempts to generalize the structure of the category of relations to handle what might be called "probabilistic relations". The compact closed ..."
Abstract

Cited by 28 (10 self)
 Add to MetaCart
We generalize the notion of nuclear maps from functional analysis by defining nuclear ideals in tensored categories. The motivation for this study came from attempts to generalize the structure of the category of relations to handle what might be called "probabilistic relations". The compact closed structure associated with the category of relations does not generalize directly, instead one obtains nuclear ideals. Most tensored categories have a large class of morphisms which behave as if they were part of a compact closed category, i.e. they allow one to transfer variables between the domain and the codomain. We introduce the notion of nuclear ideals to analyze these classes of morphisms. In compact closed tensored categories, all morphisms are nuclear, and in the tensored category of Hilbert spaces, the nuclear morphisms are the HilbertSchmidt maps. We also introduce two new examples of tensored categories, in which integration plays the role of composition. In the first, mor...
Kernel dimension reduction in regression
, 2006
"... Acknowledgements. The authors thank the editor and anonymous referees for their helpful comments. The authors also thank Dr. Yoichi Nishiyama for his helpful comments on the uniform convergence of empirical processes. We would like to acknowledge support from JSPS KAKENHI 15700241, ..."
Abstract

Cited by 27 (11 self)
 Add to MetaCart
Acknowledgements. The authors thank the editor and anonymous referees for their helpful comments. The authors also thank Dr. Yoichi Nishiyama for his helpful comments on the uniform convergence of empirical processes. We would like to acknowledge support from JSPS KAKENHI 15700241,
Intertwining Multiresolution Analyses and the Construction of Piecewise Polynomial Wavelets
, 1994
"... Let (Vp ) be a local multiresolution analysis (MRA) of L 2 (R) of multiplicity r 1, i.e., V0 is generated by r compactly supported scaling functions. If the scaling functions generate an orthogonal basis of V0 then (Vp) is called an orthogonal MRA. We prove that there exists an orthogonal local M ..."
Abstract

Cited by 26 (6 self)
 Add to MetaCart
Let (Vp ) be a local multiresolution analysis (MRA) of L 2 (R) of multiplicity r 1, i.e., V0 is generated by r compactly supported scaling functions. If the scaling functions generate an orthogonal basis of V0 then (Vp) is called an orthogonal MRA. We prove that there exists an orthogonal local MRA (V 0 p ) of multiplicity r 0 such that Vq ae V 0 0 ae Vq+n for some integers q 0, n 1 and r 0 ? 1. In particular, this shows that compactly supported orthogonal polynomial spline wavelets and scaling functions (of mulitplicity r 0 ? 1) of arbitrary regularity exist and we give several such examples. 1 Introduction The starting point for most wavelet constructions is a single function OE 2 L 2 (R) called a scaling function whose integer translates form a Riesz basis for a closed linear subspace V 0 ae L 2 (R). If the scaling function is compactly supported and generates an orthogonal basis of V 0 , then the associated wavelet will also be compactly supported and generate...
Using Local Planar Geometric Invariants to Match and Model Images of Line Segments
 J. OF COMP. VISION AND IMAGE UNDERST
, 1998
"... Image matching consists of finding features in different images that represent the same feature of the observed scene. It is a basic process in vision whenever several images are used. This paper describes a matching algorithm for lines segments in two images. The key idea of the algorithm is to ass ..."
Abstract

Cited by 20 (4 self)
 Add to MetaCart
Image matching consists of finding features in different images that represent the same feature of the observed scene. It is a basic process in vision whenever several images are used. This paper describes a matching algorithm for lines segments in two images. The key idea of the algorithm is to assume that the apparent motion between the two images can be approximated by a planar geometric transformation (a similarity or an affine transformation) and to compute such an approximation. Under such an assumption, local planar invariants related the kind of transformation used as approximation, should have the same value in both images. Such invariants are computed for simple segment configurations in both images and matched according to their values. A global constraint is added to insure a global coherency between all the possible matches: all the local matches must define approximately the same geometric transformation between the two images. These first matches are verified and complet...
On the existence of transmission eigenvalues in an inhomogeneous medium, (will appear as an article
 in Applicable Analysis), Technical report, n o RR6779, INRIA, 2008, http://hal.inria.fr/ inria00347840/fr
"... apport de recherche ..."
Discrete KaluzaKlein from scalar fluctuations in noncommutative geometry
 hepth/0104108, J. Math. Phys
, 2002
"... We compute the metric associated to noncommutative spaces described by a tensor product of spectral triples. Wellknown results of the twosheets model (distance on a sheet, distance between the sheets) are extended to any product of two spectral triples. The distance between different points on dif ..."
Abstract

Cited by 16 (10 self)
 Add to MetaCart
We compute the metric associated to noncommutative spaces described by a tensor product of spectral triples. Wellknown results of the twosheets model (distance on a sheet, distance between the sheets) are extended to any product of two spectral triples. The distance between different points on different fibres is investigated. When one of the triples describes a manifold, one finds a Pythagorean theorem as soon as the direct sum of the internal states (viewed as projections) commutes with the internal Dirac operator. Scalar fluctuations yield a discrete KaluzaKlein model in which the extra component of the metric is given by the internal part of the geometry. In the standard model, this extra component comes from the Higgs field. 1
The modeling and estimation of statistically selfsimilar processes in a multiresolution framework
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1999
"... Statistically selfsimilar (SSS) processes can be used to describe a variety of physical phenomena, yet modeling these phenomena has proved challenging. Most of the proposed models for SSS and approximately SSS processes have power spectra that behave as 1=f, such as fractional Brownian motion (fBm ..."
Abstract

Cited by 16 (3 self)
 Add to MetaCart
Statistically selfsimilar (SSS) processes can be used to describe a variety of physical phenomena, yet modeling these phenomena has proved challenging. Most of the proposed models for SSS and approximately SSS processes have power spectra that behave as 1=f, such as fractional Brownian motion (fBm), fractionally differenced noise, and waveletbased syntheses. The most flexible framework is perhaps that based on wavelets, which provides a powerful tool for the synthesis and estimation of 1=f processes, but assumes a particular distribution of the measurements. An alternative framework is the class of multiresolution processes proposed by Chou et al. [1994], which has already been shown to be useful for the identification of the parameters of fBm. These multiresolution processes are defined by an autoregression in scale that makes them naturally suited to the representation of SSS (and approximately SSS) phenomena, both stationary and nonstationary. Also, this multiresolution framework is accompanied by an efficient estimator, likelihood calculator, and conditional simulator that make no assumptions about the distribution of the measurements. In this paper, we show how to use the multiscale framework to represent SSS (or approximately SSS) processes such as fBm and fractionally differenced Gaussian noise. The multiscale models are realized by using canonical correlations (CC) and by exploiting the selfsimilarity and possible stationarity or stationary increments of the desired process. A number of examples are provided to demonstrate the utility of the multiscale framework in simulating and estimating SSS processes.
Rough solutions of the Einstein constraints on closed manifolds without nearCMC conditions. Submitted for publication. Available as arXiv:0712.0798v1 [grqc
"... ABSTRACT. We consider the conformal decomposition of Einstein’s constraint equations introduced by Lichnerowicz and York, on a closed manifold. We establish existence of nonCMC weak solutions using a combination of a priori estimates for the individual Hamiltonian and momentum constraints, barrier ..."
Abstract

Cited by 15 (11 self)
 Add to MetaCart
ABSTRACT. We consider the conformal decomposition of Einstein’s constraint equations introduced by Lichnerowicz and York, on a closed manifold. We establish existence of nonCMC weak solutions using a combination of a priori estimates for the individual Hamiltonian and momentum constraints, barrier constructions and fixedpoint techniques for the Hamiltonian constraint, RieszSchauder theory for the momentum constraint, together with a topological fixedpoint argument for the coupled system. Although we present general existence results for nonCMC weak solutions when the rescaled background metric is in any of the three Yamabe classes, an important new feature of the results we present for the positive Yamabe class is the absence of the nearCMC assumption, if the freely specifiable part of the data given by the tracelesstransverse part of the rescaled extrinsic curvature and the matter fields are sufficiently small, and if the energy density of matter is not identically zero. In this case, the mean extrinsic curvature can be taken to be an arbitrary smooth function without restrictions on the size of its spatial derivatives, so that it can be arbitrarily far from constant, giving what is apparently the first existence results for nonCMC solutions without the
The existence of an infinite discrete set of transmission eigenvalues
"... Abstract. We prove the existence of an infinite discrete set of transmission eigenvalues corresponding to the scattering problem for isotropic and anisotropic inhomogeneous media for both the Helmholtz and Maxwell’s equations. Our discussion includes the case of the interior transmission problem for ..."
Abstract

Cited by 15 (11 self)
 Add to MetaCart
Abstract. We prove the existence of an infinite discrete set of transmission eigenvalues corresponding to the scattering problem for isotropic and anisotropic inhomogeneous media for both the Helmholtz and Maxwell’s equations. Our discussion includes the case of the interior transmission problem for an inhomogeneous medium with cavities, i.e. subregions with contrast zero. Key words. Interior transmission problem, transmission eigenvalues, inhomogeneous medium, inverse scattering. AMS subject classifications. 35R30, 35Q60, 35J40, 78A25. 1. Introduction. The