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On the isoperimetric problem for radial logconvex densities
 Calc. Var. Partial Differential Equations
"... Abstract. Given a smooth, radial, uniformly logconvex density eV on Rn, n ≥ 2, we characterize isoperimetric sets E with respect to weighted perimeter R ∂E eV dHn−1 and weighted volume m = R E eV as balls centered at the origin, provided m ∈ [0, m0) for some (potentially computable) m0> 0; this ..."
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Cited by 12 (3 self)
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Abstract. Given a smooth, radial, uniformly logconvex density eV on Rn, n ≥ 2, we characterize isoperimetric sets E with respect to weighted perimeter R ∂E eV dHn−1 and weighted volume m = R E eV as balls centered at the origin, provided m ∈ [0, m0) for some (potentially computable) m0> 0
On the isoperimetric problem in Euclidean space with density Calc
 Var. Partial Differential Equations
, 2008
"... ABSTRACT. We study the isoperimetric problem for Euclidean space endowed with a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher dimensions, we prove existence results and we derive stability conditions, which lead to the conjecture that f ..."
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Cited by 40 (5 self)
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that for a radial logconvex density, balls about the origin are isoperimetric regions. Finally, we prove this conjecture and the uniqueness of minimizers for the density exp(x  2) by using symmetrization techniques. 1.
PROOF OF THE LOGCONVEX DENSITY CONJECTURE
"... Abstract. We completely characterize isoperimetric regions in Rn with density eh, where h is convex, smooth, and radially symmetric. In particular, balls around the origin constitute isoperimetric regions of any given volume, proving the LogConvex Density Conjecture due to Kenneth Brakke. ..."
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Abstract. We completely characterize isoperimetric regions in Rn with density eh, where h is convex, smooth, and radially symmetric. In particular, balls around the origin constitute isoperimetric regions of any given volume, proving the LogConvex Density Conjecture due to Kenneth Brakke.
1Two adaptive rejection sampling schemes for probability density functions logconvex
"... tails ..."
Mixture Density Estimation
 IN ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 12
, 1999
"... Gaussian mixtures (or socalled radial basis function networks) for density estimation provide a natural counterpart to sigmoidal neural networks for function fitting and approximation. In both cases, it is possible to give simple expressions for the iterative improvement of performance as component ..."
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Cited by 85 (3 self)
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Gaussian mixtures (or socalled radial basis function networks) for density estimation provide a natural counterpart to sigmoidal neural networks for function fitting and approximation. In both cases, it is possible to give simple expressions for the iterative improvement of performance
Marine gravity anomaly from Geosat and ERS1 satellite altimetry
 J. Geophys. Res
, 1997
"... Abstract. Closely spaced satellite altimeter profiles collecte during the Geosat Geodetic Mission (6 km) and the ERS 1 Geodetic Phase (8 km) are easily converted to grids of vertical gravity gradient and gravity anomaly. The longwavelength radial orbit error is suppressed below the noise level of ..."
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Cited by 211 (8 self)
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Abstract. Closely spaced satellite altimeter profiles collecte during the Geosat Geodetic Mission (6 km) and the ERS 1 Geodetic Phase (8 km) are easily converted to grids of vertical gravity gradient and gravity anomaly. The longwavelength radial orbit error is suppressed below the noise level
Local Error Estimates for Radial Basis Function Interpolation of Scattered Data
 IMA J. Numer. Anal
, 1992
"... Introducing a suitable variational formulation for the local error of scattered data interpolation by radial basis functions OE(r), the error can be bounded by a term depending on the Fourier transform of the interpolated function f and a certain "Kriging function", which allows a formulat ..."
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Cited by 120 (24 self)
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Introducing a suitable variational formulation for the local error of scattered data interpolation by radial basis functions OE(r), the error can be bounded by a term depending on the Fourier transform of the interpolated function f and a certain "Kriging function", which allows a
RADIAL DENSITY IN APOLLONIAN PACKINGS
"... Abstract. Given P, an Apollonian Circle Packing, and a circle C0 = ∂B(z0, r0) in P, color the set of disks in P tangent to C0 red. What proportion of the concentric circle C = ∂B(z0, r0 + ) is red, and what is the behavior of this quantity as → 0? Using equidistribution of closed horocycles on t ..."
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on the modular surface H2/SL(2,Z), we show that the answer is 3 pi = 0.9549... We also describe an observation due to Alex Kontorovich connecting the rate of this convergence in the FareyFord packing to the Riemann Hypothesis. For the analogous problem for Soddy Sphere packings, we find that the limiting radial
Multistep scattered data interpolation using compactly supported radial basis functions
 J. Comp. Appl. Math
, 1996
"... Abstract. A hierarchical scheme is presented for smoothly interpolating scattered data with radial basis functions of compact support. A nested sequence of subsets of the data is computed efficiently using successive Delaunay triangulations. The scale of the basis function at each level is determine ..."
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Cited by 81 (12 self)
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is determined from the current density of the points using information from the triangulation. The method is rotationally invariant and has good reproduction properties. Moreover the solution can be calculated and evaluated in acceptable computing time. During the last two decades radial basis functions have
Results 1  10
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3,673