Search results for "Gauss"

showing 10 items of 701 documents

Interior Eigenvalue Density of Jordan Matrices with Random Perturbations

2017

International audience; We study the eigenvalue distribution of a large Jordan block subject to a small random Gaussian perturbation. A result by E. B. Davies and M. Hager shows that as the dimension of the matrix gets large, with probability close to 1, most of the eigenvalues are close to a circle.We study the expected eigenvalue density of the perturbed Jordan block in the interior of that circle and give a precise asymptotic description.; Nous étudions la distribution de valeurs propres d’un grand bloc de Jordan soumis à une petite perturbation gaussienne aléatoire. Un résultat de E. B. Davies et M. Hager montre que quand la dimension de la matrice devient grande, alors avec probabilité…

[ MATH ] Mathematics [math]Jordan matrixSpectral theoryGaussian010102 general mathematicsMathematical analysisPerturbation (astronomy)Mathematics::Spectral Theory01 natural sciences010104 statistics & probabilityMatrix (mathematics)symbols.namesakesymbolsRandom perturbations[MATH]Mathematics [math]MSC: 47A10 47B80 47H40 47A550101 mathematicsDivide-and-conquer eigenvalue algorithmSpectral theoryEigenvalue perturbationEigenvalues and eigenvectorsNon-self-adjoint operatorsMathematics
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Optimal control of an ensemble of Bloch equations with applications in MRI

2016

International audience; The optimal control of an ensemble of Bloch equations describing the evolution of an ensemble of spins is the mathematical model used in Nuclear Resonance Imaging and the associated costs lead to consider Mayer optimal control problems. The Maximum Principle allows to parameterize the optimal control and the dynamics is analyzed in the framework of geometric optimal control. This lead to numerical implementations or suboptimal controls using averaging principle.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologySpins010102 general mathematicsNuclear resonance[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]02 engineering and technologyOptimal controlLinear-quadratic-Gaussian control01 natural sciences020901 industrial engineering & automationMaximum principleControl theoryBloch equationsApplied mathematics[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Boundary value problem0101 mathematicsComputingMilieux_MISCELLANEOUSMathematics2016 IEEE 55th Conference on Decision and Control (CDC)
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Geometric and numerical techniques to compute conjugate and cut loci on Riemannian surfaces

2014

International audience; We combine geometric and numerical techniques - the Hampath code - to compute conjugate and cut loci on Riemannian surfaces using three test bed examples: ellipsoids of revolution, general ellipsoids, and metrics with singularities on S2 associated to spin dynamics.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Code (set theory)Spin dynamicsGeometryspin dynamics01 natural sciencesoptimal controlsymbols.namesakeGaussian curvature0101 mathematicsGeneral ellipsoidMathematics010102 general mathematics[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Optimal controlUmbilical pointEllipsoidOptimal controlCalcul parallèle distribué et partagé010101 applied mathematicsSpindynaicssymbolsgeneral ellipsoidGravitational singularity[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Conjugate and cut lociConjugate
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All-fibered high-quality low duty-cycle 160-GHz femtosecond pulse source

2008

International audience; In this paper, we report the experimental demonstration of an all-optical fiber-based 160-GHz femtosecond pulse source exhibiting a duty cycle as low as 1/17. The 380-fs wellseparated Gaussian pulses are generated thanks to the strong temporal compression of an initial beat-signal propagating into three distinct segments of optical fiber. Experimental results are supported by numerical simulations based on the generalized nonlinear Schrödinger equation. (© 2008 by Astro Ltd., Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA)

[PHYS.PHYS.PHYS-OPTICS] Physics [physics]/Physics [physics]/Optics [physics.optics]Femtosecond pulse shapingOptical fiberPhysics and Astronomy (miscellaneous)GaussianFemtosecond02 engineering and technology01 natural scienceslaw.invention010309 opticssymbols.namesake020210 optoelectronics & photonicsQuality (physics)Opticslaw0103 physical sciences0202 electrical engineering electronic engineering information engineeringInstrumentationNonlinear Schrödinger equationComputingMilieux_MISCELLANEOUSPhysics[PHYS.PHYS.PHYS-OPTICS]Physics [physics]/Physics [physics]/Optics [physics.optics][ PHYS.PHYS.PHYS-OPTICS ] Physics [physics]/Physics [physics]/Optics [physics.optics]business.industryLow duty cyclePulse compressionDuty cyclePulse compressionFemtosecondsymbolsNonlinear optics in fibersOptoelectronicsbusiness
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Parabolic pulse generation through passive reshaping of gaussian pulses in a normally dispersive fiber

2007

We numerically and experimentally demonstrate that a Gaussian pulse can be reshaped into a pulse with a stable parabolic intensity profile during propagation in normally dispersive nonlinear fibers.

[PHYS.PHYS.PHYS-OPTICS] Physics [physics]/Physics [physics]/Optics [physics.optics]Materials scienceGaussianPhysics::Optics02 engineering and technology01 natural sciences010309 opticssymbols.namesake020210 optoelectronics & photonicsOpticsFiber Bragg grating0103 physical sciences0202 electrical engineering electronic engineering information engineeringFiberGaussian processComputer Science::DatabasesComputingMilieux_MISCELLANEOUS[PHYS.PHYS.PHYS-OPTICS]Physics [physics]/Physics [physics]/Optics [physics.optics][ PHYS.PHYS.PHYS-OPTICS ] Physics [physics]/Physics [physics]/Optics [physics.optics]Pulse (signal processing)business.industrySecond-harmonic generationNonlinear opticsPulse shapingsymbolsbusiness
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Pulsating Dissipative Light Bullets

2009

Finding domains of existence for (3+1)D spatio-temporal dissipative solitons, also called “dissipative light bullets”, by direct numerical solving of a cubic-quintic Ginzburg-Landau equation (CGLE) is a lengthy procedure [1,2]. Variational approaches pave the way for quicker soliton solution mapping, as long as tractable trial functions remain suitable approximations for exact solutions [3,4].

[PHYS.PHYS.PHYS-OPTICS] Physics [physics]/Physics [physics]/Optics [physics.optics]Physics[PHYS.PHYS.PHYS-OPTICS]Physics [physics]/Physics [physics]/Optics [physics.optics][ PHYS.PHYS.PHYS-OPTICS ] Physics [physics]/Physics [physics]/Optics [physics.optics]Nonlinear optics01 natural sciences010305 fluids & plasmassymbols.namesakeDissipative solitonClassical mechanics0103 physical sciencessymbolsDissipative systemGinzburg–Landau theorySoliton010306 general physicsDispersion (water waves)Nonlinear Sciences::Pattern Formation and SolitonsGaussian processBifurcationComputingMilieux_MISCELLANEOUS
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New developments in the study of optical parabolic pulses in normally dispersive fibers

2011

International audience; We report two recent studies dealing with the evolution of parabolic pulses in normally dispersive fibers. On the one hand, the nonlinear reshaping from a Gaussian intensity profile towards the asymptotic parabolic shape is experimentally investigated in a Raman amplifier. On the other hand, the significant impact of the fourth order dispersion on a passive propagation is theoretically discussed: we numerically demonstrate flat-top, coherent supercontinuum generation in an all-normal dispersion-flattened photonic crystal fiber. This shape is associated to a strong reshaping of the temporal profile what becomes triangular.

[PHYS.PHYS.PHYS-OPTICS] Physics [physics]/Physics [physics]/Optics [physics.optics][PHYS.PHYS.PHYS-OPTICS]Physics [physics]/Physics [physics]/Optics [physics.optics]Materials scienceRaman amplification[ PHYS.PHYS.PHYS-OPTICS ] Physics [physics]/Physics [physics]/Optics [physics.optics]business.industryGaussianNonlinear opticsPhysics::Optics01 natural sciencesSupercontinuum010309 opticssymbols.namesakeOptics0103 physical sciencesDispersion (optics)symbolsStimulated emission010306 general physicsbusinessPhotonic-crystal fiberPhotonic crystal
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Evaluation of the areal material distribution of paper from its optical transmission image

2011

International audience; The goal of this study was to evaluate the areal mass distribution (defined as the X-ray transmission image) of paper from its optical transmission image. A Bayesian inversion framework was used in the related deconvolution process so as to combine indirect optical information with a priori knowledge about the type of paper imaged. The a priori knowledge was expressed in the form of an empirical Besov space prior distribution constructed in a computationally effective way using the wavelet transform. The estimation process took the form of a large-scale optimization problem, which was in turn solved using the gradient descent method of Barzilai and Borwein. It was de…

[PHYS]Physics [physics]ta114Computer scienceGaussianWavelet transform010103 numerical & computational mathematicsCondensed Matter Physics01 natural sciences030218 nuclear medicine & medical imagingElectronic Optical and Magnetic MaterialsTikhonov regularization03 medical and health sciencessymbols.namesake0302 clinical medicinePrior probabilityPhysical SciencessymbolsBesov spaceA priori and a posterioriDeconvolution0101 mathematicsGradient descentInstrumentationAlgorithm
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Nonlinear radial-harmonic correlation using binary decomposition for scale-invariant pattern recognition

2003

We introduce a new scale-invariant pattern-recognition method that uses nonlinear correlation. We applied several common linear correlations to images decomposed into disjoint binary images, which is very discriminant even when the target is embedded in strong noise. We combine our sliced orthogonal nonlinear generalized correlation method and the radial-harmonic expansion in order to achieve scale-invariant pattern recognition. The information from a radial harmonic for each binary slice of the reference object is combined with binary slices of the target. The method avoids the time-consuming process of finding expansion centers for the radial harmonics. The stability of the correlation pe…

business.industryBinary imageBinary numberPattern recognitionScale invarianceAtomic and Molecular Physics and OpticsElectronic Optical and Magnetic MaterialsBackground noiseNonlinear systemsymbols.namesakeNoiseOpticsGaussian noiseHarmonicsymbolsArtificial intelligenceElectrical and Electronic EngineeringPhysical and Theoretical ChemistrybusinessMathematicsOptics Communications
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Improved rotation invariant pattern recognition using circular harmonics of binary gray level slices

2000

We introduce a new rotation invariant pattern recognition method based on nonlinear correlation. The images are decomposed into disjoint binary slices and then correlated using the common linear correlation. This operation is very discriminant even when the target is embedded in strong noise. We extend our sliced orthogonal nonlinear generalized correlation method to rotation invariant pattern recognition by combining the information of a circular harmonic (CH) of each binary slice of the reference object with binary slices of the target. In addition to improved discrimination capability, the method avoids the time-consuming process of finding proper centers for the CHs. Results are present…

business.industryBinary numberDisjoint setsAtomic and Molecular Physics and OpticsElectronic Optical and Magnetic MaterialsBackground noiseNoisesymbols.namesakeOpticsGaussian noisePattern recognition (psychology)symbolsRotational invarianceElectrical and Electronic EngineeringPhysical and Theoretical ChemistrybusinessRotation (mathematics)MathematicsOptics Communications
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