Search results for "polynomials"

showing 10 items of 144 documents

Removing Batch Effects from Longitudinal Gene Expression - Quantile Normalization Plus ComBat as Best Approach for Microarray Transcriptome Data

2016

International audience; Technical variation plays an important role in microarray-based gene expression studies, and batch effects explain a large proportion of this noise. It is therefore mandatory to eliminate technical variation while maintaining biological variability. Several strategies have been proposed for the removal of batch effects, although they have not been evaluated in large-scale longitudinal gene expression data. In this study, we aimed at identifying a suitable method for batch effect removal in a large study of microarray-based longitudinal gene expression. Monocytic gene expression was measured in 1092 participants of the Gutenberg Health Study at baseline and 5-year fol…

Male0301 basic medicineMolecular biologyMicroarrayslcsh:MedicineGene ExpressionPolynomialsMonocytesMathematical and Statistical Techniques0302 clinical medicineLongitudinal StudiesProspective Studieslcsh:ScienceOligonucleotide Array Sequence AnalysisGeneticsPrincipal Component Analysis[SDV.MHEP] Life Sciences [q-bio]/Human health and pathologyMultidisciplinaryGenomicsReplicateMiddle AgedRegressionRNA isolationBioassays and Physiological Analysis030220 oncology & carcinogenesisPhysical SciencesPrincipal component analysisFemaleRNA hybridizationDNA microarrayTranscriptome AnalysisStatistics (Mathematics)Research ArticleAdultComputational biologyBiologyBiomolecular isolationGeneralized linear mixed model03 medical and health sciencesDeming regressionExtraction techniquesGeneticsHumansStatistical MethodsAgedQuantile normalizationMolecular probe techniquesGene Expression Profilinglcsh:RBiology and Life SciencesComputational BiologyGenome AnalysisProbe hybridizationRNA extractionResearch and analysis methodsGene expression profilingMolecular biology techniquesAlgebra030104 developmental biologyNonlinear DynamicsMultivariate Analysislcsh:QMathematics[SDV.MHEP]Life Sciences [q-bio]/Human health and pathology
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Influence of trifocal intraocular lenses on standard autorefraction and aberrometer-based autorefraction.

2019

To study the agreement between manifest refraction and objective refraction measured with two autorefractor models and an aberrometer in eyes implanted with a trifocal diffractive intraocular lens (IOL).IOA Madrid Innova Ocular, Madrid, Spain.Prospective comparative cohort study.An autorefractor keratometer (KR-8800), based on a Scheiner double pinhole, and a 3-dimension wavefront topography aberrometer system (OPD-Scan III), based on the scanning-slit retinoscopy principle, were used to obtain objective refraction readings. In addition, lower-order Zernike coefficients (Z) were used to calculate objective refraction. A set of 7 different results was obtained in power vector notation (spher…

MaleCorneal Wavefront AberrationPseudophakiaMesopic visionZernike polynomialsmedicine.medical_treatmentVisual AcuityIntraocular lensRefraction OcularPupillaw.inventionsymbols.namesakeLens Implantation IntraocularlawmedicineHumansProspective StudiesRetinoscopyMathematicsAgedPhacoemulsificationmedicine.diagnostic_testKeratometerAberrometryMiddle AgedMultifocal Intraocular LensesSensory SystemsOphthalmologyAutorefractorsymbolsOptometrySurgeryFemalePhotopic visionJournal of cataract and refractive surgery
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Three-Dimensional Reconstruction of the Bony Nasolacrimal Canal by Automated Segmentation of Computed Tomography Images.

2016

Objective To apply a fully automated method to quantify the 3D structure of the bony nasolacrimal canal (NLC) from CT scans whereby the size and main morphometric characteristics of the canal can be determined. Design Cross-sectional study. Subjects 36 eyes of 18 healthy individuals. Methods Using software designed to detect the boundaries of the NLC on CT images, 36 NLC reconstructions were prepared. These reconstructions were then used to calculate NLC volume. The NLC axis in each case was determined according to a polygonal model and to 2nd, 3rd and 4th degree polynomials. From these models, NLC sectional areas and length were determined. For each variable, descriptive statistics and nor…

MaleModels AnatomicCritical Care and Emergency Medicinelcsh:MedicineComputed tomographyPolynomialsDiagnostic RadiologyNormality test0302 clinical medicineMedicine and Health SciencesSegmentationDegree of a polynomiallcsh:ScienceTomographyMusculoskeletal SystemTrauma MedicineMathematicsMultidisciplinaryNasolacrimal ductmedicine.diagnostic_testRadiology and ImagingAnatomyMiddle Agedmedicine.anatomical_structureSurgery Computer-AssistedPhysical SciencesNasolacrimal canalFemaleAnatomyResearch ArticleAdultComputer and Information SciencesImaging TechniquesTrauma SurgeryAutomated segmentationNeuroimagingSurgical and Invasive Medical ProceduresResearch and Analysis MethodsBone and BonesComputer Software03 medical and health sciencesImaging Three-DimensionalDiagnostic MedicinemedicineHumansSkeletonAgedMorphometrySkulllcsh:RBiology and Life SciencesComputing MethodsComputed Axial TomographyCross-Sectional StudiesAlgebra030221 ophthalmology & optometrylcsh:QTomography X-Ray ComputedNasolacrimal DuctMathematics030217 neurology & neurosurgeryNeuroscienceBiomedical engineeringVolume (compression)PLoS ONE
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Reliability of a new analysis to compute time to stabilization following a single leg drop jump landing in children.

2019

Although a number of different methods have been proposed to assess the time to stabilization (TTS), none is reliable in every axis and no tests of this type have been carried out on children. The purpose of this study was thus to develop a new computational method to obtain TTS using a time-scale (frequency) approach [i.e. continuous wavelet transformation (WAV)] in children. Thirty normally-developed children (mean age 10.16 years, SD = 1.52) participated in the study. Every participant performed 30 single-leg drop jump landings with the dominant lower limb (barefoot) on a force plate from three different heights (15cm, 20cm and 25cm). Five signals were used to compute the TTS: i) Raw, ii…

MaleResearch ValidityMuscle PhysiologyTime FactorsPhysiologyIntraclass correlationPolynomialsSignalRoot mean square0302 clinical medicineContinuous waveletStatisticsMedicine and Health SciencesBiomechanicsChildMusculoskeletal SystemReliability (statistics)MathematicsSignal processingMultidisciplinaryQRResearch AssessmentBiomechanical PhenomenaSignal FilteringPhysiological ParametersPhysical SciencesEngineering and TechnologyLegsMedicineFemaleAnatomyResearch ArticleMovementScienceResearch and Analysis Methods03 medical and health sciencesHumansMechanical PhenomenaLegBody WeightBiology and Life SciencesReproducibility of Results030229 sport sciencesAlgebraTransformation (function)Standard errorBody LimbsSignal ProcessingMusculoskeletal MechanicsMathematics030217 neurology & neurosurgeryPLoS ONE
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A new hyperelastic model for anisotropic hyperelastic materials with one fiber family

2016

International audience; The main goal of this study is to propose a practical application of a new family of transverse anisotropic invariants by designing a strain energy function (SEF) for incompressible fiber-reinforced materials. In order to validate the usability and creativeness of the proposed model, two different fiber-reinforced rubber materials under uniaxial and shear testing are considered. For each kind of material, numerical simulations based on the proposed model are consistent with experimental results and provide information about the effect of the new family of invariants in the construction of the SEF.

Materials science02 engineering and technologyStrain energy0203 mechanical engineeringNatural rubberGeneral Materials ScienceBiomechanicsAnisotropyPolynomial (hyperelastic model)Fiber (mathematics)business.industryApplied MathematicsMechanical EngineeringFunction (mathematics)Structural engineering[SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]021001 nanoscience & nanotechnologyCondensed Matter PhysicsAnisotropic hyperelasticity020303 mechanical engineering & transportsMechanics of MaterialsModeling and Simulationvisual_artHyperelastic materialvisual_art.visual_art_mediumCompressibilityTheory of invariant polynomials0210 nano-technologybusiness
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Bohr radii of vector valued holomorphic functions

2012

Abstract Motivated by the scalar case we study Bohr radii of the N -dimensional polydisc D N for holomorphic functions defined on D N with values in Banach spaces.

Mathematics(all)Mathematics::Functional AnalysisMathematics::Complex VariablesGeneral MathematicsMathematical analysisScalar (mathematics)Banach spaceHolomorphic functionPower seriesPolydiscPolynomialsBohr modelBanach spacessymbols.namesakesymbolsBohr radiusMathematical physicsMathematicsAdvances in Mathematics
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The Vector QD Algorithm for Smooth Functions (f, f′)

1996

AbstractWe deal with the functionz↦(f(z), f′(z)) wheref(z)=∑i⩾0aizi, (ai∈C) with limi→∞ai+1×ai−1/(ai)2=q. We investigate the convergence of the vector QD algorithm. We give the asymptotic behaviour of the generalized Hankel determinants. A convergence result on the vector orthogonal polynomials is proved.

Mathematics(all)Numerical AnalysisGeneral MathematicsApplied Mathematics010102 general mathematics010103 numerical & computational mathematics01 natural sciencesConvergence (routing)Orthogonal polynomials0101 mathematicsAlgorithmComputingMilieux_MISCELLANEOUS[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]AnalysisMathematicsJournal of Approximation Theory
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Indefinite integrals of special functions from inhomogeneous differential equations

2018

A method is presented for deriving integrals of special functions which obey inhomogeneous second-order linear differential equations. Inhomogeneous equations are readily derived for functions sati...

Mathematics::General MathematicsDifferential equationApplied Mathematics010102 general mathematicsMathematical analysis010103 numerical & computational mathematicsParabolic cylinder function01 natural sciencesLegendre functionsymbols.namesakeLinear differential equationSpecial functionsOrthogonal polynomialssymbols0101 mathematicsAnalysisBessel functionMathematicsIntegral Transforms and Special Functions
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Construction of a fundamental set of solutions of an arbitrary homogeneous linear difference equation

2002

Abstract The detailed construction of a prefixed fundamental set of solutions of a linear homogeneous difference equation of any order with arbitrarily variable coefficients is reported. The usefulness of the resulting resolutive formula is illustrated by simple applications to the Hermite polynomials and to the Fibonacci sequence.

Matrix difference equationFibonacci numberHermite polynomialsDifferential equationMathematical analysisMathematicsofComputing_NUMERICALANALYSISCharacteristic equationStatistical and Nonlinear PhysicsDifference equation matrix calculations Fibonacci sequence.Homogeneous differential equationComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONLinear difference equationMathematical PhysicsVariable (mathematics)MathematicsReports on Mathematical Physics
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Adaptive estimation of Laguerre models with time-varying delay

2000

Abstract An Orthonormal Basis Functions (OBF) approach is effectively used in adaptive parameter estimation of linear(ized) open-loop stable, possibly nonminimum phase plants with time-varying delay. In particular, discrete Laguerre models are considered in detail. A special attention is paid to the numerical conditioning issue in case of ’poor’ excitation of a plant under control, where OBF models are of particular value. Closed-loop predictive control simulations confirm the usefulness of adaptive OBF modelling, especially for systems with time-varying delays.

Model predictive controlAdaptive controlEstimation theoryControl theoryAdaptive systemLaguerre polynomialsPhase (waves)System identificationOrthonormal basis functionsMathematicsIFAC Proceedings Volumes
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