Search results for "Affine"

showing 10 items of 183 documents

Bézier surfaces of minimal area

2002

There are minimal surfaces admitting a Bezier form. We study the properties that the associated net of control points must satisfy. We show that in the bicubical case all minimal surfaces are, up to an affine transformation, pieces of the Enneper's surface.

Surface (mathematics)Computer Science::GraphicsMinimal surfaceNet (polyhedron)Bézier curveGeometryAffine transformationMathematics
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Automorphisms of $mathbb{A}^{1}$-fibered affine surfaces

2011

We develop technics of birational geometry to study automorphisms of affine surfaces admitting many distinct rational fibrations, with a particular focus on the interactions between automorphisms and these fibrations. In particular, we associate to each surface S of this type a graph encoding equivalence classes of rational fibrations from which it is possible to decide for instance if the automorphism group of S is generated by automorphisms preserving these fibrations.

Surface (mathematics)Graph encodingPure mathematicsApplied MathematicsGeneral MathematicsFibered knotBirational geometryType (model theory)AutomorphismMathematics::Algebraic TopologyMathematics::Group TheoryMathematics::Algebraic GeometryAffine transformationddc:510Focus (optics)Mathematics::Symplectic GeometryMathematics
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Quasi-Conformal Technique for Integrating and Validating Myocardial Tissue Characterization in MRI with Ex-Vivo Human Histological Data

2017

Ventricular tachycardia caused by a circuit of re-entry is one of the most critical arrhythmias. It is usually related with heterogeneous scar regions where slow velocity of conduction tissue is mixed with non-conductive tissue, creating pathways (CC) responsible for the tachycardia. Pre-operative DE-MRI can provide information on myocardial tissue viability and then improve therapy planning. However, the current DE-MRI resolution is not sufficient for identifying small CCs and therefore they have to be identified during the intervention, which requires considerable operator experience. In this work, we studied the relationship of histological data (with 10 \(\mu \)m resolution), with in-vi…

TachycardiaPixelFibrosisComputer sciencemedicineConformal mapHistologyAffine transformationmedicine.symptomVentricular tachycardiamedicine.diseaseEx vivoBiomedical engineering
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Annihilators of tensor density modules

2007

Abstract We describe the two-sided ideals in the universal enveloping algebras of the Lie algebras of vector fields on the line and the circle which annihilate the tensor density modules. Both of these Lie algebras contain the projective subalgebra, a copy of sl 2 . The restrictions of the tensor density modules to this subalgebra are duals of Verma modules (of sl 2 ) for Vec ( R ) and principal series modules (of sl 2 ) for Vec ( S 1 ) . Thus our results are related to the well-known theorem of Duflo describing the annihilating ideals of Verma modules of reductive Lie algebras. We find that, in general, the annihilator of a tensor density module of Vec ( R ) or Vec ( S 1 ) is generated by …

Tensor density modulesPure mathematicsVerma moduleAlgebra and Number TheorySubalgebraMathematics::Rings and AlgebrasUniversal enveloping algebraGeneralized Verma moduleAffine Lie algebraLie conformal algebraAnnihilating idealsMathematics::Quantum AlgebraTensor product of modulesTensor densityMathematics::Representation TheoryMathematicsJournal of Algebra
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A basic analysis toolkit for biological sequences

2007

This paper presents a software library, nicknamed BATS, for some basic sequence analysis tasks. Namely, local alignments, via approximate string matching, and global alignments, via longest common subsequence and alignments with affine and concave gap cost functions. Moreover, it also supports filtering operations to select strings from a set and establish their statistical significance, via z-score computation. None of the algorithms is new, but although they are generally regarded as fundamental for sequence analysis, they have not been implemented in a single and consistent software package, as we do here. Therefore, our main contribution is to fill this gap between algorithmic theory an…

Theoretical computer sciencelcsh:QH426-470Computer sciencebusiness.industrysoftwareComputationApplied MathematicsString searching algorithmApproximate string matchingSoftware ArticleSet (abstract data type)Longest common subsequence problemlcsh:GeneticsSoftwareComputational Theory and Mathematicslcsh:Biology (General)Structural BiologyAffine transformationPerlbusinesscomputerMolecular Biologylcsh:QH301-705.5computer.programming_language
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Min-max control of uncertain multi-inventory systems with multiplicative uncertainties

2001

In this note, we consider production-distribution systems with buffer and capacity constraints. For such systems, we assume that the model is not known exactly. More precisely, the entries of the matrix representing the system structure may be affine functions of some uncertain time-varying parameters that take values within assigned bounds. We give stabilizability conditions that can be checked, in principle, by solving a min-max problem on the surface of the state-space (buffer level space) unit ball. Then, we consider a special case in which each uncertain parameter affects a single column of the system matrix and is independent of all the other ones. In this case, we propose a mixed int…

Unit sphereMathematical optimizationMatrix (mathematics)Linear programmingControl and Systems EngineeringStochastic processMultiplicative functionAffine transformationElectrical and Electronic EngineeringSpecial caseInteger programmingComputer Science ApplicationsMathematics
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THE CARMA INTEREST RATE MODEL

2014

In this paper, we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This model is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provides closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.

Vasicek modelBond optionInterest rate model short rate forward rate term structure CARMA process bond pricing bond option pricing yield curve volatility curve calibrationImplied volatilityBond valuationShort-rate modelForward rateShort rateForward volatilityEconometricsEconomicsLIBOR market modelYield curveVolatility (finance)General Economics Econometrics and FinanceFinanceAffine term structure modelRendleman–Bartter modelMathematicsInternational Journal of Theoretical and Applied Finance
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Spatial correction in dynamic photon emission by affine transformation matrix estimation

2014

International audience; Photon emission microscopy and Time Resolved Imaging have proved their efficiency for defect localization on VLSI. A common process to find defect candidate locations is to draw a comparison between acquisitions on a normally working device and a faulty one. In order to be accurate and meaningful, this method requires that the acquisition scene remains the same between the two parts. In practice, it can be difficult to set. In this paper, a method to correct position by affine matrix transformation is suggested. It is based on image features detection, description and matching and affine transformation estimation.

[ INFO.INFO-TS ] Computer Science [cs]/Signal and Image ProcessingMatching (graph theory)Computer science[INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing[SPI.NANO] Engineering Sciences [physics]/Micro and nanotechnologies/Microelectronics02 engineering and technology[ SPI.SIGNAL ] Engineering Sciences [physics]/Signal and Image processing[INFO.INFO-TS]Computer Science [cs]/Signal and Image ProcessingPosition (vector)020204 information systems0202 electrical engineering electronic engineering information engineeringComputer vision[SPI.NANO]Engineering Sciences [physics]/Micro and nanotechnologies/Microelectronics[SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processingVery-large-scale integrationHarris affine region detectorbusiness.industryProcess (computing)Affine shape adaptationTransformation (function)020201 artificial intelligence & image processing[ SPI.NANO ] Engineering Sciences [physics]/Micro and nanotechnologies/MicroelectronicsArtificial intelligenceAffine transformationbusiness[SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
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Categorical action of the extended braid group of affine type $A$

2017

Using a quiver algebra of a cyclic quiver, we construct a faithful categorical action of the extended braid group of affine type A on its bounded homotopy category of finitely generated projective modules. The algebra is trigraded and we identify the trigraded dimensions of the space of morphisms of this category with intersection numbers coming from the topological origin of the group.

[ MATH ] Mathematics [math]Pure mathematicsGeneral MathematicsCategorificationBraid groupGeometric intersection01 natural sciencesMathematics - Geometric TopologyMorphismMathematics::Category TheoryQuiverMathematics - Quantum Algebra0103 physical sciencesFOS: MathematicsQuantum Algebra (math.QA)Representation Theory (math.RT)0101 mathematics[MATH]Mathematics [math]MathematicsHomotopy categoryGroup (mathematics)Applied Mathematics010102 general mathematicsQuiverBraid groupsGeometric Topology (math.GT)16. Peace & justiceCategorificationCategorical actionBounded functionMSC: 20F36 18E30 57M99 13D99010307 mathematical physicsAffine transformationMathematics - Representation Theory
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Asymptotics of accessibility sets along an abnormal trajectory

2001

We describe precisely, under generic conditions, the contact of the accessibility set at time $T$ with an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-Riemannian system of rank 2. As a consequence we obtain in sub-Riemannian geometry a new splitting-up of the sphere near an abnormal minimizer $\gamma$ into two sectors, bordered by the first Pontryagin's cone along $\gamma$, called the $\xLinfty$-sector and the $\xLtwo$-sector. Moreover we find again necessary and sufficient conditions of optimality of an abnormal trajectory for such systems, for any optimization problem.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyControl and OptimizationOptimization problemRank (linear algebra)02 engineering and technologycontrol-affine systems01 natural sciencesSet (abstract data type)020901 industrial engineering & automationFOS: Mathematicssingular trajectories0101 mathematicsMathematics - Optimization and ControlMathematics010102 general mathematicsMathematical analysisConstraint (information theory)Computational MathematicsCone (topology)Optimization and Control (math.OC)Control and Systems EngineeringControl systemTrajectoryAffine transformation[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
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