Search results for "canonical"

showing 10 items of 221 documents

Fast nosological imaging using canonical correlation analysis of brain data obtained by two-dimensional turbo spectroscopic imaging.

2007

A new fast and accurate tissue typing technique has recently been successfully applied to prostate MR spectroscopic imaging (MRSI) data. This technique is based on canonical correlation analysis (CCA), a statistical method able to simultaneously exploit the spectral and spatial information characterizing the MRSI data. Here, the performance of CCA is further investigated by using brain data obtained by two-dimensional turbo spectroscopic imaging (2DTSI) from patients affected by glioblastoma. The purpose of this study is to investigate the applicability of CCA when typing tissues of heterogeneous tumors. The performance of CCA is also compared with that of ordinary correlation analysis on s…

Diagnostic ImagingMagnetic Resonance SpectroscopyComputer scienceTurboNuclear magnetic resonanceRobustness (computer science)medicineHumansRadiology Nuclear Medicine and imagingComputer SimulationSpatial analysisSpectroscopyTissue segmentationbiologybusiness.industryBrainPattern recognitionbiology.organism_classificationmedicine.diseaseCorrelation analysisMr spectroscopic imagingMolecular MedicineArtificial intelligenceCanonical correlationbusinessGlioblastomaGlioblastomaNMR in biomedicine
researchProduct

The overlap algebra of regular opens

2010

Abstract Overlap algebras are complete lattices enriched with an extra primitive relation, called “overlap”. The new notion of overlap relation satisfies a set of axioms intended to capture, in a positive way, the properties which hold for two elements with non-zero infimum. For each set, its powerset is an example of overlap algebra where two subsets overlap each other when their intersection is inhabited. Moreover, atomic overlap algebras are naturally isomorphic to the powerset of the set of their atoms. Overlap algebras can be seen as particular open (or overt) locales and, from a classical point of view, they essentially coincide with complete Boolean algebras. Contrary to the latter, …

Discrete mathematicsAlgebra and Number Theoryoverlap algebrasNon-associative algebraBoolean algebras canonically definedComplete Boolean algebraconstructive topologyAlgebraQuadratic algebraInterior algebraComplete latticeHeyting algebraNest algebraconstructive topology; overlap algebrasMathematics
researchProduct

A decidable word problem without equivalent canonical term rewriting system

1989

We present a weak associative single-axiom system having the following property: the word problem is decidable with an efficient algorithm even though there does not exist any finite equivalent canonical term rewriting system.

Discrete mathematicsApplied MathematicsPost canonical systemComputer Science ApplicationsDecidabilityPhilosophy of languageComputational Theory and MathematicsConfluenceComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONWord problem (mathematics)RewritingEquivalence (formal languages)Computer Science::Formal Languages and Automata TheoryAssociative propertyMathematicsInternational Journal of Computer Mathematics
researchProduct

Unitary Groups Acting on Grassmannians Associated with a Quadratic Extension of Fields

2006

Let (V, H) be an anisotropic Hermitian space of finite dimension over the algebraic closure of a real closed field K. We determine the orbits of the group of isometries of (V, H) in the set of K-subspaces of V . Throughout the paper K denotes a real closed field and K its algebraic closure. Then it is well known (see, for example, [4, Chapter 2], [23]; see also [8]) that K = K(i) with i = √−1. Also we let (V,H) be an anisotropic Hermitian space (with respect to the involution underlying the quadratic field extension K/K) of finite dimension n over K. In this context we consider the natural action of the unitary group U = U(V,H) of isometries of (V,H) on the set Xd of all ddimensional K-subs…

Discrete mathematicsClassical groupPure mathematicsDouble cosetProjective unitary groupGeneral Mathematics15A21Unitary matrixSettore MAT/04 - Matematiche ComplementariAlgebraic closure11E39Unitary group51N30Quadratic fieldGeometry of classical groups Canonical forms reductions classificationSpecial unitary groupMathematicsRocky Mountain Journal of Mathematics
researchProduct

On Rough Sets in Topological Boolean Algebras

1994

We have focused on rough sets in topological Boolean algebras. Our main ideas on rough sets are taken from concepts of Pawlak [4] and certain generalizations of his constructions which were offered by Wiweger [7]. One of the most important results of this note is a characterization of the rough sets determined by regular open and regular closed elements.

Discrete mathematicsInterior algebraRough setField of setsBoolean algebras canonically definedCharacterization (mathematics)Stone's representation theorem for Boolean algebrasTopologyComplete Boolean algebraMathematics
researchProduct

The structure of the state representation of shift invariant controllable and observable group codes

2000

AbstractIn this paper an investigation on the structure of the canonical trellis section of shift invariant, l-controllable and m-observable group codes is carried out. Necessary and sufficient conditions for a set of group homomorphisms in order that they represent the trellis section of this class of codes are established.

Discrete mathematicsNumerical AnalysisAlgebra and Number TheoryObservableCanonical representationsBehavioral analysisGroup codeGroup codesDiscrete Mathematics and CombinatoricsHomomorphismCanonical formGeometry and TopologyInvariant (mathematics)Behavioral approachState representationComputer Science::Information TheoryMathematics
researchProduct

The Action of the Symplectic Group Associated with a Quadratic Extension of Fields

1999

Abstract Given a quadratic extension L/K of fields and a regular alternating space (V, f) of finite dimension over L, we classify K-subspaces of V which do not split into the orthogonal sum of two proper K-subspaces. This allows one to determine the orbits of the group SpL(V, f) in the set of K-subspaces of V.

Discrete mathematicsPure mathematicsSymplectic groupAlgebra and Number TheoryGroup (mathematics)Symplectic representationSymplectic vector spaceQuadratic equationDimension (vector space)Metaplectic groupSettore MAT/03 - GeometriaMoment mapMathematicsGeometry of classical groups Canonical forms reduction classificationJournal of Algebra
researchProduct

The cup product of Hilbert schemes for K3 surfaces

2003

To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A [n] so that there is canonical isomorphism of rings (H *(X;ℚ)[2]) [n] ≅H *(X [n] ;ℚ)[2n] for the Hilbert scheme X [n] of generalised n-tuples of any smooth projective surface X with numerically trivial canonical bundle.

Discrete mathematicsSurface (mathematics)Hilbert series and Hilbert polynomialSequencePure mathematicsMathematics::Commutative AlgebraGeneral Mathematics010102 general mathematics01 natural sciencesCanonical bundlesymbols.namesakeHilbert schemeCup product0103 physical sciencesFrobenius algebrasymbols[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]010307 mathematical physicsIsomorphism0101 mathematicsComputingMilieux_MISCELLANEOUSMathematicsInventiones Mathematicae
researchProduct

The Hamilton–Jacobi Equation

2001

We already know that canonical transformations are useful for solving mechanical problems. We now want to look for a canonical transformation that transforms the 2N coordinates (q i , p i ) to 2N constant values (Q i , P i ), e.g., to the 2N initial values \((q_{i}^{0},p_{i}^{0})\) at time t = 0. Then the problem would be solved, q = q(q0, p0, t), p = p(q0, p0, t).

Dispersionless equationCombinatoricsPhysicsOmega equationCharacteristic equationCanonical transformationSummation equationCahn–Hilliard equationKadomtsev–Petviashvili equationHamilton–Jacobi equation
researchProduct

Online Detection and Removal of Eye Blink Artifacts from Electroencephalogram

2020

The most prominent type of artifact contaminating electroencephalogram (EEG)signals are the eyeblink (EB) artifacts, which could potentially lead tomisinterpretation of the EEG signal. Online detection and removal of eyeblink artifacts from EEG signals are essential in applications such a Brain-Computer Interfaces (BCI), neurofeedback and epilepsy diagnosis. In this thesis, algorithms that combine unsupervised eyeblink artifact detection (eADA) with enhanced Empirical Mode Decomposition (FastEMD) and Canonical Correlation Analysis (CCA) are proposed,i.e. FastEMD-CCA2 and FastCCA, to automatically identify eyeblink artifacts andremove them in an online setting. FastEMD-CCA2 and FastCCA have …

ElectroencephalogramDécomposition modale empirique[INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV]Canonical Correlation AnalysisÉlectroencéphalogrammeClignement de l'œilEmpirical Mode DecompositionEyeblink ArtifactsAnalyse par corrélation canonique
researchProduct