Search results for " basis"

showing 10 items of 224 documents

Numerical Solution of Foodstuff Freezing Problems Using Radial Basis Functions

2013

This work presents a novel numerical approach for the solution of time dependent non-linear freezing processes in terms of radial basis function Hermite approach. The proposed scheme is applied to a mashed potato sample during its freezing; evaluation of time evolution of the temperature profile at the core of the sample is carried out. Food thermal properties are highly dependent on temperature and the mathematical problem becomes highly non-linear and therefore particularly difficult to solve. Incorporating a Kirchhoff transformation significantly reduces the non-linearity. The robustness of the scheme is tested by comparison with experimental results available in literature.

Health (social science)Materials scienceGeneral Computer ScienceGeneral MathematicsGeneral EngineeringThermodynamicsMechanicsEducationHermite functionGeneral EnergyFreezing processeTemperature profileSettore ING-IND/10 - Fisica Tecnica IndustrialeRadial basis functionGeneral Environmental ScienceAdvanced Science Letters
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Integration of functions ranging in complex Riesz space and some applications in harmonic analysis

2015

The theory of Henstock—Kurzweil integral is generalized to the case of functions ranging in complex Riesz space R and defined on any zero-dimensional compact Abelian group. The constructed integral is used to solve the problem of recovering the R-valued coefficients of series in systems of characters of these groups by using generalized Fourier formulas.

Henstock integralSeries (mathematics)Riesz representation theoremRiesz potentialintegral transformGeneral MathematicsMathematical analysisMathematics::Classical Analysis and ODEsHilbert spacegroup characterRiesz spacezero-dimensional compact Abelian groupcharacterHenstock—Kurzweil integralComplex Riesz space character Henstock integral basis integral transform.Riesz transformsymbols.namesakeFourier transformM. Riesz extension theorembasissymbolsMathematics (all)complex Riesz spaceMathematicsMathematical Notes
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ON THE DEFORMATION QUANTIZATION OF AFFINE ALGEBRAIC VARIETIES

2004

We compute an explicit algebraic deformation quantization for an affine Poisson variety described by an ideal in a polynomial ring, and inheriting its Poisson structure from the ambient space.

High Energy Physics - TheoryFunction field of an algebraic varietyMathematics::Commutative AlgebraGeneral MathematicsFOS: Physical sciencesFísicaAlgebraic varietyDimension of an algebraic varietyAlgebraic cycleAlgebraGröbner basisHigh Energy Physics - Theory (hep-th)DEFORMATION QUANTIZATIONMathematics - Quantum AlgebraFOS: MathematicsQuantum Algebra (math.QA)Affine transformationAffine varietyMathematicsSingular point of an algebraic varietyInternational Journal of Mathematics
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Universal formulas for characteristic classes on the Hilbert schemes of points on surfaces

2007

This article can be seen as a sequel to the first author's article ``Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane'', where he calculates the total Chern class of the Hilbert schemes of points on the affine plane by proving a result on the existence of certain universal formulas expressing characteristic classes on the Hilbert schemes in term of Nakajima's creation operators. The purpose of this work is (at least) two-fold. First of all, we clarify the notion of ``universality'' of certain formulas about the cohomology of the Hilbert schemes by defining a universal algebra of creation operators. This helps us to reformulate and extend a lot of the f…

Hilbert manifoldHilbert's basis theoremHilbert matrix01 natural sciencesMathematics - Algebraic Geometrysymbols.namesakeCharacteristic classesPrimary 14C05Secondary 14C170103 physical sciencesFOS: Mathematics[MATH]Mathematics [math]0101 mathematicsAlgebraic Geometry (math.AG)ComputingMilieux_MISCELLANEOUSMathematicsHilbert–Poincaré seriesHilbert's second problemHilbert series and Hilbert polynomialAlgebra and Number Theory010102 general mathematicsHilbert's fourteenth problemUniversal formulasPrimary 14C05; Secondary 14C17Hilbert schemes of pointsAlgebraHilbert schemesymbols[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]010307 mathematical physics
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Rolle's Theorem for Polynomials of Degree Four in a Hilbert Space

2002

AbstractIn an infinite-dimensional real Hilbert space, we introduce a class of fourth-degree polynomials which do not satisfy Rolle's Theorem in the unit ball. Extending what happens in the finite-dimensional case, we show that every fourth-degree polynomial defined by a compact operator satisfies Rolle's Theorem.

Hilbert spacesDiscrete mathematicsHilbert manifoldRolle's theorempolynomialsApplied MathematicsHilbert spaceHilbert's basis theoremCompact operator on Hilbert spacesymbols.namesakeVon Neumann's theoremHilbert schemeRolle's TheoremsymbolsBrouwer fixed-point theoremAnalysisMathematicsJournal of Mathematical Analysis and Applications
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A Novel System for Multi-level Crohn’s Disease Classification and Grading Based on a Multiclass Support Vector Machine

2020

Crohn’s disease (CD) is a chronic inflammatory condition of the gastrointestinal tract that can highly alter patient’s quality of life. Diagnostic imaging, such as Enterography Magnetic Resonance Imaging (E-MRI), provides crucial information for CD activity assessment. Automatic learning methods play a fundamental role in the classification of CD and allow to avoid the long and expensive manual classification process by radiologists. This paper presents a novel classification method that uses a multiclass Support Vector Machine (SVM) based on a Radial Basis Function (RBF) kernel for the grading of CD inflammatory activity. To validate the system, we have used a dataset composed of 800 E-MRI…

Hyperparameterbusiness.industryComputer scienceMulticlass support vector machineBayesian optimizationSupervised learningFeature extractionFeature reductionCrohn’s disease multi-level classification and gradingK-fold cross-validationPattern recognitionSupport vector machineRadial basis function kernelMedical imagingFeature extractionArtificial intelligencebusinessClassifier (UML)Supervised learningBayesian optimization
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Il Paradigma della Città Fluida

2013

Nella recente crisi globale i poderosi flussi di capitali finanziari, sociali e relazionali che hanno alimentato la riqualificazione urbana nel corso degli ultimi quindici anni non sono più disponibili ad essere intercettati in maniera indiscriminata così come è stato possibile fino a qualche anno fa. Nell'era della crisi strutturale le città più dinamiche non sono più quelle in grado di attrarre progetti urbani iconici ed investitori spinti dal mercato immobiliare o dalla redditività delle attività ricreative, ma quelle città che, a partire dalle loro profonde e diversificate risorse culturali, saranno capaci di attuare una vera e propria “metamorfosi” per usarle come base per la creazione…

In current global crisis the strong flows of financial social and relational capitals that powered urban regeneration over the last fifteen years are no longer available to be tapped in an indiscriminate manner as was the case until just a few years ago. The most dynamic cities in the future will no longer be those that are able to attract urban projects and investors driven by the real estate market or leisure-based development but the cities that have deep and different cultural resources and that are able to use them as the basis for creating new urban cultures and for generating new economic values. Revitalising waterfront is no longer easy opportunity for long-term investments or for using the financial capital gains of corporation or hedge funds but a more creative-driven port city has to provide precious opportunities for real development – not only quantitative but more and more qualitative – that is able to produce effects in both the domain of collective assets and that of private capitals.Settore ICAR/21 - Urbanistica
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Learning with the kernel signal to noise ratio

2012

This paper presents the application of the kernel signal to noise ratio (KSNR) in the context of feature extraction to general machine learning and signal processing domains. The proposed approach maximizes the signal variance while minimizes the estimated noise variance in a reproducing kernel Hilbert space (RKHS). The KSNR can be used in any kernel method to deal with correlated (possibly non-Gaussian) noise. We illustrate the method in nonlinear regression examples, dependence estimation and causal inference, nonlinear channel equalization, and nonlinear feature extraction from high-dimensional satellite images. Results show that the proposed KSNR yields more fitted solutions and extract…

Kernel methodSignal-to-noise ratioKernel embedding of distributionsPolynomial kernelbusiness.industryVariable kernel density estimationKernel (statistics)Radial basis function kernelPattern recognitionArtificial intelligencebusinessKernel principal component analysisMathematics2012 IEEE International Workshop on Machine Learning for Signal Processing
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Predicting the structure and vibrational frequencies of ethylene using harmonic and anharmonic approaches at the Kohn–Sham complete basis set limit

2016

In this work, regular convergence patterns of the structural, harmonic, and VPT2-calculated anharmonic vibrational parameters of ethylene towards the Kohn–Sham complete basis set (KS CBS) limit are demonstrated for the first time. The performance of the VPT2 scheme implemented using density functional theory (DFT-BLYP and DFT-B3LYP) in combination with two Pople basis sets (6-311++G** and 6-311++G(3df,2pd)), the polarization-consistent basis sets pc-n, aug-pc-n, and pcseg-n (n = 0, 1, 2, 3, 4), and the correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5, 6) was tested. The BLYP-calculated harmonic frequencies were found to be markedly closer than the B3LYP-calculated h…

Kohn–Sham equationsAnharmonic vibrationPolarization-consistent basis sets010402 general chemistry01 natural sciencesDFTSTO-nG basis setsCatalysisCBSInorganic ChemistryEthyleneQuantum mechanicsCorrelation-consistent basis sets0103 physical sciencesLimit (mathematics)Physical and Theoretical ChemistryVPT2Basis setPhysicsOriginal Paper010304 chemical physicsBasis (linear algebra)AnharmonicityOrganic Chemistry0104 chemical sciencesComputer Science ApplicationsComputational Theory and MathematicsHarmonicDensity functional theoryJournal of Molecular Modeling
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Distributed learning automata for solving a classification task

2016

In this paper, we propose a novel classifier in two-dimensional feature spaces based on the theory of Learning Automata (LA). The essence of our scheme is to search for a separator in the feature space by imposing a LA based random walk in a grid system. To each node in the gird we attach an LA, whose actions are the choice of the edges forming the separator. The walk is self-enclosing, i.e, a new random walk is started whenever the walker returns to starting node forming a closed classification path yielding a many edged polygon. In our approach, the different LA attached at the different nodes search for a polygon that best encircles and separates each class. Based on the obtained polygon…

Learning automataFeature vector020206 networking & telecommunications02 engineering and technologySupport vector machinesymbols.namesakeKernel methodKernel (statistics)PolygonRadial basis function kernel0202 electrical engineering electronic engineering information engineeringGaussian functionsymbols020201 artificial intelligence & image processingAlgorithmMathematics2016 IEEE Congress on Evolutionary Computation (CEC)
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