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Research talks;Computer Science;Numerical Analysis and Scientific Computing
Classical invariant theory has essentially addressed the action of the general linear group on homogeneous polynomials. Yet the orthogonal group arises in applications as the relevant group of transformations, especially in 3 dimensional space. Having a complete set of invariants for its action on ternary quartics, i.e. degree 4 homogeneous polynomials in 3 variables, is, for instance, relevant in determining biomarkers for white matter from diffusion MRI.
We characterize a generating set of rational invariants of the orthogonal group acting on even degree forms by their restriction on a slice. These restrictions are invariant under the octahedral group and their explicit formulae are given compactly in terms of equivariant maps. The invariants of the orthogonal group can then be obtained in an explicit way, but their numerical evaluation can be achieved more robustly using their restrictions. The exhibited set of generators futhermore allows us to solve the inverse problem and the rewriting.
Central in obtaining the invariants for higher degree forms is the preliminary construction, with explicit formulae, for a basis of harmonic polynomials with octahedral symmetry, dif- ferent, though related, to cubic harmonics.
This is joint work with Paul Görlach (now at MPI Leipzig), in a joint project with Téo Papadopoulo (Inria Méditerranée).
Classical invariant theory has essentially addressed the action of the general linear group on homogeneous polynomials. Yet the orthogonal group arises in applications as the relevant group of transformations, especially in 3 dimensional space. Having a complete set of invariants for its action on ternary quartics, i.e. degree 4 homogeneous polynomials in 3 variables, is, for instance, relevant in determining biomarkers for white matter from ...
05E05 ; 13A50 ; 13P10 ; 68W30 ; 92C55
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Research talks;Numerical Analysis and Scientific Computing;Partial Differential Equations
We consider photoacoustic tomography in the presence of approximation and modelling errors. The inverse problem, i.e. estimation of the initial pressure from photoacoustic time-series measured on the boundary of the target, is approached in the framework of Bayesian inverse problems. The posterior distribution is examined in situations in which the forward model contains errors or uncertainties for example due to numerical approximations or uncertainties in the acoustic parameters. Modelling of these errors and its impact on the posterior distribution are investigated.
This is joint work with Teemu Sahlstrm, Jenni Tick and Aki Pulkkinen.
We consider photoacoustic tomography in the presence of approximation and modelling errors. The inverse problem, i.e. estimation of the initial pressure from photoacoustic time-series measured on the boundary of the target, is approached in the framework of Bayesian inverse problems. The posterior distribution is examined in situations in which the forward model contains errors or uncertainties for example due to numerical approximations or ...
35R30 ; 35Q60 ; 65R32 ; 65C20 ; 92C55
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- viii; 198 p.
ISBN 978-1-4614-4132-8
Fields institute communications , 0063
Localisation : Collection 1er étage
optimisation # informatique biomédicale # imagerie biomédicale # programmation
92-06 ; 92C55 ; 62P10 ; 68U99 ; 90C90 ; 00B25
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- 196 p.
ISBN 978-83-86806-33-1
Banach center publications , 0109
Localisation : Salle des périodiques 1er étage
fractale # histologie # science biomédicale # courbe de Lissajous # théorie quantique # biométrie # mécanique statistique
00B25 ; 28-06 ; 28A80 ; 92-06 ; 92C55 ; 11-06 ; 81-06
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- xv, 228 p.
ISBN 978-3-642-03443-5
Lecture notes in mathematics , 1983
Localisation : Collection 1er étage
tomographie # biologie # application médicale # modèlisation mathématique # imagerie médicale
92C55 ; 31A25 ; 31A10 ; 35B25 ; 35J55 ; 35J65 ; 34A55
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- 192 p.
ISBN 978-3-540-78545-3
Lecture notes in mathematics , 1943
Localisation : Collection 1er étage
équation intégrale # problème inverse # transformation intégrale # transformation de radon # traitement du signal # transfert radiatif # image biomédicale # équation pour la mécanique quantique
65R32 ; 44A12 ; 92C55 ; 85A25 ; 35Q40
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- 158 p.
ISBN 978-0-8218-3930-0
Proceedings of symposia in applied mathematics , 0063
Localisation : Collection 1er étage
transformation de Radon # problème inverse # tomogrpahie # imagerie médicale # transformation intégrale # échantillonage # ondelette
44-06 ; 44A12 ; 65-06 ; 92-06 ; 92C55 ; 65R32 ; 65R10 ; 94A20 ; 42C40
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- 381 p.
ISBN 978-0-8218-3755-9
Contemporary mathematics , 0405
Localisation : Collection 1er étage
géométrie intégrale # tomographie # transformation aléatoire # imagerie biomédicale # EDP # équation d'onde # problème inverse # intégrale singulière # ondelette # analyse sur des espaces homogènes
44A12 ; 92C55 ; 35B05 ; 35L05 ; 35R30 ; 42B20 ; 42C40 ; 43A85 ; 94C12
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- 162 p.
ISBN 978-0-8176-4358-4
Progress in mathematics , 0238
Localisation : Collection 1er étage
analyse harmonique # traitement du signal # complexité calculatoire # problème de Cauchy #idéal arithmétique # idéal analytique # EDP # opérateur d'Hermite # groupe d'Heisenberg # fonction subharmonique # structure discrète # variété hyperbolique # condition de Phragmen-Lindelöf # déconvolation locale # projection orthogonale # espace hyperbolique # ondelette
05C05 ; 05C50 ; 31C20 ; 32A26 ; 32A50 ; 35C15 ; 35N05 ; 35R30 ; 42A85 ; 42B10 ; 42B35 ; 43A85 ; 44A12 ; 46F12 ; 65R30 ; 92C55 ; 94A12
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- 261 p.
ISBN 978-0-8218-2135-0
Contemporary mathematics , 0278
Localisation : Collection 1er étage
transformation intégrale # analyse numérique # tranformation de Radon # tomographie # application # imagerie médicale # traitement du signal # ondelette # problème inverse # analyse microlocale # twisteur # groupe de Lie # analyse harmonique # théorie de la distribution # problème de Pompeiu
44A12 ; 92C55 ; 92F05 ; 35R30 ; 65T60
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- 219 p.
ISBN 978-0-8218-2096-4
DIMACS series in discrete mathematics and theoretical computer science , 0055
Localisation : Collection 1er étage
mathématiques appliquées # médecine # informatique # biomathématique # combinatoire # optimisation combinatoire # application médicale # imagerie médicale # traitement du signal
92-06 ; 05-06 ; 90C27 ; 92C50 ; 92C55
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Localisation : Colloque 1er étage (MARS)
imagerie médicale # imagerie par résonnance magnétique fonctionnelle # mathématique appliquée # méthode de Monte-Carlo appliquée # statistique appliquée
62-99 ; 92C50 ; 92C55
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ISBN 978-1-57146-008-0
Conference proceedings and lecture notes in mathematical physics , 0004
Localisation : Colloque 1er étage (VIEN)
Radon # a plusieurs variables # biographie # espace symétrique # groupe de Lie # géométrie différentielle # théorie de la diffusion # tomographie # transformée de Fourier # transformée de Radon
44A12 ; 53C35 ; 57T15 ; 81Uxx ; 92C55
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- 297 p.
ISBN 978-0-8218-0337-0
Lectures in applied mathematics , 0030
Localisation : Collection 1er étage
déficit Wilmore de surface convexe # géométrie intégrale # image d'impédance # méthode de propagation arrière en acoustique inverse # perturbation de Laplacien # problème inverse # tomographie diffuse de dimension 3 # tomographie à rayon X 3D # tomographie à émission de position # transformée de Radon horocyclique # équation différentielle
35R30 ; 42A12 ; 92C55
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Research talks;Mathematical Physics;Mathematics in Science and Technology;Numerical Analysis and Scientific Computing
The heart undergoes some highly complex multi-scale multi-physics phenomena that must be accounted for in order to adequately model the biomechanical behavior of the complete organ. In this respect, a major focus of our work has been on formulating modeling ingredients that satisfy the most crucial thermomechanical requirements - in particular as regards energy balances - throughout the various forms of physical and scale-related couplings. This has led to a "beating heart" model for which some experimental and clinical validations have already been obtained. Concurrently, with the objective of building "patient-specific" heart models, we have investigated some original approaches inspired from data assimilation concepts to benefit from the available clinical data, with a particular concern for medical imaging. By combining the two fundamental sources of information represented by the model and the data, we are able to extract some most valuable quantitative knowledge on a given heart, e.g. as regards some uncertain constitutive parameter values characterizing a possible pathology, with important perspectives in diagnosis assistance. In addition, once the overall uncertainty has been adequately controlled via this adjustment process, the model can be expected to become "predictive", hence should provide clinically-relevant quantitative information, both in the current state of the patient and under various scenarii of future evolutions, such as for therapy planning.
The heart undergoes some highly complex multi-scale multi-physics phenomena that must be accounted for in order to adequately model the biomechanical behavior of the complete organ. In this respect, a major focus of our work has been on formulating modeling ingredients that satisfy the most crucial thermomechanical requirements - in particular as regards energy balances - throughout the various forms of physical and scale-related couplings. This ...
92C10 ; 92C55 ; 74H15
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Special events;30 Years of Wavelets;Mathematical Physics;Mathematics in Science and Technology
Breast cancer is the most common type of cancer among women and despite recent advances in the medical field, there are still some inherent limitations in the currently used screening techniques. The radiological interpretation of X-ray mammograms often leads to over-diagnosis and, as a consequence, to unnecessary traumatic and painful biopsies. First we use the 1D Wavelet Transform Modulus Maxima (WTMM) method to reveal changes in skin temperature dynamics of women breasts with and without malignant tumor. We show that the statistics of temperature temporal fluctuations about the cardiogenic and vasomotor perfusion oscillations do not change across time-scales for cancerous breasts as the signature of homogeneous monofractal fluctuations. This contrasts with the continuous change of temperature fluctuation statistics observed for healthy breasts as the hallmark of complex multifractal scaling. When using the 2D WTMM method to analyze the roughness fluctuations of X-ray mammograms, we reveal some drastic loss of roughness spatial correlations that likely results from some deep architectural change in the microenvironment of a breast tumor. This local breast disorganisation may deeply affect heat transfer and related thermomechanics in the breast tissue and in turn explain the loss of multifractal complexity of temperature temporal fluctuations previously observed in mammary glands with malignant tumor. These promising findings could lead to the future use of combined wavelet-based multifractal processing of dynamic IR thermograms and X-ray mammograms to help identifying women with high risk of breast cancer prior to more traumatic examinations. Besides potential clinical impact, these results shed a new light on physiological changes that may precede anatomical alterations in breast cancer development.
Keywords: breast cancer - X-ray mammography - infrared thermography - multifractal analysis - wavelet transform - wavelet transform modulus maxima method
Breast cancer is the most common type of cancer among women and despite recent advances in the medical field, there are still some inherent limitations in the currently used screening techniques. The radiological interpretation of X-ray mammograms often leads to over-diagnosis and, as a consequence, to unnecessary traumatic and painful biopsies. First we use the 1D Wavelet Transform Modulus Maxima (WTMM) method to reveal changes in skin ...
92-08 ; 92C50 ; 92C55
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Research talks;Partial Differential Equations;Mathematics in Science and Technology
Multiwave aspects of thermoacoustic imaging and range verification during particle therapy will be discussed.
Thermoacoustic images are generated from acoustic pulses induced by heating due to lossy electromagnetic wave propagation. Quantitative thermoacoustic imaging is feasible when the electric field pattern can be accurately modeled throughout the imaging field of view and delivered quickly enough to ensure stress confinement.
Therapeutic ions slow from relativistic speeds to a dead stop within nanoseconds, generating extraordinarily high temperature and pressure spikes within a thermal core of nanometer diameter along their tracks.
Possibilities for utilizing these phenomena to verify the ion beam location within the patient will be considered.
Multiwave aspects of thermoacoustic imaging and range verification during particle therapy will be discussed.
Thermoacoustic images are generated from acoustic pulses induced by heating due to lossy electromagnetic wave propagation. Quantitative thermoacoustic imaging is feasible when the electric field pattern can be accurately modeled throughout the imaging field of view and delivered quickly enough to ensure stress confinement.
Therapeutic ...
35L05 ; 35R30 ; 92C55 ; 92C50
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