Numerical solution of two delays Volterra Integral Equations is considered and the stability is studied on a nonlinear test equation
by carrying out a parallel investigation both on the continuous and the discrete problem.
Direct Quadrature methods
Double delays
Stability;
Volterra Integral Equations
Fusing in vivo and ex vivo NMR sources of information for brain tumor classification
CroitorSava A R
;
MartinezBisbal MC
;
Laudadio T
;
Piquer J
;
Celda B
;
Heerschap A
;
Sima DM
;
Van Huffel S
In this study we classify short echo-time brain magnetic resonance spectroscopic imaging (MRSI) data by applying a model-based canonical correlation analyses algorithm and by using, as prior knowledge, multimodal sources of information coming from high-resolution magic angle spinning (HR-MAS), MRSI and magnetic resonance imaging. The potential and limitations of fusing in vivo and ex vivo nuclear magnetic resonance sources to detect brain tumors is investigated. We present various modalities for multimodal data fusion, study the effect and the impact of using multimodal information for classifying MRSI brain glial tumors data and analyze which parameters influence the classification results by means of extensive simulation and in vivo studies. Special attention is drawn to the possibility of considering HR-MAS data as a complementary dataset when dealing with a lack of MRSI data needed to build a classifier. Results show that HR-MAS information can have added value in the process of classifying MRSI data.
Canonical Correlation Analysis
Multimodal data fusion
brain tumor
classification
High Resolution Magic Angle Spinning
Lattice Boltzmann Methods for Multiphase Flow Simulations across Scales
Falcucci Giacomo
;
Ubertini Stefano
;
Biscarini Chiara
;
Di Francesco Silvia
;
Chiappini Daniele
;
Palpacelli Silvia
;
De Maio Alessandro
;
Succi Sauro
The simulation of multiphase flows is an outstanding challenge, due to the inherent complexity of the underlying physical phenomena and to the fact that multiphase flows are very diverse in nature, and so are the laws governing their dynamics. In the last two decades, a new class of mesoscopic methods, based on minimal lattice formulation of Boltzmann kinetic equation, has gained significant interest as an efficient alternative to continuum methods based on the discretisation of the NS equations for non ideal fluids. In this paper, three different multiphase models based on the lattice Boltzmann method (LBM) are discussed, in order to assess the capability of the method to deal with multiphase flows on a wide spectrum of operating conditions and multiphase phenomena. In particular, the range of application of each method is highlighted and its effectiveness is qualitatively assessed through comparison with numerical and experimental literature data.
Bartlett's decomposition provides the distributional properties of the elements of the Cholesky factor of $A=G^TG$ where the elements of $G$ are i.i.d. standard Gaussian random variables.
In this paper the most general case where the elements of $G$ have a joint multivariate Gaussian density is considered.
