74,256 research outputs found
Efficient schemes on solving fractional integro-differential equations
Fractional integro-differential equation (FIDE) emerges in various modelling of
physical phenomena. In most cases, finding the exact analytical solution for FIDE is
difficult or not possible. Hence, the methods producing highly accurate numerical
solution in efficient ways are often sought after. This research has designed some
methods to find the approximate solution of FIDE. The analytical expression of
Genocchi polynomial operational matrix for left-sided and right-sided Caputo’s
derivative and kernel matrix has been derived. Linear independence of Genocchi
polynomials has been proved by deriving the expression for Genocchi polynomial
Gram determinant. Genocchi polynomial method with collocation has been
introduced and applied in solving both linear and system of linear FIDE. The
numerical results of solving linear FIDE by Genocchi polynomial are compared with
certain existing methods. The analytical expression of Bernoulli polynomial
operational matrix of right-sided Caputo’s fractional derivative and the Bernoulli
expansion coefficient for a two-variable function is derived. Linear FIDE with mixed
left and right-sided Caputo’s derivative is first considered and solved by applying the
Bernoulli polynomial with spectral-tau method. Numerical results obtained show that
the method proposed achieves very high accuracy. The upper bounds for th
Generalizing GAMETH: Inference rule procedure..
In this paper we present a generalisation of GAMETH framework, that play an important role in identifying crucial knowledge. Thus, we have developed a method based on three phases. In the first phase, we have used GAMETH to identify the set of “reference knowledge”. During the second phase, decision rules are inferred, through rough sets theory, from decision assignments provided by the decision maker(s). In the third phase, a multicriteria classification of “potential crucial knowledge” is performed on the basis of the decision rules that have been collectively identified by the decision maker(s).Knowledge Management; Knowledge Capitalizing; Managing knowledge; crucial knowledge;
FEATURE SELECTION APPLIED TO THE TIME-FREQUENCY REPRESENTATION OF MUSCLE NEAR-INFRARED SPECTROSCOPY (NIRS) SIGNALS: CHARACTERIZATION OF DIABETIC OXYGENATION PATTERNS
Diabetic patients might present peripheral microcirculation impairment and might benefit from physical training. Thirty-nine diabetic patients underwent the monitoring of the tibialis anterior muscle oxygenation during a series of voluntary ankle flexo-extensions by near-infrared spectroscopy (NIRS). NIRS signals were acquired before and after training protocols. Sixteen control subjects were tested with the same protocol. Time-frequency distributions of the Cohen's class were used to process the NIRS signals relative to the concentration changes of oxygenated and reduced hemoglobin. A total of 24 variables were measured for each subject and the most discriminative were selected by using four feature selection algorithms: QuickReduct, Genetic Rough-Set Attribute Reduction, Ant Rough-Set Attribute Reduction, and traditional ANOVA. Artificial neural networks were used to validate the discriminative power of the selected features. Results showed that different algorithms extracted different sets of variables, but all the combinations were discriminative. The best classification accuracy was about 70%. The oxygenation variables were selected when comparing controls to diabetic patients or diabetic patients before and after training. This preliminary study showed the importance of feature selection techniques in NIRS assessment of diabetic peripheral vascular impairmen
Application of a nudging technique to thermoacoustic tomography
ThermoAcoustic Tomography (TAT) is a promising, non invasive, medical imaging
technique whose inverse problem can be formulated as an initial condition
reconstruction. In this paper, we introduce a new algorithm originally designed
to correct the state of an evolution model, the \emph{back and forth nudging}
(BFN), for the TAT inverse problem. We show that the flexibility of this
algorithm enables to consider a quite general framework for TAT. The backward
nudging algorithm is studied and a proof of the geometrical convergence rate of
the BFN is given. A method based on Conjugate Gradient (CG) is also introduced.
Finally, numerical experiments validate the theoretical results with a better
BFN convergence rate for more realistic setups and a comparison is established
between BFN, CG and a usual inversion method.Comment: Preprint version of the articl
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