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This paper presents spatio-temporal modeling and analysis methods to fMRI data. Based on the nonlinear autoregressive with exogenous inputs (NARX) model realized by the Bayesian radial basis function (RBF) neural networks, two methods (NARX-1 and NARX-2) are proposed to capture the unknown complex dynamics of the brain activities. Simulation results on both synthetic and real fMRI data clearly show that the proposed schemes outperform the conventional t-test method in detecting the activated regions of the brain.

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modeling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is finite difference method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of FPDEs.

The linear and nonlinear flexure analysis of laminated plates with twenty theories with the five variable higher order shear deformation theory (HSDT) is investigated using multiquadratic radial basis function based meshfree method. The mathematical formulation of the actual physical problem of the plate subjected to transverse loading is presented utilizing von Karman nonlinear kinematics. These non-linear governing differential equations of equilibrium are linearized using quadratic extrapolation technique. The different results for deflection and stresses are obtained for thin to a thick plate and compared with some published results. It is observed that some of the theories taken here are well suited for analysis of thin as well as a thick plate while some theories are suited only for thin plates.

This paper presents the torsional analysis of isotropic, orthotropic, and functionally graded material (FGM) triangular and rectangular sections. The formulation of the governing equation of the torsion problem is done using the Saint–Venant torsion theory. Classical power law has been considered for the modeling of FGM material. A meshfree technique based on various radial basis functions is used for the solution of the governing differential equation. MATLAB code is developed to solve the discretized partial differential equations. To demonstrate the effectiveness and accuracy of this technique, convergence study and numerical examples are presented by varying the various parameters. The torsional rigidity factors and shear stress factors are obtained for different new conditions. The solution presented here is validated from the analytical and numerical results along with some new results, which shows the satisfactory performance of the present method.

This study proposes a diagnosis system for liver masses based on the improved radial basis function (RBF) neural networks. In this article, RBF networks are improved by sigmoid function and the growing and pruning algorithm. The proposed improved RBF networks adopt the sigmoid function as their kernel due to its increased flexibility over the Gaussian kernel. Furthermore, the growing and pruning algorithm is used to adjust the network size dynamically according to the neuron's significance. This investigation formulates discriminating among cysts, hepatoma, cavernous hemangioma, and normal tissue as a supervised learning problem. The current work calculates several texture and gray-level features derived from regions of interest as input in the proposed classifier. Receiver operating characteristic (ROC) curves evaluate the diagnosis performance, and demonstrate the proposed method's good performance.