An approach for solving forward and inverse boundary-value problems has been proposed using symbolic computation. Finite element or boundary element calculation of a given system is performed with the symbolic parameters expressing its shape or material properties. This allows direct sensitivity analysis ...
matlab animate_sph_harm.m -- create animations of spherical harmonics Rscript interp_vs_reg.R -- plot the difference between linear interpolation and regression Rscript plot_nearly-even-spacing.R -- show the result of the linear transport problem on finding nearly-evenly spaced pointsAbout...
MRI improves EEG Forward Problem (FP) and Inverse Problem (IP) compared to three concentric spheres or an Average Head (AH). Acquisition is often impractical. We propose an alternative approach based on a database. Some previous attempts are described in the literature. We solved FP for 305 ...
In order to solve the problem, the semisupervised ELM integrates manifold regularization into ELM to extend ELM to the area of semisupervised learning [6]. Suppose that there are labeled data samples (xi,ti)i=1l,x∈Rd,ti∈Rm and unlabeled samples (xi)i=1u,x∈Rd. The SS-ELM algorithm ...
Let us start by concentrating on the problem of computing data-driven solutions to partial differential equations (i.e., the first problem outlined above) of the general formut+N[u]=0,x∈Ω,t∈[0,T], where u(t,x) denotes the latent (hidden) solution, N[⋅] is a nonlinear differe...
The dependence between the measurements y and the unknown of the inverse problem x in question, e.g., a source localization problem, is here assumed be of the following linear form Lx = y + n, (1) The current FE meshing strategy employed in ZI treats the conductivity as an isotropic ...
Reaching the optimum implies having solved the integration problem and eliminates the need for the Monte Carlo procedure. Satisfaction means that the result can be obtained within an acceptable time, and in practice means finding a compromise between the number of terms needed, and the complexity ...
The mesencephalic locomotor region (MLR) is a brain stem area whose stimulation triggers graded forward locomotion. How MLR neurons recruit downstream vsx2+ (V2a) reticulospinal neurons (RSNs) is poorly understood. Here, to overcome this challenge, we un
To overcome the endogeneity problem, an instrumental variable approach can be used. However, it is often difficult to find reliable instruments, which should be associated with explanatory variables but not with error terms. In the empirical literature, a GMM-based dynamic panel data estimator ...
We consider first the problem of pricing an option where the underlying asset price follows a binomial process in discrete time (Fig. 1(a)). Thus, if the current price of the underlying asset is S, then, at time t+1, the price will take one of two values (in the binomial example ...