While parietal cortex is thought to be critical for representing numerical magnitudes, we recently reported an event-related potential (ERP) study demonstrating selective neural sensitivity to numerosity over midline occipital sites very early in the time course, suggesting the involvement of early visual cortex in numerosity processing. However, which specific brain area underlies such early a...

In this paper, we investigate two numerical methods for pricing Asian options: Laplace transform inversion and Monte Carlo simulation. In attempting to numerically invert the Laplace transform of the Asian call option that has been derived previously in the literature, we point out some of the potential difficulties inherent in this approach. We investigate the effectiveness of two easy-to-impl...

Two depth inversion algorithms applicable to coastal waters are developed, calibrated, and validated based on results of computations of periodic waves shoaling over mild slopes, in a two-dimensional numerical wave tank based on fully nonlinear potential flow theory. In actual field situations, these algorithms would be used to predict the cross-shore depth variation h based on sets of values o...

We present a study of the numerical solution of the two dimensional electrical impedance tomography problem, with noisy measurements of the Dirichlet to Neumann map. The inversion uses parametrizations of the conductivity on optimal grids. The grids are optimal in the sense that finite volume discretizations on them give spectrally accurate approximations of the Dirichlet to Neumann map. The ap...

In this paper, we introduce artificial boundary conditions for the linearized Green-Naghdi system of equations. The derivation of such continuous (respectively discrete) boundary conditions include the inversion of Laplace transform (respectively Z-transform) and these boundary conditions are in turn non local in time. In the case of continuous boundary conditions, the inversion is done explici...

One important parameter for an ultrasonic transducer is the echo it yields from a pointlike reflector. It can be measured directly but there are however certain problems connected with this. We propose an alternative method to calculate the echo from a pointlike reflector by measuring the echoes from sliding halfplanes. Using a tomographic way of reasoning, we can calculate the point echoes fro...

With the development of computational power, there has been an increased focus on data-fitting related seismic inversion techniques for high fidelity seismic velocity model and image, such as full-waveform inversion and least square migration. However, though more advanced than conventional methods, these data fitting methods can be very expensive in terms of computational cost. Recently, vario...

In this thesis I present a new algorithm OPT for matrix inversion that builds on a matrix multiplication subroutine. It is combined of Strassen’s matrix inversion algorithm and Newton approximation. OPT overcomes the linear lower bound in parallel runtime of Strassen’s inversion algorithm and traditional Gaussian elimination without the log-factor more work of Newton approximation. In particula...