We propose a Standing Wave Decomposition (SWD) approximation to Gaussian Process regression (GP). GP involves a costly matrix inversion operation, which limits applicability to large data analysis. For an input space that can be approximated by a grid and when correlations among data are short-ranged, the kernel matrix inversion can be replaced by analytic diagonalization using the SWD. We show...

We investigate the properties of block matrices with block banded inverses to derive efficient matrix inversion algorithms for such matrices. In particular, we derive the following: (1) a recursive algorithm to invert a full matrix whose inverse is structured as a block tridiagonal matrix; (2) a recursive algorithm to compute the inverse of a structured block tridiagonal matrix. These algorithm...

This paper proposes an alternative approach to the output leastsquares (OLS) seismic inversion for layered-media. The latter cannot guarantee a reliable solution for either synthetic or field data, because of the existence of many spurious local minima of the objective function for typical data, which lack low-frequency energy. To recover the low-frequency lacuna of typical data, we formulate w...

Packet switching networks lead mostly to M/GI/1 queue models. In this paper, computing methods are designed in order to get quickly approximate values for response time of these networks. Laplace transform is a powerful tool to study such queuing systems. But inversion of the Laplace transform on the real line is well known to be an illconditioned problem and usual numerical methods of inversio...

Reliability function is defined under suitable assumptions for dynamic stressstrength scenarios where strength degrades and stress accumulates over time. Methods for numerical evaluation of reliability are suggested under deterministic strength degradation and cumulative damage due to shocks arriving according to a Poisson process using simulation method and inversion theorem. These methods are...

A convolutional two-level hidden Markov model is defined and evaluated. The bottom level contains an unobserved categorical Markov chain, and given the variables in this level the middle level contains unobserved conditionally independent Gaussian variables. The top level contains observable variables that are a convolution of the variables in the middle level plus additive Gaussian errors. The...

helicopter-borne electromagnetic (hem) is a fast and high resolution airborne electromagnetic (aem) method that is frequently used for imaging of the subsurface resistivity structures. this is a versatile and cost effective method, frequently has used in mineral and groundwater exploration and various environmental problems. modern frequency-domain hem systems utilize small electromagnetic, mag...

We study spatial symmetry in general ABA-stacked multilayer graphene to illustrate how electronic spectra at the two valleys are related in a magnetic field. We show that the lattice of multilayers with an even number of layers as well as that of monolayer graphene satisfy spatial inversion symmetry, which rigorously guarantees valley degeneracy in the absence of time-reversal symmetry. A multi...

A new method is presented for tomographic reconstruction of objects with homogeneous attenuation. The method is based on parametric representation with Non-Uniform Rational B-Splines (NURBS) and statistical inversion with a Markov Chain Monte Carlo (MCMC) algorithm. The method recovers the approximate boundary curve shape and the attenuation value of two-dimensional homogeneous objects. The bou...

In order to determine the conductivity of a body or of a region of the Earth using electrical prospecting, currents are injected on the surface, surface voltage responses are measured, and the data are inverted to a conductivity distribution. In the present paper a new approach to the inverse problem is considered for measurements containing noise in which data are optimally chosen using availa...