Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Statistics for Spatial Data.

Large linear systems of saddle point type arise in a wide variety of applications throughout computational science and engineering. Due to their indefiniteness and often poor spectral properties, such linear systems represent a significant challenge for solver developers. In recent years there has been a surge of interest in saddle point problems, and numerous solution techniques have been proposed for this type of system. The aim of this paper is to present and discuss a large selection of solution methods for linear systems in saddle point form, with an emphasis on iterative methods for large and sparse problems.

/pdf/numerical-solution-of-saddle-point-problems-l583iob5c2.pdf

Numerical solution of saddle point problems

Statistics For Spatial Data

Geotechnical variability is a complex attribute that results from many disparate sources of uncertainties. The three primary sources of geotechnical uncertainties are inherent variability, measurem...

Characterization of geotechnical variability

SUMMARY

The finite element (FE) simulation of large-scale soil–structure interaction problems (e.g. piled-raft, tunnelling, and excavation) typically involves structural and geomaterials with significant differences in stiffness and permeability. The symmetric quasi-minimal residual solver coupled with recently developed generalized Jacobi, modified symmetric successive over-relaxation (MSSOR), or standard incomplete LU factorization (ILU) preconditioners can be ineffective for this class of problems. Inexact block diagonal preconditioners that are inexpensive approximations of the theoretical form are systematically evaluated for mitigating the coupled adverse effects because of such heterogeneous material properties (stiffness and permeability) and because of the percentage of the structural component in the system in piled-raft foundations. Such mitigation led the proposed preconditioners to offer a significant saving in runtime (up to more than 10 times faster) in comparison with generalized Jacobi, modified symmetric successive over-relaxation, and ILU preconditioners in simulating piled-raft foundations. Copyright © 2012 John Wiley & Sons, Ltd.

Effective block diagonal preconditioners for Biot's consolidation equations in piled‐raft foundations

Estimation of horizontal transition probability matrix for coupled Markov chain

The undrained shear strength (su) of a clay is not a constant. In particular, su of a clay evaluated by different test procedures are different because these tests may have different stress states, stress histories, degrees of sampling disturbance, and strain rates. This study summarizes the mean value and variability of the normalized undrained shear strength (su/ ’v) from various test procedures based on a large clay database. These second-moment statistics can be seen as a probabilistic extension of Eq-4.55 developed in Kulhawy & Mayne (1990), which provides an estimation of the normalized undrained shear strength based on three factors accounting for test mode, overconsolidation ratio, and strain rate. The second-moment statistics are essential for reliability analysis and reliability-based design.

Second-Moment Characterization of Undrained Shear Strengths from Different Test Procedures

Finite-element analysis of many soil-structure interaction problems involves material zones of widely differing stiffnesses. The large relative differences in material stiffnesses usually result in an ill-conditioned system for which practical preconditioners become ineffec- tive for the iterative solution of such systems. The study suggests that a block diagonal preconditioner can exploit such differences. However, the theoretical preconditioner is expensive for practical use. Less costly block diagonal preconditioners are numerically evaluated for various inexact forms of the blocks in conjunction with conjugate gradient solver. The study includes analysis of two representative soil-structure in- teraction problems and proposes two simplified block diagonal preconditioners that effectively mitigate such material ill conditionings. DOI: 10.1061/(ASCE)GM.1943-5622.0000197. © 2013 American Society of Civil Engineers. CE Database subject headings: Stiffness; Soil-structure interactions; Preconditions; Blocks; Finite element method; Material stiffness. Author keywords: Stiffness ratio; Soil-structure interaction problem; Block diagonal preconditioner; Preconditioned conjugate gradient.

Inexact Block Diagonal Preconditioners to Mitigate the Effects of Relative Differences in Material Stiffnesses

Prediction of changes in pore-water pressure response due to rainfall events

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