XAFS spectroscopy. I. Extracting the fine structure from the absorption spectra

Three independent techniques are used to separate fine structure from the absorption spectra, the background function in which is approximated by (i) smoothing spline. We propose a new reliable criterion for determination of smoothing parameter and the method for raising of stability with respect to k_min variation; (ii) interpolation spline with the varied knots; (iii) the line obtained from bayesian smoothing. This methods considers various prior information and includes a natural way to determine the errors of XAFS extraction. Particular attention has been given to the estimation of uncertainties in XAFS data. Experimental noise is shown to be essentially smaller than the errors of the background approximation, and it is the latter that determines the variances of structural parameters in subsequent fitting.Comment: 16 pages, 7 figures, for freeware XAFS analysis program, see http://www.crosswinds.net/~klmn/viper.htm

PDE Face: A Novel 3D Face Model

YesWe introduce a novel approach to face models, which exploits the use of Partial Differential Equations (PDE) to generate the 3D face. This addresses some common problems of existing face models. The PDE face benefits from seamless merging of surface patches by using only a relatively small number of parameters based on boundary curves. The PDE face also provides users with a great degree of freedom to individualise the 3D face by adjusting a set of facial boundary curves. Furthermore, we introduce a uv-mesh texture mapping method. By associating the texels of the texture map with the vertices of the uv mesh in the PDE face, the new texture mapping method eliminates the 3D-to-2D association routine in texture mapping. Any specific PDE face can be textured without the need for the facial expression in the texture map to match exactly that of the 3D face model

Approximation of CNC part program within a given tolerance band

Freeform surfaces are widely used in various fields of engineering design such as automotive, aerospace and mold and die industries. With the geometric model designed by freeform surfaces in the CAD system, the tool path will be next constructed and sampled by the CAM system according to the predefined chordal deviation. The sequentially sampled short linear blocks are stored in the file called the part program, which is later interpreted by the CNC system to control the machine tool and mill the workpiece. In order to deliver the desired motion smoothly and rapidly, the short linear blocks in the part program will be approximated with smooth spline curves within a specified tolerance band. With spline curves, which consist of longer polynomial pieces, the attainable feed rate of the machine tool can be greatly enhanced. In addition, with minimization of curvature variation, velocity and acceleration jumps in the relevant machine axes and undesired mechanical oscillation of the machine can be reduced significantly. This allows higher traversing speeds and reduces the vibration of the machine, thus improves the surface quality

Functional Regression

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and Silverman called replication and regularization, respectively. This article will focus on functional regression, the area of FDA that has received the most attention in applications and methodological development. First will be an introduction to basis functions, key building blocks for regularization in functional regression methods, followed by an overview of functional regression methods, split into three types: [1] functional predictor regression (scalar-on-function), [2] functional response regression (function-on-scalar) and [3] function-on-function regression. For each, the role of replication and regularization will be discussed and the methodological development described in a roughly chronological manner, at times deviating from the historical timeline to group together similar methods. The primary focus is on modeling and methodology, highlighting the modeling structures that have been developed and the various regularization approaches employed. At the end is a brief discussion describing potential areas of future development in this field

Doctor of Philosophy

dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest