In many areas of science, especially geophysics, geography and meteorology, the data are often directions or axes rather than scalars or unrestricted vectors. Directional statistics considers data which are mainly unit vectors lying in two- or three-dimensional space (R² or R³).…
The extended Kalman lter (EKF) has a long history in the field of non-linear tracking. More recently, statistically-based estimators have emerged that avoid the need for a deterministic linearisation process. The Unscented Kalman filter (UKF) is one such technique that has been …
Spline smoothing is a popular technique for creating maps of a spatial phenomenon. Most smoothers use the Euclidean metric to measure the distance between data. This approach is flawed since the distances between points in the domain as experienced by the objects within the doma…
Numerical schemes often develop inaccuracies when used to solve parabolic partial differential equations with nonsinooth data e.g., from high frequency components. For homogeneous parabolic PDEs with nonsinooth data, Luskin and Rannacher [60, 61] discovered for the case of Crank…
Smoothing is the practice of modeling data in order to eliminate random variation from the observed data and provide estimates of the underlying process. Models are developed here beginning with an additive model that incorporates spatio-temporal smoothing of the observed mortal…
Smoothing a probability distribution so that it generalizes well is a hard machine learning problem. It is particularly challenging when building a statistical language model with insufficient training data. We have developed a new smoothing algorithm (called AlphaRank) to overc…
Proteins have highly specific three-dimensional structures. It is the structure of a protein that determines how it functions in the cell, i.e. its biological activity. Thus, in order to understand how the cell works it is crucial to know the three-dimensional structure of prote…
Bezier polynomials are used frequently in computer graphics for interactive generation of smooth curves. As these polynomials have parametric equation forms, only a small number of guiding points are required to specify a desired curve. The inverse problem of finding an optimal …
The goal of this thesis is to modify the traditional linear prediction (LP) analysis in such way that the fluctuations of the LP coefficients are reduced, while the pitch pulse shape evolves slowly. These modifications can lead to an increase in the coding efficiency and/or an i…
It has long been known that high frequency components, typically from nonsmooth data, can cause spurious oscillations in numerical schemes. Luskin and Rannacher for the Crank-Nicolson scheme, and Rannacher for diagonal Padé schemes in general, discovered that the use of (m − 1, …