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No description available.

Wind power is one of the most promising renewable energy resources to replace conventional generation which carries high carbon footprints. Due to the abundance of wind and its relatively cheap installation costs, it is likely that wind power will become the most important energy resource in the near future. The successful development of wind power relies heavily on the ability to integrate wind power effciently into electricity grids. To optimize the value of wind power through careful power dispatches, techniques in forecasting the level of wind power and the associated variability are critical. Ideally, one would like to obtain reliable probability density forecasts for the wind power distributions. As wind is intermittent and wind turbines have non-linear power curves, this is a challenging task and many ongoing studies relate to the topic of wind power forecasting. For this reason, this thesis aims at contributing to the literature on wind power forecasting by constructing and analyzing various time series models and spatiotemporal models for wind power production. By exploring the key features of a portfolio of wind power data from Ireland and Denmark, we investigate different types of appropriate models. For instance, we develop anisotropic spatiotemporal correlation models to account for the propagation of weather fronts. We also develop twostage models to accommodate the probability masses that occur in wind power distributions due to chains of zeros. We apply the models to generate multi-step probability forecasts for both the individual and aggregated wind power using extensive data sets from Ireland and Denmark. From the evaluation of probability forecasts, valuable insights are obtained and deeper understanding of the strengths of various models could be applied to improve wind power forecasts in the future.

This thesis describes signal analysis methods for single-molecule fluorescence data. The primary factor motivating method development is the need to distinguish single-molecule FRET fluctuations due to conformational dynamics from fluctuations due to distance-independent FRET changes. Single-molecule Förster resonance energy transfer (FRET) promises a distinct advantage compared to alternative biochemical methods in its potential to relate biomolecular structure to function. Standard measurements assume that the mean transfer efficiency between two fluorescent probes, a donor and an acceptor, corresponds to the mean donor-acceptor distance, thus providing structural information. Accordingly, measurement analysis assumes that mean transfer efficiency fluctuations entail mean donor-acceptor distance fluctuations. Detecting such fluctuations is important in resolving molecular dynamics, as molecular function often necessitates structural changes. A problem arises, however, in that factors other than donor-acceptor distance changes may induce mean transfer efficiency fluctuations. We refer to these factors as distance-independent FRET changes. We present analysis methods to detect distance-independent photophysical dynamics and to determine their correlation with distance-dependent FRET dynamics. First, we review a theory of photon statistics and show how we can use the theory to detect FRET fluctuations. Second, we extend the theory to alternating laser excitation (ALEx) measurements and demonstrate how fluorophore stoichiometry, a measure of fluorophore brightness, reports on distance-independent photophysical dynamics. Next, we provide a measure to determine the extent to which stoichiometry fluctuations account for FRET dynamics. Finally, we use a framework similar to the preceding along with recent advances in the theory of total internal reflection fluorescence (TIRF) microscopy FRET measurements to detect TIRF FRET fluctuations which occur on a timescale faster than the measurement temporal resolution. We validate our methods with simulations and demonstrate their utility in delineating RNA polymerase open complex conformational dynamics.

Conventional feed forward Neural Networks have used the sum-of-squares cost function for training. A new cost function is presented here with a description length interpretation based on Rissanen's Minimum Description Length principle. It is a heuristic that has a rough interpretation as the number of data points fit by the model. Not concerned with finding optimal descriptions, the cost function prefers to form minimum descriptions in a naive way for computational convenience. The cost function is called the Naive Description Length cost function. Finding minimum description models will be shown to be closely related to the identification of clusters in the data. As a consequence the minimum of this cost function approximates the most probable mode of the data rather than the sum-of-squares cost function that approximates the mean. The new cost function is shown to provide information about the structure of the data. This is done by inspecting the dependence of the error to the amount of regularisation. This structure provides a method of selecting regularisation parameters as an alternative or supplement to Bayesian methods. The new cost function is tested on a number of multi-valued problems such as a simple inverse kinematics problem. It is also tested on a number of classification and regression problems. The mode-seeking property of this cost function is shown to improve prediction in time series problems. Description length principles are used in a similar fashion to derive a regulariser to control network complexity.

This thesis is about the study of relationships between experimental dynamical systems. The basic approach is to fit radial basis function maps between time delay embeddings of manifolds. We have shown that under certain conditions these maps are generically diffeomorphisms, and can be analysed to determine whether or not the manifolds in question are diffeomorphically related to each other. If not, a study of the distribution of errors may provide information about the lack of equivalence between the two. The method has applications wherever two or more sensors are used to measure a single system, or where a single sensor can respond on more than one time scale: their respective time series can be tested to determine whether or not they are coupled, and to what degree. One application which we have explored is the determination of a minimum embedding dimension for dynamical system reconstruction. In this special case the diffeomorphism in question is closely related to the predictor for the time series itself. Linear transformations of delay embedded manifolds can also be shown to have nonlinear inverses under the right conditions, and we have used radial basis functions to approximate these inverse maps in a variety of contexts. This method is particularly useful when the linear transformation corresponds to the delay embedding of a finite impulse response filtered time series. One application of fitting an inverse to this linear map is the detection of periodic orbits in chaotic attractors, using suitably tuned filters. This method has also been used to separate signals with known bandwidths from deterministic noise, by tuning a filter to stop the signal and then recovering the chaos with the nonlinear inverse. The method may have applications to the cancellation of noise generated by mechanical or electrical systems. In the course of this research a sophisticated piece of software has been developed. The program allows the construction of a hierarchy of delay embeddings from scalar and multi-valued time series. The embedded objects can be analysed graphically, and radial basis function maps can be fitted between them asynchronously, in parallel, on a multi-processor machine. In addition to a graphical user interface, the program can be driven by a batch mode command language, incorporating the concept of parallel and sequential instruction groups and enabling complex sequences of experiments to be performed in parallel in a resource-efficient manner.

University of Macau / Faculty of Science and Technology. / Department of Computer and Information Science