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The surface electrocardiogram (ECG) is a periodic signal portraying the electrical activity of the heart from the torso. The past fifty years have witnessed a proliferation of computer algorithms destined for ECG analysis. Signal averaging is a noise reduction technique believed to enable the surface ECG to act as a non-invasive surrogate for cardiac electrophysiology. The P wave and the QRS complex of the ECG respectively depict atrial and ventricular depolarization. QRS detection is a pre-requisite to P wave and QRS averaging. A novel algorithm for robust QRS detection in mice achieves a four-fold reduction in false detections compared to leading commercial software, while its human version boasts an error rate of just 0.29% on a public database containing ECGs with varying morphologies and degrees of noise. A fully automated P wave and QRS averaging and onset/offset detection algorithm is also proposed. This approach is shown to predict atrial fibrillation, a common cardiac arrhythmia which could cause stroke or heart failure, from normal asymptomatic ECGs, with 93% sensitivity and 100% specificity. Automated signal averaging also proves to be slightly more reproducible in consecutive recordings than manual signal averaging performed by expert users. Several studies postulated that high-frequency energy content in the signal-averaged QRS may be a marker of sudden cardiac death. Traditional frequency spectrum analysis techniques have failed to consistently validate this hypothesis. Layered Symbolic Decomposition (LSD), a novel algorithmic time-scale analysis approach requiring no basis function assumptions, is presented. LSD proves more reproducible than state-of-the-art algorithms, and capable of predicting sudden cardiac death in the general population from the surface ECG with 97% sensitivity and 96% specificity. A link between atrial refractory period and high-frequency energy content of the signal-averaged P wave is also considered, but neither LSD nor other algorithms find a meaningful correlation. LSD is not ECG-specific and may be effective in countless other signals with no known single basis function, such as other bio-potentials, geophysical signals, and socio-economic trends. / Thesis (Ph.D, Computing) -- Queen's University, 2013-09-30 23:54:21.137

Missing data creates various problems in analysing and processing of data in databases. Due to this reason missing data has been an area of research in various disciplines for a quite long time. This report intro- duces a new method aimed at approximating missing data in a database using a combination of genetic algorithms and neural networks. The proposed method uses genetic algorithm to minimise an error function derived from an auto-associative neural network. The error function is expressed as the square of the di®erence between the actual observa- tions and predicted values from an auto-associative neural network. In the event of missing data, all the values of the actual observations are not known hence, the error function is decomposed to depend on the known and unknown (missing) values. Multi Layer Perceptron (MLP), and Radial Basis Function (RBF) neural networks are employed to train the neural networks. The research focus also lies on the investigation of using the proposed method in approximating missing data with great accuracy as the number of missing cases within a single record increases. The research also investigates the impact of using di®erent neural net- work architecture in training the neural network and the approximation ii found to the missing values. It is observed that approximations of miss- ing data obtained using the proposed model to be highly accurate with 95% correlation coe±cient between the actual missing values and cor- responding approximated values using the proposed model. It is found that results obtained using RBF are better than MLP. Results found us- ing the combination of both MLP and RBF are found to be better than those obtained using either MLP or RBF. It is also observed that there is no signi¯cant reduction in accuracy of results as the number of missing cases in a single record increases. Approximations found for missing data are also found to depend on the particular neural network architecture employed in training the data set.

Leung Chi Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 52-57). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivations --- p.1 / Chapter 1.2 --- Related work --- p.3 / Chapter 1.2.1 --- Fixed-parameter tractability --- p.3 / Chapter 1.2.2 --- Maximum k-vertex cover --- p.4 / Chapter 1.2.3 --- Dominating set --- p.4 / Chapter 1.3 --- Overview of the thesis --- p.5 / Chapter 2 --- Preliminaries --- p.6 / Chapter 2.1 --- Notation and definitions --- p.6 / Chapter 2.1.1 --- Basic definitions --- p.6 / Chapter 2.1.2 --- Partial t-trees --- p.7 / Chapter 2.1.3 --- Cographs --- p.9 / Chapter 2.1.4 --- Chordal graphs and interval graphs --- p.11 / Chapter 2.2 --- Upper bound --- p.12 / Chapter 2.3 --- Extension method --- p.14 / Chapter 3 --- Planar Graphs --- p.17 / Chapter 3.1 --- Trees --- p.17 / Chapter 3.2 --- Partial t-trees --- p.23 / Chapter 3.3 --- Planar graphs --- p.30 / Chapter 4 --- Perfect Graphs --- p.34 / Chapter 4.1 --- Maximum k-vertex cover in cographs --- p.34 / Chapter 4.2 --- Maximum dominating k-set in interval graphs --- p.39 / Chapter 4.3 --- Maximum k-vertex subgraph in chordal graphs --- p.46 / Chapter 4.3.1 --- Maximum k-vertex subgraph in partial t- trees --- p.46 / Chapter 4.3.2 --- Maximum k-vertex subgraph in chordal graphs --- p.47 / Chapter 5 --- Concluding Remarks --- p.49 / Chapter 5.1 --- Summary of results --- p.49 / Chapter 5.2 --- Open problems --- p.50

Ho Man Lam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 51-54). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Statement of problems --- p.1 / Chapter 1.2 --- Notation and definitions --- p.3 / Chapter 1.3 --- Graph families --- p.4 / Chapter 1.4 --- Related work --- p.5 / Chapter 1.4.1 --- Graph modification problems --- p.5 / Chapter 1.4.2 --- Independent set --- p.6 / Chapter 1.5 --- Overview of the thesis --- p.7 / Chapter 2 --- Recognition of Nearly Chordal Graphs --- p.8 / Chapter 2.1 --- Critical edges not in triangles --- p.9 / Chapter 2.2 --- Critical edges in triangles --- p.10 / Chapter 2.3 --- A linear time algorithm --- p.13 / Chapter 3 --- Recognition of Almost Chordal Graphs --- p.15 / Chapter 3.1 --- Minimal separator --- p.16 / Chapter 3.2 --- "All chordless cycles passing through the minimal (x, z)-separator S" --- p.18 / Chapter 3.3 --- Algorithm for almost chordal graphs recognition --- p.22 / Chapter 3.4 --- Another approach to find a critical vertex if all chordless cycles pass through S --- p.26 / Chapter 3.5 --- A linear algorithm for all chordless cycles passing through S --- p.28 / Chapter 4 --- Maximum Independent Bases of Chordal Graphs --- p.32 / Chapter 4.1 --- Maximum independent base --- p.32 / Chapter 4.1.1 --- Finding a maximum independent set of a chordal graph . --- p.33 / Chapter 4.1.2 --- Another approach to prove the algorithm --- p.33 / Chapter 4.1.3 --- Maximum independent base --- p.34 / Chapter 4.1.4 --- Vertices in the maximum independent base --- p.36 / Chapter 4.1.5 --- A linear time algorithm --- p.38 / Chapter 4.2 --- Generating all maximum independent sets --- p.39 / Chapter 4.2.1 --- Relation between two maximum independent sets --- p.39 / Chapter 4.2.2 --- Algorithm --- p.40 / Chapter 4.3 --- Maximum induced split graph of a chordal graph --- p.43 / Chapter 4.3.1 --- Property of maximum induced split subgraph --- p.44 / Chapter 4.3.2 --- A linear time algorithm --- p.45 / Chapter 5 --- Concluding Remarks --- p.48 / Chapter 5.1 --- Summary of results --- p.48 / Chapter 5.2 --- Open problems --- p.48 / Bibliography --- p.51

It has often been said that the problem of creating timetables for scheduling university courses is hard, even as hard as solving an NP-Complete problem. There are many papers in the literature that make this assertion but rarely are precise problem definitions provided and no papers were found which offered proofs that the university course scheduling problem being discussed is NP-Complete. This thesis defines a scheduling problem that has realistic constraints. It schedules professors to sections of courses they are willing to teach at times when they are available without overloading them. Both decision and optimization versions are precisely defined. An algorithm is then provided which solves the optimization problem in polynomial time. From this it is concluded that the decision problem is unlikely to be NP-Complete because indeed it is in P. A second more complex timetable design problem, that additionally seeks to assign appropriate rooms in which the professors can teach the courses, is then introduced. Here too both decision and optimization versions are defined. The second major contribution of this thesis is to prove that this decision problem is NP-Complete and hence the corresponding optimization problem is NP-Hard.