School of Engineering and Physical Sciences - Department of Physics

Final Report: Edinburgh Multidisciplinary Consortium (EMC) for Advanced Nonlinear Analysis of Complex Systems

General:
The Consortium was established in May 1998, in partnership with the Royal Infirmary of Edinburgh, Laerdal Medical Ltd., and the Standard Life.

Aims:
The Consortium interfaces academics with doctors and financiers to undertake fundamental and strategic research into modelling, simulation, and prediction of real-life complex systems. It aims to develop new strategies and methodology to improve risk-assessment and management in Healthcare, and management and business process engineering in Finance.

Summary of Work:
In this three-year programme the techniques of nonlinear dynamical systems theory and neural networks have been developed and combined to demonstrate an effective new strategy for analysis of real-world complex systems. The results of this preliminary work are a benchmark in the field of advanced data analysis, establishing a new methodology for discovering underlying structures within the seemingly random behaviour of such complex systems. This new approach has been applied with effect to several critical areas within Healthcare, in particular (in collaboration with the Royal Infirmary of Edinburgh, Laerdal Medical Limited and other partners): modelling, prediction, and determining outcome of the lethal arrhythmia Ventricular Fibrillation, and also for more accurate classification of breast cancer through neural net analysis. In collaboration with the Center for Disease Control in Atlanta, neural networks have been successfully used in areas of Behavioural Science; in particular for identifying World Health Inequalities and health care promotion direction for countries, and within the US identifying the evolution of health status among its states. In Finance, nonlinear data analysis, in conjunction with wavelets, and neural networks has led to improved prediction accuracy; and techniques derived from this work have been incorporated into Neural Network and data analysis procedures at Standard Life. The Consortium has established a world-wide network of collaborators, and has been highly productive in published output, conference presentations, study visits; media coverage of our work has resulted in increased public awareness of this new field of analysis. For more specific information, see Research Highlights.

*now with BaySpec, CA, USA; ** now with Hong Kong Polytechnic University; *** now with University of Exeter

Partners
Dr C. Robertson, Dr G. Clegg Royal Infirmary of Edinburgh
Dr K. Morallee Laerdal Medical Limited
Dr D. Jubb, Mr H. Smith Standard Life (Investment)

Finance
Contact Grant Office at Heriot-Watt University.

Output

Collaborations
While expertise in data analysis is provided within the Nonlinear Dynamics group at Heriot-Watt University the nature of this project requires interdisciplinary collaborations with theoretical and experimental biologists, physicians and financiers. The EMC provides a framework for some of these collaborations; others exist outside of this organisation:

·  Prof Arun Holden, Dr Richard Clayton and Dr V.N. Biktashev; Computational Biology Group, Department of Physiology, University of Leeds, Leeds, UK

·  Prof Keith Fox and Dr Neil Grubb; Cardiovascular Research Unit, Royal Infirmary of Edinburgh, Edinburgh, UK.

·  Dr Paul Addison and Mr. Jamie Watson; Department of Civil and Transportation Engineering, Napier University, Edinburgh, UK.

·  Prof Fritz Sterz and Dr Michael Holzer; Abteilung Fur Notfallmedizin, Universitatskliniken Allgemeines Krankenhaus des Stat Wein, Austria.

·  Prof P.A. Steen; Department of Anaesthesia, University of Oslo, Oslo, Norway.

·  Dr Trygve Eftestöl; Signal Processing Group, Högskolen i Stavanger, Stavanger, Norway.

·  Prof. L Oxley; Economics Department, Waikato University, New Zealand

·  Dr D. McQueen; Centre of Disease Control (CDC), Atlanta, USA

·  Prof. C. Diks; CeNDEF, Amsterdam

·  Members in EPSRC "Engineering Virtual Tissues and Organs" Network

·  Prof. Mark Spano; Naval Surface Warfare Center, USA

·  Prof. Bill Ditto; Applied Chaos Laboratory, Georgia Institute of Technology, Atlanta, USA

Publications
Group total of 43 publications, 26 in peer-reviewed journals. For a complete list, see  Publications List at end of document.

Conference Presentations
Group total of 22 conference presentations, 17 proceedings papers. For a complete list, see  Conference Presentations and Proceedings List at end of document.

Public lectures:

·  Chaos and complexity in healthcare, by R. G. Harrison in the Edinburgh Science Festival, Aug. 2000.

·  Fractals and Nonlinearity in the Human body: complexity is good for you!, by J. Simonotto at the Physics Forum, Heriot-Watt University, 10 May 2001.

Workshop Meetings

·  Data Analysis of Ventricular Fibrillation (Edinburgh, 03/1999)

·  Analysis Tools of Ventricular Fibrillation (Leeds, 06/2000)

·  Validation of Virtual Cardiac Tissue (Leeds, 06/2001)

Study visits:

1998-1999

·  R.G. Harrison to University of Utah and to College of Physicians and Surgeons of Columbia University

·  Dr. R. Clayton from Leeds University to the Consortium

·  M. Small to School of Biomedical Sciences at Leeds University

1999-2000

·  R.G. Harrison and Z. Yang to CDC (Atlanta) twice

·  Dr D. McQueen from CDC to Consortium

·  Prof. M. Spano, NSWC, Navy, USA

·  Prof A.V. Holden from Leeds University to Consortium

·  D. Yu, W. Lu, M. Small and J. Simonotto to School of Biomedical Sciences at Leeds University

·  J. Simonotto, and D. Yu to Leeds University

·  Dr K. Judd from Oxford to the Consortium

2000-2001

·  J. Simonotto to Leeds University

·  Dr. A. Zaikin (University of Potsdam) to Consortium

·  J. Simonotto to University of Potsdam and Humboldt University in Berlin, Germany.

·  J. Simonotto to Center for Neurodynamics at University Missouri at St. Louis, USA

Grants

·  Development of Market Analysis and Forecasting Systems for Standard Life (£21,575, 1999).

·  Pattern Recognition and Classification of VF ECG Traces by Combined Neural Network Statistics Method (£44,070, 2000-2001, EPSRC).

·  EPSRC Network: Engineering Virtual Tissues and Organs (Leeds, Heriot-Watt, Liverpool, UMIST, Manchester and Oxford University and Freeman Hospital) (£49,700, EPSRC, 2000-2003).

·  Modelling, simulations and Analysis of Ventricular Fibrillation (£300K, EPSRC, invited resubmission, joint with University of Leeds).

Research Highlights

Data analysis methodology overview
Nonlinear dynamics: Nonlinear dynamics (NLD) and the techniques of nonlinear time series analysis are employed to extract mathematical order from apparently random behaviour. Some of the techniques provide a probabilistic assessment of nonlinearity (surrogate data analysis). Other techniques aim to quantify nonlinearity in numerical measurements (correlation dimension, entropy, and Lyapunov exponents: so-called system invariants). These measurements provide an experimental estimate of how chaotic, how nonlinear, and how random a system is. Still further techniques attempt to mimic the mathematical equations underlying apparently random behaviour (nonlinear modelling) and describe the nature of this behaviour (bifurcation analysis, unstable periodic orbits and first return maps). The principle of these techniques is that by producing a computational model of the underlying behaviour one can apply the machinery of nonlinear dynamics and describe the system's characteristics.

Artificial neural network analysis: Artificial neural networks (ANNs) are computationally intensive tools used for knowledge acquisition and inference. They learn from data without a prior knowledge of the relationship between input and output variables, the interaction among the input variables, or the underlying statistical distribution. The final target of our real-world data analysis using this approach is to support decision-making. There are many artificial neural network algorithms. Probabilistic neural networks (PNNs), which implement Bayesian theory, are the most successful tools in dealing with uncertainty in decision making. This is achieved by combining our empirical experience and prior knowledge efficiently to minimise the probability of misclassification. Of these we choose two recently developed PNNs, one of which has the advantages of parsimonious structure, called the common covariance matrix probabilistic neural network (COPNN), while the other is robust in dealing with noise in data and is called robust heteroscedastic probabilistic neural network (RHPNN).

Data analysis algorithms (with CeNDEF and Exeter university)
The nonlinear dynamics algorithms used for the characterisation and prediction of time series data when applied to real world data are commonly handicapped by problems of nonstationarity and noise contamination. In this work we covered each of these aspects: 1): Two new reliable test methods for detecting nonstationarity in a given time series were developed [1,3,38]; 2): An improved phase space prediction algorithm was proposed and found to yield improved prediction results and robustness to the presence of noise and the use of short data sets [2]; 3): An efficient implementation of the Gaussian kernel algorithm was developed to allow the improved estimation of noise level and system invariants directly from contaminated time series [7]; and 4): Improvements were made in the existing tools for nonlinear model accuracy[9,14,25]. In [1,3] the distribution of phase-space nearest neighbour time-indices is used to account for the presence of dynamical nonstationarity. A new local linear modelling technique is described in [5] and adapted in [11] for detecting changes is periodic behaviour in noisy data. A novel statistical test to distinguish a noisy periodic system from complex nonlinear dynamics has been developed and is introduced and applied in [10,12,23,46,48]. In [2], a combination of phase space transformation, weighted regression, and singular value decomposition is used to produce a superior local linear prediction function. Finally, the efficient implementation of the Gaussian kernel algorithm in [7] has allowed for fast, reliable determination of correlation dimension, entropy and noise level over a wider range of limits and problems than had previously been established.

Medical applications

Modelling, data analysis and prediction of Ventricular Fibrillation (with EMC partners: Cardiovascular Research Unit, Royal Infirmary of Edinburgh; Universitatskliniken Allgemeines Krankenhaus des Stat, Wein, Austria; Stavanger College of Technology, Oslo, Norway; Högskolen i Stavanger, Stavanger, Norway).

Ventricular Fibrillation (VF) is a leading cause of death in the industrialised world. During VF the electrical impulses across the surface of the lower chambers of the heart (the ventricles) behave in an uncoordinated, apparently random, fashion. This prevents the heart from functioning effectively and if VF continues, permanent damage or death will result. Most commonly VF is treated with a large electrical shock delivered directly to the fibrillating heart (defibrillation). While in-hospital treatment via defibrillation has been observed to be successful in about 90% of cases, the success rate for out-of-hospital treatment is far more dismal (3–5%). The actual mechanism of VF is still poorly understood, and inappropriate application of defibrillation may actually initiate arrhythmia or result in serious tissue damage.

Towards understanding the dynamics of electrical activity over the entire heart we have found, through comparative analysis of real data and computational models [16,43], that the human cardiac system during sinus rhythm and ventricular arrhythmia cannot be described by a simple linear system. Analyses of experimental recordings in swine [6,8,31,32] and humans [15,33] have show that ventricular arrhythmia and sinus rhythms are not adequately modelled as linear stochastic systems. During a normal sinus rhythm, long-term determinism is evident and the system exhibits a low dimensional attractor, entirely consistent with the hypothesis that cardiac output measured by ECG exhibits chaotic dynamics. A comparative analysis of human VF ECG recordings and computational simulations indicates that the computational model (a cuboid cardiac caricature with FitzHugh-Nagumo dynamics initiated with spiral and scroll waves of excitation) is simplistic but consistent with the electrical behaviour observed in human subjects [16]. We found correlation dimension estimates, surrogate analysis and first return maps to be consistent between computational simulations and human data. These results indicate that spiral wave break-up is a likely origin of VF in humans.

We have also applied standard and novel nonlinear statistical descriptions of time series to aid the identification of precursors to the initiation of and evolution during VF [16]. Estimating these statistics (treated as characteristics of VF) from patient data may enable us to identify the critical points in the evolution of VF, discover statistically significant precursors of VF (prediction of an arrhythmia), and to be more successful in patient defibrillation. In experimental swine subjects we observed characteristic changes in the underlying period of VF following initiation, while in human ECG data we found that a period doubling bifurcation mechanism provides the most compact and accurate description of the physiological changes in rhythm prior to onset of VF [24,44]. This was observed consistently in the initial group of data collected for this program from the CCU at Edinburgh Royal Infirmary[42].

Another aspect of our work has been on predicting the outcome of defibrillation from the status of the patient through the use of ANNs to classify pre-shock VF ECGs into those of shockable and non-shockable, corresponding to a return of spontaneous circulation (ROSC) and non-return (non-ROSC). Few studies have so far been made in this critical area and where so success has been limited. We have applied two probabilistic neural networks, using the common covariance matrix (COPNN) and robust heteroscedastic variance (RHPNN). Data was collected from the Medical Control Module (MCM) of the defibrillator, Heartstart 3000 (Laerdal Medical, Stavanger, Norway) and the regular Utetein registration in Ulleval University Hospital, Oslo, Norway, for 156 patients with out-of-hospital cardiac arrest. A total of 883 shocks were classified. Greatly improved predictions were obtained for patients with and without ROSC; the expectations of sensitivity and specificity being 93.6% and 74.0% respectively; both networks achieve similar results. More significantly, we have for the first time performed with similar results, two further levels of predictions for those patients with ROSC, that of sustained ROSC vs. non-sustained ROSC and, of the sustained ROSC, that of survival vs. non-survival [26]. These results are a first step to the development of smart software diagnostics for interface with in-ambulance defibrillators.

VF in humans is therefore nonlinear and is amenable to analysis using the techniques of NLD systems theory and ANN analysis. Characteristic nonlinear changes in rhythm are observed to precede onset of arrhythmia and may therefore be exploited to predict imminent VF; neural nets allows the further categorisation of the state of VF of a patient into a shockable or nonshockable treatment regime. With additional data and further analysis, nonlinear dynamic measures may prove an invaluable aid in diagnosing patients at immediate risk of cardiac arrhythmia. Continued collection of data from the CCU (Edinburgh) and MCM (Norway) will provide the necessary data to determine if these conclusions are physiologically significant and potentially lead to new methods of predicting cardiac arrhythmia. Furthermore, analysis of computational simulations derived from more complete models of the human heart will provide verification of the accuracy of these models and an improved understanding of the origin of VF.

Detection of false benign breast cancer diagnosis.

The true features (the most meaningful features) for detecting breast cancer, are a source of hidden information. Such features can be missed by many complicated factors, such as poor image quality, radiologist fatigue and human oversight resulting in reduced performance in diagnosing cancer. We assume that the true features may not exist within the collected features and the interrelationship between the collected features is complex. This leads us to explore a new approach using artificial neural networks (ANNs) for finding the true features based on the information provided by the collected features. From this, key features are selected from the collected features according to the probabilistic relationship between the true features and the collected features; the key features are used for diagnosis. The ANN method produces a 98.14% total correct classification rate with nine key features. By comparison, the Wills' Lambda rule generates a noticeably lower total correct classification rate of 96.5% with a higher number (13) of key features for Wisconsin diagnostic breast cancer (WDBC) data 1.

Misclassification of a malignant patient as a benign patient occurs if the medical features of a malignant patient are too close to those of a false benign patient. As a result, a diagnostic model with this problem will result in a bias when implemented in the diagnosis of breast cancer i.e. a patient is more likely to be identified as benign than malignant. Detecting false benign patients is therefore critical before a breast cancer diagnostic model can be put into clinical use. We have applied the RHPNN to detect false benign patients. The method gave an estimated accuracy of breast cancer diagnosis of 98.5% of the total correct classification rate using Wisconsin diagnostic breast cancer (WDBC) data 2 [20, 40] This is to be compared with 94% using normal procedure of adjusting the proportion of cost functions of the benign and malignant patients. The RHPNN method is superior to that of normal clinical procedure in maintaining a 100% correct classification rate of malignant patient while substantially reducing through misclassification rate of benign patients. Importantly, a false benign analysis table has been formulated in this work for clinical use in detecting false benign diagnosis.

Survival data analysis

This is an important issue in medicine because it estimates how long a patient will survive so that a necessary surgery plan can be correctly made. We compare the different modes, different methodologies and different ANNs to find which is most suitable to medical survival data analysis; specifically minimization of the mean error of survival time prediction. Using several different ANNs described in the Ventricular Fibrillation section above, we investigated which method gave best minimization of mean error results. Results are compared on three data sets: two myeloma data sets and the Wisconsin prognostic breast cancer (WPBC) data 3. Medical survival data analysis using the joint domain general regression neural network, which is developed in this project for survivor function estimation, is the most accurate, giving the lowest normalized mean error.

Behavioural science (with the Centre of Decease Control (CDC), Atlanta, and USA)
Word Health Inequality Analysis

In order to promote human health in the next century, the World Health Organization (WHO) has identified five goals of health systems, of which two are dependent on identifying health inequalities between countries. Most social scientists focus on identifying health inequalities from socioeconomic health indicators (mortality, dietary, socioeconomic position, market etc) through using univariate and linear statistical analysis. Complicated hidden relationship between health inequalities and health indicators cannot be accounted for through such analysis thereby reducing the accuracy with which health inequalities between countries may be identified. To obtain a more accurate formulation of health inequalities, we assess the ability of ANNs in the analysis of WHO data (webpage, http://www.who.int/whosis/basic/). Our result [13,21,29,41] show that the 191 countries of the world may be clustered into nine groups and health inequalities identified. A Probabilistic Transition Graph is designed for identifying health inequalities and indicating health promotion direction for countries as well as providing the key indicators for promoting the health direction.

Health status Analysis of the States of USA

Health status is usually described by a set of health indicators, such as the 22 indicators given by CDC for the USA. From these data sets, the indicators are shown to be apparently variable among the 50 states; the health status of these states therefore varies. Through the use of a similar ANN strategy to that above (see Section on Word Health Inequality Analysis) this work first establishes [13,21] an overall distribution pattern of the health status of all the states in the USA. The health status of the 50 states is further analysed in the form of ranking maps, which ranks them from high to low, based on benchmark national average indicators. Changes of the distributions in the ranking maps, from 1992-1996, illustrate the evolution of health status among these states.

Finance (with Standard Life and University of Exeter)

Financial time series are seemingly random. However, in our NLD analysis of financial market data, we have found evidence of chaotic or semi-chaotic behaviour [4,27,30]. During the examination of such market data it is often difficult to estimate the embedding dimension and lags with which to reconstruct the phase space and understand how the system works (recognizable through patterns in the time-series data). The alternative, trial-and-error is time consuming and the input vectors constructed by the embedding dimension and lags using NLD may not produce optimal prediction results. In this work we have applied an evolutionary programming technique to search for the optimal combination of stacked financial time series predictors with multiple window scales and sampling gaps. The evolutionary process is ensured to proceed smoothly towards the optimal solution by using a control strategy based on the similarity level between the genotypes from two successive generations. The experiments on S&P500 price index shows that the method significantly improves the prediction accuracy compared with the constrained least squared regression[4,27].

Additionally, we have also used neural networks[17,18,19,22] and wavelet analysis to examine financial time series data [30,39]. Specifically, we have used the ability of wavelet analysis to decompose such series into multiple orthogonal series that delineate market moves over different investment horizons. In [30], this was our starting point for the analysis of detrending techniques for financial data, which is typically highly nonstationary. This work [39] was a further step to understanding market data by looking for both persistence and coherent structure. Techniques derived from this work have been incorporated into artificial neural network and data analysis procedures at Standard Life. These methods have ultimately become part of the technical analysis input into the decision making process at Standard Life.

Publications in Peer-Reviewed Journals (listed in chronological order):

1. D. Yu, W. Lu and R.G. Harrison, Space time-index plots for probing dynamical nonstationarity, Phys. Lett. A 250, 323 (1998)
2. D. Yu, W. Lu and R.G. Harrison, Phase space prediction of chaotic time series, Dynamics and Stability of Systems, 13 (3), 219 (1998)
3. D. Yu, W. Lu and R.G. Harrison, Detecting dynamical nonstationarity in time series data, Chaos, 9(4), 865-870 (1999).
4. R.G. Harrison, D. Yu, L. Oxley, W. Lu and D. George, Nonlinear noise reduction and detecting chaos: Some evidence from the S&P composite price index, Math. & Comps. in Simulations, 48(4-6), 497-502 (1999).
5. M. Small and K. Judd. Detecting periodicity in experimental data using linear modelling techniques. Phys. Rev. E, 59, 1379-1385 (1999).
6. M. Small, D. Yu, R.G. Harrison, C. Robertson, G. Clegg, M. Holzer, and F. Sterz. Deterministic nonlinearity in ventricular fibrillation. Chaos, 10, 268–277 (2000).
7. D. Yu, M. Small, R.G. Harrison, and C. Diks. Efficient implementation of the Gaussian kernel algorithm in estimating invariants and noise level from noisy time series data. Phys Rev E, 61, 3750–3756 (2000).
8. D. Yu, M. Small, R.G. Harrison, C. Robertson, G. Clegg, M. Holzer, and F. Sterz. Measuring temporal complexity of ventricular fibrillation. Phys Lett A, 265, 68–75 (2000).
9. K. Judd and M. Small. Towards long-term prediction. Physica D, 136, 31-44, (2000).
10. M. Small, D. Yu, and R. G. Harrison. A surrogate test for pseudo-periodic time series data. Phys Rev Lett, 87(18), 188101 (2001).
11. M. Small, D.J. Yu and R.G. Harrison. Variation in the dominant period during ventricular fibrillation. IEEE Trans. Biomed. Eng., 48, 1056-1061 (2001).
12. M. Small, K. Judd and A. Mees. Nonlinear surrogates for hypothesis testing. Statistics and Computing, 11, 257-268 (2001).
13. Z.R. Yang, Analysing health inequalities using SOM, Advances in Self-organising Maps, 47-53, Springer, 2001.
14. K. Judd and M. Small. Achieving Good Nonlinear Models: Keep it Simple, Vary the Embedding, and Get the Dynamics Right. Nonlinear Dynamics and Statistics, ed. A.I. Mees, pages 65-80, Birkhauser Boston, 2001.
15. M. Small, D. Yu, J. Simonotto, R.G. Harrison, N. Grubb, and K.A.A. Fox. Uncovering nonlinear structure in human ECG recordings. Chaos, Solitons and Fractals, (2001), to appear.
16. M. Small, D.J. Yu, R. Clayton, T. Eftestol, K. Sunde, P.A. Steen and R.G. Harrison. Temporal evolution of nonlinear dynamics in ventricular arrhythmia. Int. J. Bifurcations and Chaos, 11, (2001), to appear.
17. Z. R. Yang, W. Lu and R.G. Harrison, Evolving stacked regressions for time series, Neural Processing Letters. (2001), to appear.
18. Z.R. Yang, W.P. Lu and R. Harrison, Virtual object for prediction interpretation, Decision Support Systems, (2001), to appear.
19. Z.R. Yang and R. Harrison, Analysing Company Performance Using Templates, Intelligent Data Analysis, 6(1), (2001), to appear.
20. Z.R.Yang and R.G. Harrison, Artificial neural networks for breast cancer diagnosis, IEEE Trans. On Neural Networks (2000), submitted.
21. Z.R.Yang and R.G. Harrison, Artificial neural networks for health promotion, IEEE Trans. On Neural Networks (2000), submitted.
22. Z.R.Yang, A new methodology for company failure prediction, predict it and interpret it, Journal of Accounting Research (2000), submitted.
23. M. Small and C.K. Tse. Applying the method of surrogate data to cyclic time series. Physica D (2001), submitted.
24. M. Small, D.J. Yu and R.G. Harrison. Observation of a period doubling bifurcation during onset of human ventricular fibrillation. Int. J. Bifurcations and Chaos (2001), submitted.
25. M. Small, K. Judd and A. Mees. Modelling continuous processes from data. Phys. Rev. E (2001), submitted.
26. Z.R. Yang, Z.J. Yang, W.P. Lu, R.G. Harrison, Heteroscedastic probabilistic neural network as the predictive classifier of out-of-hospital defibrillation outcomes, manuscript in preparation.

Conference Presentations and Proceedings (listed in chronological order):

1. R.G. Harrison, Dejin Yu, L. Oxley and Weiping Lu, Nonlinear noise reduction and detecting chaos: Some evidence from the S&P composite price index, Proceedings of the International Congress on Modelling and Simulation, 3, A.D. McDonald and M. McAleer (eds.), University of Tasmania, Hobart, 1997, 1254-1258 (Hobart, Australia, 1997).
2. D. Yu and R. G. Harrison, Dynamical Nature and Measurement of Ventricular Fibrillation, International Symposium on Computation and Mathematics, Warwick, UK, 14-25 September 1998.
3. Z. R Yang, W. P.Lu and R. G. Harrison, Virtual object theory for finance, Europhysics Conference on Applications of Physics in Financial Analysis , Dublin (July 1999), International Journal of Theoretical and Applied Finance 3, 605-605, July 2000.
4. B. Fleming, D. Yu, D. Jubb, H. Smith and R. G. Harrison, Analysis of effect of detrending on time-frequency structures of financial data using discrete wavelet transform, Applications of Physics in Financial Analysis, Trinity College Dublin, Ireland, 15 - 17 July, 1999, International Journal of Theoretical and Applied Finance 3(3), 375-379, July 2000.
5. D. Yu, M. Small, R. G. Harrison, C. Robertson, G. Clegg, M. Holzer and F. Sterz, Complexity Measurements for Analysis and Diagnosis of Early Ventricular Fibrillation, Computers in Cardiology, Hanover, Germany, 26-29 September 1999, Comput. Cardiol., 26:21–24, 1999.
6. M. Small, D. Yu, R. G. Harrison, C. Robertson, G. Clegg, M. Holzer and F. Sterz, Characterizing Nonlinearity in Ventricular Fibrillation, Computers in Cardiology, Hanover, Germany, 26-29 September 1999,Comput. Cardiol., 26:17–20, 1999.
7. R.H. Clayton, D. Yu, M. Small, V.N. Biktashev, R.G. Harrison, A.V. Holden, Relationship between characteristics of simulated ECG signals and action potential propagation during simulations of arrhythmia, Computers in Cardiology, Hanover, Germany, 26-29 September 1999,Comput. Cardiol., 26:479–482, 1999.
8. R. G. Harrison, Artificial Neural Networks for Healthcare, Analysis, Interpretation, and Use of Complex Social and Behavioural Surveillance Data: Looking back in order to Go Forward, Savannah, USA, June 2000.
9. D. Yu, M. Small, J. Simonotto and R.G. Harrison, Nonlinear Data Analysis of Ventricular Fibrillation, EPSRC Network workshop on Tools for virtual tissue engineering ,Leeds, UK, June 2000.
10. J. Simonotto, M. Small, R.G. Harrison, D. Yu, Automatic Identification and Recording of Cardiac Arrhythmias, EPSRC Virtual Tissue Engineering Network Workshop, Leeds, UK, June 2000.
11. M. Small, D. Yu, R. Clayton and R. G. Harrison, Temporal evolution analysis of complex nonlinear dynamics in computational simulations of ventricular arrhythmia, Proceedings of School on Space Time Chaos: Characterization, Control and Synchronization, Pamplona, Navarra, Spain, 19-23 June 2000.
12. M. Small, Dejin Yu and R.G. Harrison, Nonstationarity as an embedding problem, Proceedings of School on Space-Time Chaos: Characterization, Control and Synchronization, ed. by S. Boccaletti et al., pp 3-17 (Pamplona, Spain), 2001.
13. B. Fleming, R. G. Harrison, Wavelet Transform Based Detection of Coherent Structures and Self-Affinity in Financial Data, Europhysics Conference on Applications of Physics in Financial Analysis II, Liège (July 2000), Eur. Phys. J. B 20, 543-546 (2001).
14. Z. Yang, W. Lu, D Yu and R.G. Harrison, Detecting false benign in breast cancer diagnosis, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks, Grand Hotel di Como, Como, Italy, 24-27 July 2000.
15. Z. Yang, R.G. Harrison and W. Lu, Identifying health inequalities using artificial neural networks (WHO data), Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks, Grand Hotel di Como, Como, Italy, 24-27 July 2000.
16. M. Small, D.J. Yu, N. Grubb, J. Simonotto, K. Fox and R.G. Harrison, Automatic Identification And Recording Of Cardiac Arrhythmia, Computers in Cardiology, Boston, Cambridge, Massachusetts, 24-27 September 2000 Comput. Cardiol., 27:355–358, 2000.
17. D.J. Yu, M. Small and R.G. Harrison, Nonlinear Analysis Of Human ECG During Sinus Rhythm And Arrhythmia, Computers in Cardiology , Boston, Cambridge, Massachusetts, 24-27 September 2000, Comput. Cardiol., 27:147–150, 2000.
18. M. Small, D.J. Yu, R. Clayton, R.G. Harrison, Evolution Of Ventricular Fibrillation Revealed By First Return Plots, Computers in Cardiology , Boston, Cambridge, Massachusetts, 24-27 September 2000,Comput. Cardiol., 27:525–528, 2000.
19. Z.R.Yang, Stability analysis of financial ratios, Proceedings of the 2nd International Conference on Intelligent Data Engineering and Automated Learning, Hong Kong, December 13 - 15, 2000.
20. M. Small, R.G. Harrison and C.K. Tse. Testing Pseudo-Periodic Time Series for Additional Determinism, Proceedings of the 6th Experimental Chaos Conference, Potsdam, Germany, 22-26 June 2001.
21. M. Small, D.J. Yu and R.G. Harrison. "Evidence of a Period Doubling Bifurcation Route to Chaos in Human Ventricular Fibrillation." (Poster) The 6^th Experimental Chaos Conference, Potsdam, Germany, 22-26 June 2001.
22. M. Small, R.G. Harrison and C.K. Tse. A Surrogate Test for Inter-Cycle Determinism in Oscillatory Time Series Data, Proceeding of the International Symposium on Nonlinear Theory and its Applications, Miyagi, Japan, 28 October – 1 November 2001.

Date of Submission: 14/11/2001

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