Identification of Point Process Systems With Application to Complex Neuronal Networks

Amjad, Abdul Majeed (1989) Identification of Point Process Systems With Application to Complex Neuronal Networks. PhD thesis, University of Glasgow.

Abstract

The main aim of the thesis is to develop and apply statistical and computational techniques for the system identification of the complex interactions that occur between the components of neuronal networks within the central nervous system. An analysis of these interactions will provide a basis for understading the operations that the central nervous system uses to carry out particular tasks. In order to work effectively, it is necessary for a statistician to become familiar with the background for understanding the physiological problems. In Chapter 1, a brief description of the neuromuscular control system followed by a more detailed discussion of the muscle spindle, a particular component of the neuromuscular control system we are interested in, is given. The next section describes the problems we will be studying in this thesis. The final part of this chapter presents the basic data sets mainly obtained on the muscle spindle under different experimental conditions, and which will form the experimental material for our studies. Chapter 2 presents a review of the general theory of point processes. In Chapter 3 we introduce a univariate point process. Certain parameters are defined in both the time and frequency domain. In Chapter 4, Introducing a blvarlate stationary point process, we define certain parameters useful for measuring the association and timing relation between two processes in both domains. The main aim of this chapter is again to compare the procedures in both domains. Chapter 5 presents an extensive development of the wide range of applicability of a Fourier-based approach to measures of association and related problems. In Chapter 6 we extend the linear point process system Identification techniques to the systems which are assumed to be non-linear. The simplest non-linear case is quadratic. Certain third order (quadratic) time domain parameters, e.g., the third order product density, conditional density, and cumulant density, are defined and their estimates are considered. It is shown by a simulated study that all the three parameters give different informations about the non-linearities. The application of these parameters is demonstrated by using the real data on muscle spindle. The third order parameters are further extended to order-4. The aim is to have more insight into the processes under investigation. Estimates of the fourth order product density are considered. Asymptotic confidence intervals are constructed and Illustrated. In the frequency domain, the third order spectrum is defined and illustrated. A quadratic model relating a single output to a single input is introduced and developed which leads to the quadratic coherence, a measure of quadratic effects that the input has on the output. The estimation and application of the quadratic coherence is demonstrated. The final section of this chapter extends the quadratic model in order to include a second input. The model is solved under the assumption that the inputs are two independent Poisson processes, and which leads to a simple solution for the identification of a non-linear system with two inputs (independent Poisson processes). The results obtained in both domains reveal significant non-linear features of the muscle spindle. Chapter 7, considering the situations and problems for future work, gives a list of possible ways in which the work of this thesis may be extended. (Abstract shortened by ProQuest.).

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Adviser: Peter Breeze
• Keywords: Statistics, Computer science, Artificial intelligence
• Date of Award: 1989
• Depositing User: Enlighten Team
• Unique ID: glathesis:1989-76496
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 19 Nov 2019 14:16
• Last Modified: 19 Nov 2019 14:16
• URI: https://theses.gla.ac.uk/id/eprint/76496