Locomotor patterns and persistent activity in self-organizing neural models

The thesis investigates principles of self-organization that may account for the observed structure and behaviour of neural networks that generate locomotor behaviour and complex spatiotemporal patterns such as spiral waves, metastable states and persistent activity. This relates to the general neuroscience problem of finding the correspondence between the structure of neural networks and their function. This question is both extremely important and difficult to answer because the structure of a neural network defines a specific type of neural dynamics which underpins some function of the neural system and also influences the structure and parameters of the network including connection strengths. This loop of influences results in a stable and reliable neural dynamics that realises a neural function. In order to study the relationship between neural network structure and spatiotemporal dynamics, several computational models of plastic neural networks with different architectures are developed. Plasticity includes both modification of synaptic connection strengths and adaptation of neuronal thresholds. This approach is based on a consideration of general modelling concepts and focuses on a relatively simple neural network which is still complex enough to generate a broad spectrum of spatio-temporal patterns of neural activity such as spiral waves, persistent activity, metastability and phase transitions. Having considered the dynamics of networks with fixed architectures, we go on to consider the question of how a neural circuit which realizes some particular function establishes its architecture of connections. The approach adopted here is to model the developmental process which results in a particular neural network structure which is relevant to some particular functionality; specifically we develop a biologically realistic model of the tadpole spinal cord. This model describes the self-organized process through which the anatomical structure of the full spinal cord of the tadpole develops. Electrophysiological modelling shows that this architecture can generate electrical activity corresponding to the experimentally observed swimming behaviour

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...

Spatiotemporal behavior and nonlinear dynamics in a phase conjugate resonator

The work described can be divided into two parts. The first part is an investigation of the transient behavior and stability property of a phase conjugate resonator (PCR) below threshold. The second part is an experimental and theoretical study of the PCR's spatiotemporal dynamics above threshold. The time-dependent coupled wave equations for four-wave mixing (FWM) in a photorefractive crystal, with two distinct interaction regions caused by feedback from an ordinary mirror, was used to model the transient dynamics of a PCR below threshold. The conditions for self-oscillation were determined and the solutions were used to define the PCR's transfer function and analyze its stability. Experimental results for the buildup and decay times confirmed qualitatively the predicted behavior. Experiments were carried out above threshold to study the spatiotemporal dynamics of the PCR as a function of Pragg detuning and the resonator's Fresnel number. The existence of optical vortices in the wavefront were identified by optical interferometry. It was possible to describe the transverse dynamics and the spatiotemporal instabilities by modeling the three-dimensional-coupled wave equations in photorefractive FWM using a truncated modal expansion approach

WORKING MEMORY AND TEMPORAL PATTERNS: THE IMPLICATIONS OF NEURAL POPULATIONS

Working memory, the ability to temporarily retain information which will be used to guidesubsequent behavior, is a central component of our cognitive abilities. Almost 40 years ago,electrophysiological experiments in monkeys established that persistent activity may be theneuronal substrate of working memory. Many computational models have been proposedin order to explain persistent activity, with recurrent connections playing a prominent rolein many of these. No model, however, has captured all the important features in workingmemory networks. This work presents three related models which seek to understand someof these features. In particular, the first model explores the formation of firing rate patternsduring the delay period of working memory tasks; the second model explores the dynamicsof working memory networks with reduced inhibition, and their possible role in epilepsy;the third model explores the formation of temporal sequences and closed loops of activity.The three models assume the existence of densely connected neural populations (such asminicolumns), which respond similarly to the same stimuli. Another common feature is therole of dynamic synapses: the first two models rely on synaptic facilitation, whereas thethird uses temporally asymmetric Hebbian plasticity