Neural activity inspired asymmetric basis function TV-NARX model for the identification of time-varying dynamic systems

Inspired by the unique neuronal activities, a new time-varying nonlinear autoregressive with exogenous input (TV-NARX) model is proposed for modelling nonstationary processes. The NARX nonlinear process mimics the action potential initiation and the time-varying parameters are approximated with a series of postsynaptic current like asymmetric basis functions to mimic the ion channels of the inter-neuron propagation. In the model, the time-varying parameters of the process terms are sparsely represented as the superposition of a series of asymmetric alpha basis functions in an over-complete frame. Combining the alpha basis functions with the model process terms, the system identification of the TV-NARX model from observed input and output can equivalently be treated as the system identification of a corresponding time-invariant system. The locally regularised orthogonal forward regression (LROFR) algorithm is then employed to detect the sparse model structure and estimate the associated coefficients. The excellent performance in both numerical studies and modelling of real physiological signals showed that the TV-NARX model with asymmetric basis function is more powerful and efficient in tracking both smooth trends and capturing the abrupt changes in the time-varying parameters than its symmetric counterparts

Harnessing Neural Dynamics as a Computational Resource

Researchers study nervous systems at levels of scale spanning several orders of magnitude, both in terms of time and space. While some parts of the brain are well understood at specific levels of description, there are few overarching theories that systematically bridge low-level mechanism and high-level function. The Neural Engineering Framework (NEF) is an attempt at providing such a theory. The NEF enables researchers to systematically map dynamical systems—corresponding to some hypothesised brain function—onto biologically constrained spiking neural networks. In this thesis, we present several extensions to the NEF that broaden both the range of neural resources that can be harnessed for spatiotemporal computation and the range of available biological constraints. Specifically, we suggest a method for harnessing the dynamics inherent in passive dendritic trees for computation, allowing us to construct single-layer spiking neural networks that, for some functions, achieve substantially lower errors than larger multi-layer networks. Furthermore, we suggest “temporal tuning” as a unifying approach to harnessing temporal resources for computation through time. This allows modellers to directly constrain networks to temporal tuning observed in nature, in ways not previously well-supported by the NEF. We then explore specific examples of neurally plausible dynamics using these techniques. In particular, we propose a new “information erasure” technique for constructing LTI systems generating temporal bases. Such LTI systems can be used to establish an optimal basis for spatiotemporal computation. We demonstrate how this captures “time cells” that have been observed throughout the brain. As well, we demonstrate the viability of our extensions by constructing an adaptive filter model of the cerebellum that successfully reproduces key features of eyeblink conditioning observed in neurobiological experiments. Outside the cognitive sciences, our work can help exploit resources available on existing neuromorphic computers, and inform future neuromorphic hardware design. In machine learning, our spatiotemporal NEF populations map cleanly onto the Legendre Memory Unit (LMU), a promising artificial neural network architecture for stream-to-stream processing that outperforms competing approaches. We find that one of our LTI systems derived through “information erasure” may serve as a computationally less expensive alternative to the LTI system commonly used in the LMU

Mathematical Modelling in Engineering & Human Behaviour 2018

This book includes papers in cross-disciplinary applications of mathematical modelling: from medicine to linguistics, social problems, and more. Based on cutting-edge research, each chapter is focused on a different problem of modelling human behaviour or engineering problems at different levels. The reader would find this book to be a useful reference in identifying problems of interest in social, medicine and engineering sciences, and in developing mathematical models that could be used to successfully predict behaviours and obtain practical information for specialised practitioners. This book is a must-read for anyone interested in the new developments of applied mathematics in connection with epidemics, medical modelling, social issues, random differential equations and numerical methods

Development and use of bioanalytical instrumentation and signal analysis methods for rapid sampling microdialysis monitoring of neuro-intensive care patients

This thesis focuses on the development and use of analysis tools to monitor brain injury patients. For this purpose, an online amperometric analyzer of cerebral microdialysis samples for glucose and lactate has been developed and optimized within the Boutelle group. The initial aim of this thesis was to significantly improve the signal-to-noise ratio and limit of detection of the assay to allow reliable quantification of the analytical data. The first approach was to re-design the electronic instrumentation of the assay. Printed-circuit boards were fabricated and proved very low noise, stable and much smaller than the previous potentiostats. The second approach was to develop generic data processing algorithms to remove three complex types of noise that commonly contaminate analytical signals: spikes, non-stationary ripples and baseline drift. The general strategy consisted in identifying the types of noise, characterising them, and subsequently subtracting them from the otherwise unprocessed data set. Spikes were effectively removed with 96.8% success and ripples were removed with minimal distortion of the signal resulting in an increased signal-to-noise ratio by up to 250%. This allowed reliable quantification of traces from ten patients monitored with the online microdialysis assay. Ninety-six spontaneous metabolic events in response to spreading depolarizations were resolved. These were characterized by a fall in glucose by -32.0 μM and a rise in lactate by +23.1 μM (median values) for over a 20-minute time-period. With frequently repeating events, this led to a progressive depletion of brain glucose. Finally, to improve the temporal coupling between the metabolic data and the electro-cortical signals, a flow-cell was engineered to integrate a potassium selective electrode into the microdialysate flow stream. With good stability over hours of continuous use and a 90% response time of 65 seconds, this flow cell was used for preliminary in vivo experiments the Max Planck Institute in Cologne

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Hilbert-Huang Transform: biosignal analysis and practical implementation

Any system, however trivial, is subjected to data analysis on the signals it produces. Over the last 50 years the influx of new techniques and expansions of older ones have allowed a number of new applications, in a variety of fields, to be analysed and to some degree understood. One of the industries that is benefiting from this growth is the medical field and has been further progressed with the growth of interdisciplinary collaboration. From a signal processing perspective, the challenge comes from the complex and sometimes chaotic nature of the signals that we measure from the body, such as those from the brain and to some degree the heart. In this work we will make a contribution to dealing with such systems, in the form of a recent time-frequency data analysis method, the Hilbert-Huang Transform (HHT), and extensions to it. This thesis presents an analysis of the state of the art in seizure and heart arrhythmia detection and prediction methods. We then present a novel real-time implementation of the algorithm both in software and hardware and the motivations for doing so. First, we present our software implementation, encompassing realtime capabilities and identifying elements that need to be considered for practical use. We then translated this software into hardware to aid real-time implementation and integration. With these implementations in place we apply the HHT method to the topic of epilepsy (seizures) and additionally make contributions to heart arrhythmias and neonate brain dynamics. We use the HHT and some additional algorithms to quantify features associated with each application for detection and prediction. We also quantify significance of activity in such a way as to merge prediction and detection into one framework. Finally, we assess the real-time capabilities of our methods for practical use as a biosignal analysis tool

Designing sound : procedural audio research based on the book by Andy Farnell

In procedural media, data normally acquired by measuring something, commonly described as sampling, is replaced by a set of computational rules (procedure) that defines the typical structure and/or behaviour of that thing. Here, a general approach to sound as a definable process, rather than a recording, is developed. By analysis of their physical and perceptual qualities, natural objects or processes that produce sound are modelled by digital Sounding Objects for use in arts and entertainments. This Thesis discusses different aspects of Procedural Audio introducing several new approaches and solutions to this emerging field of Sound Design.Em Media Procedimental, os dados os dados normalmente adquiridos através da medição de algo habitualmente designado como amostragem, são substituídos por um conjunto de regras computacionais (procedimento) que definem a estrutura típica, ou comportamento, desse elemento. Neste caso é desenvolvida uma abordagem ao som definível como um procedimento em vez de uma gravação. Através da análise das suas características físicas e perceptuais , objetos naturais ou processos que produzem som, são modelados como objetos sonoros digitais para utilização nas Artes e Entretenimento. Nesta Tese são discutidos diferentes aspectos de Áudio Procedimental, sendo introduzidas várias novas abordagens e soluções para o campo emergente do Design Sonoro

SciCADE 95: International conference on scientific computation and differential equations

This report consists of abstracts from the conference. Topics include algorithms, computer codes, and numerical solutions for differential equations. Linear and nonlinear as well as boundary-value and initial-value problems are covered. Various applications of these problems are also included