Decision region approximation by polynomials or neural networks

We give degree of approximation results for decision regions which are defined by polynomial and neural network parametrizations. The volume of the misclassified region is used to measure the approximation error, and results for the degree of L1 approximation of functions are used. For polynomial parametrizations, we show that the degree of approximation is at least 1, whereas for neural network parametrizations we prove the slightly weaker result that the degree of approximation is at least r, where r can be any number in the open interval (0, 1)

Autoregressive models for biomedical signal processing

Autoregressive models are ubiquitous tools for the analysis of time series in many domains such as computational neuroscience and biomedical engineering. In these domains, data is, for example, collected from measurements of brain activity. Crucially, this data is subject to measurement errors as well as uncertainties in the underlying system model. As a result, standard signal processing using autoregressive model estimators may be biased. We present a framework for autoregressive modelling that incorporates these uncertainties explicitly via an overparameterised loss function. To optimise this loss, we derive an algorithm that alternates between state and parameter estimation. Our work shows that the procedure is able to successfully denoise time series and successfully reconstruct system parameters. This new paradigm can be used in a multitude of applications in neuroscience such as brain-computer interface data analysis and better understanding of brain dynamics in diseases such as epilepsy

Path Signatures for Seizure Forecasting

Forecasting the state of a system from an observed time series is the subject of research in many domains, such as computational neuroscience. Here, the prediction of epileptic seizures from brain measurements is an unresolved problem. There are neither complete models describing underlying brain dynamics, nor do individual patients exhibit a single seizure onset pattern, which complicates the development of a `one-size-fits-all' solution. Based on a longitudinal patient data set, we address the automated discovery and quantification of statistical features (biomarkers) that can be used to forecast seizures in a patient-specific way. We use existing and novel feature extraction algorithms, in particular the path signature, a recent development in time series analysis. Of particular interest is how this set of complex, nonlinear features performs compared to simpler, linear features on this task. Our inference is based on statistical classification algorithms with in-built subset selection to discern time series with and without an impending seizure while selecting only a small number of relevant features. This study may be seen as a step towards a generalisable pattern recognition pipeline for time series in a broader context

Nonlinear energy-based control method for aircraft automatic landing systems

In this paper we present an aircraft automatic landing system using the nonlinear energy-based control method (NEM). This technique is based on aircraft energy management. NEM is based on the passivity-based control technique (PBC) and similar to Total Energy Control Systems (TECS). A physical interpretation of the NEM controller for the system is presented. We demonstrate that NEM provides insight into aircraft modeling and control while it achieves a satisfactory automatic flight control system (AFCS). The aircraft dynamics are presented via the energy functions. By modifying these functions, stabilization and tracking can be achieved. The automatic landing system is designed for a twin-engine civil aircraft, developed by the Group for Aeronautical Research and Technology in Europe (GARTEUR). Singular perturbation ideas are used to deal with the separation of the short-period and the phugoid dynamics. The proposed control laws appear to behave well even under extreme flight conditions