Statistical models for natural sounds

It is important to understand the rich structure of natural sounds in order to solve important tasks, like automatic speech recognition, and to understand auditory processing in the brain. This thesis takes a step in this direction by characterising the statistics of simple natural sounds. We focus on the statistics because perception often appears to depend on them, rather than on the raw waveform. For example the perception of auditory textures, like running water, wind, fire and rain, depends on summary-statistics, like the rate of falling rain droplets, rather than on the exact details of the physical source. In order to analyse the statistics of sounds accurately it is necessary to improve a number of traditional signal processing methods, including those for amplitude demodulation, time-frequency analysis, and sub-band demodulation. These estimation tasks are ill-posed and therefore it is natural to treat them as Bayesian inference problems. The new probabilistic versions of these methods have several advantages. For example, they perform more accurately on natural signals and are more robust to noise, they can also fill-in missing sections of data, and provide error-bars. Furthermore, free-parameters can be learned from the signal. Using these new algorithms we demonstrate that the energy, sparsity, modulation depth and modulation time-scale in each sub-band of a signal are critical statistics, together with the dependencies between the sub-band modulators. In order to validate this claim, a model containing co-modulated coloured noise carriers is shown to be capable of generating a range of realistic sounding auditory textures. Finally, we explored the connection between the statistics of natural sounds and perception. We demonstrate that inference in the model for auditory textures qualitatively replicates the primitive grouping rules that listeners use to understand simple acoustic scenes. This suggests that the auditory system is optimised for the statistics of natural sounds

A Statistical Perspective of the Empirical Mode Decomposition

This research focuses on non-stationary basis decompositions methods in time-frequency analysis. Classical methodologies in this field such as Fourier Analysis and Wavelet Transforms rely on strong assumptions of the underlying moment generating process, which, may not be valid in real data scenarios or modern applications of machine learning. The literature on non-stationary methods is still in its infancy, and the research contained in this thesis aims to address challenges arising in this area. Among several alternatives, this work is based on the method known as the Empirical Mode Decomposition (EMD). The EMD is a non-parametric time-series decomposition technique that produces a set of time-series functions denoted as Intrinsic Mode Functions (IMFs), which carry specific statistical properties. The main focus is providing a general and flexible family of basis extraction methods with minimal requirements compared to those within the Fourier or Wavelet techniques. This is highly important for two main reasons: first, more universal applications can be taken into account; secondly, the EMD has very little a priori knowledge of the process required to apply it, and as such, it can have greater generalisation properties in statistical applications across a wide array of applications and data types. The contributions of this work deal with several aspects of the decomposition. The first set regards the construction of an IMF from several perspectives: (1) achieving a semi-parametric representation of each basis; (2) extracting such semi-parametric functional forms in a computationally efficient and statistically robust framework. The EMD belongs to the class of path-based decompositions and, therefore, they are often not treated as a stochastic representation. (3) A major contribution involves the embedding of the deterministic pathwise decomposition framework into a formal stochastic process setting. One of the assumptions proper of the EMD construction is the requirement for a continuous function to apply the decomposition. In general, this may not be the case within many applications. (4) Various multi-kernel Gaussian Process formulations of the EMD will be proposed through the introduced stochastic embedding. Particularly, two different models will be proposed: one modelling the temporal mode of oscillations of the EMD and the other one capturing instantaneous frequencies location in specific frequency regions or bandwidths. (5) The construction of the second stochastic embedding will be achieved with an optimisation method called the cross-entropy method. Two formulations will be provided and explored in this regard. Application on speech time-series are explored to study such methodological extensions given that they are non-stationary

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics

Modelling and control techniques for multiphase electric drives: a phase variable approach

Multiphase electric drives are today one of the most relevant research topics for the electrical engineering scientific community, thanks to the many advantages they offer over standard three-phase solutions (e.g., power segmentation, fault-tolerance, optimized performances, torque/power sharing strategies, etc...). They are considered promising solutions in many application areas, like industry, traction and renewable energy integration, and especially in presence of high-power or high-reliability requirements. However, contrarily to the three-phase counterparts, multiphase drives can assume a wider variety of different configurations, concerning both the electrical machine (e.g., symmetrical/asymmetrical windings disposition, concentrated/distributed windings, etc...) and the overall drive topology (e.g., single-star configuration, multiple-star configuration, open-end windings, etc…). This aspect, together with the higher number of variables of the system, can make their analysis and control more challenging, especially when dealing with reconfigurable systems (e.g., in post-fault scenarios). This Ph.D. thesis is focused on the mathematical modelling and on the control of multiphase electric drives. The aim of this research is to develop a generalized model-based approach that can be used in multiple configurations and scenarios, requiring minimal reconfigurations to deal with different machine designs and/or different converter topologies, and suitable both in healthy and in faulty operating conditions. Standard field-oriented approaches for the analysis and control of multiphase drives, directly derived as extensions of the three-phase equivalents, despite being relatively easy and convenient solutions to deal with symmetrical machines, may suffer some hurdles when applied to some asymmetrical configurations, including post-fault layouts. To address these issues, a different approach, completely derived in the phase variable domain, is here developed. The method does not require any vector space decomposition or rotational transformation but instead explicitly considers the mathematical properties of the multiphase machine and the effects of the drive topology (which typically introduces some constraints on the system variables). In this thesis work, the proposed approach is particularized for multiphase permanent magnet synchronous machines and for multiphase synchronous reluctance machines. All the results are obtained through rigorous mathematical derivations, and are supported and validated by both numerical analysis and experimental tests. As proven considering many different configurations and scenarios, the main benefits of the proposed methodology are its generality and flexibility, which make it a viable alternative to standard modelling and control algorithms

Differential-Algebraic Equations

Differential-Algebraic Equations (DAE) are today an independent field of research, which is gaining in importance and becoming of increasing interest for applications and mathematics itself. This workshop has drawn the balance after about 25 years investigations of DAEs and the research aims of the future were intensively discussed

Guided Matching Pursuit and its Application to Sound Source Separation

In the last couple of decades there has been an increasing interest in the application of source separation technologies to musical signal processing. Given a signal that consists of a mixture of musical sources, source separation aims at extracting and/or isolating the signals that correspond to the original sources. A system capable of high quality source separation could be an invaluable tool for the sound engineer as well as the end user. Applications of source separation include, but are not limited to, remixing, up-mixing, spatial re-configuration, individual source modification such as filtering, pitch detection/correction and time stretching, music transcription, voice recognition and source-specific audio coding to name a few. Of particular interest is the problem of separating sources from a mixture comprising two channels (2.0 format) since this is still the most commonly used format in the music industry and most domestic listening environments. When the number of sources is greater than the number of mixtures (which is usually the case with stereophonic recordings) then the problem of source separation becomes under-determined and traditional source separation techniques, such as “Independent Component Analysis” (ICA) cannot be successfully applied. In such cases a family of techniques known as “Sparse Component Analysis” (SCA) are better suited. In short a mixture signal is decomposed into a new domain were the individual sources are sparsely represented which implies that their corresponding coefficients will have disjoint (or almost) disjoint supports. Taking advantage of this property along with the spatial information within the mixture and other prior information that could be available, it is possible to identify the sources in the new domain and separate them by going back to the time domain. It is a fact that sparse representations lead to higher quality separation. Regardless, the most commonly used front-end for a SCA system is the ubiquitous short-time Fourier transform (STFT) which although is a sparsifying transform it is not the best choice for this job. A better alternative is the matching pursuit (MP) decomposition. MP is an iterative algorithm that decomposes a signal into a set of elementary waveforms called atoms chosen from an over-complete dictionary in such a way so that they represent the inherent signal structures. A crucial part of MP is the creation of the dictionary which directly affects the results of the decomposition and subsequently the quality of source separation. Selecting an appropriate dictionary could prove a difficult task and an adaptive approach would be appropriate. This work proposes a new MP variant termed guided matching pursuit (GMP) which adds a new pre-processing step into the main sequence of the MP algorithm. The purpose of this step is to perform an analysis of the signal and extract important features, termed guide maps, that are used to create dynamic mini-dictionaries comprising atoms which are expected to correlate well with the underlying signal structures thus leading to focused and more efficient searches around particular supports of the signal. This algorithm is accompanied by a modular and highly flexible MATLAB implementation which is suited to the processing of long duration audio signals. Finally the new algorithm is applied to the source separation of two-channel linear instantaneous mixtures and preliminary testing demonstrates that the performance of GMP is on par with the performance of state of the art systems

Elementary approaches to microbial growth rate maximisation

This thesis, called Elementary approaches to microbial growth rate maximisation, reports on a theoretical search for principles underlying single cell growth, in particular for microbial species that are selected for fast growth rates. First, the optimally growing cell is characterised in terms of its elementary modes. We prove an extremum principle: a cell that maximises a metabolic rate uses few Elementary Flux Modes (EFMs, the minimal pathways that support steady-state metabolism). The number of active EFMs is bounded by the number of growth-limiting constraints. Later, this extremum principle is extended in a theory that explicitly accounts for self-fabrication. For this, we had to define the elementary modes that underlie balanced self-fabrication: minimal self-supporting sets of expressed enzymes that we call Elementary Growth Modes (EGMs). It turns out that many of the results for EFMs can be extended to their more general self-fabrication analogue. Where the above extremum principles tell us that few elementary modes are used by a rate-maximising cell, it does not tell us how the cell can find them. Therefore, we also search for an elementary adaptation method. It turns out that stochastic phenotype switching with growth rate dependent switching rates provides an adaptation mechanism that is often competitive with more conventional regulatory-circuitry based mechanisms. The derived theory is applied in two ways. First, the extremum principles are used to review the mathematical fundaments of all optimisation-based explanations of overflow metabolism. Second, a computational tool is presented that enumerates Elementary Conversion Modes. These elementary modes can be computed for larger networks than EFMs and EGMs, and still provide an overview of the metabolic capabilities of an organism

Unsupervised methods for large-scale, cell-resolution neural data analysis

In order to keep up with the volume of data, as well as the complexity of experiments and models in modern neuroscience, we need scalable and principled analytic programmes that take into account the scientific goals and the challenges of biological experiments. This work focuses on algorithms that tackle problems throughout the whole data analysis process. I first investigate how to best transform two-photon calcium imaging microscopy recordings – sets of contiguous images – into an easier-to-analyse matrix containing time courses of individual neurons. For this I first estimate how the true fluorescence signal gets transformed by tissue artefacts and the microscope setup, by learning the parameters of a realistic physical model from recorded data. Next, I describe how individual neural cell bodies may be segmented from the images, based on a cost function tailored to neural characteristics. Finally, I describe an interpretable non-linear dynamical model of neural population activity, which provides immediate scientific insight into complex system behaviour, and may spawn a new way of investigating stochastic non-linear dynamical systems. I hope the algorithms described here will not only be integrated into analytic pipelines of neural recordings, but also point out that algorithmic design should be informed by communication with the broader community, understanding and tackling the challenges inherent in experimental biological science