The Fourier analysis of saccadic eye movements

This thesis examines saccadic eye movements in the frequency domain and develops sensitive tools for characterising their dynamics. It tests a variety of saccade models and provides the first strong empirical evidence that saccades are time-optimal. By enabling inferences on the neural command, it also allows for better clinical differentiation of abnormalities and the evaluation of putative mechanisms for the development of congenital nystagmus. Chapters 3 and 4 show how Fourier transforms reveal sharp minima in saccade frequency spectra, which are robust to instrument noise. The minima allow models based purely on the output trajectory, purely on the neural input, or both, to be directly compared and distinguished. The standard, most commonly accepted model based on bang-bang control theory is discounted. Chapter 5 provides the first empirical evidence that saccades are time-optimal by demonstrating that saccade bandwidths overlap across amplitude onto a single slope at high frequencies. In Chapter 6, the overlap also allows optimal (Wiener) filtering in the frequency domain without a priori assumptions. Deconvolution of the aggregate neural driving signal is then possible for current models of the oculomotor plant. The final two chapters apply these Fourier techniques to the quick phases of physiological (optokinetic) nystagmus and of pathological (congenital) nystagmus. These quick phases are commonly assumed to be saccadic in origin. This assumption is thoroughly tested and found to hold, but with subtle differences implying that the smooth pursuit system interacts with the saccade system during the movement. This interaction is taken into account in Chapter 8 in the assessment of congenital nystagmus quick phases, which are found to be essentially normal. Congenital nystagmus models based on saccadic abnormalities are appraised

Problems In High-Dimensional Statistics And Applications In Genomics, Metabolomics And Microbiomics

With rapid technological advancements in data collection and processing, massive large-scale and complex datasets are widely available nowadays in diverse research fields such as genomics, metabolomics and microbiomics. The analysis of large datasets with complex structures poses significant challenges and calls for new theory and methodology. In this dissertation, we address several high-dimensional statistical problems, and develop novel statistical theory and methods for analyzing datasets generated from such data-driven interdisciplinary research. In the first part of the dissertation (Chapter 1 and Chapter 2), motivated by the ubiquitous availability of high-dimensional datasets with binary outcomes and the need of powerful methods for analyzing them, we develop novel bias-correction techniques for inferring low-dimensional components or functionals of high-dimensional objects, and propose computationally efficient procedures for parameter estimation, global and simultaneous hypotheses testing, and confidence intervals in high-dimensional logistic regression(s). The theoretical properties of the proposed methods, including their minimax optimality, are carefully studied. We show empirically the effectiveness and stability of our methods in extracting useful information from high-dimensional noisy datasets. By applying our methods to a real metabolomic dataset, we unveil the associations between fecal metabolites and pediatric Crohn’s disease as well as the effects of dietary treatment on such associations (Chapter 1); by analyzing a real genetic dataset, we obtain novel insights about the shared genetic architecture between ten pediatric autoimmune diseases (Chapter 2). In the second part of the dissertation (Chapter 3 and Chapter 4), motivated by important questions in large-scale human microbiome and metagenomic research, as well as other applications, we propose a novel permuted monotone matrix model and build up new principles, theories and methods for inferring the underlying model parameters. In particular, we focus on two interrelated problems, namely, optimal permutation recovery from noisy observations (Chapter 3), and extreme value estimation in permuted low-rank monotone matrices (Chapter 4), and propose an efficient spectral approach to attack these problems. The proposed methods are rigorously justified by statistical theory, including their convergence rates and the minimax optimality. Numerical experiments through simulated and synthetic microbiome metagenomic data are presented to show the superiority of the proposed methods over the alternatives. The methods are applied to two real datasets to compare the growth rates of gut bacteria between inflammatory bowel disease patients and/or normal controls

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

Wavelet Theory

The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior

Nineteenth Annual Conference on Manual Control

No abstract availabl

Contributions to Structural Modeling and Estimation

The first chapter of my thesis develops and estimates a dynamicstructural partial equilibrium model of schooling and workdecisions.  The estimated model explicitly accounts for thesimultaneous choice of enrolling in school and working.  It alsoallows for endogenous leisure choices, intertemporalnonseparabilities in preferences, aggregate skill specificproductivity shocks, aggregate consumption price effects, andindividual heterogeneity.  Times spent on schooling, working, andleisure are treated as continuous choice variables.  The estimatedmodel is solved and two counterfactual simulation exercises areperformed.  The first is the case where a subsidy is given toindividuals who enroll in school and do not participate in the labormarket.  The second is the case where the demands of the schoolcurriculum are increased so that a young man enrolled in schoolnecessarily spends more time studying.   The conclusion is that thelatter policy is more effective in enhancing educationalachievements and future wages.The second chapter of my thesis develops a semiparametric estimatorfor a dynamic nonlinear single index panel data model.  Flexibilityof the model is achieved by assuming that the index function isunknown.  Flexibility in individual heterogeneity is achieved byassuming that the individual effect is an unknown function of someobservable random variable.  The paper proposes an algorithm thatestimates each of the finite and infinite dimensional parameters. Inparticular, the full data generating process is estimated.  This isimportant if the predicted outcomes are used as plug-in estimators,as in the multistage estimation of dynamic structural models.The final chapter of my thesis develops a powerful new algorithm tosolve single object first price auctions where bidders drawindependent private values from heterogeneous distributions.  Thealgorithm allows for the scenario in which groups of symmetric andasymmetric bidders may collude, and for the auctioneer to set areserve price.  The paper also provides operational univariatequadratures to evaluate the probabilities of winning as well as theexpected revenues for the bidders and the auctioneer.  The expectedrevenue function is used to the compute optimal reserve underasymmetric environments.</p