Objective. The P300 speller is a brain-computer interface (BCI) that can possibly restore communication abilities to individuals with severe neuromuscular disabilities, such as amyotrophic lateral sclerosis (ALS), by exploiting elicited brain signals in electroencephalography (EEG) data. However, accurate spelling with BCIs is slow due to the need to average data over multiple trials to increase the signal-to-noise ratio (SNR) of the elicited brain signals. Probabilistic approaches to dynamically control data collection have shown improved performance in non-disabled populations; however, validation of these approaches in a target BCI user population has not occurred. Approach. We have developed a data-driven algorithm for the P300 speller based on Bayesian inference that improves spelling time by adaptively selecting the number of trials based on the acute SNR of a user's EEG data. We further enhanced the algorithm by incorporating information about the user's language. In this current study, we test and validate the algorithms online in a target BCI user population, by comparing the performance of the dynamic stopping (DS) (or early stopping) algorithms against the current state-of-the-art method, static data collection, where the amount of data collected is fixed prior to online operation. Main results. Results from online testing of the DS algorithms in participants with ALS demonstrate a significant increase in communication rate as measured in bits/min (100-300%), and theoretical bit rate (100-550%), while maintaining selection accuracy. Participants also overwhelmingly preferred the DS algorithms. Significance. We have developed a viable BCI algorithm that has been tested in a target BCI population which has the potential for translation to improve BCI speller performance towards more practical use for communication.

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The research in this dissertation addresses reduced rank adaptive signal processing, with specific emphasis on the multistage Wiener filter (MWF). The MWF is a generalization of the classical Wiener filter that performs a stage-by-stage decomposition based on orthogonal projections. Truncation of this decomposition produces a reduced rank filter with many benefits, for example, improved performance. This dissertation extends knowledge of the MWF in four areas. The first area is rank and sample support compression. This dissertation examines, under a wide variety of conditions, the size of the adaptive subspace required by the MWF (i.e., the rank) as well as the required number of training samples. Comparisons are made with other algorithms such as the eigenvector-based principal components algorithm. The second area investigated in this dissertation concerns "soft stops", i.e., the insertion of diagonal loading into the MWF. Several methods for inserting loading into the MWF are described, as well as methods for choosing the amount of loading. The next area investigated is MWF rank selection. The MWF will outperform the classical Wiener filter when the rank is properly chosen. This dissertation presents six approaches for selecting MWF rank. The algorithms are compared to one another and an overall design space taxonomy is presented. Finally, as digital modelling capabilities become more sophisticated there is emerging interest in augmenting adaptive processing algorithms to incorporate prior knowledge. This dissertation presents two methods for augmenting the MWF, one based on linear constraints and a second based on non-zero weight vector initialization. Both approaches are evaluated under ideal and perturbed conditions. Together the research described in this dissertation increases the utility and robustness of the multistage Wiener filter. The analysis is presented in the context of adaptive array processing, both spatial array processing and space-time adaptive processing for airborne radar. The results, however, are applicable across the entire spectrum of adaptive signal processing applications. / Ph. D.

With autonomy becoming a reality for passenger cars, developing an autonomous for tractor-trailers is the next step for driverless roads. Tractor-trailers are heavy, large, and have a pivot joint between the tractor and trailer that makes the movement between the two more complicated. The purpose of the research presented here is to determine the best forward "looking" perception sensor that will see far out enough for the vehicle to stop in time to avoid hitting an object. In order to determine the best sensor, a review of previous sensors and autonomous vehicle sensors will be explored along with the various perception technology. Additionally, a simulation of a tractor-trailer stopping was created to determine the range necessary for a forward perception sensor and when jackknifing may occur. The best brake type for a tractor-trailer will be recommended as well. Finally, the best forward sensor and senor layout for an autonomous tractor-trailer is made based upon the simulation results for the stopping distance of a tractor-trailer. The work, however, is not fully complete. A discussion of the future work and validation of the sensors selected will give future research goals. / Master of Science / With autonomy becoming a reality for passenger cars, developing an autonomous for tractor-trailers is the next step for driverless roads. Tractor-trailers are heavy, large, and have a pivot joint between the tractor and trailer that makes the movement between the two more complicated. The purpose of the research presented here is to determine the best forward “looking” perception sensor that will see far out enough for the vehicle to stop in time to avoid hitting an object. In order to determine the best sensor, a review of previous sensors and autonomous vehicle sensors will be explored along with the various perception technology. Additionally, a simulation of a tractor-trailer stopping was created to determine the range necessary for a forward perception sensor and when jackknifing may occur. The best brake type for a tractor-trailer will be recommended as well. Finally, the best forward sensor and senor layout for an autonomous tractor trailer is made based upon the simulation results for the stopping distance of a tractor-trailer. The work, however, is not fully complete. A discussion of the future work and validation of the sensors selected will give future research goals.

This thesis consists of an introduction and five articles in the field of financial mathematics. The main topics of the papers comprise credit risk modelling, optimal stopping theory, and Dynkin games. An underlying theme in all of the articles is valuation of various financial instruments. Namely, Paper I deals with valuation of a game version of a perpetual American option where the parties disagree about the distributional properties of the underlying process, Papers II and III investigate pricing of default-sensitive contingent claims, Paper IV treats CVA (credit value adjustment) modelling for a portfolio consisting of American options, and Paper V studies a problem motivated by model calibration in pricing of corporate bonds. In each of the articles, we deal with an underlying stochastic process that is continuous in time and defined on some probability space. Namely, Papers I-IV treat stochastic processes with continuous paths, whereas Paper V assumes that the underlying process is a jump-diffusion with finite jump intensity. The information level in Paper I is the filtration generated by the stock value. In articles III and IV, we consider investors whose information flow is designed as a progressive enlargement with default time of the filtration generated by the stock price, whereas in Paper II the information flow is an initial enlargement. Paper V assumes that the default is a hitting time of the firm's value and thus the underlying filtration is the one generated by the process modelling this value. Moreover, in all of the papers the risk-free bonds are assumed for simplicity to have deterministic prices so that the focus is on the uncertainty coming from the stock price and default risk.

Accurate knowledge of stopping powers is essential for these for quantitative analysis and surface characterization of thin films using ion beam analysis (IBA). These values are also of interest in radiobiology and radiotherapy, and in ion- implantation technology where shrinking feature sizes puts high demands on the accuracy of range calculations. A theory that predicts stopping powers and ranges for all projectile-target combinations is needed. The most important database used to report the stopping powers is the SRIM/TRIM program developed by Ziegler and coworkers. However, other researchers report that at times, these values differ significantly from experimental values. In this study the stopping powers of Si, P and S ions have been measured in Ni, Cu, Ge and GaAs absorbers in the energy range ~ 2-10 MeV. For elemental films of Ni, Cu and Ge, the stopping of heavy ions was measured using a novel ERD (Elastic Recoil Detection) based technique. In which an elastically recoiled lighter atom is used to indirectly measure the energy of the incoming heavy ion using a surface barrier detector. In this way it was possible to reduce the damage and to improve the FWHM of the detector. The results were compared to SRIM-2000 predictions and other experimental measurements. A new technique derived from Molecular Beam Epitaxy (MBE) was developed to prepare stoichiometric GaAs films on thin carbon films for use in transmission ion beam experiments. The GaAs films were characterized using X-ray Photoelectron Spectroscopy (XPS) and Particle Induced X-ray Emission (PIXE). These films were used to investigate the stopping powers of energetic heavy ions in GaAs and to provide data for the calculation of Bethe-Bloch parameters in the framework of the Modified Bethe-Bloch theory. As a result of this study, stopping power data are available for the first time for Si and P ions in the energy range 2-10 MeV stopping in GaAs absorbers.

In Chapter 1 the classical secretary problem is introduced. Chapters 2 and 3 are variations of this problem. Chapter 2, discusses the problem of maximizing the probability of stopping with one of the two highest values in a Bernoulli random walk with arbitrary parameter p and finite time horizon n. The optimal strategy (continue or stop) depends on a sequence of threshold values (critical probabilities) which has an oscillating pattern. Several properties of this sequence have been proved by Dr. Allaart. Further properties have been recently proved. In Chapter 3, a gambler will observe a finite sequence of continuous random variables. After he observes a value he must decide to stop or continue taking observations. He can play two different games A) Win at the maximum or B) Win within a proportion of the maximum. In the first section the sequence to be observed is independent. It is shown that for each n>1, theoptimal win probability in game A is bounded below by (1-1/n)^{n-1}. It is accomplished by reducing the problem to that of choosing the maximum of a special sequence of two-valued random variables and applying the sum-the-odds theorem of Bruss (2000). Secondly, it is assumed the sequence is i.i.d. The best lower bounds are provided for the winning probabilities in game B given any continuous distribution. These bounds are the optimal win probabilities of a game A which was examined by Gilbert and Mosteller (1966).

This study presents a procedure for the estimation of stopping behavior of industrial robots with a trained neural network. This trained network is presented as a single channel in a redundant architecture for safety control applications, where its potential for future integration with an analytical model of robot stopping is discussed. Basic physical relations for simplified articulated manipulators are derived, which motivate a choice of quantities to predict robot stopping behavior and inform the training and testing of a network for prediction of stopping distances and times. Robot stopping behavior is considered in the context of relevant standards ISO 10218-1, ISO/TS 15066 and IS0 13849-1, which inform the definitions for safety related stopping distances and times used in this study. Prior work on the estimation of robot stopping behavior is discussed alongside applications of machine learning to the broader field of industrial robotics, and particularly to the cases of prediction of forward and inverse kinematics with trained networks. A state-driven data collection program is developed to perform repeated stopping experiments for a controlled stop on path within a specified sampling domain. This program is used to collect data for a simulated and real robot system. Special attention is given to the identification of meaningful stopping times, which includes the separation of stopping into pre-deceleration and post-deceleration phases. A definition is provided for stopping of a robot in a safety context, based on the observation that residual motion over short distances (less than 1 mm) and at very low velocities (less than 1 mm/s) is not relevant to robot safety. A network architecture and hyperparameters are developed for the prediction of stopping distances and times for the first three joints of the manipulator without the inclusion of payloads. The result is a dual-network structure, where stopping distance predictions from the distance prediction network serve as inputs to the stopping time prediction network. The networks are validated on their capacity to interpolate and extrapolate predictions of robot stopping behavior in the presence of initial conditions not included in the training and testing data. A method is devised for the calculation of prediction errors for training training, testing and validation data. This method is applied both to interpolation and extrapolation to new initial velocity and positional conditions of the manipulator. In prediction of stopping distances and times, the network is highly successful at interpolation, resulting in comparable or nominally higher errors for the validation data set when compared to the errors for training and testing data. In extrapolation to new initial velocity and positional conditions, notably higher errors in the validation data predictions are observed for the networks considered. Future work in the areas of predictions of stopping behavior with payloads and tooling, further applications to collaborative robotics, analytical models of stopping behavior, inclusion of additional stopping functions, use of explainable AI methods and physics-informed networks are discussed. / Master of Science / As the uses for industrial robots continue to grow and expand, so do the need for robust safety measures to avoid, control, or limit the risks posed to human operators and collaborators. This is exemplified by Isaac Asimov's famous first law of robotics - "A robot may not injure a human being, or, through inaction, allow a human being to come to harm." As applications for industrial robots continue to expand, it is beneficial for robots and human operators to collaborate in work environments without fences. In order to ethically implement such increasingly complex and collaborative industrial robotic systems, the ability to limit robot motion with safety functions in a predictable and reliable way (as outlined by international standards) is paramount. In the event of either a technical failure (due to malfunction of sensors or mechanical hardware) or change in environmental conditions, it is important to be able to stop an industrial robot from any position in a safe and controlled manner. This requires real-time knowledge of the stopping distance and time for the manipulator. To understand stopping distances and times reliability, multiple independent methods can be used and compared to predict stopping behavior. The use of machine learning methods is of particular interest in this context due to their speed of processing and the potential for basis on real recorded data. In this study, we will attempt to evaluate the efficacy of machine learning algorithms to predict stopping behavior and assess their potential for implementation alongside analytical models. A reliable, multi-method approach for estimating stopping distances and times could also enable further methods for safety in collaborative robotics such as Speed and Separation Monitoring (SSM), which monitors both human and robot positions to ensure that a safe stop is always possible. A program for testing and recording the stopping distances and times for the robot is developed. As stopping behavior varies based on the positions and speeds of the robot at the time of stopping, a variety of these criteria are tested with the robot stopping program. This data is then used to train an artificial neural network, a machine learning method that mimics the structure of human and animal brains to learn relationships between data inputs and outputs. This network is used to predict both the stopping distance and time of the robot. The network is shown to produce reasonable predictions, especially for positions and speeds that are intermediate to those used to train the network. Future improvements are suggested and a method is suggested for use of stopping distance and time quantities in robot safety applications.

La famille des matériaux semiconducteurs III-N présente des propriétés adéquates pour diversesapplications que ce soit dans le domaine de l’optique ou de l’électronique. Certaines de ces applicationsconsistent à intégrer ces matériaux dans des environnements hostiles et notamment soumis à l’actiond’ions lourds à différentes énergies. Lors de cette thèse, le travail consistait tout d’abord à comprendrel’évolution microstructurale sous irradiation du substrat alpha-Al2O3, puis du film mince GaN, afin d’établirun profil de l’évolution de l’endommagement en fonction de la profondeur. Un comportement assezsimilaire concernant l’évolution des paramètres de maille a été observé pour les deux matériaux. Dansla direction parallèle à la trajectoire du faisceau d’ions, une importante augmentation du paramètre demaille a été mise en évidence tandis que peu de variations ont été relevées perpendiculairement à latrajectoire du faisceau d’ions. Les formations de couche amorphe pour l’alpha-Al2O3 et de couche fortementendommagée pour le GaN ont été observées en surface. Les épaisseurs de ces couches augmentent enfonction de la fluence, associé à l’augmentation des contraintes résiduelles au sein du matériau. Al’aide d’hypothèses et des différents résultats obtenus, deux profils d’endommagement en profondeuront été proposés. D’autre part, la nanoindentation a montré que les paramètres de dureté et de moduled’élasticité évoluent fortement sous irradiation en fonction de la fluence. / Nitride semiconductors are attractive materials for the development of optical and electronic devices.Some of these applications can expose materials to extreme environments and especially radiation ofheavy ions at different energies. In this thesis, the study focused first on behaviour evolution underirradiation of alpha-Al2O3 and then of GaN thin film, in order to establish a profile of damage evolution asfunction of the depth. Concerning lattice parameter, a similar behaviour was observed for both materials.An important increase of lattice parameter parallel to ion beam was highlighted while few variations wasnoted for the lattice parameter perpendicular to ion beam. Formation of amorphous layer for alpha-Al2O3and highly disordered layer for GaN were observed in surface. Layers thicknesses increase as functionof the fluence with an increase of residual stresses in material. Using different results and assumptions,two damage profiles as function of the depth have been proposed. In addition, nanoindentation hasshown hardness and modulus of elasticity parameter evolve highly under irradiation as function of thefluence.

Ill-posed inverse problems have wide applications in many fields such as oceanography, signal processing, machine learning, biomedical imaging, remote sensing, geophysics, and others. In this dissertation, we address the problem of solving unstable operator equations with iteratively regularized Newton-type algorithms. Important practical questions such as selection of regularization parameters, construction of generating (filtering) functions based on a priori information available for different models, algorithms for stopping rules and error estimates are investigated with equal attention given to theoretical study and numerical experiments.