State estimation and tracking (also known as filtering) is an integral part of any system performing inference in a partially observable environment, whether it is a robot that is gauging an environment through noisy sensors or a natural language processing system that is trying to model a sequence of characters without full knowledge of the syntactic or semantic state of the text. In this work, we develop a framework for constructing state estimators. The framework consists of a model class, referred to as predictive state models, and a learning algorithm, referred to as two-stage regression. Our framework is based on two key concepts: (1) predictive state: where our belief about the latent state of the environment is represented as a prediction of future observation features and (2) instrumental regression: where features of previous observations are used to remove sampling noise from future observation statistics, allowing for unbiased estimation of system dynamics. These two concepts allow us to develop efficient and tractable learning methods that reduce the unsupervised problem of learning an environment model to a supervised regression problem: first, a regressor is used to remove noise from future observation statistics. Then another regressor uses the denoised observation features to estimate the dynamics of the environment. We show that our proposed framework enjoys a number of theoretical and practical advantages over existing methods, and we demonstrate its efficacy in a prediction setting, where the task is to predict future observations, as well as a control setting, where the task is to optimize a control policy via reinforcement learning.

The close-by orbits of the ongoing Juno mission allow measuring with unprecedented accuracy Jupiter's low-degree even gravity moments J(2), J(4), J(6), and J(8). These can be used to better determine Jupiter's internal density profile and constrain its core mass. Yet the largest unknown on these gravity moments comes from the effect of differential rotation, which gives a degree of freedom unaccounted for by internal structure models. Here considering a wide range of possible internal flow structures and dynamical considerations, we provide upper bounds to the effect of dynamics (differential rotation) on the low-degree gravity moments. In light of the recent Juno gravity measurements and their small uncertainties, this allows differentiating between the various models suggested for Jupiter's internal structure.

>Magister Scientiae - MSc / There exists an extensive statistics literature dealing with non-parametric deconvolution, the estimation of the underlying population probability density when sample values are subject to measurement errors. In parametric deconvolution, on the other hand, the data are known to be from a specific distribution. In this case the parameters of the distribution can be estimated by e.g. maximum likelihood. In realistic cases the measurement errors may be heteroscedastic and there may be unknown parameters associated with the distribution. The specific realistic case is investigated in which the measurement error standard deviation is proportional to the true sample values. In this case it is shown that the method of moment’s estimation is particularly simple. Estimation by maximum likelihood is computationally very expensive, since numerical integration needs to be performed for each data point, for each evaluation of the likelihood function. Method of moment’s estimation sometimes fails to give physically meaningful estimates. The origin of this problem lies in the large sampling variations of the third moment. Possible remedies are considered. Due to the fact that a convolution integral needed to be calculated for each data point, and that this has to be repeated for each iteration towards the solution, maximum likelihood computing cost is very high. New preliminary work suggests that saddle point approximations could sometimes be used for the convolution integrals. This allows much larger datasets to be dealt with. Application of the theory is illustrated with simulation and real data.

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An optical study of Mn and Mo isotopes has been performed in two contrasting regions of the nuclear chart. Collinear laser spectroscopic methods were employed using the Ion Guide Separator On-Line (IGISOL) at the University of Jyväskylä, Finland. Optical pumping in an ion-trap with the use of frequency quadrupled titanium sapphire lasers, greatly improved the efficiency of the spectroscopy performed.For the first time, the change in mean-square charge radius was determined for ground and isomeric states in 50-56Mn with a sharp shell closure seen across N = 28. Nuclear quadrupole moments in 50m,53,54,56Mn were also extracted, displaying trends similar to those of the charge radii. Newly extracted hyperfine structures and isotope shifts of 90-92,94-98,100,102-106,108Mo span the N = 50 shell closure and well-known N = 60 shape change. Unlike the Z = 38 - 41 isotopic chains, Mo exhibits a smooth increase in mean-square charge radius, with no sudden onset of deformation at N = 60. These measurements signify the end point of this strongly deformed A ~ 100 region in both Z and N. In the Z ~ 40 region, the charge radii follow the trends in the mass measurements near perfectly. However, in the Mn measurements a clear disparity between the mass and charge radii measurements is seen across the N = 28 magic shell closure. The absence of any shell effects in the Mn mass measurements show the importance of charge radii measurements, with pertinent implications for future investigations in the N = 40 region. Additionally, a portable data acquisition system for laser spectroscopy has been successfully tested. It is based on the LabJack system which will directly interface to a USB connection. It is able to register individual photons from amplified and converted photomultiplier tube signals (with bunched or continuous ion beams). The device drives a Cooknell voltage supply, which steps the voltage across the laser-ion interaction region. The introduction of an accurate 100 ms time window into the LabJack system has enabled a precise photon detection system for future off-line testing and on-line use. Further to this, a new method of locating hyperfine resonances has been introduced into our spectroscopy.

The search for physics beyond the Standard Model has been a main focus of the scientific community for several decades. Unknown physics in the form of new interactions violating the simultaneous reversal of charge and parity symmetries (CP) would, for example, provide a significant step towards understanding the baryon matter-antimatter asymmetry observed in the Universe. Such parameters are predicted to also manifest themselves in atomic and molecular systems in the form of both: permanent electric dipole moments and nuclear charge distribution asymmetries described by the nuclear Schiff moment. Both can be measured to a high degree of precision in modern experiments, allowing us to place stringent limits on parameters appearing in new fundamental theories. The Cold Molecule Nuclear Time Reversal Experiment (CeNTREX) is the latest approach to probing these effects. CeNTREX is a molecular beam experiment that uses thallium fluoride (²⁰⁵Tl⁹F) as its test species to measure energy shifts induced by the interaction of thallium's nuclear Schiff moment. It does so by performing nuclear magnetic resonance using a separate oscillatory fields technique. The precision of this measurement is dictated by the free precession time and the number of interrogated molecules, and is significantly enhanced by thallium fluoride's inherent properties. Employing novel methods, CeNTREX strives to achieve significant improvements to limits placed on the fundamental parameters. One such method is rotational cooling. It was thoroughly analyzed, simulated and experimentally confirmed - with the help of optical and microwave pumping, we collapsed the initial Boltzmann distribution of molecules amongst their rotational states into one chosen hyperfine state of the ground rotational state manifold. The efficiency of this process depends on multiple factors, the most crucial being the approach towards dark state destabilization and remixing. After careful investigation, we chose the most appropriate method and devised an efficient rotational cooling scheme. Experimental confirmation showed an enhancement factor of r𝑓23.70±1.13, very close to our theoretical predictions. This allows us to conclude that CeNTREX should provide a 2500-fold improvement over the current best measurements of the nuclear Schiff moment in thallium nucleus.

This dissertation proposes the development of a new quantile-based generalized logistic distribution GLDQB, by using the quantile function of the generalized logistic distribution (GLO) as the basic building block. This four-parameter distribution is highly flexible with respect to distributional shape in that it explains extensive levels of skewness and kurtosis through the inclusion of two shape parameters. The parameter space as well as the distributional shape properties are discussed at length. The distribution is characterized through its -moments and an estimation algorithm is presented for estimating the distribution’s parameters with method of -moments estimation. This new distribution is then used to fit and approximate the probability of a data set. / Dissertation (MSc)--University of Pretoria, 2014. / Statistics / MSc / Unrestricted

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