This thesis explores the possibility of using parallel algorithms to calculate the dynamics of driven quantum systems prevalent in atomic physics. In this process, new as well as existing algorithms are considered. The thesis is split into three parts. In the first part an attempt is made to develop a new formalism of the time dependent Schroedinger equation (TDSE) in the hope that the new formalism could lead to a parallel algorithm. The TDSE is written as an eigenvalue problem, the ground state of which represents the solution to the original TDSE. Even though mathematically sound and correct, it turns out the ground state of this eigenvalue problem cannot be easily found numerically, rendering the original hope a false one. In the second part we borrow a Bayesian global optimisation method from the machine learning community in an effort to find the optimum conditions in different systems quicker than textbook optimisation algorithms. This algorithm is specifically designed to find the optimum of expensive functions, and is used in this thesis to 1. maximise the electron yield of hydrogen, 2. maximise the asymmetry in the photo-electron angular distribution of hydrogen, 3. maximise the higher harmonic generation yield within a certain frequency range, 4. generate short pulses via combining higher harmonics generated by hydrogen. In the last part, the phenomenon of dynamic interference (temporal equivalent of the double-slit experiment) is discussed. The necessary conditions are derived from first principles and it is shown where some of the previous analytical and numerical studies have gone wrong; it turns out the choice of gauge plays a crucial role. Furthermore, a number of different scenarios are presented where interference in the photo-electron spectrum is expected to occur.

Gaussian processes (GPs) as a Bayesian regressionmethod have been around for some time. Since proven advant-ageous for sparse and noisy data, we explore the potential ofGaussian process regression (GPR) as a tool for estimating radiochannel characteristics.Specifically, we consider the estimation of a time-varyingcontinuous transfer function from discrete samples. We introducethe basic theory of GPR, and employ both GPR and its deep-learning counterpart deep Gaussian process regression (DGPR)for estimation. We find that both perform well, even with fewsamples. Additionally, we relate the channel coherence bandwidthto a GPR hyperparameter called length-scale. The results show atendency towards proportionality, suggesting that our approachoffers an alternative way to approximate the coherence band-width. / Gaussiska processer (Gaussian processes,GPs) har länge använts för Bayesiansk regression. Då de visat sigfördelaktiga för gles och brusig data utforskar vi möjligheternaför GP-regression (Gaussian process regression, GPR) som ettverktyg för att estimera egenskaper hos radiokanaler.Isynnerhetbetraktasskattningaventidsvarierandeöverföringsfunktion utifrån diskreta samplingar. Vi presenterarden grundläggande teorin kring GPR, och använder både GPRoch dess djupinlärningsmotsvarighet DGPR (deep Gaussian pro-cess regression) för skattning. Båda ger goda resultat, även när samplingarna är få. Utöver detta så relaterar vi koherens-bandbredden hos en radiokanal till en hyperparameter i GPR-modellen. Resultaten visar på en tendens till proportionalitet,vilket antyder att vår metod kan användas som ett alternativt sätt att approximera koherensbandbredden. / Kandidatexjobb i elektroteknik 2020, KTH, Stockholm

Thesis (MSc (Physics))--University of Stellenbosch, 2005. / It was Wigner that in the 1950’s first introduced the idea of modelling physical reality with an ensemble of random matrices while studying the energy levels of heavy atomic nuclei. Since then, the field of Random Matrix Theory has grown tremendously, with applications ranging from fluctuations on the economic markets to M-theory. It is the purpose of this thesis to discuss the basic concepts of Random Matrix Theory, using the ensembles of random matrices originally introduced by Wigner, the Gaussian ensembles, as a starting point. As Random Matrix Theory is classically concerned with the statistical properties of levels sequences, we start with a brief introduction to the statistical analysis of a level sequence before getting to the introduction of the Gaussian ensembles. With the ensembles defined, we move on to the statistical properties that they predict. In the light of these predictions, a few of the classical applications of Random Matrix Theory are discussed, and as an example of some of the important concepts, the Anderson model of localization is investigated in some detail.

We present a unifying framework for the global optimization of functions which are expensive to evaluate. The framework is based on a Bayesian interpretation of radial basis function interpolation which incorporates existing methods such as Kriging, Gaussian process regression and neural networks. This viewpoint enables the application of Bayesian decision theory to derive a sequential global optimization algorithm which can be extended to include existing algorithms of this type in the literature. By posing the optimization problem as a sequence of sampling decisions, we optimize a general cost function at each stage of the algorithm. An extension to multi-stage decision processes is also discussed. The key idea of the framework is to replace the underlying expensive function by a cheap surrogate approximation. This enables the use of existing branch and bound techniques to globally optimize the cost function. We present a rigorous analysis of the canonical branch and bound algorithm in this setting as well as newly developed algorithms for other domains including convex sets. In particular, by making use of Lipschitz continuity of the surrogate approximation, we develop an entirely new algorithm based on overlapping balls. An application of the framework to the integration of expensive functions over rectangular domains and spherical surfaces in low dimensions is also considered. To assess performance of the framework, we apply it to canonical examples from the literature as well as an industrial model problem from oil reservoir simulation.

The area of misfire detection is important because of the effects of misfires on both the environment and the exhaust system. Increasing requirements on the detection performance means that improvements are always of interest. In this thesis, potential improvements to an existing misfire detection algorithm are evaluated. The improvements evaluated are: using Gaussian processes to model the classifier, alternative signal treatments for detection of multiple misfires, and effects of where flywheel tooth angle error estimation is performed. The improvements are also evaluated for their suitability for use on-line. Both the use of Gaussian processes and the detection of multiple misfires are hard problems to solve while maintaining detection performance. Gaussian processes most likely loses performance due to loss of dependence between the weights of the classifier. It can give performance similar to the original classifier, but with greatly increased complexity. For multiple misfires, the performance can be slightly improved without loss of single misfire performance. Greater improvements are possible, but at the cost of single misfire performance. The decision is in the end down to the desired trade-off. The flywheel tooth angle error compensation gives nearly identical performance regardless of where it is estimated. Consequently the error estimation can be separated from the signal processing, allowing the implementation to be modular. Using an EKF for estimating the flywheel errors on-line is found to be both feasible and give good performance. Combining the separation of the error estimation from the signal treatment with a, after initial convergence, heavily restricted EKF gives a vastly reduced computational load for only a moderate loss of performance.

La majeure partie de cette thèse est consacrée à l'inégalité de Blaschke-Santaló, qui s'énonce ainsi : parmi les ensembles symétriques, la boule euclidienne maximise le produit vol(K) vol(K°), K° désignant le polaire de K. Il existe des versions fonctionnelles de cette inégalité, découvertes par plusieurs auteurs (Ball, Artstein, Klartag, Milman, Fradelizi, Meyer. . .), mais elles sont toutes dérivées de l'inégalité ensembliste. L'objet de cette thèse est de proposer des démonstrations directes de ces inégalités fonctionnelles. On obtient ainsi de nouvelles preuves de l'inégalité de Santaló, parfois très simples. La dernière partie est un peu à part et concerne le chaos gaussien : on démontre une majoration précise des moments du chaos gaussien due à Lataªa par des arguments de chaînage à la Talagrand / This thesis is mostly about the Blaschke-Santaló inequality, which states that among symmetric sets, the Euclidean ball maximises the product vol(K) vol(K°), where K° is the polar body of K. Several authors (Ball, Artstein, Klartag, Milman, Fradelizi, Meyer. . .) were able to derive functional inequalities from this inequality. The purpose of this thesis is to give direct proofs of these functional Santaló inequalities. This provides new proofs of Santaló, some of which are very simple. The last chapter is about Gaussian chaoses. We obtain a sharp bound for moments of Gaussian chaoses due to Lataªa, using the generic chaining of Talagrand

<p>Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, the spectral mixture (SM) kernel was proposed to model the spectral density of a single task in a Gaussian process framework. This work develops a novel covariance kernel for multiple outputs, called the cross-spectral mixture (CSM) kernel. This new, flexible kernel represents both the power and phase relationship between multiple observation channels. The expressive capabilities of the CSM kernel are demonstrated through implementation of 1) a Bayesian hidden Markov model, where the emission distribution is a multi-output Gaussian process with a CSM covariance kernel, and 2) a Gaussian process factor analysis model, where factor scores represent the utilization of cross-spectral neural circuits. Results are presented for measured multi-region electrophysiological data.</p> / Dissertation

A research report submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, in partial fulfilment of the requirements for the degree of Master of Science in Mining Engineering. February, 2016 / Mineral Resource estimation provides an assessment of the quantity, quality, shape and grade distribution of a mineralised deposit. The resource estimation process involves; the assessment of data available, creation of geological and/or grade models for the deposit, statistical and geostatistical analyses of the data, as well as determination of the appropriate grade interpolation methods. In the grade estimation process, grades are interpolated/extrapolated into a two or three – dimensional resource block model of a deposit. The process uses a search volume ellipsoid, centred on each block, to select samples used for estimation. Traditionally, a global orientated search ellipsoid is used during the estimation process. An improvement in the estimation process can be achieved if the direction and continuity of mineralisation is acknowledged by aligning the search ellipsoid accordingly. The misalignment of the search ellipsoid by just a few degrees can impact the estimation results. Representing grade continuity in undulating and folded structures can be a challenge to correct grade estimation. One solution to this problem is to apply the method of Dynamic Anisotropy in the estimation process. This method allows for the anisotropy rotation angles defining the search ellipsoid and variogram model, to directly follow the trend of the mineralisation for each cell within a block model. This research report will describe the application of Dynamic Anisotropy to a slightly undulating area which lies on a gently folded limb of a syncline at Driefontein gold mine and where Ordinary Kriging is used as the method of estimation. In addition, the optimal Dynamic Anisotropy resolution that will provide an improvement in grade estimates will be determined. This will be achieved by executing the estimation process on various block model grid sizes. The geostatistical literature research carried out for this research report highlights the importance of Dynamic Anisotropy in resource estimation. Through the application and analysis on a real-life dataset, this research report will put theories and opinions about Dynamic Anisotropy to the test.

A research project report submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, in fulfilment of the requirements for the degree of Masters of Science in Engineering, 2017 / The assessment of local and spatial uncertainty associated with a regionalised variable such as nickel grade at Hunters Road magmatic sulphide deposit is one of the critical elements in the resource estimation. The study focused on the application of Multiple Indicator Kriging (MIK) and Sequential Gaussian Simulation (SGS) in the estimation of recoverable resources and the assessment of grade uncertainty at Hunters Road’s Western orebody. The Hunters Road Western orebody was divided into two domains namely the Eastern and the Western domains and was evaluated based on 172 drill holes. MIK and SGS were performed using Datamine Studio RM module. The combined Mineral Resources estimate for the Western orebody at a cut-off grade of 0.40%Ni is 32.30Mt at an average grade of 0.57%Ni, equivalent to 183kt of contained nickel metal. SGS results indicated low uncertainty associated with Hunters Road nickel project with 90% probability of an average true grade above cut-off, lying within +/-3% of the estimated block grade. The estimate of the mean based on SGS was 0.55%Ni and 0.57% Ni for the Western and Eastern domains respectively. MIK results were highly comparable with SGS E-type estimates while the most recent Ordinary Kriging (OK) based estimates by BNC dated May 2006, overstated the resources tonnage and underestimated the grade compared to the MIK estimates. It was concluded that MIK produced better estimates of recoverable resources than OK. However, since only E-type estimates were produced by MIK, post processing of “composite” conditional cumulative distribution function (ccdf) results using a relevant change of support algorithm such as affine correction is recommended. Although SGS produced a good measure of uncertainty around nickel grades, post processing of realisations using a different software such as Isatis has been recommended together with combined simulation of both grade and tonnage. / XL2018

Affective computing has gained significant attention from researchers in the last decade due to the wide variety of applications that can benefit from this technology. Often, researchers describe affect using emotional dimensions such as arousal and valence. Valence refers to the spectrum of negative to positive emotions while arousal determines the level of excitement. Describing emotions through continuous dimensions (e.g. valence and arousal) allows us to encode subtle and complex affects as opposed to discrete emotions, such as the basic six emotions: happy, anger, fear, disgust, sad and neutral. Recognizing spontaneous and subtle emotions remains a challenging problem for computers. In our work, we employ two modalities of information: video and audio. Hence, we extract visual and audio features using deep neural network models. Given that emotions are time-dependent, we apply the Temporal Convolutional Neural Network (TCN) to model the variations in emotions. Additionally, we investigate an alternative model that combines a Convolutional Neural Network (CNN) and a Recurrent Neural Network (RNN). Given our inability to fit the latter deep model into the main memory, we divide the RNN into smaller segments and propose a scheme to back-propagate gradients across all segments. We configure the hyperparameters of all models using Gaussian processes to obtain a fair comparison between the proposed models. Our results show that TCN outperforms RNN for the recognition of the arousal and valence emotional dimensions. Therefore, we propose the adoption of TCN for emotion detection problems as a baseline method for future work. Our experimental results show that TCN outperforms all RNN based models yielding a concordance correlation coefficient of 0.7895 (vs. 0.7544) on valence and 0.8207 (vs. 0.7357) on arousal on the validation dataset of SEWA dataset for emotion prediction.