O filtro cuno faz parte do circuito de tratamento de água do reator IEA-R1 que , quando saturado, é substituído, se tornando um rejeito radioativo que deve ser gerenciado. Neste trabalho foi realizada a caracterização primária do filtro cuno do reator nuclear IEA-R1 do IPEN utilizando-se espectrometria gama associada ao método de Monte Carlo. A espectrometria gama foi realizada utilizando-se um detector de germânio hiperpuro (HPGe). O cristal de germânio representa o volume ativo de detecção do detector HPGe, que possui uma região denominada camada morta ou camada inativa. Na literatura tem sido reportada uma diferença entre os valores experimentais e teóricos na obtenção da curva de eficiência desses detectores. Neste trabalho foi utilizado o código MCNP-4C para a obtenção da calibração em eficiência do detector para a geometria do filtro cuno, onde foram estudadas as influências da camada morta e do efeito de soma em cascata no detector HPGe. As correções dos valores de camada morta foram realizadas variando-se a espessura e o raio do cristal de germânio. O detector possui 75,83 cm3 de volume ativo de detecção, segundo informações fornecidas pelo fabricante. Entretanto os resultados encontrados mostraram que o valor de volume ativo real é menor do que o especificado, onde a camada morta representa 16% do volume total do cristal. A análise do filtro cuno por meio da espectrometria gama, permitiu a identificação de picos de energia. Por meio desses picos foram identificados três radionuclídeos no filtro: 108mAg, 110mAg e 60Co. A partir da calibração em eficiência obtida pelo método de Monte Carlo, o valor de atividade estimado para esses radionuclídeos está na ordem de MBq. / The Cuno filter is part of the water processing circuit of the IEA-R1 reactor and, when saturated, it is replaced and becomes a radioactive waste, which must be managed. In this work, the primary characterization of the Cuno filter of the IEA-R1 nuclear reactor at IPEN was carried out using gamma spectrometry associated with the Monte Carlo method. The gamma spectrometry was performed using a hyperpure germanium detector (HPGe). The germanium crystal represents the detection active volume of the HPGe detector, which has a region called dead layer or inactive layer. It has been reported in the literature a difference between the theoretical and experimental values when obtaining the efficiency curve of these detectors. In this study we used the MCNP-4C code to obtain the detector calibration efficiency for the geometry of the Cuno filter, and the influence of the dead layer and the effect of sum in cascade at the HPGe detector were studied. The correction of the dead layer values were made by varying the thickness and the radius of the germanium crystal. The detector has 75.83 cm3 of active volume of detection, according to information provided by the manufacturer. Nevertheless, the results showed that the actual value of active volume is less than the one specified, where the dead layer represents 16% of the total volume of the crystal. A Cuno filter analysis by gamma spectrometry has enabled identifying energy peaks. Using these peaks, three radionuclides were identified in the filter: 108mAg, 110mAg and 60Co. From the calibration efficiency obtained by the Monte Carlo method, the value of activity estimated for these radionuclides is in the order of MBq.

The purpose of this research is to investigate properties of diffusion processes in porous media. Porous media are modelled by random Sierpinski carpets, each carpet is constructed by mixing two different generators with the same linear size. Diffusion on porous media is studied by performing random walks on random Sierpinski carpets and is characterized by the random walk dimension $d_w$. In the first part of this work we study $d_w$ as a function of the ratio of constituents in a mixture. The simulation results show that the resulting $d_w$ can be the same as, higher or lower than $d_w$ of carpets made by a single constituent generator. In the second part, we discuss the influence of static external fields on the behavior of diffusion. The biased random walk is used to model these phenomena and we report on many simulations with different field strengths and field directions. The results show that one structural feature of Sierpinski carpets called traps can have a strong influence on the observed diffusion properties. In the third part, we investigate the effect of diffusion under the influence of external fields which change direction back and forth after a certain duration. The results show a strong dependence on the period of oscillation, the field strength and structural properties of the carpet.

The purpose of this research is to investigate properties of diffusion processes in porous media. Porous media are modelled by random Sierpinski carpets, each carpet is constructed by mixing two different generators with the same linear size. Diffusion on porous media is studied by performing random walks on random Sierpinski carpets and is characterized by the random walk dimension $d_w$. In the first part of this work we study $d_w$ as a function of the ratio of constituents in a mixture. The simulation results show that the resulting $d_w$ can be the same as, higher or lower than $d_w$ of carpets made by a single constituent generator. In the second part, we discuss the influence of static external fields on the behavior of diffusion. The biased random walk is used to model these phenomena and we report on many simulations with different field strengths and field directions. The results show that one structural feature of Sierpinski carpets called traps can have a strong influence on the observed diffusion properties. In the third part, we investigate the effect of diffusion under the influence of external fields which change direction back and forth after a certain duration. The results show a strong dependence on the period of oscillation, the field strength and structural properties of the carpet.

No / Nonadiabatic Monte Carlo transition-state theory is used to explore competing C¿Cl and C¿Br bond fission processes in a simple model of 1[n,pi*(CO)] photoexcited bromoacetyl chloride. Morse potentials are used to represent bond stretching coordinates, and the positions and magnitudes of nonadiabatic coupling between excited state potentials are modeled using ab initio data. The main effect of nonadiabaticity is to favor C¿Cl fission over C¿Br, despite a larger barrier to C¿Cl dissociation. The absolute values of the rate constants are smaller than observed experimentally, but the calculated branching ratios are close to the experimental value. For C¿Cl fission, it is shown that the minimum energy crossing point is not sufficient to describe the rate constant, suggesting that care must be taken when using alternative models which make this assumption.

Computational methods for predicting the binding affinity of small organic molecules tobiological macromolecules cover a vast range of theoretical and physical complexity. Generally, as the required accuracy increases so does the computational cost, thereby making the user choose a method that suits their needs within the parameters of the project. We present how WScore, a rigid-receptor docking program normally consigned to structure-based hit discovery in drug design projects, is systematically ameliorated to perform accurately enough for lead optimization with a set of ROCK1 complexes and congeneric ligands from a structure-activity relationship study. Initial WScore results from the Schrödinger 2019-3 release show poor correlation (R² ∼0.0), large errors in predicted binding affinity (RMSE = 2.30 kcal/mol), and bad native pose prediction (two RMSD > 4Å) for the six ROCK1 crystal structures and associated active congeneric ligands. Improvements to WScore’s treatment of desolvation, myriad code fixes, and a simple ensemble consensus scoring protocol improved the correlation (R² = 0.613), the predicted affinity accuracy (RMSE = 1.34 kcal/mol), and native pose prediction (one RMSD > 1.5Å). Then we evaluate a physically and thermodynamically rigorous free energy perturbation (FEP) method, FEP+, against CryoEM structures of the Machilis hrabei olfactory receptor, MhOR5, and associated dose-response assays of a panel of small molecules with the wild-type and mutants. Augmented with an induced-fit docking method, IFD-MD, FEP+ performs well for ligand mutating relative binding FEP (RBFEP) calculations which correlate with experimental log(EC50)with an R² = 0.551. Ligand absolute binding FEP (ABFEP) on a set of disparate ligands from the MhOR5 panel has poor correlation (R² = 0.106) for ligands with log(EC50) within the assay range. But qualitative predictions correctly identify the ligands with the lowest potency. Protein mutation calculations have no log(EC50) correlation and consistently fail to predict the loss of potency for a majority of MhOR5 single point mutations. Prediction of ligand efficacy (the magnitude of receptor response) is also an unsolved problem as the canonical active and inactive conformations of the receptor are absent in the FEP simulations. We believe that structural insights of the mutants for both bound and unbound (apo) states are required to better understand the shortcomings of the current FEP+ methods for protein mutation RBFEP. Finally, improvements to GPU-accelerated linear algebra functions in an Auxiliary-Field Quantum Monte Carlo (AFQMC) program effect an average 50-fold reduction in GPU kernel compute time using optimized GPU library routines instead of custom made GPU kernels. Also MPI parallelization of the population control algorithm that destroys low-weight walkers has a bottleneck removed in large, multi-node AFQMC calculations.Computational methods for predicting the binding affinity of small organic molecules tobiological macromolecules cover a vast range of theoretical and physical complexity. Generally, as the required accuracy increases so does the computational cost, thereby making the user choose a method that suits their needs within the parameters of the project. We present how WScore, a rigid-receptor docking program normally consigned to structure-based hit discovery in drug design projects, is systematically ameliorated to perform accurately enough for lead optimization with a set of ROCK1 complexes and congeneric ligands from a structure-activity relationship study. Initial WScore results from the Schrödinger 2019-3 release show poor correlation (R² ∼0.0), large errors in predicted binding affinity (RMSE = 2.30 kcal/mol), and bad native pose prediction (two RMSD > 4Å) for the six ROCK1 crystal structures and associated active congeneric ligands. Improvements to WScore’s treatment of desolvation, myriad code fixes, and a simple ensemble consensus scoring protocol improved the correlation (R² = 0.613), the predicted affinity accuracy (RMSE = 1.34 kcal/mol), and native pose prediction (one RMSD > 1.5Å). Then we evaluate a physically and thermodynamically rigorous free energy perturbation (FEP) method, FEP+, against CryoEM structures of the Machilis hrabei olfactory receptor, MhOR5, and associated dose-response assays of a panel of small molecules with the wild-type and mutants. Augmented with an induced-fit docking method, IFD-MD, FEP+ performs well for ligand mutating relative binding FEP (RBFEP) calculations which correlate with experimental log(EC50)with an R² = 0.551. Ligand absolute binding FEP (ABFEP) on a set of disparate ligands from the MhOR5 panel has poor correlation (R² = 0.106) for ligands with log(EC50) within the assay range. But qualitative predictions correctly identify the ligands with the lowest potency. Protein mutation calculations have no log(EC50) correlation and consistently fail to predict the loss of potency for a majority of MhOR5 single point mutations. Prediction of ligand efficacy (the magnitude of receptor response) is also an unsolved problem as the canonical active and inactive conformations of the receptor are absent in the FEP simulations. We believe that structural insights of the mutants for both bound and unbound (apo) states are required to better understand the shortcomings of the current FEP+ methods for protein mutation RBFEP. Finally, improvements to GPU-accelerated linear algebra functions in an Auxiliary-Field Quantum Monte Carlo (AFQMC) program effect an average 50-fold reduction in GPU kernel compute time using optimized GPU library routines instead of custom made GPU kernels. Also MPI parallelization of the population control algorithm that destroys low-weight walkers has a bottleneck removed in large, multi-node AFQMC calculations.

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Thesis (MSc (Applied Mathematics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: In this dissertation we study the machine learning subfield of Reinforcement Learning (RL). After developing a coherent background, we apply a Monte Carlo (MC) control algorithm with exploring starts (MCES), as well as an off-policy Temporal-Difference (TD) learning control algorithm, Q-learning, to a simplified version of the Weapon Assignment (WA) problem. For the MCES control algorithm, a discount parameter of τ = 1 is used. This gives very promising results when applied to 7 × 7 grids, as well as 71 × 71 grids. The same discount parameter cannot be applied to the Q-learning algorithm, as it causes the Q-values to diverge. We take a greedy approach, setting ε = 0, and vary the learning rate (α ) and the discount parameter (τ). Experimentation shows that the best results are found with set to 0.1 and constrained in the region 0.4 ≤ τ ≤ 0.7. The MC control algorithm with exploring starts gives promising results when applied to the WA problem. It performs significantly better than the off-policy TD algorithm, Q-learning, even though it is almost twice as slow. The modern battlefield is a fast paced, information rich environment, where discovery of intent, situation awareness and the rapid evolution of concepts of operation and doctrine are critical success factors. Combining the techniques investigated and tested in this work with other techniques in Artificial Intelligence (AI) and modern computational techniques may hold the key to solving some of the problems we now face in warfare. / AFRIKAANSE OPSOMMING: Die fokus van hierdie verhandeling is die masjienleer-algoritmes in die veld van versterkingsleer. ’n Koherente agtergrond van die veld word gevolg deur die toepassing van ’n Monte Carlo (MC) beheer-algoritme met ondersoekende begintoestande, sowel as ’n afbeleid Temporale-Verskil beheer-algoritme, Q-leer, op ’n vereenvoudigde weergawe van die wapentoekenningsprobleem. Vir die MC beheer-algoritme word ’n afslagparameter van τ = 1 gebruik. Dit lewer belowende resultate wanneer toegepas op 7 × 7 roosters, asook op 71 × 71 roosters. Dieselfde afslagparameter kan nie op die Q-leer algoritme toegepas word nie, aangesien dit veroorsaak dat die Q-waardes divergeer. Ons neem ’n gulsige aanslag deur die gulsigheidsparameter te verstel na ε = 0. Ons varieer dan die leertempo ( α) en die afslagparameter (τ). Die beste eksperimentele resultate is behaal wanneer = 0.1 en as die afslagparameter vasgehou word in die gebied 0.4 ≤ τ ≤ 0.7. Die MC beheer-algoritme lewer belowende resultate wanneer toegepas op die wapentoekenningsprobleem. Dit lewer beduidend beter resultate as die Q-leer algoritme, al neem dit omtrent twee keer so lank om uit te voer. Die moderne slagveld is ’n omgewing ryk aan inligting, waar dit kritiek belangrik is om vinnig die vyand se planne te verstaan, om bedag te wees op die omgewing en die konteks van gebeure, en waar die snelle ontwikkeling van die konsepte van operasie en doktrine lei tot sukses. Die tegniekes wat in die verhandeling ondersoek en getoets is, en ander kunsmatige intelligensie tegnieke en moderne berekeningstegnieke saamgesnoer, mag dalk die sleutel hou tot die oplossing van die probleme wat ons tans in die gesig staar in oorlogvoering.

In this thesis, we consider some popular stochastic differential equation models used in finance, such as the Vasicek Interest Rate model, the Heston model and a new fractional Heston model. We discuss how to perform inference about unknown quantities associated with these models in the Bayesian framework. We describe sequential importance sampling, the particle filter and the auxiliary particle filter. We apply these inference methods to the Vasicek Interest Rate model and the standard stochastic volatility model, both to sample from the posterior distribution of the underlying processes and to update the posterior distribution of the parameters sequentially, as data arrive over time. We discuss the sensitivity of our results to prior assumptions. We then consider the use of Markov chain Monte Carlo (MCMC) methodology to sample from the posterior distribution of the underlying volatility process and of the unknown model parameters in the Heston model. The particle filter and the auxiliary particle filter are also employed to perform sequential inference. Next we extend the Heston model to the fractional Heston model, by replacing the Brownian motions that drive the underlying stochastic differential equations by fractional Brownian motions, so allowing a richer dependence structure across time. Again, we use a variety of methods to perform inference. We apply our methodology to simulated and real financial data with success. We then discuss how to make forecasts using both the Heston and the fractional Heston model. We make comparisons between the models and show that using our new fractional Heston model can lead to improve forecasts for real financial data.

The problem of this study was to determine the differences in experimentwise and comparisonwise Type I error rate among six multiple comparison procedures when applied to twenty-eight combinations of normally distributed data. These were the Least Significant Difference, the Fisher-protected Least Significant Difference, the Student Newman-Keuls Test, the Duncan Multiple Range Test, the Tukey Honestly Significant Difference, and the Scheffe Significant Difference. The Spjøtvoll-Stoline and Tukey—Kramer HSD modifications were used for unequal n conditions. A Monte Carlo simulation was used for twenty-eight combinations of k and n. The scores were normally distributed (µ=100; σ=10). Specified multiple comparison procedures were applied under two conditions: (a) all experiments and (b) experiments in which the F-ratio was significant (0.05). Error counts were maintained over 1000 repetitions. The FLSD held experimentwise Type I error rate to nominal alpha for the complete null hypothesis. The FLSD was more sensitive to sample mean differences than the HSD while protecting against experimentwise error. The unprotected LSD was the only procedure to yield comparisonwise Type I error rate at nominal alpha. The SNK and MRT error rates fell between the FLSD and HSD rates. The SSD error rate was the most conservative. Use of the harmonic mean of the two unequal sample n's (HSD-TK) yielded uniformly better results than use of the minimum n (HSD-SS). Bernhardson's formulas controlled the experimentwise Type I error rate of the LSD and MRT to nominal alpha, but pushed the HSD below the 0.95 confidence interval. Use of the unprotected HSD produced fewer significant departures from nominal alpha. The formulas had no effect on the SSD.

Title: Sequential Monte Carlo Methods Author: David Coufal Department: Department of Probability and Mathematical Statistics Supervisor: prof. RNDr. Viktor Beneš, DrSc. Abstract: The thesis summarizes theoretical foundations of sequential Monte Carlo methods with a focus on the application in the area of particle filters; and basic results from the theory of nonparametric kernel density estimation. The summary creates the basis for investigation of application of kernel meth- ods for approximation of densities of distributions generated by particle filters. The main results of the work are the proof of convergence of kernel estimates to related theoretical densities and the specification of the development of approx- imation error with respect to time evolution of a filter. The work is completed by an experimental part demonstrating the work of presented algorithms by simulations in the MATLABR⃝ computational environment. Keywords: sequential Monte Carlo methods, particle filters, nonparametric kernel estimates