O presente trabalho estuda o modelo de Blume-Capel na rede aleatória e também analisa a inclusão de um termo de campo cristalino aleatório e de um termo de campo local aleatório. Ao resolver o modelo na rede aleatória, uma técnica de conectividade finita foi utilizada, na qual cada spin é conectado a um número finito de outros spins. Os spins foram conectados de acordo com uma distribuição de Poisson, os termos de campo aleatório seguiram uma distribuição bimodal e as interações entre os spins foram consideradas uniformes. Desse modo, só há desordem nas conexões entre os spins. O foco desse trabalho foi determinar como a natureza da transição de fase é alterada com a conectividade e se há um comportamento reentrante das linhas de transição de fase. A técnica de réplicas é usada para obter equações de ponto de sela para a distribuição de campos locais. Um Ansatz de simetria de réplicas foi utilizado para a função de ordem e esse foi escrito em termos de uma distribuição bidimensional de campos efetivos, onde uma das componentes é associada com um termo linear dos spins e a outra com o termo de campo cristalino. Com isso, equações para as funções de ordem e a energia livre podem ser obtidas. Uma técnica de dinâmica populacional é usada para resolver numericamente a equação auto-consistente para a distribuição de campos locais e outros parâmetros, como a magnetização, a atividade da rede e a energia livre. Os resultados indicam que a natureza da transição ferromagnética-paramagnética, a posição do ponto tricrítico e a existência de reentrância dependem fortemente do valor da conectividade e, nos casos com um termo de campo aleatório, dependem da intensidade dos campos aleatórios. No caso em que o campo cristalino é aleatório, o ponto tricrítico é suprimido para valores acima de um certo valor de aleatoriedade. / The present work studies the Blume-Capel model in a random network and also analyses the inclusion of a random crystal-field term and a random field term. To solve the model in a random network a finite connectivity technique is used, in which each spin is connected to a finite number of other spins. The spins were connected according a Poisson distribution, the random field terms followed a bimodal distribution and the bonds between the spins were considered uniform. Thus, there is only a connection disorder. The focus of this work was on determining how the nature of the phase transition changes with the connectivity and the random fields and if there is a reentrant behavior of the phase boundaries. The replica technique is used to obtain saddle-point equations for the effective local-field distribution. The replica symmetric Ansatz for the order function is written in terms of a two-dimensional effective-field distribution, where one of the components is associated with a linear form in the spins and the other with the crystal-field term. This allows one to derive equations for the order function and for the free-energy. A population dynamics procedure is used to solve numerically a self-consistency equation for the distribution of the local field and with it some physical parameters, like magnetization and free-energy. The results obtained indicate that the nature of the F-P transition, the location of the tricritical point and the presence of a reentrant phase depend strongly on the connectivity. In the cases with a random field term, those are also dependent on the intensity of the fields. For the case with a random crystal-field term, the tricritical point is supressed above a certain value of randomness.

It is foreseeable that device-to-device (D2D) communication will become a standard feature in the future, for the reason that it offloads the data traffic from network infrastructures to user devices. Recent researches prove that delivering delay-tolerant contents through content delivery network (CDN) by D2D helps network operators increase spectral and energy efficiency. However, protecting the private information of mobile users in D2D assistant CDN is the primary concern, which directly affects the willingness of mobile users to share their resources with others. In this thesis, we proposed a privacy concerned top layer system for selecting the sub-optimal set of mobile nodes as initial mobile content provider (MCP) for content delivery in any general D2D communications, which implies that our proposed system does not rely on private user information such as location, affinity, and personal preferences. We model the initial content carrier set problem as an incentive maximization problem to optimize the rewards for network operators and content providers. Then, we utilized the Markov random field (MRF) theory to build a probabilistic graphical model to make an inference on the observation of delivered contents. Furthermore, we proposed a greedy algorithm to solve the non-linear binary integer programming (NLBIP) problem for selecting the optimal initial content carrier set. The evaluations of the proposed system are based on both a simulated dataset and a real-world collected dataset corresponding to the off-line and on-line scenarios.

Land cover information is a key input to many earth system models, and thus accurate and consistent land cover maps are critically important to global change science. However, existing global land cover products show unrealistically high levels of year-to-year change. This thesis explores methods to improve accuracies for global land cover classifications, with a focus on reducing spurious year-to-year variation in results derived from MODIS data. In the first part of this thesis I use clustering to identify spectrally distinct sub-groupings within defined land cover classes, and assess the spectral separability of the resulting sub-classes. Many of the sub-classes are difficult to separate due to a high degree of overlap in spectral space. In the second part of this thesis, I examine two methods to reduce year-to-year variation in classification labels. First, I evaluate a technique to construct training data for a per-pixel supervised classification algorithm by combining multiple years of spectral measurements. The resulting classifier achieves higher accuracy and lower levels of year-to-year change than a reference classifier trained using a single year of data. Second, I use a spatio-temporal Markov Random Field (MRF) model to post-process the predictions of a per-pixel classifier. The MRF framework reduces spurious label change to a level comparable to that achieved by a post-hoc heuristic stabilization technique. The timing of label change in the MRF processed maps better matched disturbance events in a reference data, whereas the heuristic stabilization results in label changes that lag several years behind disturbance events.

Three dimensional reconstruction of large macromolecules like viruses at resolutions below 8 Ã… - 10 Ã… requires a large set of projection images and the particle identification step becomes a bottleneck. Several automatic and semi-automatic particle detection algorithms have been developed along the years. We present a general technique designed to automatically identify the projection images of particles. The method utilizes Markov random field modelling of the projected images and involves a preprocessing of electron micrographs followed by image segmentation and post processing for boxing of the particle projections. Due to the typically extensive computational requirements for extracting hundreds of thousands of particle projections, parallel processing becomes essential. We present parallel algorithms and load balancing schemes for our algorithms. The lack of a standard benchmark for relative performance analysis of particle identification algorithms has prompted us to develop a benchmark suite. Further, we present a collection of metrics for the relative performance analysis of particle identification algorithms on the micrograph images in the suite, and discuss the design of the benchmark suite.

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Computational systems biology is an inter-disciplinary field that aims to develop computational approaches for a system-level understanding of biological systems. Advances in high-throughput biotechnology offer broad scope and high resolution in multiple disciplines. However, it is still a major challenge to extract biologically meaningful information from the overwhelming amount of data generated from biological systems. Effective computational approaches are of pressing need to reveal the functional components. Thus, in this dissertation work, we aim to develop computational approaches for differential analysis of RNA-seq and methylation data to detect aberrant events associated with cancers. We develop a novel Bayesian approach, BayesIso, to identify differentially expressed isoforms from RNA-seq data. BayesIso features a joint model of the variability of RNA-seq data and the differential state of isoforms. BayesIso can not only account for the variability of RNA-seq data but also combines the differential states of isoforms as hidden variables for differential analysis. The differential states of isoforms are estimated jointly with other model parameters through a sampling process, providing an improved performance in detecting isoforms of less differentially expressed. We propose to develop a novel probabilistic approach, DM-BLD, in a Bayesian framework to identify differentially methylated genes. The DM-BLD approach features a hierarchical model, built upon Markov random field models, to capture both the local dependency of measured loci and the dependency of methylation change. A Gibbs sampling procedure is designed to estimate the posterior distribution of the methylation change of CpG sites. Then, the differential methylation score of a gene is calculated from the estimated methylation changes of the involved CpG sites and the significance of genes is assessed by permutation-based statistical tests. We have demonstrated the advantage of the proposed Bayesian approaches over conventional methods for differential analysis of RNA-seq data and methylation data. The joint estimation of the posterior distributions of the variables and model parameters using sampling procedure has demonstrated the advantage in detecting isoforms or methylated genes of less differential. The applications to breast cancer data shed light on understanding the molecular mechanisms underlying breast cancer recurrence, aiming to identify new molecular targets for breast cancer treatment. / Ph. D.

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A..=2b, where A 2 Rnn is a large, sparse symmetric positive definite matrix and b 2 Rn is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LLT is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L..T z, with x = A..1=2z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form n = A..=2b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t..=2 and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A..=2b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

The new General Data Protection Regulation (GDPR) Act will apply to all companies within the European Union after 25 May. This means stricter legal requirements for companies that in some way store personal data. The goal of this project is therefore to make it easier for companies to meet the new legal requirements. This by creating a tool that searches file systems and visually shows the user in a graphical user interface which files contain personal data. The tool uses Named entity recognition with the Linear chain conditional random field algorithm which is a type of supervised learning method in machine learning. This algorithm is used in the project to find names and addresses in files. The different models are trained with different parameters and the training is done using the stanford NER library in Java. The models are tested by a test file containing 45,000 words where the models themselves can predict all classes to the words in the file. The models are then compared with each other using the measurements of precision, recall and F-score to find the best model. The tool also uses Regular Expression to find emails, IP numbers, and social security numbers. The result of the final machine learning model shows that it does not find all names and addresses, but that can be improved by increasing exercise data. However, this is something that requires a more powerful computer than the one used in this project. An analysis of how the Swedish language is built would also need to be done to apply the most appropriate parameters for the training of the model. / Den nya lagen General data protection regulation (GDPR) började gälla för alla företag inom Europeiska unionen efter den 25 maj. Detta innebär att det blir strängare lagkrav för företag som på något sätt lagrar personuppgifter. Målet med detta projekt är därför att underlätta för företag att uppfylla de nya lagkraven. Detta genom att skapa ett verktyg som söker igenom filsystem och visuellt visar användaren i ett grafiskt användargränssnitt vilka filer som innehåller personuppgifter. Verktyget använder Named Entity Recognition med algoritmen Linear Chain Conditional Random Field som är en typ av ”supervised” learning metod inom maskininlärning. Denna algoritm används för att hitta namn och adresser i filer. De olika modellerna tränas med olika parametrar och träningen sker med hjälp av biblioteket Stanford NER i Java. Modellerna testas genom en testfil som innehåller 45 000 ord där modellerna själva får förutspå alla klasser till orden i filen. Modellerna jämförs sedan med varandra med hjälp av mätvärdena precision, recall och F-score för att hitta den bästa modellen. Verktyget använder även Regular expression för att hitta e- mails, IP-nummer och personnummer. Resultatet på den slutgiltiga maskininlärnings modellen visar att den inte hittar alla namn och adresser men att det är något som kan förbättras genom att öka träningsdata. Detta är dock något som kräver en kraftfullare dator än den som användes i detta projekt. En undersökning på hur det svenska språket är uppbyggt skulle även också behöva göras för att använda de lämpligaste parametrarna vid träningen av modellen.