Tesis Magíster
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Browsing Tesis Magíster by Subject "Algoritmos"
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Item Análogos del décimo problema de Hilbert = Analogues of hilbert's tenth problem.(Universidad de Concepción, 2010) Utreras Alarcón, Javier Antonio; Vidaux Negre, XavierThe tenth problem in D. Hilbert's famous list asked the following : Devise an algorithm to decide whether a polynomial equation with integer coe cients has an integer solution. (These equations are called Diophantine equations.) In the year 1970, 70 years after Hilbert posed it, Y. Matiyasevich (based on work of M. Davis, J. Robinson and H. Putnam) proved that such an algorithm does not exist [10]. Knowing that the decision problem for integer solutions of Diophantine equations had a negative answer, the problem shifted to smaller classes of equations. For example, it follows from Matiyasevich's negative answer that there exists no algorithm to decide whether a system of second-degree Diophantine equations has integral solutions; while, on the other hand, a result of M. Presburger (1929) implies that an analogous algorithm for systems of linear Diophantine equations exists [15]. Consider all systems of second degree Diophantine equations in where every unknown appears squared in all of its ocurrences. These systems form a subset of all systems of second degree Diophantine equations, and it can be shown that every linear Diophantine equation can be written as such (just because any integer can be written as x2+y2z2 for some integers x, y and z). Thus, the decision problem for integer solutions to this kind of systems of equations is \in between" the two already known results mentioned in the previous paragraph. This problem is known as the Problem of representation by diagonal quadratic forms, and is currently open.Item Classification of major galaxy mergers using machine learning algorithms trained with N-body simulations.(Universidad de Concepción, 2024) Saavedra Bastidas, Jorge Eduardo; Schleicher, DominikGalaxy mergers are significant events in astronomy, driving the morphological transformation from spiral to elliptical galaxies and disrupting internal gas mechanics, increasing star formation, enhancing nuclear activity, and contributing to the formation and evolution of supermassive black holes. Traditional detection methods for galaxy mergers lack the effectiveness and efficiency required to handle large datasets. In this study, we perform a systematic comparison of different machine learning models as classifiers for major galaxy mergers and their merger stages, relying solely on morphological information. We test ensemble-based classifiers like Random Forest (RF) and Extreme Gradient Boosting (XGboost) and deep learning architectures like Convolutional Neural Networks (CNNs). We propose the implementation of images extracted from N-body simulations designed to replicate the morphological features of galaxy-galaxy interactions as training data for the classification algorithms. We evaluate the performance of these models across three levels of observational realism: highly idealized galaxies extracted from our simulations, galaxies convoluted with a Gaussian point spread function (PSF), and galaxies convoluted with the Gaussian PSF and complemented with real background noise. We found that models with the best performance on the highest observational realism synthetic test set are those trained on data from the same distribution. CNNs achieved an average area under the receiver operating characteristic curve of 95.2%, while XGBoost and RF obtained 93.5% and 93.0%, respectively. Despite being in second place, XGBoost shows greater stability than CNNs when predicting mergers from galaxies provided by different data distributions. We test XGBoost on a sample of massive, low-redshift (z ≤ 0.15) galaxies from the Dark Energy Camera Legacy Survey - Galaxy Zoo Data Release 5, showing the ability to differentiate galaxy pairs effectively. We conclude that morphological features are a solid base for training a machine learning classifier for galaxy mergers, however, the differences between isolated galaxies and recent post-mergers require more detailed physics to completely characterize both stages.Item Trapezoidal Kumaraswamy distribution and sem algorithm.(Universidad de Concepción, 2021) Toledo Balboa, Juan Guillermo; Figueroa Zúñiga, Jorge IsaacModels involving the Kumaraswamy distribution have been a very studied in the past years in the analysis and modeling of bounded continuos variables. In this paper we focus on one in particular: the Trapezoidal Kumaraswamy model. We present an estimation method for its parameters based on bayesian approaches: the Stochastic EM algorithm (SEM), which avoids the most common issues of the classical EM. Then, we apply this method to the daily covid-19 cases in Chile using this model.