In the last decade, over a million stars were monitored to detect transiting planets. Manual interpretation of potential exoplanet candidates is labour intensive and subject to human error, the results of which are difficult to quantify. Here we present a new method of detecting exoplanet candidates in large planetary search projects that, unlike current methods, uses a neural network. Neural networks, also called 'deep learning' or 'deep nets', are designed to give a computer perception into a specific problem by training it to recognize patterns. Unlike past transit detection algorithms, deep nets learn to recognize planet features instead of relying on hand-coded metrics that humans perceive as the most representative. Our convolutional neural network is capable of detecting Earth-like exoplanets in noisy time series data with a greater accuracy than a least-squares method. Deep nets are highly generalizable allowing data to be evaluated from different time series after interpolation without compromising performance. As validated by our deep net analysis of Kepler light curves, we detect periodic transits consistent with the true period without any model fitting. Our study indicates that machine learning will facilitate the characterization of exoplanets in future analysis of large astronomy data sets.

The diploma thesis is focused on possibilities of application of cartographic methods to display and analyze migration. In the introduction part is defined the term of migration and methods of its description and analyzing, there are introduced also the basis of cartographic methods. The main part is devoted to concrete usage of cartographic methods. Three attitudes to description of migration are distinguished - using aggregate (one-dimensional) data, delimitation of regions of migration and migration flows. For all of these are suggested possible display methods, including their advantages and disadvantages. Some of the suggested methods were applied in maps, and final applications were evaluated. The results are resumed in conclusion. Evaluation of partial maps is included in appendix.

There is a large degree of variety in the optical variability of quasars and it is unclear whether this is all attributable to a single (set of) physical mechanism(s). We present the results of a systematic search for major flares in active galactic nucleus (AGN) in the Catalina Real-time Transient Survey as part of a broader study into extreme quasar variability. Such flares are defined in a quantitative manner as being atop of the normal, stochastic variability of quasars. We have identified 51 events from over 900 000 known quasars and high-probability quasar candidates, typically lasting 900 d and with a median peak amplitude of Delta m = 1.25 mag. Characterizing the flare profile with a Weibull distribution, we find that nine of the sources are well described by a single-point single-lens model. This supports the proposal by Lawrence et al. that microlensing is a plausible physical mechanism for extreme variability. However, we attribute the majority of our events to explosive stellar-related activity in the accretion disc: superluminous supernovae, tidal disruption events and mergers of stellar mass black holes.

Various models are currently in existence for determining the deflection of lithospheric plates under an applied transverse load. The most popular models treat lithospheric plates as thin elastic or thin viscoelastic plates. The equations governing the deflection of such plates have been solved successfully in two dimensions using integral transform techniques. Three dimensional models have been solved using Fourier Series expansions assuming a sinusoidal variation for the load and deflection. In the engineering context, the finite element technique has also been employed. The current aim, however, is to develop an efficient solver for the three dimensional elastic and viscoelastic problems using finite difference techniques. A variety of loading functions may therefore be considered with minimum work involved in obtaining a solution for different forcing functions once the main program has been developed. The proposed method would therefore provide a valuable technique for assessing new models for the loading of lithospheric plates as well as a useful educational tool for use in geophysics laboratories. The multigrid method, which has proved to be a fast, efficient solver for elliptic partial differential equations, is examined as the basis for a solver of both the elastic and viscoelastic problems. The viscoelastic problem, being explicitly time-dependent, is the more challenging of the two and will receive particular attention. Multigrid proves to be a very effective method applicable to the solution of both the elastic and viscoelastic problems. / Science, Faculty of / Mathematics, Department of / Graduate

This master´s thesis deals with the evaluation of the financial situation of the company using selected methods of financial analysis. It is focussed on detection of shortcomings in financial management and their causes. In conclusion of the thesis are suggested possible solutions for the improvement of the current financial situations of the company.

Smoothed Particle Hydrodynamics (SPH) is a meshless numerical method which has long been put into practice for scientific and engineering applications. It arises as a numerical discretization of convolution-like integral operators that approximate local differential operators. There have been many studies on the SPH with an emphasis on its role as a numerical scheme for partial differential equations while little attention is paid to the underlying continuum nonlocal models that lie intermediate between the two. The main goal of this thesis is to provide mathematical understanding of the SPH-like meshless methods by means of ongoing developments in studies of nonlocal models with a finite range of nonlocal interactions. It is timely for such a work to be initiated with growing interests in the nonlocal models. The thesis touches on numerical, theoretical and modeling aspects of the nonlocal integro-differential equations pertaining to the SPH-like schemes. As illustrative examples of each aspect it presents robust SPH-like schemes for advection-convection equations, discusses the stabilities of nonsymmetric nonlocal gradient operators, and proposes a new formulation of nonlocal Dirichlet-like type boundary conditions.

The astronomical size of spectral data cubes that will result from the SKA pathfinders planned large HI surveys such as LADUMA; Fornax HI survey; DINGO; WALLABY; etc. necessitate fully automated three-dimensional (3D) source finding and parametrization tools. A fraction of the percentage difference in the performance of these automated tools corresponds to a significant number of galaxies being detected or undetected. Failure or success to resolve satellites around big spirals will affect both the low and the high mass end of the HI mass function. As a result, the performance and efficiency of these automated tools are of great importance, especially in the epoch of big data. Here I present the comprehensive comparison of performance between the fully automated source identification and parametrization software: SOFIA, the visual galaxy identification method and the semi-automated galaxy identification method. Each galaxy identification method has been applied to the same ∼ 35 gigabytes 3D HI data cube. The data cube results from the blind HI imaging survey conducted using the Westerbork Synthesis Radio Telescope (WSRT). The survey mapped the overdensity corresponding to the Perseus-Pisces Supercluster filament crossing the Zone-of-Avoidance (ZoA), at (`, b) ≈ (160◦ , 0.5◦ ). A total of 211 galaxies detected using the semi-automated method by Ramatsoku et al. [2016]. In this work, I detected 194 galaxies (using the visual identification method) of which 89.7% (174) have cross-matches/counterparts on the galaxy catalogue produced through semi-automated identification method. A total of 130 detections were made using SOFIA of which 89 were also identified by the two other methods. I used the sample of 174 visual detections with semi-automated counterparts as a Testbed to calculate the reliability and completeness achieved by SOFIA. The achieved reliability is ∼ 0.68 whereas completeness is ∼ 0.51. Further parameter fine-tuning is necessary to have a better handle on all SOFIA parameters and achieve higher reliability and completeness values.

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<p> A detailed synopsis of the state-of-the-art in the field of the Structural Analysis of sandwich beams is presented. Deficiencies, inaccuracies, lack of clarity, and the imposition of unnecessary assumptions of behaviour found in the related bibliography are presented in a comparative fashion. A method of analysis with obvious advantages over the others studied in this thesis is derived, and its use is suggested. The presentation of all methods of analysis is made under the most general cases of dimensions and loadings to make them as applicable as possible to the common cases encountered in sandwich components for the building industry.</p> <p> Experimental work carried out on several materials with some potential to be used in sandwich members for buildings and the tests carried out on some sandwich beams and beam-columns are reported.</p> / Thesis / Master of Engineering (MEngr)

<p> Clustering involves partitioning a given data set into several groups based on some similarity/dissimilarity measurements. Cluster analysis has been widely used in information retrieval, text and web mining, pattern recognition, image segmentation and software reverse engineering.</p> <p> K-means is the most intuitive and popular clustering algorithm and the working horse for clustering. However, the classical K-means suffers from several flaws. First, the algorithm is very sensitive to the initialization method and can be easily trapped at a local minimum regarding to the measurement (the sum of squared errors) used in the model. On the other hand, it has been proved that finding a global minimal sum of the squared errors is NP-hard even when k = 2. In the present model for K-means clustering, all the variables are required to be discrete and the objective is nonlinear and nonconvex.</p> <p> In the first part of the thesis, we consider the issue of how to derive an optimization model to the minimum sum of squared errors for a given data set based on continuous convex optimization. For this, we first transfer the K-means clustering into a novel optimization model, 0-1 semidefinite programming where the eigenvalues of involved matrix argument must be 0 or 1. This provides an unified way for many other clustering approaches such as spectral clustering and normalized cut. Moreover, the new optimization model also allows us to attack the original problem based on the relaxed linear and semidefinite programming.</p> <p> Moreover, we consider the issue of how to get a feasible solution of the original clustering from an approximate solution of the relaxed problem. By using principal component analysis, we construct a rounding procedure to extract a feasible clustering and show that our algorithm can provide a 2-approximation to the global solution of the original problem. The complexity of our rounding procedure is O(n^(k2(k-1)/2)), which improves substantially a similar rounding procedure in the literature with a complexity O(n^k3/2). In particular, when k = 2, our rounding procedure runs in O(n log n) time. To the best of our knowledge, this is the lowest complexity that has been reported in the literature to find a solution to K-means clustering with guaranteed quality.</p> <p> In the second part of the thesis, we consider approximation methods for the so-called balanced bi-clustering. By using a simple heuristics, we prove that we can improve slightly the constrained K-means for bi-clustering. For the special case where the size of each cluster is fixed, we develop a new algorithm, called Q means, to find a 2-approximation solution to the balanced bi-clustering. We prove that the Q-means has a complexity O(n^2).</p> <p> Numerical results based our approaches will be reported in the thesis as well.</p> / Thesis / Master of Science (MSc)