Doctoral Dissertations
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Jelović, Ana (Beograd , 2022)[more][less]
Abstract: n the first part of this dissertation different repeat types are defined as well as repeats that satisfy motif masks. A method for precise repeat finding in input sequences of arbitrary length has been described. As the input sequences can be very long, the number of found repeats can also be large. For that reason it is important that the method also includes filtering found repeats based on the expected number of their occurrences. The method was first applied to protein sequences in which experimentally confirmed Tcell epitopes from the IEDB database were registered. Association rules were applied to the found repeats in order to construct a model that would enable the prediction of the positions of Tcell epitopes in protein sequences. In this way, it would indicate to researchers a region in the protein sequence where an epitope can be expected with high confidence. In the case of Tcell epitopes, a large number of rules with high confidence was found. These rules can be considered as reliable predictors of the position of Tcell epitopes within the protein sequences. Based on the results found, association rules were formed that characterize the epitopes and the repeats associated with them in more detail. As a large number of results were found, only their part is presented in this disser tation. On the basis of the strings that determine the repeat, a motif mask that the repeat needs to satisfy was searched for. The entire procedure was applied to both direct noncomplementary repeats and indirect noncomplementary repeats. With similar results, the entire procedure was applied to Bcell epitopes on data from the IEDB database. Data on experimentally confirmed short linear motifs were taken from the ELM database. In protein sequences where short linear motifs were registered, repeats were searched for and association rules were applied to them. The rules with high confidence have been singled out in particular. On the basis of the results found, motif masks that repeats with high confidence would satisfy were searched for. URI: http://hdl.handle.net/123456789/5442 Files in this item: 1
Ana_Jelovic_tekst_doktorata.pdf ( 6.127Mb ) 
Mitrašinović, Ana (Beograd , 2022)[more][less]
Abstract: The subject of this dissertation is to study the effects of galaxy flybys on the structural evolution of galaxies. Galaxy flybys are very close interactions that do not result in a merger. With the high frequency in the late Universe, their role in the evolution of galaxies is significant. Earlier studies focused on equalmass flybys, which are extremely rare. We focus on typical flybys with a lower mass ratio. We aim to explore the structure and evolution of galaxies in greater detail and demonstrate that these flybys are just as important as equalmass ones. We performed a series of N body simulations of typical flybys with varying impact para meters. We demonstrated the applicability and importance of isolated N body simulations and developed an efficient method for reliable bar detection in galaxy discs. For the first time, we examined the evolution of the secondary galaxy, focusing on its dark matter mass loss. The results show that the leftover mass follows logarithmic growth law with impact parameter and suggest that flybys contribute to the formation of dark matterdeficient galaxies. The primary galaxy is affected in a similar way as in equalmass flybys. Bars form in closer flybys, twoarmed spirals form during all flybys, and the dark matter halo spins up. Most of the parameters of these structures are correlated or anticorrelated with the impact parameter. We also noticed that a double bar could form as evolving spirals wrap around the earlyformed bar. We successfully demonstrated that frequent, typical flybys with lower mass ratios signifi cantly affect the evolution of galaxies, producing various observed effects. Our results should serve as a warning not to disregard these interactions in future studies. URI: http://hdl.handle.net/123456789/5441 Files in this item: 1
mitrasinovic_ana.pdf ( 5.370Mb ) 
Jovanović, Jasmina (Beograd , 2022)[more][less]
Abstract: The analysis of biological sequence similarity between different species is significant in identifying functional, structural or evolutionary relationships among the species. Biological sequence similarity and analysis of newly discovered nucleotide and amino acid sequences are demanding tasks in bioinformatics. As biological data is growing exponentially, new and innovative algorithms are needed to be constantly developed to get faster and more effective data processing. The challenge in sequence similarity analysis algorithms is that sequence does not always have obvious features and the dimension of sequence features may be very high for applying regular feature selection methods on sequences. It is important to have a simple and effective algorithm for determining biological sequence relationships. This thesis proposes two new methods for sequence transformation in feature vectors that takes into consideration statistically significant repetitive parts of analyzed sequences, as well as includes different approaches for determination of nucleotide sequence similarity and sequence classification for predicting taxonomy groups of biological sequence data. The first method is based on information theory and fact that both position and frequency of repeated sequences are not expected to occur with the identical presence in a random sequence of the same length. The second method includes building signatures of biological sequences and profiles of taxonomic classes based on repetitive parts of sequences and distances between these repeats. Proposed methods have been validated on multiple data sets and compared with results obtained using different well known and accepted methods in this field like BLAST, Clustal Omega and methods based on kmers. Resulted precision for proposed methods is close to values provided for existing methods for the majority of tested datasets, and time performance depends strictly to used infrastructure and sequence type. Methods provide results that are comparable with other commonly used methods focused on resolving the same problem, taking into consideration statistically significant repetitive parts of sequences with different characteristics. URI: http://hdl.handle.net/123456789/5440 Files in this item: 1
JasminaJovanovic.pdf ( 3.984Mb ) 
Ivanović, Marija (Beograd , 2022)[more][less]
Abstract: This dissertation focuses on the Roman domination problem and its two modifications. Improvements and relaxations of two integer linear programming for mulations for the Roman domination problem from the literature are introduced, proved to be equivalent to the existing ones despite of the variables relaxation and usage of fewer number of constraints and compared by standard optimization solvers, CPLEX and Gurobi. Improved formulations can be equally used as original ones, but, as it can be seen from numerical results, for some instances, they can be more useful. Given the fact that old and new formulations can not be used for some large size instances, and that algorithms for solving Roman domination problem are mostly defined for some particular graph classes, the aim of this research was to find a new algorithm that can be used for solving Roman domination problem on all graph classes and all graph sizes. Although the Roman domination problem belongs to the class NP, presented algorithm is able to find solution value equal to optimal solution value on very large number of instances in less then a second. For the first modification of the Roman domination problem, named Restrained Roman domination problem, a new mixed integer linear programming formulation is intro duced and, to the best of the author’s knowledge, this formulation is the first in the literature. For the second modification of the Roman domination problem, the Weak Roman domination problem, an improved integer linear programming formu lation is presented. Improved formulation is also proved to be correct, equivalent to the existing formulation from the literature and compared using standard op timization solvers, CPLEX and Gurobi. Numerical results showed the advantage of the improved formulation on almost all tested instances. Additionally, an im proved lineartime algorithm for solving the Weak Roman domination problem on block graphs is introduced and, similarly to the Roman domination problem, a new algorithm, based on the variable neighborhood search method is presented. With the new variable neighborhood search based algorithm we aimed to find solution of the Weak Roman domination problem equal to the optimal on very large number of tested instances. For instances for which some solution value is found but not proved to be an optimal, presented algorithm provided the new lowerbounds. Even more, for some instances, where optimization solvers were not able to prove optimality or to find any solution, new solutions are found. URI: http://hdl.handle.net/123456789/5431 Files in this item: 1
MarijaIvanovic_ ... a_saPotpisanimIzjavama.pdf ( 1.958Mb ) 
Jovanović Spasojević, Tanja (Beograd , 2022)[more][less]
Abstract: In this thesis, subjects of consideration are the embeddings theorems of weighted Bergman spaces in Lpspaces, as well as embeddings theorems of harmonic mixed norm spaces. The first part of the thesis generalizes the theorems of embeddings Bergman spaces into Lp(μ)spaces, where μ is a Borel measure on a given domain. They have been earlier studied on domains such as unit ball and upper halfspace. Generalization refers to bounded domains Ω ⊂ Rn with C1 boundary. This embedding will be valid to any p > 0, whenever the measure of the spaces Lp satisfies the Carledon condition. Reverse the direction will be valid only in case if p > 1 + α+2 n−2 . The second part of the dissertation also generalizes the embeddings theorems of mixed norm spaces of harmonic functions on a unit ball, where the generalization is applied to the domain Ω ⊂ Rn with C1 boundary. However, in addition we are obtaining another important result relating to the limitation of the maximum operators in the mixed norm on the general domain for the class of QNS functions. URI: http://hdl.handle.net/123456789/5378 Files in this item: 1
Jovanovic_Spasojevic_Tanja.pdf ( 1.643Mb )