Doctoral Dissertations
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Čvorović - Hajdinjak, Iva (Beograd , 2025)[more][less]
Abstract: This doctoral dissertation addresses the development and application of advanced methods for analyzing the temporal variability of active galactic nuclei (AGN) through the modeling of their optical light curves. The research integrates unsupervised and generative learning techniques, by combining Self- Organizing Maps (SOM) for data preprocessing and Conditional Neural Processes (CNP) for light curve prediction. For the first time in the study of AGN light curves, clustering via SOM has been implemented for preprocessing, alongside the application of CNP for modeling variability. This innovative approach facilitates a more effective modeling of light curves characterized by uneven sampling and missing observations. The QNPy software package was developed and optimized for large-scale parallel processing of extensive time series data. The proposed methodology was validated using light curves from the All-Sky Automated Survey for SuperNovae (ASAS-SN) and the SWIFT/BAT mission, covering a broad range of time scales and variability. The analysis prove that clustering light curves with SOM enhances the performance of neural process, particularly for objects exhibiting simpler variability patterns. The effects of SOM hyperparameters on clustering and prediction performance were carefully examined. The models were validated using loss function and mean squared error evaluations on real data. The proposed methodology shows strong potential for scalable processing of the large time-series data, anticipated in upcoming projects such as the Vera C. Rubin Observatory’s Legacy Survey of Space and Time, enabling automated classification, anomaly detection, and the extraction of scientifically significant objects from catalogs containing hundreds of millions of sources. URI: http://hdl.handle.net/123456789/5766 Files in this item: 1
doktorska_disertacija_iva_cvorovic_hajdinjak.pdf ( 7.248Mb ) -
Srdanović, Vladimir (University of Belgrade , 1987)[more][less]
Abstract: The dissertation relates to the elements of medical decision-making, modeled by a consultative expert system, characteristic to the domain of rheumatology and potentially other domains of medicine with a similar structure. URI: http://hdl.handle.net/123456789/5764 Files in this item: 1
Konsultativni ekspertni sistem.pdf ( 7.218Mb ) -
Stefanović, Seđan (Beograd , 2025)[more][less]
Abstract: The subject of the dissertation is the investigation of the relation of strong BJ orthogonality in C∗-algebras. For two elements a and b of C∗-algebra A, we say that a is strong BJ orthogonal to b, if for all c ∈ A holds ‖a + bc‖ ⩾ ‖a‖ and we write a ⊥S b. If it is also true that b ⊥S a, then we say that a and b are mutual strong BJ orthogonal and write a ⊥⊥S b. To this relation, we associate an undirected graph Γ(A) (which we call an orthograf), where the vertices are the nonzero elements of the C∗-algebra A, with the identification of an element and its scalar multiple; while there is an edge between two vertices a and b if a ⊥⊥S b. We will show that for any C∗-algebra A, different from three simple C∗-algebras, and for any two non-isolated vertices a and b in the orthograph, we can find vertices c1, c2, c3 ∈ Γ(A) such that a ⊥⊥S c1 ⊥⊥S c2 ⊥⊥S c3 ⊥⊥S b. We will also describe the isolated vertices of the graph Γ(A) for any C∗-algebra A. Finally, in the case of finite-dimensional C -algebras, we will determine the diameter of Γ(A), i.e., the minimum number of elements required to connect any two vertices. URI: http://hdl.handle.net/123456789/5754 Files in this item: 1
Stefanovic_Srdjan_doktorska_disertacija.pdf ( 990.4Kb ) -
Jovanović, Milica (Beograd , 2024)[more][less]
Abstract: The analysis of Grassmann manifolds, which were first introduced in the 19th century, is one of the classical problems in the algebraic topology. When analyzing topological spaces, it is always useful to determine their cohomology algebra. The cohomology of Grassmann manifolds is already well known, but their covering spaces, so called oriented Grassmann manifolds, are far less examined. The oriented Grassmann manifold ˜Gn,k is defined to be the space of oriented k-dimensional subspaces of Rn. In this dissertation we analyze the cohomology algebra of oriented Grassmann manifolds ˜Gn,k with integer and modulo 2 coe!cients, predominantly the case k = 3. The dissertation comprises three chapters. The first chapter is an introduction where an overview of known results and necessary tools is given. In the second chapter we study the cohomology with the modulo 2 coe!cients. First of all, the known results in the case k = 2 are presented. Next, we move onto the case k = 3 where the partial description of the cohomology algebra is given. This section is based on papers published in the last several years. We give an overview of these results in the thesis, and we also present original results for n close to a power of two. In the last part of this chapter, we investigate the cohomology algebra of the manifold ˜G2t,4, and that is as far as we have come with the examination of modulo 2 cohomology. The third chapter is dedicated to the integral cohomology. This chapter, like the previous one, also splits in several sections, depending on the value of k. When k = 2, the integral cohomology is completely determined, and we present the proof for n odd. When k = 3, only the integral cohomology of ˜Gn,3, n → {6, 8, 10}, has been determined so far, while for k ↭ 4 only some partial results are known. In this segment we also analyze the connection between the integer and the modulo 2 cohomology algebra of these Grassmannians by analyzing the morphism between them induced by the modulo 2 reduction. URI: http://hdl.handle.net/123456789/5751 Files in this item: 1
Milica_Jovanovic_doktorat.pdf ( 1.723Mb ) -
Mrkela, Lazar (Beograd , 2024)[more][less]
Abstract: This dissertation examines two discrete location problems and their bi- objective variants. The first problem under consideration is the maximal covering location problem with user preferences and budget constraints imposed on facility opening. This variant of the maximal covering problem has not been previously studied in the literature. Unlike the classical maximal covering problem, the variant proposed in this dissertation includes user preferences for locations, where users are assigned to the location with opened facility that they prefer the most. Additionally, different locations have different costs for establishing facilities, and the available budget for opening facilities is limited. This problem is solved using the Variable Neighborhood Search (VNS) method, and the results were compared with the ones obtained by an exact solver on modified instances from the literature. Furthermore, an existing variant of the maximal covering problem is also addressed, which imposes the limit on the number of opened facilities instead of limiting the budget for opening facilities. The second problem examined is the regenerator placement in optical networks. In optical networks, signal quality degrades with distance, necessitating the place- ment of costly devices to restore the signal. This dissertation studies an existing model where the set of possible regenerator locations and the set of user nodes are different, defining the problem as generalized. The generalized regenerator place- ment problem in optical networks is also solved using the Variable Neighborhood Search method, with results compared to the best available solutions from the lit- erature. Bi-objective variants of these problems are defined as well. For the maximal covering location problem, user preferences are included as weighted factors in the total covered demand, forming the first objective function. The second objective function represents the number of uncovered users and aims to ensure fairness in the model. In the regenerator placement problem for optical networks, it is assumed that, due to budget constraints, uninterrupted communication between all pairs of user nodes may not be feasible. Each pair is assigned a weight, and the sum of the weights of connected pairs constitutes the first objective function, while the second objective function represents the cost of placing regenerators. These bi-objective variants are solved using an adapted multi-objective version of the Variable Neigh- borhood Search method, and the results are compared with general evolutionary algorithms. URI: http://hdl.handle.net/123456789/5750 Files in this item: 1
lazar_mrkela_doktorska_disertacija.pdf ( 17.56Mb )