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Vicanović, Jelena (Beograd , 2024)[more][less]
Abstract: A convex continuoustime maximization problem is formulated and the nec essary optimality conditions in the infinitedimensional case are obtained. As a main tool for obtaining optimal conditions in this dissertation we use the new theorem of the alternative. Since there’s no a differentiability assumption, we perform a linearization of the problem using subdifferentials. It is proved that the multiplier with the objective function won’t be equal to zero. It was also shown that if the linear and nonlinear constraints are separated, with additional assumptions it can be guaranteed that the multiplier with nonlinear constraints will also be nonzero. In the following, an integral constraint is added to the original convex problem, so that a Lyapunovtype problem, i.e. an isoperimetric problem, is considered. Lin earization of the problem using subdifferentials proved to be a practical way to ignore the lack of differentiability, so the optimality conditions were derived in a similar way. It is shown that the obtained results will also be valid for the vector case of the isoperimetric problem. Additionally, the optimality conditions for the smooth problem were considered. On the minimization problem, it was shown that the necessary conditions of KarushKuhnTucker type will be valid with the additional regularity constraint condition. Also, any point that satisfies the mentioned optimality conditions will be a global minimum. URI: http://hdl.handle.net/123456789/5676 Files in this item: 1
J.Vicanovic_doktorska_disertacija.pdf ( 2.198Mb ) 
Kostić, Petar (b , 2023)[more][less]
Abstract: The models of radio synchrotron emission of supernova remnants (SNRs) imply uniform density ahead of shock wave, so the evolution of luminosity is usu ally studied in such an environment, most often through the surfacebrightnessto diameter dependence, the Σ–D relation. This field aims to better understand the SNR evolution, the emission models, but also the methods for determining their distance. It is not an easy task because of a very large scatter in the Σ–D Milky Way sample. The dissertation puts a different perspective at the Σ–D relation (usually treated as powerlaw function), assuming that nonuniform environment around the stars considerably affects its shape and slope, that may vary during the SNR expansion. It makes the ambient density structure an important factor whose impact must be investigated. The numerical code for hydrodynamic (HD) simulations and the emission model were developed. The 3D HD simulations were performed in different nonuniform environments, including lowdensity bubbles and a variety of clumpy models. Based on the simulation results, a semianalytical 3D sphericallysymmetric model of HD and Σ–D evolution of SNRs in clumpy medium was developed, which is used to generate large Σ–D samples. The results show that after entering the clumpy medium the SNR brightness enhances, but afterward the Σ–D slope steepens, shortening the brightness evolu tion lifetime. Despite the evident increase in slope in clumpy medium, the Galactic sample average slope flattens at ≈ 13–50 pc. After analyzing the generated SNR samples in clumpy medium it is concluded that the significant flattening and scatter in Galactic sample originates in sporadic emission jumps of individual SNRs in a limited diameter interval. The additional analyses of selection effects are needed to investigate these issues. URI: http://hdl.handle.net/123456789/5606 Files in this item: 1
Kostic_Petar_disertacija.pdf ( 1.947Mb ) 
Protić, Danijela (Beograd , 2023)[more][less]
Abstract: Anomaly detection is the recognition of suspicious computer network behavior by comparing unknown network traffic to a statistical model of normal network behavior. Binary classifiers based on supervised machine learning are good candidates for normality detection. This thesis presents five standard binary classifiers: the knearest neighbors, weighted knearest neighbors, decision trees, support vector machines and feedforward neural network. The main problem with supervised learning is that it takes a lot of data to train highprecision classifiers. To reduce the training time with minimal degradation of the accuracy of the models, a twophase preprocessing step is performed. In the first phase, numeric attributes are selected to reduce the dataset. The second phase is a novel normalization method based on hyperbolic the tangent function and the damping strategy of the LevenbergMarquardt algorithm. The Kyoto 2006+ dataset, the only publicly available data set of realworld network traffic intended solely for anomaly detection research in computer networks, was used to demonstrate the positive impact of such preprocessing on classifier training time and accuracy. Of all the selected classifiers, the feedforward neural network has the highest processing speed, while the weighted knearest neighbor model proved to be the most accurate. The assumption is that when the classifiers work concurrently, they should detect either an anomaly or normal network traffic, which occasionally is not the case, resulting in different decision about the anomaly, i.e. a conflict arises. The conflicting decision detector performs a logical exclusive OR (XOR) operation on the outputs of the classifiers. If both classifiers simultaneously detected an anomaly or recognized traffic as normal, their decision was no conflict had occurred. Otherwise a conflict is detected. The number of conflicts detected provides an opportunity for additional detection of changes in computer network behavior. URI: http://hdl.handle.net/123456789/5599 Files in this item: 1
Danijela Protic  Doktorska Disertacija.pdf ( 3.143Mb ) 
Kovjanić, Milorad (Beograd , 2023)[more][less]
URI: http://hdl.handle.net/123456789/5598 Files in this item: 1
Milorad Kovjanić  Disertacija.pdf ( 2.190Mb ) 
Radosavljević, Jovan (Beograd , 2023)[more][less]
Abstract: Graph G = (V,E) is an ordered pair of set of nodes V and branches E. Order graph G is the number of nodes V , and its size is the number of branches E. Knots u, v ∈ V are adjacent if there is a branch uv ∈ E between them. Distance dist(u, v) nodes u and v G is the length of the shortest path from u to v. The diameter of the graph G is the largest distance dist(u, v) let two nodes in, v. They are discussed in the dissertation graphs of diameter 2. Intuitively, the notion that graphs are dia meters 2 simple structures; however, they are known to be asymptotically close all graphs of diameter 2. That is why a narrower class is interesting — class D2C of critical graphs of diameter 2, i.e. graphs where the removal of any branches leads to an increase in diameter. In addition, a narrower class of pri mitive D2C (PD2C) graphs, i.e. D2C graphs that do not have two nodes with the same set of neighbors. In the introductory chapter 2, the basic concepts, algorithms and dings used in the dissertation. They are presented in the following chapters original results regarding diameter graphs 2. Chapter 3 describes the procedure for obtaining a list of D2C graphs of order up to 13. With builtin parallelization, the creation of a list of D2C graphs of order up to 13 it lasted a month. This was a step forward, because previously there was a spi around all graphs of diameter 2 lines up to 10. The obtained results were used for testing several known hypotheses about graphs of diameter 2. In chapter 4 it is shown that for every m ⩾ 3 a D2C graph containing cli a ku of size m must have at least 2m nodes. At the same time, with accuracy up to isomorphism, there is exactly one graph of size 2m that contains a clique of characters m. Chapter 5 discusses PD2C graphs with the smallest number of branches. From list of all PD2C graphs of order n ⩽ 13 are selected PD2C graphs of size at most 2n − 4. Only three of the isolated graphs are of size 2n − 5, which is in accordance with the statement of the ErdesRenji theorem about the lower bound for the size graphs of diameter 2 that do not contain a node adjacent to all other nodes (that limit is 2n − 5). PD2C graphs of size 2n − 4 rows up to 13 sorted are in three groups: • The first group belongs to the Z family, defined in the dissertation, which for each n ⩾ 6 contains exactly one PD2C graph of order n of size 2n − 4. • The second group consists of seven Hamiltonian PD2C graphs of order at most 9 of size 2n−4. In the dissertation it was proved that there is no such Hamil tone graph of order greater than 11, i.e. that the seven graphs found are the only ones Hamiltonian PD2C graphs of size 2n − 4. • The third group consists of a unique graph that does not belong to any of the first two groups. Based on these results, the hypothesis was formulated that all PD2C graphs re that n ⩾ 10 and sizes 2n − 4 belong to the family Z. Keywords: graphs, critical graphs of diameter 2, primitive graph You Scientific field: Computing and informatics Narrower scientific field: Graph theory UDC number: 004.415.5(519.1 URI: http://hdl.handle.net/123456789/5594 Files in this item: 1
disertacijaJovanRadosavljevic.pdf ( 746.0Kb )