Browsing Doctoral Dissertations by Title
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Grbić, Milana (Beograd , 2020)[more][less]
Abstract: In this dissertation some actual problems of bioinformatics and computational biology are explored,together with the methods for solving them. The following problems are considered: partitioning ofsparse biological networks intok-plexsubnetworks, prediction of the role of metabolites in metabolicreactions, partitioning of biological networks into highly connectedcomponents and the problem ofidentification of significant groups of proteins by adding new edges to the weighted protein interacti-ons network. The aforementioned problems have theoretical importance in areas of machine learningand optimization, and practical application in biological research. Inaddition to solving the afore-mentioned problems from the computational aspect, the dissertation explores further application ofthe obtained results in the fields of biology and biochemistry, as well as the integration of resultswithin existing bioinformatics tools.The problem of predicting the role of metabolites in metabolic reactions is solved by a predictivemachine learning method based on the conditional random fields, whilefor the remaining threeproblems the algorithams based on variable neighbourhood search are developed. For solving theproblem of identification of significant groups of proteins by adding new edges to the weighted proteininteractions network, the variable neighbourhood search is only the first phase of the proposedsolution, while in the second and the third phase of the proposed method, the integration withadditional biological information and bioinformatics tools are performed.The proposed computational methods of partitioning and groupingin biological networks confirmexisting findings in a new manner and lead to new discoveries about biological elements and theconnections between them. By solving these problems and by interpreting the obtained resultsin this dissertation, a scientific contribution was made to the scientific field of computer science,particularly to the scientific disciplines of bioinformatics and computational biology. URI: http://hdl.handle.net/123456789/5088 Files in this item: 1
grbic_Milana_disertacija.pdf ( 8.740Mb ) -
Davidović, Tatjana (Belgrade , 2006)[more][less]
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Radović, Viktor (Beograd , 2017)[more][less]
Abstract: The main goal of this dissertation is improvement of an approach for identi- cation of the members of asteroid families, based on the hierarchical clustering method. An additional step is introduced in order to reduce a so-called chaining e ect. The introduced algorithm consists of four main steps. In the rst step, the hierarchical clustering method is applied to the initial catalogue of proper elements in order to obtain a preliminary list of family members. In the second step, using available physical properties, and based upon the de ned criteria, the interlopers are identi ed. In the third step, objects identi ed as interlopers in the second step, are excluded from the initial catalogue of proper orbital elements, producing a modi ed catalogue. Finally, in the fourth step, the HCM analysis is performed again, but this time using the modi ed catalogue of proper elements. It is shown that in this way a number of potential interlopers among family members is signi cantly reduced. Moreover, an on-line based portal (Asteroids Families Portal; AFP) to apply this procedure is developed, and is freely available to all interested researchers. The second goal of the dissertation is to determine the limitations of the backward integration method, used for estimation of ages of young asteroid families. This aim is achieved through numerical simulations of the evolution of a ctitious family. By determining instants of secular angles i $ clustering, a linear relationship is found between the depth of a clustering and the age of a family. According to the obtained results, the backward integration method could be successfully applied to families not older than 18 Myrs. URI: http://hdl.handle.net/123456789/4504 Files in this item: 1
Radovic_teza.pdf ( 22.32Mb ) -
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 k-mers. Resulted precision for proposed methods is close to values provided for existing methods for the majority of tested data-sets, 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 ) -
Perović, Vladimir (Beograd , 2013)[more][less]
Abstract: Although long-range intermolecular interactions (interactions acting on distances >5Å) play an important role in recognition and targeting between molecules in biological systems, there is no one appropriate software package allowing use of this important property in investigation of biologically active molecules. The multifunctional EIIP/ISM software, which is based on physical parameters determining long-range molecular properties, was developed in this thesis. This novel and unique platform allows (i) investigation of protein-protein and protein-small molecule interactions, (ii) analysis of structure/function relationship of proteins, (iii) assessment of biological effects of mutations in proteins, (iv) monitoring of the functional evolution of proteins, (v) ―de novo‖ design of molecules with desired biological function and (vi) selection of candidate therapeutic molecules. Results of application of the EIIP/ISM platform on diverse problems (e.g. the evolution of influenza A viruses, assessment of biological effects of mutations on the LPL protein, representing a risk factor for cardiovascular diseases, identification of therapeutic targets for HIV and influenza viruses, virtual screening of molecular libraries for candidate antibiotics and anti-HIV drugs) which are presented in this thesis, confirm the applicability of this platform on broad spectrum of problems in molecular biology, biomedicine and pharmacology. URI: http://hdl.handle.net/123456789/4230 Files in this item: 1
phdPerovic_Vladimir.pdf ( 11.95Mb ) -
Baranović, Nives (Beograd , 2022)[more][less]
Abstract: Future primary education teachers should acquire appropriate mathematical knowledge, skills, and abilities to provide a suitable environment for developing their prospective students' responding knowledge, skills, and abilities. Various studies in education show that students of all ages have difficulties mastering geometric concepts and making functional connections between them, especially at the transition from school to university level. Therefore, a quasi-experimental study was conducted with non-equivalent groups of future primary education teachers. The study aimed to determine a particular teaching method's effectiveness for developing visualization skills, geometric thinking, and optimizing geometry learning outcomes. Three tests were used before and after teaching to collect data on the characteristics of the research participants. The tests were: the VH test to measure the level of geometric thinking, the GEO test to gain insight into geometric knowledge and visual skills, and the SPAC test to measure the unique visual-spatial ability to establish connections between 3D figures and their networks. In the experimental group, a specific teaching approach was applied. The teaching approach is based on the visual-analytical method and directed observation and balancing of three ways of expression: linguistic, visual, and symbolic. Van Hiele's five stages of learning were used in the structuring and selecting of teaching activities. The pre-test results confirmed the relatively weak prior knowledge, visualization skills, and level of geometric thinking of all participants, and the possession of appropriate visual-spatial abilities that predict possible success. The t-test confirmed no statistically significant difference between the participants at the beginning of the teaching. The Spearman correlation coefficient determined a positive, statistically significant correlation between all three tests, indicating a possibility for mutual development. The post-test results confirmed the effectiveness of the applied strategies and teaching methods in achieving better geometry learning outcomes, developing visual literacy, and progress in the levels of geometric thinking of the participants in the experimental group. The experimental group participants had statistically significantly better results on the post-test than the results they achieved on the pre-test compared to the results achieved by the control group participants who were taught more traditionally. Participants in the control group also improved, but these improvements were not statistically significant. The above confirmed that it is possible to develop geometry and visual literacy through systematic learning and teaching at different levels of the educational system. URI: http://hdl.handle.net/123456789/5453 Files in this item: 1
Doktorat _Baranovic 2022 Final NB.pdf ( 7.954Mb ) -
Vidović, Zoran (Beograd , 2020)[more][less]
Abstract: From a sequence of observations, the ones that exceed previous ones in a time seriesare called records. The pioneer paper of record theory is considered to be Chandler [39]. Thistheory gained its popularity doe to significant public interest towards records. As a result, largenumber of papers are published on this topic.Record values are very important in statistics. Record values are applied in parameterestimation issues, characterization issues, hypothesis and stationarity tests, etc. Also, theirusefulness in probability theory and in theory of random process is tremendous.This dissertation discusses applications of records through numerical evaluations of maximumlikelihood estimators of parameters of the three-parameter extensions of Weibull distributionfamily, new recurrence relations of record moments, records in Bayesian inference, applicationsof records in characterization issues for random chord length distributions as well with theasymptotic behaviour of extremes of random chord lengths. This dissertation consists on sixchapters.Several examples of records are presented in the first chapter.Second chapter discusses the strict formulations of records from a sequence of independentand identically distributed random variables. Their application and their extensions from thesame model are presented, as well with several interesting results.The problem of existence and uniqueness of maximum likelihood estimators based on recordsis elaborated in the third chapter. In this chapter, we present sufficient conditions that confirmthe existence and uniqueness of maximum likelihood estimators for a three-parameter extensionsof Weibull distributions. Also, several well known results are presented as examples. Severalresults from this chapter could be found in [135].The fourth chapter is dedicated to moment recurrence relations of a three-parameter ex-tension of Weibull distribution based on records with possible applications. These results arepublished in [136].Fifth chapter deals with Bayesian prediction of order statistics based on record values. Here,we expand the applicability of records in real problems and provide a better understanding oftheir significance. Several results presented in this chapter could be found in [136].In the sixth chapter the random chord length issue is considered through the record valuetheory. A new generation method of random chords is presented. The study of limit behaviourof maximum length of random chords for all cases of generation is also conducted. Character-ization results for random chord length distributions based on record moments are obtained. Several results presented in this chapter could be found in [134]. URI: http://hdl.handle.net/123456789/5089 Files in this item: 1
disertacija_Z_Vidovic.pdf ( 2.262Mb ) -
Banković, Dragić (Belgrade , 1980)[more][less]
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Savić, Branko (Belgrade)[more][less]
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Đenić, Aleksandar (Beograd , 2018)[more][less]
Abstract: This pap er considers two discrete lo cation problems: Bus Terminal Lo cation Problem (BTLP) and Long-term Care Facility Lo cation Problem (LTCFLP). Vari- able Neighb orho o d Search (VNS) metho d for solving BTLP and LTCFLP is pre- sented in this pap er. VNS is a single-solution based metaheuristic based on system- atic change of neighb orho o ds while searching for optimal solution of the problem. It consists two main phases: shake phase and lo cal search phase. BTLP is a discrete lo cation problem which considers lo cating bus terminals in order to provide the highest p ossible quality of public service to the clients. Clients are presented as public transp ortation stations, such as bus or metro stations. VNS algorithm is used for solving BTLP. This algorithm uses improved lo cal search based on e cient neighb orho o d interchange. VNS is parallelized (PVNS) which leads to signi cant time improvement in function of the pro cessor core count. Computa- tional results show that prop osed PVNS metho d improves existing results from the literature in terms of quality. Larger instances, based on instances from the Trav- eling Salesman Problem library, are presented and computational results for those instances are rep orted. LTCFLP is created as a part of health care infrastructure planning in South Korea. Clients are considered as groups of patients with a need of long-term health care, while established facilities present lo cations where the centers that provide health care services should b e built. Prede ned are n lo cations where centers are to b e established. This problem seeks at most K lo cations to establish health centers so they are to b e equally loaded with clients demand. For solving LTCFLP, by using VNS algorithm, data structure based on fast interchange is presented. It reduces the time complexity of one iteration of lo cal search algorithm to O ( n · max( n,K 2 )) comparing to the known time complexity from the literature O ( K 2 · n 2 ) . Reduced time complexity of the presented VNS leads to b etter quality solutions, due to larger numb er of VNS iterations that can b e p erformed in less computational time. This pap er presents computational results that outp erform the b est known results from the literature. URI: http://hdl.handle.net/123456789/4744 Files in this item: 1
Aleksandar_Djenic_phd.pdf ( 2.183Mb ) -
Pantić, Dražen (Belgrade)[more][less]
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Mišković, Stefan (Beograd , 2016)[more][less]
Abstract: In this dissertation, three NP-hard min-max discrete optimization problems are considered. The rst considered problem is multi-period emergency service location problem, the second one is dynamic maximal covering location problem with multiple covering radii, and the third one is uncapacitated multiple allocation p-hub center problem. In many practical situations, input parameters (such as user demands, transportation time or cost) often vary with unknown distributions. Therefore, it is necessary to involve these uncertainties in the deterministic variants of the problems by applying robust optimization approach. Mathematical models for the deterministic and non-deterministic variants of all three problems are developed, except for the deterministic uncapacitated multiple allocation p-hub center problem, which has already been addressed in the literature. In addition, for the rst time in the literature, it was proven that the emergency service location problem is NP-hard. The considered problems and their robust variants have numerous applications, due to the fact that in real-life situations input parameters are often subject to uncertainty. Multi-period emergency service location problem may be used when determining optimal locations for police stations, re brigades, ambulances, and other emergency units in the given region. The dynamic maximal covering location problem with multiple covering radii is useful when choosing the optimal strategy for establishing resources (service centers, suppliers, facilities, etc.) with maximal satisfaction of customer demands in a certain region, by assuming that the service e ciency directly depends on the distance between customer and service center (i.e., the selected coverage radius). The uncapacitated multiple allocation p-hub center problem has signi cant applications in designing telecommunication and transportation networks, postal delivery systems, emergency systems, supply networks, etc. Since exact methods provide optimal solutions only for problem instances of small dimensions, hybrid metaheuristic algorithms are developed to solve both deterministic and robust variants of the considered problems. The proposed hybrid algorithms are obtained by combining particle swarm optimization, with local search heuristic { classical local search or variable neighborhood search method. For dynamic maximal covering location problem with multiple covering radii, a hybridization of metaheuristic algorithm with exact method based on linear programming is developed. All elements of the proposed algorithms are adopted to the problems under consideration. Di erent strategies are implemented for improving the e ciency of proposed algorithms, especially for the calculation of the objective function value and the local search part. The in uence of di erent parameters of hybrid algorithms on the solution quality is analyzed in detail. All parameters are adjusted by using analysis of variance. For all considered problems (both deterministic and robust variant), the performance of the proposed hybrid algorithms is evaluated on adequate test data sets. The proposed algorithms are compared with existing heuristic from the literature and exact methods incorporated in commercial CPLEX solver. The obtained experimental results indicate the e ciency of proposed algorithms in obtaining high quality solutions for all considered test instances. The presented comparative analysis indicates the advantages of the proposed hybrid algorithms over existing methods in the sense of solution quality and/or required computational time, especially in the case of large problem dimensions. The results presented in this paper represent a contribution to the eld of discrete optimization, robust optimization and metaheuristic methods. URI: http://hdl.handle.net/123456789/4423 Files in this item: 1
Miskovic_Stefan_teza.pdf ( 1.773Mb ) -
Lepović, Mirko (Beograd , 1991)[more][less]
URI: http://hdl.handle.net/123456789/4138 Files in this item: 1
Spektralna_teorija_grafova.PDF ( 4.283Mb ) -
Marić, Miroslav (Belgrade)[more][less]
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Lazić, Mirjana (Kragujevac, Serbia , 2011)[more][less]
Abstract: This doctoral dissertation belongs to the Spectral theory of finite and infinite graphs, which joins elements of Graph theory and Linear algebra. The dissertation, beside Preface and References with 24 items, consists of four chapters divided in sections and Appendix. In Chapter 1 some results on the reduced energy of graphs are given. All connected graphs whose reduced energy does not exceed 3 are described. In Chapter 2 all finite and infinite graphs with seven nonzero eigenvalues are determined. Some results on integral graphs are given in Chapter 3. Finally, Chapter 4 contains some results on symmetric double starlike trees. The definitions of starlike tree and double starlike tree are given and we proved that there exist no two cospectral non-isomorphic symmetric double starlike trees. URI: http://hdl.handle.net/123456789/1879 Files in this item: 1
dokdis.pdf ( 713.4Kb ) -
Matić, Dragan (Beograd , 2013)[more][less]
Abstract: In this work some actual combinatorial optimization problems are investigated. Several di erent methods are suggested for solving the following NP hard problems: maximally balanced connected partition problem in graph, general maximally balanced problem with q partitions (q ≥ 2), maximum set splitting problem and p-ary transitive reduction problem in digraphs. Together with investigation of combinatorial optimization methods for solving these problems, the applying of these problems in education is also considered in the dissertation. For solving each of these problems, metaheuristics are developed: variable neighborhood search is developed for each problem and genetic algorithm is used for solving p-ary transitive reduction problem in digraphs. For maximally balanced connected partition problem a mixed linear programming model is established, which enables to solve the problem exactly for the instances of lower dimensions. Achieved numerical results indicate the high level of reliability and usability of the proposed methods. Problems solved in this research are of a great interest both in theoretical and practical points of view. They are used in production, computer networks, engineering, image processing, biology, social sciences and also in various elds of applied mathematics and computer science. In this work the applying of some problems in educational issues is also considered. It is shown that approaches of nding maximally balanced connected partition in graph and nding maximum splitting of the set can be successfully used in course organization, which is veri ed on the concrete examples. Based on the objective indicators and professor's assessment, the techniques for the identifying the connections between the lessons, as well as the weights of the lessons are developed. Thus, whole course can be represented as a connected weighted graph, enabling the resolving of the lesson partition problem by mathematical approaches. By assigning the lessons into the appropriate categories (topics area) inside a iv course, a collection of subsets (corresponding to the topics) of the set of lessons is created. If we set the requirement that lessons should be split into two disjoint subsets (e.g. into the winter and summer semesters), in a way that corresponding topics are processed in both subsets, then the mathematical model of the requirement and its solution corresponds to the set splitting problem. By the developed models of course organization, from which the NP hard problems arise, in addition to the scienti c contributions in the elds of mathematical programming and operational research, contributions in educational aspects are added, especially in the methodology of teaching mathematics and computer science. URI: http://hdl.handle.net/123456789/4229 Files in this item: 1
phd_matic_dragan.pdf ( 1.438Mb ) -
Matić, Dragan (Beograd , 2013)[more][less]
Abstract: In this work some actual combinatorial optimization problems are investigated. Several di erent methods are suggested for solving the following NP hard problems: maximally balanced connected partition problem in graph, general maximally balanced problem with q partitions (q ≥ 2), maximum set splitting problem and p-ary transitive reduction problem in digraphs. Together with investigation of combinatorial optimization methods for solving these problems, the applying of these problems in education is also considered in the dissertation. For solving each of these problems, metaheuristics are developed: variable neighborhood search is developed for each problem and genetic algorithm is used for solving p-ary transitive reduction problem in digraphs. For maximally balanced connected partition problem a mixed linear programming model is established, which enables to solve the problem exactly for the instances of lower dimensions. Achieved numerical results indicate the high level of reliability and usability of the proposed methods. Problems solved in this research are of a great interest both in theoretical and practical points of view. They are used in production, computer networks, engineering, image processing, biology, social sciences and also in various elds of applied mathematics and computer science. In this work the applying of some problems in educational issues is also considered. It is shown that approaches of nding maximally balanced connected partition in graph and nding maximum splitting of the set can be successfully used in course organization, which is veri ed on the concrete examples. Based on the objective indicators and professor's assessment, the techniques for the identifying the connections between the lessons, as well as the weights of the lessons are developed. Thus, whole course can be represented as a connected weighted graph, enabling the resolving of the lesson partition problem by mathematical approaches. By assigning the lessons into the appropriate categories (topics area) inside a iv course, a collection of subsets (corresponding to the topics) of the set of lessons is created. If we set the requirement that lessons should be split into two disjoint subsets (e.g. into the winter and summer semesters), in a way that corresponding topics are processed in both subsets, then the mathematical model of the requirement and its solution corresponds to the set splitting problem. By the developed models of course organization, from which the NP hard problems arise, in addition to the scienti c contributions in the elds of mathematical programming and operational research, contributions in educational aspects are added, especially in the methodology of teaching mathematics and computer science. URI: http://hdl.handle.net/123456789/3050 Files in this item: 1
phd_matic_dragan.pdf ( 1.438Mb ) -
Stojadinović, Mirko (Beograd , 2016)[more][less]
Abstract: Many real-world problems can be modeled as constraint satisfaction problems (CSPs) and then solved by one of many available techniques for solving these problems. One of the techniques is reduction to SAT, i.e. Boolean Satisfiability Problem. Variables and constraints of CSP are translated (encoded) to SAT instance, that is then solved by state-of-the-art SAT solvers and solution, if exists, is translated to the solution of the original CSP. The main aim of this thesis is to improve CSP solving techniques that are using reduction to SAT. Two new hybrid encodings of CSPs to SAT are presented and they combine good sides of the existing encodings. We give the proof of correctness of one encoding that did not exist in literature. We developed system meSAT that enables reduction of CSPs to SAT by using 4 basic and 2 hybrid encodings. The system also enables solving of CSPs by reduction to two problems related to SAT, SMT and PB. We developed a portfolio for automated selection of encoding/solver to be used on some new instance that needs to be solved. The developed portfolio is comparable with the state-of-the-art portfolios. We developed a hybrid approach based on short solving timeouts with the aim of significantly reducing the preparation time of a portfolio. By using this approach, we got results comparable to the ones obtained by using preparation time of usual length. We made comparison between several machine learning techniques with the aim to find out which one is the best suited for the short training approach. The problem of assigning air traffic controllers to shifts is described and three models of this problem are presented. We used a large number of different solving methods and a diverse set of solvers for solving this problem. We developed optimization techniques that aim to find optimal solutions of the problem. A hybrid technique combining reduction to SAT and local search is shown to be the most efficient one. We also considered sudoku puzzles and the existing techniques of solving the puzzles of greater size than 9 9. Amongst the used techniques, the existing reduction to SAT is the most efficient in solving these puzzles. We improved the existing algorithm for generating large sudoku puzzles. It is shown that simple preprocessing rules additionally improve speed of generating large sudokus. URI: http://hdl.handle.net/123456789/4427 Files in this item: 1
MirkoStojadinovicTeza.pdf ( 2.030Mb ) -
Todorčević, Stevo (Belgrade)[more][less]
Abstract: The thesis consists of four chapters and one appendix. The relation between trees and ordering types, especially the relation between tree-subtree and the type-subtype are considered in Chapter 1. By using Jensens’s principle, Aronszajn’s tree which does not contain any Aronszajn’s subtree and Cantor’s subtree are constructed. Moreover, it is shown that in the model ZFC+GCH each ω_2- Aronszajn’s tree contains Aronszajn’s and Cantor’s subtree. In the first part of Chapter 2 the problem of the existence of Boolean algebras which have non-trivial automorphisms and endomorptisms are studied. It is shown that for each cardinal k, k>ω, there are exactly 2^k types of isomorphic Boolean algebras without non-trivial automorphisms. In the second part of that chapter the problem of isomorphism and automorhism of ω_1-trees is studied. It is shown that there are 2^ω1 types of isomorphic total rigid Aronszajn’s trees, so one Aronszajn’s tree does not have any nontrivial automorphism. Several problems of the partition relations of cardinal numbers are solved in Chapter 3. The appendix contains the proof of the property that in ZFC the σ-dense partial ordered set of power ω_1 does not exist. It is shown that in ZFC there is not any linearly ordered topological space with weight less or equal ω_1 which satisfies Kurepa’s generalization of the notion of separable topological space. It is also shown that if ¬ω Kurepa’s hypothesis + Martin’s axiom + ¬Continuum hypothesis is assumed, then each perfect normal non - Arhimedian space whose weight is ω1 is measurable. URI: http://hdl.handle.net/123456789/316 Files in this item: 1
phdStevoTodorcevic.pdf ( 18.19Mb ) -
Dragović, Vladimir (Beograd , 1992)[more][less]