Browsing Doctoral Dissertations by Title

Pavlović, Miroljub (Belgrade)[more][less]

Doder, Dragan (Beograd , 2011)[more][less]

Kartelj, Aleksandar (Beograd , 2014)[more][less]
Abstract: This work investigates the potential of improving the classi cation process through solving three classi cationrelated problems: feature selection, feature weighting and parameter selection. All three problems are challenging and currently in the focus of scienti c researches in the eld of machine learning. Each problem is solved by using populationbased metaheruistic method called electromagnetismlike method. This method is used for combinatorial and global optimization. It is inspired by laws of attraction and repulsion among charged particles. Each particle is represented by a vector of real values. The solution of the problem of interest is then obtained by mapping these realvalued vectors to the feasible solution domain. Particles representing better solutions achieve higher level of charge, which consequently produces greater impact on other particles. The search process is performed by iterating the particle movement, induced by charges. Through implementing the methods, two key aspects are managed: 1) the classi cation quality obtained after applying the optimization method and 2) the e ciency of the proposed methods from the perspective of time and space resources. All methods are equiped with problemspeci c local search procedures which tend to increase the solution quality. The bene t of applying feature selection for the classi cation process is twofold. Firstly, the elimination of unnecessary features decreases the data set noise, which degrades the quality of the classi cation model. Secondly, the problem dimension is decreased, thus the e ciency is increased. Feature selection problem is very e  ciently solved by the proposed method. The classi cation quality is in the majority of cases (instances) improved relative to the methods from literature. For some of the instances, computational times are up to several hundred times smaller than those of the competing methods. Feature weighting and parameter selection problem share similar underlying solution representation, based on the vectors of real values. Since the representation of charged particles is based on the same underlying domain, the transition from the particle to the solution domain behaves smoothly. The quality of the method for iv feature weighting is demonstrated through nearest neighbors classi cation model. The testing of the method is conducted on di erent collection of instances, and after that, the comparison to several methods from literature is made. In the majority of cases, the proposed method outperformed the comparison methods. The parameter selection, in classi cation, has a great impact on the classi cation quality. The proposed method for parameter selection is applied on the support vector machihe, which has a complex parametric structure when the number of parameters and the size of their domains is in question. By using heuristic initialization procedure, the detection of high quality regions for parameter combinations is accelerated. Exhaustive tests are performed on various instances in terms of their dimension and feature structure: homogenous and heterogeneous. Single kernel learning is adopted for homogenous, and multiple kernel learning for heterogeneous instances. The comparison with methods from literature showed superiority of the proposed method when single and multiple kernel learning based on radial basis function is considered. The method shows to be competitive in other cases. All proposed methods improved the classi cation quality. Because of the way, the problem is being solved, all three methods can be generalized and applied to a wide class of classi cation models and/or classi cation problem. URI: http://hdl.handle.net/123456789/4234 Files in this item: 1
phdAleksandarKartelj.pdf ( 2.121Mb ) 
Andrejić, Vladica (Beograd , 2010)[more][less]
Abstract: U ovom radu posmatramo princip dualnosti (i jake dualnosti) za Osermanove mnogostrukosti i uopxtavamo ga za pseudoRimanov sluqaj. Osnovni ci je dokazati princip dualnosti za Osermanove mnogostrukosti u opxtem sluqaju ili konstrukcija eventualnih kon traprimera. Za sada smo u sta u da damo samo rezultate pod speci fiqnim dodatnim uslovima. Prva mogu nost je mali indeks pseudo Rimanove mnogostrukosti, gde dokazujemo da jaka dualnost va i za Rimanove i Lorencove prostore. Druga mogu nost su prostori malih dimenzija gde dokazujemo da jaka dualnost va i kad dimenzija nije ve a od qetiri. Posled a olakxavaju a okolnost sa kojom radimo tiqe se malog broja sopstvenih vrednosti redukovanog Jakobijevog operatora, gde posmatramo dvolisnoOsermanove tenzore krivine. U tom sluqaju radimo sa jakim uslovima iz definicije kvazispecijalnih Osermanovih tenzora krivine i elimo da doka emo da pod ima va i princip dualnosti. Konaqan rezultat je da skorospecijalan Oser manov tenzor krivine mora biti specijalan Osermanov. U nastavku postav amo obratan problem, te pokuxavamo da istra imo pod kojim uslovima algebarski tenzor krivine za koji va i princip dualnosti mora biti Osermanov. Potvrdan rezultat dobili smo u dimenziji tri, kao i u sluqaju kada se Fidlerova suma sastoji od samo jednog qlana. URI: http://hdl.handle.net/123456789/2479 Files in this item: 1
phdAndrejicVladica.pdf ( 513.6Kb ) 
Dajović, Slobodan (Belgrade)[more][less]

Đorđević, Radosav (Kragujevac , 1991)[more][less]
Abstract: The thesis consists of six chapters. Chapter 1 contains the structures, in which the probability logics are realized, and the basic methods of nonstandard analysis which are used in the other chapters. In Chapter 2 the syntax and semantics of the following probability logics are presented: the logic with the probability quantifiers L_Ap, the logic with the integral operators L_A_∫ , the logic with the operator of conditional expectation L_AE and adapted probability logic L_ad. Moreover, the certain important results about these logics are given. The problems of Barwise’s completeness, completeness, compactness, the existence of analytic and hyperfinite models for biprobability logics LA_P1_P2, LA_∫_1_∫_2 and L_ad in absolute continuous and singular cases are solved in Chapter 3. The manyprobability logic BC{L_AP_i:i∊I}, I∊A obtained by Boolean combinations of probability logics L_AP is introduced and some modeltheoretical properties of that logic are given in Chapter 4. In Chapter 5 the probability logic L^2AP∀ of second order is introduced, which is motivated by Keisler’ s problems with L_AP∀ and some topological logics. The problem of completeness for the logic L^2AP∀ is proved. In Chapter 6 cylinder probability algebras are introduced and some possibilities to solve problems for these algebras (which are characteristics of standard cylinder algebras, as the representation, axiomatization and decidability) are presented. URI: http://hdl.handle.net/123456789/189 Files in this item: 1
phdRadosavSDjordjevic.pdf ( 2.407Mb ) 
Djerasimović, Božidar (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/140 Files in this item: 1
phdBozidarPDjerasimovic.pdf ( 2.343Mb ) 
Stančić, Olivera (Beograd , 2018)[more][less]
Abstract: Hub Location Problems (HLP) represent an important class of optimiza tion problems due to their numerous applications in many areas of real life. They often arise from practical situations that require routing of the flow from origin node (supplier) to the destination node (customer) under given conditions, such that the value of considered objective function is optimal. Hubs are special objects (nodes in the network) that represent centres for consolidation and flow collection between two selected locations  suppliers and customers. As transportation costs (per unit of flow) along the links that connect hub nodes are lower compared to other links in the network, directing the flow to hubs may lead to significant reductions of transportation cost in the network. The subject of this doctoral dissertation is one class of hub location problems, denoted as Hub Maximal Covering Problems (HMCPs) in the literature. The goal of HMCPs is to determine optimal locations for establishing certain number of hubs in order to maximize the total flow between all the covered origindestination pairs, under the assumption of binary or partial covering. Three variants of the hub maximal covering problem are considered: uncapacitated single allocation p hub maximal covering problem (USApHMCP), uncapacitated multiple allocation p hub maximal covering problem (UMApHMCP) and uncapacitated r allocation p hub maximal covering problem (UrApHMCP). Note that the UrApHMCP has not been studied in the literature so far. All three considered problems are proven to be NP hard. In case of USApHMCP, for the given set of hubs, the obtained subproblem of optimal allocation of nonhub nodes by established hubs is also NPhard. In this dissertation, new mathematical models for USApHMCP with binary and partial covering are proposed. The main advantage of the newly proposed models, in respect to existing ones from the literature, is the fact that small modifications of the new models enable their transformation to new models for p hub maximal covering problems with different allocation schemes. More precisely, new models for UMApHMCP and UrApHMCP can be obtained from the newly proposed mod els for USApHMCP in both coverage cases. All proposed models for USApHMCP and UMApHMCP are compared with the existing ones from the literature in the terms of efficiency within the framework of exact CPLEX 12.6 solver. Several hub data sets from the literature are used in numerical experiments when comparing the formulations. The obtained experimental results indicate that new models for UMApHMCP with both binary and partial coverage show the best performance in terms of solutions’ quality and execution times. For UrApHMCP and both coverage criteria, three mathematical models are proposed, and compared in terms of effi ciency using the exact CPLEX 12.6 solver. It turns out that the exact solver finds optimal or feasible solutions only for smallsize problem instances. Having in mind the complexity of all three problems under consideration and the results obtained by CPLEX 12.6 solver, the conclusion is that, in practice, exact methods can not provide solutions for large problem dimensions. For this reason, it was necessary to implement adequate heuristic or metaheuristic methods, in order to obtain highquality solutions in short execution times, even in the case of large problem dimensions. Up to now, only simple but insufficiently effective heuris tic methods for solving USApHMCP and UMApHMCP with binary coverage have been proposed in the literature, while the HMCP variants with partial coverage have not been previosly solved by using metaheuristic methods. As UrApHMCP with binary and partial coverage has not been previously considered in the litera ture, no solution methods suggested for this problem existed up to now. Inspired by previous successful applications of variable neighborhood search method (VNS) to other hub location problems from the literature, this metaheuristic approach is applied to the considered HMCP problems. In this dissertation, several variants of VNS metaheuristic are designed and implemented: General Variable Neighborhood Search (GVNS) for USApHMCP, Basic Variable Neighborhood Search (BVNS) for UMApHMCP and a variant of General Variable Neighborhood Search (GVNSR) for UrApHMCP. In the case of UrApHMCP, two additional metaheuristic meth ods are proposed: Greedy Randomized Adaptive Search Procedure with Variable Neighborhood Descent (GRASPVND) and Genetic Algorithm (GA). Constructive components of all proposed metaheuristics are adapted to the characteristics of the considered problems. Experimental study was conducted on the existing hub data sets from the lit erature, which include instances with up to 1000 nodes in the network. The ob tained results show that the proposed metaheuristics for the considered problems reach all known optimal solutions previously obtained by CPLEX 12.6 solver or establish new bestknown solutions in significantly shorter CPU time compared to CPLEX 12.6. The proposed GVNS and BVNS metaheuristics quickly reach all known optimal solutions on smallsize problem instances when solving USApHMCP and UMApHMCP, respectively. In the case of largesize problem instances, which have not been previously used for testing purposes for these problems, the proposed GVNS and BVNS return their best solutions in short execution times. The results obtained by the proposed GVNSR and GRASPVND for UrApHMCP on largesize problem instances indicate their effectiveness in both coverage cases. The proposed GA method showed to be successful only for UrApHMCP in binary covering, on instances up to 200 nodes. The variants of hub maximal covering problems considered in this dissertation are important from both theoretical and practical points of view. The new mathe matical models proposed in this dissertation for the considered variants of HMCP, represent a scientific contribution to the theory of hub location problems, mathemat ical modeling and optimization. Designed and implemented metaheuristic methods for solving the studied variants of HMCP are the scientific contribution to the field of optimization methods for solving location problems, as well as the development of software. The considered variants of HMCP have numerous applications in the optimization of telecommunication and transport systems, air passenger and goods transport, emergency services, postal and other delivery systems, so that the results obtained in this doctoral dissertation can be applied in practice, partially or com pletely. URI: http://hdl.handle.net/123456789/4750 Files in this item: 1
StancicOliveradisertacija.pdf ( 1.688Mb ) 
Stojanović, Stevan (Belgrade , 1969)[more][less]

Berisha, Muharrem (Pristina , 1979)[more][less]

Mateljević, Miodrag (Belgrade)[more][less]

Melentijević, Petar (Beograd , 2018)[more][less]
Abstract: In this thesis we study sharp estimates of gradients and operator norm estimates in harmonic function theory. First, we obtain Schwarztype inequalities for holomorphic mappings from the unit ball B n to the unit ball B m , and then analoguous inequalities for holomorphic functions on the disk D without zeros and pluriharmonic functions from the unit ball B n to ( − 1 , 1) . These extend results from [ 32 ] and [ 18 ]. Also, we give a new proof of the fact that positive harmonic function in the upperhalf plane is a contraction with resprect to hyperbolic metrics on both H and R + ([ 47 ]). Besides that, in the second chapter, we construct the examples to show that the analoguous does not hold for the higherdimensional upperhalf spaces. All mentioned results are from the authors’ paper [55]. In the third chapter we intend to calculate the exact seminorm of the weighted Berezin transform considered as an operator from L ∞ ( B n ) to the ”smooth” Bloch space ([57]). The fourth chapter contains results concerning Bergman projection. We solve the problem posed by Kalaj and Marković in [ 28 ] on determining the exact seminorm of the Bergman projections from L ∞ ( B n ) to the B ( B n ) . The crucial obstacle is the fact that B ( B n ) is equipped with M− invariant gradient seminorm. Also, we provide the sharp gradient estimates of the Bergman projection of an L p function in the unit ball B n , as well as its consequences on Cauchy projection and certain gradient estimates for the functions from the Hardy and Bergman spaces.We obtain the exact values of the Bloch’s seminorms and norms for the Cauchy projection on L ∞ ( S n ) . These results are based on the papers [56] and [58]. The last chapter contains the proof of the one part of HollenbeckVerbitsky conjecture from [ 26 ]. Exactly, we find the exact norms of (  P +  s +  P −  s ) 1 s for 0 < s ≤ 2 on L p ( T ) , where P + is the Riesz projection and P − = I − P + . Also we give the appropriate dual estimates and prove that they are sharp. The paper [ 45 ] is motivated by the results from [25] and [33]. URI: http://hdl.handle.net/123456789/4749 Files in this item: 1
doktorat_Petar_merged.pdf ( 1.507Mb ) 
Popović, Biljana (Belgrade)[more][less]

Stanimirović, Predrag (Niš)[more][less]
URI: http://hdl.handle.net/123456789/190 Files in this item: 1
phdPredragStanimirovic.pdf ( 5.471Mb ) 
Oskanjan, Vasilije (Belgrade)[more][less]

Dotlić, Milan (Beograd , 2015)[more][less]
Abstract: The thesis considers numerical methods for the computation of subsurface flow and transport of mass and energy in an anisotropic piecewise continuous medium. This kind of problems arises in hidrology, petroleum engineering, ecology and other fields. Subsurface flow in a saturated medium is described by a linear partial differential equation, while in an unsaturated medium it is described by the Richards nonlinear partial differential equation. Transport of mass and energy is described by advectiondiffusion equations. The thesis considers several finite volume methods for the discretization of diffusive and advective terms. An interpolation method for discretization of diffusion through discontinuous media is presented. This method is applicable to several nonlinear finite volume schemes. The presence of a well in the reservoir determines the subsurface flow to a large extent. Standard numerical methods produce a completely wrong flux and an inaccurate hydraulic head distribution in the well viscinity. Two methods for the well flux correction are introduced in this thesis. One of these methods gives secondorder accuracy for the hydraulic head and firstorder accuracy for the flux. Explicit and implicit time discretizations are presented. Preservation of the maximum and minimum principles in all considered schemes is analyzed. All considered schemes are tested using numerical examples that confirm teoretical results. URI: http://hdl.handle.net/123456789/4236 Files in this item: 1
phdDotlic_Milan.pdf ( 5.137Mb ) 
Milosavljević, Dragan (Belgrade , 1986)[more][less]
URI: http://hdl.handle.net/123456789/238 Files in this item: 1
phdDraganMilosavljevic.PDF ( 6.718Mb ) 
Georgijević, Dušan (Belgrade)[more][less]

Miličić, Pavle (Belgrade)[more][less]

Trifunović, Miodrag (Novi Sad)[more][less]