Browsing Doctoral Dissertations by Title
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Jocković, Jelena (Beograd , 2012)[more][less]
Abstract: Statistical methodology for dealing with extremes depend on how extreme values are defined. One way to extract extremes from a given sample x1, x2, ..., xN is to consider maxima (minima). The other way is to consider values y1 = x1 − u, y2 = x2 − u, . . . , yn = xn − u, where y1, y2, . . . , yn are sample members above (below) a given predetermined threshold u. These two methods lead to two different approaches in extreme value theory. This doctoral dissertation has two main goals. One of them is to apply the techniques from extreme value framework to certain type of combinatorial problems. The other goal is to contribute to the field of statistical modeling of extremes. The dissertation consists of three chapters. In the first chapter, we introduce generalized extreme value distributions and generalized Pareto distributions (GPD). These two families play key roles in the two approaches to modeling extremes. We set out the theoretical background for both approaches. In the second chapter, we apply the extremal techniques to combinatorial waiting time problems. Precisely, we consider Coupon collector’s problem, defined as follows: elements are sampled with replacement from the set Nn = {1, 2, . . . , n} under assumption that each element has probability 1/n of being drawn. The subject of interest is the waiting time Mn until all elements of Nn or some other pattern are sampled. We focus our attention to the following two cases: 1. Mn is the waiting time until all elements of Nn are sampled at least r times, where r is a positive integer; 2. Mn is the waiting time until all pairs of elements jj, j ∈ Nn are sampled. We present new results related to the asymptotic behavior of the waiting time Mn, if it is known that a large number of trials was performed and the experiment is not over. For both cases, we determine the limiting distribution of exceedances of Mn over high thresholds, and answer some related questions: how to choose a suitable high threshold (depending on n) in order to obtain a limiting distribution; under what conditions the limit does not depend on the threshold; are the generalized Pareto distributions the only possible limits. We also estimate the speed of convergence in both cases. The third chapter of the dissertation is devoted to estimation of parameters and quantiles of the generalized Pareto distributions. We restrict the attention to the two-parameter version of GPD, defined as: Wγ,σ(x) = 1 − e−x , x ≥ 0, γ = 0 1 − 1 + γ σx −1 , x ≥ 0, γ > 0 1 − 1 + γ σx −1 , x ∈ h 0,−σ γ i , γ < 0. Well known problem with this model is inconsistency with the sample data, which is that one or more sample observations exceed the estimated upper bound in case when γ < 0. We propose a new, general technique to overcome the inconsistency problem and improve performance of the existing GPD estimation methods. We apply the proposed technique to methodof- moments and method-of-probability-weighted-moments estimates, investigate its performance through computer simulation and provide some real data examples. Finally, we address the problem of estimating high GPD quantiles. We evaluate the robustness of some estimation methods through simulation study and present a case study from finance (value-at-risk estimation), with special emphasis to certain difficulties related to this field of application. URI: http://hdl.handle.net/123456789/4271 Files in this item: 1
phdJockovic_Jelena.pdf ( 1.687Mb ) -
Jocković, M. Jelena (Belgrade , 2012)[more][less]
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Petruševski, Ljiljana (Belgrade , 1986)[more][less]
URI: http://hdl.handle.net/123456789/51 Files in this item: 1
phdLjiljanaPetrusevski.pdf ( 1.651Mb ) -
Todorović, Nataša (Beograd , 2012)[more][less]
Abstract: Nehoroševljeva teorema (1977) igra veoma značajnu ulogu u razumevanju prirode hamiltonijanskih sistema. Pored činjenice da daje prikaz celokupne dinamike faznog prostora, ova teorema obezbeđuje i stabilnost kvazi-integrabilnih sistema u smislu da se vremena stabilnosti dejstava eksponencijalno produžavaju smanjenjem parametra poremećaja. Jedan od uslova teoreme je da integrabilna aproksimacija hamiltonijanske funkcije zadovoljava takozvani uslov strmosti. Pretpostavka izneta u dokazu teoreme je da pored parametra poremećaja, i strmost utiče na stabilizaciju sistema. Cilj doktorske teze bio je da se ova pretpostavka proveri numeričkim putem, kao i da se ilustruje uticaj strmosti na dinamiku sistema. Korišćen je model četvorodimenzione kvazi-integrabilne strme simplektičke mape, na kojoj se intenzitet strmosti lako podešava pomoću odgovarajućeg parametra. Oslanjajući se na tzv. Brzi indikator Ljapunova (Fast Lyapunov Indicator- FLI), numeričku metodu za detekciju haosa, prikazana je rezonantna struktura modela i merena je difuzija Arnoldovog tipa na odabranoj rezonanci. U prvom delu eksperimenta su za fiksirane vrednosti parametra strmosti merene promene difuzije u odnosu na smanjenje poremećaja, i potvrđeno je da se vrednost eksponenata fitovane funkcije povećava (sistem se stabilizuje) što je sistem strmiji. Otkriveno je i da eksponencijalna funkcija u strmoj nekonveksnoj oblasti u izvesnom smislu osciluje, što je rezultat koji još uvek nema svoju teorijsku interpretaciju. Takođe, primećeno je da se sa povećanjem strmosti, hiperboličke tačke zajedno sa svojom okolinom izmeštaju sa rezonantne krive. I konačno, u eksperimentu u kojem je meren direktan uticaj strmosti na brzinu difuzije, potvrđena je pretpostavka iz dokaza Nehoroševljeve teoreme, o postojanju kritične vrednosti parametra strmosti. Za vrednosti koje su manje od kritične, strmost nema uticaj na brzinu difuzije, dok je za vrednosti koje su veće od kritične, ovaj uticaj eksponencijalan. Štaviše, vrednost eksponenta ove funkcije u izvesnom smislu ima opšti karakter to jest ne zavisi od ostalih parametara sistema. Detaljnije analitičko objašnjenje ovog rezulata, svakako je jedan od budućih zadataka u interpretaciji Nehoroševljeve teoreme. URI: http://hdl.handle.net/123456789/3569 Files in this item: 1
Ntodorovic_Doktorat_1R.pdf ( 2.955Mb ) -
Blagojević, Dragan (Belgrade)[more][less]
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Mihnjević, Danilo (Belgrade)[more][less]
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Kovačević, Jovana (Beograd , 2015)[more][less]
Abstract: Proteins represent the most important groups of biomoleculs. Di erent functions that they carry out in each organism are unique and irreplaceable, including versatile cellular processes, structural role of proteins, catalytic function, a number of metabolic functions and so on. Knowing and under- standing protein function is therefore essential in investigation of any biolo- gical process, especially of human diseases since a lot of them are caused by functional mutations. In this paper, we represent investigation of protein function domain through two di erent approaches. In the rst one, protein function is represented by GO ontologies with the structure of a directed acyclic graph. There are three GO ontologies: one for functions regarding biological processes, one for functions regarding cellular components and one for molecular functions. Each ontology contains several thousands of nodes, where every node deter- mines more speci c function than his ascendants. The task of this part of research was to develop a software for predicting protein function from its primary sequence based on structural support vector machines method which represents generalization of well-known support vector machines method on structural output. Structure-function paradigm is one of basic concepts in molecular biology, stating that 3D proten structure is closely connected to its role in organism. It has been detected that disordered proteins (the ones that lack 3D struc- ture) and disordered regions of proteins are related with severe contemporary illnesses, which contributed to their popularity in modern research. In an- other aspect, we investigated the relationship between proteins' functional categories and their disorder, as well ad with other physico-chemical char- acteristics of proteins. Here, protein function has been observed through 25 elementary functions grouped in 4 functional groups. In this work, we present results of thorough analysis over large protein dataset where dis- order has been determined computationally, using publicly available tools. URI: http://hdl.handle.net/123456789/4451 Files in this item: 1
DoktoratJK2015.pdf ( 1.116Mb ) -
Stamenković, Blagoje (Belgrade)[more][less]
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Gjergji, Rexhep (Priština)[more][less]
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Martinović, Mihailo (, 2016)[more][less]
Abstract: The quasi-thermal noise spectroscopy is an accurate method of determination of density and temperature in space plasmas. When an electric antenna is immersed into a plasma, it is able to measure electrostatic uctuations caused by the thermal motion of plasma particles. These uctuations are detected as the power spectral density at the antenna terminals, observing a spectrum at frequencies comparable to the electron plasma frequency for both electrons and protons, since the proton signal is strongly Doppler-shifted towards higher frequencies due to the solar wind drift velocity. Beside inducing the uctuating electric eld, some of the electrons are impacting the antenna surface, causing disturbances of the antenna electric potential. The signal caused by this population is directly proportional to the ux of plasma electrons impacting the antenna and is dominant if the antenna has a large surface area. In this work, we use the orbit limited theory to calculate the incoming particle ux for a non-thermal plasma described by velocity distribution function, commonly measured in the solar wind. The increase in the particle collection by cylindrical and spherical objects is quanti ed and presented as a function of the surface electrostatic potential and the fraction of supra-thermal particles. Including these results into the theory has turned out to be absolutely necessary for accurate measurements of the plasma parameters whenever the shot noise is the dominant component in the power spectrum. This is the case for STEREO because the impact noise is overwhelming on this probe, due to the presence of short and thick antennas. The comprehensive study of data on this mission is motivated by the fact that the electron analyzers are malfunctioning since launch and no information on thermal electrons is available. Results obtained are veri ed by comparing with the results from Wind, showing a good match between the values measured by the two spacecraft. Uncertainties of the measurements are determined by the uncertainties of the instruments used and are estimated to be around 40%. The nal outcome of this work will be establishing a database of the electron moments in both STEREO A and B that will be covering the entire duration of the mission. In the second part of the thesis, we use the kinetic approach to expand the theory of the quasi-thermal noise to plasmas where electron-neutral collisions play a dominant role. This technique is able to measure the electron density, temperature and the collision frequency as independent parameters using the wide frequency range both below and above the plasma frequency, if the ratio of the collisional to plasma frequency is not smaller than 0.1. The results presented here have can be potentially applied in laboratory plasmas and unmagnetized ionospheres, while at the ionosphere of Earth their use is limited to low frequencies due to the presence of the magnetic field. URI: http://hdl.handle.net/123456789/4476 Files in this item: 1
MMartinovic_Thesis.pdf ( 16.42Mb ) -
Petrović, Mihailo (Paris)[more][less]
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Adamović, Dušan (Belgrade , 1965)[more][less]
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Gajić, Ljiljana (Novi Sad , 1982)[more][less]
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Laković, Bosiljka (Titograd , 1979)[more][less]
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Laković, Bosiljka (Belgrade)[more][less]
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Jablan, Slavik (Belgrade , 1984)[more][less]
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Spasić, Slađana (Belgrade)[more][less]
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Cvetković, Ljiljana (Novi Sad)[more][less]
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Janikijevik, Ljiljana (Skopje , 1973)[more][less]
URI: http://hdl.handle.net/123456789/157 Files in this item: 1
phdLjiljanaJanikijevik.pdf ( 4.625Mb ) -
Teorija onfinitezimalnih transformacija i njihova primena na integraljenje diferencijalnih jednačinaOkiljević, Blažo (Belgrade , 1986)[more][less]