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Disertacijos darbo tikslas – įrodyti universalias tiksliąsias nelygybes atsitiktinių dydžių funkcijų nukrypimo nuo vidurkio tikimybėms. Universalios nelygybės pažymi, kad jos yra tolygios pagal tam tikras bendras skirstinių klases ir pagal atsitiktinių dydžių kiekį, kartais ir pagal kitus parametrus. Nelygybės vadinamos tiksliosiomis, jeigu pavyksta sukonstruoti atsitiktinių dydžių seką, kuriai nelygybės virsta lygybėmis. Tokios nelygybės labai naudingos, pavyzdžiui, draudimo matematikoje, konstruojant efektyvius algoritmus. Disertaciją sudaro šeši skyriai. Pirmasis skyrius yra įvadas, kuriame neformaliai pristatomas disertacijoje tiriamas objektas, pateikiamas bendras darbo aprašymas ir motyvacija. Detalesnė kitų autorių rezultatų apžvalga pateikiama atskirai kiekviename skyriuje. Antrasis skyrius skirtas atvejui, kai atsitiktiniai dydžiai yra aprėžti ir simetriniai. Trečiajame skyriuje įrodomos nelygybės atsitiktiniams dydžiams, tenkinantiems dispersijos aprėžtumo sąlygą. Ketvirtajame skyriuje nagrinėjamos sąlyginai aprėžtų atsitiktinių dydžių sumos. Penktajame skyriuje tiriamos atsitiktinių dydžių sekos, sudarančios martingalą arba supermartingalą, ir joms gaunamos universaliosios tikimybinės nelygybės ir sukonstruojama nehomogeninė Markovo grandinė, kuri yra martingalas, ir kuriai minėtos nelygybės virsta lygybėmis. Šeštajame skyriuje rezultatai yra apibendrinami atsitiktinių dydžių sekos Lipšico funkcijoms.

The purpose of the dissertation is to prove universal tight bounds for deviation from the mean probability inequalities for functions of random variables. Universal bounds shows that they are uniform with respect to some class of distributions and quantity of variables and other parameters. The bounds are called tight, if we can construct a sequence of random variables, such that the upper bounds are achieved. Such inequalities are useful for example in insurance mathematics, for constructing effective algorithms. We extend the results for Lipschitz functions on general probability metric spaces.

Advisors/Committee Members: KUBILIUS, KĘSTUTIS (Doctoral dissertation committee chair), DUČINSKAS, KĘSTUTIS (Doctoral dissertation committee member), PAULAUSKAS, VYGANTAS (Doctoral dissertation committee member), SURGAILIS, DONATAS (Doctoral dissertation committee member), ŠIAUČIŪNAS, DARIUS (Doctoral dissertation committee member), BIKELIS, ALGIMANTAS JONAS (Doctoral dissertation opponent), RADAVIČIUS, MARIJUS (Doctoral dissertation opponent).

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The purpose of the dissertation is to prove universal tight bounds for deviation from the mean probability inequalities for functions of random variables. Universal bounds shows that they are uniform with respect to some class of distributions and quantity of variables and other parameters. The bounds are called tight, if we can construct a sequence of random variables, such that the upper bounds are achieved. Such inequalities are useful for example in insurance mathematics, for constructing effective algorithms. We extend the results for Lipschitz functions on general probability metric spaces.

Disertacijos darbo tikslas – įrodyti universalias tiksliąsias nelygybes atsitiktinių dydžių funkcijų nukrypimo nuo vidurkio tikimybėms. Universalios nelygybės pažymi, kad jos yra tolygios pagal tam tikras bendras skirstinių klases ir pagal atsitiktinių dydžių kiekį, kartais ir pagal kitus parametrus. Nelygybės vadinamos tiksliosiomis, jeigu pavyksta sukonstruoti atsitiktinių dydžių seką, kuriai nelygybės virsta lygybėmis. Tokios nelygybės labai naudingos, pavyzdžiui, draudimo matematikoje, konstruojant efektyvius algoritmus. Disertaciją sudaro šeši skyriai. Pirmasis skyrius yra įvadas, kuriame neformaliai pristatomas disertacijoje tiriamas objektas, pateikiamas bendras darbo aprašymas ir motyvacija. Detalesnė kitų autorių rezultatų apžvalga pateikiama atskirai kiekviename skyriuje. Antrasis skyrius skirtas atvejui, kai atsitiktiniai dydžiai yra aprėžti ir simetriniai. Trečiajame skyriuje įrodomos nelygybės atsitiktiniams dydžiams, tenkinantiems dispersijos aprėžtumo sąlygą. Ketvirtajame skyriuje nagrinėjamos sąlyginai aprėžtų atsitiktinių dydžių sumos. Penktajame skyriuje tiriamos atsitiktinių dydžių sekos, sudarančios martingalą arba supermartingalą, ir joms gaunamos universaliosios tikimybinės nelygybės ir sukonstruojama nehomogeninė Markovo grandinė, kuri yra martingalas, ir kuriai minėtos nelygybės virsta lygybėmis. Šeštajame skyriuje rezultatai yra apibendrinami atsitiktinių dydžių sekos Lipšico funkcijoms.

Advisors/Committee Members: KUBILIUS, KĘSTUTIS (Doctoral dissertation committee chair), DUČINSKAS, KĘSTUTIS (Doctoral dissertation committee member), PAULAUSKAS, VYGANTAS (Doctoral dissertation committee member), SURGAILIS, DONATAS (Doctoral dissertation committee member), ŠIAUČIŪNAS, DARIUS (Doctoral dissertation committee member), BIKELIS, ALGIMANTAS JONAS (Doctoral dissertation opponent), RADAVIČIUS, MARIJUS (Doctoral dissertation opponent).

Darbe pateiktos alternatyvios ARCH(2) stacionarumo sąlygos, analogiškos egzistuojančioms. Taip pat suformuluotos hipotetinės HARCH(2) proceso stacionarumo sąlygos.

There are given alternative conditions of stationarity of ARCH(2) process similar to the existing ones. Also hypothetical conditions of stationarity of HARCH(2) are stated.

Advisors/Committee Members: Kazakevičius, Vytautas (Master's thesis supervisor).

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Darbo tikslas: Įvertinti neinvazinių ir invazinių tyrimų galimybes bei vertę diagnozuojant odos melanomą ir jos išplitimą, renkantis optimalią chirurginio gydymo metodiką. Darbo uždaviniai: 1. Nustatyti neinvazinio ultragarsinio tyrimo sąsajas su morfologinio tyrimo rezultatais, vertinant odos melanomos storį, svarbų chirurginio gydymo taktikai. 2. Įvertinti dviejų invazinių diagnostikos metodų taikymo tikslingumą, surandant sarginį (-ius) limfmazgius, kai aplink naviką arba pooperacinį randą suleidžiamas audinių dažas ir RF. 3. Palyginti sarginių limfmazgių skaičių ir mikrometastazių dažnį dviejose sergančių odos melanoma pacientų grupėse: operuotųjų vieno etapo operacija – radikali naviko ekscizija ir sarginių limfmazgių biopsija („V“ tiriamųjų grupė) ir operuotųjų dviem etapais – pirminė diagnostinė naviko ekscizija 0,5 cm atstumu nuo naviko kraštų, po to radikali pooperacinio rando reekscizija su sarginių limfmazgių biopsija („D“ tiriamųjų grupė).

The aim The aim of this study was to evaluate the potential and value of non-invasive and invasive tests in diagnosing cutaneous melanoma and assessment of its dissemination, and to justify optimal technique for surgical management. Objectives 1. To determine correlation between non-invasive ultrasound investigation and results of morphologic examination in assessment of cutaneous melanoma thickness influencing surgical treatment strategy. 2. To evaluate the expedience of using two invasive diagnostic methods (tissue stain and RA injection at the site of the tumour) in detection of sentinel lymph node(s). 3. To compare the count of sentinel lymph nodes and the rate of micrometastases between two groups of patients with cutaneous melanoma: patients who underwent one-stage surgery – radical excision of the tumour and sentinel lymph node biopsy (group “V”), and patients who underwent two-stage surgery – primary diagnostic excision of the tumour (0.5 cm from borders of the lesion) followed by a radical re-excision of the postoperative scar and sentinel lymph node biopsy (group “D”).

Advisors/Committee Members: Pundzius, Juozas (Doctoral dissertation supervisor), Endzinas, Žilvinas (Doctoral dissertation committee chair), Inčiūra, Arturas (Doctoral dissertation committee member), Mickevičius, Antanas (Doctoral dissertation committee member), Marčiukaitienė, Irena (Doctoral dissertation committee member), Characiejus, Dainius (Doctoral dissertation committee member), Juozaitytė, Elona (Doctoral dissertation opponent), Gancevičienė, Rūta (Doctoral dissertation opponent), Pundzius, Juozas (Doctoral dissertation advisor).

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Aggregated data appears in many areas such as econimics, sociology, geography, etc. This motivates an importance of studying the (dis)aggregation problem. One of the most important reasons why the contemporaneous aggregation become an object of research is the possibility of obtaining the long memory phenomena in processes. The aggregation provides an explanation of the long-memory effect in time series and a simulation method of such series as well. Accumulation of short-memory non-ergodic random processes can lead to the long memory ergodic process, that can be used for the forecasts of the macro and micro variables. We explore the aggregation scheme of AR(1) processes and nearest-neighbour random fields with infinite variance. We provide results on the existence of limit aggregated processes, and find conditions under which it has long memory properties in certain sense. For the random fields on Z², we introduce the notion of (an)isotropic long memory based on the behavior of partial sums. In L₂ case, the known aggregation of independent AR(1) processes leads to the Gaussian limit. While we describe a new model of aggregation based on independent triangular arrays. This scheme gives the limit aggregated process with finite variance which is not necessary Gaussian. We study a discrete time risk insurance model with stationary claims, modeled by the aggregated heavy-tailed process. We establish the asymptotic properties of the ruin probability and the dependence structure... [to full text]

Agreguoti duomenys naudojami daugelyje mokslo sričių tokių kaip ekonomika, sociologija, geografija ir kt. Tai motyvuoja tirti (de)agregavimo uždavinį. Viena iš pagrindinių priežasčių kodėl vienalaikis agregavimas tapo tyrimų objektu yra galimybė gauti ilgos atminties procesus. Agregavimas paaiškina ilgos atminties atsiradima procesuose ir yra vienas iš būdų tokius procesus generuoti. Agreguodami trumpos atminties neergodiškus atsitiktinius procesus, galime gauti ilgos atminties ergodišką procesą, kuris gali būti naudojamas mikro ir makro kintamųjų prognozavimui. Disertacijoje nagrinėjama AR(1) procesų bei artimiausio kaimyno atsitiktinių laukų, turinčių begalinę dispersiją, agregavimo schema, randamos sąlygos, kurioms esant ribinis agreguotas procesas egzistuoja, ir turi ilgąją atmintį tam tikra prasme. Atsitiktinių laukų atveju, įvedamas anizotropinės/izotropinės ilgos atminties apibrėžimas, kuris yra paremtas dalinių sumų elgesiu. Baigtinės dispersijos atveju yra gerai žinoma nepriklausomų AR(1) procesų schema, kuri rezultate duoda Gauso ribinį agreguotą procesą. Disertacijoje aprašoma trikampio masyvo agregavimo modelis, kuris baigtinės dispersijos atveju duoda nebūtinai Gauso ribinį agreguotą procesą. Taip pat disertacijoje nagrinėjama bankroto tikimybės asimptotika, kai žalos yra aprašomos sunkiauodegiu agreguotu procesu, nusakoma priklausomybė tarp žalų, apibūdinama žalų ilga atmintis.

Advisors/Committee Members: PAULAUSKAS, VYGANTAS (Doctoral dissertation committee chair), DAVYDOV, YOURI (Doctoral dissertation committee member), LEIPUS, REMIGIJUS (Doctoral dissertation committee member), RAČKAUSKAS, ALFREDAS (Doctoral dissertation committee member), SUQUET, CHARLES (Doctoral dissertation committee member), JAKUBOWKI, ADAM (Doctoral dissertation opponent), SOULIER, PHILIPPE (Doctoral dissertation opponent), SURGAILIS, DONATAS (Doctoral dissertation supervisor), PHILIPPE, ANNE (Doctoral dissertation advisor).

▼ We consider k maximum’s multiplication where factors are independently distributed random extremes of independent identically distributed random variables which are distributed uniformly over (0, 1). We find distribution function, limiting distribution function and estimate convergence rate. Advisors/Committee Members: Saulius, Leonas (Master’s degree committee chair), Barauskas, Arūnas (Master’s degree committee member), Janilionis, Vytautas (Master’s degree committee member), Valakevičius, Eimutis (Master’s degree session secretary), Padvelskis, Kazimieras (Master’s thesis reviewer), Aksomaitis, Jonas Algimantas (Master’s thesis supervisor), Pekarskas, Vidmantas Povilas (Master’s degree committee member), Rudzkis, Rimantas (Master’s degree committee member), Navickas, Zenonas (Master’s degree committee member), Aksomaitis, Jonas Algimantas (Master’s degree committee member).

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Apsidairykite aplink ir Jūs suprasite, kad pasaulį valdo atsitiktinumai – jie visur: nuo radijo imtuvo triukšmo iki Loto ir kortų žaidimų, nuo rusiškos ruletės iki ... sėkmės gyvenime. Tačiau nepaisant mus supančio pasaulio “atsitiktinumų”, gauti absoliučiai atsitiktinę skaičių seką – pakankamai sudėtinga užduotis, netgi neskaitant to, kad šiai dienai atsitiktinių sekų paklausa - milžiniška. Šiame darbe nagrinėjami atsitiktinių skaičių generatoriai. Darbo tikslas - išsiaiškinti įvairių atsitiktinių skaičių generatorių (ASG) galimybes ir jų kokybės charakteristikas; ištirti jų darbą; palyginti ir įvertinti generatorių kokybę. Darbą sudaro trys pagrindinės dalys: 1. Apžvalginė dalis. Ši dalis skirta atsitiktinių skaičių generavimo klausimams, tiksliau: kas yra atsitiktinis skaičius, kas yra atsitiktinių skaičių generatorius, kokie būna generatoriai, pseudoatsitiktinių skaičių gavimo metodai, generatorių darbo kokybės patikrinimas 2. Antroje dalyje kalbama apie pseudoatsitiktinių sekų tyrimą. Aprašomi tyrimo metodai, Diehard testai. 3. Trečia dalis – eksperimentinė. Tikslas – išanalizuoti ASG (įvairių programavimo kalbų (Turbo Pascal, Lazarus, Dev C++, Visual Basic), o taip pat Excel ir Matlab standartinių funkcijų) galimybes. Darbo pabaigoje pateikiamos išvados apie atliktą analizę. Naudojamų programavimo kalbų kodai ir duomenų lentelės pateikiami prieduose.

Looking around our daily life it easy to realize that the world is managed by coincidence - they are everywhere, from wite noise comming from you radio to lotto games or Russian roulette, even ... success in your life. The real world is full of coincidence’s which is normally we surround by, although to obtain completely random sequence of numbers - a relatively complex task. Even withdrawing the fact that at this day’s the demand for random sequences is enormous. The random number generators will be review by this work. The purpose - to find various random number generator (RNG) functionality and quality characteristics, to examine their work principles, compare and evaluate the quality of the generator. The work consists of three main parts: 1. Overview. This part contains principles of generating of the random number’s, namely: what is a random number, what is a random number generator, what mean generating a pseudorandom number and methods for obtaining, review of generating quality. 2. The second part deals with pseudo-random sequence analysis. It will describe the research methods, Diehard tests. 3. Part three – experimental part. The purpose of this part is to analyze the RNG capability via various programming languages (Turbo Pascal, Lazarus Dev C + +, Visual Basic) as well as Excel and MatLab standard function. End of this document contains the conclusion of performed analysis. Annexes will contain programs and all the data tables which was used for code this work.

Advisors/Committee Members: Kazlauskas, Kazys (Master’s degree committee chair), Stankevičienė, Eglė (Master’s degree session secretary), Petkus, Tomas (Master’s degree committee member), Kligienė, Nerutė (Master’s degree committee member), Dzemyda, Gintautas (Master’s degree committee member), Lipeikienė, Joana (Master’s degree committee member), Kazlauskas, Kazys (Master’s thesis reviewer), Ivanikovas, Sergėjus (Master’s thesis supervisor).

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The dissertation consists of two parts. In the first part several asymptotic properties of random intersection graphs are studied. They include birth thresholds for small complete subgraphs in the binomial random intersection graph, the clique number in sparse random intersection graphs and the chromatic index of random uniform hypergraphs. Several new methods and theoretically and practically relevant algorithms are proposed. Some results are illustrated with data from real-world networks. The second part deals with asymptotic enumeration and properties of graphs from minor-closed classes in the case when the excluded minors are disjoint. The class of graphs without k+1 (vertex-)disjoint cycles and more general classes of graphs without k+1 disjoint excluded minors (satisfying a condition related to fans) are considered. Typical graphs in such classes are shown to have a simple “k apex vertex” structure. Other asymptotic properties (connectivity, number of components, chromatic number, vertex degrees) are also determined. Finally, it is shown that typical graphs without k+1 disjoint minors K4 have a more complicated “2k+1 apex vertex” structure, and properties of such graphs are investigated. Part of the results is proved in greater generality. A variety of methods from computer science, graph theory, combinatorics and the theory of generating functions are applied.

Disertacijoje yra dvi pagrindinės dalys. Pirmojoje dalyje gaunami keli nauji rezultatai uždaviniams, susijusiems su atsitiktiniais sankirtų grafais. Nagrinėjamas pilnojo pografio gimimo slenkstis binominiame atsitiktiniame sankirtų grafe, didžiausios klikos eilė atsitiktiniame retame sankirtų grafe ir chromatinio indekso eilė atsitiktiniame reguliariajame hipergrafe. Sprendimams pasiūloma keletas naujų metodų, taip pat pateikiami teoriškai ir praktiškai svarbūs algoritmai. Kai kurie rezultatai iliustruojami duomenimis iš realių tinklų. Antrojoje dalyje pristatomi rezultatai grafų su uždraustaisiais minorais tematikoje, nagrinėjamas atvejis kai uždraustieji minorai yra nejungūs. Čia tiriamas asimptotinis grafų, neturinčių k+1 nepriklausomų ciklų, skaičius, rezultatai apibendrinami grafų, neturinčių k+1 uždraustųjų minorų, tačiau tenkinančių tam tikrą „vėduoklės“ apribojimą, klasėms. Įrodoma, kad tipiniai tokių klasių grafai turi paprastą „k dydžio blokatoriaus“ struktūrą, nustatomos kitos tokių grafų asimptotinės savybės (jungumas, komponenčių skaičius, viršūnių laipsniai). Galiausiai parodoma, kad tipiniai grafai, neturintys k+1 nepriklausomų minorų K4 turi sudėtingesnę „2k+1 dydžio blokatoriaus“ struktūrą ir ištiriamos kitos jų savybės. Dalis šių rezultatų įrodoma daug bendresniu atveju. Darbe pasitelkiami įvairūs informatikos, kombinatorikos, grafų, tikimybių ir generuojančiųjų funkcijų teorijos metodai.

Advisors/Committee Members: MANSTAVIČIUS, EUGENIJUS (Doctoral dissertation committee chair), BAREIKIS, GINTAUTAS (Doctoral dissertation committee member), BIKELIS, ALGIMANTAS JONAS (Doctoral dissertation committee member), DUBICKAS, ARTŪRAS (Doctoral dissertation committee member), JANUŠKEVIČIUS, ROMANAS (Doctoral dissertation committee member), KRYLOVAS, ALEKSANDRAS (Doctoral dissertation opponent), MAČIULIS, ALGIRDAS (Doctoral dissertation opponent).

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Nagrinėjama silpnai priklausomų atsitiktinių dydžių statistika. Šio magistrinio darbo tikslas, turimą sumą, suvesti į nepriklausomų atsitiktinių dydžių sumą, kuri leistų tolimesniam tyrimui, pritaikyti žinomas teoremas, skaičiavimus bei rezultatus iš nepriklausomų atsitiktinių dydžių teorijos.

We analyze of weakly dependent random variables statistics. The objective of this master thesis is to deduce sum to independent random variables sum, which will be useful for applaying known theorems, calculations and results from the theory in independent random variables.

Advisors/Committee Members: Bikelis, Algimantas (Master’s thesis supervisor), Padvelskis, Kazimieras (Master’s thesis reviewer).

▼ Please note: This degree was awarded by the University of Kwazulu-Natal. Permission was granted to archive it in this database for teaching purposes.This study reports the development and use of an original methodology to measure inflation credibility, as well as the first results of such measurement in terms of an inflation credibility barometer. The barometer is an instrument measuring the degree of acceptance of the accuracy of historic inflation figures. Despite the lack of knowledge about inflation and the low inflation credibility recorded by this first calculation of an inflation credibility barometer for South Africa, valuable information about inflation is unveiled to the authorities. The research results serve as a benchmark, but cannot be compared to earlier research, as this study represents the first systematic measurement of inflation credibility in South Africa. The barometer yields better results than the limited current international measurement of perceptions of the accuracy of historic inflation figures. The barometer (i) reports the credibility of inflation figures as a figure between zero and 100; (ii) will highlight changes in credibility over time with repeated use; (iii) can be explained easily to the general public; (iv) provides for international comparison between countries; and (v) can be used by all countries. The use of inflation credibility barometers and changes in barometer readings over time can also serve as an early warning system for changes in inflation perceptions that might feed through to inflation expectations. Sampling results used to calculate a South African inflation credibility barometer show little public understanding of the rate of inflation. Owing to an increased focus on inflation figures in countries using an inflation-targeting monetary policy, central banks entrusted with such a policy should adopt a communication strategy highlighting the calculation and measurement of the rate of inflation. This study shows that no generally accepted international benchmarks for successful central-bank communication strategies have been developed, but the use of the methodology developed in this study will assist in the assessment of the effectiveness of communication strategies. This study makes three further contributions of significance to available literature on inflation in South Africa. The first is an analysis of prices increases and inflation over a period of 85 years (1921 to 2006) and a selected comparison of salaries and remuneration over a period of 78 years (1929 to 2006). To this end data sets were developed for comparative purposes, thereby distinguishing between perception and reality about the accuracy of inflation figures over time. As this comparison has not been done before, a methodology was developed that can be used in future research. Based on these comparisons an inflation accuracy indicator (IAI) is developed for the first time. The research showed no systematic over or under-reporting of price increases, therefore confirming the general accuracy of… Advisors/Committee Members: Padayachee, Vishnu (advisor).

▼ Please note: This degree was awarded by the University of Kwazulu-Natal. Permission was granted to archive it in this database for teaching purposes.This study reports the development and use of an original methodology to measure inflation credibility, as well as the first results of such measurement in terms of an inflation credibility barometer. The barometer is an instrument measuring the degree of acceptance of the accuracy of historic inflation figures. Despite the lack of knowledge about inflation and the low inflation credibility recorded by this first calculation of an inflation credibility barometer for South Africa, valuable information about inflation is unveiled to the authorities. The research results serve as a benchmark, but cannot be compared to earlier research, as this study represents the first systematic measurement of inflation credibility in South Africa. The barometer yields better results than the limited current international measurement of perceptions of the accuracy of historic inflation figures. The barometer (i) reports the credibility of inflation figures as a figure between zero and 100; (ii) will highlight changes in credibility over time with repeated use; (iii) can be explained easily to the general public; (iv) provides for international comparison between countries; and (v) can be used by all countries. The use of inflation credibility barometers and changes in barometer readings over time can also serve as an early warning system for changes in inflation perceptions that might feed through to inflation expectations. Sampling results used to calculate a South African inflation credibility barometer show little public understanding of the rate of inflation. Owing to an increased focus on inflation figures in countries using an inflation-targeting monetary policy, central banks entrusted with such a policy should adopt a communication strategy highlighting the calculation and measurement of the rate of inflation. This study shows that no generally accepted international benchmarks for successful central-bank communication strategies have been developed, but the use of the methodology developed in this study will assist in the assessment of the effectiveness of communication strategies. This study makes three further contributions of significance to available literature on inflation in South Africa. The first is an analysis of prices increases and inflation over a period of 85 years (1921 to 2006) and a selected comparison of salaries and remuneration over a period of 78 years (1929 to 2006). To this end data sets were developed for comparative purposes, thereby distinguishing between perception and reality about the accuracy of inflation figures over time. As this comparison has not been done before, a methodology was developed that can be used in future research. Based on these comparisons an inflation accuracy indicator (IAI) is developed for the first time. The research showed no systematic over or under-reporting of price increases, therefore confirming the general accuracy of… Advisors/Committee Members: Padayachee, Vishnu (advisor).

▼ Introduction: Prior in vitro work has shown that implants restored with aftermarket (AM) abutments are more prone to leakage at the implant-abutment interface (IAI) than implants seated with their original equipment manufacturer (OEM) abutments. The goal of the current study was to examine the relationship between bacterial colonisation at the IAI and implant parameters using OEM or AM abutments on identical implants. It was hypothesised that microbial colonisation at the IAI may increase peri-implant inflammatory cell accumulation and lead to increased bone and soft tissue loss around the AM abutments. Method: Sixty ø4/3 mm x 10 mm implants were placed into healed mandibular post-extraction ridges in ten mature ewes. Abutments were placed immediately or at 2nd stage surgery after 2 months. Six groups (n=10) were evaluated as follows: Delayed aftermarket abutment (A), delayed OEM abutment (B), immediate aftermarket abutment (C and D), immediate OEM abutment (E and F). Radiographs and microbial sampling were taken at baseline, 2 months, and 4 months. Identification and relative quantification of DNA for oral microbial species was performed using Polymerisation Chain Reaction (PCR) (IAI Padotest, Switzerland). Mean percent bone- to-implant contact (%BIC) and distance to first bone contact were calculated from two images per implant using Image J software. Linear mixed models were used to look for between group differences and mixed logistic regression models used for the binary outcomes. Analyses were conducted using Stata 14.1 and p<0.05 was considered statistically significant. Results: While there were more failures of the implants restored with aftermarket abutments (14 vs. 8) this difference failed to reach statistical significance (p=0.17). There was no statistical difference between OEM vs. aftermarket for %BIC, first bone contact, radiographic bone changes, height of soft tissue, bone density, or microbial colonisation. There was no correlation between microbial leakage and implant outcomes. Conclusion: This animal study found no difference in microbial leakage between OEM and AM abutments. There was no apparent relationship between increased microbial leakage and implant outcomes. Statistical analysis was complicated by the higher-than-expected number of implant failures. While some intriguing trends were noticed, a larger human study is now recommended to further explore this relationship. Advisors/Committee Members: Duncan, Warwick (advisor).

▼  Today there are many different Cad-applications on the market for engineers. Because of big building projects it has become more and more important to work with the same application or to have access to a neutral file type to be able to transfer files between different ones. This report studies the single objects and how they react when transferring them between ADT and ArchiCAD via the neutral type IFC. We have also been looking at problems during the transfer between and if there are some connections between these problems. Afterwards we created a neutral object model of a small country house to see if the objects appeared different. The result shows no differences. But looking at the problems that appeared during the transmissions they felt small and no logical. Today it is not possible to save in a neutral type without facing small problems. But with small corrections it would become possible to use IFC without any difficulties. If we get IFC to work properly it would save a lot of time, effort and the possibility to store your projects for the future.

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Šiame magistriniame darbe yra nagrinėjami nepriklausomi vienodai pasiskirstę atsitiktiniai dydžiai, turintys visus absoliutinius baigtinius momentus. Magistrinio darbo tikslas - atlikti konvergavimo greičio į normalųjį dėsnį įvertinimą. Darbą sudaro aštuoni skyriai. Įvade aprašoma problema ir visi tyrimo parametrai. Antrasis skyrius skirtas teoriniai analizei. Šiame skyriuje pateikiamos svarbiausios teorinės žinios ir metodai, kurie bus taikomi magistrinio darbo uždaviniams bei tikslams įgyvendinti. Trečiame skyriuje nagrinėjami kumuliantai Bernulio schemos atveju, o ketvirtame - analizuojamas Čebyšovo asimptotinis skleidinys ir pasinaudojus matematiniu paketu Maple, grafiniu būdu, tyrinėjamas jo konvergavimas. Aproksimacijos normaliuoju dėsniu tikslumui įvertinti naudojamas charakteristinių funkcijų metodas, todėl penktasis skyrius yra skiriamas suglodinimo nelygybių patikslinimui. Šeštame skyriuje, pasinaudojus turimais rezultatais, realizuojamas magistrinio darbo tikslas, o septintame - patikrinamas absoliutinės paklaidos įvertis Bernulio schemos atveju. Išvados ir rezultatai glaustai išdėstomi aštuntame skyriuje.

This master thesis considers independiant and identically distributed random variables, having absolute finite moments. The main task is to determine error estimate of the normal approximation. The work consists of eight chapters. In the introduction are considered problems and all subjects of research. The second chapter is designed for the theory analysis. Here are placed the main theoretical studies and methods that are used to solve the aims of the master thesis. The third chapter is intended to deal with cumulants in case of the Bernoulli’s distribution, the fourth one - is analyzing the Čebyšova’s asymptotic expansion and it convergence with the help of the mathematical package Maple. The method of characteristic’s functions is used to find the remainder term of the normal approximation, so the fifth chapter is designed to specify smoothing inequalities. Based on these results, the main task of the master thesis was obtained and specified in the sixth chapter. In the seventh one the error estimate in case of Bernoulli’s distribution, was examined with a mathematical package Maple. The short conclusions and results are placed in the eighth chapter.

Advisors/Committee Members: Padvelskis, Kazimieras (Master’s thesis supervisor), Sapagovas, Jonas (Master’s thesis reviewer), Saulis, Leonas (Master’s degree committee chair).

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Šioje santraukoje trumpai aprašoma V. Kurausko disertacija. Pristatomos abi disertacijos dalys, įvedami atsitiktinių sankirtų grafų ir digrafų modeliai, apibrėžiamos minorinės grafų klasės, suformuluojami sprendžiami uždaviniai bei pateikiami pagrindiniai rezultatai.

This paper summarizes (in Lithuanian) the doctoral dissertation "On two models of random graphs" (in English) by V. Kurauskas. We introduce the random graph models (random intersection graphs, graphs with disjoint excluded minors) studied in the thesis, overview the problems and state the main results.

Advisors/Committee Members: MANSTAVIČIUS, EUGENIJUS (Doctoral dissertation committee chair), BAREIKIS, GINTAUTAS (Doctoral dissertation committee member), BIKELIS, ALGIMANTAS JONAS (Doctoral dissertation committee member), DUBICKAS, ARTŪRAS (Doctoral dissertation committee member), JANUŠKEVIČIUS, ROMANAS (Doctoral dissertation committee member), KRYLOVAS, ALEKSANDRAS (Doctoral dissertation opponent), MAČIULIS, ALGIRDAS (Doctoral dissertation opponent).

▼ The novelty and originality of the work consists in the fact that in order to obtain asymptotic expansions with optimal values of the remainder terms in the zone of large deviations, along with the cumulant method the classical method of characteristic functions has to be used. In addition, when solving the problems stated in the work, other than the well known results in the problems of limit theorems of the probability theory and mathematical statistics, we have to estimate constants. Technically it is frequently rather a complicated task. The results obtained in the work have good opportunities to be applied in probability theory, mathematical statistics, econometric, etc. That is illustrated in the last section of the work in which theorems of large deviations are proved in the summation of weighted random variables with weights as well as discounted limit theorems. Advisors/Committee Members: Januškevičius, Romanas (Doctoral dissertation committee member), Bloznelis, Mindaugas (Doctoral dissertation opponent), Krylovas, Aleksandras (Doctoral dissertation committee member), Rudzkis, Rimantas (Doctoral dissertation committee member), Čiegis, Raimondas (Doctoral dissertation committee chair), Sunklodas, Jonas Kazys (Doctoral dissertation opponent), Laurinčikas, Antanas (Doctoral dissertation committee member).

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Our aim is to investigate Poisson type approximations to the sums of dependent integer-valued random variables. In this thesis, only one type of dependence is considered, namely m-dependent random variables. The accuracy of approximation is measured in the total variation, local, uniform (Kolmogorov) and Wasserstein metrics. Results can be divided into four parts. The first part is devoted to 2-runs, when pi=p. We generalize Theorem 5.2 from A.D. Barbour and A. Xia “Poisson perturbations” in two directions: by estimating the second order asymptotic expansion and asymptotic expansion in the exponent. Moreover, lower bound estimates are established, proving the optimality of upper bound estimates. Since, the method of proof does not allow to get small constants, in certain cases, we calculate asymptotically sharp constants. In the second part, we consider sums of 1-dependent random variables, concentrated on nonnegative integers and satisfying analogue of Franken's condition. All results of this part are comparable to the known results for independent summands. In the third part, we consider Poisson type approximations for sums of 1-dependent symmetric three-point distributions. We are unaware about any Poisson-type approximation result for dependent random variables, when symmetry of the distribution is taken into account. In the last part, we consider 1-dependent non-identically distributed Bernoulli random variables. It is shown, that even for this simple generalization of... [to full text]

Disertacijoje tiriamas diskrečių m-priklausomų atsitiktinių dydžių aproksimavimo Puasono tipo matais tikslumas. Silpnai priklausomų atsitiktinių dydžių sumos yra natūralus nepriklausomų atsitiktinių dydžių sumų apibendrinimas. Vis dėlto atsitiktinių dydžių priklausomybė žymiai pasunkina tokių sumų tyrimą. Disertacijoje pagrindinis dėmesys skiriamas dviparametrėms ir triparametrėms diskrečiosioms aproksimacijoms. Gautus rezultatus galima suskirstyti į keturias dalis. Pirmoje dalyje nagrinėjant dviejų narių serijų statistikos aproksimaciją Puasono ir sudėtiniais Puasono skirstiniais buvo nustatyta, kad dviparametrė sudėtinė Puasono aproksimacija yra tikslesnė už Puasono dėsnio asimptotinį skleidinį su vienu asimptotikos nariu. Aproksimacijos tikslumas įvertintas pilnosios variacijos ir lokalioje metrikoje. Specialiu atveju apskaičiuotos asimptotiškai tikslios konstantos. Taip pat nustatyta, kad gautieji įverčiai iš apačios yra tos pačios eilės, kaip ir įverčiai iš viršaus. Antroje dalyje buvo gauta, kad sveikaskaičiai atsitiktiniai dydžiai, tenkinantys Frankeno sąlygos analogą, gali būti naudojami perėjimui nuo m-priklausomų prie 1-priklausomų atsitiktinių dydžių. Nustatyta, kad ženklą keičiančios sudėtinės Puasono aproksimacijos yra tokios pačios tikslumo eilės, kaip žinomi rezultatai nepriklausomų atsitiktinių dydžių sumoms. Trečioje dalyje nustatyta, kad kai atsitiktiniai dydžiai yra simetriniai, tuomet sudėtinio Puasono aproksimacijos tikslumas yra daug geresnis nei... [toliau žr. visą tekstą]

Advisors/Committee Members: Čekanavičius, Vydas (Doctoral dissertation supervisor), Račkauskas, Alfredas (Doctoral dissertation committee chair), Leipus, Remigijus (Doctoral dissertation committee member), Bloznelis, Mindaugas (Doctoral dissertation committee member), Januškevičius, Romanas (Doctoral dissertation committee member), Krapavickaitė, Danutė (Doctoral dissertation committee member), Bikelis, Algimantas (Doctoral dissertation opponent), Sunklodas, Jonas Kazys (Doctoral dissertation opponent).

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Individuali veikla, kaip teisinė kategorija, Lietuvoje egzistuoja nuo 2003 m. sausio 1 d., kai įsigaliojo GPMĮ. Teisinės prielaidos užsiimti savarankiška veikla nesteigiant juridinio asmens fiksuojamos ir anksčiau – iki 2002 m. gruodžio 31 d. galiojo patentų sistema. Veikla su patentu buvo traktuojama per daug siaurai – tai lėmė savarankiškos veiklos teisinio reguliavimo pokyčius pereinant prie individualios veiklos instituto. Galima teigti, jog pagal dabartinį teisinį reguliavimą ši verslo organizavimo forma yra visapusiškai inkorporuota į verslo sistemą, ji sudaro smulkiausiąjį verslo segmentą, o jos subjektai yra pilnateisiai verslo atstovai, galintys pasinaudoti pakankamai plačiomis verslo galimybėmis. Individualios veiklos sąvokos įtvirtinimas įstatymuose bei bandymas formalizuotai pateikti atskirus tokios veiklos požymius sukūrė kritišką visuomenės požiūrį dėl sąvokos apibrėžtumo stokos bei galimybės kiekvieną iš požymių traktuoti itin plačiai. Netobula individualios veiklos definicijos formuluotė doktrinoje įvardijama kaip pagrindinė priežastis dėl nuolat augančių mokestinių ginčų skaičiaus, kuriuose ginčo dalykas – gautų pajamų pripažinimas iš individualios veiklos gautomis pajamomis. Magistro darbe darbo autorė problematikos užuomazgų ieško platesniame kontekste. Siekiant užsibrėžto tikslo – identifikuoti individualios veiklos ribas, darbe nuosekliai analizuojami visi individualios veiklos požymiai (tęstinumas, savarankiškumas, ekonominės naudos siekimas), remiantis... [toliau žr. visą tekstą]

Individual activity, as legal rank, has being prevailed in Lithuania since 1 January 2003 when the Law on Personal Income tax was inured. Legal premise to perform an independent activity without establishing a legal entity was fixed earlier, because till 31 December 2002 it was available under patent system. Activity with patent was treated too much constricted and this determined changes in juridical regulation of independent activity by passing to insitute of Individual Activity. It can be stated, that this form of business today is fully incorporated in the enterprise system and today it forms the smallest section of business, moreover it must be pointed up, that representatives of individual activity have wide possibilities to operate in business market. When the definition of individual activity appeared in the Law on Personal Income tax and the features of it were determined, the critical public opinion arose because of lack of specification and possibility to interpret each of the features very widely. The widespread opinion of imperfect definition is considered as the main reason of frequent litigations. In the master’s work author tried to look for the primary reasons of this problem in much wider way. Having an aim to find the framework of individual activity, author analysed all features of the definition of an individual activity (succession, independence, economic benefit) according to the practice of institutions which judge taxation related issues, judgments of... [to full text]

Advisors/Committee Members: Medelienė, Aistė (Master's thesis supervisor).