Euroregionai Europoje egzistuoja jau nuo šeštojo XX a. dešimtmečio. Tačiau universalios euroregiono sampratos dar nėra. Pateikiamuose euroregiono apibrėžimuose aiškiai pabrėžiama, kad tai struktūros, turinčios teritorinį apibrėžtumą. Svarbus aspektas – euroregioną sudarančių narių lygybė bei teisinis pamatas, reglamentuojantis veiklą. Euroregionų skirtingumui įtakos turi įkūrimo tikslų bei uždavinių įvairumas, veiklos prioritetų nevienodumas. Magistro darbe siekiama supažindinti su euroregionų veikla bei vystymuisi nuo 2000 iki 2008 metų. Pagrindinis tyrimo aspektas – makroekonominių rodiklių kaitos dinamika ir išsivystymo skirtumai skirtingose teritorijose esančiuose euroregionuose. Analizuojam bendrosios pridėtinės vertės (BPV), bendrojo vidaus produkto (BVP), materialinių investicijų, tiesioginių užsienio investicijų, ir eksporto rodikliai euroregionuose. Tyrimu siekiama statistiškai pagrįsti objekto (šiuo atveju euroregiono) esminius požymius, jo funkcionavimo veiksnius. Euroregionas pateikiamas kaip vientisa sudėtinga sistema turinti begalę trūkumų, kurių pagrindinis – daugiamatiškumas. Darbe siekiama kuo labiau atsiriboti nuo istorinio ir socialinio konteksto ir rezultatus pateikti tik ekonominiame kontekste. Magistro darbas parašytas naudojantis aprašomaisiais, statistinių ir kitų šaltinių analizės bei grafiniu metodais. / Euregions in Europe there is already the sixth of the twentieth century decade. However, the universal concept of the Euroregion yet. Submissions Euroregion definition clearly states that this structure, a spatial predictability. An important aspect - making up the Euroregion equality and legal basis regulating the activities. Euroregions the difference is affected by the establishment of diversity goals and objectives, operational priorities of inequality. Master work to make the Euroregion activities and development from 2000 to 2008. The main aspect of the study - macroeconomic dynamics of change and development in the different territories of the Euroregion. Analyzed the gross value added (GVA), gross domestic product (GDP), capital investment, foreign direct investment and export performance of the Euroregion. The study seeks to statistically justify the object (in this case, the Euroregion) the essential features of the functioning of factors. Euroregion presented as an integrated complex system with myriad shortcomings, the principal - daugiamatiškumas. The paper aims to maximize distance from the historical and social context, and results only in an economic context. Master thesis is written using descriptive, statistical and other sources for analysis and graphical methods.

The research problem of this dissertation is the use of securitization in a small open economy. During the process of securitization bank’s illiquid assets are replaced by liquid assets – asset-backed securities, what allows increasing and diversifying bank’s financial resources. Having in mind the relevance of the economic situation in Lithuania, the utility of securitisation for Lithuania is analyzed in this dissertation. Dissertation also analyses positive and negative aspects of the experience of other countries in using securitization. Research showed that there is a strong correlation between GDP and credit resources in Lithuania. This fact means that country's economic growth could be promoted by finding ways to supplement the financial resources available to the banks and by encouraging them to lend out these resources. Thus, the use of the funds received after issuing asset-backed securities for further lending by banks would have a direct positive impact on the level of GDP in Lithuania. In order to successfully develop asset securitization in the country Lithuanian banks should concentrate their resources and expertise. This would help to achieve the necessary economies of scale and acceptable transaction costs. Analysis showed that Lithuanian legal framework for securitization should be also improved considering best practices from other countries in order to create greater legal certainty, reduce the administrative burden and ensure investor protection. / Disertacijoje nagrinėjama mokslinė problema yra sekiuritizacijos panaudojimas mažoje atviroje ekonomikoje. Sekiuritizacijos metu nelikvidus turtas yra pakeičiamas likvidžiu turtu – turtu padengtais vertybiniais popieriais, kuris leidžia padidinti ir diversifikuoti bankų turimus kreditinius išteklius. Atsižvelgus į darbo aktualumą Lietuvos ekonominei situacijai, darbe vertinamas sekiuritizacijos panaudojimo Lietuvoje naudingumas, analizuojami sekiuritizacijos teigiami ir neigiami aspektai, kitų šalių patirtis ir praktika. Atliktas tyrimas parodė, kad Lietuvoje egzistuoja stiprus ryšys tarp BVP ir kreditinių išteklių, kas reiškia, kad suradus būdų kaip papildyti bankų turimus finansinius išteklius ir taip paskatinus juos skolinti, atitinkamai paspartėtų šalies ekonomikos atsigavimas bei tolesnis augimas. Tad bankams pritaikius sekiuritizaciją ir išleidus turtu padengtus vertybinius popierius, o gautas lėšas panaudojus tolesniam kreditavimui, tai turėtų tiesioginės teigiamos įtakos BVP dydžiui Lietuvoje. Siekiant sėkmingai vystyti sekiuritizaciją Lietuvoje bankams vertėtų kooperuotis sutelkiant savo išteklius bei kompetenciją, kas leistų pasiekti reikiamą masto ekonomiją ir priimtinus sekiuritizacijos sandorių kaštus. Taip pat reikėtų tobulinti Lietuvos teisinę bazę sekiuritizacijos srityje pasiremiant geriausia sekiuritizacijos reguliavimo praktika: kurti didesnį teisinį tikrumą, mažinti administracinę naštą ir užtikrinti investuotojų apsaugą.

Recording and monitoring vital signs is an essential aspect of home-based healthcare. Using contact sensors to record physiological signals can cause discomfort to patients, especially after prolonged use. Hence, remote physiological measurement approaches have attracted considerable attention as they do not require physical contact with the patient’s skin. Several studies proposed techniques to measure Heart Rate (HR) and Heart Rate Variability (HRV) by detecting the Blood Volume Pulse (BVP) from human facial video recordings while the subject is in a resting condition. In this thesis, we focus on the measurement of HR. We adopt an algorithm that uses the Independent Component Analysis (ICA) to separate the source (physiological) signal from noise in the RGB channels of a facial video. We generalize existing methods to support subject movement during video recording. When a subject is moving, the face may be turned away from the camera. We utilize multiple cameras to enable the algorithm to monitor the vital sign continuously, even if the subject leaves the frame or turns away from a subset of the system’s cameras. Furthermore, we improve the accuracy of existing methods by implementing a light equalization scheme to reduce the effect of shadows and unequal facial light on the HR estimation, a machine learning method to select the most accurate channel outputted by the ICA module, and a regression technique to adjust the initial HR estimate. We systematically test our method on eleven subjects using four cameras. The proposed method decreases the RMSE by 27% compared to the state of the art in the rest condition. When the subject is in motion, the proposed method achieves a RMSE of 1.12 bpm using a single camera and RMSE of 0.96 bpm using multiple camera.

Robôs verdadeiramente autônomos devem conhecer o ambiente para executar tarefas complexas. Em ambientes desconhecidos o robô deve concorrentemente construir o mapa do ambiente e se localizar usando sensores proprioceptivos e exteroceptivos imprecisos. Isto é problemático, uma vez que o mapa parcial e possivelmente incorreto do ambiente será usado para corrigir erros de localização. Este problema importante da robótica móvel é conhecido como Localização e Mapeamento Simultâneos (SLAM). Quando um robô autonomamente executa o algoritmo de SLAM concorrentemente com uma estratégia de exploração, o problema passa a se chamar SLAM Ativo ou Exploração Integrada. Um dos principais desafios por trás destes problemas é o tratamento de fechamento de ciclos. Ao atravessar regiões desconhecidas ou ambientes esparsos, a pose do robô e o mapa podem não ser propriamente corrigidos por falta de informação. Quando isto acontece, as incertezas da posição do robô e do mapa aumentam, podendo levar a erros irrecuperáveis. Por outro lado, quando o ciclo é fechado corretamente, estas incertezas diminuem consideravelmente. Portanto, a escolha do caminho para explorar o ambiente pode drasticamente melhorar ou degradar a qualidade do mapeamento e da localização. Uma técnica bem conhecida de exploração de ambientes é a adaptação do problema de valor de contorno (BVP) para a equação de Laplace e condições de contorno de Dirichlet. Apesar de ser fácil de implementar, resultando em trajetórias de exploração suaves, esta técnica não endereça cuidadosamente erros de SLAM, uma vez que ela segue a descida do gradiente, o que pode não possibilitar revisitas, uma limitação crucial para o SLAM Ativo. Mesmo sendo uma técnica de exploração gulosa e direcionada a fronteiras, consideramos que a flexibilidade do BVP e condições de contorno de Dirichlet ainda são pouco exploradas. Nossa proposta é modificar o algoritmo de Exploração por BVP para executar comportamentos complexos, tais como revisitas e, em particular, fechamentos de ciclo. Apresentamos duas novas abordagens: a primeira faz uso de uma condição de contorno direcionada pelo tempo combinada a distorções de potencial para gerar comportamentos de fechamento de ciclo, além de um potencial que nunca cessa de existir, mesmo após o ambiente ter sido completamente explorado; a segunda, propicia o fechamento de ciclos aproveitando a propagação do potencial em regiões desconhecidas, através de um par dinâmico de condições de contorno que funcionam como obstáculos e objetivos virtuais. Ambas abordagens aproveitam o Esqueleto de Voronoi do ambiente para reduzir o custo computacional do algoritmo. Testes em ambientes reais e simulados usando o robô Pioneer 3DX mostram que as técnicas apresentadas apresetam melhores resultados quando comparadas a técnicas concorrentes. / Truly autonomous robots must know the environment in order to execute complex tasks. In unknown environments, the robot must construct a map and localize itself using noisy proprioceptive and exteroceptive sensors. This is problematic, since the partial and possibly inaccurate map of the environment will be used to correct localization errors. This important problem of mobile robotics is known as Simultaneous Localization and Mapping (SLAM). When a robot autonomously execute a SLAM algorithm concurrently with an exploration strategy, this problem is called Active SLAM or Integrated Exploration. One of the main challenges behind both these problems is the treatment of loop closures. While the robot traverses unknown regions or sparse environments, the robot pose and the map may not be properly corrected due to lack of information. When this happens, the uncertainties about the map and the robot pose increase, which may lead to unrecoverable SLAM errors. On the other hand, when a loop is closed successfully, these uncertainties drastically decrease. Therefore, path chosen to explore the environment can considerably improve or degrade the quality of both localization and mapping. One well known way to explore the environment is the adaptation of the Boundary Value Problem (BVP) for the Laplace Equation and Dirichlet boundary conditions. Even though it is easy to implement, resulting in smooth exploration trajectories, it does not carefully address SLAM errors, since it follows a gradient decent which not always allows revisits, a crucial limitation for Active SLAM. Despite being a greedy frontier driven exploration strategy, we consider the flexibility of the BVP and Dirichlet boundary conditions still under-explored for Active SLAM. Our proposal is to modify the BVP Exploration algorithm to execute complex exploration behaviors, such as revisits and, in particular, loop-closures. We present two new approaches: the first makes use of a time driven boundary value condition together with potential distortions to generate loop closing behaviors and a potential field that never ceases to exist, even after the exploration ends; the second enables loop closure behaviors with BVP by taking advantage of potential propagation in unknown space generated by a pair of dynamic boundary conditions functioning as virtual walls and goals. Both approaches take advantage of a local optimization that uses the Voronoi Skeleton to reduce the computational cost of the algorithm. Tests in real and simulated environments using a Pioneer 3DX show that the proposed approaches present better results when compared with competing approaches.

Robôs verdadeiramente autônomos devem conhecer o ambiente para executar tarefas complexas. Em ambientes desconhecidos o robô deve concorrentemente construir o mapa do ambiente e se localizar usando sensores proprioceptivos e exteroceptivos imprecisos. Isto é problemático, uma vez que o mapa parcial e possivelmente incorreto do ambiente será usado para corrigir erros de localização. Este problema importante da robótica móvel é conhecido como Localização e Mapeamento Simultâneos (SLAM). Quando um robô autonomamente executa o algoritmo de SLAM concorrentemente com uma estratégia de exploração, o problema passa a se chamar SLAM Ativo ou Exploração Integrada. Um dos principais desafios por trás destes problemas é o tratamento de fechamento de ciclos. Ao atravessar regiões desconhecidas ou ambientes esparsos, a pose do robô e o mapa podem não ser propriamente corrigidos por falta de informação. Quando isto acontece, as incertezas da posição do robô e do mapa aumentam, podendo levar a erros irrecuperáveis. Por outro lado, quando o ciclo é fechado corretamente, estas incertezas diminuem consideravelmente. Portanto, a escolha do caminho para explorar o ambiente pode drasticamente melhorar ou degradar a qualidade do mapeamento e da localização. Uma técnica bem conhecida de exploração de ambientes é a adaptação do problema de valor de contorno (BVP) para a equação de Laplace e condições de contorno de Dirichlet. Apesar de ser fácil de implementar, resultando em trajetórias de exploração suaves, esta técnica não endereça cuidadosamente erros de SLAM, uma vez que ela segue a descida do gradiente, o que pode não possibilitar revisitas, uma limitação crucial para o SLAM Ativo. Mesmo sendo uma técnica de exploração gulosa e direcionada a fronteiras, consideramos que a flexibilidade do BVP e condições de contorno de Dirichlet ainda são pouco exploradas. Nossa proposta é modificar o algoritmo de Exploração por BVP para executar comportamentos complexos, tais como revisitas e, em particular, fechamentos de ciclo. Apresentamos duas novas abordagens: a primeira faz uso de uma condição de contorno direcionada pelo tempo combinada a distorções de potencial para gerar comportamentos de fechamento de ciclo, além de um potencial que nunca cessa de existir, mesmo após o ambiente ter sido completamente explorado; a segunda, propicia o fechamento de ciclos aproveitando a propagação do potencial em regiões desconhecidas, através de um par dinâmico de condições de contorno que funcionam como obstáculos e objetivos virtuais. Ambas abordagens aproveitam o Esqueleto de Voronoi do ambiente para reduzir o custo computacional do algoritmo. Testes em ambientes reais e simulados usando o robô Pioneer 3DX mostram que as técnicas apresentadas apresetam melhores resultados quando comparadas a técnicas concorrentes. / Truly autonomous robots must know the environment in order to execute complex tasks. In unknown environments, the robot must construct a map and localize itself using noisy proprioceptive and exteroceptive sensors. This is problematic, since the partial and possibly inaccurate map of the environment will be used to correct localization errors. This important problem of mobile robotics is known as Simultaneous Localization and Mapping (SLAM). When a robot autonomously execute a SLAM algorithm concurrently with an exploration strategy, this problem is called Active SLAM or Integrated Exploration. One of the main challenges behind both these problems is the treatment of loop closures. While the robot traverses unknown regions or sparse environments, the robot pose and the map may not be properly corrected due to lack of information. When this happens, the uncertainties about the map and the robot pose increase, which may lead to unrecoverable SLAM errors. On the other hand, when a loop is closed successfully, these uncertainties drastically decrease. Therefore, path chosen to explore the environment can considerably improve or degrade the quality of both localization and mapping. One well known way to explore the environment is the adaptation of the Boundary Value Problem (BVP) for the Laplace Equation and Dirichlet boundary conditions. Even though it is easy to implement, resulting in smooth exploration trajectories, it does not carefully address SLAM errors, since it follows a gradient decent which not always allows revisits, a crucial limitation for Active SLAM. Despite being a greedy frontier driven exploration strategy, we consider the flexibility of the BVP and Dirichlet boundary conditions still under-explored for Active SLAM. Our proposal is to modify the BVP Exploration algorithm to execute complex exploration behaviors, such as revisits and, in particular, loop-closures. We present two new approaches: the first makes use of a time driven boundary value condition together with potential distortions to generate loop closing behaviors and a potential field that never ceases to exist, even after the exploration ends; the second enables loop closure behaviors with BVP by taking advantage of potential propagation in unknown space generated by a pair of dynamic boundary conditions functioning as virtual walls and goals. Both approaches take advantage of a local optimization that uses the Voronoi Skeleton to reduce the computational cost of the algorithm. Tests in real and simulated environments using a Pioneer 3DX show that the proposed approaches present better results when compared with competing approaches.

In this paper, we investigate the question of the spectrally equivalence of the so- called Pseudo-Laplacian to the usual discrete Laplacian in order to use hierarchical preconditioners for this more complicate matrix. The spectral equivalence is shown to be equivalent to a Brezzi-type inequality, which is fulfilled for the finite element spaces considered here.

In this paper, we investigate the question of the spectrally equivalence of the so- called Pseudo-Laplacian to the usual discrete Laplacian in order to use hierarchical preconditioners for this more complicate matrix. The spectral equivalence is shown to be equivalent to a Brezzi-type inequality, which is fulfilled for the finite element spaces considered here.

Valstybės skola ir jos atsiradimo priežastys svarbios ekonomikos mokslo dalykui, nes tai valstybės ekonomikos vystimuisi reikšmingas veiksnys. Didelė valstybės skola yra našta šalies ekonomikai, kadangi kuo didesnė skola, tuo daugiau valstybės biudžeto lėšų reikia skirti jos aptarnavimui, t.y. palūkanų mokėjimams ir pačios skolos grąžinimui. Tačiau nesiskolinti valstybė taip pat negali. Biudžeto deficitas, stambūs investiciniai projektai, kurių įgyvendinimui reikalingos didelės lėšos ir kitos priežastys lemia skolos atsiradimą ir tolesnį jos vystimąsi. Šiuolaikiniam šalies gyventojui yra aktuali valstybės biudžeto tvarkymo sistema, kadangi nuo to, koks valstybės biudžetas ir valstybės skola, priklauso gyventojų socialinė aplinka, net gyvenimo lygis, tad svarbu išsiaiškinti, koks optimalus turi būti skolos dydis, kad teigiamai veiktų ekonomiką, ir būtinai rasti būdų, kaip tinkamai ir racionaliai vykdyti valstybės skolos valdymą. / Public debt and the causes of economic research relevant to the subject matter, as the state of economic development is a significant factor. High level of debt is a burden to the economy because the larger the debt, the more the state budget funds should be used with its service, ie interest payments and repayment of the debt. Nesiskolinti But the state also can not. The budget deficit, large investment projects, whose implementation would require significant resources and other reasons for the emergence of the debt and further development. Tje budget management system is topical for the modern capita of the state, since that what the state budget and public debt, the population belongs to the social environment, even the standard of living, it is important to clarify what must be the optimal amount of debt, make a positive contribution to the economy, and it must find ways to the proper and rational exercise of public debt management.

Pastarąjį dešimtmetį kilusios problemos dėl ekonomikos raidos bei mokesčių vaidmens šiuolaikinėje ekonomikoje skatino diskusijas apie fiskalinės politikos poveikį konkurencingumui. Tyrimai stokoja vertinimo argumentacijos, dauguma vertinimų grindžiamos tik BVP kitimo tendencijomis, kurios nerodo socialinių pokyčių. Mokslinė problema: kaip įvertinti mokesčių naštos ir ekonomikos konkurencingumo sąveiką socialinės aplinkos kontekste? Mokesčių naštos poveikio ekonomikos konkurencingumui vertinimas socialinės aplinkos kontekste modelis sudarytas, vadovaujantis teorinėmis, istorinėmis ir praktinėmis mokesčių kitimo ir įtakos ekonomikos, konkurencingumo, socialinio aplinkos lygio raidai bei valstybės dalyvavimo ekonominėje veikloje vertinimui ir yra argumentuotas instrumentas, tinkamas vertinti mokesčių vaidmenį ekonomikos konkurencingumo formavime socialinės aplinkos kontekste. Atlikti mokesčių naštos lygio ekonomikos aplinkos pokyčiams tyrimo rezultatai rodo, kad mokesčiai yra svarbi ekonomikos vystymosi aplinkybė, kuri šiuolaikinėje aplinkoje turi būti vertinama plačiau, ne tik valstybės dalyvavimo ekonomikoje lygio aspektu. Mokestinės naštos poveikį aktualu įvertinti ekonominio potencialo, konkurencingumo, socialinės aplinkos lygio ir viešųjų išlaidų poreikio kontekste. Kompleksinis mokesčių vertinimas leidžia atskleisti mokesčių naštos poveikį ne tik ekonomikos pokyčiams, bet parodo ir mokestinių pajamų perskirstymo vaidmenį ekonomikos konkurencingumo ir socialinės aplinkos... [toliau žr. visą tekstą] / Over the last decade, problems with the economic development and role of taxation in the modern economy, encouraged debate on fiscal policy impact on competitiveness. Studies lack reasoning, most estimates are based only on the GDP change trends, which do not reflect social changes. The scientific problem: how to assess the interaction of tax burden and economic competitiveness in the context of social environment? The model “Assessment of the tax burden impact on competitiveness of economy in context of the social environment” was created in accordance with the theoretical, historical and practical taxation changes and their impact on assessment of economy, competitiveness, social environment development level and state participation in economic activities. The model is reasoned assessment tool, suitable for evaluation of the role of taxation in the formation of economic competitiveness in social environment context. Results of the performed study of tax burden impact on economic environment changes show that taxes are an important factor in economic development, which in today's environment must be regarded as more, than just a level of state involvement in the economy. It is relevant to assess impact of tax burden in the context of economic potential, competitiveness, social environment level and public expenditure need. Complex assessment of taxes allows not only to reveal the impact of tax burden on changes in the economy, but also shows the role of tax revenue... [to full text]

In the field of singularly perturbed reaction- or convection-diffusion boundary value problems the research area of a priori error analysis for the finite element method, has already been thoroughly investigated. In particular, for mesh adapted methods and/or various stabilization techniques, works have been done that prove optimal rates of convergence or supercloseness uniformly in the perturbation parameter epsilon. Commonly, however, it is assumed that the exact solution behaves nicely in that it obeys certain regularity assumptions although in general, e.g. due to corner singularities, these regularity requirements are not satisfied. So far, insufficient regularity has been met by assuming compatibility conditions on the data. The present thesis originated from the question: What can be shown if these rather unrealistic additional assumptions are dropped? We are interested in epsilon-uniform a priori estimates for convergence and superconvergence that include some regularity parameter that is adjustable to the smoothness of the exact solution. A major difficulty that occurs when seeking the numerical error decay is that the exact solution is not known. Since we strive for reliable rates of convergence we want to avoid the standard approach of the "double-mesh principle". Our choice is to use reference solutions as a substitute for the exact solution. Numerical experiments are intended to confirm the theoretical results and to bring further insights into the interplay between layers and singularities. To computationally realize the thereby arising demanding practical aspects of the finite element method, a new software is developed that turns out to be particularly suited for the needs of the numerical analyst. Its design, features and implementation is described in detail in the second part of the thesis.