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The random walk is a powerful model. Chemistry, Physics, and Finance are just a few of the disciplines that model with the random walk. It is clear from its varied uses that despite its simplicity, the simple random walk it very flexible. There is one major drawback, however, to the simple random walk and the geometric random walk. The limiting distribution is either normal, lognormal, or a levy process with infinite variance. This thesis introduces an new random walk aimed at overcoming this drawback. Because the simple random walk and the geometric random walk are special cases of the proposed walk, it is called a generalized random walk. Several properties of the generalized random walk are considered. First, the limiting distribution of the generalized random walk is shown to include a large class of distributions. Second and in conjunction with the first, the generalized random walk is compared to the geometric random walk. It is shown that when parametrized properly, the generalized random walk does converge to the lognormal distribution. Third, and perhaps most interesting, is one of the limiting properties of the generalized random walk. In the limit, generalized random walks are closely connected with a u function. The u function is the key link between generalized random walks and its difference equation. Last, we apply the generalized random walk to option pricing.

No description available.

It is believed that in the long time limit, the limiting behavior of the discrete-time quantum random walk will cross from quantum to classical if we take into account of the decoherence. The computer simulation has already shown that for the discrete-time one-dimensional Hadamard quantum random walk with coin decoherence such that the measurement operators on the coin space are defined by A0 = Ic √1 − p, A1 = |R > < R| √p and A2 = |L > < L > < L| √p is diffusive when 0 < p ≤ 1 and it is ballistic when P = 0. In this thesis, we are going to let p to be dynamical depending on the step t, that is, we consider p = 1/tß, ß ≥ 0 and we found that it has sub-ballistic behavior for 0 < ß < 1. Furthermore, we study not only the coin decoherence, but the total decoherence, that means the measurement operators apply on the Hilbert space H = Hp ⊗ Hc instead of the coin space only. We find that the results are both sub-ballistic for the coin and total decoherence when 0 < ß < 1. Moreover, according to the model given in [T. A. Brun, H. A. Carteret, and A. Ambainis, Phys. Rev. A 67, 032304 (2003)], we know that if the walker has chance to hop to the second nearest neighbor lattice in one step, the long-time behavior is also sub-ballistic and it is similar to that the walker can hop to the third nearest neighbor lattice in one step. By the way, we also find that if we combine the classical part of the model given in [Jing Zhao and Peiqing Tong. One-dimensional quantum walks subject to next nearest neighbor hopping decoherence, Nanjing Normal University, preprint (2014)] with different step length, then this decoherence will also cross from quantum to classical. Finally, we define the quantum γ-stable walk and obtain the quantum γ-stable law with decoherence. By this decoherence, we can see that the limiting behavior of the quantum stable walk will also cross from quantum to classical and we shows that it spreads out faster than the classical stable walk. / Mathematics

Cryptosystems based on elliptic curves are in wide-spread use, they are considered secure because of the difficulty to solve the elliptic curve discrete logarithm problem. Pollard's rho method is regarded as the best method for attacking the logarithm problem to date, yet it is still not efficient enough to break an elliptic curve cryptosystem. This is because its time complexity is O(√n) and for uses in cryptography the value of n will be very large. The objective of this thesis is to see if there are ways to improve Pollard's rho method. To do this, we study some modifications of the original functions used in the method. We also investigate some different functions proposed by other researchers to see if we can find a version that will improve the performance. From the experiments conducted on these modifications and functions, we can conclude that we get an improvement in the performance for some of them.

Introdução: As doenças cardíacas ou do aparelho circulatório são as principais causas de morte na população brasileira, sendo responsável por um terço dos óbitos. Embora o tratamento conservador seja amplamente adotado, grande parte das doenças cardiovasculares necessita e tem como tratamento a cirurgia cardíaca, da qual as mais comuns são a cirurgia de revascularização do miocárdio (CRVM) e de troca valvar. Atualmente existem diversos estudos avaliando a função pulmonar ou a capacidade funcional para o acompanhamento do tratamento conservador ou em situação pré-operatória, porém estudos avaliando e correlacionando essas variáveis no pré-cirúrgico são escassos na literatura científica não sendo possível averiguar a existência da relação entre os níveis de nitrito e nitrato e o desempenho nos testes de capacidade funcional. Objetivo: Avaliar a correlação nitrito/nitrato (NOx) do condensado do exalado pulmonar (CEP) e a distância caminhada nos testes de caminhada de 6 minutos (TC6) e shuttle walk test (SWT), além de verificar se a utilização de medicações contendo betabloqueadores, nitrato ou enzima conversora de angiotensina (IECA) podem influenciar nas concentrações de nitrito/nitrato no CEP e nas distâncias caminhadas no TC6 e no SWT e comparar seu comportamento entre valvopatas e coronariopatas no pré operatório de cirurgia cardíaca. Metodologia: Foram selecionados 73 pacientes, dos quais 28 eram coronariopatas e 45 valvopatas, de ambos os sexos, com idade entre 20 e 80 anos, feita coleta do CEP para análise do NOx e submetidos ao TC6 e ao SWT para avaliação da distância caminhada. Resultados: Na análise das concentrações de NOx do CEP não foi encontrada diferença estatisticamente significativa entre as medicações utilizadas via oral contendo nitrato (dinitrato de isossorbida), IECA (captopril ou enalapril) e/ou betabloqueador ou entre os pacientes do grupo coronariopata e grupo valvopata (p>0,05). Houve diferença estatisticamente significativa no TC6 nos valores de frequência cardíaca (FC) inicial, final e repouso e no valor referente à dispnéia final, e no SWT nos valores de FC inicial, final e repouso, na pressão arterial sistólica (PAS) inicial e no valor referente à dispnéia final entre os grupos coronariopata e valvopata. No entanto, foram interrompidos 4 TC6 e 7 SWT do grupo coronariopata devido ao desencadeamento de dor precordial, fato não ocorrido no grupo valvopata, apresentando nível de significância. A FC inicial e de repouso no TC6 e a FC final no SWT dos pacientes que não ingeriram nenhum medicamento antes do teste é diferente em relação à dos pacientes que fizeram uso de quaisquer medicamentos descritos antes do teste sugerindo a ação de medicamentos que modulam a FC como os betabloqueadores. Foi constatado correlação positiva moderada entre o NOx do CEP e os valores de PAS inicial e final de coronariopatas e correlação negativa fraca a moderada entre o NOx do CEP e os valores de FC final e de dispnéia final nos valvopatas no TC6, além da correlação positiva moderada entre o NOx do CEP e os valores de PAS inicial de indivíduos coronariopatas e correlação negativa fraca a moderada entre o NOx do CEP e os valores de FC inicial nos valvopatas no SWT. Foi identificado correlação negativa moderada na distância caminhada no TC6 e no SWT apenas nos indivíduos coronariopatas. Conclusões: Não foram identificadas influências do uso de medicações betabloqueadoras, nitrato ou IECA sobre a dosagem de NOx ou a distância caminhada em nenhum dos testes e em nenhum dos grupos, no entanto coronariopatas com níveis mais elevados de NOx apresentaram uma distância deambulada menor. / Introduction: Heart disease or circulatory system diseases are the leading causes of death in our population, accounting for one third of deaths. Although conservative treatment is widely adopted, part of cardiovascular disease treatment demands heart surgery, of which the most common are coronary artery bypass grafting (CABG) and valve replacement. Currently there are many studies evaluating lung function or functional capacity for monitoring of conservative treatment or preoperative situation, but studies assessing and correlating these variables in pre surgical are rare in the literature is not possible to ascertain the existence of the relationship between levels of nitrite and nitrate (NOx) in exhaled breath condensate (EBC) and performance in functional ability tests. Methods: were selected 73 patients, 28 with coronary artery diseas and 45 with heart valve disease of both genders, aged 20 to 80 years old. The EBC was collected for analysis of NOx and performed the six minutes walking test (6MWT) and shuttle walk test (SWT) to evaluate the distance walked. Results: the analysis of the concentrations of NOx in EBC has no statistically significant difference found between the medications used, such as oral nitrate (isosorbide dinitrate), ace inhibitors (captopril or enalapril) and/or beta-blockers in both coronary artery disease and heart valve disease (p> 0.05). There was a statistically significant difference in 6MWT for HR initial, final and rest and final dyspnea, and in SWT for HR initial, final and rest, the initial SBP and the final dyspnea between the coronary artery disease e heart valve disease. However, were interrupted 4 6MWT and 7 SWT from coronary artery disease related to chest pain, this fact was not related in patients with valve disease, presenting a significance level. The initial and resting HR during the 6MWT and in SWT final HRr patients not ingesting any medication before the test is different from patients who used any medications before the test, suggesting the action of drugs that modulate the HR, such as beta blockers. Moderate positive correlation was found between the NOx in EBC and SBP initial and final in coronary disease and weak to moderate correlation between the NOx in EBC and final HR and final dyspnea in 6MWT from heart valve disease. Besides the positive moderate correlation between NOx in the EBC and the SBP initial in coronary disease during 6MWT and weak to moderate negative correlation between NOx in the EBC and the HR initial in valve disease during SWT. Moderate negative correlation was identified in the distance walked during the 6MWT and SWT only between individuals with coronary artery disease. Conclusions: the use of beta-blocker drugs, ace inhibitors or nitrate evidenciates no influence on the NOx or on the distance walked in any tests, and none of the groups, however, individuals with coronary artery disease showed higher NOx levels and performed lower distance walked.

Introdução: As doenças cardíacas ou do aparelho circulatório são as principais causas de morte na população brasileira, sendo responsável por um terço dos óbitos. Embora o tratamento conservador seja amplamente adotado, grande parte das doenças cardiovasculares necessita e tem como tratamento a cirurgia cardíaca, da qual as mais comuns são a cirurgia de revascularização do miocárdio (CRVM) e de troca valvar. Atualmente existem diversos estudos avaliando a função pulmonar ou a capacidade funcional para o acompanhamento do tratamento conservador ou em situação pré-operatória, porém estudos avaliando e correlacionando essas variáveis no pré-cirúrgico são escassos na literatura científica não sendo possível averiguar a existência da relação entre os níveis de nitrito e nitrato e o desempenho nos testes de capacidade funcional. Objetivo: Avaliar a correlação nitrito/nitrato (NOx) do condensado do exalado pulmonar (CEP) e a distância caminhada nos testes de caminhada de 6 minutos (TC6) e shuttle walk test (SWT), além de verificar se a utilização de medicações contendo betabloqueadores, nitrato ou enzima conversora de angiotensina (IECA) podem influenciar nas concentrações de nitrito/nitrato no CEP e nas distâncias caminhadas no TC6 e no SWT e comparar seu comportamento entre valvopatas e coronariopatas no pré operatório de cirurgia cardíaca. Metodologia: Foram selecionados 73 pacientes, dos quais 28 eram coronariopatas e 45 valvopatas, de ambos os sexos, com idade entre 20 e 80 anos, feita coleta do CEP para análise do NOx e submetidos ao TC6 e ao SWT para avaliação da distância caminhada. Resultados: Na análise das concentrações de NOx do CEP não foi encontrada diferença estatisticamente significativa entre as medicações utilizadas via oral contendo nitrato (dinitrato de isossorbida), IECA (captopril ou enalapril) e/ou betabloqueador ou entre os pacientes do grupo coronariopata e grupo valvopata (p>0,05). Houve diferença estatisticamente significativa no TC6 nos valores de frequência cardíaca (FC) inicial, final e repouso e no valor referente à dispnéia final, e no SWT nos valores de FC inicial, final e repouso, na pressão arterial sistólica (PAS) inicial e no valor referente à dispnéia final entre os grupos coronariopata e valvopata. No entanto, foram interrompidos 4 TC6 e 7 SWT do grupo coronariopata devido ao desencadeamento de dor precordial, fato não ocorrido no grupo valvopata, apresentando nível de significância. A FC inicial e de repouso no TC6 e a FC final no SWT dos pacientes que não ingeriram nenhum medicamento antes do teste é diferente em relação à dos pacientes que fizeram uso de quaisquer medicamentos descritos antes do teste sugerindo a ação de medicamentos que modulam a FC como os betabloqueadores. Foi constatado correlação positiva moderada entre o NOx do CEP e os valores de PAS inicial e final de coronariopatas e correlação negativa fraca a moderada entre o NOx do CEP e os valores de FC final e de dispnéia final nos valvopatas no TC6, além da correlação positiva moderada entre o NOx do CEP e os valores de PAS inicial de indivíduos coronariopatas e correlação negativa fraca a moderada entre o NOx do CEP e os valores de FC inicial nos valvopatas no SWT. Foi identificado correlação negativa moderada na distância caminhada no TC6 e no SWT apenas nos indivíduos coronariopatas. Conclusões: Não foram identificadas influências do uso de medicações betabloqueadoras, nitrato ou IECA sobre a dosagem de NOx ou a distância caminhada em nenhum dos testes e em nenhum dos grupos, no entanto coronariopatas com níveis mais elevados de NOx apresentaram uma distância deambulada menor. / Introduction: Heart disease or circulatory system diseases are the leading causes of death in our population, accounting for one third of deaths. Although conservative treatment is widely adopted, part of cardiovascular disease treatment demands heart surgery, of which the most common are coronary artery bypass grafting (CABG) and valve replacement. Currently there are many studies evaluating lung function or functional capacity for monitoring of conservative treatment or preoperative situation, but studies assessing and correlating these variables in pre surgical are rare in the literature is not possible to ascertain the existence of the relationship between levels of nitrite and nitrate (NOx) in exhaled breath condensate (EBC) and performance in functional ability tests. Methods: were selected 73 patients, 28 with coronary artery diseas and 45 with heart valve disease of both genders, aged 20 to 80 years old. The EBC was collected for analysis of NOx and performed the six minutes walking test (6MWT) and shuttle walk test (SWT) to evaluate the distance walked. Results: the analysis of the concentrations of NOx in EBC has no statistically significant difference found between the medications used, such as oral nitrate (isosorbide dinitrate), ace inhibitors (captopril or enalapril) and/or beta-blockers in both coronary artery disease and heart valve disease (p> 0.05). There was a statistically significant difference in 6MWT for HR initial, final and rest and final dyspnea, and in SWT for HR initial, final and rest, the initial SBP and the final dyspnea between the coronary artery disease e heart valve disease. However, were interrupted 4 6MWT and 7 SWT from coronary artery disease related to chest pain, this fact was not related in patients with valve disease, presenting a significance level. The initial and resting HR during the 6MWT and in SWT final HRr patients not ingesting any medication before the test is different from patients who used any medications before the test, suggesting the action of drugs that modulate the HR, such as beta blockers. Moderate positive correlation was found between the NOx in EBC and SBP initial and final in coronary disease and weak to moderate correlation between the NOx in EBC and final HR and final dyspnea in 6MWT from heart valve disease. Besides the positive moderate correlation between NOx in the EBC and the SBP initial in coronary disease during 6MWT and weak to moderate negative correlation between NOx in the EBC and the HR initial in valve disease during SWT. Moderate negative correlation was identified in the distance walked during the 6MWT and SWT only between individuals with coronary artery disease. Conclusions: the use of beta-blocker drugs, ace inhibitors or nitrate evidenciates no influence on the NOx or on the distance walked in any tests, and none of the groups, however, individuals with coronary artery disease showed higher NOx levels and performed lower distance walked.

För närvarande utforskas quantum walk som en potentiell metod för att analysera medicinska bilder. Med inspiration från Gradys random walk-algoritm för bildbehandling har vi utvecklat en metod som bygger på de kvantmekaniska fördelar som quantum walk innehar för att detektera och segmentera medicinska bilder. Vidare har de segmenterade bilderna utvärderats utifrån klinisk relevans. Teoretiskt sett kan quantum walk-algoritmer erbjuda en mer effektiv metod för bildanalys inom medicin jämfört med traditionella metoder för bildsegmentering som exempelvis klassisk random walk, som inte bygger på kvantmekanik. Inom området finns omfattande potential för utveckling, och det är av yttersta vikt att fortsätta utforska och förbättra metoder. För närvarande kan det konstateras att det är en lång väg att vandra innan detta är något som kan appliceras i en klinisk miljö. / Currently, quantum walk is being explored as a potential method for analyzing medical images. Taking inspiration from Grady's random walk algorithm for image processing, we have developed an approach that leverages the quantum mechanical advantages inherent in quantum walk to detect and segment medical images. Furthermore, the segmented images have been evaluated in terms of clinical relevance. Theoretically, quantum walk algorithms have the potential to offer a more efficient method for medical image analysis compared to traditional methods of image segmentation, such as classical random walk, which do not rely on quantum mechanics. Within this field, there is significant potential for development, and it is of utmost importance to continue exploring and refining these methods. However, it should be noted that there is a long way to go before this becomes something that can be applied in a clinical environment.

<p> </p><p>I uppsatsen undersöks effektiviteten av de tre nordiska aktieindexterminerna OMXS30, OBX och OMXC20 vars underliggande index representerar den svenska, norska respektive den danska aktiemarknaden. Analysen baseras på den svaga formen av den effektiva marknadshypotesen och den närbesläktade random walk hypotesen. Aktieindexterminerna undersöks under perioden januari 1997 till december 2008 samt under perioder då den nordiska marknaden karaktäriseras av bull och bear perioder. Testresultaten av Augmented Dickey-Fuller (ADF) samt Kwiatkowski, Phillips, Schmidt och Shin (KPSS) testet tyder på att aktieindexterminerna följer en random walk och att nordiska aktieindexterminer är effektiva under den undersökta perioden. Då testen utförs för de kortare bull och bear perioderna erhålls motsägelsefulla resultat vilket medför att slutsatser om huruvida aktieindexterminerna är effektiva under dessa perioder ej kan dras.</p><p> </p>

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