Introdução: As diversas armadilhas apresentam rendimento diferenciado na captura, havendo a necessidade de buscar instrumentos que amostrem porções representativas das populações de mosquitos. Levanta-se a hipótese de que as armadilhas Mosquito Magnet Independence e CDC com CO2+Lurex3 sejam mais eficazes na captura de culicídeos do que a armadilha CDC luminosa. Objetivos: Avaliar a eficácia das armadilhas Mosquito Magnet Independence e CDC+CO2+Lurex3, em relação à CDC-luminosa, para a captura de culicídeos adultos em área agrícola na Fazenda Experimental em Pariquera-Açu, Vale do Ribeira, São Paulo, Brasil. Material e Métodos: Capturas mensais, das 15h00 às 21h00, por meio do delineamento em quadrado latino 3X3, no período de dezembro/2010 a novembro/2011. Perfis de diversidade de Rényi e índices de riqueza, dominância, diversidade, equabilidade e similaridade foram estimados para cada armadilha para compará-las. Resultados: Capturou-se 6.055 de 70 espécies e 12 gêneros. A CDC-luminosa amostrou 990 indivíduos de 42 espécies e 10 gêneros,a CDC+CO2+lurex31.419 indivíduos em 41 espécies e 10 gêneros e a Mosquito Magnet 3151 indivíduos de 46 espécies e 11 gêneros. A riqueza, pelo índice de Margalef e Perfil de Rényi, não apresentou diferença estatística para nenhuma armadilha no período dez/mai. A Mosquito Magnet obteve maior rendimento na mensuração da diversidade, segundos os índices de Shannon e Simpson, observados no perfil de Rényi. A dominância, pelo índice de Berger-Parker isolado,foi maior na Mosquito Magnet do que nas demais, nos dois períodos de capturas. O perfil de Rényi não apontou diferença significante para dominância. Índice de Pielou não mostrou significância em relação à CDC-luminosa para nenhuma das armadilhas nos dois períodos avaliados. Índices de Jaccard e Sorensen apontaram maior similaridade na composição de espécies entre a Mosquito Magnet e CDC+CO2+lurex3. Conclusões: A Mosquito Magnet Independence e CDC+CO2+Lurex3 apresentaram rendimento semelhante, nos meses mais frios e secos do ano. A utilização dessas armadilhas para a captura de determinados táxons pode ser importante ponto na estratégia de vigilância de espécies vetoras. Estudos com maior esforço amostral devem ser realizados para avaliar o rendimento das armadilhas Mosquito Magnet Independence e CDC+CO2 +lurex3 em áreas de ambiente alterado de Floresta Atlântica. / Introduction: The several traps have different performance in sampling mosquitoes,with the need to seek that capture representative portions of mosquito population. Formulate the hypothesis that the Mosquito Magnet trap and CDC+CO2+lurex3 are more effective in catching mosquitoes than the CDC light trap. Objectives: To evaluate the effectiveness the Mosquito Magnet Independence and CDC+CO2+lurex3 in relation to CDC light trap, to catching adult mosquitoes in the agricultural area at the Experimental Station in Pariquera-Açu, Vale do Ribeira, São Paulo, Brazil. Methods: Monthly captures, from 03:00pm-09:00pm, through the 3X3 Latin square from the December 2010 to November 2011. Rényi diversity profiles and indexes of the richness, dominance, diversity, evenness and similarity were estimated for each trap to compare them. Results: Were captured 6055 mosquitoes of the 70 species and 12 genera. CDC light traps sampled 990 specimens of 42 species and 10 genera, the CDC+CO2+lurex3 sampled 1419 specimens in 41 species and 10 genera and 3151 specimens were captured in the Mosquito Magnet belonging to 46 species and 11 genera. The richness, by the Margalef index on profile Rényi, showed no statistical difference for any trap in the period Dez/Mai. The Mosquito Magnet trap obtained higher yield in the measurement of diversity, according indexes of Shannon and Simpson, seen in profile Rényi. The dominance, by Berger-Parker index isolated, was higher in the Mosquito Magnet than in the other traps in both periods of captures. The profile Rényi showed no significant difference for dominance. Pielou index was not significant in relation to CDC light trap for any of the periods. Jaccard and Sorensen indexes showed greater similarity in composition of species between the CDC+CO2+lurex3 and Mosquito Magnet. Conclusions: The Mosquito Magnet Independence and CDC+CO2+ Lurex3 showed similar performance in colder and drier months of the year. The use of these traps to capture certain taxa can be important point in the surveillance approach vector species. Studies with greater sampling effort should be made to evaluate the performance of the Mosquito Magnet Independence and CDC+CO +lurex3 traps changed environment in areas of Atlantic Forest.

Introdução: As diversas armadilhas apresentam rendimento diferenciado na captura, havendo a necessidade de buscar instrumentos que amostrem porções representativas das populações de mosquitos. Levanta-se a hipótese de que as armadilhas Mosquito Magnet Independence e CDC com CO2+Lurex3 sejam mais eficazes na captura de culicídeos do que a armadilha CDC luminosa. Objetivos: Avaliar a eficácia das armadilhas Mosquito Magnet Independence e CDC+CO2+Lurex3, em relação à CDC-luminosa, para a captura de culicídeos adultos em área agrícola na Fazenda Experimental em Pariquera-Açu, Vale do Ribeira, São Paulo, Brasil. Material e Métodos: Capturas mensais, das 15h00 às 21h00, por meio do delineamento em quadrado latino 3X3, no período de dezembro/2010 a novembro/2011. Perfis de diversidade de Rényi e índices de riqueza, dominância, diversidade, equabilidade e similaridade foram estimados para cada armadilha para compará-las. Resultados: Capturou-se 6.055 de 70 espécies e 12 gêneros. A CDC-luminosa amostrou 990 indivíduos de 42 espécies e 10 gêneros,a CDC+CO2+lurex31.419 indivíduos em 41 espécies e 10 gêneros e a Mosquito Magnet 3151 indivíduos de 46 espécies e 11 gêneros. A riqueza, pelo índice de Margalef e Perfil de Rényi, não apresentou diferença estatística para nenhuma armadilha no período dez/mai. A Mosquito Magnet obteve maior rendimento na mensuração da diversidade, segundos os índices de Shannon e Simpson, observados no perfil de Rényi. A dominância, pelo índice de Berger-Parker isolado,foi maior na Mosquito Magnet do que nas demais, nos dois períodos de capturas. O perfil de Rényi não apontou diferença significante para dominância. Índice de Pielou não mostrou significância em relação à CDC-luminosa para nenhuma das armadilhas nos dois períodos avaliados. Índices de Jaccard e Sorensen apontaram maior similaridade na composição de espécies entre a Mosquito Magnet e CDC+CO2+lurex3. Conclusões: A Mosquito Magnet Independence e CDC+CO2+Lurex3 apresentaram rendimento semelhante, nos meses mais frios e secos do ano. A utilização dessas armadilhas para a captura de determinados táxons pode ser importante ponto na estratégia de vigilância de espécies vetoras. Estudos com maior esforço amostral devem ser realizados para avaliar o rendimento das armadilhas Mosquito Magnet Independence e CDC+CO2 +lurex3 em áreas de ambiente alterado de Floresta Atlântica. / Introduction: The several traps have different performance in sampling mosquitoes,with the need to seek that capture representative portions of mosquito population. Formulate the hypothesis that the Mosquito Magnet trap and CDC+CO2+lurex3 are more effective in catching mosquitoes than the CDC light trap. Objectives: To evaluate the effectiveness the Mosquito Magnet Independence and CDC+CO2+lurex3 in relation to CDC light trap, to catching adult mosquitoes in the agricultural area at the Experimental Station in Pariquera-Açu, Vale do Ribeira, São Paulo, Brazil. Methods: Monthly captures, from 03:00pm-09:00pm, through the 3X3 Latin square from the December 2010 to November 2011. Rényi diversity profiles and indexes of the richness, dominance, diversity, evenness and similarity were estimated for each trap to compare them. Results: Were captured 6055 mosquitoes of the 70 species and 12 genera. CDC light traps sampled 990 specimens of 42 species and 10 genera, the CDC+CO2+lurex3 sampled 1419 specimens in 41 species and 10 genera and 3151 specimens were captured in the Mosquito Magnet belonging to 46 species and 11 genera. The richness, by the Margalef index on profile Rényi, showed no statistical difference for any trap in the period Dez/Mai. The Mosquito Magnet trap obtained higher yield in the measurement of diversity, according indexes of Shannon and Simpson, seen in profile Rényi. The dominance, by Berger-Parker index isolated, was higher in the Mosquito Magnet than in the other traps in both periods of captures. The profile Rényi showed no significant difference for dominance. Pielou index was not significant in relation to CDC light trap for any of the periods. Jaccard and Sorensen indexes showed greater similarity in composition of species between the CDC+CO2+lurex3 and Mosquito Magnet. Conclusions: The Mosquito Magnet Independence and CDC+CO2+ Lurex3 showed similar performance in colder and drier months of the year. The use of these traps to capture certain taxa can be important point in the surveillance approach vector species. Studies with greater sampling effort should be made to evaluate the performance of the Mosquito Magnet Independence and CDC+CO +lurex3 traps changed environment in areas of Atlantic Forest.

This thesis examines the utility of mathematical complexity measures for the analysis of stratospheric dynamics. Through theoretical considerations and tests with artificial data sets, e.g., the iteration of the logistic map, suitable parameters are determined for the application of the statistical entropy measures sample entropy (SE) and Rényi entropy (RE) to methane (a long-lived stratospheric tracer) data from simulations of the SOCOL chemistry-climate model. The SE is shown to be useful for quantifying the variability of recurring patterns in a time series and is able to identify tropical patterns similar to those reported by previous studies of the ``tropical pipe'' region. However, the SE is found to be unsuitable for use in polar regions, due to the non-stationarity of the methane data at extra-tropical latitudes. It is concluded that the SE cannot be used to analyse climate complexity on a global scale. The focus is turned to the RE, which is a complexity measure of probability distribution functions (PDFs). Using the second order RE and a normalisation factor, zonal PDFs of ten consecutive days of methane data are created with a Bayesian optimal binning technique. From these, the RE is calculated for every day (moving 10-day window). The results indicate that the RE is a promising tool for identifying stratospheric mixing barriers. In Southern Hemisphere winter and early spring, RE produces patterns similar to those found in other studies of stratospheric mixing. High values of RE are found to be indicative of the strong fluctuations in tracer distributions associated with relatively unmixed air in general, and with gradients in the vicinity of mixing barriers, in particular. Lower values suggest more thoroughly mixed air masses. The analysis is extended to eleven years of model data. Realistic inter-annual variability of some of the RE structures is observed, particularly in the Southern Hemisphere. By calculating a climatological mean of the RE for this period, additional mixing patterns are identified in the Northern Hemisphere. The validity of the RE analysis and its interpretation is underlined by showing that qualitatively similar patterns can be seen when using observational satellite data of a different tracer. Compared to previous techniques, the RE has the advantage that it requires significantly less computational effort, as it can be used to derive dynamical information from model or measurement tracer data without relying on any additional input such as wind fields. The results presented in this thesis strongly suggest that the RE is a useful new metric for analysing stratospheric mixing and its variability from climate model data. Furthermore, it is shown that the RE measure is very robust with respect to data gaps, which makes it ideal for application to observations. Hence, using the RE for comparing observations of tracer distributions with those from model simulations potentially presents a novel approach for analysing mixing in the stratosphere.

Cette thèse porte sur le lien entre la tomographie et la notion de copule. La tomographie à rayons X consiste à (re)construire la structure cachée d'un objet (une densité de matière, la distribution d'une quantité physique, ou une densité de loi conjointe) à partir de certaines données obtenues ou mesurées de l'objet (les projections, les radiographies, les densités marginales). Le lien entre les mesures et l'objet se modélise mathématiquement par la Transformée à Rayons X ou la Transformée de Radon. Par exemple, dans les problèmes d'imagerie en géométrie parallèle, lorsqu'on a seulement deux projections à deux angles de 0 et pi/2 (horizontale et verticale), le problème peut être identifié comme un autre problème très important en mathématique qui est la détermination d'une densité conjointe à partir de ses marginales. En se limitant à deux projections, les deux problèmes sont des problèmes mal posés au sens de Hadamard. Il faut alors ajouter de l'information a priori, ou bien des contraintes supplémentaires. L'apport principal de cette thèse est l'utilisation des critères de plusieurs entropies (Rényi, Tsallis, Burg, Shannon) permettant d'aboutir à une solution régularisée. Ce travail couvre alors différents domaines. Les aspects mathématiques de la tomographie via l'élément fondamental qui est la transformée de Radon. En probabilité sur la recherche d'une loi conjointe connaissant ses lois marginales d'où la notion de ``copule'' via le théorème de Sklar. Avec seulement deux projections, ce problème est extrêmement difficile. Mais en assimilant les deux projections (normalisées) aux densités marginales et l'image à reconstruire à une densité de probabilité, le lien se fait et les deux problèmes sont équivalents et peuvent se transposer dans le cadre statistique. Pour caractériser toutes les images possibles à reconstruire on a choisi alors l'outil de la théorie de probabilité, c'est-à-dire les copules. Et pour faire notre choix parmi les copules ou les images nous avons imposé le critère d'information a priori qui se base sur différentes entropies. L'entropie est une quantité scientifique importante car elle est utilisée dans divers domaines (en Thermodynamique, en théorie de l'information, etc). Ainsi, en utilisant par exemple l'entropie de Rényi nous avons découvert de nouvelles classes de copules. Cette thèse apporte de nouvelles contributions à l'imagerie, par l'interaction entre les domaines qui sont la tomographie et la théorie des probabilités et statistiques. / This thesis studies the relationship between Computed Tomography (CT) and the notion of copula. In X-ray tomography the objective is to (re)construct an image representing the distribution of a physical quantity (density of matter) inside of an object from the radiographs obtained all around the object called projections. The link between these images and the object is described by the X-ray transform or the Radon transform. In 2D, when only two projections at two angles 0 and pi/2 (horizontal and vertical) are available, the problem can be identified as another problem in mathematics which is the determination of a joint density from its marginals, hence the notion of copula. Both problems are ill-posed in the sense of Hadamard. It requires prior information or additional criteria or constraints. The main contribution of this thesis is the use of entropy as a constraint that provides a regularized solution to this ill-posed inverse problem. Our work covers different areas. The mathematics aspects of X-ray tomography where the fundamental model to obtain projections is based mainly on the Radon transform. In general this transform does not provide all necessary projections which need to be associated with certain regularization techniques. We have two projections, which makes the problem extremely difficult, and ill-posed but noting that if a link can be done, that is, if the two projections can be equated with marginal densities and the image to reconstruct to a probability density, the problem translates into the statistical framework via Sklar's theorem. And the tool of probability theory called "copula" that characterizes all possible reconstructed images is suitable. Hence the choice of the image that will be the best and most reliable arises. Then we must find techniques or a criterion of a priori information, one of the criteria most often used, we have chosen is a criterion of entropy. Entropy is an important scientific quantity because it is used in various areas, originally in thermodynamics, but also in information theory. Different types of entropy exist (Rényi, Tsallis, Burg, Shannon), we have chosen some as criteria. Using the Rényi entropy we have discovered new copulas. This thesis provides new contributions to CT imaging, the interaction between areas that are tomography and probability theory and statistics.

<p>Quantum key growing, often called quantum cryptography or quantum key distribution, is a method using some properties of quantum mechanics to create a secret shared cryptography key even if an eavesdropper has access to unlimited computational power. A vital but often neglected part of the method is unconditionally secure message authentication. This thesis examines the security aspects of authentication in quantum key growing. Important concepts are formalized as Python program source code, a comparison between quantum key growing and a classical system using trusted couriers is included, and the chain rule of entropy is generalized to any Rényi entropy. Finally and most importantly, a security flaw is identified which makes the probability to eavesdrop on the system undetected approach unity as the system is in use for a long time, and a solution to this problem is provided.</p>

Quantum key growing, often called quantum cryptography or quantum key distribution, is a method using some properties of quantum mechanics to create a secret shared cryptography key even if an eavesdropper has access to unlimited computational power. A vital but often neglected part of the method is unconditionally secure message authentication. This thesis examines the security aspects of authentication in quantum key growing. Important concepts are formalized as Python program source code, a comparison between quantum key growing and a classical system using trusted couriers is included, and the chain rule of entropy is generalized to any Rényi entropy. Finally and most importantly, a security flaw is identified which makes the probability to eavesdrop on the system undetected approach unity as the system is in use for a long time, and a solution to this problem is provided. / ICG QC

Ziel dieser Arbeit ist die Untersuchung der Sub- und Superdiffusion in fraktalen Strukturen. Der Fokus liegt auf zwei separaten Ansätzen, die entsprechend des Diffusionbereiches gewählt und variiert werden. Dadurch erhält man ein tieferes Verständnis und eine bessere Beschreibungsweise für beide Bereiche. Im ersten Teil betrachten wir subdiffusive Prozesse, die vor allem bei Transportvorgängen, z. B. in lebenden Geweben, eine grundlegende Rolle spielen. Hierbei modellieren wir den fraktalen Zustandsraum durch endliche Sierpinski Teppiche mit absorbierenden Randbedingungen und lösen dann die Mastergleichung zur Berechnung der Zeitentwicklung der Wahrscheinlichkeitsverteilung. Zur Charakterisierung der Diffusion auf regelmäßigen und zufälligen Teppichen bestimmen wir die Abfallzeit der Wahrscheinlichkeitsverteilung, die mittlere Austrittszeit und die Random Walk Dimension. Somit können wir den Einfluss zufälliger Strukturen auf die Diffusion aufzeigen. Superdiffusive Prozesse werden im zweiten Teil der Arbeit mit Hilfe der Diffusionsgleichung untersucht. Deren zweite Ableitung im Ort erweitern wir auf nichtganzzahlige Ordnungen, um die fraktalen Eigenschaften der Umgebung darzustellen. Die resultierende raum-fraktionale Diffusionsgleichung spannt ein Übergangsregime von der irreversiblen Diffusionsgleichung zur reversiblen Wellengleichung auf. Deren Lösungen untersuchen wir mittels verschiedener Entropien, wie Shannon, Tsallis oder Rényi Entropien, und deren Entropieproduktionsraten, welche natürliche Maße für die Irreversibilität sind. Das dabei gefundene Entropieproduktions-Paradoxon, d. h. ein unerwarteter Anstieg der Entropieproduktionsrate bei sinkender Irreversibilität des Prozesses, können wir nach geeigneter Reskalierung der Entropien auflösen. / The aim of this thesis is the examination of sub- and superdiffusive processes in fractal structures. The focus of the work concentrates on two separate approaches that are chosen and varied according to the corresponding regime. Thus, we obtain new insights about the underlying mechanisms and a more appropriate way of description for both regimes. In the first part subdiffusion is considered, which plays a crucial role for transport processes, as in living tissues. First, we model the fractal state space via finite Sierpinski carpets with absorbing boundary conditions and we solve the master equation to compute the time development of the probability distribution. To characterize the diffusion on regular as well as random carpets we determine the longest decay time of the probability distribution, the mean exit time and the Random walk dimension. Thus, we can verify the influence of random structures on the diffusive dynamics. In the second part of this thesis superdiffusive processes are studied by means of the diffusion equation. Its second order space derivative is extended to fractional order, which represents the fractal properties of the surrounding media. The resulting space-fractional diffusion equations span a linking regime from the irreversible diffusion equation to the reversible (half) wave equation. The corresponding solutions are analyzed by different entropies, as the Shannon, Tsallis or Rényi entropies and their entropy production rates, which are natural measures of irreversibility. We find an entropy production paradox, i. e. an unexpected increase of the entropy production rate by decreasing irreversibility of the processes. Due to an appropriate rescaling of the entropy we are able to resolve the paradox.

Cette thèse porte sur le lien entre la tomographie et la notion de copule. La tomographie à rayons X consiste à (re)construire la structure cachée d'un objet (une densité de matière, la distribution d'une quantité physique, ou une densité de loi conjointe) à partir de certaines données obtenues ou mesurées de l'objet (les projections, les radiographies, les densités marginales). Le lien entre les mesures et l'objet se modélise mathématiquement par la Transformée à Rayons X ou la Transformée de Radon. Par exemple, dans les problèmes d'imagerie en géométrie parallèle, lorsqu'on a seulement deux projections à deux angles de 0 et pi/2 (horizontale et verticale), le problème peut être identifié comme un autre problème très important en mathématique qui est la détermination d'une densité conjointe à partir de ses marginales. En se limitant à deux projections, les deux problèmes sont des problèmes mal posés au sens de Hadamard. Il faut alors ajouter de l'information a priori, ou bien des contraintes supplémentaires. L'apport principal de cette thèse est l'utilisation des critères de plusieurs entropies (Rényi, Tsallis, Burg, Shannon) permettant d'aboutir à une solution régularisée. Ce travail couvre alors différents domaines. Les aspects mathématiques de la tomographie via l'élément fondamental qui est la transformée de Radon. En probabilité sur la recherche d'une loi conjointe connaissant ses lois marginales d'où la notion de ''copule'' via le théorème de Sklar. Avec seulement deux projections, ce problème est extrêmement difficile. Mais en assimilant les deux projections (normalisées) aux densités marginales et l'image à reconstruire à une densité de probabilité, le lien se fait et les deux problèmes sont équivalents et peuvent se transposer dans le cadre statistique. Pour caractériser toutes les images possibles à reconstruire on a choisi alors l'outil de la théorie de probabilité, c'est-à-dire les copules. Et pour faire notre choix parmi les copules ou les images nous avons imposé le critère d'information a priori qui se base sur différentes entropies. L'entropie est une quantité scientifique importante car elle est utilisée dans divers domaines (en Thermodynamique, en théorie de l'information, etc). Ainsi, en utilisant par exemple l'entropie de Rényi nous avons découvert de nouvelles classes de copules. Cette thèse apporte de nouvelles contributions à l'imagerie, par l'interaction entre les domaines qui sont la tomographie et la théorie des probabilités et statistiques.

This thesis examines the utility of mathematical complexity measures for the analysis of stratospheric dynamics. Through theoretical considerations and tests with artificial data sets, e.g., the iteration of the logistic map, suitable parameters are determined for the application of the statistical entropy measures sample entropy (SE) and Rényi entropy (RE) to methane (a long-lived stratospheric tracer) data from simulations of the SOCOL chemistry-climate model. The SE is shown to be useful for quantifying the variability of recurring patterns in a time series and is able to identify tropical patterns similar to those reported by previous studies of the ``tropical pipe'' region. However, the SE is found to be unsuitable for use in polar regions, due to the non-stationarity of the methane data at extra-tropical latitudes. It is concluded that the SE cannot be used to analyse climate complexity on a global scale. The focus is turned to the RE, which is a complexity measure of probability distribution functions (PDFs). Using the second order RE and a normalisation factor, zonal PDFs of ten consecutive days of methane data are created with a Bayesian optimal binning technique. From these, the RE is calculated for every day (moving 10-day window). The results indicate that the RE is a promising tool for identifying stratospheric mixing barriers. In Southern Hemisphere winter and early spring, RE produces patterns similar to those found in other studies of stratospheric mixing. High values of RE are found to be indicative of the strong fluctuations in tracer distributions associated with relatively unmixed air in general, and with gradients in the vicinity of mixing barriers, in particular. Lower values suggest more thoroughly mixed air masses. The analysis is extended to eleven years of model data. Realistic inter-annual variability of some of the RE structures is observed, particularly in the Southern Hemisphere. By calculating a climatological mean of the RE for this period, additional mixing patterns are identified in the Northern Hemisphere. The validity of the RE analysis and its interpretation is underlined by showing that qualitatively similar patterns can be seen when using observational satellite data of a different tracer. Compared to previous techniques, the RE has the advantage that it requires significantly less computational effort, as it can be used to derive dynamical information from model or measurement tracer data without relying on any additional input such as wind fields. The results presented in this thesis strongly suggest that the RE is a useful new metric for analysing stratospheric mixing and its variability from climate model data. Furthermore, it is shown that the RE measure is very robust with respect to data gaps, which makes it ideal for application to observations. Hence, using the RE for comparing observations of tracer distributions with those from model simulations potentially presents a novel approach for analysing mixing in the stratosphere.

Ziel dieser Arbeit ist die Untersuchung der Sub- und Superdiffusion in fraktalen Strukturen. Der Fokus liegt auf zwei separaten Ansätzen, die entsprechend des Diffusionbereiches gewählt und variiert werden. Dadurch erhält man ein tieferes Verständnis und eine bessere Beschreibungsweise für beide Bereiche. Im ersten Teil betrachten wir subdiffusive Prozesse, die vor allem bei Transportvorgängen, z. B. in lebenden Geweben, eine grundlegende Rolle spielen. Hierbei modellieren wir den fraktalen Zustandsraum durch endliche Sierpinski Teppiche mit absorbierenden Randbedingungen und lösen dann die Mastergleichung zur Berechnung der Zeitentwicklung der Wahrscheinlichkeitsverteilung. Zur Charakterisierung der Diffusion auf regelmäßigen und zufälligen Teppichen bestimmen wir die Abfallzeit der Wahrscheinlichkeitsverteilung, die mittlere Austrittszeit und die Random Walk Dimension. Somit können wir den Einfluss zufälliger Strukturen auf die Diffusion aufzeigen. Superdiffusive Prozesse werden im zweiten Teil der Arbeit mit Hilfe der Diffusionsgleichung untersucht. Deren zweite Ableitung im Ort erweitern wir auf nichtganzzahlige Ordnungen, um die fraktalen Eigenschaften der Umgebung darzustellen. Die resultierende raum-fraktionale Diffusionsgleichung spannt ein Übergangsregime von der irreversiblen Diffusionsgleichung zur reversiblen Wellengleichung auf. Deren Lösungen untersuchen wir mittels verschiedener Entropien, wie Shannon, Tsallis oder Rényi Entropien, und deren Entropieproduktionsraten, welche natürliche Maße für die Irreversibilität sind. Das dabei gefundene Entropieproduktions-Paradoxon, d. h. ein unerwarteter Anstieg der Entropieproduktionsrate bei sinkender Irreversibilität des Prozesses, können wir nach geeigneter Reskalierung der Entropien auflösen. / The aim of this thesis is the examination of sub- and superdiffusive processes in fractal structures. The focus of the work concentrates on two separate approaches that are chosen and varied according to the corresponding regime. Thus, we obtain new insights about the underlying mechanisms and a more appropriate way of description for both regimes. In the first part subdiffusion is considered, which plays a crucial role for transport processes, as in living tissues. First, we model the fractal state space via finite Sierpinski carpets with absorbing boundary conditions and we solve the master equation to compute the time development of the probability distribution. To characterize the diffusion on regular as well as random carpets we determine the longest decay time of the probability distribution, the mean exit time and the Random walk dimension. Thus, we can verify the influence of random structures on the diffusive dynamics. In the second part of this thesis superdiffusive processes are studied by means of the diffusion equation. Its second order space derivative is extended to fractional order, which represents the fractal properties of the surrounding media. The resulting space-fractional diffusion equations span a linking regime from the irreversible diffusion equation to the reversible (half) wave equation. The corresponding solutions are analyzed by different entropies, as the Shannon, Tsallis or Rényi entropies and their entropy production rates, which are natural measures of irreversibility. We find an entropy production paradox, i. e. an unexpected increase of the entropy production rate by decreasing irreversibility of the processes. Due to an appropriate rescaling of the entropy we are able to resolve the paradox.