<p>Historically, evolution has been studied either by looking at morphological traits in living organisms and the fossil record, or by using bioinformatics and comparative genomics. While highly useful for deducing evolutionary history, these approaches are not particularly well suited for studying the mechanisms of evolution. In order to address such issues, other methods are needed. Mathematical modelling is one of the most powerful options available, and it is the approach used in this thesis. By constructing models of biological systems, the work aims to resolve some of the many unresolved questions regarding evolutionary processes, such as how new genes evolve and how selection acts in fragmented populations. Some answers have been reached, and thus the thesis makes a small contribution to our overall understanding of evolution.</p><p>The creation of novel genes was studied both directly and by extension of an analogous system, which revolved around reversion of a frameshift mutant. The results pointed to gene amplification as a likely mechanism for both reversion of the frameshift mutant and creation of new genes.</p><p>Selection in fragmented populations is shown to be effective even when sub-populations, rather than individuals, are competing against each other. Modeling of a system of bacterial symbionts living in aphids indicates that, although the bacterial population within a single host is small and subject to rampant genetic drift, the bacterial population as a whole is regulated by selection on the host level. Thus, deleterious mutations do no accumulate and the population maintains its fitness over time.</p>

Historically, evolution has been studied either by looking at morphological traits in living organisms and the fossil record, or by using bioinformatics and comparative genomics. While highly useful for deducing evolutionary history, these approaches are not particularly well suited for studying the mechanisms of evolution. In order to address such issues, other methods are needed. Mathematical modelling is one of the most powerful options available, and it is the approach used in this thesis. By constructing models of biological systems, the work aims to resolve some of the many unresolved questions regarding evolutionary processes, such as how new genes evolve and how selection acts in fragmented populations. Some answers have been reached, and thus the thesis makes a small contribution to our overall understanding of evolution. The creation of novel genes was studied both directly and by extension of an analogous system, which revolved around reversion of a frameshift mutant. The results pointed to gene amplification as a likely mechanism for both reversion of the frameshift mutant and creation of new genes. Selection in fragmented populations is shown to be effective even when sub-populations, rather than individuals, are competing against each other. Modeling of a system of bacterial symbionts living in aphids indicates that, although the bacterial population within a single host is small and subject to rampant genetic drift, the bacterial population as a whole is regulated by selection on the host level. Thus, deleterious mutations do no accumulate and the population maintains its fitness over time.

Inhomogeneities in the earth (fractures, layering, shape, composition) are responsible for seismic wave scattering and contribute towards amplitude, travel time, frequency and spectral fluctuations observed in seismic records. This thesis presents findings that complement our understanding of seismic scattering and imaging in heterogeneous media. Interest focused on probing the correlation between spatial variations in attributes that characterize the state (physical, chemical) of rocks and seismic waveform data with consideration towards potential implications for seismic survey design to optimize imaging, imaging with converted waves, microseismic monitoring, velocity modeling and imaging of lithological boundaries. The highlights of the research strategy include: • The use of stochastic methods to build realistic earth models that characterize the 1D, 2D and 3D spatial variations in rock properties. These petrophysical earth models are conditioned by experimental (“hard”) data such as geology, wave velocities and density from case study areas like the Bosumtwi impact crater and the base metal deposits in Nash Creek (Canada) and Thompson (Canada). The distributions of the sulfide mineralization at Nash Creek and at Thompson represent two end members of the heterogeneity spectrum. While the sulfide mineralization at Nash Creek is highly disseminated in nature, the sulfide rich zones at Thompson occur as well defined volumes (lens-shaped) having a strong density contrast with respect to the host rocks. • Analysis of modeled forward (transmitted) and backward scattered wave propagation in the heterogeneous earth models. As a result of a study aimed at correlating resonant frequencies to scale length parameters, it is observed that the efficiency of the spectral ratio method is undermined by its sensitivity to the interference between P- and S-waves as well as the impedance contrast. It is also demonstrated that travel time of direct arrivals (transmitted waves) can be used to infer structural heterogeneity and velocity distribution beyond borehole locations. However, the success of imaging with transmitted waves is subject to the influence of geology which must factor in the choice of acquisition geometry. For the first time, multivariate and multidimensional (3D) heterogeneous earth models that are conditioned by hard data from multiple boreholes are constructed. The methodology requires having at least one physical rock property attribute that is sampled along the whole borehole length. This approach helped to characterize the uncertainty in the distribution of rock densities and metal content in a study region of the Nash Creek property. The density data suggests the sulfides are disseminated and this poses challenges for both gravity and seismic imaging methods. Modeling studies suggest seismic methods will not be suited for imaging zones with such disseminated mineralization. On the other hand, when dealing with massive sulfide mineralization that has complex geology (steep dip) like the case in Thompson, the success of the seismic imaging process relies very much on the acquisition geometry as well as the variability of the physical properties of the host rock. Elastic modeling results show that a Vertical Seismic Profiling (VSP) geometry is better suited to capture the down-dip scattered wavefield from the orebody. While surface acquisition geometry with sufficient extended length in the down dip direction can also be used to detect the dipping orebody, its efficiency can however be undermined by background heterogeneity: when the scale length along the direction of dip is comparable to the dimensions of the orebody, the scattered wavefields are strong enough to mask the diffraction hyperbola generated from the ore. Moreover, the study also corroborates that converted waves generated from the scattering processes hold promise as an imaging tool for a dipping orebody as they are least affected by the scattering processes of background heterogeneity.

Inhomogeneities in the earth (fractures, layering, shape, composition) are responsible for seismic wave scattering and contribute towards amplitude, travel time, frequency and spectral fluctuations observed in seismic records. This thesis presents findings that complement our understanding of seismic scattering and imaging in heterogeneous media. Interest focused on probing the correlation between spatial variations in attributes that characterize the state (physical, chemical) of rocks and seismic waveform data with consideration towards potential implications for seismic survey design to optimize imaging, imaging with converted waves, microseismic monitoring, velocity modeling and imaging of lithological boundaries. The highlights of the research strategy include: • The use of stochastic methods to build realistic earth models that characterize the 1D, 2D and 3D spatial variations in rock properties. These petrophysical earth models are conditioned by experimental (“hard”) data such as geology, wave velocities and density from case study areas like the Bosumtwi impact crater and the base metal deposits in Nash Creek (Canada) and Thompson (Canada). The distributions of the sulfide mineralization at Nash Creek and at Thompson represent two end members of the heterogeneity spectrum. While the sulfide mineralization at Nash Creek is highly disseminated in nature, the sulfide rich zones at Thompson occur as well defined volumes (lens-shaped) having a strong density contrast with respect to the host rocks. • Analysis of modeled forward (transmitted) and backward scattered wave propagation in the heterogeneous earth models. As a result of a study aimed at correlating resonant frequencies to scale length parameters, it is observed that the efficiency of the spectral ratio method is undermined by its sensitivity to the interference between P- and S-waves as well as the impedance contrast. It is also demonstrated that travel time of direct arrivals (transmitted waves) can be used to infer structural heterogeneity and velocity distribution beyond borehole locations. However, the success of imaging with transmitted waves is subject to the influence of geology which must factor in the choice of acquisition geometry. For the first time, multivariate and multidimensional (3D) heterogeneous earth models that are conditioned by hard data from multiple boreholes are constructed. The methodology requires having at least one physical rock property attribute that is sampled along the whole borehole length. This approach helped to characterize the uncertainty in the distribution of rock densities and metal content in a study region of the Nash Creek property. The density data suggests the sulfides are disseminated and this poses challenges for both gravity and seismic imaging methods. Modeling studies suggest seismic methods will not be suited for imaging zones with such disseminated mineralization. On the other hand, when dealing with massive sulfide mineralization that has complex geology (steep dip) like the case in Thompson, the success of the seismic imaging process relies very much on the acquisition geometry as well as the variability of the physical properties of the host rock. Elastic modeling results show that a Vertical Seismic Profiling (VSP) geometry is better suited to capture the down-dip scattered wavefield from the orebody. While surface acquisition geometry with sufficient extended length in the down dip direction can also be used to detect the dipping orebody, its efficiency can however be undermined by background heterogeneity: when the scale length along the direction of dip is comparable to the dimensions of the orebody, the scattered wavefields are strong enough to mask the diffraction hyperbola generated from the ore. Moreover, the study also corroborates that converted waves generated from the scattering processes hold promise as an imaging tool for a dipping orebody as they are least affected by the scattering processes of background heterogeneity.

The risk-based life-cycle management of engineering systems in a nuclear power plant is intended to ensure safe and economically efficient operation of energy generation infrastructure over its entire service life. An important element of life-cycle management is to understand, model and forecast the effect of various degradation mechanisms affecting the performance of engineering systems, structures and components. The modeling of degradation in nuclear plant components is confounded by large sampling and temporal uncertainties. The reason is that nuclear systems are not readily accessible for inspections due to high level of radiation and large costs associated with remote data collection methods. The models of degradation used by industry are largely derived from ordinary linear regression methods. The main objective of this thesis is to develop more advanced techniques based on stochastic process theory to model deterioration in engineering components with the purpose of providing more scientific basis to life-cycle management of aging nuclear power plants. This thesis proposes a stochastic gamma process (GP) model for deterioration and develops a suite of statistical techniques for calibrating the model parameters. The gamma process is a versatile and mathematically tractable stochastic model for a wide variety of degradation phenomena, and another desirable property is its nonnegative, monotonically increasing sample paths. In the thesis, the GP model is extended by including additional covariates and also modeling for random effects. The optimization of age-based replacement and condition-based maintenance strategies is also presented. The thesis also investigates improved regression techniques for modeling deterioration. A linear mixed-effects (LME) regression model is presented to resolve an inconsistency of the traditional regression models. The proposed LME model assumes that the randomness in deterioration is decomposed into two parts: the unobserved heterogeneity of individual units and additive measurement errors. Another common way to model deterioration in civil engineering is to treat the rate of deterioration as a random variable. In the context of condition-based maintenance, the thesis shows that the random variable rate (RV) model is inadequate to incorporate temporal variability, because the deterioration along a specific sample path becomes deterministic. This distinction between the RV and GP models has profound implications to the optimization of maintenance strategies. The thesis presents detailed practical applications of the proposed models to feeder pipe systems and fuel channels in CANDU nuclear reactors. In summary, a careful consideration of the nature of uncertainties associated with deterioration is important for credible life-cycle management of engineering systems. If the deterioration process is affected by temporal uncertainty, it is important to model it as a stochastic process.

The risk-based life-cycle management of engineering systems in a nuclear power plant is intended to ensure safe and economically efficient operation of energy generation infrastructure over its entire service life. An important element of life-cycle management is to understand, model and forecast the effect of various degradation mechanisms affecting the performance of engineering systems, structures and components. The modeling of degradation in nuclear plant components is confounded by large sampling and temporal uncertainties. The reason is that nuclear systems are not readily accessible for inspections due to high level of radiation and large costs associated with remote data collection methods. The models of degradation used by industry are largely derived from ordinary linear regression methods. The main objective of this thesis is to develop more advanced techniques based on stochastic process theory to model deterioration in engineering components with the purpose of providing more scientific basis to life-cycle management of aging nuclear power plants. This thesis proposes a stochastic gamma process (GP) model for deterioration and develops a suite of statistical techniques for calibrating the model parameters. The gamma process is a versatile and mathematically tractable stochastic model for a wide variety of degradation phenomena, and another desirable property is its nonnegative, monotonically increasing sample paths. In the thesis, the GP model is extended by including additional covariates and also modeling for random effects. The optimization of age-based replacement and condition-based maintenance strategies is also presented. The thesis also investigates improved regression techniques for modeling deterioration. A linear mixed-effects (LME) regression model is presented to resolve an inconsistency of the traditional regression models. The proposed LME model assumes that the randomness in deterioration is decomposed into two parts: the unobserved heterogeneity of individual units and additive measurement errors. Another common way to model deterioration in civil engineering is to treat the rate of deterioration as a random variable. In the context of condition-based maintenance, the thesis shows that the random variable rate (RV) model is inadequate to incorporate temporal variability, because the deterioration along a specific sample path becomes deterministic. This distinction between the RV and GP models has profound implications to the optimization of maintenance strategies. The thesis presents detailed practical applications of the proposed models to feeder pipe systems and fuel channels in CANDU nuclear reactors. In summary, a careful consideration of the nature of uncertainties associated with deterioration is important for credible life-cycle management of engineering systems. If the deterioration process is affected by temporal uncertainty, it is important to model it as a stochastic process.

The use of hazardous toxic substances is very common in the industrial sector. The substances are often stored in tanks in storage compartments or transported between industrial premises. In case of an accident involving these substances, severe harm can affect both population and the environment. This leaves a demand for an accurate prediction of the substance concentration distribution to mitigate the risks as much as possible and in advance create suitable safety measures. Toxic gases and vapors are often denser than air making it affected by negative buoyancy forces. This will make the gas descend and spread horizontally when reaching the ground. Swedish Defence Research Agency (FOI) carries today a model called LillPello for simulating the dispersion of gases, yet it does not account for the specific case of a dense gas. Therefore, this thesis aims to implement the necessary effects needed to accurately simulate the dispersion of a dense gas. These effects were implemented in Fortran 90 by solving five conservation equations for energy, momentum (vertical and horizontal) and mass. The model was compared against experimental data of a leak of ammonia (NH3). By analyzing the result of the simulations in this thesis, we can conclude that the overall result is satisfactory. We can notice a small concentration underestimation at all measurement points and the model produced a concentration power law coefficient which lands inside the expected range. Two out of the three statistical quantities Geometric Mean (MG), Geometric Variance (VG) and Factor of 2 (FA2) produced values within the ranges of acceptable values. The drawback of the model as it is implemented today is its efficiency, so the main priority for the future of this thesis is to improve this. The model should also be analyzed on more experiments to further validate its accuracy. / Användandet av giftiga ämnen är vanligt inom den industriella sektorn. Ämnena är oftast lagrade i behållare positionerade i lagringsutrymmen eller så transporteras ämnena mellan industrilokaler. I samband med en olycka innehållande dessa substanser kan stora skador drabba både befolkning och miljön. Detta leder till ett behov av att noggrant kunna förutspå koncentrationsfördelningen för att minska riskerna, samt i förväg kunna skapa lämpliga säkerhetsåtgärder. Giftiga gaser och ångor är oftast tyngre än luft vilket gör att gasen blir påverkad av negativ bärkraft. Detta gör att gasen sjunker och sprids horisontalt när den når marken. Totalförsvarets Forskningsinstitut (FOI) besitter idag en modell kallad LillPello som simulerar spridning av gaser, men den hanterar inte det specifika fallet av en tunggas. Därför siktar detta projekt på att, in i LillPello, implementera de nödvändiga effekterna som behövs för att korrekt kunna simulera spridningen av en tunggas. Dessa effekter är implementerad i Fortran 90 genom att lösa fem konserveringsekvationer för energi, momentum (vertikal och horisontell) samt massa. Modellen jämfördes mot data från ett fältexperiment där ammoniak (NH3) släpptes ut. Genom att analysera resultatet från simuleringar kan vi dra slutsatsen att det övergripande resultatet är tillfredsställande. Vi kan notera en underskattning för alla koncentrationsmätningar i simuleringarna och modellen producerade en potenslagsexponent vars värde hamnade innanför den accepterade gränsen. Två utav de tre beräknade statistiska kvantiteterna: Geometriskt medelvärde (MG), Geometrisk varians (VG) och Faktor av 2 (FA2) producerade värden inom de acceptabla gränserna. Största nackdelen med modellen är dess effektivitet och därför är största prioritet för det fortsatta arbetet inom detta projekt att effektivisera implementeringen. Modellen ska även bli vidare analyserad mot fler experiment för att validera dess noggrannhet.

This thesis uses methods and models from non-equilibrium statistical physics to describe intracellular processes. Bidirectional microtubule-based transport within axons is modeled as a quasi-one-dimensional stochastic lattice gas with two particle species moving in opposite directions under mutual exclusion interaction. Generically occurring clusters of particles in current models for intracellular transport can be dissolved by additionally considering the dynamics of the transport lattice, i.e., the microtubule. An idealized model for the lattice dynamics is used to create a phase transition toward a homogenous state with efficient transport in both directions. In the thermodynamic limit, a steady state property of the dynamic lattice limits the maximal size of clusters. Lane formation mechanisms which are due to specific particle-particle interactions turn out to be very sensitive to the model assumptions. Furthermore, even if some particle-particle interaction is considered, taking the lattice dynamics into account almost always improves transport. Thus the lattice dynamics seems to be the key aspect in understanding how nature regulates intracellular traffic. The last part introduces a model for the dynamics of a microtubule which is limited in its growth by the cell boundary. The action of a rescue-enhancing protein which is added to the growing tip of a microtubule and then slowly dissociates leads to interesting aging effects which should be experimentally observable.

This dissertation presents a stochastic framework for modeling the degradation processes of components in complex engineering systems using sensor based signals. Chapters 1 and 2 discuses the challenges and the existing literature in monitoring and predicting the performance of complex engineering systems. Chapter 3 presents the degradation model with the absorbing failure threshold for a single unit and the RLD estimation using the first-passage-time approach. Subsequently, we develop the estimate of the RLD using the first-passage-time approach for two cases: information prior distributions and non-informative prior distributions. A case study is presented using real-world data from rolling elements bearing applications. Chapter 4 presents a stochastic methodology for modeling degradation signals from components functioning under dynamically evolving environmental conditions. We utilize in-situ sensor signals related to the degradation process, as well as the environmental conditions, to predict and continuously update, in real-time, the distribution of a component’s residual lifetime. Two distinct models are presented. The first considers future environmental profiles that evolve in a deterministic manner while the second assumes the environment evolves as a continuous-time Markov chain. Chapters 5 and 6 generalize the failure-dependent models and develop a general model that examines the interactions among the degradation processes of interconnected components/subsystems. In particular, we model how the degradation level of one component affects the degradation rates of other components in the system. Hereafter, we refer to this type of component-to-component interaction caused by their stochastic dependence as degradation-rate-interaction (DRI). Chapter 5 focuses on the scenario in which these changes occur in a discrete manner, whereas, Chapter 6 focuses on the scenario, in which DRIs occur in a continuous manner. We demonstrate that incorporating the effects of component interactions significantly improves the prediction accuracy of RLDs. Finally, we outline the conclusion remarks and a future work plan in Chapter 7.

There are a huge number of pathogens with multi-component transmission cycles, involving ampli_er hosts, vectors, complex pathogen life cycles and particular environmental conditions. These complex systems present challenges in terms of modeling and policy development. The deadliest tick-borne infectious disease in the world, the Brazilian Spotted Fever (BSF), is a relevant example of that. The current increase of human cases of BSF has been associated with the presence and expansion of capybaras Hydrochoerus hydrochaeris, amplifer host for the agent Rickettsia rickettsii and primary host for the tick vector Amblyomma sculptum. The objective of this thesis was to analyze the dynamics of the FMB with the purpose of providing bases for the planning of strategies focused on the prevention of human cases. We proposed diferent approaches to evaluating: i) the contribution of hosts and vectors in the transmission of BSF, ii) potential risk areas and anthropogenic parameters associated with the occurrence of human cases, iii) the pattern and the spatial propagation velocity of BSF, and iv) climatic and landscape factors that could be related to the distribution of the vector. The proposed approaches elucidated how BSF control and prevention strategies can be focused on the management of amplifier hosts populations. We found that geographical barriers generated, for example, by areas of riparian reforestation, could prevent the spatial spread of BSF, since a positive association between the occurrence of human cases and the increment of sugarcane crop was determined, as well as a higher propagation velocity of BSF in places with higher carrying capacity. This thesis was interdisciplinary and required, on one hand, expertise in biology, computational epidemiology, mathematics and statistics and on the other hand, a datarich environment such as the Laboratory of Parasitology of the VPS/FMVZ/USP. The results of this thesis can be usefulness in the planning of public health policies related to the prevention of BSF. Furthermore, this work will open the path to further mathematical and computational studies focused on the dynamics and prevention of other vector-borne infectious diseases. / Existe um grande número de agentes patogênicos com ciclos de transmissão complexos, envolvendo hospedeiros amplificadores, vetores e condições ambientais particulares. Esses sistemas complexos apresentam desafios quanto a modelagem e desenvolvimento de políticas públicas. A Febre Maculosa Brasileira (FMB) é a doença transmitida por carrapatos mais letal do mundo e é um claro exemplo de um sistema complexo. O aumento atual de casos humanos de BSF tem sido associado à presença e expansão de capivaras Hydrochoerus hydrochaeris, hospedeiros amplificadores do agente Rickettsia rickettsii e hospedeiros primários do carrapato vetor Amblyomma sculptum. O objetivo desta tese foi analisar a dinâmica da FMB com o propósito de fornecer bases para o delineamento de estratégias de prevenção de casos em humanos. Diferentes abordagens foram propostas para avaliar: i) a contribuição específica de hospedeiros e vetores na transmissão da FMB, ii) os parâmetros antropogênicos associados com a ocorrência dos casos e potenciais áreas de risco, iii) o padrão e a velocidade de propagação espacial e da doença, e iv) os fatores climáticos e paisagísticos que poderiam estar relacionados à distribuição do vetor. Os modelos propostos elucidaram que as estratégias de controle e prevenção da FMB podem estar focadas em práticas de manejo das populações de hospedeiros amplificadores. Uma vez que uma associação positiva entre ocorrência de casos humanos e o incremento de cultura de cana-de-açúcar foi determinada, assim como uma maior velocidade de propagação da FMB em locais com alta quantidade desta cultura, barreiras geográficas geradas, por exemplo, por zonas de reflorestamento ciliar, poderiam impedir a disseminação da FMB. Esta tese foi interdisciplinar e exigiu, por um lado, conhecimentos em biologia, epidemiologia computacional, matemática e estatística e, em contrapartida, um ambiente rico em dados biológicos como o Laboratório de Parasitologia do VPS/USP. Os resultados desta tese poderão ser utilizados na planificação de políticas de saúde pública enfocadas à prevenção da FMB. Complementarmente, este trabalho abrirá o caminho para futuros estudos matemáticos e computacionais orientados no estudo da dinâmica e prevenção de outras doenças infecciosas transmitidas por vetores.