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This study focuses on the development of a stochastic simulation methodology to study the effects of cure kinetics uncertainty, in plane fibre misalignment and boundary conditions uncertainty on the cure process of composite materials. Differential Scanning Calorimetry was used to characterise cure kinetics variability of a commercial epoxy resin used in aerospace applications. It was found that cure kinetics uncertainty is associated with variations in the initial degree of cure, activation energy and reaction order. Image analysis was employed to characterise in plane fibre misalignment in a carbon fibre ±45º non-crimp fabric. The experimental results showed that variability in tow orientation was significant with a standard deviation of about 1.2º. A set of experiments using an infusion set-up was carried out to quantify boundary conditions uncertainty related to tool temperature, ambient temperature and surface heat transfer coefficient using thermocouples (tool/ambient temperature) and heat flux sensors (surface heat transfer coefficient). It was concluded that boundary conditions uncertainty can show considerable short term and long term variability. Conventional Monte Carlo and Probabilistic Collocation Method were integrated with a thermo-mechanical cure simulation model in order to investigate the effect of cure kinetics, fibre misalignment and boundary conditions variability on process outcome. The cure model was developed and implemented using a finite element model incorporating appropriate material sub-models of cure kinetics, specific heat capacity, thermal conductivity, moduli, thermal expansion and cure shrinkage. The effect of cure kinetics uncertainty on the temperature overshoot of a thick carbon fibre epoxy flat panel was investigated using the two stochastic simulation schemes. The stochastic simulation results showed that variability in cure kinetics can introduce a significant scatter in temperature overshoot, presenting a coefficient of variation of about 30%. Furthermore, it was shown that the collocation method can offer an efficient solution with significantly lower computational cost compared to Monte Carlo at comparable accuracy. Stochastic simulation of the cure of an angle shaped carbon fibre-epoxy component within the Monte Carlo scheme showed that fibre misalignment can cause considerable variability in the process outcome. The coefficient of variation of maximum residual stress can reach up to approximately 2% (standard deviation of 1 MPa) whilst qualitative and quantitative variations in final distortion of the cured part occur with the standard deviation in twist and corner angle reaching values of 0.4 º and 0.05º respectively. Simulation of the cure of a thin carbon fibre-epoxy panel within the Monte Carlo scheme indicated that surface heat transfer and tool temperature variability dominate variability in cure time, resulting in a coefficient of variation of about 22%. In addition to Monte Carlo, the effect of surface heat transfer coefficient and tool temperature variations on cure time was addressed using the collocation method. It was found that probabilistic collocation is capable of capturing variability propagation with good accuracy while offering tremendous benefits in terms of computational costs.

One of the principle causes for deviations between predicted and simulated performance of buildings relates to the stochastic nature of their occupants: their presence, activities whilst present, activity dependent behaviours and the consequent implications for their perceived comfort. A growing research community is active in the development and validation of stochastic models addressing these issues; and considerable progress has been made. Specifically models in the areas of presence, activities while present, shading devices, window openings and lighting usage. One key outstanding challenge relates to the integration of these prototype models with building simulation in a coherent and generalizable way; meaning that emerging models can be integrated with a range of building simulation software. This thesis describes our proof of concept platform that integrates stochastic occupancy models within a multi agent simulation platform, which communicates directly with building simulation software. The tool is called Nottingham Multi-Agent Stochastic Simulation (No-MASS). No-MASS is tested with a building performance simulation solver to demonstrate the effectiveness of the integrated stochastic models on a residential building and a non-residential building. To account for diversity between occupants No-MASS makes use of archetypical behaviours within the stochastic models of windows, shades and activities. Thus providing designers with means to evaluate the performance of their designs in response to the range of expected behaviours and to evaluate the robustness of their design solutions; which is not possible using current simplistic deterministic representations. A methodology for including rule based models is built into No-MASS, this allows for testing what-if scenarios with building performance simulation and provides a pragmatic basis for the modelling of the behaviours for which there is insufficient data to develop stochastic models. A Belief-Desire-Intention model is used to develop a set of goals and plans that an agent must follow to influence the environment based on their beliefs about current environmental conditions. Recommendations for the future development of stochastic models are presented based on the sensitivity analysis of the plans. A social interactions framework is developed within No-MASS to resolve conflicts between competing agents. This framework resolves situations where each agent may have different desires, for example one may wish to have a window open and another closed based on the outputs of the stochastic models. A votes casting system determines the agent choice, the most votes becomes the action acted on. No-MASS employs agent machine learning techniques that allow them to learn how to respond to the processes taking place within a building and agents can choose a strategy without the need for context specific rules. Employing these complementary techniques to support the comprehensive simulation of occupants presence and behaviour, integrated within a single platform that can readily interface with a range of building (and urban) energy simulation programs is the key contribution to knowledge from this thesis. Nevertheless, there is significant scope to extend this work to further reduce the performance gap between simulated and real world buildings.

To comprehend the immense complexity that drives biological systems, it is necessary to generate hypotheses of system behaviour. This is because one can observe the results of a biological process and have knowledge of the molecular/genetic components, but not directly witness biochemical interaction mechanisms. Hypotheses can be tested in silico which is considerably cheaper and faster than “wet” lab trialand- error experimentation. Bio-systems are traditionally modelled using ordinary differential equations (ODEs). ODEs are generally suitable for the approximation of a (test tube sized) in vitro system trajectory, but cannot account for inherent system noise or discrete event behaviour. Most in vivo biochemical interactions occur within small spatially compartmentalised units commonly known as cells, which are prone to stochastic noise due to relatively low intracellular molecular populations. Stochastic simulation algorithms (SSAs) provide an exact mechanistic account of the temporal evolution of a bio-system, and can account for noise and discrete cellular transcription and signalling behaviour. Whilst this reaction-by-reaction account of system trajectory elucidates biological mechanisms more comprehensively than ODE execution, it comes at increased computational expense. Scaling to the demands of modern biology requires ever larger and more detailed models to be executed. Scientists evaluating and engineering tissue-scale and bacterial colony sized biosystems can be limited by the tractability of their computational hypothesis testing techniques. This thesis evaluates a hypothesised relationship between SSA computational performance and biochemical model characteristics. This relationship leads to the possibility of predicting the fastest SSA for an arbitrary model - a method that can provide computational headroom for more complex models to be executed. The research output of this thesis is realised as a software package for meta-stochastic simulation called ssapredict. Ssapredict uses statistical classification to predict SSA performance, and also provides high performance stochastic simulation implementations to the wider community.

Peer-to-Peer (P2P) networks provide an alternative approach to distributed systems, relaxing the requirements for dedicated servers from the client-server model. A P2P network operates as an overlay at application layer, on top of the physical network. In the early years of P2P, most applications lacked mechanisms for enforcing a particular overlay topology. This resulted in inefficient communication schemes, such as flooding or the maintenance of large numbers of connections with other peers. However, researchers and practitioners have realized the importance of constructing and maintaining appropriate overlay topologies for efficient and robust P2P systems. P2P-based Voice over IP (VoIP) networks, such as Skype, distinguish client peers from super peers. This results in a two-level hierarchy: Peers with powerful CPU, more free memory and greater bandwidth take on server-like responsibilities and provide services to a set of client peers. But building and maintaining a super peer-based overlay topology is not easy. In particular, the uncontrollable and unpredictable behaviour of peers results in volatile overlay topologies. This makes it challenging to design reconfigurable and stable networks that provide good Quality of Service (QoS). Various solutions have been proposed. However, peer dynamics, scale and complexity make it hard and expensive to validate them by testing. Simulation can help to validate network designs and protocols, but most existing approaches cannot cope with unbounded dynamic change of network topology. We propose a new approach to the modelling and simulation of P2P network reconfigurations using graph transformation, a visual rule based formalism. Based on existing alternatives we classify network design variations by means of a feature tree. Focussing on P2P VoIP applications, we develop a structural model and transformation rules to compare alternative solutions to the problems of selection and connection to super peers, peer promotion, and load balancing, evaluating their QoS properties. We validate the model using statistics from the real Skype network and experimental data in the literature.

This study focuses on the development of an inversion procedure based on Markov Chain Monte Carlo (MCMC) integrating composites process monitoring with simulation to provide real time probabilistic estimations of process outcomes. The simulation incorporates material and boundary condition uncertainty. Quantification of resin viscosity uncertainty showed a variability of 30% in initial values, introducing variations of an equivalent magnitude in the filling stage of Liquid Composite Moulding (LCM). A surrogate model based on Kriging was developed to enable the use of process models iteratively within a stochastic simulation or optimisation loop. The Kriging model reduces run times by 99% compared to finite element simulation, introducing only an error below 2%. A dielectric sensor appropriate for flow and cure monitoring in the presence carbon reinforcement was developed overcoming limitations of electrical sorting and interference with the electric field. The sensor functionality was demonstrated in both flow and cure LCM trials. Real time flow monitoring was integrated with simulation into an inverse algorithm achieving on line estimation of unknown variables and of the resulting flow field with an error lower than 5%, compared to visual measurements. The inversion was also used in curing, by combining thermal monitoring with simulation to identify the thermal conductivity and heat transfer coefficient probabilistically, leading to estimation of cure duration and final degree of cure with an error below 1%. A stochastic multi-objective optimisation methodology has been developed as a first step towards model based stochastic control of composite manufacturing. The method, which is based on Genetic Algorithms (GA), is capable of identifying process settings that optimise process objectives and their variance. In the case of cure of thick composites, the optimisation identifies cure profiles which achieve 40% reduction in temperature overshoot and process duration compared to standard profiles, whilst achieving increased process robustness through minimisation of the variance.

Noise is ubiquitous in biology. Recent studies have demonstrated that both gene expression and physiological processes, such as growth, can be noisy. The cell-to-cell variation resulting from this stochasticity has been implicated in survival strategies for bacterial populations. However, it remains unclear how single cells couple gene expression with growth to implement these strategies. In this thesis we show how noisy expression of a key stress response regulator, RpoS, allows E. coli to modulate its noisy growth dynamics to survive future adverse environments. We first demonstrate that single cells in bulk, exponential phase cultures have heterogeneous rpoS expression. Combining microfluidics and time-lapse microscopy we reveal multi-generation RpoS activity pulses are responsible for this heterogeneity. We next show that RpoS and growth have stochastic dynamics and are anti-correlated. With a stochastic simulation of chemical reactions coupled to a deterministic cell growth model we show that a mutual inhibition loop between RpoS activity and growth rate is sufficient to capture the observed dynamics. We test our model by performing experimental perturbations and find good agreement between theory and experiment. Next, we demonstrate the functionality of this phenotypic variability by using the microfluidic platform to apply a short, intense period of oxidative stress. By tracking cells prior to the stress and testing for survival after the stress we reveal that E. coli prepare for sudden stressful events by entering prolonged periods of slow growth mediated by RpoS. This dynamic phenotype is captured by the RpoS-growth feedback model. Our synthesis of noisy gene expression, growth, and survival paves the way for further exploration of functional phenotypic variability.

Modelling and simulation are essential to modern research in cell biology. This thesis follows a journey starting from the construction of new stochastic methods for discrete biochemical systems to using them to simulate a population of interacting haematopoietic stem cell lineages. The first part of this thesis is on discrete stochastic methods. We develop two new methods, the stochastic extrapolation framework and the Stochastic Bulirsch-Stoer methods. These are based on the Richardson extrapolation technique, which is widely used in ordinary differential equation solvers. We believed that it would also be useful in the stochastic regime, and this turned out to be true. The stochastic extrapolation framework is a scheme that admits any stochastic method with a fixed stepsize and known global error expansion. It can improve the weak order of the moments of these methods by cancelling the leading terms in the global error. Using numerical simulations, we demonstrate that this is the case up to second order, and postulate that this also follows for higher order. Our simulations show that extrapolation can greatly improve the accuracy of a numerical method. The Stochastic Bulirsch-Stoer method is another highly accurate stochastic solver. Furthermore, using numerical simulations we find that it is able to better retain its high accuracy for larger timesteps than competing methods, meaning it remains accurate even when simulation time is speeded up. This is a useful property for simulating the complex systems that researchers are often interested in today. The second part of the thesis is concerned with modelling a haematopoietic stem cell system, which consists of many interacting niche lineages. We use a vectorised tau-leap method to examine the differences between a deterministic and a stochastic model of the system, and investigate how coupling niche lineages affects the dynamics of the system at the homeostatic state as well as after a perturbation. We find that larger coupling allows the system to find the optimal steady state blood cell levels. In addition, when the perturbation is applied randomly to the entire system, larger coupling also results in smaller post-perturbation cell fluctuations compared to non-coupled cells. In brief, this thesis contains four main sets of contributions: two new high-accuracy discrete stochastic methods that have been numerically tested, an improvement that can be used with any leaping method that introduces vectorisation as well as how to use a common stepsize adapting scheme, and an investigation of the effects of coupling lineages in a heterogeneous population of haematopoietic stem cell niche lineages.

This thesis is concerned with mathematical modelling of oncolytic virotherapy: the use of genetically modified viruses to selectively spread, replicate and destroy cancerous cells in solid tumours. Traditional spatially-dependent modelling approaches have previously assumed that virus spread is due to viral diffusion in solid tumours, and also neglect the time delay introduced by the lytic cycle for viral replication within host cells. A deterministic, age-structured reaction-diffusion model is developed for the spatially-dependent interactions of uninfected cells, infected cells and virus particles, with the spread of virus particles facilitated by infected cell motility and delay. Evidence of travelling wave behaviour is shown, and an asymptotic approximation for the wave speed is derived as a function of key parameters. Next, the same physical assumptions as in the continuum model are used to develop an equivalent discrete, probabilistic model for that is valid in the limit of low particle concentrations. This mesoscopic, compartment-based model is then validated against known test cases, and it is shown that the localised nature of infected cell bursts leads to inconsistencies between the discrete and continuum models. The qualitative behaviour of this stochastic model is then analysed for a range of key experimentally-controllable parameters. Two-dimensional simulations of in vivo and in vitro therapies are then analysed to determine the effects of virus burst size, length of lytic cycle, infected cell motility, and initial viral distribution on the wave speed, consistency of results and overall success of therapy. Finally, the experimental difficulty of measuring the effective motility of cells is addressed by considering effective medium approximations of diffusion through heterogeneous tumours. Considering an idealised tumour consisting of periodic obstacles in free space, a two-scale homogenisation technique is used to show the effects of obstacle shape on the effective diffusivity. A novel method for calculating the effective continuum behaviour of random walks on lattices is then developed for the limiting case where microscopic interactions are discrete.

Quantification of hurricane hazard, which includes wind, rainfall and storm surge, is essential for engineering design as well as financial loss assessment. The objective of this study is to develop a stochastic simulation framework which integrates the simulation process of hurricane rainfall and wind hazard. This study is divided into two parts. The main objective of the first part is to develop a method for the estimation of the hurricane wind field parameters radius to maximum wind speeds (R_max) and Holland B parameter (B). The second part develops a stochastic model to simulate hurricane rainfall, which is named the ‘NormRain’ model. The first part develops a hurricane wind speed computation method, which is validated by comparing with wind speed observations from meteorological stations. Then, a method to estimate R_max and B for historical storms is developed using this wind speed computation algorithm. Finally, based on the analysis of historical storms using the R_max and B estimation method, equations for stochastic simulation of R_max and B time history are developed. These equations can simulate the temporal correlation (i.e. correlation of the simulated value in current time-step with the previous timesteps) of R_max and B, which is an improvement over other commonly used method. Besides R_max and B estimation, another important application of the wind speed computation framework is to develop a database of hurricane wind speed hazard curves for the 30 Eastern US states, which is expected to aid the research of performance-based wind engineering. The hurricane rainfall distribution about the storm center can be very asymmetric and irregular, with high rainfall rates far from storm center. The existing statistical models for hurricane rainfall usually estimate the mean rainfall rate profile, and do not explicitly consider the total rainfall volume. However, the mean rainfall rate profiles cannot account for high localized rainfall rates which can be much larger than the mean value and can contribute a significant portion of the total rainfall volume. To overcome this limitation, this study develops a rainfall simulation model which explicitly simulates total rainfall volume using central pressure, relative vorticity and total precipitable water. Since the irregular shape of hurricane rain field is difficult to describe using equations, this study simulates the hurricane rain field using the concept of normalized rain field shape from historical storms. The hurricane simulation model can thus simulate realistic hurricane rain fields. The hurricane rain simulation model ‘NormRain’ developed in the second part of this study consists of two parts. The first part estimates the total rainfall volume and extent of hurricane rain field at any time-step, and the second part determines how the rainfall rates associated with this rainfall volume are distributed within the rain field extent.

Since its inception, quantum information processing (QIP) has been branched into many new directions. As well as well-known applications such as teleportation and metrology, researchers are beginning to investigate interdisciplinary areas such as quantum machine learning. One of the interesting areas is where quantum information science meets stochastic modelling, from the field of complexity science. Recently, it has been shown theoretically that, for simulating classical systems, quantumassisted models and simulators are more efficient in terms of memory storage they require to do simulations, compared with classical computers. That is, for most systems, classical simulators demand an excessive amount of memory storage, while quantum simulators can do the same simulation with less memory. The main focus of this thesis is on experimental realisation of quantum simulators that are capable of simulating stochastic processes with a reduced amount of memory. To implement the (nearly) exact simulation of stochastic processes using quantum simulators, it is essential to have low-noise state preparation, robust unitary operations, and high-precision read-out. These requirements, and the flexibility and precision of photonic quantum optics, make photonics the ideal system for developing the science of this new quantum advantage and for making strides towards its technological realisation. In the context of stochastic simulation, I have experimentally studied three key problems that serve as stepping stones in advancing this new field. In the first experiment, an error-tolerant quantum simulator was designed, and realised to simulate a 1D Ising spin chain, using internal states that store less information than the corresponding classical approach. Furthermore, an interesting and fundamental phenomenon named the ambiguity of simplicity is witnessed. This is the inconsistency that we observe in the order of relative complexity of two systems when we change the simulators from classical to quantum. In the second experiment, a quantum simulator was built that can simulate classical processes for more than one step of the simulation at a time, storing the information from multiple steps coherently. In the third experiment, a new type of quantum memory advantage, which is based on the dimensionality of the memory register, rather than on information entropy measure, is demonstrated. This advantage is realisable in a single simulator, in contrast to previous works. Realising the dimensionality memory advantage in practical applications does not rely on running multiple simulators in parallel.In the field of optical QIP, realising an ideal single-photon source has been a longstanding challenge. In another part of my PhD, I have worked on a source that aims to tackle some of the existing issues in this context. We built a source of high-quality entangled photons with a high heralding efficiency, which has the potential to be used in multi-photon experiments. This source was also essential to demonstrate a fundamental task in quantum non-locality, one-way steering, which was performed conclusively for the first time.

Breeding for high-yielding and broadly adapted varieties of cassava has been the primary target of the International Institute of Tropical Agriculture (IITA) cassava breeding program based in Nigeria. However, this target has been hindered due to the presence of genotype-by-environment interaction (GEI) and phenotypic recurrent selection as a traditional approach of breeding. This approach generates gains slowly due to long breeding cycle, resulting to low rate of realized genetic gain per unit time for complex traits like fresh root yield. Taking advantage of recent advances in computational resources, this study focused on exploring historical data using advance statistical techniques and stochastic simulation. The main objective was to identify a breeding scheme which optimizes the cost of field operation and rate of genetic gain. First, I used classical linear-bilinear model to dissect existing patterns of GEI of 36 elite cassava clones evaluated in 11 locations over 3 growing seasons. This aims to identify the optimum number of environments from target population of environments for future testing of genetic lines for key traits such as fresh root yield, dry matter content, and top yield. Second, I exploited the complex pattern of GEI from 96 varieties assessed in 48 trials using variance structure models on fresh root yield to identify an optimal model that captures GEI and stable clones, identify mega-environments and key environmental covariables driving GEI. Lastly, I used stochastic simulation to assess different breeding scenarios to identify an optimal breeding scheme which maximized genetic gain for cassava in Nigeria by investing the breeding resources in one breeding program for broad adaptation or splitting the resources into two sets of testing locations for narrow adaptation. Key lessons from these studies include: (1) Regardless the number of environments sampled to represent TPE, prediction accuracy of fresh root yield is lower than that of dry matter content and top yield. (2) The testing locations within the same geographic region were clustered and dissimilar from locations in other regions indicating some locations within each cluster may be dropped for field trial to maximize the budget cost. (2) A factor analytic statistical model with three factors was identified as the parsimonious model whose common latent factors captured 79.0% of total genetic variability. (3) Maximization of covariance between latent factor loadings and weather variables was an effective approach for identifying weather conditions driving genotypic response to testing environments. (4) The rate of genetic gain per unit time from genomic-enabled breeding programs were consistently higher than that of phenotypic-based conventional breeding program.

Thanks to advanced computing and modeling technologies, computer simulations are becoming more widely used for the reliability evaluation of complex systems. Yet, as simulation models represent physical systems more accurately and utilize a large number of random variables to reflect various uncertainties, high computational costs remain a major challenge in analyzing the system reliability. The objective of this dissertation research is to provide new solutions for saving computational time of simulation-based reliability evaluation that considers large uncertainties within the simulation. This dissertation develops (a) a variance reduction technique for stochastic simulation models, (b) an uncertainty quantification method for the variance reduction technique, and (c) an adaptive approach of the variance reduction technique. First, among several variance reduction techniques, importance sampling has been widely used to improve the efficiency of simulation-based reliability evaluation using deterministic simulation models. In contrast to deterministic simulation models whose simulation output is uniquely determined given a fixed input, stochastic simulation models produce random outputs. We extend the theory of importance sampling to efficiently estimate a system's reliability with stochastic simulation models. Second, to quantify the uncertainty of the reliability estimation with stochastic simulation models, we can repeat the simulation experiment multiple times. It, however, multiplies computational burden. To overcome this, we establish the central limit theorem for the reliability estimator with stochastic simulation models, and construct an asymptotically valid confidence interval using data from a single simulation experiment. Lastly, theoretically optimal importance sampling densities require approximations in practice. As a candidate density to approximate the optimal density, a mixture of parametric densities can be used in the cross-entropy method that aims to minimize the cross-entropy between the optimal density and the candidate density. We propose an information criterion to identify an appropriate number of mixture densities. This criterion enables us to adaptively find the importance sampling density as we gather data through an iterative procedure. Case studies, using computationally intensive aeroelastic wind turbine simulators developed by the U.S. Department of Energy (DOE)'s National Renewable Energy Laboratory (NREL), demonstrate the superiority of the proposed approaches over alternative methods in estimating the system reliability using stochastic simulation models.

Traditionally investigation into helicopter accidents has focused heavily on building complex, deterministic FE models and attempting to validate them with a small number of full size crash tests. One of the major drawbacks of this methodology is that it does not address the dissimilarity of loads generated in nominally identical crashes. To take into account inherent uncertainties in the helicopter crashes, the classic deterministic approach has been replaced in this work by simulation using stochastic algorithms. The chaotic nature, due to complexity in helicopter accidents, requires a much more robust simulation framework to capture a broad spectrum of potential crash scenarios. The thesis aims to investigate helicopter accidents resulting from engine failure by using stochastic simulation methods. An innovative, hierarchical block structure for a stochastic simulation is developed for investigating the variability in a full crash event reduced to two phases: flight emergency simulation and structure crash simulation. Non-parametric analysis is performed on the stochastic injury responses which attempt to predict the severity of the occupant’s injuries caused by helicopter accidents. The modelling framework establishes correlations between the critical parameters prior to helicopter accidents and possible occupant injury metrics. To achieve this aim, various stochastic algorithms are performed throughout the stochastic framework for the typical helicopter accidents. An investigation into helicopter accidents after engine failure is investigated by simulating auto-rotational flight within a range of sampled pre-event flight conditions to establish the correlation between initial flight parameters and the impact response. The structural crash simulation uses impact loads randomly selected from within the boundary of the flight simulation results to determine accelerations at the seat position. The potential injury is predicted by the stochastically generated acceleration peak-values the human body is subjected to and is evaluated by the resulting robust solution based on a computational geometry algorithm. A highly flexible, hierarchical, stochastic simulation framework has been established for investigating helicopter accidents. It has been demonstrated for the case of complete engine failure during flight leading to autorotation. The significance of this approach is the resulting combination of a complete crash event into a single framework which can be robustly analysed to study the limits of occupant harm. This work will lead to strategies for minimizing occupant harm and maximizing survivability for a wide range of helicopter accident scenarios by both structural modification and flight procedural changes. Some techniques supporting the stochastic analysis are successfully used offering the possibility of projecting the methodology into other engineering domains.

Stochastic effects in cellular systems are usually modeled and simulated with Gillespie's stochastic simulation algorithm (SSA), which follows the same theoretical derivation as the chemical master equation (CME), but the low efficiency of SSA limits its application to large chemical networks. To improve efficiency of stochastic simulations, Haseltine and Rawlings proposed a hybrid of ODE and SSA algorithm, which combines ordinary differential equations (ODEs) for traditional deterministic models and SSA for stochastic models. In this dissertation, accuracy analysis, efficient implementation strategies, and application of of Haseltine and Rawlings's hybrid method (HR) to a budding yeast cell cycle model are discussed. Accuracy of the hybrid method HR is studied based on a linear chain reaction system, motivated from the modeling practice used for the budding yeast cell cycle control mechanism. Mathematical analysis and numerical results both show that the hybrid method HR is accurate if either numbers of molecules of reactants in fast reactions are above certain thresholds, or rate constants of fast reactions are much larger than rate constants of slow reactions. Our analysis also shows that the hybrid method HR allows for a much greater region in system parameter space than those for the slow scale SSA (ssSSA) and the stochastic quasi steady state assumption (SQSSA) method. Implementation of the hybrid method HR requires a stiff ODE solver for numerical integration and an efficient event-handling strategy for slow reaction firings. In this dissertation, an event-handling strategy is developed based on inverse interpolation. Performances of five wildly used stiff ODE solvers are measured in three numerical experiments. Furthermore, inspired by the strategy of the hybrid method HR, a hybrid of ODE and SSA stochastic models for the budding yeast cell cycle is developed, based on a deterministic model in the literature. Simulation results of this hybrid model match very well with biological experimental data, and this model is the first to do so with these recently available experimental data. This study demonstrates that the hybrid method HR has great potential for stochastic modeling and simulation of large biochemical networks.

Fueled by a growing number of applications in science and engineering, the development of stochastic simulation metamodeling methodologies has gained momentum in recent years. A majority of the existing methods, such as stochastic kriging (SK), only focus on efficiently metamodeling the mean response surface implied by a stochastic simulation experiment. As the simulation outputs are stochastic with the simulation variance varying significantly across the design space, suitable methods for variance modeling are required. This thesis takes a dual metamodeling perspective and aims at exploiting the benefits of fitting the mean and variance functions simultaneously for achieving an improved predictive performance. We first explore the effects of replacing the sample variances with various smoothed variance estimates on the performance of SK and propose a dual metamodeling approach to obtain an efficient simulation budget allocation rule. Second, we articulate the links between SK and least-square support vector regression and propose to use a ``dense and shallow'' initial design to facilitate selection of important design points and efficient allocation of the computational budget. Third, we propose a variational Bayesian inference-based Gaussian process (VBGP) metamodeling approach to accommodate the situation where either one or multiple simulation replications are available at every design point. VBGP can fit the mean and variance response surfaces simultaneously, while taking into full account the uncertainty in the heteroscedastic variance. Lastly, we generalize VBGP for handling large-scale heteroscedastic datasets based on the idea of ``transductive combination of GP experts.''

With the fast development of computing power over the last few decades, simulation models become increasingly popular in many applications when running actual experiments are expensive or even impossible. In particular, this dissertation considers stochastic simulation models that generate random outputs with multiple simulation runs at the same input. In order to fully reflect high level uncertainties in reality, modern simulation models tend to embed a large number of random variables for generating stochastic outputs. Thus, stochastic simulation models have been employed in many applications including wind energy. One important use of the simulation models is to analyze extreme events for complex systems. However, heavy computational requirement for running stochastic simulation models brings great challenges in the system reliability analysis. A system failure is often defined as an event where the system response exceeds a certain threshold level. Mathematically the threshold level, when it is associated with a small failure probability, refers to the extreme quantile of the random response. This dissertation aims to provide computationally efficient methods to estimate the extreme quantile for random responses and quantify the estimation uncertainty via stochastic simulation. This dissertation consists of three main chapters, including (a) a variance reduction method for extreme quantile estimation using stochastic simulation models, (b) uncertainty quantification for the extreme quantile estimation with the variance reduction method, (c) an adaptive variance reduction method for the extreme quantile estimation. First, we propose using importance sampling combined with order statistics to estimate extreme quantiles via stochastic simulation models. Importance sampling has been known as one of the most powerful variance reduction techniques. The proposed method reduces the computational burden significantly while achieving much better estimation accuracy, compared with existing methods. We present our method with a wind turbine case study for estimating extreme load responses. Second, to quantify the uncertainty of the extreme quantile estimation with stochastic simulation models, we build confidence intervals for the extreme quantile. We consider multiple approaches, including theoretical approach, batching-based approaches, bootstrapping and Jackknife. We validate asymptotic properties for extreme quantile estimator and show that the quantile estimator is asymptotically normal following the central limit theorem. The immediate result is a theoretically valid confidence interval in an explicit form. Building on the theoretical validity of the quantile estimator, confidence intervals using three batching-based approaches, namely, batching, sectioning and sectioning-batching, are presented. We present numerical results to compare the confidence interval estimation performance of all studied methods. Lastly, we develop a new adaptive importance sampling method for estimating extreme quantiles using stochastic simulation models in a more computationally efficient way. In our first study, we employ importance sampling to estimate extreme quantile with stochastic simulation model and show its computational advantage over alternative methods. However, a good choice of the importance sampling density relies on information about the unknown extreme quantile. Faced with this challenge, we develop an adaptive method that refines the importance sampling density parameter toward the unknown target quantile along the iterations. The proposed adaptive scheme allows us to use the simulation outcomes obtained in previous iterations for steering the simulation process to focus on important input areas. We prove consistency properties of the proposed method and show that our approach can achieve variance reduction over crude Monte Carlo sampling. We demonstrate its estimation efficiency through both numerical examples and wind turbine case study.

Stochastic models are widely used in the simulation of biochemical systems at a cellular level. For well mixed models, the system state can be represented by the population of each species. The probabilities for the system to be in each state are governed by the Chemical Master Equation (CME), which is generally a huge ordinary differential equation (ODE) system. The cost of solving the CME directly is generally prohibitive, due to its huge size.The Stochastic Simulation Algorithm (SSA) provides a kinetic Monte Carlo approach to obtain the solution to the CME. It does this by simulating every reaction event in the system. A great many stochastic realizations must be performed, to obtain accurate probabilities for the states. The SSA can generate a highly accurate result, however the computation of many SSA realizations may be expensive if there are many reaction events. Tau-leaping is an approximate algorithm that can speed up the simulation for many systems. It advances the system with a selected stepsize. In each step, it directly samples the number of reaction events in each reaction channel, which yields a faster simulation than SSA. The error in tau-leaping is controlled by selecting the stepsize properly.We have developed a new, accelerated tau-leaping algorithm for discrete stochastic simulation that make use of the fact that exact (time-dependent) solutions are known for some of the most common reaction motifs (subgraphs of the network of chemical species and reactants). This idea can be extended to spatial stochastic simulation, by treating the diffusion network as a special motif for which there is an exact time dependent solution. We describe the well-mixed and spatial stochastic time dependent solution algorithms, along with numerical experiments illustrating their effectiveness.

A biological pathway represents a network of complex reactions at the molecular level of living cells. Pathways model how biological molecules interact to carry out a biological function and how they respond to external stimuli. The pathway models are derived through scientific experimentation and data analysis. Modeling biochemical reactions is a component in studying and analyzing biological pathways. The modeling and control of biological pathways is extremely important in understanding various biological phenomena. Biological pathways can be controlled in the laboratory and this process has applications in medicine and also in the invention of certain biologically based components for computer circuits or bio-circuits. However, direct experimental study of the pathways is expensive and also time consuming. Mathematical modeling and stochastic simulation techniques provide an affordable and easy to use experimental platform. Mathematical modeling and stochastic simulations, based on biochemical rate equations, provide us with rigorous tools to understand the intricacies involved in biological pathways. In this thesis we model the Phage Lambda system, which functions as a biological switch, and the Bioluminescence system, which provides a model of communication. We use the stochastic simulation techniques based on Gibson and Bruck’s Next Reaction Method. We compare our results with the results of simulations using Gillespie’s Algorithm and with the results from an agent-based model. We also provide easy-to-use templates for the simulations to support future research in this area.

Wind turbines in a wind plant do not always experience free-stream flow fields. The flow fields inside a wind plant or wind farm, waked by upwind turbines, exhibit different dynamic characteristics. The International Electrotechnical Commission (IEC) standard 61400-1 for the design of wind turbines only considers a deterministic wake model for the design of a wind plant. This study is focused on the stochastic modeling of waked wind fields for assessing turbine loads using a regression-based approach. The waked wind velocity field is generated using Large-Eddy Simulation (LES). Stochastic characteristics of the generated waked wind velocity field, including the mean and turbulence components, are analyzed. Proper orthogonal decomposition (POD) and spectral methods are proposed to develop reduced-order engineering model-based wind velocity fields as alternatives to the LES-generated waked fields. The reduced-order model-based simulation employs either a subset of the POD eigenmodes or Fourier-based spectral simulation with parameters derived from LES in illustrations with a wake-generating turbine. With the spectral model, wake-related spectral parameters are estimated using Multivariate Multiple Linear Regression (MMLR). To validate the simulated wind fields based on the reduced-order models, wind turbine tower and blade loads are generated using aeroelastic simulation for a utility-scale wind turbine model and compared with those based on LES. This study also discusses the construction of a stochastic expanded-wake model for wind turbines experiencing fully and partially waked situations. The study's overall objective is to offer efficient stochastic approaches that are computationally tractable, when assessing the performance and loads of turbines operating in wakes. Validation studies are carried out by comparion with loads computed directly from LES wake fields.

Water distribution systems are critical infrastructure systems enabling the social and economic welfare of a community. While normal failures are expected and repaired quickly, low-probability and high consequence disruptive events have potential to cause severe damage to the infrastructure and significantly reduce their performance or even stop their function altogether. Resilient infrastructure is a necessary component towards achieving resilient and sustainable communities. Resilience concepts allow improved decision making in relation with risk assessment and management in water utilities. However, in order to operationalize infrastructure resilience concepts, it is fundamental to develop practical resilience assessment methods such as the methodology and tool proposed in this research, named Effective Resilience Assessment Methodology for Utilities (ERASMUS). ERASMUS utilizes a stochastic simulation model to evaluate the probability of resilient response from a water distribution system in case of disruption. This methodology utilizes a parametric concept of resilience, in which a resilient infrastructure system is defined in terms of a set of performance parameters compared with their socially acceptable values under a variety of disruptive events. The methodology is applied to two actual water distribution networks in the East and West coasts of the US.

The advent of large scale data, particularly from the biological sciences, has accelerated interest in developing computational methods for analysis and prediction.Implementing such methods often requires software to either automate computational tasks or to carry out calculations that elude analytic techniques. This work focuses on the latter while paying respect to useful and elegant abstractions from mathematical theory.The diverse set of topics in this dissertation span applied probability, mathematical optimization, and epidemiological modelling. First, we investigate simulation techniques for stochastic processes. Second, we elaborate on the proximal distance technique of constrained optimization as a computational framework with examples in orthogonal projection, clustering, regression, and imaging. Third, we use deterministic equation modelling to evaluate school reopening strategies under pandemic conditions. Finally, we conclude with preliminary work on an application of the proximal distance method to hierarchical linear models.

In this thesis, I examine several situations in which one can improve the efficiency of a stochastic simulation algorithm by adaptively exploiting special structure of the problem at hand. The thesis is comprised of three independent papers. In the first paper, I propose a new variance reduction technique in the setting of comparing the performance of two stochastic systems. The technique is a natural generalization of common random number sampling, a well-known sampling strategy that may reduce variance in certain situations. Common random number sampling entails sampling the underlying uniform random variates according to a particular copula; my proposed method considers more general copulae. I identify properties such a copula must have in order to induce a valid sampling strategy, give examples of situations in which copulae exist that outperform common random numbers, and give an algorithm for computing an effective Gaussian copula. In the second paper, I discuss an automated procedure for computing a control variate for the pricing of American options. The control variate is equal to the value of a particular martingale at the time the option is exercised. The martingale is constructed using an approximation of the value function in a backward dynamic program. We use adaptive linear regression splines to create the functional approximation. These splines have properties of which make them computationally convenient for constructing a martingale-based control variate of this type. In the third paper, I describe and analyze a novel root-finding procedure for monotone, convex univariate functions in the presence of noise. The main result of the analysis is a probabilistic performance guarantee for the algorithm. Specifically, given an indifference parameter delta and a confidence level alpha, the algorithm returns a point whose absolute function value is less than delta with probability at least one minus alpha. The total amount of work required by the algorithm may be bounded in terms of the length of the compact interval on which the function is defined and the Lipschitz constant of the function.

Distinct localisation of macromolecular structures relative to cell shape is a common feature across the domains of life. One mechanism for achieving spatiotemporal intracellular organisation is the Turing reaction-diffusion system (e.g. Min system in the bacterium Escherichia coli controlling in cell division). In this thesis, I explore potential Turing systems in archaea and eukaryotes as well as the effects of subdiffusion. Recently, a MinD homologue, MinD4, in the archaeon Haloferax volcanii was found to form a dynamic spatiotemporal pattern that is distinct from E. coli in its localisation and function. I investigate all four archaeal Min paralogue systems in H. volcanii by identifying four putative MinD activator proteins based on their genomic location and show that they alter motility but do not control MinD4 patterning. Additionally, one of these proteins shows remarkably fast dynamic motion with speeds comparable to eukaryotic molecular motors, while its function appears to be to control motility via interaction with the archaellum. In metazoa, neurons are highly specialised cells whose functions rely on the proper segregation of proteins to the axonal and somatodendritic compartments. These compartments are bounded by a structure called the axon initial segment (AIS) which is precisely positioned in the proximal axonal region during early neuronal development. How neurons control these self-organised localisations is poorly understood. Using a top-down analysis of developing neurons in vitro, I show that the AIS lies at the nodal plane of the first non-homogeneous spatial harmonic of the neuron shape while a key axonal protein, Tau, is distributed with a concentration that matches the same harmonic. These results are consistent with an underlying Turing patterning system which remains to be identified. The complex intracellular environment often gives rise to the subdiffusive dynamics of molecules that may affect patterning. To simulate the subdiffusive transport of biopolymers, I develop a stochastic simulation algorithm based on the continuous time random walk framework, which is then applied to a model of a dimeric molecular motor. This provides insight into the effects of subdiffusion on motor dynamics, where subdiffusion reduces motor speed while increasing the stall force. Overall, this thesis makes progress towards understanding intracellular patterning systems in different organisms, across the domains of life.

Combustion-generated nanoparticles (diameter less than or equal to 100 nm) are prevalent in modern society. Carbonaceous nanoparticles (CNPs) are especially important, finding applications as pigments in ink, in composite materials, or as catalysts. Despite such useful applications, CNPs have attracted the most attention as hazardous emissions from combustion sources like automotive engines, especially as aggregate particles known as soot, as their primary constituents are carcinogenic polycyclic aromatic hydrocarbons (PAHs). Critically, the formation of CNPs in combustion environments remains an area of considerable uncertainty, particularly the growth from gas phase precursors through the nucleation of solid phase particles. Towards elucidating PAH formation via chemical reactions, a significant element of the growth process, a novel simulation software was developed, named the Stochastic Nanoparticle Simulator (SNAPS), along with a corresponding PAH chemical reaction mechanism. This software was then applied to investigate the chemical and physical properties of PAHs formed in combustion. SNAPS simulations were corroborated through comparisons with existing experimental measurements in flames utilizing a variety of fuels. Furthermore, simulations provided molecular-level detail that revealed key aspects of a complex chemical growth process. Importantly, these simulations provided insights into chemical reaction and composition details beyond those typically inaccessible by experiment. For all studied flames, analysis of the major chemical reactions and PAH species involved in simulations contrasted with conventional theories. Simulations showed that PAH growth is characterized by complex sequences of highly reversible reactions, leading to a variety of species that far exceeds the relatively narrow range that has traditionally been the focus of investigations. SNAPS therefore represents an important tool for synthesizing experimental observations and theoretical predictions, towards building a comprehensive and accurate description of CNP growth. Most importantly, the current work is only one application of the software. The extensibility of SNAPS will enable modeling of many different systems involving heterogeneous nucleation and growth of nanoparticles, which illustrates its potential for wide impact. Altogether, this work represents a strong framework that will support and drive future investigations of nanoparticle growth and contribute to the development of novel combustion technologies that will positively impact society.

With the embrace of the seismic resilience concept as a measure of the ability of constructed facilities and communities to contain the effects of an earthquake and achieve a timely recovery, the critical role of tall buildings in supporting community functionality, has been brought to the forefront. This study presents a series of frameworks for performing post-earthquake assessment and optimal decision-making for tall buildings. A machine learning framework to assess structural safety is first proposed and applied to a low-rise frame building. A similar methodology is then adapted for tall buildings, while incorporating robust techniques to deal with the high-dimension feature space that arises because of the large number of structural components. Seismic risk assessment is then carried out for the tall building by comparing the time-dependent probability of exceeding various response demand limits over a pre-defined period considering both mainshock-only and mainshock-aftershock hazard. The risk-based consistency of the limit state acceptance criteria for engineering demand parameters is also examined. Finally, a methodology to support optimal decision-making following the mainshock is developed with the goal of minimizing expected financial losses and, at the same time, ensuring life safety. The proposed prediction model, risk assessment methodology and optimal decision-making strategy can provide critical insights into the seismic performance of mainshock-damaged tall buildings and inform the post-earthquake actions of occupants, structural engineers, insurance companies and policymakers.

Computer simulation models have the potential to aid decision-making in many industries. They are particularly beneficial when applied to situations that would be too costly or impractical to experiment with in reality. In the railway domain, such applications may include making infrastructure changes or updating a timetable. A simulation is a representation of a system or object, not an exact copy. However, to be a meaningful planning aid, the output of a simulation needs to be sufficiently realistic. A review of existing railway simulation software identifies two features where established modelling techniques limit the realism of the output: train movements and signalling decisions. This thesis develops a stochastic simulation that models train movements and signalling decisions using supervised machine learning. Train movements are modelled using quantile regression. The models are applied to replicate the distribution of travel durations without requiring any underlying assumptions about the properties of the distribution. Probabilistic classification is employed to predict signallers' actions, achieving accuracies of over 89%. Experiments were conducted by running the stochastic simulation for a week's worth of activity on a section of the British network for 600 iterations. The outputs were compared to the true activity of the selected week. The true total travel duration of all the trains fell within the simulated minimum and maximum values achieved across all iterations. Moreover, the median total travel duration across all iterations settled to within 1% of the true value. The results demonstrate that machine learning-assisted simulation modelling can be applied to make realistic performance assessments in the railway domain. There is the possibility to use such a model to compare alternative train regulation policies or to investigate the performance of a new timetable.

Simulation is widely used to identify the best of a finite set of proposed systems, where 'best' is defined in terms of the maximum (or minimum) mean value of simulation output. There is therefore considerable interest in selection procedures that allocate computing resources to identify the best system. Commonly-used 'indifference-zone' procedures that allocate computing resources to infer the best system (i) are designed with a statistically conservative least favorable configuration assumption, (ii) consider only the probability correct selection (PCS), and (iii) assume that the cost of simulating each system is the same. Recent Bayesian work improves the efficiency of selecting the best and considers opportunity cost rather than PCS, but assumes that the simulation output variance is known, an assumption that is typically violated in simulation. This dissertation addresses both the efficiency and the generality of the selection problem and presents new two-stage and sequential procedures for identifying the best system. We consider the reduction of either the expected opportunity cost loss or the probability of incorrect selection, different replication costs for each system, and base the analysis on normally distributed output with unknown mean and variance that may differ for each system. The approach in this dissertation is decision-theoretic: we derive Bonferroni-like approximation for the expected risk (loss plus cost of replications) for selecting the system with the maximum expected mean, then determine an asymptotically optimal allocation. In addition, this dissertation presents new two-stage procedures when common random numbers are utilized. Furthermore, we compare our procedures with several other procedures for many selection problems. Numerical experiments indicate that our new procedures outperform the existing procedures with respect to several criteria.

In this thesis we study stochastic modeling and simulation methods for biochemical systems. The thesis is focused on systems with multi-state and multi-scale features and divided into two parts. In the first part, we propose new algorithms that improve existing multi-state simulation methods. We first compare the well known Gillespie\\\'s stochastic simulation algorithm (SSA) with the StochSim, an agent-based simulation method. Based on the analysis, we propose a hybrid method that possesses the advantages of both methods. Then we propose two new methods that extend the Network-Free Algorithm (NFA) for rule-based models. Numerical results are provided to show the performance improvement by our new methods. In the second part, we investigate two simulation schemes for the multi-scale feature: Haseltine and Rawlings\\\' hybrid method and the quasi-steady-state stochastic simulation method. We first propose an efficient partitioning strategy for the hybrid method and an efficient way of building stochastic cell cycle models with this new partitioning strategy. Then, to understand conditions where the two simulation methods can be applied, we develop a way to estimate the relaxation time of the fast sub-network, and compare it with the firing interval of the slow sub-network. Our analysis are verified by numerical experiments on different realistic biochemical models.

In order for scientists to learn more about molecular biology, it is imperative that they have the ability to construct and evaluate models. Model statistics consistent with the chemical master equation can be obtained using Gillespie's stochastic simulation algorithm (SSA). Due to the stochastic nature of the Monte Carlo simulations, large numbers of simulations must be run in order to get accurate statistics for the species populations and reactions. However, the algorithm tends to be computationally heavy and leads to long simulation runtimes for large systems. In this research, the performance of Gillespie's stochastic simulation algorithm is analyzed and optimized using a number of techniques and architectures. These techniques include parallelizing simulations using streaming SIMD extensions (SSE), message passing interface with multicore systems and computer cluters, and CUDA with NVIDIA graphics processing units. This research is an attempt to make using the SSA a better option for modeling biological and chemical systems. Through this work, it will be shown that accelerating the algorithm in both of the serial and SSE implementations proved to be beneficial, while the CUDA implementation had lower than expected results.

The ability to accurately and efficiently simulate computer models of biochemical systems is of growing importance to the molecular biology and pharmaceutical research communities. Exact stochastic simulation is a popular approach for simulating such systems because it properly represents genetic noise and it accurately represents systems with small populations of chemical species. Unfortunately, the computational demands of exact stochastic simulation often limit its applicability. To enable next-generation whole-cell and multi-cell stochastic modeling, advanced tools and techniques must be developed to increase simulation efficiency. This work assesses the applicability of a variety of hardware and software acceleration approaches for exact stochastic simulation including serial algorithm improvements, parallel computing, reconfigurable computing, and cluster computing. Through this analysis, improved simulation techniques for biological systems are explored and evaluated.

Currently, the applicability of computer modeling to whole-cell and multi-cell biochemical models is limited by the accuracy and efficiency of the simulation tools used to model gene regulatory networks. It is widely accepted that exact stochastic simulation algorithms, originally developed by Gillespie and improved by Gibson and Bruck, accurately depict the time-evolution of a spatially homogeneous biochemical model, but these algorithms are often abandoned by modelers because their execution time can be on the order of days to months. Other modeling techniques exist that simulate models much more quickly, such as approximate stochastic simulation and differential equations modeling, but these techniques can be inaccurate for biochemical models with small populations of chemical species. This work analyzes the performance of exact stochastic simulation algorithms by developing software implementations of exact stochastic simulation algorithms and measuring their performance for a wide variety of models. Through this study, several techniques are developed and tested that improve the performance of certain algorithms for specific models. A new algorithm called the Adaptive Method is then presented which attempts to select the optimal simulation algorithm for the particular model based on periodic measurements of simulator performance during execution. Other algorithmic changes are proposed to aid in the development of hardware accelerators for exact stochastic simulation. The work serves as another step in the process of making exact stochastic simulation a practical modeling solution for molecular biologists.

This thesis is concerned with two topics rooted in the analysis of time-series. In the first, we improve the estimation of rare-event probabilities by stochastic simulation. The proposed method, quasi-monotone splitting uses generalized splitting to estimate integrals with respect to intractable target distributions by instead estimating them with respect to the terminal state of a certain Markov chain, allowing us to use time series methods to study them. We employ two innovations to this end: Problem constraints are exploited to derive a simple, efficient estimation strategy automatically for a tractable problem class, and The performance of the estimator is improved through the use of survival analysis and extreme value theory, in which near-optimal parameters can be derived with minimal intervention. We demonstrate applications of this algorithm to a variety of wireless reliability problems. The performance of the resulting algorithms are competitive with specialized Monte Carlo estimators for specific problems, and provide novel estimators for problems previously lacking known, efficient estimators. Some of the methods in this section were developed for a paper with several co-authors which has now been published. The second topic is audio signal analysis. An important task here is style transfer, which attempts to synthesize a new signal from two others, a source and a target. The new synthetic signal should possess the microscopic “stylistic” statistics of the source, and the macroscopic “semantic” statistics of the target. We solve this problem using mosaicing style transfer, which decomposes the source signal into microscopic sub-samples, superimposing them to produce the new synthetic signal whose macroscopic statistics approximate the target. In such models, one chooses parameters by minimising some loss function which ideally approximates acoustic similarity as perceived by a human listener. We leverage the insight that human pitch perception is related to the local autocorrelogram of a signal to construct a novel loss function based on a difference between autocorrelograms. This, in combination with a signal approximation method based on orthogonal matching pursuits, results in a novel synthesis algorithm called autocorrelogram mosaicing. This algorithm is the only one we know of with public code that can mosaic with arbitrary pitch transposition of source audio, enabling style transfer between differently tuned instruments while maintaining musical consonance. The strength and weakness of this algorithm for various source materials is demonstrated.

Uncertainty in revenue for grain and oilseed operations located across Nebraska exists due to commodity price volatility and yield variability. Several risk management tools enable producers to deal with financial losses from revenue declines including crop insurance, marketing strategies, and government farm programs. Producers may need to combine multiple tools for an effective risk management strategy, but research lacks on integrating these tools currently available to producers across the state. Actions amongst individuals actively engaged in the industry show their plans to deal with revenue declines may lead to less than optimal strategies. Stochastic simulation utilizing eight representative farms across Nebraska allows for the analysis of risk management strategies. Attributes of these farms reflect the average size, productivity, and variability, expressed by operations across the eight National Agricultural Statistical Districts of the state. Also, the simulation of national, state, district, and county yields or prices are generated for the necessary parameters in the evaluation of various programs or products. Conclusion drawn from these simulations indicate the optimal risk management strategy for a region of Nebraska, given a set of feasible prices and base 2011 yield and price parameters. Current program participation and product utilization rates indicate strategies employed by the majority of producers in the state do not sway far from these simulated outcomes. Participating in higher levels of revenue protection crop insurance, direct and counter-cyclical government programs, and using a short futures hedge when marketing grain provided the greatest level of revenue protection subject to a producer’s risk preference. Findings may change substantially dependent upon different price, yield, or guarantee levels. Advisor: Bradley D. Lubben

In this thesis, I propose a general stochastic simulation algorithm for particle based lattice model using the concepts of Gillespie's stochastic simulation algorithm, which was originally designed for well-stirred systems. I describe the details about this method and analyze its complexity compared with the StochSim algorithm, another simulation algorithm originally proposed to simulate stochastic lattice model. I compare the performance of both algorithms with application to two different examples: the May-Leonard model and Ziff-Gulari-Barshad model. Comparison between the simulation results from both algorithms has validate our claim that our new proposed algorithm is comparable to the StochSim in simulation accuracy. I also compare the efficiency of both algorithms using the CPU cost of each code and conclude that the new algorithm is as efficient as the StochSim in most test cases, while performing even better for certain specific cases.

Alzheimer disease (AD) attacks the brain and is the most common cause of dementia worldwide and it is classified to be the main cause of cognitive impairment in elderly people. Beta-amyloids (Aβ) and tau are aggregated to produce respectively plaques and tangles that are classified to be prime suspects for cell deaths in Alzheimer’s brain. Plaques target nerve cells to prevent their ability to contact each other in the correct way while tangles attack the transport system made of protein to be destroyed. However, the mechanisms that link Aβ and tau are still not fully understood. A recent proposed model (known immunization in AD model) not only examines pathways (DNA damage, p53 regulation, GSK3β activity, Aβ production and aggregation and tau dynamic and aggregation) involved in this relationship, but also how passive and active immunization against Aβ can indirectly reduce the level of tau pathologies. In this research, we stochastically model immunization in AD for better understanding of the relationship between Aβ and tau since noise in biology is a rule rather than expectation. This modelling is done using a proposed approach that combines Mapping Reduction Method (MRM) and Gillespie Stochastic Simulation Algorithm (GSSA). This combination increases the performance of GSSA by accelerating a single run of GSSA and explicitly includes concurrency feature. To validate MRM/GSSA, we compare it with GSSA itself and the modified Tau leap method classified to be one of the fastest version of GSSA. MRM/GSSA is not only faster than GSSA and comparable with the modified Tau-leap method, but also has more ability to represent stochastic feature and more reliable to be used for modelling any biochemical system than the modified tau leap method. Local sensitivity analysis (LSA) is stochastically and deterministically performed using MRM/GSSA and ordinary differential equations (ODEs) to investigate the behaviour of the immunization in AD model when parameters are perturbed, one at a time. A finite difference approximation method (FDM) is used to deterministically to perform LSA while FDM in conjunction with the common random number (CRN) is used to stochastically perform LSA. LSA is performed to (1) determine the maximum and minimum ranges of each parameter, (2) classify the most important species that contribute to the overall behaviour of the system and (3) identify pathways that dramatically changed in response to parameter perturbation. LSA using ODEs and MRM/GSSA indicates that p53 regulation, DNA damage pathway and GSK3β activity are not contributing to the overall behaviour of the system. Aβ production and aggregation, Tau dynamic and aggregation and immunisation pathways (passive and active) are the most important pathways that dramatically contribute to the overall behaviour of the system. LSA also demonstrates that parameters specific to p53, Mdm2 and Aβ are the most important parameters that contribute most to the variation in the system. Latin Hypercube Sampling and Partial Rank Correlation Coefficient (LHS/PRCC) are powerful tool employed with a minimum number of computer simulations in uncertainty analysis to monotonically relate the model outputs to the input parameters. We use LHS/PRCC to not only deterministically (ODEs), but also stochastically (MRM/GSSA) investigate the epistemic uncertainties of parameters of immunization in AD model. We explore at three different time points the effects of parameters on the key outputs of immunization in AD model (selected from the included pathways). This is to discover the most important parameters that uncertainties contribute to predication imprecision and rank these parameters by their importance in contributing to this imprecision. PRCC analysis using ODEs and MRM/GG demonstrates that binding relationship between p53 and Mdm2 and Mdm2 synthesis are the most important reactions that contribute to the behaviour of nearly all selected species in response to combination of LHS matrix. PRCC analysis using MRM/GSSA indicates some other parameters such as kgenROSGila and kbinE2UB also have strong correlation with the key outputs.

Mathematical and statistical modeling of biological systems is a desired goal for many years. Many biochemical models are often evaluated using a deterministic approach, which uses differential equations to describe the chemical interactions. However, such an approach is inaccurate for small species populations as it neglects the discrete representation of population values, presents the possibility of negative populations, and does not represent the stochastic nature of biochemical systems. The Stochastic Simulation Algorithm (SSA) developed by Gillespie is able to properly account for these inherent noise fluctuations. Due to the stochastic nature of the Monte Carlo simulations, large numbers of simulations must be run in order to get accurate statistics for the species populations and reactions. However, the algorithm tends to be computationally heavy and leads to long simulation runtimes for large systems. Therefore, this thesis explores implementing the SSA on a Field Programmable Gate Array (FPGA) to improve performance. Employing the Field programmable Gate Arrays exploits the parallelism present in the SSA, providing speedup over the software implementations that execute sequentially. In contrast to prior work that requires re-construction and re-synthesis of the design to simulate a new biochemical system, this work explores the use of reconfigurable hardware in implementing a generic biochemical simulator.

Gillespie's stochastic simulation algorithm (SSA) has been a conventional method for stochastic modeling and simulation of biochemical systems. However, its population-based scheme faces the challenge from multi-state situations in many biochemical models. To tackle this problem, Morton-Firth and Bray's stochastic simulator (StochSim) was proposed with a particle-based scheme. The thesis first provides a detailed comparison between these two methods, and then proposes improvements on StochSim and a hybrid method to combine the advantages of the two methods. Analysis and numerical experiment results demonstrate that the hybrid method exhibits extraordinary performance for systems with both the multi-state feature and a high total population. In order to deal with the combinatorial complexity caused by the multi-state situation, the rules-based modeling was proposed by Hlavacek's group and the particle-based Network-Free Algorithm (NFA) has been used for its simulation. In this thesis, we improve the NFA so that it has both the population-based and particle-based features. We also propose a population-based method for simulation of the rule-based models. The bacterial chemotaxis model has served as a good biological example involving multi-state species. We implemented different simulation methods on this model. Then we constructed a graphical interface and compared the behaviors of the bacterium under different mechanisms, including simplified mathematical models and chemically reacting networks which are simulated stochastically.

MtDNA mutations in mammalian cells are implicated in cellular ageing and encephalomyopathies, although mechanisms involved are not completely understood. The mitochondrial genetic bottleneck has puzzled biologists for a long time. Approximate models of genetic bottleneck proposed in the literature do not accurately model underlying biology. Recent studies indicate mitochondrial morphology changes during cellular aging in culture. In particular, the rates of mitochondrial fission and fusion are shown to be in tight balance, though this rate decreases with age. Some proteins involved in mitochondrial morphology maintenance are implicated in apoptosis. Hence, mitochondrial genetic and morphologic dynamics are critical to the life and death of cells. By working closely with experimental collaborators and by utilizing data derived from literature, we have developed stochastic simulation models of mitochondrial genetic and morphologic dynamics. Hypotheses from the mitochondrial genetic dynamics model include: (1) the decay of mtDNA heteroplasmy in blood is exponential and not linear as reported in literature. (2) Blood heteroplasmy measurements are a good proxy for the blood stem cell heteroplasmy. (3) By analyzing our simulation results in tandem with published longitudinal clinical data, we propose for the first time, a way to correct for the patient's age in the analysis of heteroplasmy data. (4) We develop a direct model of the genetic bottleneck process during mouse embryogenesis. (5) Partitioning of mtDNA into daughter cells during blastocyst formation and relaxed replication of mtDNA during the exponential growth phase of primordial germ cells leads to the variation in heteroplasmy inherited by offspring from the same mother. (6) We develop a “simulation control” for experimental studies on mtDNA heteroplasmy variation in cell cultures. Hypothesis from the mitochondrial morphologic dynamics model: (7) A cell adjusts the mitochondrial fusion rate to compensate for the fluctuations in the fission rate, but not vice versa. A deterministic model for this control is proposed. Contributions: extensible simulation models of mitochondrial genetic and morphologic dynamics to aide in the powerful analysis of published and new experimental data. Our results have direct relevance to cell biology and clinical diagnosis. The work also illustrates scientific success by tight integration of theory with practice.