Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic integrators, and often, these techniques are developed for well-understood Hamiltonian systems such as Hill’s lunar equation. In this presentation, we explore how well symplectic techniques developed for well-understood systems (specifically, Hill’s Lunar equation) address discretization errors in MD systems which fail for one or more reasons.

For this project, we use a modified version of a previously developed mathematical model, which describes the relationships among matrix metalloproteinases (MMPs), their tissue inhibitors (TIMPs), and extracellular matrix (ECM). Our ultimate goal is to quantify and understand differences in parameter estimates between patients in order to predict future responses and individualize treatment for each patient. By analyzing parameter confidence intervals and confidence and prediction intervals for the state variables, we develop a parameter space reduction algorithm that results in better future response predictions for each individual patient. Moreover, use of another subset selection method, namely Structured Covariance Analysis, that considers identifiability of parameters, has been included in this work. Furthermore, to estimate parameters more efficiently and accurately, the standard error (SE- )optimal design method is employed, which calculates optimal observation times for clinical data to be collected. Finally, by combining different parameter subset selection methods and an optimal design problem, different cases for both finding optimal time points and intervals have been investigated.

Dropped object are defined as any object that fall under its own weight from a previously static position or fell due to an applied force from equipment or a moving object. It is among the top ten causes of injuries and fatality in oil and gas industry. To solve this problem, several in-house tools and guidelines is developed over time to assess the risk of dropped objects on the sub-sea structures. This thesis focuses on compiling and comparing those methods in hope to improve the recommended practices available in the market. A simple modification is done on the in-house tools to better predict the landing point distribution of the dropped cylindrical objects on the seabed by imposing the random three-dimensional rotation around the water depth axis. This tool is then used to compare the result of annual hit frequency using the recommended practice and further compared with the available experimental data.

<div>Given a parametrized family of Iterated Function System (IFS) we give sufficient conditions for a parameter on the boundary of the connectedness locus, M, to be accessible from the complement of M.</div><div>Moreover, we provide a few examples of such parameters and describe how they are connected to Misiurewicz parameter in the Mandelbrot set, i.e. the connectedness locus of the quadratic family z^2+c.<br></div>

No description available.

Model reduction is a powerful and ubiquitous tool used to reduce the complexity of a dynamical system while preserving the input-output behavior. It has been applied throughout many different disciplines, including controls, fluid and structural dynamics. Model reduction via proper orthogonal decomposition (POD) is utilized for of control of partial differential equations. In this thesis, the analytical expressions of POD modes are derived for the heat equation. The autocorrelation function of the latter is viewed as the kernel of a self adjoint compact operator, and the POD modes and corresponding eigenvalues are computed by solving homogeneous integral equations of the second kind. The computed POD modes are compared to the modes obtained from snapshots for both the one-dimensional and two-dimensional heat equation. Boundary feedback control is obtained through reduced-order POD models of the heat equation and the effectiveness of reduced-order control is compared to the full-order control. Moreover, the explicit computation of the POD modes and eigenvalues are shown to allow the computation of different n-widths approximations for the heat equation, including the linear, Kolmogorov, Gelfand, and Bernstein n-widths.

No description available.

Species of Argulus are macro-, ecto-parasites known to infect a wide variety of fish, but in the UK mainly cause problems in rainbow (Oncorhynchus mykiss) and brown trout (Salmo trutta). Argulus foliaceus is estimated to have caused problems in over 25% of stillwater trout fisheries in the UK. While A. foliaceus does not usually cause high levels of mortality, the parasite affects fish welfare, and also makes fish harder to catch due to morbidity and reduced appetite. This can cause severe economic problems for the fishery, resulting in reduced angler attendance due to poor capture rates and the reduced aesthetic appearance of fish; in the worst-case scenario this can result in the closure of the fishery. Current methods of control include chemical treatment with chemotherapeutant emamectin benzoate (Slice), physical intervention with egg-laying boards which are removed periodically and cleaned in order to reduce the number of parasites hatching into the environment, and the complete draining and liming of the lake to remove all free-living and egg stages of the parasite. While these treatments have all been shown to reduce parasite numbers, none are known to have resulted in permament eradication of the parasite. There is evidence to suggest that A. foliaceus will eventually develop resistance to Slice - the only currently available chemical treatment against the infection - and egg-laying boards and the draining and liming of the lake are both time- and labour-intensive. Previous studies have shown that slow fish turnover is a risk factor with respect to A. foliaceus infections, and with a wide variety of stocking practices occurring in the UK one of the first aims of this project was to determine their impact on the host-parasite dynamics. Mathematical models provide a cost-effective way of examining the impact of such practices, and after a literature review (chapter one), in chapter two a three-compartment mathematical model was adapted for use in the A. foliaceus-trout system. Four generalised stocking methods were then incorporated and analysed, and a minimum threshold host density was found to be necessary to sustain the parasite. Including a function which reduced the capture rate as the parasite burden increased allowed the parasite to survive at a lower host density, as susceptible fish were removed from the water at a slower rate, and attached parasites also remained in the water for longer. This resulted in hysteresis in the model, as the invasion threshold for the parasite remained the same, but once established the parasite became harder to eradicate, requiring significant reductions in the host density. In chapter three the model was further developed in order to improve its biological real- ism. Several features were added and these included: natural host mortalities, a separate compartment for the parasite egg population, and parasite survival after the natural or parasite-induced mortality of its host. In chapter four seasonality was added by incorporating temperature-dependent egg-laying rates and an over-wintering period during which the parasite was unable to reproduce. The model was then fit to the available data, and estimates for the rate of parasite-induced host mortalities and the parasite’s rate of attachment to a host were found. In chapter five we returned to stocking methods, this time looking at the frequency and timing of stocking events and the impact of imposing a rod limit (whereby anglers are only permitted to capture four fish per visit); it was concluded that while current guidelines suggest that very frequent trickle stocking is recommended when dealing with Argulus spp. infections, monthly stocking does not appear to worsen the infection, and if the fish capture rate is high then less-frequent stocking may also be permissable - particularly if stocking occurs towards the end of the year when the parasite is no longer active. This practice may, however, be detrimental to the fishery due to low fish densities in the summer months. In chapter six treatment with Slice was included in the model, and it was demonstrated that with constant treatment, and in the absence of reservoir hosts and a withdrawal period from the drug prior to stocking treated fish into the fishery, the parasite was eradicated. Under current veterinary cascade guidelines, however, trout are required to undergo a withdrawal period of 500 degree days prior to being made available for human consumption. When this was included in the model the drug still decreased parasite abundance, but did not eradicate it - this is in agreement with results reported by communications with fishery managers currently treating fish with Slice. A reduction in the withdrawal period of 25% was shown to further decrease parasite abundance, but still did not result in parasite extinction. As constant treatment with Slice is not advisable due to the potential for resistance build-up, we then sought to find time at which to apply a single treatment of Slice, and found that this was in August when the temperature was highest and the parasite was reproducing and attaching to hosts quickly. Egg-laying boards were also incorporated into the model and similarly to findings by Fenton et al. [11] the success of this treatment was mostly dependent on the proportion of eggs being laid on the boards (as opposed to natural substrates). In contrast with the A. coregoni system, however, the boards would have to be cleaned and replaced more frequently that once per year, as several cohorts of A. foliaceus emerge during a single year.

To understand how the components of a complex system like the biological cell interact and regulate each other, we need to collect data for how the components respond to system perturbations. Such data can then be used to solve the inverse problem of inferring a network that describes how the pieces influence each other. The work in this thesis deals with modelling the cell regulatory system, often represented as a network, with tools and concepts derived from systems biology. The first investigation focuses on network sparsity and algorithmic biases introduced by penalised network inference procedures. Many contemporary network inference methods rely on a sparsity parameter such as the L1 penalty term used in the LASSO. However, a poor choice of the sparsity parameter can give highly incorrect network estimates. In order to avoid such poor choices, we devised a method to optimise the sparsity parameter, which maximises the accuracy of the inferred network. We showed that it is effective on in silico data sets with a reasonable level of informativeness and demonstrated that accurate prediction of network sparsity is key to elucidate the correct network parameters. The second investigation focuses on how knowledge from association networks can be transferred to regulatory network inference procedures. It is common that the quality of expression data is inadequate for reliable gene regulatory network inference. Therefore, we constructed an algorithm to incorporate prior knowledge and demonstrated that it increases the accuracy of network inference when the quality of the data is low. The third investigation aimed to understand the influence of system and data properties on network inference accuracy. L1 regularisation methods commonly produce poor network estimates when the data used for inference is ill-conditioned, even when the signal to noise ratio is so high that all links in the network can be proven to exist for the given significance. In this study we elucidated some general principles for under what conditions we expect strongly degraded accuracy. Moreover, it allowed us to estimate expected accuracy from conditions of simulated data, which was used to predict the performance of inference algorithms on biological data. Finally, we built a software package GeneSPIDER for solving problems encountered during previous investigations. The software package supports highly controllable network and data generation as well as data analysis and exploration in the context of network inference. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Manuscript.</p><p> </p>

Type 2 diabetes is a global disease which affects an increasing number of peopleevery year. At the heart of the disease lies insulin resistance in the target tissues,primarily fat and muscle. The insulin resistance is caused by the failure of a complexsignalling network, and several mechanistic hypotheses for this failure havebeen proposed. Herein, we evaluate a hypothesis that revolves around the proteinmammalian target of rapamycin (mTOR) and its feedback signals to insulin receptorsubstrate-1 (IRS1). In particular, we have re-examined this hypothesis andrelevant biological data using a mathematical modelling approach. During the course of modelling we gained several important insights. For instance,the model was unable to reproduce the relation between the EC50-valuesin the dose-response curves for IRS1 and its serine residue 312 (Ser-312). Thisimplies that the presented hypothesis, where the phosphorylation of Ser-312 liesdownstream of the tyrosine phosphorylation of IRS1, is inconsistent with the provideddata, and that the hypothesis or the data might be incorrect. Similarly, wealso realized that in order to fully account for the information in the dose-responsedata, time curves needed to be incorporated into the model. A preliminary model is presented, which explains most of the data-sets, butstill is unable to describe all the details in the data. The originally proposed hypothesisas an explanation to the given data has been revised, and our analysisserves to exemplify that an evaluation of a mechanistic hypothesis by mere biochemicalreasoning often misses out on important details, and/or leads to incorrectconclusions. A model-based approach, on the other hand, can efficiently pin-pointsuch weaknesses, and if combined with a comprehensive understanding of biologicalvariation and generation of experimental data, mathematical modelling canprove to be a method of great potential in the search for mechanistic explanationsto the cause of insulin resistance in type 2 diabetics.