Biostatistics News

Estimation of Odds Rati

Optimized auxiliary oscillators for the simulation of general open quantum systems

A method for the systematic construction of few-body damped harmonic oscillator networks accurately reproducing the effect of general bosonic environments in open quantum systems is presented. Under the sole assumptions of a Gaussian environment and regardless of the system coupled to it, an algorithm to determine the parameters of an equivalent set of interacting damped oscillators obeying a Markovian quantum master equation is introduced. By choosing a suitable coupling to the system and minimizing an appropriate distance between the two-time correlation function of this effective bath and that of the target environment, the error induced in the reduced dynamics of the system is brought under rigorous control. The interactions among the effective modes provide remarkable flexibility in replicating non-Markovian effects on the system even with a small number of oscillators, and the resulting Lindblad equation may therefore be integrated at a very reasonable computational cost using standard methods for Markovian problems, even in strongly non-perturbative coupling regimes and at arbitrary temperatures including zero. We apply the method to an exactly solvable problem in order to demonstrate its accuracy, and present a study based on current research in the context of coherent transport in biological aggregates as a more realistic example of its use; performance and versatility are highlighted, and theoretical and numerical advantages over existing methods, as well as possible future improvements, are discussed.Comment: 23 + 9 pages, 11 + 2 figures. No changes from previous version except publication info and updated author affiliation

Rationalising the inhibition of M. tuberculosis MshB by a series of inhibitors constructed from plumbagin conjugated via a viariable alkyl linker to a phenyl thioglycoside

Infection by M. tuberculosis results in an estimated 1.7 million TB related deaths worldwide. Mycothiol is produced in M. tuberculosis as the dominant low molecular weight thiol and is thought to protect the bacteria against oxidative stress. Since mycothiol is unique to Actinomycetes and is also proposed to play an important role in the dormant state of Mycobacteria, the pseudo-dissacharide is seen as a potential target for novel anti-tuberculars. Targeting the mycothiol redox cycle has led to MshB inhibition by a series of substrate analogues. Kinetics studied showed that the competitive inhibition increased when the alkyl linker was lengthened. The binding of the inhibitors was investigated using computational techniques in order to rationalise the observed trend in inhibition

Implementation of gaussian process models for non-linear system identification

This thesis is concerned with investigating the use of Gaussian Process (GP) models for the identification of nonlinear dynamic systems. The Gaussian Process model is a non-parametric approach to system identification where the model of the underlying system is to be identified through the application of Bayesian analysis to empirical data. The GP modelling approach has been proposed as an alternative to more conventional methods of system identification due to a number of attractive features. In particular, the Bayesian probabilistic framework employed by the GP model has been shown to have potential in tackling the problems found in the optimisation of complex nonlinear models such as those based on multiple model or neural network structures. Furthermore, due to this probabilistic framework, the predictions made by the GP model are probability distributions composed of mean and variance components. This is in contrast to more conventional methods where a predictive point estimate is typically the output of the model. This additional variance component of the model output has been shown to be of potential use in model-predictive or adaptive control implementations. A further property that is of potential interest to those working on system identification problems is that the GP model has been shown to be particularly effective in identifying models from sparse datasets. Therefore, the GP model has been proposed for the identification of models in off-equilibrium regions of operating space, where more established methods might struggle due to a lack of data. The majority of the existing research into modelling with GPs has concentrated on detailing the mathematical methodology and theoretical possibilities of the approach. Furthermore, much of this research has focused on the application of the method toward statistics and machine learning problems. This thesis investigates the use of the GP model for identifying nonlinear dynamic systems from an engineering perspective. In particular, it is the implementation aspects of the GP model that are the main focus of this work. Due to its non-parametric nature, the GP model may also be considered a ‘black-box’ method as the identification process relies almost exclusively on empirical data, and not on prior knowledge of the system. As a result, the methods used to collect and process this data are of great importance, and the experimental design and data pre-processing aspects of the system identification procedure are investigated in detail. Therefore, in the research presented here the inclusion of prior system knowledge into the overall modelling procedure is shown to be an invaluable asset in improving the overall performance of the GP model. In previous research, the computational implementation of the GP modelling approach has been shown to become problematic for applications where the size of training dataset is large (i.e. one thousand or more points). This is due to the requirement in the GP modelling approach for repeated inversion of a covariance matrix whose size is dictated by the number of points included in the training dataset. Therefore, in order to maintain the computational viability of the approach, a number of different strategies have been proposed to lessen the computational burden. Many of these methods seek to make the covariance matrix sparse through the selection of a subset of existing training data. However, instead of operating on an existing training dataset, in this thesis an alternative approach is proposed where the training dataset is specifically designed to be as small as possible whilst still containing as much information. In order to achieve this goal of improving the ‘efficiency’ of the training dataset, the basis of the experimental design involves adopting a more deterministic approach to exciting the system, rather than the more common random excitation approach used for the identification of black-box models. This strategy is made possible through the active use of prior knowledge of the system. The implementation of the GP modelling approach has been demonstrated on a range of simulated and real-world examples. The simulated examples investigated include both static and dynamic systems. The GP model is then applied to two laboratory-scale nonlinear systems: a Coupled Tanks system where the volume of liquid in the second tank must be predicted, and a Heat Transfer system where the temperature of the airflow along a tube must be predicted. Further extensions to the GP model are also investigated including the propagation of uncertainty from one prediction to the next, the application of sparse matrix methods, and also the use of derivative observations. A feature of the application of GP modelling approach to nonlinear system identification problems is the reliance on the squared exponential covariance function. In this thesis the benefits and limitations of this particular covariance function are made clear, and the use of alternative covariance functions and ‘mixed-model’ implementations is also discussed

A radial basis function method for solving optimal control problems.

This work presents two direct methods based on the radial basis function (RBF) interpolation and arbitrary discretization for solving continuous-time optimal control problems: RBF Collocation Method and RBF-Galerkin Method. Both methods take advantage of choosing any global RBF as the interpolant function and any arbitrary points (meshless or on a mesh) as the discretization points. The first approach is called the RBF collocation method, in which states and controls are parameterized using a global RBF, and constraints are satisfied at arbitrary discrete nodes (collocation points) to convert the continuous-time optimal control problem to a nonlinear programming (NLP) problem. The resulted NLP is quite sparse and can be efficiently solved by well-developed sparse solvers. The second proposed method is a hybrid approach combining RBF interpolation with Galerkin error projection for solving optimal control problems. The proposed solution, called the RBF-Galerkin method, applies a Galerkin projection to the residuals of the optimal control problem that make them orthogonal to every member of the RBF basis functions. Also, RBF-Galerkin costate mapping theorem will be developed describing an exact equivalency between the Karush–Kuhn–Tucker (KKT) conditions of the NLP problem resulted from the RBF-Galerkin method and discretized form of the first-order necessary conditions of the optimal control problem, if a set of conditions holds. Several examples are provided to verify the feasibility and viability of the RBF method and the RBF-Galerkin approach as means of finding accurate solutions to general optimal control problems. Then, the RBF-Galerkin method is applied to a very important drug dosing application: anemia management in chronic kidney disease. A multiple receding horizon control (MRHC) approach based on the RBF-Galerkin method is developed for individualized dosing of an anemia drug for hemodialysis patients. Simulation results are compared with a population-oriented clinical protocol as well as an individual-based control method for anemia management to investigate the efficacy of the proposed method

Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions

A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data

Fast methods for modelling fluid flow and characterising petroleum reservoirs

This thesis tackles three kinds of computationally efficient methods widely applicable in the fields of engineering, simulation and numerical modelling. First, the Non-Intrusive Reduced Order Modelling (NIROM) is discussed, reframed, generalised and tested. While NIROM is a general methodology, the main focus of this work is to evaluate its potential in the field of reservoir modelling. For this purpose a new method for constructing parameterised NIROMs is proposed and the POD-RBF approach is investigated on a number of representative test cases. A detailed analysis concludes with NIROM not being a viable practical solution at this stage; the underlying issues, their causes and future development the method are discussed in detail. Second, a method for classifying well log data is given. The method is an alternative to typical machine learning (ML) approaches, which up to date have been the only tools utilised for the purpose. Our approach is motivated by (and mitigates a number of) issues with applying ML in practical applications, in particular the lack of explainability. Instead of being a complex surrogate with a large number of degrees of freedom (cf ML), our model consists of the automatically re-scaled training set and a single additional number extracted during the training procedure. The technique proposed is characterised by a case-independent design, very high computational efficiency and relies on an intuitively meaningful operating principle; it also provides additional functionality in comparison with alternatives. It is demonstrated that (out of the box) the method outperforms the vast majority of alternatives on a realistic data set in terms of efficiency and accuracy, even when implemented in serial in an interpreted programming language. Finally, the last part of the thesis addresses the issue of efficient semi-analytical modelling of solid boundaries in Smoothed Particle Hydrodynamics (SPH) simulations. More precisely, this work focuses on the purely technical aspect of efficient evaluation of correction factors governing the boundary effects; the framework utilising their values is already well established. Mathematically, the problem is described as efficiently integrating a spherically symmetric function over its compact spherical support truncated by a surface (or a collection of surfaces) representing a solid boundary (wall). Three types of boundary geometries are considered, namely piecewise-planar, spherical and super-ellipsoid/super-toroid surfaces, with the latter two categories addressed for the first time in the literature. All methods provided are characterised by an arbitrary degree of accuracy and simplicity of implementation, especially in comparison with all to up to date alternatives. A number of representative test cases is studied.Open Acces

Efficient Ranking-Based Methodologies in the Optimal Design of Large-Scale Chemical Processes under Uncertainty

Chemical process design is still an active area of research since it largely determines the optimal and safe operation of a new process under various conditions. The design process involves a series of steps that aims to identify the most economically attractive design typically using steady-state optimization. However, optimal steady-state designs may fail to comply with the process constraints when the system under analysis is subject to uncertainties in the inputs (e.g. the composition of a reactant in a feedstream) or in the system’s parameters (e.g. the activation energy in a chemical reaction). This has motivated the development of systematic methods that explicitly account for uncertainty in optimal process design. In this work, a new efficient approach for the optimal design under uncertainty is presented. The key idea is to approximate the process constraint functions and outputs using Power Series Expansions (PSE)-based functions. A ranking-based approach is adopted where the user can assign priorities or probabilities of satisfaction for the different process constraints and process outputs considered in the analysis. The methodology was tested on a reactor-heat exchanger system, the Tennessee Eastman plant, which is an industrial benchmark process, and a post-combustion CO2 capture plant, which is a large-scale chemical plant that has recently gained attention and significance due to its potential to mitigate CO2 emissions from fossil-fired power plants. The results show that the present method is computationally attractive since the optimal process design is accomplished in shorter computational times when compared to the stochastic programming approach, which is the standard method used to address this type of problems. Furthermore, it has been shown that process dynamics play an important role while searching for the optimal process design of a system under uncertainty. Therefore, a stochastic-based simultaneous design and control methodology for the optimal design of chemical processes under uncertainty that incorporates an advanced model-based scheme such as Model Predictive Control (MPC) is also presented in this work. The key idea is to determine the time-dependent variability of the system that will be accounted for in the process design using a stochastic-based worst-case variability index. A case study of an actual wastewater treatment industrial plant has been used to test the proposed methodology. The MPC-based simultaneous design and control approach provided more economical designs when compared to a decentralized multi-loop PI control strategy, thus showing that this method is a practical approach to address the integration of design and control while using advanced model-based control strategies