Aiping Xu

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Experience sharing: Mathematical Contest in Modelling (MCM)

MSOR Connections, 2017

In January 2016, Coventry University’s sigma Mathematics Support Centre (MSC) funded three studen... more In January 2016, Coventry University’s sigma Mathematics Support Centre (MSC) funded three students for MCM, a multi-day mathematics competition held annually in the USA. This is organised by the Consortium for Mathematics and Its Applications (COMAP) and sponsored by the Mathematical Association of America (MAA), the Society of Industrial and Applied Mathematics (SIAM) and the Institute for Operations Research and the Management Sciences (INFORMS). In this article the team leader and advisor reflect on their experience.

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Maintenance affects the stability of a two-tiered microbial ‘food chain’?

Journal of Theoretical Biology, 2011

Microbial 'food chains' are fundamentally different from canonical food chains in the sense that ... more Microbial 'food chains' are fundamentally different from canonical food chains in the sense that the waste products of the organisms on one trophic level are consumed by organisms of the next trophic level rather than the organisms themselves. In the present paper we introduce a generalised model of a two-tiered microbial 'food chain' with feedback inhibition, after applying an appropriate dimensionless transformation, and investigate its stability analytically. We then parameterised the model with consensus values for syntrophic propionate degradation compiled by the IWA Task Group for Mathematical Modelling of Anaerobic Digestion Processes. Consumption of energy for all processes other than growth is called maintenance. In the absence of maintenance and decay the microbial 'food chain' is intrinsically stable, but when decay is included in the description this is not necessarily the case. We point out that this is in analogy to canonical food chains where introduction of maintenance in the description of a stable (equilibrium or limit cycle) predator-prey system generates chaos.

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Functional data clustering using principal curve methods

Communications in Statistics-theory and Methods, 2021

In this paper we propose a novel clustering method for functional data based on the principal cur... more

$Research paper thumbnail of Understanding of fraction and its application in unit conversions$

Understanding of fraction and its application in unit conversions

MSOR Connections, 2017

Many British university students lack confidence in manipulating fractions. In this paper, we tak... more Many British university students lack confidence in manipulating fractions. In this paper, we take a detailed look into the difficulties that students are experiencing across disciplines. We also introduce a method on how to effectively convert units via manipulating fraction operations. Though this approach to unit conversions is widespread in the United States, particularly in the discipline of Chemistry, it is not well documented or applied within the UK Higher Education sector to the authors’ knowledge. The method has been frequently used by the authors in Coventry's Mathematics Support Centre with very positive feedback.

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Gaussian process methods for nonparametric functional regression with mixed predictors

Computational Statistics & Data Analysis, 2019

Gaussian process methods are proposed for nonparametric functional regression for both scalar and... more Gaussian process methods are proposed for nonparametric functional regression for both scalar and functional responses with mixed multidimensional functional and scalar predictors. The proposed models allow the response variables to depend on the entire trajectories of the functional predictors. They inherit the desirable properties of Gaussian process regression, and can naturally accommodate both scalar and functional variables as the predictors, as well as easy to obtain and express uncertainty in predictions. The numerical experiments show that the proposed methods significantly outperform the competing models, and their usefulness is also demonstrated by the application to two real datasets.

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Gaussian process regression with functional covariates and multivariate response

Chemometrics and Intelligent Laboratory Systems, 2017

Gaussian process regression (GPR) has been shown to be a powerful and effective nonparametric met... more Gaussian process regression (GPR) has been shown to be a powerful and effective nonparametric method for regression, classification and interpolation, due to many of its desirable properties. However, most GPR models consider univariate or multivariate covariates only. In this paper we extend the GPR models to cases where the covariates include both functional and multivariate variables and the response is multidimensional. The model naturally incorporates two different types of covariates: multivariate and functional, and the principal component analysis is used to de-correlate the multivariate response which avoids the widely recognised difficulty in the multi-output GPR models of formulating covariance functions which have to describe the correlations not only between data points but also between responses. The usefulness of the proposed method is demonstrated through a simulated example and two real data sets in chemometrics.

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Anomalous energy yields in thermodynamic calculations: importance of accounting for pH-dependent organic acid speciation

The ISME Journal, 2010

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The thermodynamic landscape of methanogenic PAH degradation

Microbial Biotechnology, 2009

Methanogenic degradation of polycyclic aromatic hydrocarbons (PAHs) has long been considered impo... more Methanogenic degradation of polycyclic aromatic hydrocarbons (PAHs) has long been considered impossible, but evidence in contaminated near surface environments and biodegrading petroleum reservoirs suggests that this is not necessarily the case. To evaluate the thermodynamic constraints on methanogenic PAH degradation we have estimated the Gibbs free energy values for naphthalene, phenanthrene, anthracene, pyrene and chrysene in the aqueous phase, and used these values to evaluate several possible routes whereby PAHs may be converted to methane. Under standard conditions (25°C, solutes at 1 M concentrations, and gases at 1 atm), methanogenic degradation of these PAHs yields between 209 and 331 kJ mol-1. Per mole of methane produced this is 27-35 kJ mol-1 , indicating that PAHbased methanogenesis is exergonic. We evaluated the energetics of three potential PAH degradation routes: oxidation to H2/CO2, complete conversion to acetate, or incomplete oxidation to H2 plus acetate. Depending on the in situ conditions the energetically most favourable pathway for the PAH-degrading organisms is oxidation to H2/CO2 or conversion into acetate. These are not necessarily the pathways that prevail in the environment. This may be because the kinetic theory of optimal length of metabolic pathways suggests that PAH degraders may have evolved towards incomplete oxidation to acetate plus H 2 as the optimal pathway.

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Residual Generation for Fault Diagnosis in Linear Time-Varying Systems

IEEE Transactions on Automatic Control, 2004

A residual generation method for fault diagnosis in deterministic and stochastic linear time-vary... more A residual generation method for fault diagnosis in deterministic and stochastic linear time-varying systems is proposed in this note. Based on appropriate assumptions on the monitored faults and on some persistent excitation condition, it enables complete diagnosis of any number of faults, regardless of the number of output sensors. In order to generate residuals for fault diagnosis, part of the possible faults are estimated with a recently developed technique of adaptive observer. The sensitivity of the residuals to the monitored faults is rigorously analyzed, as well as their insensitivity to the faults to be ignored.

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Implicit adaptive observers for a class of nonlinear systems

Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148), 2001

Abstract The authors propose a nonlinear adaptive observer for joint state and parameter estimati... more

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