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  • Journal article
    Peach R, Yaliraki S, Lefevre D, Barahona Met al.,

    Data-driven unsupervised clustering of online learner behaviour 

    , npj Science of Learning, ISSN: 2056-7936

    The widespread adoption of online courses opens opportunities for analysing learner behaviour and optimising web-based learning adapted to observed usage. Here we introduce a mathematical framework for the analysis of time series of online learner engagement, which allows the identification of clusters of learners with similar online temporal behaviour directly from the raw data without prescribing a priori subjective reference behaviours. The method uses a dynamic time warping kernel to create a pairwise similarity between time series of learner actions, and combines it with an unsupervised multiscale graph clustering algorithm to identify groups of learners with similar temporal behaviour. To showcase our approach, we analyse task completion data from a cohort of learners taking an online post-graduate degree at Imperial Business School. Our analysis reveals clusters of learners with statistically distinct patterns of engagement, from distributed to massed learning, with different levels of regularity, adherence to pre-planned course structure and task completion. The approach also reveals outlier learners with highly sporadic behaviour. A posteriori comparison against student performance shows that, whereas high performing learners are spread across clusters with diverse temporal engagement, low performers are located significantly in the massed learning cluster, and our unsupervised clustering identifies low performers more accurately than common machine learning classification methods trained on temporal statistics of the data. Finally, we test the applicability of the method by analysing two additional datasets: a different cohort of the same course, and time series of different format from another university.

  • Journal article
    Kuntz Nussio J, Thomas P, Stan GB, Barahona Met al., 2019,

    Bounding the stationary distributions of the chemical master equation via mathematical programming

    , Journal of Chemical Physics, Vol: 151, Pages: 034109-034109, ISSN: 0021-9606

    The stochastic dynamics of biochemical networks are usually modelled with the chemical master equation (CME). The stationary distributions of CMEs are seldom solvable analytically, and numerical methods typically produce estimates with uncontrolled errors. Here, we introduce mathematical programming approaches that yield approximations of these distributions with computable error bounds which enable the verification of their accuracy. First, we use semidefinite programming to compute increasingly tighter upper and lower bounds on the moments of the stationary distributions for networks with rational propensities. Second, we use these moment bounds to formulate linear programs that yield convergent upper and lower bounds on the stationary distributions themselves, their marginals and stationary averages. The bounds obtained also provide a computational test for the uniqueness of the distribution. In the unique case, the bounds form an approximation of the stationary distribution with a computable bound on its error. In the non unique case, our approach yields converging approximations of the ergodic distributions. We illustrate our methodology through several biochemical examples taken from the literature: Schl¨ogl’s model for a chemical bifurcation, a two-dimensional toggle switch, a model for bursty gene expression, and a dimerisation model with multiple stationary distributions.

  • Journal article
    Johnston I, Hoffmann T, Greenbury S, Cominetti O, Jallow M, Kwiatkowski D, Barahona M, Jones N, Casals-Pascual Cet al., 2019,

    Precision identification of high-risk phenotypes and progression pathways in severe malaria without requiring longitudinal data

    , npj Digital Medicine, Vol: 2, ISSN: 2398-6352

    More than 400,000 deaths from severe malaria (SM) are reported every year, mainly in African children. The diversity of clinical presentations associated with SM indicates important differences in disease pathogenesis that require specific treatment, and this clinical heterogeneity of SM remains poorly understood. Here, we apply tools from machine learning and model-based inference to harness large-scale data and dissect the heterogeneity in patterns of clinical features associated with SM in 2904 Gambian children admitted to hospital with malaria. This quantitative analysis reveals features predicting the severity of individual patient outcomes, and the dynamic pathways of SM progression, notably inferred without requiring longitudinal observations. Bayesian inference of these pathways allows us assign quantitative mortality risks to individual patients. By independently surveying expert practitioners, we show that this data-driven approach agrees with and expands the current state of knowledge on malaria progression, while simultaneously providing a data-supported framework for predicting clinical risk.

  • Journal article
    Schaub MT, Delvenne JC, Lambiotte R, Barahona Met al., 2019,

    Multiscale dynamical embeddings of complex networks

    , Physical Review E, Vol: 99, Pages: 062308-1-062308-18, ISSN: 1539-3755

    Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict, and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from control theory, we propose a time-dependent dynamical similarity measure between nodes, which quantifies the effect a node-input has on the network. This dynamical similarity induces an embedding that can be employed for several analysis tasks. Here we focus on (i) dimensionality reduction, i.e., projecting nodes onto a low-dimensional space that captures dynamic similarity at different timescales, and (ii) how to exploit our embeddings to uncover functional modules. We exemplify our ideas through case studies focusing on directed networks without strong connectivity and signed networks. We further highlight how certain ideas from community detection can be generalized and linked to control theory, by using the here developed dynamical perspective.

  • Journal article
    Kuntz J, Thomas P, Stan G-B, Barahona Met al., 2019,

    Approximations of countably-infinite linear programs over bounded measure spaces

    We study a class of countably-infinite-dimensional linear programs (CILPs)whose feasible sets are bounded subsets of appropriately defined weightedspaces of measures. We show how to approximate the optimal value, optimalpoints, and minimal points of these CILPs by solving finite-dimensional linearprograms. The errors of our approximations converge to zero as the size of thefinite-dimensional program approaches that of the original problem and are easyto bound in practice. We discuss the use of our methods in the computation ofthe stationary distributions, occupation measures, and exit distributions ofMarkov~chains.

  • Journal article
    Attard M, Dawes T, Simoes Monteiro de Marvao A, Biffi C, Shi W, Wharton J, Rhodes C, Ghataorhe P, Gibbs J, Howard L, Rueckert D, Wilkins M, O'Regan Det al., 2019,

    Metabolic pathways associated with right ventricular adaptation to pulmonary hypertension: Three dimensional analysis of cardiac magnetic resonance imaging

    , EHJ Cardiovascular Imaging / European Heart Journal - Cardiovascular Imaging, Vol: 20, Pages: 668-676, ISSN: 2047-2412

    AimsWe sought to identify metabolic pathways associated with right ventricular (RV) adaptation to pulmonary hypertension (PH). We evaluated candidate metabolites, previously associated with survival in pulmonary arterial hypertension, and used automated image segmentation and parametric mapping to model their relationship to adverse patterns of remodelling and wall stress.Methods and resultsIn 312 PH subjects (47.1% female, mean age 60.8 ± 15.9 years), of which 182 (50.5% female, mean age 58.6 ± 16.8 years) had metabolomics, we modelled the relationship between the RV phenotype, haemodynamic state, and metabolite levels. Atlas-based segmentation and co-registration of cardiac magnetic resonance imaging was used to create a quantitative 3D model of RV geometry and function—including maps of regional wall stress. Increasing mean pulmonary artery pressure was associated with hypertrophy of the basal free wall (β = 0.29) and reduced relative wall thickness (β = −0.38), indicative of eccentric remodelling. Wall stress was an independent predictor of all-cause mortality (hazard ratio = 1.27, P = 0.04). Six metabolites were significantly associated with elevated wall stress (β = 0.28–0.34) including increased levels of tRNA-specific modified nucleosides and fatty acid acylcarnitines, and decreased levels (β = −0.40) of sulfated androgen.ConclusionUsing computational image phenotyping, we identify metabolic profiles, reporting on energy metabolism and cellular stress-response, which are associated with adaptive RV mechanisms to PH.

  • Journal article
    Kuntz J, Thomas P, Stan G-B, Barahona Met al., 2019,

    The exit time finite state projection scheme: bounding exit distributions and occupation measures of continuous-time Markov chains

    , SIAM Journal on Scientific Computing, Vol: 41, Pages: A748-A769, ISSN: 1064-8275

    We introduce the exit time finite state projection (ETFSP) scheme, a truncation- based method that yields approximations to the exit distribution and occupation measure associated with the time of exit from a domain (i.e., the time of first passage to the complement of the domain) of time-homogeneous continuous-time Markov chains. We prove that: (i) the computed approximations bound the measures from below; (ii) the total variation distances between the approximations and the measures decrease monotonically as states are added to the truncation; and (iii) the scheme converges, in the sense that, as the truncation tends to the entire state space, the total variation distances tend to zero. Furthermore, we give a computable bound on the total variation distance between the exit distribution and its approximation, and we delineate the cases in which the bound is sharp. We also revisit the related finite state projection scheme and give a comprehensive account of its theoretical properties. We demonstrate the use of the ETFSP scheme by applying it to two biological examples: the computation of the first passage time associated with the expression of a gene, and the fixation times of competing species subject to demographic noise.

  • Journal article
    Warren L, Clarke J, Arora S, Barahona M, Arebi N, Darzi Aet al., 2019,

    Transitions of care across hospital settings in patients with inflammatory bowel disease

    , World Journal of Gastroenterology, ISSN: 1007-9327

    BACKGROUNDInflammatory bowel disease (IBD) is a chronic, inflammatory disorder characterised by both intestinal and extra-intestinal pathology. Patients may receive both emergency and elective care from several providers, often in different hospital settings. Poorly managed transitions of care between providers can lead to inefficiencies in care and patient safety issues. To ensure that the sharing of patient information between providers is appropriate, timely, accurate and secure, effective data-sharing infrastructure needs to be developed. To optimise inter-hospital data-sharing for IBD patients, we need to better understand patterns of hospital encounters in this group.AIMTo determine the type and location of hospital services accessed by IBD patients in England.METHODSThis was a retrospective observational study using Hospital Episode Statistics, a large administrative patient data set from the National Health Service in England. Adult patients with a diagnosis of IBD following admission to hospital were followed over a 2-year period to determine the proportion of care accessed at the same hospital providing their outpatient IBD care, defined as their ‘home provider’. Secondary outcome measures included the geographic distribution of patient-sharing, regional and age-related differences in accessing services, and type and frequency of outpatient encounters.RESULTSOf 95055 patients accessed hospital services on 1760156 occasions over a 2-year follow-up period. The proportion of these encounters with their identified IBD ‘home provider’ was 73.3%, 87.8% and 83.1% for accident and emergency, inpatient and outpatient encounters respectively. Patients living in metropolitan centres and younger patients were less likely to attend their ‘home provider’ for hospital services. The most commonly attended specialty services were gastroenterology, general surgery and ophthalmology.CONCLUSIONTransitions of care between secondary care sett

  • Journal article
    Bello G, Dawes T, Duan J, Biffi C, Simoes Monteiro de Marvao A, Howard L, Gibbs S, Wilkins M, Cook S, Rueckert D, O'Regan Det al., 2019,

    Deep learning cardiac motion analysis for human survival prediction

    , Nature Machine Intelligence, Vol: 1, Pages: 95-104, ISSN: 2522-5839

    Motion analysis is used in computer vision to understand the behaviour of moving objects in sequences of images. Optimizing the interpretation of dynamic biological systems requires accurate and precise motion tracking as well as efficient representations of high-dimensional motion trajectories so that these can be used for prediction tasks. Here we use image sequences of the heart, acquired using cardiac magnetic resonance imaging, to create time-resolved three-dimensional segmentations using a fully convolutional network trained on anatomical shape priors. This dense motion model formed the input to a supervised denoising autoencoder (4Dsurvival), which is a hybrid network consisting of an autoencoder that learns a task-specific latent code representation trained on observed outcome data, yielding a latent representation optimized for survival prediction. To handle right-censored survival outcomes, our network used a Cox partial likelihood loss function. In a study of 302 patients, the predictive accuracy (quantified by Harrell’s C-index) was significantly higher (P = 0.0012) for our model C = 0.75 (95% CI: 0.70–0.79) than the human benchmark of C = 0.59 (95% CI: 0.53–0.65). This work demonstrates how a complex computer vision task using high-dimensional medical image data can efficiently predict human survival.

  • Journal article
    Tonn M, Thomas P, Barahona M, Oyarzun D, Tonn M, Thomas P, Barahona M, Oyarzun Det al., 2019,

    Stochastic modelling reveals mechanisms of metabolic heterogeneity

    , Communications Biology, Vol: 2, ISSN: 2399-3642

    Phenotypic variation is a hallmark of cellular physiology. Metabolic heterogeneity, in particular, underpins single-cell phenomena such as microbial drug tolerance and growth variability. Much research has focussed on transcriptomic and proteomic heterogeneity, yet it remains unclear if such variation permeates to the metabolic state of a cell. Here we propose a stochastic model to show that complex forms of metabolic heterogeneity emerge from fluctuations in enzyme expression and catalysis. The analysis predicts clonal populations to split into two or more metabolically distinct subpopulations. We reveal mechanisms not seen in deterministic models, in which enzymes with unimodal expression distributions lead to metabolites with a bimodal or multimodal distribution across the population. Based on published data, the results suggest that metabolite heterogeneity may be more pervasive than previously thought. Our work casts light on links between gene expression and metabolism, and provides a theory to probe the sources of metabolite heterogeneity.

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