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  • Journal article
    Kuntz Nussio J, Thomas P, Stan G, Barahona Met al., 2021,

    Approximations of countably-infinite linear programs over bounded measure spaces

    , SIAM Journal on Optimization, ISSN: 1052-6234

    We study a class of countably-infinite-dimensional linear programs (CILPs)whose feasible sets are bounded subsets of appropriately defined spaces ofmeasures. The optimal value, optimal points, and minimal points of these CILPscan be approximated by solving finite-dimensional linear programs. We show howto construct finite-dimensional programs that lead to approximations witheasy-to-evaluate error bounds, and we prove that the errors converge to zero asthe size of the finite-dimensional programs approaches that of the originalproblem. We discuss the use of our methods in the computation of the stationarydistributions, occupation measures, and exit distributions of Markov~chains.

  • Journal article
    Kuntz J, Thomas P, Stan G-B, Barahona Met al., 2020,

    Stationary distributions of continuous-time Markov chains: a review of theory and truncation-based approximations

    , SIAM Review, ISSN: 0036-1445

    Computing the stationary distributions of a continuous-time Markov chaininvolves solving a set of linear equations. In most cases of interest, thenumber of equations is infinite or too large, and cannot be solved analyticallyor numerically. Several approximation schemes overcome this issue by truncatingthe state space to a manageable size. In this review, we first give acomprehensive theoretical account of the stationary distributions and theirrelation to the long-term behaviour of the Markov chain, which is readilyaccessible to non-experts and free of irreducibility assumptions made instandard texts. We then review truncation-based approximation schemes payingparticular attention to their convergence and to the errors they introduce, andwe illustrate their performance with an example of a stochastic reactionnetwork of relevance in biology and chemistry. We conclude by elaborating oncomputational trade-offs associated with error control and some open questions.

  • Journal article
    Clarke J, Murray A, Markar S, Barahona M, Kinross Jet al., 2020,

    A new geographic model of care to manage the post-COVID-19 elective surgery aftershock in England: a retrospective observational study

    , BMJ Open, ISSN: 2044-6055

    Objectives The suspension of elective surgery during the COVID pandemic is unprecedented and has resulted in record volumes of patients waiting for operations. Novel approaches that maximise capacity and efficiency of surgical care are urgently required. This study applies Markov Multiscale Community Detection (MMCD), an unsupervised graph-based clustering framework, to identify new surgical care models based on pooled waiting lists delivered across an expanded network of surgical providers. DesignRetrospective observational study using Hospital Episode Statistics.SettingPublic and private hospitals providing surgical care to National Health Service (NHS) patients in England. ParticipantsAll adult patients resident in England undergoing NHS-funded planned surgical procedures between 1st April 2017 and 31st March 2018. Main outcome measuresThe identification of the most common planned surgical procedures in England (High Volume Procedures – HVP) and proportion of low, medium and high-risk patients undergoing each HVP. The mapping of hospitals providing surgical care onto optimised groupings based on patient usage data.ResultsA total of 7,811,891 planned operations were identified in 4,284,925 adults during the one-year period of our study. The 28 most common surgical procedures accounted for a combined 3,907,474 operations (50.0% of the total). 2,412,613 (61.7%) of these most common procedures involved ‘low risk’ patients. Patients travelled an average of 11.3 km for these procedures. Based on the data, MMCD partitioned England into 45, 16 and 7 mutually exclusive and collectively exhaustive natural surgical communities of increasing coarseness. The coarser partitions into 16 and 7 surgical communities were shown to be associated with balanced supply and demand for surgical care within communities.ConclusionsPooled waiting lists for low risk elective procedures and patients across integrated, expanded natural surgical community networks have the pot

  • Journal article
    Bai W, Suzuki H, Huang J, Francis C, Wang S, Tarroni G, Guitton F, Aung N, Fung K, Petersen SE, Piechnik SK, Neubauer S, Evangelou E, Dehghan A, O'Regan DP, Wilkins MR, Guo Y, Matthews PM, Rueckert Det al., 2020,

    A population-based phenome-wide association study of cardiac and aortic structure and function

    , Nature Medicine, Vol: 26, Pages: 1654-1662, ISSN: 1078-8956

    Differences in cardiac and aortic structure and function are associated with cardiovascular diseases and a wide range of other types of disease. Here we analyzed cardiovascular magnetic resonance images from a population-based study, the UK Biobank, using an automated machine-learning-based analysis pipeline. We report a comprehensive range of structural and functional phenotypes for the heart and aorta across 26,893 participants, and explore how these phenotypes vary according to sex, age and major cardiovascular risk factors. We extended this analysis with a phenome-wide association study, in which we tested for correlations of a wide range of non-imaging phenotypes of the participants with imaging phenotypes. We further explored the associations of imaging phenotypes with early-life factors, mental health and cognitive function using both observational analysis and Mendelian randomization. Our study illustrates how population-based cardiac and aortic imaging phenotypes can be used to better define cardiovascular disease risks as well as heart–brain health interactions, highlighting new opportunities for studying disease mechanisms and developing image-based biomarkers.

  • Journal article
    Meyer H, Dawes T, Serrani M, Bai W, Tokarczuk P, Cai J, Simoes Monteiro de Marvao A, Henry A, Lumbers T, Gierten J, Thumberger T, Wittbrodt J, Ware J, Rueckert D, Matthews P, Prasad S, Costantino M, Cook S, Birney E, O'Regan Det al., 2020,

    Genetic and functional insights into the fractal structure of the heart

    , Nature, Vol: 584, Pages: 589-594, ISSN: 0028-0836

    The inner surfaces of the human heart are covered by a complex network of muscular strands that is thought to be a vestigeof embryonic development.1,2 The function of these trabeculae in adults and their genetic architecture are unknown. Toinvestigate this we performed a genome-wide association study using fractal analysis of trabecular morphology as animage-derived phenotype in 18,096 UK Biobank participants. We identified 16 significant loci containing genes associatedwith haemodynamic phenotypes and regulation of cytoskeletal arborisation.3,4 Using biomechanical simulations and humanobservational data, we demonstrate that trabecular morphology is an important determinant of cardiac performance. Throughgenetic association studies with cardiac disease phenotypes and Mendelian randomisation, we find a causal relationshipbetween trabecular morphology and cardiovascular disease risk. These findings suggest an unexpected role for myocardialtrabeculae in the function of the adult heart, identify conserved pathways that regulate structural complexity, and reveal theirinfluence on susceptibility to disease

  • Journal article
    Greenbury SF, Barahona M, Johnston IG, 2020,

    HyperTraPS: Inferring Probabilistic Patterns of Trait Acquisition in Evolutionary and Disease Progression Pathways.

    , Cell Syst, Vol: 10, Pages: 39-51.e10

    The explosion of data throughout the biomedical sciences provides unprecedented opportunities to learn about the dynamics of evolution and disease progression, but harnessing these large and diverse datasets remains challenging. Here, we describe a highly generalizable statistical platform to infer the dynamic pathways by which many, potentially interacting, traits are acquired or lost over time. We use HyperTraPS (hypercubic transition path sampling) to efficiently learn progression pathways from cross-sectional, longitudinal, or phylogenetically linked data, readily distinguishing multiple competing pathways, and identifying the most parsimonious mechanisms underlying given observations. This Bayesian approach allows inclusion of prior knowledge, quantifies uncertainty in pathway structure, and allows predictions, such as which symptom a patient will acquire next. We provide visualization tools for intuitive assessment of multiple, variable pathways. We apply the method to ovarian cancer progression and the evolution of multidrug resistance in tuberculosis, demonstrating its power to reveal previously undetected dynamic pathways.

  • Journal article
    Maes A, Barahona M, Clopath C, 2020,

    Learning spatiotemporal signals using a recurrent spiking network that discretizes time

    , PLoS Computational Biology, Vol: 16, Pages: 1-26, ISSN: 1553-734X

    Learning to produce spatiotemporal sequences is a common task that the brain has to solve. The same neural substrate may be used by the brain to produce different sequential behaviours. The way the brain learns and encodes such tasks remains unknown as current computational models do not typically use realistic biologically-plausible learning. Here, we propose a model where a spiking recurrent network of excitatory and inhibitory biophysical neurons drives a read-out layer: the dynamics of the driver recurrent network is trained to encode time which is then mapped through the read-out neurons to encode another dimension, such as space or a phase. Different spatiotemporal patterns can be learned and encoded through the synaptic weights to the read-out neurons that follow common Hebbian learning rules. We demonstrate that the model is able to learn spatiotemporal dynamics on time scales that are behaviourally relevant and we show that the learned sequences are robustly replayed during a regime of spontaneous activity.

  • Journal article
    Liu Z, Barahona M, 2020,

    Graph-based data clustering via multiscale community detection

    , Applied Network Science, Vol: 5, Pages: 1-20, ISSN: 2364-8228

    We present a graph-theoretical approach to data clustering, which combines the creation of a graph from the data with Markov Stability, a multiscale community detection framework. We show how the multiscale capabilities of the method allow the estimation of the number of clusters, as well as alleviating the sensitivity to the parameters in graph construction. We use both synthetic and benchmark real datasets to compare and evaluate several graph construction methods and clustering algorithms, and show that multiscale graph-based clustering achieves improved performance compared to popular clustering methods without the need to set externally the number of clusters.

  • Journal article
    Tonn MK, Thomas P, Barahona M, OyarzĂșn DAet al., 2020,

    Computation of Single-Cell Metabolite Distributions Using Mixture Models.

    , Front Cell Dev Biol, Vol: 8, ISSN: 2296-634X

    Metabolic heterogeneity is widely recognized as the next challenge in our understanding of non-genetic variation. A growing body of evidence suggests that metabolic heterogeneity may result from the inherent stochasticity of intracellular events. However, metabolism has been traditionally viewed as a purely deterministic process, on the basis that highly abundant metabolites tend to filter out stochastic phenomena. Here we bridge this gap with a general method for prediction of metabolite distributions across single cells. By exploiting the separation of time scales between enzyme expression and enzyme kinetics, our method produces estimates for metabolite distributions without the lengthy stochastic simulations that would be typically required for large metabolic models. The metabolite distributions take the form of Gaussian mixture models that are directly computable from single-cell expression data and standard deterministic models for metabolic pathways. The proposed mixture models provide a systematic method to predict the impact of biochemical parameters on metabolite distributions. Our method lays the groundwork for identifying the molecular processes that shape metabolic heterogeneity and its functional implications in disease.

  • Journal article
    Hodges M, Yaliraki SN, Barahona M, 2019,

    Edge-based formulation of elastic network models

    , Physical Review Research, Pages: 033211-033211

    We present an edge-based framework for the study of geometric elastic networkmodels to model mechanical interactions in physical systems. We use aformulation in the edge space, instead of the usual node-centric approach, tocharacterise edge fluctuations of geometric networks defined in d- dimensionalspace and define the edge mechanical embeddedness, an edge mechanicalsusceptibility measuring the force felt on each edge given a force applied onthe whole system. We further show that this formulation can be directly relatedto the infinitesimal rigidity of the network, which additionally permits three-and four-centre forces to be included in the network description. We exemplifythe approach in protein systems, at both the residue and atomistic levels ofdescription.

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