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  • 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.,

    Genetic and functional insights into the fractal structure of the heart

    , Nature, 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
    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
    Maes A, Barahona M, Clopath C, 2020,

    Learning spatiotemporal signals using a recurrent spiking network that discretizes time.

    , PLoS Comput Biol, Vol: 16

    Learning to produce spatiotemporal sequences is a common task that the brain has to solve. The same neurons may be used 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 spiking 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
    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.

  • Book chapter
    Schaub MT, Delvenne J-C, Lambiotte R, Barahona Met al., 2019,

    Structured networks and coarse-grained descriptions: a dynamical perspective

    , Advances in Network Clustering and Blockmodeling, Editors: Doreian, Batagelj, Ferligoj, Publisher: John Wiley and Sons, Ltd, Pages: 333-361, ISBN: 9781119224709

    This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We thus aim to gain a reduced description of the system that takes into account both its structure and dynamics. In the first part, we introduce the general mathematical setup for the types of dynamics we consider throughout the chapter. We provide two guiding examples, namely consensus dynamics and diffusion processes (random walks), motivating their connection to social network analysis, and provide a brief discussion on the general dynamical framework and its possible extensions. In the second part, we focus on the influence of graph structure on the dynamics taking place on the network, focusing on three concepts that allow us to gain insight into this notion. First, we describe how time scale separation can appear in the dynamics on a network as a consequence of graph structure. Second, we discuss how the presence of particular symmetries in the network give rise to invariant dynamical subspaces that can be precisely described by graph partitions. Third, we show how this dynamical viewpoint can be extended to study dynamics on networks with signed edges, which allow us to discuss connections to concepts in social network analysis, such as structural balance. In the third part, we discuss how to use dynamical processes unfolding on the network to detect meaningful network substructures. We then show how such dynamical measures can be related to seemingly different algorithm for community detection and coarse-graining proposed in the literature. We conclude with a brief summary and highlight interesting open future directions.

  • Journal article
    Peach R, Yaliraki S, Lefevre D, Barahona Met al., 2019,

    Data-driven unsupervised clustering of online learner behaviour 

    , npj Science of Learning, Vol: 4, 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, 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.

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