arXiv subjects

Mauricio Barahona

Publications and source records attributed to Mauricio Barahona.

At least 73 records · Page 4Linked to original sources

arXiv2019

An edge-based formulation of elastic network models

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

physics.chem-ph↗

arXiv2019

Allostery and cooperativity in multimeric proteins: bond-to-bond propensities in ATCase

Aspartate carbamoyltransferase (ATCase) is a large dodecameric enzyme with six active sites that exhibits allostery: its catalytic rate is modulated by the binding of various substrates at distal points from the active sites. A recently developed method, bond-to-bond propensity analysis, has proven capable of predicting allosteric sites in a wide range of proteins using an energy-weighted atomistic graph obtained from the protein structure and given knowledge only of the location of the active site. Bond-to-bond propensity establishes if energy fluctuations at given bonds have significant effects on any other bond in the protein, by considering their propagation through the protein graph. In this work, we use bond-to-bond propensity analysis to study different aspects of ATCase activity using three different protein structures and sources of fluctuations. First, we predict key residues and bonds involved in the transition between inactive (T) and active (R) states of ATCase by analysing allosteric substrate binding as a source of energy perturbations in the protein graph. Our computational results also indicate that the effect of multiple allosteric binding is non linear: a switching effect is observed after a particular number and arrangement of substrates is bound suggesting a form of long range communication between the distantly arranged allosteric sites. Second, cooperativity is explored by considering a bisubstrate analogue as the source of energy fluctuations at the active site, also leading to the identification of highly significant residues to the T-R transition that enhance cooperativity across active sites. Finally, the inactive (T) structure is shown to exhibit a strong, non linear communication between the allosteric sites and the interface between catalytic subunits, rather than the active site.

q-bio.QM↗

arXiv2019

Semi-supervised classification on graphs using explicit diffusion dynamics

Classification tasks based on feature vectors can be significantly improved by including within deep learning a graph that summarises pairwise relationships between the samples. Intuitively, the graph acts as a conduit to channel and bias the inference of class labels. Here, we study classification methods that consider the graph as the originator of an explicit graph diffusion. We show that appending graph diffusion to feature-based learning as an \textit{a posteriori} refinement achieves state-of-the-art classification accuracy. This method, which we call Graph Diffusion Reclassification (GDR), uses overshooting events of a diffusive graph dynamics to reclassify individual nodes. The method uses intrinsic measures of node influence, which are distinct for each node, and allows the evaluation of the relationship and importance of features and graph for classification. We also present diff-GCN, a simple extension of Graph Convolutional Neural Network (GCN) architectures that leverages explicit diffusion dynamics, and allows the natural use of directed graphs. To showcase our methods, we use benchmark datasets of documents with associated citation data.

cs.LG↗

arXiv2019

Extracting information from free text through unsupervised graph-based clustering: an application to patient incident records

The large volume of text in electronic healthcare records often remains underused due to a lack of methodologies to extract interpretable content. Here we present an unsupervised framework for the analysis of free text that combines text-embedding with paragraph vectors and graph-theoretical multiscale community detection. We analyse text from a corpus of patient incident reports from the National Health Service in England to find content-based clusters of reports in an unsupervised manner and at different levels of resolution. Our unsupervised method extracts groups with high intrinsic textual consistency and compares well against categories hand-coded by healthcare personnel. We also show how to use our content-driven clusters to improve the supervised prediction of the degree of harm of the incident based on the text of the report. Finally, we discuss future directions to monitor reports over time, and to detect emerging trends outside pre-existing categories.

cs.LG↗

arXiv2019

Data-driven unsupervised clustering of online learner behaviour

The widespread adoption of online courses opens opportunities for the analysis of learner behaviour and for the optimisation of web-based material adapted to observed usage. Here we introduce a mathematical framework for the analysis of time series collected from online engagement of learners, which allows the identification of clusters of learners with similar online behaviour directly from the data, i.e., the groups of learners are not pre-determined subjectively but emerge algorithmically from the analysis and the data.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 cluster groups of learners with similar patterns of behaviour. We showcase our approach on online engagement data of adult learners taking six web-based courses as part of a post-graduate degree at Imperial Business School. Our analysis identifies clusters of learners with statistically distinct patterns of engagement, ranging from distributed to massed learning, with different levels of adherence to pre-planned course structure and/or task completion, and also revealing outlier learners with highly sporadic behaviour. A posteriori comparison with performance showed that, although the majority of low-performing learners are part of in the massed learning cluster, the high performing learners are distributed across clusters with different traits of online engagement. We also show that our methodology is able to identify low performing learners more accurately than common classification methods based on raw statistics extracted from the data.

cs.SI↗

arXiv2019

Rigorous bounds on the stationary distributions of the chemical master equation via mathematical programming

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: Schlögl'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.

math.PR↗

arXiv2019

Multiscale dynamical embeddings of complex networks

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 time scales, 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.

cs.SI↗

arXiv2019

Stochastic modelling reveals mechanisms of metabolic heterogeneity

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.

q-bio.MN↗

arXiv2019

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

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.

math.PR↗

arXiv2018

Collective search with finite perception: transient dynamics and search efficiency

Motile organisms often use finite spatial perception of their surroundings to navigate and search their habitats. Yet standard models of search are usually based on purely local sensory information. To model how a finite perceptual horizon affects ecological search, we propose a framework for optimal navigation that combines concepts from random walks and optimal control theory. We show that, while local strategies are optimal on asymptotically long and short search times, finite perception yields faster convergence and increased search efficiency over transient time scales relevant in biological systems. The benefit of the finite horizon can be maintained by the searchers tuning their response sensitivity to the length scale of the stimulant in the environment, and is enhanced when the agents interact as a result of increased consensus within subpopulations. Our framework sheds light on the role of spatial perception and transients in search movement and collective sensing of the environment.

physics.bio-ph↗

arXiv2018

From Free Text to Clusters of Content in Health Records: An Unsupervised Graph Partitioning Approach

Electronic Healthcare records contain large volumes of unstructured data in different forms. Free text constitutes a large portion of such data, yet this source of richly detailed information often remains under-used in practice because of a lack of suitable methodologies to extract interpretable content in a timely manner. Here we apply network-theoretical tools to the analysis of free text in Hospital Patient Incident reports in the English National Health Service, to find clusters of reports in an unsupervised manner and at different levels of resolution based directly on the free text descriptions contained within them. To do so, we combine recently developed deep neural network text-embedding methodologies based on paragraph vectors with multi-scale Markov Stability community detection applied to a similarity graph of documents obtained from sparsified text vector similarities. We showcase the approach with the analysis of incident reports submitted in Imperial College Healthcare NHS Trust, London. The multiscale community structure reveals levels of meaning with different resolution in the topics of the dataset, as shown by relevant descriptive terms extracted from the groups of records, as well as by comparing a posteriori against hand-coded categories assigned by healthcare personnel. Our content communities exhibit good correspondence with well-defined hand-coded categories, yet our results also provide further medical detail in certain areas as well as revealing complementary descriptors of incidents beyond the external classification. We also discuss how the method can be used to monitor reports over time and across different healthcare providers, and to detect emerging trends that fall outside of pre-existing categories.

cs.CL↗

arXiv2018

Global Network Prediction from Local Node Dynamics

The study of dynamical systems on networks, describing complex interactive processes, provides insight into how network structure affects global behaviour. Yet many methods for network dynamics fail to cope with large or partially-known networks, a ubiquitous situation in real-world applications. Here we propose a localised method, applicable to a broad class of dynamical models on networks, whereby individual nodes monitor and store the evolution of their own state and use these values to approximate, via a simple computation, their own steady state solution. Hence the nodes predict their own final state without actually reaching it. Furthermore, the localised formulation enables nodes to compute global network metrics without knowledge of the full network structure. The method can be used to compute global rankings in the network from local information; to detect community detection from fast, local transient dynamics; and to identify key nodes that compute global network metrics ahead of others. We illustrate some of the applications of the algorithm by efficiently performing web-page ranking for a large internet network and identifying the dynamic roles of inter-neurons in the C. Elegans neural network. The mathematical formulation is simple, widely applicable and easily scalable to real-world datasets suggesting how local computation can provide an approach to the study of large-scale network dynamics.

physics.soc-ph↗

arXiv2018

Content-driven, unsupervised clustering of news articles through multiscale graph partitioning

The explosion in the amount of news and journalistic content being generated across the globe, coupled with extended and instantaneous access to information through online media, makes it difficult and time-consuming to monitor news developments and opinion formation in real time. There is an increasing need for tools that can pre-process, analyse and classify raw text to extract interpretable content; specifically, identifying topics and content-driven groupings of articles. We present here such a methodology that brings together powerful vector embeddings from Natural Language Processing with tools from Graph Theory that exploit diffusive dynamics on graphs to reveal natural partitions across scales. Our framework uses a recent deep neural network text analysis methodology (Doc2vec) to represent text in vector form and then applies a multi-scale community detection method (Markov Stability) to partition a similarity graph of document vectors. The method allows us to obtain clusters of documents with similar content, at different levels of resolution, in an unsupervised manner. We showcase our approach with the analysis of a corpus of 9,000 news articles published by Vox Media over one year. Our results show consistent groupings of documents according to content without a priori assumptions about the number or type of clusters to be found. The multilevel clustering reveals a quasi-hierarchy of topics and subtopics with increased intelligibility and improved topic coherence as compared to external taxonomy services and standard topic detection methods.

cs.CL↗

arXiv2018

From Text to Topics in Healthcare Records: An Unsupervised Graph Partitioning Methodology

Electronic Healthcare Records contain large volumes of unstructured data, including extensive free text. Yet this source of detailed information often remains under-used because of a lack of methodologies to extract interpretable content in a timely manner. Here we apply network-theoretical tools to analyse free text in Hospital Patient Incident reports from the National Health Service, to find clusters of documents with similar content in an unsupervised manner at different levels of resolution. We combine deep neural network paragraph vector text-embedding with multiscale Markov Stability community detection applied to a sparsified similarity graph of document vectors, and showcase the approach on incident reports from Imperial College Healthcare NHS Trust, London. The multiscale community structure reveals different levels of meaning in the topics of the dataset, as shown by descriptive terms extracted from the clusters of records. We also compare a posteriori against hand-coded categories assigned by healthcare personnel, and show that our approach outperforms LDA-based models. Our content clusters exhibit good correspondence with two levels of hand-coded categories, yet they also provide further medical detail in certain areas and reveal complementary descriptors of incidents beyond the external classification taxonomy.

cs.CL↗

arXiv2018

Structured networks and coarse-grained descriptions: a dynamical perspective

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.

cs.SI↗

arXiv2018

Flux-dependent graphs for metabolic networks

Cells adapt their metabolic fluxes in response to changes in the environment. We present a framework for the systematic construction of flux-based graphs derived from organism-wide metabolic networks. Our graphs encode the directionality of metabolic fluxes via edges that represent the flow of metabolites from source to target reactions. The methodology can be applied in the absence of a specific biological context by modelling fluxes probabilistically, or can be tailored to different environmental conditions by incorporating flux distributions computed through constraint-based approaches such as Flux Balance Analysis. We illustrate our approach on the central carbon metabolism of Escherichia coli and on a metabolic model of human hepatocytes. The flux-dependent graphs under various environmental conditions and genetic perturbations exhibit systemic changes in their topological and community structure, which capture the re-routing of metabolic fluxes and the varying importance of specific reactions and pathways. By integrating constraint-based models and tools from network science, our framework allows the study of context-specific metabolic responses at a system level beyond standard pathway descriptions.

q-bio.MN↗

arXiv2017

Geometric Multiscale Community Detection: Markov Stability and Vector Partitioning

Multiscale community detection can be viewed from a dynamical perspective within the Markov Stability framework, which uses the diffusion of a Markov process on the graph to uncover intrinsic network substructures across all scales. Here we reformulate multiscale community detection as a max-sum length vector partitioning problem with respect to the set of time-dependent node vectors expressed in terms of eigenvectors of the transition matrix. This formulation provides a geometric interpretation of Markov Stability in terms of a time-dependent spectral embedding, where the Markov time acts as an inhomogeneous geometric resolution factor that zooms the components of the node vectors at different rates. Our geometric formulation encompasses both modularity and the multi-resolution Potts model, which are shown to correspond to vector partitioning in a pseudo-Euclidean space, and is also linked to spectral partitioning methods, where the number of eigenvectors used corresponds to the dimensionality of the underlying embedding vector space. Inspired by the Louvain optimisation for community detection, we then propose an algorithm based on a graph-theoretical heuristic for the vector partitioning problem. We apply the algorithm to the spectral optimisation of modularity and Markov Stability community detection. The spectral embedding based on the transition matrix eigenvectors leads to improved partitions with higher information content and higher modularity than the eigen-decomposition of the modularity matrix. We illustrate the results with random network benchmarks.

cs.SI↗

arXiv2017

GlnK facilitates the dynamic regulation of bacterial nitrogen assimilation

Ammonium assimilation in E. coli is regulated by two paralogous proteins (GlnB and GlnK), which orchestrate interactions with regulators of gene expression, transport proteins and metabolic pathways. Yet how they conjointly modulate the activity of glutamine synthetase (GS), the key enzyme for nitrogen assimilation, is poorly understood. We combine experiments and theory to study the dynamic roles of GlnB and GlnK during nitrogen starvation and upshift. We measure time-resolved in vivo concentrations of metabolites, total and post-translationally modified proteins, and develop a concise biochemical model of GlnB and GlnK that incorporates competition for active and allosteric sites, as well as functional sequestration of GlnK. The model predicts the responses of GS, GlnB and GlnK under time-varying external ammonium level in the wild type and two genetic knock-outs. Our results show that GlnK is tightly regulated under nitrogen-rich conditions, yet it is expressed during ammonium run-out and starvation. This suggests a role for GlnK as a buffer of nitrogen shock after starvation, and provides a further functional link between nitrogen and carbon metabolisms.

q-bio.SC↗