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• JOURNAL ARTICLE
Grandjean L, Gilman RH, Iwamoto T, Koser CU, Coronel J, Zimic M, Torok ME, Ayabina D, Kendall M, Fraser C, Harris S, Parkhill J, Peacock SJ, Moore DAJ, Colijn Cet al., 2017,

### Convergent evolution and topologically disruptive polymorphisms among multidrug-resistant tuberculosis in Peru

, PLOS ONE, Vol: 12, ISSN: 1932-6203
• JOURNAL ARTICLE
Kiselev VY, Kirschner K, Schaub MT, Andrews T, Yiu A, Chandra T, Natarajan KN, Reik W, Barahona M, Green AR, Hemberg Met al., 2017,

### SC3: consensus clustering of single-cell RNA-seq data

, NATURE METHODS, Vol: 14, Pages: 483-+, ISSN: 1548-7091
• JOURNAL ARTICLE
Kuntz J, Thomas P, Stan G-B, Barahona Met al., 2017,

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

The stochastic dynamics of networks of biochemical reactions in living cellsare typically modelled using chemical master equations (CMEs). The stationarydistributions of CMEs are seldom solvable analytically, and few methods existthat yield numerical estimates with computable error bounds. Here, we presenttwo such methods based on mathematical programming techniques. First, we usesemidefinite programming to obtain increasingly tighter upper and lower boundson the moments of the stationary distribution for networks with rationalpropensities. Second, we employ linear programming to compute convergent upperand lower bounds on the stationary distributions themselves. The boundsobtained provide a computational test for the uniqueness of the stationarydistribution. In the unique case, the bounds collectively form an approximationof the stationary distribution accompanied with a computable $\ell^1$-errorbound. In the non-unique case, we explain how to adapt our approach so that ityields approximations of the ergodic distributions, also accompanied withcomputable error bounds. We illustrate our methodology through two biologicalexamples: Schl\"ogl's model and a toggle switch model.

• JOURNAL ARTICLE
Liu Z, Barahona M, 2017,

### Geometric multiscale community detection: Markov stability and vector partitioning

, Journal of Complex Networks, ISSN: 2051-1329

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 optimization 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 optimization 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.

• JOURNAL ARTICLE
Amor BRC, Schaub MT, Yaliraki SN, Barahona Met al., 2016,

### Prediction of allosteric sites and mediating interactions through bond-to-bond propensities

, NATURE COMMUNICATIONS, Vol: 7, ISSN: 2041-1723
• BOOK CHAPTER
Amor BRC, Vuik SI, Callahan R, Darzi A, Yaliraki SN, Barahona Met al., 2016,

### Community detection and role identification in directed networks: Understanding the twitter network of the care.data debate

, Dynamic Networks and Cyber-Security, Pages: 111-136, ISBN: 9781786340757

© 2016 by World Scientific Publishing Europe Ltd. All rights reserved. With the rise of social media as an important channel for the debate and discussion of public affairs, online social networks such as Twitter have become important platforms for public information and engagement by policy makers. To communicate effectively through Twitter, policy makers need to understand how influence and interest propagate within its network of users. In this chapter, we use graph-theoretic methods to analyse the Twitter debate surrounding NHS England's controversial care.data scheme. Directionality is a crucial feature of the Twitter social graph - information flows from the followed to the followers - but is often ignored in social network analyses; our methods are based on the behaviour of dynamic processes on the network and can be applied naturally to directed networks. We uncover robust communities of users and show that these communities reflect how information flows through the Twitter network. We are also able to classify users by their differing roles in directing the flow of information through the network. Our methods and results will be useful to policy makers who would like to use Twitter effectively as a communication medium.

• JOURNAL ARTICLE
Bacik KA, Schaub MT, Beguerisse-Diaz M, Billeh YN, Barahona Met al., 2016,

### Flow-Based Network Analysis of the Caenorhabditis elegans Connectome

, PLOS Computational Biology, Vol: 12, ISSN: 1553-734X

We exploit flow propagation on the directed neuronal network of the nematode C. elegans to reveal dynamically relevant features of its connectome. We find flow-based groupings of neurons at different levels of granularity, which we relate to functional and anatomical constituents of its nervous system. A systematic in silico evaluation of the full set of single and double neuron ablations is used to identify deletions that induce the most severe disruptions of the multi-resolution flow structure. Such ablations are linked to functionally relevant neurons, and suggest potential candidates for further in vivo investigation. In addition, we use the directional patterns of incoming and outgoing network flows at all scales to identify flow profiles for the neurons in the connectome, without pre-imposing a priori categories. The four flow roles identified are linked to signal propagation motivated by biological input-response scenarios.

• JOURNAL ARTICLE
Beguerisse Diaz M, Desikan R, Barahona M, 2016,

### Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction

, Journal of the Royal Society Interface, Vol: 13, ISSN: 1742-5689

Cellular signal transduction usually involves activation cascades, the sequential activation of a series of proteins following the reception of an input signal. Here we study the classic model of weakly activated cascades and obtain analytical solutions for a variety of inputs. We show that in the special but important case of optimal-gain cascades (i.e., when the deactivation rates are identical) the downstream output of the cascade can be represented exactly as a lumped nonlinear module containing an incomplete gamma function with real parameters that depend on the rates and length of the cascade, as well as parameters of the input signal. The expressions obtained can be applied to the non-identical case when the deactivation rates are random to capture the variability in the cascade outputs. We also show that cascades can be rearranged so that blocks with similar rates can be lumped and represented through our nonlinear modules. Our results can be used both to represent cascades in computational models of differential equations and to fit data efficiently, by reducing the number of equations and parameters involved. In particular, the length of the cascade appears as a real-valued parameter and can thus be fitted in the same manner as Hill coefficients. Finally, we show how the obtained nonlinear modules can be used instead of delay differential equations to model delays in signal transduction.

• JOURNAL ARTICLE
Johnston IG, Jones NS, 2016,

### Evolution of Cell-to-Cell Variability in Stochastic, Controlled, Heteroplasmic mtDNA Populations

, AMERICAN JOURNAL OF HUMAN GENETICS, Vol: 99, Pages: 1150-1162, ISSN: 0002-9297
• JOURNAL ARTICLE
Kuntz J, Ottobre M, Stan G-B, Barahona Met al., 2016,

### BOUNDING STATIONARY AVERAGES OF POLYNOMIAL DIFFUSIONS VIA SEMIDEFINITE PROGRAMMING

, SIAM JOURNAL ON SCIENTIFIC COMPUTING, Vol: 38, Pages: A3891-A3920, ISSN: 1064-8275

This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.

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