Mauricio Barahona

Michael T. Schaub, Jean-Charles Delvenne, Renaud Lambiotte et al.

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.

Adam Gosztolai, Robert L. Peach, Alexis Arnaudon et al.

The dynamics of neuron populations commonly evolve on low-dimensional manifolds. Thus, we need methods that learn the dynamical processes over neural manifolds to infer interpretable and consistent latent representations. We introduce a representation learning method, MARBLE, that decomposes on-manifold dynamics into local flow fields and maps them into a common latent space using unsupervised geometric deep learning. In simulated non-linear dynamical systems, recurrent neural networks, and experimental single-neuron recordings from primates and rodents, we discover emergent low-dimensional latent representations that parametrise high-dimensional neural dynamics during gain modulation, decision-making, and changes in the internal state. These representations are consistent across neural networks and animals, enabling the robust comparison of cognitive computations. Extensive benchmarking demonstrates state-of-the-art within- and across-animal decoding accuracy of MARBLE compared with current representation learning approaches, with minimal user input. Our results suggest that manifold structure provides a powerful inductive bias to develop powerful decoding algorithms and assimilate data across experiments.

Aivar Sootla, Natalja Strelkowa, Damien Ernst et al.

In this paper, we consider the periodic reference tracking problem in the framework of batch-mode reinforcement learning, which studies methods for solving optimal control problems from the sole knowledge of a set of trajectories. In particular, we extend an existing batch-mode reinforcement learning algorithm, known as Fitted Q Iteration, to the periodic reference tracking problem. The presented periodic reference tracking algorithm explicitly exploits a priori knowledge of the future values of the reference trajectory and its periodicity. We discuss the properties of our approach and illustrate it on the problem of reference tracking for a synthetic biology gene regulatory network known as the generalised repressilator. This system can produce decaying but long-lived oscillations, which makes it an interesting system for the tracking problem. In our companion paper we also take a look at the regulation problem of the toggle switch system, where the main goal is to drive the system's states to a specific bounded region in the state space.

Mariano Beguerisse-Diaz, Baojun Wang, Radhika Desikan et al.

Motivation: Estimating parameters from data is a key stage of the modelling process, particularly in biological systems where many parameters need to be estimated from sparse and noisy data sets. Over the years, a variety of heuristics have been proposed to solve this complex optimisation problem, with good results in some cases yet with limitations in the biological setting. Results: In this work, we develop an algorithm for model parameter fitting that combines ideas from evolutionary algorithms, sequential Monte Carlo and direct search optimisation. Our method performs well even when the order of magnitude and/or the range of the parameters is unknown. The method refines iteratively a sequence of parameter distributions through local optimisation combined with partial resampling from a historical prior defined over the support of all previous iterations. We exemplify our method with biological models using both simulated and real experimental data and estimate the parameters efficiently even in the absence of a priori knowledge about the parameters.

Zhaolu Liu, Robert L. Peach, Pedro A. M. Mediano et al.

Models that rely solely on pairwise relationships often fail to capture the complete statistical structure of the complex multivariate data found in diverse domains, such as socio-economic, ecological, or biomedical systems. Non-trivial dependencies between groups of more than two variables can play a significant role in the analysis and modelling of such systems, yet extracting such high-order interactions from data remains challenging. Here, we introduce a hierarchy of $d$-order ($d \geq 2$) interaction measures, increasingly inclusive of possible factorisations of the joint probability distribution, and define non-parametric, kernel-based tests to establish systematically the statistical significance of $d$-order interactions. We also establish mathematical links with lattice theory, which elucidate the derivation of the interaction measures and their composite permutation tests; clarify the connection of simplicial complexes with kernel matrix centring; and provide a means to enhance computational efficiency. We illustrate our results numerically with validations on synthetic data, and through an application to neuroimaging data.

Thomas Wong, Mauricio Barahona

This paper is a work in progress. We are looking for collaborators to provide us financial datasets in Equity/Futures market to conduct more bench-marking studies. The authors have papers employing similar methods applied on the Numerai dataset, which is freely available but obfuscated. We apply different feature engineering methods for time-series to US market price data. The predictive power of models are tested against Numerai-Signals targets.

Asem Alaa, Erik Mayer, Mauricio Barahona

Early diagnosis of disease can lead to improved health outcomes, including higher survival rates and lower treatment costs. With the massive amount of information available in electronic health records (EHRs), there is great potential to use machine learning (ML) methods to model disease progression aimed at early prediction of disease onset and other outcomes. In this work, we employ recent innovations in neural ODEs combined with rich semantic embeddings of clinical codes to harness the full temporal information of EHRs. We propose ICE-NODE (Integration of Clinical Embeddings with Neural Ordinary Differential Equations), an architecture that temporally integrates embeddings of clinical codes and neural ODEs to learn and predict patient trajectories in EHRs. We apply our method to the publicly available MIMIC-III and MIMIC-IV datasets, and we find improved prediction results compared to state-of-the-art methods, specifically for clinical codes that are not frequently observed in EHRs. We also show that ICE-NODE is more competent at predicting certain medical conditions, like acute renal failure, pulmonary heart disease and birth-related problems, where the full temporal information could provide important information. Furthermore, ICE-NODE is also able to produce patient risk trajectories over time that can be exploited for further detailed predictions of disease evolution.

Felix Laumann, Zhaolu Liu, Mauricio Barahona

The Hilbert-Schmidt Independence Criterion (HSIC) and its joint-independence extension $d\mathrm{HSIC}$ are degenerate $V$-statistics whose data-dependent weighted-$χ^2$ null limits force a permutation calibration that multiplies the per-test cost by the number of permutations, in practice two orders of magnitude. Adapting the recent martingale MMD construction for two-sample testing to the (joint) independence problem, we introduce two studentised statistics whose null distributions are standard normal regardless of the data law, so that a single normal-quantile lookup replaces the permutation step entirely. The first, $m\mathrm{HSIC}$, is a self-normalised lower-triangular sum of the Hadamard product of two empirically centred Gram matrices. Under independence and bounded-fourth-moment kernels it converges to a standard normal. It is consistent against every fixed alternative, and runs at quadratic cost in the sample size without any sample split, matching the biased HSIC $V$-statistic. Our second statistic, $md\mathrm{HSIC}$, achieves finite-sample consistency with a single half-sample split: the centring is estimated on one half and the lower-triangular self-normalised martingale is run on the other, shrinking the conditional-mean residual to a quantity that is exponentially small in $d$, so the statistic is asymptotically standard normal at every fixed number of jointly tested variables, with a per-test cost that grows only linearly in $d$. On synthetic data with per-variable input dimension from $1$ to $500$ and between $2$ and $10$ jointly tested variables, both statistics match the empirical type-I error rate and test power of permutation-calibrated baselines while running $25$ to $60\times$ faster.

Mihir Dhanakshirur, Felix Laumann, Junhyung Park et al.

Understanding and adequately assessing the difference between a true and a learnt causal graphs is crucial for causal inference under interventions. As an extension to the graph-based structural Hamming distance and structural intervention distance, we propose a novel continuous-measured metric that considers the underlying data in addition to the graph structure for its calculation of the difference between a true and a learnt causal graph. The distance is based on embedding intervention distributions over each pair of nodes as conditional mean embeddings into reproducing kernel Hilbert spaces and estimating their difference by the maximum (conditional) mean discrepancy. We show theoretical results which we validate with numerical experiments on synthetic data.

Sung En Chiang, Zhaolu Liu, Robert L. Peach et al.

Analyzing causality in multivariate systems involves establishing how information is generated, distributed and combined. Traditional causal discovery frameworks are capable of multivariate reasoning but their intrinsic pairwise graph topology restricts them to do so only indirectly by integrating multivariate information across pairwise edges. Higher-order information theory provides direct tools that can explicitly model higher-order interactions. In particular, Partial Information Decomposition (PID) allows the decomposition of the information that a set of sources provides about a target into redundant, unique, and synergistic components. Yet the mathematical connection between such higher-order information-theoretic measures and causal structure remains undeveloped. Here we establish the first theoretical correspondence between PID components and causal structure in both Bayesian networks and hypergraphs. We first show that in Bayesian networks unique information precisely characterizes direct causal neighbors, while synergy identifies collider relationships. This establishes a localist causal discovery paradigm in which the structure surrounding each variable can be recovered from its immediate informational footprint, eliminating the need for global search over graph space. Extending these results to more expressive causal representation, we prove that PID signatures in Bayesian hypergraphs differentiate parents, children, co-heads, and co-tails, revealing a novel collider effect unique to multi-tail hyperedges. Our results position PID as a rigorous, model-agnostic foundation for inferring both pairwise and higher-order causal structure, and introduce a fundamentally local information-theoretic viewpoint on causal discovery.

Thomas Wong, Mauricio Barahona

The application of deep learning to non-stationary temporal datasets can lead to overfitted models that underperform under regime changes. In this work, we propose a modular machine learning pipeline for ranking predictions on temporal panel datasets which is robust under regime changes. The modularity of the pipeline allows the use of different models, including Gradient Boosting Decision Trees (GBDTs) and Neural Networks, with and without feature engineering. We evaluate our framework on financial data for stock portfolio prediction, and find that GBDT models with dropout display high performance, robustness and generalisability with reduced complexity and computational cost. We then demonstrate how online learning techniques, which require no retraining of models, can be used post-prediction to enhance the results. First, we show that dynamic feature projection improves robustness by reducing drawdown in regime changes. Second, we demonstrate that dynamical model ensembling based on selection of models with good recent performance leads to improved Sharpe and Calmar ratios of out-of-sample predictions. We also evaluate the robustness of our pipeline across different data splits and random seeds with good reproducibility.

Thomas Wong, Mauricio Barahona

We present a robust deep incremental learning framework for regression tasks on financial temporal tabular datasets which is built upon the incremental use of commonly available tabular and time series prediction models to adapt to distributional shifts typical of financial datasets. The framework uses a simple basic building block (decision trees) to build self-similar models of any required complexity to deliver robust performance under adverse situations such as regime changes, fat-tailed distributions, and low signal-to-noise ratios. As a detailed study, we demonstrate our scheme using XGBoost models trained on the Numerai dataset and show that a two layer deep ensemble of XGBoost models over different model snapshots delivers high quality predictions under different market regimes. We also show that the performance of XGBoost models with different number of boosting rounds in three scenarios (small, standard and large) is monotonically increasing with respect to model size and converges towards the generalisation upper bound. We also evaluate the robustness of the model under variability of different hyperparameters, such as model complexity and data sampling settings. Our model has low hardware requirements as no specialised neural architectures are used and each base model can be independently trained in parallel.

Dimitar Georgiev, Álvaro Fernández-Galiana, Simon Vilms Pedersen et al.

Raman spectroscopy is widely used across scientific domains to characterize the chemical composition of samples in a non-destructive, label-free manner. Many applications entail the unmixing of signals from mixtures of molecular species to identify the individual components present and their proportions, yet conventional methods for chemometrics often struggle with complex mixture scenarios encountered in practice. Here, we develop hyperspectral unmixing algorithms based on autoencoder neural networks, and we systematically validate them using both synthetic and experimental benchmark datasets created in-house. Our results demonstrate that unmixing autoencoders provide improved accuracy, robustness and efficiency compared to standard unmixing methods. We also showcase the applicability of autoencoders to complex biological settings by showing improved biochemical characterization of volumetric Raman imaging data from a monocytic cell.

Juni Schindler, Mauricio Barahona

Datasets often possess an intrinsic multiscale structure with meaningful descriptions at different levels of coarseness. Such datasets are naturally described as multi-resolution clusterings, i.e., not necessarily hierarchical sequences of partitions across scales. To analyse and compare such sequences, we use tools from topological data analysis and define the Multiscale Clustering Bifiltration (MCbiF), a 2-parameter filtration of abstract simplicial complexes that encodes cluster intersection patterns across scales. The MCbiF can be interpreted as a higher-order extension of Sankey diagrams and reduces to a dendrogram for hierarchical sequences. We show that the multiparameter persistent homology (MPH) of the MCbiF yields a finitely presented and block decomposable module, and its stable Hilbert functions characterise the topological autocorrelation of the sequence of partitions. In particular, at dimension zero, the MPH captures violations of the refinement order of partitions, whereas at dimension one, the MPH captures higher-order inconsistencies between clusters across scales. We demonstrate through experiments the use of MCbiF Hilbert functions as topological feature maps for downstream machine learning tasks. MCbiF feature maps outperform information-based baseline features on both regression and classification tasks on synthetic sets of non-hierarchical sequences of partitions. We also show an application of MCbiF to real-world data to measure non-hierarchies in wild mice social grouping patterns across time.

Juni Schindler, Sneha Jha, Xixuan Zhang et al.

We present Local Graph-based Dictionary Expansion (LGDE), a method for data-driven discovery of the semantic neighbourhood of words using tools from manifold learning and network science. At the heart of LGDE lies the creation of a word similarity graph from the geometry of word embeddings followed by local community detection based on graph diffusion. The diffusion in the local graph manifold allows the exploration of the complex nonlinear geometry of word embeddings to capture word similarities based on paths of semantic association, over and above direct pairwise similarities. Exploiting such semantic neighbourhoods enables the expansion of dictionaries of pre-selected keywords, an important step for tasks in information retrieval, such as database queries and online data collection. We validate LGDE on two user-generated English-language corpora and show that LGDE enriches the list of keywords with improved performance relative to methods based on direct word similarities or co-occurrences. We further demonstrate our method through a real-world use case from communication science, where LGDE is evaluated quantitatively on the expansion of a conspiracy-related dictionary from online data collected and analysed by domain experts. Our empirical results and expert user assessment indicate that LGDE expands the seed dictionary with more useful keywords due to the manifold-learning-based similarity network.

Juni Schindler, Mauricio Barahona

In data clustering, it is often desirable to find not just a single partition into clusters but a sequence of partitions that describes the data at different scales (or levels of coarseness). A natural problem then is to analyse and compare the (not necessarily hierarchical) sequences of partitions that underpin such multiscale descriptions. Here, we use tools from topological data analysis and introduce the Multiscale Clustering Filtration (MCF), a well-defined and stable filtration of abstract simplicial complexes that encodes arbitrary cluster assignments in a sequence of partitions across scales of increasing coarseness. We show that the zero-dimensional persistent homology of the MCF measures the degree of hierarchy of this sequence, and the higher-dimensional persistent homology tracks the emergence and resolution of conflicts between cluster assignments across the sequence of partitions. To broaden the theoretical foundations of the MCF, we provide an equivalent construction via a nerve complex filtration, and we show that, in the hierarchical case, the MCF reduces to a Vietoris-Rips filtration of an ultrametric space. Using synthetic data, we then illustrate how the persistence diagram of the MCF provides a feature map that can serve to characterise and classify multiscale clusterings.

Zijing Liu, Mauricio Barahona

We propose a similarity measure for sparsely sampled time course data in the form of a log-likelihood ratio of Gaussian processes (GP). The proposed GP similarity is similar to a Bayes factor and provides enhanced robustness to noise in sparse time series, such as those found in various biological settings, e.g., gene transcriptomics. We show that the GP measure is equivalent to the Euclidean distance when the noise variance in the GP is negligible compared to the noise variance of the signal. Our numerical experiments on both synthetic and real data show improved performance of the GP similarity when used in conjunction with two distance-based clustering methods.

M. Tarik Altuncu, Sophia N. Yaliraki, Mauricio Barahona

Production of news content is growing at an astonishing rate. To help manage and monitor the sheer amount of text, there is an increasing need to develop efficient methods that can provide insights into emerging content areas, and stratify unstructured corpora of text into `topics' that stem intrinsically from content similarity. Here we present an unsupervised framework that brings together powerful vector embeddings from natural language processing with tools from multiscale graph partitioning that can reveal natural partitions at different resolutions without making a priori assumptions about the number of clusters in the corpus. We show the advantages of graph-based clustering through end-to-end comparisons with other popular clustering and topic modelling methods, and also evaluate different text vector embeddings, from classic Bag-of-Words to Doc2Vec to the recent transformers based model Bert. This comparative work is showcased through an analysis of a corpus of US news coverage during the presidential election year of 2016.

Yun William Yu, Jean-Charles Delvenne, Sophia N. Yaliraki et al.

A major goal of dynamical systems theory is the search for simplified descriptions of the dynamics of a large number of interacting states. For overwhelmingly complex dynamical systems, the derivation of a reduced description on the entire dynamics at once is computationally infeasible. Other complex systems are so expansive that despite the continual onslaught of new data only partial information is available. To address this challenge, we define and optimise for a local quality function severability for measuring the dynamical coherency of a set of states over time. The theoretical underpinnings of severability lie in our local adaptation of the Simon-Ando-Fisher time-scale separation theorem, which formalises the intuition of local wells in the Markov landscape of a dynamical process, or the separation between a microscopic and a macroscopic dynamics. Finally, we demonstrate the practical relevance of severability by applying it to examples drawn from power networks, image segmentation, social networks, metabolic networks, and word association.

Stamatina Lamprinakou, Mauricio Barahona, Seth Flaxman et al.

The effectiveness of Bayesian Additive Regression Trees (BART) has been demonstrated in a variety of contexts including non-parametric regression and classification. A BART scheme for estimating the intensity of inhomogeneous Poisson processes is introduced. Poisson intensity estimation is a vital task in various applications including medical imaging, astrophysics and network traffic analysis. The new approach enables full posterior inference of the intensity in a non-parametric regression setting. The performance of the novel scheme is demonstrated through simulation studies on synthetic and real datasets up to five dimensions, and the new scheme is compared with alternative approaches.

Yifan Qian, Paul Expert, Pietro Panzarasa et al.

Traditional classification tasks learn to assign samples to given classes based solely on sample features. This paradigm is evolving to include other sources of information, such as known relations between samples. Here we show that, even if additional relational information is not available in the data set, one can improve classification by constructing geometric graphs from the features themselves, and using them within a Graph Convolutional Network. The improvement in classification accuracy is maximized by graphs that capture sample similarity with relatively low edge density. We show that such feature-derived graphs increase the alignment of the data to the ground truth while improving class separation. We also demonstrate that the graphs can be made more efficient using spectral sparsification, which reduces the number of edges while still improving classification performance. We illustrate our findings using synthetic and real-world data sets from various scientific domains.

Robert L. Peach, Alexis Arnaudon, Mauricio Barahona

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.

Zijing Liu, Mauricio Barahona

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.

M. Tarik Altuncu, Eloise Sorin, Joshua D. Symons et al.

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.

Amadeus Maes, Mauricio Barahona, Claudia Clopath

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.

Yifan Qian, Paul Expert, Tom Rieu et al.

We show that the classification performance of graph convolutional networks (GCNs) is related to the alignment between features, graph, and ground truth, which we quantify using a subspace alignment measure (SAM) corresponding to the Frobenius norm of the matrix of pairwise chordal distances between three subspaces associated with features, graph, and ground truth. The proposed measure is based on the principal angles between subspaces and has both spectral and geometrical interpretations. We showcase the relationship between the SAM and the classification performance through the study of limiting cases of GCNs and systematic randomizations of both features and graph structure applied to a constructive example and several examples of citation networks of different origins. The analysis also reveals the relative importance of the graph and features for classification purposes.

M. Tarik Altuncu, Erik Mayer, Sophia N. Yaliraki et al.

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.

M. Tarik Altuncu, Sophia N. Yaliraki, Mauricio Barahona

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.

M. Tarik Altuncu, Erik Mayer, Sophia N. Yaliraki et al.

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.

Michael T. Schaub, Neave O'Clery, Yazan N. Billeh et al.

Synchronization over networks depends strongly on the structure of the coupling between the oscillators. When the coupling presents certain regularities, the dynamics can be coarse-grained into clusters by means of External Equitable Partitions of the network graph and their associated quotient graphs. We exploit this graph-theoretical concept to study the phenomenon of cluster synchronization, in which different groups of nodes converge to distinct behaviors. We derive conditions and properties of networks in which such clustered behavior emerges, and show that the ensuing dynamics is the result of the localization of the eigenvectors of the associated graph Laplacians linked to the existence of invariant subspaces. The framework is applied to both linear and non-linear models, first for the standard case of networks with positive edges, before being generalized to the case of signed networks with both positive and negative interactions. We illustrate our results with examples of both signed and unsigned graphs for consensus dynamics and for partial synchronization of oscillator networks under the master stability function as well as Kuramoto oscillators.

Mariano Beguerisse-Díaz, Amy K. McLennan, Guillermo Garduño-Hernández et al.

Social media are being increasingly used for health promotion, yet the landscape of users, messages and interactions in such fora is poorly understood. Studies of social media and diabetes have focused mostly on patients, or public agencies addressing it, but have not looked broadly at all the participants or the diversity of content they contribute. We study Twitter conversations about diabetes through the systematic analysis of 2.5 million tweets collected over 8 months and the interactions between their authors. We address three questions: (1) what themes arise in these tweets?, (2) who are the most influential users?, (3) which type of users contribute to which themes? We answer these questions using a mixed-methods approach, integrating techniques from anthropology, network science and information retrieval such as thematic coding, temporal network analysis, and community and topic detection. Diabetes-related tweets fall within broad thematic groups: health information, news, social interaction, and commercial. At the same time, humorous messages and references to popular culture appear consistently, more than any other type of tweet. We classify authors according to their temporal 'hub' and 'authority' scores. Whereas the hub landscape is diffuse and fluid over time, top authorities are highly persistent across time and comprise bloggers, advocacy groups and NGOs related to diabetes, as well as for-profit entities without specific diabetes expertise. Top authorities fall into seven interest communities as derived from their Twitter follower network. Our findings have implications for public health professionals and policy makers who seek to use social media as an engagement tool and to inform policy design.

Aivar Sootla, Natalja Strelkowa, Damien Ernst et al.

In this paper, we consider the problem of optimal exogenous control of gene regulatory networks. Our approach consists in adapting an established reinforcement learning algorithm called the fitted Q iteration. This algorithm infers the control law directly from the measurements of the system's response to external control inputs without the use of a mathematical model of the system. The measurement data set can either be collected from wet-lab experiments or artificially created by computer simulations of dynamical models of the system. The algorithm is applicable to a wide range of biological systems due to its ability to deal with nonlinear and stochastic system dynamics. To illustrate the application of the algorithm to a gene regulatory network, the regulation of the toggle switch system is considered. The control objective of this problem is to drive the concentrations of two specific proteins to a target region in the state space.