Imperial College London

Till Hoffmann

Faculty of Natural SciencesDepartment of Mathematics

Academic Visitor







Sir Ernst Chain BuildingSouth Kensington Campus





Publication Type

6 results found

Hoffmann T, Jones NS, 2020, Inference of a universal social scale and segregation measures using social connectivity kernels, Journal of the Royal Society Interface, Vol: 17, ISSN: 1742-5662

How people connect with one another is a fundamental question in the social sciences, and the resulting social networks can have a profound impact on our daily lives. Blau offered a powerful explanation: people connect with one another based on their positions in a social space. Yet a principled measure of social distance, allowing comparison within and between societies, remains elusive.We use the connectivity kernel of conditionally-independent edge models to develop a family of segregation statistics with desirable properties: they offer an intuitive and universal characteristic scale on social space (facilitating comparison across datasets and societies), are applicable to multivariate and mixed node attributes, and capture segregation at the level of individuals, pairs of individuals, and society as a whole. We show that the segregation statistics can induce a metric on Blau space (a space spanned by the attributes of the members of society) and provide maps of two societies.Under a Bayesian paradigm, we infer the parameters of the connectivity kernel from eleven ego-network datasets collected in four surveys in the United Kingdom and United States. The importance of different dimensions of Blau space is similar across time and location, suggesting a macroscopically stable social fabric. Physical separation and age differences have the most significant impact on segregation within friendship networks with implications for intergenerational mixing and isolation in later stages of life.

Journal article

Hoffmann T, Peel L, Lambiotte R, Jones Net al., 2020, Community detection in networks without observing edges, Science Advances, Vol: 6, ISSN: 2375-2548

We develop a Bayesian hierarchical model to identify communities of time series. Fitting the model provides an end-to-end community detection algorithmthat does not extract information as a sequence of point estimates but propagates uncertainties from the raw data to the community labels. Our approachnaturally supports multiscale community detection as well as the selection ofan optimal scale using model comparison. We study the properties of the algorithm using synthetic data and apply it to daily returns of constituents of theS&P100 index as well as climate data from US cities.

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

Hoffmann T, Lambiotte R, Porter MA, 2013, Decentralized routing on spatial networks with stochastic edge weights, Physical Review E, Vol: 88, ISSN: 1539-3755

Journal article

Hoffmann TA, Porter MA, Lambiotte R, 2013, Random Walks on Stochastic Temporal Networks, Temporal Networks, Editors: Holme, Saramäki, Publisher: Springer Verlag, Pages: 295-313, ISBN: 9783642364600

In the study of dynamical processes on networks, there has been intense focus on network structure—i.e., the arrangement of edges and their associated weights—but the effects of the temporal patterns of edges remains poorly understood. In this chapter, we develop a mathematical framework for random walks on temporal networks using an approach that provides a compromise between abstract but unrealistic models and data-driven but non-mathematical approaches. To do this, we introduce a stochastic modelfor temporal networks in which we summarize the temporal and structural organization of a system using a matrix of waiting-time distributions. We show that random walks on stochastic temporal networks can be described exactly by an integro-differential master equation and derive an analytical expression for its asymptotic steady state. We also discuss how our work might be useful to help build centrality measures for temporal networks.

Book chapter

Hoffmann T, Porter MA, Lambiotte R, 2012, Generalized master equations for non-Poisson dynamics on networks, Physical Review E, Vol: 86, ISSN: 1539-3755

Journal article

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