Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes

Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model on weighted simplicial complexes with phases supported on simplices of any order k, we introduce linear and non-linear frustration terms independent of the orientation of the k + 1 simplices, as a natural generalization of the Sakaguchi-Kuramoto model to simplicial complexes. With increasingly complex simplicial complexes, we study the the dynamics of the edge simplicial Sakaguchi-Kuramoto model with nonlinear frustration to highlight the complexity of emerging dynamical behaviors. We discover various dynamical phenomena, such as the partial loss of synchronization in subspaces aligned with the Hodge subspaces and the emergence of simplicial phase re-locking in regimes of high frustration

Kernel-based Joint Independence Tests for Multivariate Stationary and Non-stationary Time Series

Multivariate time series data that capture the temporal evolution of interconnected systems are ubiquitous in diverse areas. Understanding the complex relationships and potential dependencies among co-observed variables is crucial for the accurate statistical modelling and analysis of such systems. Here, we introduce kernel-based statistical tests of joint independence in multivariate time series by extending the $d$-variable Hilbert-Schmidt independence criterion (dHSIC) to encompass both stationary and non-stationary processes, thus allowing broader real-world applications. By leveraging resampling techniques tailored for both single- and multiple-realisation time series, we show how the method robustly uncovers significant higher-order dependencies in synthetic examples, including frequency mixing data and logic gates, as well as real-world climate and socioeconomic data. Our method adds to the mathematical toolbox for the analysis of multivariate time series and can aid in uncovering high-order interactions in data.Comment: 15 pages, 7 figure

Bostonia. Volume 13

Founded in 1900, Bostonia magazine is Boston University's main alumni publication, which covers alumni and student life, as well as university activities, events, and programs

A unified framework for Simplicial Kuramoto models

Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models, categorized into three main groups: "simple" models, "Hodge-coupled" models, and "order-coupled" (Dirac) models. Our framework is based on topology, discrete differential geometry as well as gradient flows and frustrations, and permits a systematic analysis of their properties. We establish an equivalence between the simple simplicial Kuramoto model and the standard Kuramoto model on pairwise networks under the condition of manifoldness of the simplicial complex. Then, starting from simple models, we describe the notion of simplicial synchronization and derive bounds on the coupling strength necessary or sufficient for achieving it. For some variants, we generalize these results and provide new ones, such as the controllability of equilibrium solutions. Finally, we explore a potential application in the reconstruction of brain functional connectivity from structural connectomes and find that simple edge-based Kuramoto models perform competitively or even outperform complex extensions of node-based models.Comment: 36 pages, 11 figure

Network memory in the movement of hospital patients carrying antimicrobial-resistant bacteria

Hospitals constitute highly interconnected systems that bring into contact an abundance of infectious pathogens and susceptible individuals, thus making infection outbreaks both common and challenging. In recent years, there has been a sharp incidence of antimicrobial-resistance amongst healthcare-associated infections, a situation now considered endemic in many countries. Here we present network-based analyses of a data set capturing the movement of patients harbouring drug-resistant bacteria across three large London hospitals. We show that there are substantial memory effects in the movement of hospital patients colonised with drug-resistant bacteria. Such memory effects break first-order Markovian transitive assumptions and substantially alter the conclusions from the analysis, specifically on node rankings and the evolution of diffusive processes. We capture variable length memory effects by constructing a lumped-state memory network, which we then use to identify overlapping communities of wards. We find that these communities of wards display a quasi-hierarchical structure at different levels of granularity which is consistent with different aspects of patient flows related to hospital locations and medical specialties

Informing antimicrobial management in the context of COVID-19:Understanding the longitudinal dynamics of C-reactive protein and procalcitonin

Background: To characterise the longitudinal dynamics of C-reactive protein (CRP) and Procalcitonin (PCT) in a cohort of hospitalised patients with COVID-19 and support antimicrobial decision-making. Methods: Longitudinal CRP and PCT concentrations and trajectories of 237 hospitalised patients with COVID-19 were modelled. The dataset comprised of 2,021 data points for CRP and 284 points for PCT. Pairwise comparisons were performed between: (i) those with or without significant bacterial growth from cultures, and (ii) those who survived or died in hospital. Results: CRP concentrations were higher over time in COVID-19 patients with positive microbiology (day 9: 236 vs 123 mg/L, p < 0.0001) and in those who died (day 8: 226 vs 152 mg/L, p < 0.0001) but only after day 7 of COVID-related symptom onset. Failure for CRP to reduce in the first week of hospital admission was associated with significantly higher odds of death. PCT concentrations were higher in patients with COVID-19 and positive microbiology or in those who died, although these differences were not statistically significant. Conclusions: Both the absolute CRP concentration and the trajectory during the first week of hospital admission are important factors predicting microbiology culture positivity and outcome in patients hospitalised with COVID-19. Further work is needed to describe the role of PCT for co-infection. Understanding relationships of these biomarkers can support development of risk models and inform optimal antimicrobial strategies