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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 and discrete differential geometry, as well as gradient systems 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., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

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 to encompass both stationary and non-stationary processes, thus allowing broader real-world applications. By leveraging resampling techniques tailored for both single- and multiple-realization 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, neuroscience and socio-economic 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., Competing Interests: We declare we have no competing interests., (© 2023 The Authors.)

Background: Real-time prediction is key to prevention and control of infections associated with health-care settings. Contacts enable spread of many infections, yet most risk prediction frameworks fail to account for their dynamics. We developed, tested, and internationally validated a real-time machine-learning framework, incorporating dynamic patient-contact networks to predict hospital-onset COVID-19 infections (HOCIs) at the individual level., Methods: We report an international retrospective cohort study of our framework, which extracted patient-contact networks from routine hospital data and combined network-derived variables with clinical and contextual information to predict individual infection risk. We trained and tested the framework on HOCIs using the data from 51 157 hospital inpatients admitted to a UK National Health Service hospital group (Imperial College Healthcare NHS Trust) between April 1, 2020, and April 1, 2021, intersecting the first two COVID-19 surges. We validated the framework using data from a Swiss hospital group (Department of Rehabilitation, Geneva University Hospitals) during a COVID-19 surge (from March 1 to May 31, 2020; 40 057 inpatients) and from the same UK group after COVID-19 surges (from April 2 to Aug 13, 2021; 43 375 inpatients). All inpatients with a bed allocation during the study periods were included in the computation of network-derived and contextual variables. In predicting patient-level HOCI risk, only inpatients spending 3 or more days in hospital during the study period were examined for HOCI acquisition risk., Findings: The framework was highly predictive across test data with all variable types (area under the curve [AUC]-receiver operating characteristic curve [ROC] 0·89 [95% CI 0·88-0·90]) and similarly predictive using only contact-network variables (0·88 [0·86-0·90]). Prediction was reduced when using only hospital contextual (AUC-ROC 0·82 [95% CI 0·80-0·84]) or patient clinical (0·64 [0·62-0·66]) variables. A model with only three variables (ie, network closeness, direct contacts with infectious patients [network derived], and hospital COVID-19 prevalence [hospital contextual]) achieved AUC-ROC 0·85 (95% CI 0·82-0·88). Incorporating contact-network variables improved performance across both validation datasets (AUC-ROC in the Geneva dataset increased from 0·84 [95% CI 0·82-0·86] to 0·88 [0·86-0·90]; AUC-ROC in the UK post-surge dataset increased from 0·49 [0·46-0·52] to 0·68 [0·64-0·70])., Interpretation: Dynamic contact networks are robust predictors of individual patient risk of HOCIs. Their integration in clinical care could enhance individualised infection prevention and early diagnosis of COVID-19 and other nosocomial infections., Funding: Medical Research Foundation, WHO, Engineering and Physical Sciences Research Council, National Institute for Health Research (NIHR), Swiss National Science Foundation, and German Research Foundation., Competing Interests: Declaration of interests After the analysis in this paper was completed, AM and MB received funding from UKRI Research England via the MedTech SuperConnector (awarded on June 1, 2022) for commercial viability testing of infection prevention models. All other authors declare no competing interests., (Copyright © 2022 The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 license. Published by Elsevier Ltd.. All rights reserved.)

The current mental health crisis is a growing public health issue requiring a large-scale response that cannot be met with traditional services alone. Digital support tools are proliferating, yet most are not systematically evaluated, and we know little about their users and their needs. Shout is a free mental health text messaging service run by the charity Mental Health Innovations, which provides support for individuals in the UK experiencing mental or emotional distress and seeking help. Here we study a large data set of anonymised text message conversations and post-conversation surveys compiled through Shout. This data provides an opportunity to hear at scale from those experiencing distress; to better understand mental health needs for people not using traditional mental health services; and to evaluate the impact of a novel form of crisis support. We use natural language processing (NLP) to assess the adherence of volunteers to conversation techniques and formats, and to gain insight into demographic user groups and their behavioural expressions of distress. Our textual analyses achieve accurate classification of conversation stages (weighted accuracy = 88%), behaviours (1-hamming loss = 95%) and texter demographics (weighted accuracy = 96%), exemplifying how the application of NLP to frontline mental health data sets can aid with post-hoc analysis and evaluation of quality of service provision in digital mental health services., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Liu, Peach, Lawrance, Noble, Ungless and Barahona.)

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., (© 2021. The Author(s).)

TOR1A is the most common inherited form of dystonia with still unclear pathophysiology and reduced penetrance of 30-40%. ∆ETorA rats mimic the TOR1A disease by expression of the human TOR1A mutation without presenting a dystonic phenotype. We aimed to induce dystonia-like symptoms in male ∆ETorA rats by peripheral nerve injury and to identify central mechanism of dystonia development. Dystonia-like movements (DLM) were assessed using the tail suspension test and implementing a pipeline of deep learning applications. Neuron numbers of striatal parvalbumin + , nNOS + , calretinin + , ChAT + interneurons and Nissl + cells were estimated by unbiased stereology. Striatal dopaminergic metabolism was analyzed via in vivo microdialysis, qPCR and western blot. Local field potentials (LFP) were recorded from the central motor network. Deep brain stimulation (DBS) of the entopeduncular nucleus (EP) was performed. Nerve-injured ∆ETorA rats developed long-lasting DLM over 12 weeks. No changes in striatal structure were observed. Dystonic-like ∆ETorA rats presented a higher striatal dopaminergic turnover and stimulus-induced elevation of dopamine efflux compared to the control groups. Higher LFP theta power in the EP of dystonic-like ∆ETorA compared to wt rats was recorded. Chronic EP-DBS over 3 weeks led to improvement of DLM. Our data emphasizes the role of environmental factors in TOR1A symptomatogenesis. LFP analyses indicate that the pathologically enhanced theta power is a physiomarker of DLM. This TOR1A model replicates key features of the human TOR1A pathology on multiple biological levels and is therefore suited for further analysis of dystonia pathomechanism., (Copyright © 2021 The Author(s). Published by Elsevier Inc. All rights reserved.)

Networks are widely used as mathematical models of complex systems across many scientific disciplines. Decades of work have produced a vast corpus of research characterizing the topological, combinatorial, statistical, and spectral properties of graphs. Each graph property can be thought of as a feature that captures important (and sometimes overlapping) characteristics of a network. In this paper, we introduce HCGA, a framework for highly comparative analysis of graph datasets that computes several thousands of graph features from any given network. HCGA also offers a suite of statistical learning and data analysis tools for automated identification and selection of important and interpretable features underpinning the characterization of graph datasets. We show that HCGA outperforms other methodologies on supervised classification tasks on benchmark datasets while retaining the interpretability of network features. We exemplify HCGA by predicting the charge transfer in organic semiconductors and clustering a dataset of neuronal morphology images., Competing Interests: The authors declare no competing interests., (© 2021 The Authors.)

The intrinsic temporality of learning demands the adoption of methodologies capable of exploiting time-series information. In this study we leverage the sequence data framework and show how data-driven analysis of temporal sequences of task completion in online courses can be used to characterise personal and group learners' behaviors, and to identify critical tasks and course sessions in a given course design. We also introduce a recently developed probabilistic Bayesian model to learn sequential behaviours of students and predict student performance. The application of our data-driven sequence-based analyses to data from learners undertaking an on-line Business Management course reveals distinct behaviors within the cohort of learners, identifying learners or groups of learners that deviate from the nominal order expected in the course. Using course grades a posteriori, we explore differences in behavior between high and low performing learners. We find that high performing learners follow the progression between weekly sessions more regularly than low performing learners, yet within each weekly session high performing learners are less tied to the nominal task order. We then model the sequences of high and low performance students using the probablistic Bayesian model and show that we can learn engagement behaviors associated with performance. We also show that the data sequence framework can be used for task-centric analysis; we identify critical junctures and differences among types of tasks within the course design. We find that non-rote learning tasks, such as interactive tasks or discussion posts, are correlated with higher performance. We discuss the application of such analytical techniques as an aid to course design, intervention, and student supervision.

Aberrant neural oscillations hallmark numerous brain disorders. Here, we first report a method to track the phase of neural oscillations in real-time via endpoint-corrected Hilbert transform (ecHT) that mitigates the characteristic Gibbs distortion. We then used ecHT to show that the aberrant neural oscillation that hallmarks essential tremor (ET) syndrome, the most common adult movement disorder, can be transiently suppressed via transcranial electrical stimulation of the cerebellum phase-locked to the tremor. The tremor suppression is sustained shortly after the end of the stimulation and can be phenomenologically predicted. Finally, we use feature-based statistical-learning and neurophysiological-modelling to show that the suppression of ET is mechanistically attributed to a disruption of the temporal coherence of the aberrant oscillations in the olivocerebellar loop, thus establishing its causal role. The suppression of aberrant neural oscillation via phase-locked driven disruption of temporal coherence may in the future represent a powerful neuromodulatory strategy to treat brain disorders.

The widespread adoption of online courses opens opportunities for analysing learner behaviour and optimising web-based learning adapted to observed usage. Here, we introduce a mathematical framework for the analysis of time-series of online learner engagement, which allows the identification of clusters of learners with similar online temporal behaviour directly from the raw data without prescribing a priori subjective reference behaviours. The method uses a dynamic time warping kernel to create a pair-wise similarity between time-series of learner actions, and combines it with an unsupervised multiscale graph clustering algorithm to identify groups of learners with similar temporal behaviour. To showcase our approach, we analyse task completion data from a cohort of learners taking an online post-graduate degree at Imperial Business School. Our analysis reveals clusters of learners with statistically distinct patterns of engagement, from distributed to massed learning, with different levels of regularity, adherence to pre-planned course structure and task completion. The approach also reveals outlier learners with highly sporadic behaviour. A posteriori comparison against student performance shows that, whereas high-performing learners are spread across clusters with diverse temporal engagement, low performers are located significantly in the massed learning cluster, and our unsupervised clustering identifies low performers more accurately than common machine learning classification methods trained on temporal statistics of the data. Finally, we test the applicability of the method by analysing two additional data sets: a different cohort of the same course, and time-series of different format from another university., Competing Interests: Competing interestsThe authors declare no competing interests.