Dynamics of new strain emergence on a temporal network

Multi-strain competition on networks is observed in many contexts, including infectious disease ecology, information dissemination or behavioral adaptation to epidemics. Despite a substantial body of research has been developed considering static, time-aggregated networks, it remains a challenge to understand the transmission of concurrent strains when links of the network are created and destroyed over time. Here we analyze how network dynamics shapes the outcome of the competition between an initially endemic strain and an emerging one, when both strains follow a susceptible-infected-susceptible dynamics, and spread at time scales comparable with the network evolution one. Using time-resolved data of close-proximity interactions between patients admitted to a hospital and medical health care workers, we analyze the impact of temporal patterns and initial conditions on the dominance diagram and coexistence time. We find that strong variations in activity volume cause the probability that the emerging strain replaces the endemic one to be highly sensitive to the time of emergence. The temporal structure of the network shapes the dominance diagram, with significant variations in the replacement probability (for a given set of epidemiological parameters) observed from the empirical network and a randomized version of it. Our work contributes towards the description of the complex interplay between competing pathogens on temporal networks.Comment: 9 pages, 4 figure

Reconstructing dynamical networks via feature ranking

Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the topology of networks from time-resolved observations of their node-dynamics. The methods based on physical insights often rely on strong assumptions about the properties and dynamics of the scrutinized network. Here, we use the insights from machine learning to design a new method of network reconstruction that essentially makes no such assumptions. Specifically, we interpret the available trajectories (data) as features, and use two independent feature ranking approaches -- Random forest and RReliefF -- to rank the importance of each node for predicting the value of each other node, which yields the reconstructed adjacency matrix. We show that our method is fairly robust to coupling strength, system size, trajectory length and noise. We also find that the reconstruction quality strongly depends on the dynamical regime

Evolutionary optimization of network reconstruction from derivative-variable correlations

Topologies of real-world complex networks are rarely accessible, but can often be reconstructed from experimentally obtained time series via suitable network reconstruction methods. Extending our earlier work on methods based on statistics of derivative-variable correlations, we here present a new method built on integrating an evolutionary optimization algorithm into the derivative-variable correlation method. Results obtained from our modi cation of the method in general outperform the original results, demonstrating the suitability of evolutionary optimization logic in network reconstruction problems. We show the method's usefulness in realistic scenarios where the reconstruction precision can be limited by the nature of the time series. We also discuss important limitations coming from various dynamical regimes that time series can belong to.This work was founded by the EU via H2020 Marie SklodowskaCurie project COSMOS, grant no. 642563. R G A acknowledges funding from the Volkswagen foundation, the Spanish Ministry of Economy and Competitiveness (Grant FIS2014-54177-R) and the CERCA Programme of the Generalitat de Catalunya. Z L acknowledges funding from the Slovenian Research Agency via program Complex Networks P1-0383 and project J5- 8236

Measuring synchrony in bio-medical timeseries.

Paroxysms are sudden, unpredictable, short-lived events that abound in physiological processes and pathological disorders, from cellular functions (e.g., hormone secretion and neuronal firing) to life-threatening attacks (e.g., cardiac arrhythmia, epileptic seizures, and diabetic ketoacidosis). With the increasing use of personal chronic monitoring (e.g., electrocardiography, electroencephalography, and glucose monitors), the discovery of cycles in health and disease, and the emerging possibility of forecasting paroxysms, the need for suitable methods to evaluate synchrony-or phase-clustering-between events and related underlying physiological fluctuations is pressing. Here, based on examples in epilepsy, where seizures occur preferentially in certain brain states, we characterize different methods that evaluate synchrony in a controlled timeseries simulation framework. First, we compare two methods for extracting the phase of event occurrence and deriving the phase-locking value, a measure of synchrony: (M1) fitting cycles of fixed period-length vs (M2) deriving continuous cycles from a biomarker. In our simulations, M2 provides stronger evidence for cycles. Second, by systematically testing the sensitivity of both methods to non-stationarity in the underlying cycle, we show that M2 is more robust. Third, we characterize errors in circular statistics applied to timeseries with different degrees of temporal clustering and tested with different strategies: Rayleigh test, Poisson simulations, and surrogate timeseries. Using epilepsy data from 21 human subjects, we show the superiority of testing against surrogate time-series to minimize false positives and false negatives, especially when used in combination with M1. In conclusion, we show that only time frequency analysis of continuous recordings of a related bio-marker reveals the full extent of cyclical behavior in events. Identifying and forecasting cycles in biomedical timeseries will benefit from recordings using emerging wearable and implantable devices, so long as conclusions are based on conservative statistical testing

Cues for seizure timing.

The cyclical organization of seizures in epilepsy has been described since antiquity. However, historical explanations for seizure cycles-based on celestial, hormonal, and environmental factors-have only recently become testable with the advent of chronic electroencephalography (cEEG) and modern statistical techniques. Here, factors purported over millennia to influence seizure timing are viewed through a contemporary lens. We discuss the emerging concept that seizures are organized over multiple timescales, each involving differential influences of external and endogenous rhythm generators. Leveraging large cEEG datasets and circular statistics appropriate for cyclical phenomena, we present new evidence for circadian (day-night), multidien (multi-day), and circannual (about-yearly) variation in seizure activity. Modulation of seizure timing by multiscale temporal variables has implications for diagnosis and therapy in clinical epilepsy. Uncovering the mechanistic basis for seizure cycles, particularly the factors that govern multidien periodicity, will be a major focus of future work

Inferring directed networks using a rank-based connectivity measure

Inferring the topology of a network using the knowledge of the signals of each of the interacting units is key to understanding real-world systems. One way to address this problem is using data- driven methods like cross-correlation or mutual information. However, these measures lack the ability to distinguish the direction of coupling. Here, we use a rank-based nonlinear interdependence measure originally developed for pairs of signals. This measure not only allows one to measure the strength but also the direction of the coupling. Our results for a system of coupled Lorenz dynamics show that we are able to consistently infer the underlying network for a subrange of the coupling strength and link density. Furthermore, we report that the addition of dynamical noise can benefit the reconstruction. Finally, we show an application to multichannel electroencephalographic recordings from an epilepsy patient.This work was funded by the EU via H2020 Marie SklodowskaCurie project COSMOS, grant no. 642563 (M.G.L., I.M., Z.L., and R.G.A). R.G.A. and C.G.B.M. acknowledge funding from the Spanish Ministry of Econ- omy and Competitiveness (Grant FIS2014-54177-R) and the CERCA Programme of the Generalitat de Catalunya. C.G.B.M. acknowledges the support by the Spanish Ministry of Economy and Competitiveness under the Maria de Maeztu Units of Excellence Programme (MDM-2015-0502). Z.L. acknowledges funding from the Slovenian Re- search Agency via program Complex Networks P1-0383 and project J5-8236

Forecasting seizure risk in adults with focal epilepsy: a development and validation study

Background: People with epilepsy are burdened with the apparent unpredictability of seizures. In the past decade, converging evidence from studies using chronic EEG (cEEG) revealed that epileptic brain activity shows robust cycles, operating over hours (circadian) and days (multidien). We hypothesised that these cycles can be leveraged to estimate future seizure probability, and we tested the feasibility of forecasting seizures days in advance. Methods: We did a feasibility study in distinct development and validation cohorts, involving retrospective analysis of cEEG data recorded with an implanted device in adults (age ≥18 years) with drug-resistant focal epilepsy followed at 35 centres across the USA between Jan 19, 2004, and May 18, 2018. Patients were required to have had 20 or more electrographic seizures (development cohort) or self-reported seizures (validation cohort). In all patients, the device recorded interictal epileptiform activity (IEA; ≥6 months of continuous hourly data), the fluctuations in which helped estimate varying seizure risk. Point process statistical models trained on initial portions of each patient's cEEG data (both cohorts) generated forecasts of seizure probability that were tested on subsequent unseen seizure data and evaluated against surrogate time-series. The primary outcome was the percentage of patients with forecasts showing improvement over chance (IoC). Findings: We screened 72 and 256 patients, and included 18 and 157 patients in the development and validation cohorts, respectively. Models incorporating information about multidien IEA cycles alone generated daily seizure forecasts for the next calendar day with IoC in 15 (83%) patients in the development cohort and 103 (66%) patients in the validation cohort. The forecasting horizon could be extended up to 3 days while maintaining IoC in two (11%) of 18 patients and 61 (39%) of 157 patients. Forecasts with a shorter horizon of 1 h, possible only for electrographic seizures in the development cohort, showed IoC in all 18 (100%) patients. Interpretation: This study shows that seizure probability can be forecasted days in advance by leveraging multidien IEA cycles recorded with an implanted device. This study will serve as a basis for prospective clinical trials to establish how people with epilepsy might benefit from seizure forecasting over long horizons

Inferring directed networks using a rank-based connectivity measure

Inferring the topology of a network using the knowledge of the signals of each of the interacting units is key to understanding real-world systems. One way to address this problem is using data- driven methods like cross-correlation or mutual information. However, these measures lack the ability to distinguish the direction of coupling. Here, we use a rank-based nonlinear interdependence measure originally developed for pairs of signals. This measure not only allows one to measure the strength but also the direction of the coupling. Our results for a system of coupled Lorenz dynamics show that we are able to consistently infer the underlying network for a subrange of the coupling strength and link density. Furthermore, we report that the addition of dynamical noise can benefit the reconstruction. Finally, we show an application to multichannel electroencephalographic recordings from an epilepsy patient.This work was funded by the EU via H2020 Marie SklodowskaCurie project COSMOS, grant no. 642563 (M.G.L., I.M., Z.L., and R.G.A). R.G.A. and C.G.B.M. acknowledge funding from the Spanish Ministry of Econ- omy and Competitiveness (Grant FIS2014-54177-R) and the CERCA Programme of the Generalitat de Catalunya. C.G.B.M. acknowledges the support by the Spanish Ministry of Economy and Competitiveness under the Maria de Maeztu Units of Excellence Programme (MDM-2015-0502). Z.L. acknowledges funding from the Slovenian Re- search Agency via program Complex Networks P1-0383 and project J5-8236