Spread in climate policy scenarios unravelled.

Analysis of climate policy scenarios has become an important tool for identifying mitigation strategies, as shown in the latest Intergovernmental Panel on Climate Change Working Group III report1. The key outcomes of these scenarios differ substantially not only because of model and climate target differences but also because of different assumptions on behavioural, technological and socio-economic developments2-4. A comprehensive attribution of the spread in climate policy scenarios helps policymakers, stakeholders and scientists to cope with large uncertainties in this field. Here we attribute this spread to the underlying drivers using Sobol decomposition5, yielding the importance of each driver for scenario outcomes. As expected, the climate target explains most of the spread in greenhouse gas emissions, total and sectoral fossil fuel use, total renewable energy and total carbon capture and storage in electricity generation. Unexpectedly, model differences drive variation of most other scenario outcomes, for example, in individual renewable and carbon capture and storage technologies, and energy in demand sectors, reflecting intrinsic uncertainties about long-term developments and the range of possible mitigation strategies. Only a few scenario outcomes, such as hydrogen use, are driven by other scenario assumptions, reflecting the need for more scenario differentiation. This attribution analysis distinguishes areas of consensus as well as strong model dependency, providing a crucial step in correctly interpreting scenario results for robust decision-making.

Reducing societal impacts of SARS-CoV-2 interventions through subnational implementation.

To curb the initial spread of SARS-CoV-2, many countries relied on nation-wide implementation of non-pharmaceutical intervention measures, resulting in substantial socio-economic impacts. Potentially, subnational implementations might have had less of a societal impact, but comparable epidemiological impact. Here, using the first COVID-19 wave in the Netherlands as a case in point, we address this issue by developing a high-resolution analysis framework that uses a demographically stratified population and a spatially explicit, dynamic, individual contact-pattern based epidemiology, calibrated to hospital admissions data and mobility trends extracted from mobile phone signals and Google. We demonstrate how a subnational approach could achieve similar level of epidemiological control in terms of hospital admissions, while some parts of the country could stay open for a longer period. Our framework is exportable to other countries and settings, and may be used to develop policies on subnational approach as a better strategic choice for controlling future epidemics.

Hidden dependence of spreading vulnerability on topological complexity.

Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time-commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena, which we abbreviate as its "spreading vulnerability," is often surmised to be related to the topology of the temporal network featured by the system. Yet, cleanly extracting spreading vulnerability of a complex system directly from the topological information of the temporal network remains a challenge. Here, using data from a diverse set of real-world complex systems, we develop the "entropy of temporal entanglement" as a quantity to measure topological complexities of temporal networks. We show that this parameter-free quantity naturally allows for topological comparisons across vastly different complex systems. Importantly, by simulating three different types of stochastic dynamical processes playing out on top of temporal networks, we demonstrate that the entropy of temporal entanglement serves as a quantitative embodiment of the systems' spreading vulnerability, irrespective of the details of the processes. In being able to do so, i.e., in being able to quantitatively extract a complex system's proneness to facilitate spreading phenomena from topology, this entropic measure opens itself for applications in a wide variety of natural, social, biological, and engineered systems.

Quantifying agent impacts on contact sequences in social interactions.

Human social behavior plays a crucial role in how pathogens like SARS-CoV-2 or fake news spread in a population. Social interactions determine the contact network among individuals, while spreading, requiring individual-to-individual transmission, takes place on top of the network. Studying the topological aspects of a contact network, therefore, not only has the potential of leading to valuable insights into how the behavior of individuals impacts spreading phenomena, but it may also open up possibilities for devising effective behavioral interventions. Because of the temporal nature of interactions-since the topology of the network, containing who is in contact with whom, when, for how long, and in which precise sequence, varies (rapidly) in time-analyzing them requires developing network methods and metrics that respect temporal variability, in contrast to those developed for static (i.e., time-invariant) networks. Here, by means of event mapping, we propose a method to quantify how quickly agents mingle by transforming temporal network data of agent contacts. We define a novel measure called contact sequence centrality, which quantifies the impact of an individual on the contact sequences, reflecting the individual's behavioral potential for spreading. Comparing contact sequence centrality across agents allows for ranking the impact of agents and identifying potential 'behavioral super-spreaders'. The method is applied to social interaction data collected at an art fair in Amsterdam. We relate the measure to the existing network metrics, both temporal and static, and find that (mostly at longer time scales) traditional metrics lose their resemblance to contact sequence centrality. Our work highlights the importance of accounting for the sequential nature of contacts when analyzing social interactions.

Geographic delay characterization of railway systems.

Railway systems provide pivotal support to modern societies, making their efficiency and robustness important to ensure. However, these systems are susceptible to disruptions and delays, leading to accumulating economic damage. The large spatial scale of delay spreading typically make it difficult to distinguish which regions will ultimately affected from an initial disruption, creating uncertainty for risk assessment. In this paper, we identify geographical structures that reflect how delay spreads through railway networks. We do so by proposing a graph-based, hybrid schedule and empirical-based model for delay propagation and apply spectral clustering. We apply the model to four European railway systems: the Netherlands, Germany, Switzerland and Italy. We characterize these geographical delay structures in the railway systems of these countries and interpret these regions in terms of delay severity and how dynamically disconnected they are from the rest. The method also allows us to point out important differences between these countries' railway systems. For practitioners, such geographical characterization of railways provides natural boundaries for local decision-making structures and risk assessment.

Characterizing neural phase-space trajectories via Principal Louvain Clustering.

BACKGROUND: With the growing size and richness of neuroscience datasets in terms of dimension, volume, and resolution, identifying spatiotemporal patterns in those datasets is increasingly important. Multivariate dimension-reduction methods are particularly adept at addressing these challenges. NEW METHOD: In this paper, we propose a novel method, which we refer to as Principal Louvain Clustering (PLC), to identify clusters in a low-dimensional data subspace, based on time-varying trajectories of spectral dynamics across multisite local field potential (LFP) recordings in awake behaving mice. Data were recorded from prefrontal cortex, hippocampus, and parietal cortex in eleven mice while they explored novel and familiar environments. RESULTS: PLC-identified subspaces and clusters showed high consistency across animals, and were modulated by the animals' ongoing behavior. CONCLUSIONS: PLC adds to an important growing literature on methods for characterizing dynamics in high-dimensional datasets, using a smaller number of parameters. The method is also applicable to other kinds of datasets, such as EEG or MEG.

Cascading dominates large-scale disruptions in transport over complex networks.

The core functionality of many socio-technical systems, such as supply chains, (inter)national trade and human mobility, concern transport over large geographically-spread complex networks. The dynamical intertwining of many heterogeneous operational elements, agents and locations are oft-cited generic factors to make these systems prone to large-scale disruptions: initially localised perturbations amplify and spread over the network, leading to a complete standstill of transport. Our level of understanding of such phenomena, let alone the ability to anticipate or predict their evolution in time, remains rudimentary. We approach the problem with a prime example: railways. Analysing spreading of train delays on the network by building a physical model, supported by data, reveals that the emergence of large-scale disruptions rests on the dynamic interdependencies among multiple 'layers' of operational elements (resources and services). The interdependencies provide pathways for the so-called delay cascading mechanism, which gets activated when, constrained by local unavailability of on-time resources, already-delayed ones are used to operate new services. Cascading locally amplifies delays, which in turn get transported over the network to give rise to new constraints elsewhere. This mechanism is a rich addition to some well-understood ones in, e.g., epidemiological spreading, or the spreading of rumours and opinions over (contact) networks, and stimulates rethinking spreading dynamics on complex networks. Having these concepts built into the model provides it with the ability to predict the evolution of large-scale disruptions in the railways up to 30-60 minutes up front. For transport systems, our work suggests that possible alleviation of constraints as well as a modular operational approach would arrest cascading, and therefore be effective measures against large-scale disruptions.

Predicting transitions across macroscopic states for railway systems.

Railways are classic instances of complex socio-technical systems, whose defining characteristic is that they exist and function by integrating (continuous-time) interactions among technical components and human elements. Typically, unlike physical systems, there are no governing laws for describing their dynamics. Based purely on micro-unit data, here we present a data-driven framework to analyze macro-dynamics in such systems, leading us to the identification of specific states and prediction of transitions across them. It consists of three steps, which we elucidate using data from the Dutch railways. First, we form a dimensionally reduced phase-space by extracting a few relevant components, wherein relevance is proxied by dominance in terms of explained variance, as well as by persistence in time. Secondly, we apply a clustering algorithm to the reduced phase-space, resulting in the revelation of states of the system. Specifically, we identify 'rest' and 'disrupted' states, for which the system operations deviates respectively little and strongly from the planned timetable. Third, we define an early-warning metric based on the probability of transitions across states, predict whether the system is likely to transit from one state to another within a given time-frame and evaluate the performance of this metric using the Peirce skill score. Interestingly, using case studies, we demonstrate that the framework is able to predict large-scale disruptions up to 90 minutes beforehand with significant skill, demonstrating, for the railway companies, its potential to better track the evolution of large-scale disruptions in their networks. We discuss that the applicability of the three-step framework stretches to other systems as well-i.e., not only socio-technical ones-wherein real-time monitoring can help to prevent macro-scale state transitions, albeit the methods chosen to execute each step may depend on specific system-details.