Ensemble2: Scenarios ensembling for communication and performance analysis.

Throughout the COVID-19 pandemic, scenario modeling played a crucial role in shaping the decision-making process of public health policies. Unlike forecasts, scenario projections rely on specific assumptions about the future that consider different plausible states-of-the-world that may or may not be realized and that depend on policy interventions, unpredictable changes in the epidemic outlook, etc. As a consequence, long-term scenario projections require different evaluation criteria than the ones used for traditional short-term epidemic forecasts. Here, we propose a novel ensemble procedure for assessing pandemic scenario projections using the results of the Scenario Modeling Hub (SMH) for COVID-19 in the United States (US). By defining a "scenario ensemble" for each model and the ensemble of models, termed "Ensemble2", we provide a synthesis of potential epidemic outcomes, which we use to assess projections' performance, bypassing the identification of the most plausible scenario. We find that overall the Ensemble2 models are well-calibrated and provide better performance than the scenario ensemble of individual models. The ensemble procedure accounts for the full range of plausible outcomes and highlights the importance of scenario design and effective communication. The scenario ensembling approach can be extended to any scenario design strategy, with potential refinements including weighting scenarios and allowing the ensembling process to evolve over time.

Nonlinear bias toward complex contagion in uncertain transmission settings.

Current epidemics in the biological and social domains are challenging the standard assumptions of mathematical contagion models. Chief among them are the complex patterns of transmission caused by heterogeneous group sizes and infection risk varying by orders of magnitude in different settings, like indoor versus outdoor gatherings in the COVID-19 pandemic or different moderation practices in social media communities. However, quantifying these heterogeneous levels of risk is difficult, and most models typically ignore them. Here, we include these features in an epidemic model on weighted hypergraphs to capture group-specific transmission rates. We study analytically the consequences of ignoring the heterogeneous transmissibility and find an induced superlinear infection rate during the emergence of a new outbreak, even though the underlying mechanism is a simple, linear contagion. The dynamics produced at the individual and group levels are therefore more similar to complex, nonlinear contagions, thus blurring the line between simple and complex contagions in realistic settings. We support this claim by introducing a Bayesian inference framework to quantify the nonlinearity of contagion processes. We show that simple contagions on real weighted hypergraphs are systematically biased toward the superlinear regime if the heterogeneity of the weights is ignored, greatly increasing the risk of erroneous classification as complex contagions. Our results provide an important cautionary tale for the challenging task of inferring transmission mechanisms from incidence data. Yet, it also paves the way for effective models that capture complex features of epidemics through nonlinear infection rates.

Source-sink behavioural dynamics limit institutional evolution in a group-structured society.

Social change in any society entails changes in both behaviours and institutions. We model a group-structured society in which the transmission of individual behaviour occurs in parallel with the selection of group-level institutions. We consider a cooperative behaviour that generates collective benefits for groups but does not spread between individuals on its own. Groups exhibit institutions that increase the diffusion of the behaviour within the group, but also incur a group cost. Groups adopt institutions in proportion to their fitness. Finally, the behaviour may also spread globally. We find that behaviour and institutions can be mutually reinforcing. But the model also generates behavioural source-sink dynamics when behaviour generated in institutionalized groups spreads to non-institutionalized groups and boosts their fitness. Consequently, the global diffusion of group-beneficial behaviour creates a pattern of institutional free-riding that limits the evolution of group-beneficial institutions. Our model suggests that, in a group-structured society, large-scale beneficial social change can be best achieved when the relevant behaviour and institutions remain correlated.

Universal Nonlinear Infection Kernel from Heterogeneous Exposure on Higher-Order Networks.

The collocation of individuals in different environments is an important prerequisite for exposure to infectious diseases on a social network. Standard epidemic models fail to capture the potential complexity of this scenario by (1) neglecting the higher-order structure of contacts that typically occur through environments like workplaces, restaurants, and households, and (2) assuming a linear relationship between the exposure to infected contacts and the risk of infection. Here, we leverage a hypergraph model to embrace the heterogeneity of environments and the heterogeneity of individual participation in these environments. We find that combining heterogeneous exposure with the concept of minimal infective dose induces a universal nonlinear relationship between infected contacts and infection risk. Under nonlinear infection kernels, conventional epidemic wisdom breaks down with the emergence of discontinuous transitions, superexponential spread, and hysteresis.

Master equation analysis of mesoscopic localization in contagion dynamics on higher-order networks.

Simple models of infectious diseases tend to assume random mixing of individuals, but real interactions are not random pairwise encounters: they occur within various types of gatherings such as workplaces, households, schools, and concerts, best described by a higher-order network structure. We model contagions on higher-order networks using group-based approximate master equations, in which we track all states and interactions within a group of nodes and assume a mean-field coupling between them. Using the susceptible-infected-susceptible dynamics, our approach reveals the existence of a mesoscopic localization regime, where a disease can concentrate and self-sustain only around large groups in the network overall organization. In this regime, the phase transition is smeared, characterized by an inhomogeneous activation of the groups. At the mesoscopic level, we observe that the distribution of infected nodes within groups of the same size can be very dispersed, even bimodal. When considering heterogeneous networks, both at the level of nodes and at the level of groups, we characterize analytically the region associated with mesoscopic localization in the structural parameter space. We put in perspective this phenomenon with eigenvector localization and discuss how a focus on higher-order structures is needed to discern the more subtle localization at the mesoscopic level. Finally, we discuss how mesoscopic localization affects the response to structural interventions and how this framework could provide important insights for a broad range of dynamics.

Social Confinement and Mesoscopic Localization of Epidemics on Networks.

Recommendations around epidemics tend to focus on individual behaviors, with much less efforts attempting to guide event cancellations and other collective behaviors since most models lack the higher-order structure necessary to describe large gatherings. Through a higher-order description of contagions on networks, we model the impact of a blanket cancellation of events larger than a critical size and find that epidemics can suddenly collapse when interventions operate over groups of individuals rather than at the level of individuals. We relate this phenomenon to the onset of mesoscopic localization, where contagions concentrate around dominant groups.

Inference, Model Selection, and the Combinatorics of Growing Trees.

One can often make inferences about a growing network from its current state alone. For example, it is generally possible to determine how a network changed over time or pick among plausible mechanisms explaining its growth. In practice, however, the extent to which such problems can be solved is limited by existing techniques, which are often inexact, inefficient, or both. In this Letter, we derive exact and efficient inference methods for growing trees and demonstrate them in a series of applications: network interpolation, history reconstruction, model fitting, and model selection.

Localization, epidemic transitions, and unpredictability of multistrain epidemics with an underlying genotype network.

Mathematical disease modelling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen spreading among a population. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modelling community to focus on the complexity of other factors such as population structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics. Here, we introduce a disease model with an underlying genotype network to account for two important mechanisms. One, the disease can mutate along network pathways as it spreads in a host population. Two, the genotype network allows us to define a genetic distance between strains and therefore to model the transcendence of immunity often observed in real world pathogens. We study the emergence of epidemics in this model, through its epidemic phase transitions, and highlight the role of the genotype network in driving cyclicity of diseases, large scale fluctuations, sequential epidemic transitions, as well as localization around specific strains of the associated pathogen. More generally, our model illustrates the richness of behaviours that are possible even in well-mixed host populations once we consider strain diversity and go beyond the "one disease equals one pathogen" paradigm.

Social confinement and mesoscopic localization of epidemics on networks.

Recommendations around epidemics tend to focus on individual behaviors, with much less efforts attempting to guide event cancellations and other collective behaviors since most models lack the higher-order structure necessary to describe large gatherings. Through a higher-order description of contagions on networks, we model the impact of a blanket cancellation of events larger than a critical size and find that epidemics can suddenly collapse when interventions operate over groups of individuals rather than at the level of individuals. We relate this phenomenon to the onset of mesoscopic localization, where contagions concentrate around dominant groups.

Network comparison and the within-ensemble graph distance.

Quantifying the differences between networks is a challenging and ever-present problem in network science. In recent years, a multitude of diverse, ad hoc solutions to this problem have been introduced. Here, we propose that simple and well-understood ensembles of random networks-such as Erdos-Rényi graphs, random geometric graphs, Watts-Strogatz graphs, the configuration model and preferential attachment networks-are natural benchmarks for network comparison methods. Moreover, we show that the expected distance between two networks independently sampled from a generative model is a useful property that encapsulates many key features of that model. To illustrate our results, we calculate this within-ensemble graph distance and related quantities for classic network models (and several parameterizations thereof) using 20 distance measures commonly used to compare graphs. The within-ensemble graph distance provides a new framework for developers of graph distances to better understand their creations and for practitioners to better choose an appropriate tool for their particular task.

Annually resolved Atlantic sea surface temperature variability over the past 2,900 y.

Global warming due to anthropogenic factors can be amplified or dampened by natural climate oscillations, especially those involving sea surface temperatures (SSTs) in the North Atlantic which vary on a multidecadal scale (Atlantic multidecadal variability, AMV). Because the instrumental record of AMV is short, long-term behavior of AMV is unknown, but climatic teleconnections to regions beyond the North Atlantic offer the prospect of reconstructing AMV from high-resolution records elsewhere. Annually resolved titanium from an annually laminated sedimentary record from Ellesmere Island, Canada, shows that the record is strongly influenced by AMV via atmospheric circulation anomalies. Significant correlations between this High-Arctic proxy and other highly resolved Atlantic SST proxies demonstrate that it shares the multidecadal variability seen in the Atlantic. Our record provides a reconstruction of AMV for the past ∼3 millennia at an unprecedented time resolution, indicating North Atlantic SSTs were coldest from ∼1400-1800 CE, while current SSTs are the warmest in the past ∼2,900 y.

Thresholding normally distributed data creates complex networks.

Network data sets are often constructed by some kind of thresholding procedure. The resulting networks frequently possess properties such as heavy-tailed degree distributions, clustering, large connected components, and short average shortest path lengths. These properties are considered typical of complex networks and appear in many contexts, prompting consideration of their universality. Here we introduce a simple model for correlated relational data and study the network ensemble obtained by thresholding it. We find that some, but not all, of the properties associated with complex networks can be seen after thresholding the correlated data, even though the underlying data are not "complex." In particular, we observe heavy-tailed degree distributions, a large numbers of triangles, and short path lengths, while we do not observe nonvanishing clustering or community structure.

Efficient sampling of spreading processes on complex networks using a composition and rejection algorithm.

Efficient stochastic simulation algorithms are of paramount importance to the study of spreading phenomena on complex networks. Using insights and analytical results from network science, we discuss how the structure of contacts affects the efficiency of current algorithms. We show that algorithms believed to require O ( log  N ) or even O ( 1 ) operations per update-where N is the number of nodes-display instead a polynomial scaling for networks that are either dense or sparse and heterogeneous. This significantly affects the required computation time for simulations on large networks. To circumvent the issue, we propose a node-based method combined with a composition and rejection algorithm, a sampling scheme that has an average-case complexity of O [ log ( log  N ) ] per update for general networks. This systematic approach is first set-up for Markovian dynamics, but can also be adapted to a number of non-Markovian processes and can enhance considerably the study of a wide range of dynamics on networks.

Geometric evolution of complex networks with degree correlations.

We present a general class of geometric network growth mechanisms by homogeneous attachment in which the links created at a given time t are distributed homogeneously between a new node and the existing nodes selected uniformly. This is achieved by creating links between nodes uniformly distributed in a homogeneous metric space according to a Fermi-Dirac connection probability with inverse temperature ß and general time-dependent chemical potential µ(t). The chemical potential limits the spatial extent of newly created links. Using a hidden variable framework, we obtain an analytical expression for the degree sequence and show that µ(t) can be fixed to yield any given degree distributions, including a scale-free degree distribution. Additionally, we find that depending on the order in which nodes appear in the network-its history-the degree-degree correlations can be tuned to be assortative or disassortative. The effect of the geometry on the structure is investigated through the average clustering coefficient 〈c〉. In the thermodynamic limit, we identify a phase transition between a random regime where 〈c〉→0 when ß<ß_{c} and a geometric regime where 〈c〉>0 when ß>ß_{c}.

Phase transition of the susceptible-infected-susceptible dynamics on time-varying configuration model networks.

We present a degree-based theoretical framework to study the susceptible-infected-susceptible (SIS) dynamics on time-varying (rewired) configuration model networks. Using this framework on a given degree distribution, we provide a detailed analysis of the stationary state using the rewiring rate to explore the whole range of the time variation of the structure relative to that of the SIS process. This analysis is suitable for the characterization of the phase transition and leads to three main contributions: (1) We obtain a self-consistent expression for the absorbing-state threshold, able to capture both collective and hub activation. (2) We recover the predictions of a number of existing approaches as limiting cases of our analysis, providing thereby a unifying point of view for the SIS dynamics on random networks. (3) We obtain bounds for the critical exponents of a number of quantities in the stationary state. This allows us to reinterpret the concept of hub-dominated phase transition. Within our framework, it appears as a heterogeneous critical phenomenon: observables for different degree classes have a different scaling with the infection rate. This phenomenon is followed by the successive activation of the degree classes beyond the epidemic threshold.

Are Paleomagnetic Records From U-Channels Appropriate for Studies of Reversals and Excursions?

Sampling of sediment cores using plastic U-channels has made possible the acquisition of detailed records of paleomagnetic secular variation, geomagnetic polarity, environmental magnetic studies, and relative paleointensity over the past several million years. U-channel measurements provide the great advantage of rapid measurements of long sediment cores, but the signal resolution is attenuated by the response function of the magnetometer sensors, which therefore restrains the recovery of rapid and large-amplitude field changes. Here we focus on the suitability of the dynamics of reversals and excursions derived from U-channel measurements. We compare successive individual paleomagnetic directions of 1.5 cm × 1.5 cm × 1.5 cm cubic discrete samples with those of a 1.5-m equivalent U-channel sample train obtained by placing the samples adjacent to each other. We use varying excursion and transition lengths and generate transitional directions that resemble those of the most detailed paleomagnetic records. Excursions with opposite polarity directions recorded over less than 7.5 cm are barely detected in U-channel measurements. Regarding reversals, U-channel measurements smooth the signal of low-resolution records and generate artificial transitional directions. Despite producing misleading similarities with the overall structure of transition records, longer transitional intervals fail also to reproduce the complexity of field changes. Finally, we test the convolution of magnetization by different response functions. The simulation reveals that even small response function changes can generate significant differences in results.

Exact vectorial model for nonparaxial focusing by arbitrary axisymmetric surfaces.

We present a new approach, based on Richards-Wolf formalism, to rigorously model nonparaxial focusing of radially and azimuthally polarized electromagnetic beams by axisymmetric systems without a single-point focus. Our approach is based on a combined method that uses ray tracing and diffraction integrals. Our method is validated by comparing known results obtained with a parabolic mirror. Our integral representation of the focused beams, compliant with diffraction theory, is thoroughly discussed and solved for various conics that, so far, have not been treated analytically. The extension of the method to other polarization states is straightforward.

Mid-Pleistocene climate transition drives net mass loss from rapidly uplifting St. Elias Mountains, Alaska.

Erosion, sediment production, and routing on a tectonically active continental margin reflect both tectonic and climatic processes; partitioning the relative importance of these processes remains controversial. Gulf of Alaska contains a preserved sedimentary record of the Yakutat Terrane collision with North America. Because tectonic convergence in the coastal St. Elias orogen has been roughly constant for 6 My, variations in its eroded sediments preserved in the offshore Surveyor Fan constrain a budget of tectonic material influx, erosion, and sediment output. Seismically imaged sediment volumes calibrated with chronologies derived from Integrated Ocean Drilling Program boreholes show that erosion accelerated in response to Northern Hemisphere glacial intensification (∼ 2.7 Ma) and that the 900-km-long Surveyor Channel inception appears to correlate with this event. However, tectonic influx exceeded integrated sediment efflux over the interval 2.8-1.2 Ma. Volumetric erosion accelerated following the onset of quasi-periodic (∼ 100-ky) glacial cycles in the mid-Pleistocene climate transition (1.2-0.7 Ma). Since then, erosion and transport of material out of the orogen has outpaced tectonic influx by 50-80%. Such a rapid net mass loss explains apparent increases in exhumation rates inferred onshore from exposure dates and mapped out-of-sequence fault patterns. The 1.2-My mass budget imbalance must relax back toward equilibrium in balance with tectonic influx over the timescale of orogenic wedge response (millions of years). The St. Elias Range provides a key example of how active orogenic systems respond to transient mass fluxes, and of the possible influence of climate-driven erosive processes that diverge from equilibrium on the million-year scale.

Holocene dynamics of the Arctic's largest ice shelf.

Ice shelves in the Arctic lost more than 90% of their total surface area during the 20th century and are continuing to disintegrate rapidly. The significance of these changes, however, is obscured by the poorly constrained ontogeny of Arctic ice shelves. Here we use the sedimentary record behind the largest remaining ice shelf in the Arctic, the Ward Hunt Ice Shelf (Ellesmere Island, Canada), to establish a long-term context in which to evaluate recent ice-shelf deterioration. Multiproxy analysis of sediment cores revealed pronounced biological and geochemical changes in Disraeli Fiord in response to the formation of the Ward Hunt Ice Shelf and its fluctuations through time. Our results show that the ice shelf was absent during the early Holocene and formed 4,000 years ago in response to climate cooling. Paleoecological data then indicate that the Ward Hunt Ice Shelf remained stable for almost three millennia before a major fracturing event that occurred ∼1,400 years ago. After reformation ∼800 years ago, freshwater was a constant feature of Disraeli Fiord until the catastrophic drainage of its epishelf lake in the early 21st century.