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Coordination games have been of interest to game theorists, economists, and ecologists for many years to study such problems as the emergence of local conventions and the evolution of cooperative behavior. Approaches for understanding the coordination game with discrete structure have been limited in scope, often relying on symmetric reduction of the state space, or other constraints which limit the power of the model to give insight into desired applications. In this paper, we introduce a new way of thinking about equilibria of the structured coordination game with neutral strategies by means of graph partitioning. We begin with a few elementary game theoretical results and then catalogue all the Nash equilibria of the coordination game with neutral options for graphs with seven or fewer vertices. We extend our observations through the use of simulation on larger Erd\H{o}s-R\'enyi random graphs to form the basis for proposing some conjectures about the general relationships among edge density, cluster number, and consensus stability.

When we think of model ensembling or ensemble modeling, there are many possibilities that come to mind in different disciplines. For example, one might think of a set of descriptions of a phenomenon in the world, perhaps a time series or a snapshot of multivariate space, and perhaps that set is comprised of data-independent descriptions, or perhaps it is quite intentionally fit *to* data, or even a suite of data sets with a common theme or intention. The very meaning of 'ensemble' - a collection together - conjures different ideas across and even within disciplines approaching phenomena. In this paper, we present a typology of the scope of these potential perspectives. It is not our goal to present a review of terms and concepts, nor is it to convince all disciplines to adopt a common suite of terms, which we view as futile. Rather, our goal is to disambiguate terms, concepts, and processes associated with 'ensembles' and 'ensembling' in order to facilitate communication, awareness, and possible adoption of tools across disciplines., Comment: 33 pages, 4 figures

The built environment provides an excellent setting for interdisciplinary research on the dynamics of microbial communities. The system is simplified compared to many natural settings, and to some extent the entire environment can be manipulated, from architectural design, to materials use, air flow, human traffic, and capacity to disrupt microbial communities through cleaning. Here we provide an overview of the ecology of the microbiome in the built environment. We address niche space and refugia, population and community (metagenomic) dynamics, spatial ecology within a building, including the major microbial transmission mechanisms, as well as evolution. We also address the landscape ecology connecting microbiomes between physically separated buildings. At each stage we pay particular attention to the actual and potential interface between disciplines, such as ecology, epidemiology, materials science, and human social behavior. We end by identifying some opportunities for future interdisciplinary research on the microbiome of the built environment., Comment: 23 pages

Investigations of infectious disease outbreaks often focus on identifying place- and context-dependent factors responsible for emergence and spread, resulting in phenomenological narratives ill-suited to developing generalizable predictive and preventive measures. We contend that case-control hypothesis testing is a more powerful framework for epidemiological investigation. The approach, widely used in medical research, involves identifying counterfactuals, with case-control comparisons drawn to test hypotheses about the conditions that manifest outbreaks. Here we outline the merits of applying a case-control framework as epidemiological study design. We first describe a framework for iterative multidisciplinary interrogation to discover minimally sufficient sets of factors that can lead to disease outbreaks. We then lay out how case-control comparisons can respectively center on pathogen(s), factor(s), or landscape(s) with vignettes focusing on pathogen transmission. Finally, we consider how adopting case-control approaches can promote evidence-based decision making for responding to and preventing outbreaks.

Animal communication is frequently studied with conventional network representations that link pairs of individuals who interact, for example, through vocalisation. However, acoustic signals often have multiple simultaneous receivers, or receivers integrate information from multiple signallers, meaning these interactions are not dyadic. Additionally, non-dyadic social structures often shape an individual's behavioural response to vocal communication. Recently, major advances have been made in the study of these non-dyadic, higher-order networks (e.g., hypergraphs and simplicial complexes). Here, we show how these approaches can provide new insights into vocal communication through three case studies that illustrate how higher-order network models can: a) alter predictions made about the outcome of vocally-coordinated group departures; b) generate different patterns of song synchronisation than models that only include dyadic interactions; and c) inform models of cultural evolution of vocal communication. Together, our examples highlight the potential power of higher-order networks to study animal vocal communication. We then build on our case studies to identify key challenges in applying higher-order network approaches in this context and outline important research questions these techniques could help answer.

How self-organization leads to the emergence of structure in social populations remains a fascinating and open question in the study of complex systems. One frequently observed structure that emerges again and again across systems is that of self-similar community, i.e., homophily. We use a game theoretic perspective to explore a case in which individuals choose affiliation partnerships based on only two factors: the value they place on having social contacts, and their risk tolerance for exposure to threat derived from social contact (e.g., infectious disease, threatening ideas, etc.). We show how diversity along just these two influences are sufficient to cause the emergence of self-organizing homophily in the population. We further consider a case in which extrinsic social factors influence the desire to maintain particular social ties, and show the robustness of emergent homophilic patterns to these additional influences. These results demonstrate how observable population-level homophily may arise out of individual behaviors that balance the value of social contacts against the potential risks associated with those contacts. We present and discuss these results in the context of outbreaks of infectious disease in human populations. Complementing the standard narrative about how social division alters epidemiological risk, we here show how epidemiological risk may deepen social divisions in human populations., Comment: 17 pages, 4 figures

Analyzing social networks is challenging. Key features of relational data require the use of non-standard statistical methods such as developing system-specific null, or reference, models that randomize one or more components of the observed data. Here we review a variety of randomization procedures that generate reference models for social network analysis. Reference models provide an expectation for hypothesis-testing when analyzing network data. We outline the key stages in producing an effective reference model and detail four approaches for generating reference distributions: permutation, resampling, sampling from a distribution, and generative models. We highlight when each type of approach would be appropriate and note potential pitfalls for researchers to avoid. Throughout, we illustrate our points with examples from a simulated social system. Our aim is to provide social network researchers with a deeper understanding of analytical approaches to enhance their confidence when tailoring reference models to specific research questions.

Though pandemic preparedness has been a focus of public health planning for centuries, during which our understanding of infectious disease dynamics has grown, our methodologies for managing outbreaks have remained relatively unchanged. We propose leveraging this history to identify opportunities for actual progress. We contrast current plans with historical outbreak control measures and isolate how the complexities of a modern era yield additional challenges in how best to anticipate and mitigate outbreaks. We analyze a diversity of publicly available modern preparedness plans against the context of a historically-based fictional outbreak control strategy described in Defoe's A Journal of the Plague Year (published 1720). We identify themes in preparedness planning that remain unchanged from historical settings even though they continue to be actively evaluated in planning efforts. More importantly, we isolate critical modern challenges in preparedness planning that remain predominantly unsolved. These modern, unsolved issues offer best avenues for meaningful improvement. Shifting our planning efforts to focus on identified novel issues may greatly strengthen our local- to global- capacity to deal with infectious threats.

The lack of large-scale, continuously evolving empirical data usually limits the study of networks to the analysis of snapshots in time. This approach has been used for verification of network evolution mechanisms, such as preferential attachment. However, these studies are mostly restricted to the analysis of the first links established by a new node in the network and typically ignore connections made after each node's initial introduction. Here, we show that the subsequent actions of individuals, such as their second network link, are not random and can be decoupled from the mechanism behind the first network link. We show that this feature has strong influence on the network topology. Moreover, snapshots in time can now provide information on the mechanism used to establish the second connection. We interpret these empirical results by introducing the propinquity model, in which we control and vary the distance of the second link established by a new node, and find that this can lead to networks with tunable density scaling, as found in real networks. Our work shows that sociologically meaningful mechanisms are influencing network evolution and provides indications of the importance of measuring the distance between successive connections., Comment: 32 pages, 9 figures, includes Supplementary Information

The process of destroying a complex network through node removal has been the subject of extensive interest and research. Node loss typically leaves the network disintegrated into many small and isolated clusters. Here we show that these clusters typically remain close to each other and we suggest a simple algorithm that is able to reverse the inflicted damage by restoring the network's functionality. After damage, each node decides independently whether to create a new link depending on the fraction of neighbors it has lost. In addition to relying only on local information, where nodes do not need knowledge of the global network status, we impose the additional constraint that new links should be as short as possible (i.e. that the new edge completes a shortest possible new cycle). We demonstrate that this self-healing method operates very efficiently, both in model and real networks. For example, after removing the most connected airports in USA, the self-healing algorithm re-joined almost 90\% of the surviving airports., Comment: 10 pages, 8 figures

As the understanding of the importance of social contact networks in the spread of infectious diseases has increased, so has the interest in understanding the feedback process of the disease altering the social network. While many studies have explored the influence of individual epidemiological parameters and/or underlying network topologies on the resulting disease dynamics, we here provide a systematic overview of the interactions between these two influences on population-level disease outcomes. We show that the sensitivity of the population-level disease outcomes to the combination of epidemiological parameters that describe the disease are critically dependent on the topological structure of the population's contact network. We introduce a new metric for assessing disease-driven structural damage to a network as a population-level outcome. Lastly, we discuss how the expected individual-level disease burden is influenced by the complete suite of epidemiological characteristics for the circulating disease and the ongoing process of network compromise. Our results have broad implications for prediction and mitigation of outbreaks in both natural and human populations., Comment: 23 pages, 6 figures

The ability to compare complex systems can provide new insight into the fundamental nature of the processes captured in ways that are otherwise inaccessible to observation. Here, we introduce the $n$-tangle method to directly compare two networks for structural similarity, based on the distribution of edge density in network subgraphs. We demonstrate that this method can efficiently introduce comparative analysis into network science and opens the road for many new applications. For example, we show how the construction of a phylogenetic tree across animal taxa according to their social structure can reveal commonalities in the behavioral ecology of the populations, or how students create similar networks according to the University size. Our method can be expanded to study a multitude of additional properties, such as network classification, changes during time evolution, convergence of growth models, and detection of structural changes during damage., Comment: 11 pages, 4 figures, includes Supplementary Information. For the source code, see http://www-levich.engr.ccny.cuny.edu/~lazaros/research_comparison.html