Saray Shai

Clustering Network Layers with the Strata Multilayer Stochastic Block Model

Multilayer networks are a useful data structure for simultaneously capturing multiple types of relationships between a set of nodes. In such networks, each relational definition gives rise to a layer. While each layer provides its own set of information, community structure across layers can be collectively utilized to discover and quantify underlying relational patterns between nodes. To concisely extract information from a multilayer network, we propose to identify and combine sets of layers with meaningful similarities in community structure. In this paper, we describe the “strata multilayer stochastic block model” (sMLSBM), a probabilistic model for multilayer community structure. The central extension of the model is that there exist groups of layers, called “strata”, which are defined such that all layers in a given stratum have community structure described by a common stochastic block model (SBM). That is, layers in a stratum exhibit similar node-to-community assignments and SBM probability parameters. Fitting the sMLSBM to a multilayer network provides a joint clustering that yields node-to-community and layer-to-stratum assignments, which cooperatively aid one another during inference. We describe an algorithm for separating layers into their appropriate strata and an inference technique for estimating the SBM parameters for each stratum. We demonstrate our method using synthetic networks and a multilayer network inferred from data collected in the Human Microbiome Project.

Multiplex networks in metropolitan areas: generic features and local effects

Most large cities are spanned by more than one transportation system. These different modes of transport have usually been studied separately: it is however important to understand the impact on urban systems of coupling different modes and we report in this paper an empirical analysis of the coupling between the street network and the subway for the two large metropolitan areas of London and New York. We observe a similar behaviour for network quantities related to quickest paths suggesting the existence of generic mechanisms operating beyond the local peculiarities of the specific cities studied. An analysis of the betweenness centrality distribution shows that the introduction of underground networks operate as a decentralizing force creating congestion in places located at the end of underground lines. Also, we find that increasing the speed of subways is not always beneficial and may lead to unwanted uneven spatial distributions of accessibility. In fact, for London—but not for New York—there is an optimal subway speed in terms of global congestion. These results show that it is crucial to consider the full, multimodal, multilayer network aspects of transportation systems in order to understand the behaviour of cities and to avoid possible negative side-effects of urban planning decisions.

Resilience of networks formed of interdependent modular networks

Many infrastructure networks have a modular structure and are also interdependent. While significant research has explored the resilience of interdependent networks, there has been no analysis of the effects of modularity. Here we develop a theoretical framework for attacks on interdependent modular networks and support our results by simulations. We focus on the case where each network has the same number of communities and the dependency links are restricted to be between pairs of communities of different networks. This is very realistic for infrastructure across cities. Each city has its own infrastructures and different infrastructures are dependent within the city. However, each infrastructure is connected within and between cities. For example, a power grid will connect many cities as will a communication network, yet a power station and communication tower that are interdependent will likely be in the same city. It has been shown that single networks are very susceptible to the failure of the interconnected nodes (between communities) Shai et al. and that attacks on these nodes are more crippling than attacks based on betweenness da Cunha et al. In our example of cities these nodes have long range links which are more likely to fail. For both treelike and looplike interdependent modular networks we find distinct regimes depending on the number of modules,

The scaling structure of the global road network

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Resilience of networks with community structure behaves as if under an external field

. (i) In the case where there are fewer modules with strong intraconnections, the system first separates into modules in an abrupt first-order transition and then each module undergoes a second percolation transition. (ii) When there are more modules with many interconnections between them, the system undergoes a single transition. Overall, we find that modular structure can influence the type of transitions observed in interdependent networks and should be considered in attempts to make interdependent networks more resilient.

Care Coordination and Multispecialty Teams in the Care of Colorectal Cancer Patients

Because of increasing global urbanization and its immediate consequences, including changes in patterns of food demand, circulation and land use, the next century will witness a major increase in the extent of paved roads built worldwide. To model the effects of this increase, it is crucial to understand whether possible self-organized patterns are inherent in the global road network structure. Here, we use the largest updated database comprising all major roads on the Earth, together with global urban and cropland inventories, to suggest that road length distributions within croplands are indistinguishable from urban ones, once rescaled to account for the difference in mean road length. Such similarity extends to road length distributions within urban or agricultural domains of a given area. We find two distinct regimes for the scaling of the mean road length with the associated area, holding in general at small and at large values of the latter. In suitably large urban and cropland domains, we find that mean and total road lengths increase linearly with their domain area, differently from earlier suggestions. Scaling regimes suggest that simple and universal mechanisms regulate urban and cropland road expansion at the global scale. As such, our findings bear implications for global road infrastructure growth based on land-use change and for planning policies sustaining urban expansions.

Enhanced Detectability of Community Structure in Multilayer Networks through Layer Aggregation

Significance Much work has focused on phase transitions in complex networks in which the system transitions from a resilient to a failed state. Furthermore, many of these networks have a community structure, whose effects on resilience have not yet been fully understood. Here, we show that the community structure can significantly affect the resilience of the system in that it removes the phase transition present in a single module, and the network remains resilient at this transition. In particular, we show that the effect of increasing interconnections is analogous to increasing external magnetic field in spin systems. Our findings provide insight into the resilience of many modular complex systems and clarify the important effects that community structure has on network resilience. Although detecting and characterizing community structure is key in the study of networked systems, we still do not understand how community structure affects systemic resilience and stability. We use percolation theory to develop a framework for studying the resilience of networks with a community structure. We find both analytically and numerically that interlinks (the connections among communities) affect the percolation phase transition in a way similar to an external field in a ferromagnetic– paramagnetic spin system. We also study universality class by defining the analogous critical exponents δ and γ, and we find that their values in various models and in real-world coauthor networks follow the fundamental scaling relations found in physical phase transitions. The methodology and results presented here facilitate the study of network resilience and also provide a way to understand phase transitions under external fields.

Critical tipping point distinguishing two types of transitions in modular network structures.

Objectives: To estimate the association between provider and team experience and adherence to guidelines, survival, and utilization among colorectal cancer patients in North Carolina. Subjects: The analysis cohort included 7295 patients diagnosed with incident stage II/III colorectal cancer between 2004 and 2013 who received surgery. Methods: Primary outcomes included adherence to guidelines: consultation with a medical oncologist (stage III), receipt of adjuvant chemotherapy (stage III), and receipt of surveillance colonoscopy posttreatment. Secondary outcomes included 5-year overall survival, number of surveillance radiology studies, any unplanned hospitalization, and any emergency department visit. The primary predictors were measures of provider volume and patient sharing across surgeons and medical oncologists. Regression analyses adjusted for patient and provider characteristics. Results: Patients whose surgeons shared >40% of their colorectal cancer patients in the previous year with a medical oncologist were (1) more likely to have had a consultation with a medical oncologist [marginal effect (ME)=13.3 percentage points, P-value<0.001], (2) less likely to receive a surveillance colonoscopy within 12 months (ME=3.5 percentage points, P-value=0.049), and (3) received more radiology studies (ME=0.254 studies, P-value=0.029). Patients whose surgeon and medical oncologist shared >20% of their colorectal cancer patients with each other in the previous year had a higher likelihood of receiving adjuvant chemotherapy (ME=11.5 percentage points, P-value<0.001) and surveillance colonoscopy within 12 months (ME=6.7 percentage points, P-value=0.030) and within 18 months (ME=6.2 percentage points, P-value=0.054). Conclusions: Our study shows that team experience is associated with patients’ quality of care, survival, and utilization.