In many physical networks, from neurons in the brain [ 1 , 2 ] to 3D integrated circuits [ 3 ] or underground hyphal networks [ 4 ], the nodes and links are physical objects unable to cross each other. These non-crossing conditions constrain their layout geometry and affect how these networks form, evolve and function, limitations ignored by the theoretical framework currently used to characterize real networks [ 5 , 6 , 7 , 8 , 9 , 10 ]. Indeed, most current network layout tools are variants of the Force-Directed Layout (FDL) algorithm [ 11 , 12 ], which assumes dimensionless nodes and links, hence are unable to reveal the geometry of densely packed physical networks. Here, we develop a modeling framework that accounts for the physical reality of nodes and links, allowing us to explore how the non-crossing conditions affect the geometry of the network layout. For small link thicknesses, r L , we observe a weakly interacting regime where link crossings are avoided via local link rearrangements, without altering the overall layout geometry. Once r L exceeds a threshold, a strongly interacting regime emerges, where multiple geometric quantities, from the total link length to the link curvature, scale with r L . We show that the crossover between the two regimes is driven by excluded volume interactions, allowing us to analytically derive the transition point, and show that large networks eventually end up in the strongly interacting regime. We also find that networks in the weakly interacting regime display a solid-like response to stress, whereas they behave in a gel-like fashion in the strongly interacting regime. Finally, we show that the weakly interacting regime offers avenues to 3D print networks, while the strongly interacting regime offers insight on the scaling of densely packed mammalian brains.

Environmental factors, and in particular diet, are known to play a key role in the development of Coronary Heart Disease. Many of these factors were unveiled by detailed nutritional epidemiology studies, focusing on the role of a single nutrient or food at a time. Here, we apply an Environment-Wide Association Study approach to Nurses’ Health Study data to explore comprehensively and agnostically the association of 257 nutrients and 117 foods with coronary heart disease risk (acute myocardial infarction and fatal coronary heart disease). After accounting for multiple testing, we identify 16 food items and 37 nutrients that show statistically significant association – while adjusting for potential confounding and control variables such as physical activity, smoking, calorie intake, and medication use – among which 38 associations were validated in Nurses’ Health Study II. Our implementation of Environment-Wide Association Study successfully reproduces prior knowledge of diet-coronary heart disease associations in the epidemiological literature, and helps us detect new associations that were only marginally studied, opening potential avenues for further extensive experimental validation. We also show that Environment-Wide Association Study allows us to identify a bipartite food-nutrient network, highlighting which foods drive the associations of specific nutrients with coronary heart disease risk.

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Excessive greenhouse gas emissions from the transportation sector have led companies to move towards a sustainable supply chain network design. In this study we present a new bi-objective nonlinear formulation where multiple inventory components are integrated into the location and routing decisions throughout the supply chain network. To efficiently solve the proposed model, we implement an exact method and four evolutionary algorithms for small and large-scale instances. Extensive computational results and sensitivity analysis are performed to validate the efficiency of the proposed approaches, both quantitatively and qualitatively. Besides, we run a statistical analysis to investigate whether there is any statistically significant difference between solution methods.