Balancing building and maintenance costs in growing transport networks

Random geometric graphs in high dimension

Many machine learning algorithms used for dimensional reduction and manifold learning leverage on the computation of the nearest neighbors to each point of a data set to perform their tasks. These proximity relations define a so-called geometric graph, where two nodes are linked if they are sufficiently close to each other. Random geometric graphs, where the positions of nodes are randomly generated in a subset of R^{d}, offer a null model to study typical properties of data sets and of machine learning algorithms. Up to now, most of the literature focused on the characterization of low-dimensional random geometric graphs whereas typical data sets of interest in machine learning live in high-dimensional spaces (d≫10^{2}). In this work, we consider the infinite dimensions limit of hard and soft random geometric graphs and we show how to compute the average number of subgraphs of given finite size k, e.g., the average number of k cliques. This analysis highlights that local observables display different behaviors depending on the chosen ensemble: soft random geometric graphs with continuous activation functions converge to the naive infinite-dimensional limit provided by Erdös-Rényi graphs, whereas hard random geometric graphs can show systematic deviations from it. We present numerical evidence that our analytical results, exact in infinite dimensions, provide a good approximation also for dimension d≳10.

Resilience of three-dimensional sinusoidal networks in liver tissue

Can three-dimensional, microvasculature networks still ensure blood supply if individual links fail? We address this question in the sinusoidal network, a plexus-like microvasculature network, which transports nutrient-rich blood to every hepatocyte in liver tissue, by building on recent advances in high-resolution imaging and digital reconstruction of adult mice liver tissue. We find that the topology of the three-dimensional sinusoidal network reflects its two design requirements of a space-filling network that connects all hepatocytes, while using shortest transport routes: sinusoidal networks are sub-graphs of the Delaunay graph of their set of branching points, and also contain the corresponding minimum spanning tree, both to good approximation. To overcome the spatial limitations of experimental samples and generate arbitrarily-sized networks, we developed a network generation algorithm that reproduces the statistical features of 0.3-mm-sized samples of sinusoidal networks, using multi-objective optimization for node degree and edge length distribution. Nematic order in these simulated networks implies anisotropic transport properties, characterized by an empirical linear relation between a nematic order parameter and the anisotropy of the permeability tensor. Under the assumption that all sinusoid tubes have a constant and equal flow resistance, we predict that the distribution of currents in the network is very inhomogeneous, with a small number of edges carrying a substantial part of the flow-a feature known for hierarchical networks, but unexpected for plexus-like networks. We quantify network resilience in terms of a permeability-at-risk, i.e., permeability as function of the fraction of removed edges. We find that sinusoidal networks are resilient to random removal of edges, but vulnerable to the removal of high-current edges. Our findings suggest the existence of a mechanism counteracting flow inhomogeneity to balance metabolic load on the liver.

LCC Estimation Model: A Construction Material Perspective

The growing pressure to ensure sustainable construction is also associated with stricter demands on the cost-effectiveness of construction and operation of buildings and reduction of their environmental impact. This paper presents a methodology for building life cycle cost estimation that enables investors to identify the optimum material solution for their buildings on the level of functional parts. The functionality of a comprehensive model that takes into account investor requirements and links them to a construction cost estimation database and a facility management database is verified through a case study of a “façade composition” functional part, with sublevel “external thermal insulation composite system (ETICS) with thin plaster”. The results show that there is no generally applicable optimum ETICS material solution, which is caused by differing investor requirements, as well as the unique circumstances of each building and its user. The solution presented in this paper aims to aid investor decision-making regarding the choice of the building materials while taking the Life Cycle Cost (LCC) into account.

Efficiency and shrinking in evolving networks

Characterizing the spatio-temporal evolution of networks is a central topic in many disciplines. While network expansion has been studied thoroughly, less is known about how empirical networks behave when shrinking. For transportation networks, this is especially relevant on account of their connection with the socio-economical substrate, and we focus here on the evolution of the French railway network from its birth in 1840 to 2000, in relation to the country's demographic dynamics. The network evolved in parallel with technology (e.g. faster trains) and under strong constraints, such as preserving a good population coverage and balancing cost and efficiency. We show that the shrinking phase that started in 1930 decreased the total length of the network while preserving efficiency and population coverage: efficiency and robustness remained remarkably constant while the total length of the network shrank by 50% between 1930 and 2000, and the total travel time and time-diameter decreased by more than 75% during the same period. Moreover, shrinking the network did not affect the overall accessibility with an average travel time that decreases steadily since its formation. This evolution leads naturally to an increase in transportation multimodality (such as a massive use of cars) and shows the importance of considering together transportation modes acting at different spatial scales. More generally, our results suggest that shrinking is not necessarily associated with a decay in performance and functions but can be beneficial in terms of design goals and can be part of the natural evolution of an adaptive network.