Principled network extraction from images

A mathematical perspective on Romanisation: Modelling the Roman road activation process in ancient Tunisia

Romanisation is a multi-faceted historical phenomenon with profound and lasting cultural impact on the ancient world. In the modern-day territory of Tunisia, this is particularly manifest during the first four centuries AD, under the reign of the Roman Empire. We derive a reduced, operational concept of Romanisation as a cultural diffusion process that is observable in the archaeological remains of the Roman era settlement system. We then introduce a novel mathematical model that computes spatio-temporal approximations for the Romanisation of the settlement system. The model is based on the concept of temporal road activation and makes minimal assumptions regarding input data quality. The results of our study contribute to the understanding of the time dynamics of the region's road network, under the influence of Romanisation. Our model can be applied in similar archaeological research scenarios, to generate spatio-temporal backbones for the analysis of otherwise intractably complex social processes.

Similarity and economy of scale in urban transportation networks and optimal transport-based infrastructures

Designing and optimizing the structure of urban transportation networks is a challenging task. In this study, we propose a method inspired by optimal transport theory and the principle of economy of scale that uses little information in input to generate structures that are similar to those of public transportation networks. Contrarily to standard approaches, it does not assume any initial backbone network infrastructure but rather extracts this directly from a continuous space using only a few origin and destination points, generating networks from scratch. Analyzing a set of urban train, tram and subway networks, we find a noteworthy degree of similarity in several of the studied cases between simulated and real infrastructures. By tuning one parameter, our method can simulate a range of different subway, tram and train networks that can be further used to suggest possible improvements in terms of relevant transportation properties. Outputs of our algorithm provide naturally a principled quantitative measure of similarity between two networks that can be used to automatize the selection of similar simulated networks.

Teasing out elevational trends in infraspecific Prunus taxa: A vein analysis approach

Using 33 specimens collected from across their range in Turkey, we demonstrate that the subspecies of Prunus microcarpa C.A.Mey react very differently to altitude. We first outline a simplified, flexible protocol for sectioning and removing the epidermis of small, difficult-to-image leaves for leaf vein studies. We then used venation analysis software to evaluate the two subspecies of this wild cherry in relation to altitude. We also found key differences in venation features between short-shoot and long-shoot leaves for each taxon. Differences include statistically significant negative correlation between vein density, and positive correlation between areole area and altitude in long-shoot leaves of Prunus microcarpa subsp. microcarpa, while its short-shoot leaves had a positive relationship between maximum areole area, and negative relationship between vein density, numbers of veins and endpoints. Meanwhile, P. microcarpa subsp. tortuosa (Boiss. & Hausskn.) Browicz recorded trends that were largely opposite of this, but beside vein thickness and areole area, were not statistically significant. This difference may be part of each taxon's overarching syndrome of anatomical and morphological adaptations to its external environment. RESEARCH HIGHLIGHTS: Features of vein density and thickness fell, while areole area and vein length rose with altitude in P. microcarpa. P. microcarpa subsp. tortuosa showed opposite trends, but reacted less strongly to altitude. Short-shoot and long-shoot have significantly different venation parameters. Using sections proportionate to leaf size is useful to compare venation of leaves that vary due to dimorphism. We discuss protocol strategies for imaging of difficult leaves for venation analyses.

Meshed neuronal mitochondrial networks empowered by AI-powered classifiers and immersive VR reconstruction

Mitochondrial networks are defined as a continuous matrix lumen, but the morphological feature of neuronal mitochondrial networks is not clear due to the lack of suitable analysis techniques. The aim of the present study is to develop a framework to capture and analyze the neuronal mitochondrial networks by using 4-step process composed of 2D and 3D observation, primary and secondary virtual reality (VR) analysis, with the help of artificial intelligence (AI)-powered Aivia segmentation an classifiers. In order to fulfill this purpose, we first generated the PCs-Mito-GFP mice, in which green fluorescence protein (GFP) could be expressed on the outer mitochondrial membrane specifically on the cerebellar Purkinje cells (PCs), thus all mitochondria in the giant neuronal soma, complex dendritic arborization trees and long projection axons of Purkinje cells could be easily detected under a laser scanning confocal microscope. The 4-step process resolved the complicated neuronal mitochondrial networks into discrete neuronal mitochondrial meshes. Second, we measured the two parameters of the neuronal mitochondrial meshes, and the results showed that the surface area (μm²) of mitochondrial meshes was the biggest in dendritic trees (45.30 ± 53.21), the smallest in granular-like axons (3.99 ± 1.82), and moderate in soma (27.81 ± 22.22) and silk-like axons (17.50 ± 15.19). These values showed statistically different among different subcellular locations. The volume (μm³) of mitochondrial meshes was the biggest in dendritic trees (9.97 ± 12.34), the smallest in granular-like axons (0.43 ± 0.25), and moderate in soma (6.26 ± 6.46) and silk-like axons (3.52 ± 4.29). These values showed significantly different among different subcellular locations. Finally, we found both the surface area and the volume of mitochondrial meshes in dendritic trees and soma within the Purkinje cells in PCs-Mito-GFP mice after receiving the training with the simulating long-term pilot flight concentrating increased significantly. The precise reconstruction of neuronal mitochondrial networks is extremely laborious, the present 4-step workflow powered by artificial intelligence and virtual reality reconstruction could successfully address these challenges.

Infrastructure adaptation and emergence of loops in network routing with time-dependent loads

Network routing approaches are widely used to study the evolution in time of self-adapting systems. However, few advances have been made for problems where adaptation is governed by time-dependent inputs. In this work we study a dynamical systems where the edge conductivities of a network are regulated by time-varying mass loads injected on nodes. Motivated by empirical observations, we assume that conductivities adapt slowly with respect to the characteristic time of the loads. Furthermore, assuming the loads to be periodic, we derive a dynamics where the evolution of the system is controlled by a matrix obtained with the Fourier coefficients of the input loads. Remarkably, we find a sufficient condition on these coefficients that determines when the resulting network topologies are trees. We show an example of this on the Bordeaux bus network where we tune the input loads to interpolate between loopy and tree topologies. We validate our model on several synthetic networks and provide an expression for long-time solutions of the original conductivities.

Community detection in networks by dynamical optimal transport formulation

Detecting communities in networks is important in various domains of applications. While a variety of methods exist to perform this task, recent efforts propose Optimal Transport (OT) principles combined with the geometric notion of Ollivier-Ricci curvature to classify nodes into groups by rigorously comparing the information encoded into nodes' neighborhoods. We present an OT-based approach that exploits recent advances in OT theory to allow tuning between different transportation regimes. This allows for better control of the information shared between nodes' neighborhoods. As a result, our model can flexibly capture different types of network structures and thus increase performance accuracy in recovering communities, compared to standard OT-based formulations. We test the performance of our algorithm on both synthetic and real networks, achieving a comparable or better performance than other OT-based methods in the former case, while finding communities that better represent node metadata in real data. This pushes further our understanding of geometric approaches in their ability to capture patterns in complex networks.

Sustainable optimal transport in multilayer networks

Traffic congestion is one of the major challenges faced by the transportation industry. While this problem carries a high economic and environmental cost, the need for an efficient design of optimal paths for passengers in multilayer network infrastructures is imperative. We consider an approach based on optimal transport theory to route passengers preferably along layers that are more carbon-efficient than the road, e.g., rails. By analyzing the impact of this choice on performance, we find that this approach reduces carbon emissions considerably compared to shortest-path minimization. Similarly, we find that this approach distributes traffic more homogeneously, thus alleviating the risk of traffic congestion. Our results shed light on the impact of distributing traffic flexibly across layers guided by optimal transport theory.

Multicommodity routing optimization for engineering networks

Optimizing passengers routes is crucial to design efficient transportation networks. Recent results show that optimal transport provides an efficient alternative to standard optimization methods. However, it is not yet clear if this formalism has empirical validity on engineering networks. We address this issue by considering different response functions-quantities determining the interaction between passengers-in the dynamics implementing the optimal transport formulation. Particularly, we couple passengers' fluxes by taking their sum or the sum of their squares. The first choice naturally reflects edges occupancy in transportation networks, however the second guarantees convergence to an optimal configuration of flows. Both modeling choices are applied to the Paris metro. We measure the extent of traffic bottlenecks and infrastructure resilience to node removal, showing that the two settings are equivalent in the congested transport regime, but different in the branched one. In the latter, the two formulations differ on how fluxes are distributed, with one function favoring routes consolidation, thus potentially being prone to generate traffic overload. Additionally, we compare our method to Dijkstra's algorithm to show its capacity to efficiently recover shortest-path-like graphs. Finally, we observe that optimal transport networks lie in the Pareto front drawn by the energy dissipated by passengers, and the cost to build the infrastructure.