Related papers: Fluctuations and redundancy in optimal transport n…

We study spatial networks that are designed to distribute or collect a commodity, such as gas pipelines or train tracks. We focus on the cost of a network, as represented by the total length of all its edges, and its efficiency in terms of…

A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a final distribution. The cost of the scheme encodes a higher transport efficiency…

We investigate the relation between energy minimizing maps valued into spheres having topological singularities at given points and optimal networks connecting them (e.g. Steiner trees, Gilbert-Steiner irrigation networks). We show the…

Supply chain network is critical to serving customers, so the most common practices are to determine the number, location, and capacity of facilities. But at the same time, uncertainties and risks must be taken into account in order to…

Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in…

Ecological networks such as plant-pollinator systems and food webs vary in space and time. This variability includes fluctuations in global network properties such as total number and intensity of interactions but also in the local…

Traffic congestion is one of the major challenges faced by the transportation industry. While this problem carries a high economical and environmental cost, the need for an efficient design of optimal paths for passengers in multilayer…

Distribution networks -- from vasculature to urban transportation systems -- are prevalent in both the natural and consumer worlds. These systems are intrinsically physical in composition and are embedded into real space, properties that…

Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…

A heterogeneous continuous time random walk is an analytical formalism for studying and modeling diffusion processes in heterogeneous structures on microscopic and macroscopic scales. In this paper we study both analytically and numerically…

Tree-based phylogenetic networks, which may be roughly defined as leaf-labeled networks built by adding arcs only between the original tree edges, have elegant properties for modeling evolutionary histories. We answer an open question of…

Units of complex systems -- such as neurons in the brain or individuals in societies -- must communicate efficiently to function properly: e.g., allowing electrochemical signals to travel quickly among functionally connected neuronal areas…

We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans…

The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…

Advanced integration of logistics systems has been promoted for the sake of competitiveness and sustainability. Such efforts will enable more globally optimal and flexible operations by efficiently utilizing transportation capacity. At the…

In ad hoc wireless networking, units are connected to each other rather than to a central, fixed, infrastructure. Constructing and maintaining such networks create several trade-off problems between robustness, communication speed, power…

We review the research literature investigating systems in which mobile entities can carry data while they move. These entities can be either mobile by nature (e.g., human beings and animals) or mobile by design (e.g., trains, airplanes,…

To analyze the transport of information or material from a source to every node of a network we use two quantities introduced in the study of river networks: the cost and the flow. For a network with $K$ nodes and $M$ levels, we show that…

An important feature of many complex systems, both natural and artificial, is the structure and organization of their interaction networks with interesting properties. Here we present a theory of self-organization by evolutionary adaptation…

Surfacic networks are structures built upon a two-dimensional manifold. Many systems, including transportation networks and various urban networks, fall into this category. The fluctuations of node elevations imply significant deviations…