Related papers: Water transport on infinite graphs

Equilibrium molecular dynamics simulations are used to investigate the effect of phase transitions on the transport properties of highly-confined water between parallel graphene sheets. An abrupt reduction by several orders of magnitude in…

We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind…

Suppose that under the action of gravity, liquid drains through the unit $d$-cube via a minimal-length network of channels constrained to pass through random sites and to flow with nonnegative component in one of the canonical orthogonal…

Maximization of the entropy rate is an important issue to design diffusion processes aiming at a well-mixed state. We demonstrate that it is possible to construct maximal-entropy random walks with only local information on the graph…

A unifying graph theoretic framework for the modelling of metro transportation networks is proposed. This is achieved by first introducing a basic graph framework for the modelling of the London underground system from a diffusion law point…

Multilayer networks describe well many real interconnected communication and transportation systems, ranging from computer networks to multimodal mobility infrastructures. Here, we introduce a model in which the nodes have a limited…

We consider random labelings of finite graphs conditioned on a small fixed number of peaks. We introduce a continuum framework where a combinatorial graph is associated with a metric graph and edges are identified with intervals. Next we…

A ride sharing problem is considered where we are given a graph, whose edges are equipped with a travel cost, plus a set of objects, each associated with a transportation request given by a pair of origin and destination nodes. A vehicle…

We show in full generality the stability of optimal traffic paths in branched transport: namely we prove that any limit of optimal traffic paths is optimal as well. This solves an open problem in the field (cf. Open problem 1 in the book…

Multiplex networks are representations of multilayer interconnected complex networks where the nodes are the same at every layer. They turn out to be good abstractions of the intricate connectivity of multimodal transportation networks,…

We consider a random graph in which vertices can have one of two possible colours. Each vertex switches its colour at a rate that is proportional to the number of vertices of the other colour to which it is connected by an edge. Each edge…

We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply…

We prove non-universality results for first-passage percolation on the configuration model with i.i.d. degrees having infinite variance. We focus on the weight of the optimal path between two uniform vertices. Depending on the properties of…

We consider changes in properties of a subgraph of an infinite graph resulting from the addition of open edges of Bernoulli percolation on the infinite graph to the subgraph. We give the triplet of an infinite graph, one of its subgraphs,…

Many real life queueing networks have finite buffers with overflows. To understand the behavior of such networks, we consider traffic equations that generalize the traffic equations of classic open queueing networks where some nodes are…

Computing paths in graph structures is a fundamental operation in a wide range of applications, from transportation networks to data analysis. The beer path problem, which captures the option of visiting points of interest, such as gas…

We consider data with multiple observations or reports on a network in the case when these networks themselves are connected through some form of network ties. We could take the example of a cognitive social structure where there is another…

In a former paper the concept of Bipartite PageRank was introduced and a theorem on the limit of authority flowing between nodes for personalized PageRank has been generalized. In this paper we want to extend those results to multimodal…

Generative Adversarial Networks have been shown to be powerful in generating content. To this end, they have been studied intensively in the last few years. Nonetheless, training these networks requires solving a saddle point problem that…

We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of…