Related papers: Transport Processes on Homogeneous Planar Graphs w…

In this paper we consider a wide class of discrete diffusion load balancing algorithms. The problem is defined as follows. We are given an interconnection network and a number of load items, which are arbitrarily distributed among the nodes…

Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…

We study structural feature and evolution of the Internet at the autonomous systems level. Extracting relevant parameters for the growth dynamics of the Internet topology, we construct a toy model for the Internet evolution, which includes…

We introduce a self-organized model of graph evolution associated with preferential network random walkers. The idea is developed by using two different types of walkers, the interactions of which lead to a dynamic graph. The walkers of the…

The transport phenomenon of active particles confined in 3D(three dimensional) corrugated confined channel with Gaussian noises is investigated. Large noise intensity perpendicular to the symmetry axis is good for the diffusion and current…

Graph Neural Networks have emerged as the most popular architecture for graph-level learning, including graph classification and regression tasks, which frequently arise in areas such as biochemistry and drug discovery. Achieving good…

Many foraging microorganisms rely upon cellular transport networks to deliver nutrients, fluid and organelles between different parts of the organism. Networked organisms ranging from filamentous fungi to slime molds demonstrate a…

We study stochastic processes that generate non-growing complex networks without self-loops and multiple edges (simple graphs). The work concentrates on understanding and formulation of constraints which keep the rewiring stochastic…

Quantum communication is a growing area of research, with quantum internet being one of the most promising applications. Studying the statistical properties of this network is essential to understanding its connectivity and the efficiency…

Scale-free networks constitute a fast-developing field that has already provided us with important tools to understand natural and social phenomena. From biological systems to environmental modifications, from quantum fields to high energy…

In this paper we study coordinated multipath routing at the flow-level in networks with routes of length one. As a first step the static case is considered, in which the number of flows is fixed. A clustering pattern in the rate allocation…

Leaf venation is a pervasive example of a complex biological network, endowing leaves with a transport system and mechanical resilience. Transport networks optimized for efficiency have been shown to be trees, i.e. loopless. However,…

We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance…

The transport properties of disordered systems are known to depend critically on dimensionality. We study the diffusion coefficient of a quantum particle confined to a lattice on the surface of a tube, where it scales between the 1D and 2D…

This paper investigates the effect of network topology on the fair allocation of network resources among a set of agents, an all-important issue for the efficiency of transportation networks all around us. We analyse a generic mechanism…

With high throughput networks acquiring a crucial role in supporting data-intensive applications, a variety of data center network topologies have been proposed to achieve high capacity at low cost. While this literature explores a large…

We present an efficient and robust numerical model for simulation of electrokinetic phenomena in porous networks over a wide range of applications including energy conversion, desalination, and lab-on-a-chip systems. Coupling between fluid…

Complex distribution networks are pervasive in biology. Examples include nutrient transport in the slime mold \emph{Physarum polycephalum} as well as mammalian and plant venation. Adaptive rules are believed to guide development of these…

Macroscopic link-based flow models are efficient for simulating flow propagation in urban road networks. Existing link-based flow models described traffic states of a link with two state variables of link inflow and outflow and assumed…

We present a general theoretical framework to discuss mechanisms of morphogen transport and gradient formation in a cell layer. Trafficking events on the cellular scale lead to transport on larger scales. We discuss in particular the case…