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Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
The complex spatiotemporal patterns of atmospheric flows resulting from the cooperative existence of fluctuations ranging in size from millimeters to thousands of kilometers are found to exhibit long-range spatial and temporal correlations…
In this article, we consider transport networks with uncertain demands. Network dynamics are given by linear hyperbolic partial differential equations and suitable coupling conditions, while demands are incorporated as solutions to…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
In recent years, the study of biological transportation networks has attracted significant interest, focusing on their self-regulating, demand-driven nature. This paper examines a mathematical model for these networks, featuring nonlinear…
This paper is concerned with the study of scalability in nonlinear heterogeneous networks affected by communication delays and disturbances. After formalizing the notion of scalability, we give two sufficient conditions to assess this…
We present a fluid-dynamic model for the simulation of urban traffic networks with road sections of different lengths and capacities. The model allows one to efficiently simulate the transitions between free and congested traffic, taking…
Traffic waves, the spatiotemporal propagation of congestion, are a key feature of traffic flow. As Adaptive Cruise Control (ACC) systems gain widespread adoption and show promise for improving both efficiency and safety, understanding how…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
Inspired by experiments on the actin driven propulsion of micrometer sized beads we develop and study a minimal mechanical model of a two-dimensional network of stiff elastic filaments grown from the surface of a cylinder. Starting out from…
For real-world complex system constantly enduring perturbation, to achieve survival goal in changing yet unknown environments, the central problem is constantly adapting themself to external environments according to environmental feedback.…
We investigate the properties of an autoassociative network of threshold-linear units whose synaptic connectivity is spatially structured and asymmetric. Since the methods of equilibrium statistical mechanics cannot be applied to such a…
In multi-class communication networks, traffic surges due to one class of users can significantly degrade the performance for other classes. During these transient periods, it is thus of crucial importance to implement priority mechanisms…
Robustness of routing policies for networks is a central problem which is gaining increased attention with a growing awareness to safeguard critical infrastructure networks against natural and man-induced disruptions. Routing under limited…
Several networks occurring in real life have modular structures that are arranged in an hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that,…
We derive a class of equations describing low Reynolds number steady flows of incompressible and viscous fluids in networks made of straight channels, with several sources and sinks, and adaptive conductivities. The flow is controlled by…
A complex network is said to show topological isotropy if the topological structure around a particular node looks the same in all directions of the whole network. Topologically anisotropic networks are those where the local neighborhood…
The structure of complex networks in previous research has been widely described as scale-free networks generated by the preferential attachment model. However, the preferential attachment model does not take into account the detailed…
While modern deep networks have demonstrated remarkable versatility, their training dynamics remain poorly understood--often driven more by empirical tweaks than architectural insight. This paper investigates how internal structural choices…
We study a coupled dynamics of a network and a particle system. Particles of density $\rho$ diffuse freely along edges, each of which is rewired at a rate given by a decreasing function of particle flux. We find that the coupled dynamics…