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Motivated by results of Henry, Pralat and Zhang (PNAS 108.21 (2011): 8605-8610), we propose a general scheme for evolving spatial networks in order to reduce their total edge lengths. We study the properties of the equilbria of two networks…
In this paper we propose a Godunov-based discretization of a hyperbolic system of conservation laws with discontinuous flux, modeling vehicular flow on a network. Each equation describes the density evolution of vehicles having a common…
Biological transport networks adapt through dynamic interactions between material transport and structural modification during growth and development. In this work, we present a model of transport network growth driven by local material…
Dynamical patterns in complex networks of coupled oscillators are both of theoretical and practical interest, yet to fully reveal and understand the interplay between pattern emergence and network structure remains to be an outstanding…
We consider transport over a strongly connected, directed graph. The scheduling amounts to selecting transition probabilities for a discrete-time Markov evolution which is designed to be consistent with certain initial and final marginals.…
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…
Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway or airline infrastructure over industrial manufacturing to fluid dynamics. Here, we utilize a generic…
Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of…
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
The interaction between natural selection and random mutation is frequently debated in recent years. Does similar dilemma also exist in the evolution of real networks such as biological networks? In this paper, we try to discuss this issue…
Evolving Neural Networks (NNs) has recently seen an increasing interest as an alternative path that might be more successful. It has many advantages compared to other approaches, such as learning the architecture of the NNs. However, the…
We model the robustness against random failure or intentional attack of networks with arbitrary large-scale structure. We construct a block-based model which incorporates --- in a general fashion --- both connectivity and interdependence…
A central issue in complex networks is tolerance to random failures and intentional attacks. Current literature emphasizes the dichotomy between networks with a power-law node connectivity distribution, which are robust to random failures…
Modern network systems, such as transportation and communication systems, are prone to cyber-physical disruptions and thus suffer efficiency loss. This paper studies network resiliency, in terms of throughput, and develops resilient control…
Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that…
The small-world property is known to have a profound effect on the navigation efficiency of complex networks [J. M. Kleinberg, Nature 406, 845 (2000)]. Accordingly, the proper addition of shortcuts to a regular substrate can lead to the…
We study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arises under various centrality measures, and…
Network pruning is used to reduce inference latency and power consumption in large neural networks. However, most current pruning methods rely on ad-hoc heuristics that are poorly understood. We introduce Hyperflux, a conceptually-grounded…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
The behavior of complex networks under failure or attack depends strongly on the specific scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure but appear to be especially vulnerable to…