Network Density of States

Spectral analysis connects graph structure to the eigenvalues and eigenvectors of associated matrices. Much of spectral graph theory descends directly from spectral geometry, the study of differentiable manifolds through the spectra of associated differential operators. But the translation from spectral geometry to spectral graph theory has largely focused on results involving only a few extreme eigenvalues and their associated eigenvalues. Unlike in geometry, the study of graphs through the overall distribution of eigenvalues - the spectral density - is largely limited to simple random graph models. The interior of the spectrum of real-world graphs remains largely unexplored, difficult to compute and to interpret. In this paper, we delve into the heart of spectral densities of real-world graphs. We borrow tools developed in condensed matter physics, and add novel adaptations to handle the spectral signatures of common graph motifs. The resulting methods are highly efficient, as we illustrate by computing spectral densities for graphs with over a billion edges on a single compute node. Beyond providing visually compelling fingerprints of graphs, we show how the estimation of spectral densities facilitates the computation of many common centrality measures, and use spectral densities to estimate meaningful information about graph structure that cannot be inferred from the extremal eigenpairs alone.Comment: 10 pages, 7 figure

Performance Comparison of Contention- and Schedule-based MAC Protocols in Urban Parking Sensor Networks

Network traffic model is a critical problem for urban applications, mainly because of its diversity and node density. As wireless sensor network is highly concerned with the development of smart cities, careful consideration to traffic model helps choose appropriate protocols and adapt network parameters to reach best performances on energy-latency tradeoffs. In this paper, we compare the performance of two off-the-shelf medium access control protocols on two different kinds of traffic models, and then evaluate their application-end information delay and energy consumption while varying traffic parameters and network density. From the simulation results, we highlight some limits induced by network density and occurrence frequency of event-driven applications. When it comes to realtime urban services, a protocol selection shall be taken into account - even dynamically - with a special attention to energy-delay tradeoff. To this end, we provide several insights on parking sensor networks.Comment: ACM International Workshop on Wireless and Mobile Technologies for Smart Cities (WiMobCity) (2014

Complex quantum networks as structured environments: engineering and probing

We consider structured environments modeled by bosonic quantum networks and investigate the probing of their spectral density, structure, and topology. We demonstrate how to engineer a desired spectral density by changing the network structure. Our results show that the spectral density can be very accurately detected via a locally immersed quantum probe for virtually any network configuration. Moreover, we show how the entire network structure can be reconstructed by using a single quantum probe. We illustrate our findings presenting examples of spectral densities and topology probing for networks of genuine complexity.Comment: 7 pages, 4 figures. v3: update to match published versio

Controlling chaos in a chaotic neural network

The chaotic neural network constructed with chaotic neuron shows the associative memory function, but its memory searching process cannot be stabilized in a stored state because of the chaotic motion of the network. In this paper, a pinning control method focused on the chaotic neural network is proposed. The computer simulation proves that the chaos in the chaotic neural network can be controlled with this method and the states of the network can converge in one of its stored patterns if the control strength and the pinning density are chosen suitable. It is found that in general the threshold of the control strength of a controlled network is smaller at higher pinned density and the chaos of the chaotic neural network can be controlled more easily if the pinning control is added to the variant neurons between the initial pattern and the target pattern

The Impact of Antenna Height Difference on the Performance of Downlink Cellular Networks

Capable of significantly reducing cell size and enhancing spatial reuse, network densification is shown to be one of the most dominant approaches to expand network capacity. Due to the scarcity of available spectrum resources, nevertheless, the over-deployment of network infrastructures, e.g., cellular base stations (BSs), would strengthen the inter-cell interference as well, thus in turn deteriorating the system performance. On this account, we investigate the performance of downlink cellular networks in terms of user coverage probability (CP) and network spatial throughput (ST), aiming to shed light on the limitation of network densification. Notably, it is shown that both CP and ST would be degraded and even diminish to be zero when BS density is sufficiently large, provided that practical antenna height difference (AHD) between BSs and users is involved to characterize pathloss. Moreover, the results also reveal that the increase of network ST is at the expense of the degradation of CP. Therefore, to balance the tradeoff between user and network performance, we further study the critical density, under which ST could be maximized under the CP constraint. Through a special case study, it follows that the critical density is inversely proportional to the square of AHD. The results in this work could provide helpful guideline towards the application of network densification in the next-generation wireless networks.Comment: conference submission - Mar. 201