Demystifying the Scaling Laws of Dense Wireless Networks: No Linear Scaling in Practice

We optimize the hierarchical cooperation protocol of Ozgur, Leveque and Tse, which is supposed to yield almost linear scaling of the capacity of a dense wireless network with the number of users $n$. Exploiting recent results on the optimality of "treating interference as noise" in Gaussian interference channels, we are able to optimize the achievable average per-link rate and not just its scaling law. Our optimized hierarchical cooperation protocol significantly outperforms the originally proposed scheme. On the negative side, we show that even for very large $n$, the rate scaling is far from linear, and the optimal number of stages $t$ is less than 4, instead of $t \rightarrow \infty$ as required for almost linear scaling. Combining our results and the fact that, beyond a certain user density, the network capacity is fundamentally limited by Maxwell laws, as shown by Francheschetti, Migliore and Minero, we argue that there is indeed no intermediate regime of linear scaling for dense networks in practice.Comment: 5 pages, 6 figures, ISIT 2014. arXiv admin note: substantial text overlap with arXiv:1402.181

A pairwise maximum entropy model describes energy landscape for spiral wave dynamics of cardiac fibrillation

Heart is an electrically-connected network. Spiral wave dynamics of cardiac fibrillation shows chaotic and disintegrated patterns while sinus rhythm shows synchronized excitation patterns. To determine functional interactions between cardiomyocytes during complex fibrillation states, we applied a pairwise maximum entropy model (MEM) to the sequential electrical activity maps acquired from the 2D computational simulation of human atrial fibrillation. Then, we constructed energy landscape and estimated hierarchical structure among the different local minima (attractors) to explain the dynamic properties of cardiac fibrillation. Four types of the wave dynamics were considered: sinus rhythm; single stable rotor; single rotor with wavebreak; and multiple wavelet. The MEM could describe all types of wave dynamics (both accuracy and reliability>0.9) except the multiple random wavelet. Both of the sinus rhythm and the single stable rotor showed relatively high pairwise interaction coefficients among the cardiomyocytes. Also, the local energy minima had relatively large basins and high energy barrier, showing stable attractor properties. However, in the single rotor with wavebreak, there were relatively low pairwise interaction coefficients and a similar number of the local minima separated by a relatively low energy barrier compared with the single stable rotor case. The energy landscape of the multiple wavelet consisted of a large number of the local minima separated by a relatively low energy barrier, showing unstable dynamics. These results indicate that the MEM provides information about local and global coherence among the cardiomyocytes beyond the simple structural connectivity. Energy landscape analysis can explain stability and transitional properties of complex dynamics of cardiac fibrillation, which might be determined by the presence of 'driver' such as sinus node or rotor.Comment: Presented at the 62nd Biophysical Society Annual Meeting, San Francisco, California, 201