We study delay tolerant networking (DTN) and in particular, its capacity to store, carry and forward messages so that the messages eventually reach their final destinations. We approach this broad question in the framework of percolation theory. To this end, we assume an elementary mobility model, where nodes arrive to an infinite plane according to a Poisson point process, move a certain distance L, and then depart. In this setting, we characterize the mean density of nodes required to support DTN style networking. In particular, under the given assumptions, we show that DTN is feasible when the mean node degree is greater than 4 e(g), where parameter g=L d is the ratio of the distance L to the transmission range d, and e(g) is the critical reduced number density of tilted cylinders in a directed continuum percolation model. By means of Monte Carlo simulations, we give numerical values for e(g). The asymptotic behavior of e(g) when g tends to infinity is also derived from a fluid flow analysis.
In contrast, in @cite_5 , we assumed and showed that opportunistic content dissemination schemes, such as the floating content, can be analyzed by using a three-dimensional continuum percolation model. In this paper, we adapt the same approach, but instead of approximating the process by undirected percolation model, we consider the characterizing the dissemination of messages by exactly in a DTN network. There are less results available for the directed percolation models than there are for the normal undirected percolation, and results for directed continuum models are even more scarce. The basic directed cases are the bond and site percolation models, where, e.g., bonds have fixed directions (e.g., up and right in a square lattice) @cite_15 @cite_14 . Directed models have been also studied in the context of scale-free networks @cite_6 , which arise in Internet, social networks etc.
@cite_5 @cite_15 @cite_14 @cite_6
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Many complex networks in nature have directed links, a property that affects the network’s navigability and large-scale topology. Here we study the percolation properties of such directed scale-free networks with correlated in and out degree distributions. We derive a phase diagram that indicates the existence of three regimes, determined by the values of the degree exponents. In the first regime we regain the known directed percolation mean field exponents. In contrast, the second and third regimes are characterized by anomalous exponents, which we calculate analytically. In the third regime the network is resilient to random dilution, i.e., the percolation threshold is pc!1. We propose a new end-to-end single image dehazing method, called Densely Connected Pyramid Dehazing Network (DCPDN), which can jointly learn the transmission map, atmospheric light and dehazing all together. The end-to-end learning is achieved by directly embedding the atmospheric scattering model into the network, thereby ensuring that the proposed method strictly follows the physics-driven scattering model for dehazing. Inspired by the dense network that can maximize the information flow along features from different levels, we propose a new edge-preserving densely connected encoder-decoder structure with multi-level pyramid pooling module for estimating the transmission map. This network is optimized using a newly introduced edge-preserving loss function. To further incorporate the mutual structural information between the estimated transmission map and the dehazed result, we propose a joint-discriminator based on generative adversarial network framework to decide whether the corresponding dehazed image and the estimated transmission map are real or fake. An ablation study is conducted to demonstrate the effectiveness of each module evaluated at both estimated transmission map and dehazed result. Extensive experiments demonstrate that the proposed method achieves significant improvements over the state-of-the-art methods. Code and dataset is made available at: https: github.com hezhangsprinter DCPDN We propose a new end-to-end single image dehazing method, called Densely Connected Pyramid Dehazing Network (DCPDN), which can jointly learn the transmission map, atmospheric light and dehazing all together. The end-to-end learning is achieved by directly embedding the atmospheric scattering model into the network, thereby ensuring that the proposed method strictly follows the physics-driven scattering model for dehazing. Inspired by the dense network that can maximize the information flow along features from different levels, we propose a new edge-preserving densely connected encoder-decoder structure with multi-level pyramid pooling module for estimating the transmission map. This network is optimized using a newly introduced edge-preserving loss function. To further incorporate the mutual structural information between the estimated transmission map and the dehazed result, we propose a joint-discriminator based on generative adversarial network framework to decide whether the corresponding dehazed image and the estimated transmission map are real or fake. An ablation study is conducted to demonstrate the effectiveness of each module evaluated at both estimated transmission map and dehazed result. Extensive experiments demonstrate that the proposed method achieves significant improvements over the state-of-the-art methods. Code will be made available at: this https URL We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate percolation as a message passing process and demonstrate how the resulting equations can be used to calculate, among other things, the size of the percolating cluster and the average cluster size. The calculations are exact for sparse networks when the number of short loops in the network is small, but even on networks with many short loops we find them to be highly accurate when compared with direct numerical simulations. By considering the fixed points of the message passing process, we also show that the percolation threshold on a network with few loops is given by the inverse of the leading eigenvalue of the so-called non-backtracking matrix.