No Arabic abstract
We propose an efficient scheme for generating fake network traffic to disguise the real event notification in the presence of a global eavesdropper, which is especially relevant for the quality of service in delay-intolerant applications monitoring rare and spatially sparse events, and deployed as large wireless sensor networks with single data collector. The efficiency of the scheme that provides statistical source anonymity is achieved by partitioning network nodes randomly into several node groups. Members of the same group collectively emulate both temporal and spatial distribution of the event. Under such dummy-traffic framework of the source anonymity protection, we aim to better model the global eavesdropper, especially her way of using statistical tests to detect the real event, and to present the quality of the location protection as relative to the adversarys strength. In addition, our approach aims to reduce the per-event work spent to generate the fake traffic while, most importantly, providing a guaranteed latency in reporting the event. The latency is controlled by decoupling the routing from the fake traffic schedule. We believe that the proposed source anonymity protection strategy, and the quality evaluation framework, are well justified by the abundance of the applications that monitor a rare event with known temporal statistics, and uniform spatial distribution.
Modularity is a popular metric for quantifying the degree of community structure within a network. The distribution of the largest eigenvalue of a networks edge weight or adjacency matrix is well studied and is frequently used as a substitute for modularity when performing statistical inference. However, we show that the largest eigenvalue and modularity are asymptotically uncorrelated, which suggests the need for inference directly on modularity itself when the network size is large. To this end, we derive the asymptotic distributions of modularity in the case where the networks edge weight matrix belongs to the Gaussian Orthogonal Ensemble, and study the statistical power of the corresponding test for community structure under some alternative model. We empirically explore universality extensions of the limiting distribution and demonstrate the accuracy of these asymptotic distributions through type I error simulations. We also compare the empirical powers of the modularity based tests with some existing methods. Our method is then used to test for the presence of community structure in two real data applications.
This work considers a line-of-sight underwater acoustic sensor network (UWASN) consisting of $M$ underwater sensor nodes randomly deployed according to uniform distribution within a vertical half-disc (the so-called trusted zone). The sensor nodes report their sensed data to a sink node on water surface on a shared underwater acoustic (UWA) reporting channel in a time-division multiple-access (TDMA) fashion, while an active-yet-invisible adversary (so-called Eve) is present in the close vicinity who aims to inject malicious data into the system by impersonating some Alice node. To this end, this work first considers an additive white Gaussian noise (AWGN) UWA channel, and proposes a novel, multiple-features based, two-step method at the sink node to thwart the potential impersonation attack by Eve. Specifically, the sink node exploits the noisy estimates of the distance, the angle of arrival, and the location of the transmit node as device fingerprints to carry out a number of binary hypothesis tests (for impersonation detection) as well as a number of maximum likelihood hypothesis tests (for transmitter identification when no impersonation is detected). We provide closed-form expressions for the error probabilities (i.e., the performance) of most of the hypothesis tests. We then consider the case of a UWA with colored noise and frequency-dependent pathloss, and derive a maximum-likelihood (ML) distance estimator as well as the corresponding Cramer-Rao bound (CRB). We then invoke the proposed two-step, impersonation detection framework by utilizing distance as the sole feature. Finally, we provide detailed simulation results for both AWGN UWA channel and the UWA channel with colored noise. Simulation results verify that the proposed scheme is indeed effective for a UWA channel with colored noise and frequency-dependent pathloss.
In wireless sensor networks (WSNs), the Eschenauer-Gligor (EG) key pre-distribution scheme is a widely recognized way to secure communications. Although connectivity properties of secure WSNs with the EG scheme have been extensively investigated, few results address physical transmission constraints. These constraints reflect real-world implementations of WSNs in which two sensors have to be within a certain distance from each other to communicate. In this paper, we present zero-one laws for connectivity in WSNs employing the EG scheme under transmission constraints. These laws help specify the critical transmission ranges for connectivity. Our analytical findings are confirmed via numerical experiments. In addition to secure WSNs, our theoretical results are also applied to frequency hopping in wireless networks.
We investigate the condition on transmission radius needed to achieve connectivity in duty-cycled wireless sensor networks (briefly, DC-WSN). First, we settle a conjecture of Das et. al. (2012) and prove that the connectivity condition on Random Geometric Graphs (RGG), given by Gupta and Kumar (1989), can be used to derive a weak sufficient condition to achieve connectivity in DC-WSN. To find a stronger result, we define a new vertex-based random connection model which is of independent interest. Following a proof technique of Penrose (1991) we prove that when the density of the nodes approaches infinity then a finite component of size greater than 1 exists with probability 0 in this model. We use this result to obtain an optimal condition on node transmission radius which is both necessary and sufficient to achieve connectivity and is hence optimal. The optimality of such a radius is also tested via simulation for two specific duty-cycle schemes, called the contiguous and the random selection duty-cycle scheme. Finally, we design a minimum-radius duty-cycling scheme that achieves connectivity with a transmission radius arbitrarily close to the one required in Random Geometric Graphs. The overhead in this case is that we have to spend some time computing the schedule.
We study the efficacy and efficiency of deep generative networks for approximating probability distributions. We prove that neural networks can transform a low-dimensional source distribution to a distribution that is arbitrarily close to a high-dimensional target distribution, when the closeness are measured by Wasserstein distances and maximum mean discrepancy. Upper bounds of the approximation error are obtained in terms of the width and depth of neural network. Furthermore, it is shown that the approximation error in Wasserstein distance grows at most linearly on the ambient dimension and that the approximation order only depends on the intrinsic dimension of the target distribution. On the contrary, when $f$-divergences are used as metrics of distributions, the approximation property is different. We show that in order to approximate the target distribution in $f$-divergences, the dimension of the source distribution cannot be smaller than the intrinsic dimension of the target distribution.