Multiplex networks have become increasingly more prevalent in many fields, and have emerged as a powerful tool for modeling the complexity of real networks. There is a critical need for developing inference models for multiplex networks that can take into account potential dependencies across different layers, particularly when the aim is community detection. We add to a limited literature by proposing a novel and efficient Bayesian model for community detection in multiplex networks. A key feature of our approach is the ability to model varying communities at different network layers. In contrast, many existing models assume the same communities for all layers. Moreover, our model automatically picks up the necessary number of communities at each layer (as validated by real data examples). This is appealing, since deciding the number of communities is a challenging aspect of community detection, and especially so in the multiplex setting, if one allows the communities to change across layers. Borrowing ideas from hierarchical Bayesian modeling, we use a hierarchical Dirichlet prior to model community labels across layers, allowing dependency in their structure. Given the community labels, a stochastic block model (SBM) is assumed for each layer. We develop an efficient slice sampler for sampling the posterior distribution of the community labels as well as the link probabilities between communities. In doing so, we address some unique challenges posed by coupling the complex likelihood of SBM with the hierarchical nature of the prior on the labels. An extensive empirical validation is performed on simulated and real data, demonstrating the superior performance of the model over single-layer alternatives, as well as the ability to uncover interesting structures in real networks.

Chronic kidney disease (CKD) is a major public health burden around the world. The gut microbiome may contribute to CKD progression and serve as a promising therapeutic target. Colonic dialysis has long been used in China to help remove gut-derived toxins to delay CKD progression. Since disturbances in the gut biome may influence disease progression, we wondered whether colonic dialysis may mitigate the condition by influencing the biome. We compared the gut microbiota, based on 16S rRNA gene sequencing, in fecal samples of 25 patients with CKD (stages 3–5) who were receiving colonic dialysis(group CD), 25 outpatients with CKD not receiving colonic dialysis(group OP), and 34 healthy subjects(group HS). Richness of gut microbiota was similar between patients on colonic dialysis and healthy subjects, and richness in these two groups was significantly higher than that in patients not on colonic dialysis. Colonic dialysis also altered the profile of microbes in the gut of CKD patients, bringing it closer to the profile in healthy subjects. Colonic dialysis may protect renal function in pre-dialysis CKD by mitigating dysbiosis of gut microbiota.

Adversarial examples can easily degrade the classification performance in neural networks. Empirical methods for promoting robustness to such examples have been proposed, but often lack both analytical insights and formal guarantees. Recently, some robustness certificates have appeared in the literature based on system theoretic notions. This letter proposes an incremental dissipativity-based robustness certificate for neural networks in the form of a linear matrix inequality for each layer. We also propose a sufficient spectral norm bound for this certificate which is scalable to neural networks with multiple layers. We demonstrate the improved performance against adversarial attacks on a feed-forward neural network trained on MNIST and an Alexnet trained using CIFAR-10.

It has become an increasingly common practice in modern science and engineering to collect samples of multiple network data in which a network serves as a basic data object. The increasing prevalence of multiple network data calls for developments of models and theories that can deal with inference problems for populations of networks. In this work, we propose a general procedure for hypothesis testing of networks and in particular, for differentiating distributions of two samples of networks. We consider a very general framework which allows us to perform test on large and sparse networks. Our contribution is two-fold: (1) We propose a test statistics based on the singular value of a generalized Wigner matrix. The asymptotic null distribution of the statistics is shown to follow the Tracy–Widom distribution as the number of nodes tends to infinity. The test also yields asymptotic power guarantee with the power tending to one under the alternative; (2) The test procedure is adapted for change-point detection in dynamic networks which is proven to be consistent in detecting the change-points. In addition to theoretical guarantees, another appealing feature of this adapted procedure is that it provides a principled and simple method for selecting the threshold that is also allowed to vary with time. Extensive simulation studies and real data analyses demonstrate the superior performance of our procedure with competitors.