Hierarchical Stochastic Block Model for Community Detection in Multiplex Networks

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

Failure Inference and Optimization for Step Stress Model Based on Bivariate Wiener Model

In this paper, we consider the situation under a life test, in which the failure time of the test units are not related deterministically to an observable stochastic time varying covariate. In such a case, the joint distribution of failure time and a marker value would be useful for modeling the step stress life test. The problem of accelerating such an experiment is considered as the main aim of this paper. We present a step stress accelerated model based on a bivariate Wiener process with one component as the latent (unobservable) degradation process, which determines the failure times and the other as a marker process, the degradation values of which are recorded at times of failure. Parametric inference based on the proposed model is discussed and the optimization procedure for obtaining the optimal time for changing the stress level is presented. The optimization criterion is to minimize the approximate variance of the maximum likelihood estimator of a percentile of the products' lifetime distribution

Anderson Transition in Disordered Bilayer Graphene

Employing the Kernel Polynomial method (KPM), we study the electronic properties of the graphene bilayers in the presence of diagonal disorder, within the tight-binding approximation. The KPM method enables us to calculate local density of states (LDOS) without need to exactly diagonalize the Hamiltonian. We use the geometrical averaging of the LDOS's at different lattice sites as a criterion to distinguish the localized states from extended ones. We find that bilayer graphene undergoes Anderson metal-insulator transition at a critical value of disorder strength

The upper normal limit of serum alanine aminotransferase in Golestan Province, Northeast Iran

Background: The objective of this study was to determine the upper normal limit of serum alanine aminotransferase level in a population-based study in Golestan Province, northeast Iran. Methods: From the randomly invited individuals (2,292), 698 out of the 916 males and 1,351 out of the 1,376 females participated in the study (participation rate: 76.2 and 98.1, respectively). One hundred and twenty-one participants were excluded due to positive hepatitis B surface antigen or hepatitis C virus antibody and/or drinking more than 20 grams of alcohol per day. A total of 1,928 participants (1300 females) were included. The upper normal limit of serum alanine aminotransferase level was defined as the 95th percentile. Results: The upper normal limit of serum alanine aminotransferase level in normal weight and nondiabetics was significantly lower than the total study group (36 versus 45 U/L). Serum alanine aminotransferase level was independently associated with male gender, body mass index, and diabetes mellitus (OR=2.05; 95Cl: 1.44 - 2.94, OR=2.76; 95Cl: 1.84 - 4.13, and OR=2.96; 95Cl: 1.56-5.61, respectively). Conclusion: Considering the lower calculated upper normal limit in normal weight nondiabetic participants in this study, we recommend setting new upper normal limit for serum alanine aminotransferase level, It seems reasonable to set upper normal limit for serum alanine aminotransferase level in males and females separately