Background
Integrative network methods are commonly used for interpretation of high-throughput experimental biological data: transcriptomics, proteomics, metabolomics and others. One of the common approaches is finding a connected subnetwork of a global interaction network that best encompasses significant individual changes in the data and represents a so-called active module. Usually methods implementing this approach find a single subnetwork and thus solve a hard classification problem for vertices. This subnetwork inherently contains erroneous vertices, while no instrument is provided to estimate the confidence level of any particular vertex inclusion. To address this issue, in the current study we consider the active module problem as a soft classification problem.
Results
We propose a method to estimate probabilities of each vertex to belong to the active module based on Markov chain Monte Carlo (MCMC) subnetwork sampling. As an example of the performance of our method on real data, we run it on two gene expression datasets. For the first many-replicate expression dataset we show that the proposed approach is consistent with an existing resampling-based method. On the second dataset the jackknife resampling method is inapplicable due to the small number of biological replicates, but the MCMC method can be run and shows high classification performance.
Conclusions
The proposed method allows to estimate the probability that an individual vertex belongs to the active module as well as the false discovery rate (FDR) for a given set of vertices. Given the estimated probabilities, it becomes possible to provide a connected subgraph in a consistent manner for any given FDR level: no vertex can disappear when the FDR level is relaxed. We show, on both simulated and real datasets, that the proposed method has good computational performance and high classification accuracy.
The study of fracture of thin aluminum rings due to shock loading generated by magnetic-pulse method was performed. This method provides experimental results on dynamic fracture under conditions of pure tension for a wide range of loading conditions. To simulate rapture of the ring samples a structural-temporal fracture criterion was applied. This criterion allows for analysis of the effects which are characteristic for the dynamic experiments. The fracture incubation time value and ultimate stresses are calculated for the aluminum rings subjected to pulse loading. An analytical relationship between the critical stress and the fracture time are obtained and this relation is in good agreement with the experimental data.
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