The stochastic block model (SBM) provides a popular framework for modeling community structures in networks. However, more attention has been devoted to problems concerning estimating the latent node labels and the model parameters than the issue of choosing the number of blocks. We consider an approach based on the log likelihood ratio statistic and analyze its asymptotic properties under model misspecification. We show the limiting distribution of the statistic in the case of underfitting is normal and obtain its convergence rate in the case of overfitting. These conclusions remain valid when the average degree grows at a polylog rate. The results enable us to derive the correct order of the penalty term for model complexity and arrive at a likelihood-based model selection criterion that is asymptotically consistent. Our analysis can also be extended to a degree-corrected block model (DCSBM). In practice, the likelihood function can be estimated using more computationally efficient variational methods or consistent label estimation algorithms, allowing the criterion to be applied to large networks.

With the recent increase in study sample sizes in human genetics, there has been growing interest in inferring historical population demography from genomic variation data. Here, we present an efficient inference method that can scale up to very large samples, with tens or hundreds of thousands of individuals. Specifically, by utilizing analytic results on the expected frequency spectrum under the coalescent and by leveraging the technique of automatic differentiation, which allows us to compute gradients exactly, we develop a very efficient algorithm to infer piecewise-exponential models of the historical effective population size from the distribution of sample allele frequencies. Our method is orders of magnitude faster than previous demographic inference methods based on the frequency spectrum. In addition to inferring demography, our method can also accurately estimate locus-specific mutation rates. We perform extensive validation of our method on simulated data and show that it can accurately infer multiple recent epochs of rapid exponential growth, a signal that is difficult to pick up with small sample sizes. Lastly, we use our method to analyze data from recent sequencing studies, including a large-sample exome-sequencing data set of tens of thousands of individuals assayed at a few hundred genic regions.

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Single-cell multi-omics data continues to grow at an unprecedented pace, and effectively integrating different modalities holds the promise for better characterization of cell identities. Although a number of methods have demonstrated promising results in integrating multiple modalities from the same tissue, the complexity and scale of data compositions typically present in cell atlases still pose a significant challenge for existing methods. Here we present scJoint, a transfer learning method to integrate atlas-scale, heterogeneous collections of scRNA-seq and scATAC-seq data. scJoint leverages information from annotated scRNA-seq data in a semi-supervised framework and uses a neural network to simultaneously train labeled and unlabeled data, enabling label transfer and joint visualization in an integrative framework. Using multiple atlas data and a biologically varying multi-modal data, we demonstrate scJoint is computationally efficient and 1 .

An interesting feature of microstructured optical fibers (MOFs) is that their properties can be adjusted by filling or coating of the holes. Some applications require selective filling or coating, which has proved experimentally demanding. We demonstrate selective coating of MOFs with metal and use it to fabricate an in-fiber absorptive polarizer.