Prior research has demonstrated the efficacy of balanced trees as spatially adaptive grids for large-scale simulations. However, state-of-the-art methods for balanced tree construction are restricted by the iterative nature of the ripple effect, thus failing to fully leverage the massive parallelism offered by modern GPU architectures. We propose to reframe the construction of balanced trees as a process to merge N -balanced Minimum Spanning Trees ( N -balanced MSTs) generated from a collection of seed points. To ensure optimal performance, we propose a stack-free parallel strategy for constructing all internal nodes of a specified N -balanced MST. This approach leverages two 32-bit integer registers as buffers rather than relying on an integer array as a stack during construction, which helps maintain balanced workloads across different GPU threads. We then propose a dynamic update algorithm utilizing refinement counters for all internal nodes to enable parallel insertion and deletion operations of N -balanced MSTs. This design achieves significant efficiency improvements compared to full reconstruction from scratch, thereby facilitating fluid simulations in handling dynamic moving boundaries. Our approach is fully compatible with GPU implementation and demonstrates up to an order-of-magnitude speedup compared to the state-of-the-art method [Wang et al. 2024]. The source code for the paper is publicly available at https://github.com/peridyno/peridyno.

RNA Polymerase II (Pol II) transcriptional elongation pausing is an integral part of the dynamic regulation of gene transcription in the genome of metazoans. It plays a pivotal role in many vital biological processes and disease progression. However, experimentally measuring genome-wide Pol II pausing is technically challenging and the precise governing mechanism underlying this process is not fully understood. Here, we develop RP3 (RNA Polymerase II Pausing Prediction), a network regularized logistic regression machine learning method, to predict Pol II pausing events by integrating genome sequence, histone modification, gene expression, chromatin accessibility, and protein-protein interaction data. RP3 can accurately predict Pol II pausing in diverse cellular contexts and unveil the transcription factors that are associated with the Pol II pausing machinery. Furthermore, we utilize a forward feature selection framework to systematically identify the combination of histone modification signals associated with Pol II pausing. RP3 is freely available at https://github.com/AMSSwanglab/RP3.

The DNA methyltransferases (DNMTs) (DNMT3A, DNMT3B and DNMT3L) are primarily responsible for the establishment of genomic locus-specific DNA methylation patterns, which play an important role in gene regulation and animal development. However, this important protein family's binding mechanism, i.e. how and where the DNMTs bind to genome, is still missing in most tissues and cell lines. This motivates us to explore DNMTs and TF's cooperation and develop a network regularized logistic regression model, GuidingNet, to predict DNMTs' genome-wide binding by integrating gene expression, chromatin accessibility, sequence and protein-protein interaction data. GuidingNet accurately predicted methylation experimental data validated DNMTs' binding, outperformed single data source based and sparsity regularized methods and performed well in within and across tissue prediction for several DNMTs in human and mouse. Importantly, GuidingNet can reveal transcription cofactors assisting DNMTs for methylation establishment. This provides biological understanding in the DNMTs' binding specificity in different tissues and demonstrate the advantage of network regularization. In addition to DNMTs, GuidingNet achieves good performance for other chromatin regulators' binding. GuidingNet is freely available at https://github.com/AMSSwanglab/GuidingNet.