One-step synthesis of high-entropy diborides with hierarchy structure and high hardness via aluminum-melt reaction method

Two new high-entropy metal diborides (ZrTiVCr)B2 and (ZrTiVCrMn)B2 were successfully synthesized via a novel aluminum melt reaction method. The high-entropy diboride crystals have a hexagonal structure and possess high compositional uniformity. We unexpectedly found that the Mn elements could significantly change the crystal morphology of (ZrTiVCrMn)B2, resulting in a hierarchically structured nanosheet-assembled nanoplatelet shape. Benefiting from this interesting hierarchical structure and enhanced lattice distortion, the average hardness of the (ZrTiVCrMn)B2 phase is significantly enhanced to 31.44 GPa as compared to that of (ZrTiVCr)B2 for 28.82 GPa. This work will supply a new paradigm for synthesizing high-entropy metal diborides

Secuer: Ultrafast, scalable and accurate clustering of single-cell RNA-seq data.

Identifying cell clusters is a critical step for single-cell transcriptomics study. Despite the numerous clustering tools developed recently, the rapid growth of scRNA-seq volumes prompts for a more (computationally) efficient clustering method. Here, we introduce Secuer, a Scalable and Efficient speCtral clUstERing algorithm for scRNA-seq data. By employing an anchor-based bipartite graph representation algorithm, Secuer enjoys reduced runtime and memory usage over one order of magnitude for datasets with more than 1 million cells. Meanwhile, Secuer also achieves better or comparable accuracy than competing methods in small and moderate benchmark datasets. Furthermore, we showcase that Secuer can also serve as a building block for a new consensus clustering method, Secuer-consensus, which again improves the runtime and scalability of state-of-the-art consensus clustering methods while also maintaining the accuracy. Overall, Secuer is a versatile, accurate, and scalable clustering framework suitable for small to ultra-large single-cell clustering tasks

Secuer: ultrafast, scalable and accurate clustering of single-cell RNA-seq data

Identifying cell clusters is a critical step for single-cell transcriptomics study. Despite the numerous clustering tools developed recently, the rapid growth of scRNA-seq volumes prompts for a more (computationally) efficient clustering method. Here, we introduce Secuer, a Scalable and Efficient speCtral clUstERing algorithm for scRNA-seq data. By employing an anchor-based bipartite graph representation algorithm, Secuer enjoys reduced runtime and memory usage by orders of magnitude, especially for ultra-large datasets profiling over 1 or even 10 million cells. Meanwhile, Secuer also achieves better or comparable accuracy than competing methods in small and moderate benchmark datasets. Furthermore, we showcase that Secuer can also serve as a building block for a new consensus clustering method, Secuer-consensus, which again greatly improves the runtime and scalability of state-of-the-art consensus clustering methods while also maintaining the accuracy. Overall, Secuer is a versatile, accurate, and scalable clustering framework suitable for small to ultra-large single-cell clustering tasks

Performance of Secuer and other methods on simulated datasets.

(A) The NMI of different methods on simulated datasets with different sample sizes. The simulated datasets with an increasing number of cells ranging from 10,000 to 40 million are generated from Mouse brain datasets (see Materials and Methods for more details). (B) The number of clusters estimated by Louvain in five simulated datasets with sample sizes ranging from 5 million to 9 million under different resolutions (x-axis). (C) We divided the entire clustering procedure into three steps and showed the runtime of each step taken by Secuer and vanilla spectral clustering (VSC) on four datasets, including Worm neuron, Simulation data with 10,000 samples, Mouse retina and TAM FACS with the number of cells ranging from 4,217 to 110,823. (D) The NMI of two methods on the four datasets. (TIF)</p

The Secuer-consensus parameters benchmarked on twelve datasets.

(A-C) Clustering accuracy quantified by ARI (A) and NMI (B) vs. the number of repetitions in consensus clustering (M) outputs of Secuer fed into Secuer-consensus (i.e., Secuer-C) over different datasets. (C) Runtime vs. M over different datasets. (TIF)</p

The runtime of Secuer and Secuer-consensus using parallel computation.

(A) Clustering time of Secuer (A) and Secuer-consensus (i.e., Secuer-C) (B) vs. the number of cores used in parallel computation on different datasets. (TIF)</p

Clustering performance of Secuer and U-SPEC.

(A) The differences between Secuer and U-SPEC. Here the number of clusters K in Secuer is estimated from data (i.e., data-adaptive) and in U-SPEC is user-specified (i.e., not data-adaptive). (B) ARI (left) and NMI (right) of Secuer and U-SPEC on 128 datasets from Mouse Cell Atlas, where Secuer used a locally scaled Gaussian kernel and U-SPEC used a non-locally scaled Gaussian kernel. The detailed information on these datasets is provided in S2 Table. Each point is the average over 10 runs and the dashed rectangles refer to the datasets with poor results (defined as those with ARI (TIF)</p

The performance of different methods on large real datasets.

(A) The clustering time of different methods. (B) The ARI of different methods on three large datasets. (C-I) UMAP visualization of the Mouse brain dataset for the different methods. Reference (C) illustrates the ground-truth cell type labels obtained from the original study. Secuer (D), Louvain (E), and Leiden (F) display clustering results by using their default parameters. Adjusted Louvain (G) and adjusted Leiden (H) refer to the clustering results by setting the resolution parameter to 0.3. k-means (I) represents the clustering results given the ground-truth number of clusters in (C).</p

Overview of the Secuer-consensus algorithm and the performance on fourteen scRNA-seq datasets.

(A) Secuer-consensus takes a matrix as input, with genes as the columns and cells as the rows, executes Secuer M times to acquire multiple clustering outputs, and constructs an unweighted bipartite graph, with two sets of nodes respectively representing the clusters (denoted as C) and cells (denoted as x). Finally, k-means clustering is used to obtain a consensus grouping. (B) The clustering runtime for different methods. Secuer-C: short for Secuer-consensus. (C) The ARI for four methods on 14 benchmark datasets.</p

Performance of Secuer on twelve gold and silver standard datasets.

(A) The clustering runtime of each method on all twelve datasets. (B-C) Accuracy of different methods, including k-means, Louvain, Leiden, and Secuer, on gold (B) and silver (C) standard datasets. (D) A boxplot showing the distribution of ARI of different methods on all datasets. (E-I) UMAP visualization of the ground-true cell type labels obtained from the original study, termed as reference (E) and clustering results from four different methods (F-I) on Mouse retina dataset.</p