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Nana Wei

Publications and source records attributed to Nana Wei.

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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.

q-bio.QM

The structures and decompositions of symmetries involving idempotents

Let $\mathcal{H}$ be a separable Hilbert space and $P$ be an idempotent on $\mathcal{H}.$ We denote by $$Γ_{P}=\{J: J=J^{\ast}=J^{-1} \hbox{ }\hbox{ and }\hbox{ } JPJ=I-P\}$$ and $$Δ_{P}=\{J: J=J^{\ast}=J^{-1} \hbox{ }\hbox{ and }\hbox{ } JPJ=I-P^*\}.$$ In this paper, we first get that symmetries $(2P-I)|2P-I|^{-1}$ and $(P+P^{*}-I)|P+P^{*}-I|^{-1}$ are the same. Then we show that $Γ_{P}\neq\emptyset$ if and only if $Δ_{P}\neq\emptyset.$ Also, the specific structures of all symmetries $J\inΓ_{P}$ and $J\inΔ_{P} $ are established, respectively. Moreover, we prove that $J\inΔ_{P}$ if and only if $\sqrt{-1}J(2P-I)|2P-I|^{-1}\inΓ_{P}.$

math.FA