Sparsified Block Elimination for Directed Laplacians

We show that the sparsified block elimination algorithm for solving undirected Laplacian linear systems from [Kyng-Lee-Peng-Sachdeva-Spielman STOC'16] directly works for directed Laplacians. Given access to a sparsification algorithm that, on graphs with $n$ vertices and $m$ edges, takes time $\mathcal{T}_{\rm S}(m)$ to output a sparsifier with $\mathcal{N}_{\rm S}(n)$ edges, our algorithm solves a directed Eulerian system on $n$ vertices and $m$ edges to $\epsilon$ relative accuracy in time $$O(\mathcal{T}_{\rm S}(m) + {\mathcal{N}_{\rm S}(n)\log {n}\log(n/\epsilon)}) + \tilde{O}(\mathcal{T}_{\rm S}(\mathcal{N}_{\rm S}(n)) \log n),$$ where the $\tilde{O}(\cdot)$ notation hides $\log\log(n)$ factors. By previous results, this implies improved runtimes for linear systems in strongly connected directed graphs, PageRank matrices, and asymmetric M-matrices. When combined with slower constructions of smaller Eulerian sparsifiers based on short cycle decompositions, it also gives a solver that runs in $O(n \log^{5}n \log(n / \epsilon))$ time after $O(n^2 \log^{O(1)} n)$ pre-processing. At the core of our analyses are constructions of augmented matrices whose Schur complements encode error matrices

Communication-Efficient Topologies for Decentralized Learning with O(1)O(1) Consensus Rate

Decentralized optimization is an emerging paradigm in distributed learning in which agents achieve network-wide solutions by peer-to-peer communication without the central server. Since communication tends to be slower than computation, when each agent communicates with only a few neighboring agents per iteration, they can complete iterations faster than with more agents or a central server. However, the total number of iterations to reach a network-wide solution is affected by the speed at which the agents' information is ``mixed'' by communication. We found that popular communication topologies either have large maximum degrees (such as stars and complete graphs) or are ineffective at mixing information (such as rings and grids). To address this problem, we propose a new family of topologies, EquiTopo, which has an (almost) constant degree and a network-size-independent consensus rate that is used to measure the mixing efficiency. In the proposed family, EquiStatic has a degree of $\Theta(\ln(n))$, where $n$ is the network size, and a series of time-dependent one-peer topologies, EquiDyn, has a constant degree of 1. We generate EquiDyn through a certain random sampling procedure. Both of them achieve an $n$-independent consensus rate. We apply them to decentralized SGD and decentralized gradient tracking and obtain faster communication and better convergence, theoretically and empirically. Our code is implemented through BlueFog and available at \url{https://github.com/kexinjinnn/EquiTopo}Comment: NeurIPS 202

Chromosome-level genome assembly of the caenogastropod snail Rapana venosa

Abstract The carnivorous gastropod Rapana venosa (Valenciennes, 1846) is one of the most notorious ecological invaders worldwide. Here, we present the first high-quality chromosome-scale reference R. venosa genome obtained via PacBio sequencing, Illumina paired-end sequencing, and high-throughput chromosome conformation capture scaffolding. The assembled genome has a size of 2.30 Gb, with a scaffold N50 length of 64.63 Mb, and is anchored to 35 chromosomes. It contains 29,649 protein-coding genes, 77.22% of which were functionally annotated. Given its high heterozygosity (1.41%) and large proportion of repeat sequences (57.72%), it is one of the most complex genome assemblies. This chromosome-level genome assembly of R. venosa is an important resource for understanding molluscan evolutionary adaption and provides a genetic basis for its biological invasion control

Rethinking Nano-TiO Safety: Overview of Toxic Effects in Humans and Aquatic Animals.

Titanium dioxide nanoparticles (nano-TiO2 ) are widely used in consumer products, raising environmental and health concerns. An overview of the toxic effects of nano-TiO2 on human and environmental health is provided. A meta-analysis is conducted to analyze the toxicity of nano-TiO2 to the liver, circulatory system, and DNA in humans. To assess the environmental impacts of nano-TiO2 , aquatic environments that receive high nano-TiO2 inputs are focused on, and the toxicity of nano-TiO2 to aquatic organisms is discussed with regard to the present and predicted environmental concentrations. Genotoxicity, damage to membranes, inflammation and oxidative stress emerge as the main mechanisms of nano-TiO2 toxicity. Furthermore, nano-TiO2 can bind with free radicals and signal molecules, and interfere with the biochemical reactions on plasmalemma. At the higher organizational level, nano-TiO2 toxicity is manifested as the negative effects on fitness-related organismal traits including feeding, reproduction and immunity in aquatic organisms. Bibliometric analysis reveals two major research hot spots including the molecular mechanisms of toxicity of nano-TiO2 and the combined effects of nano-TiO2 and other environmental factors such as light and pH. The possible measures to reduce the harmful effects of nano-TiO2 on humans and non-target organisms has emerged as an underexplored topic requiring further investigation