Minimum Width of Leaky-ReLU Neural Networks for Uniform Universal Approximation

The study of universal approximation properties (UAP) for neural networks (NN) has a long history. When the network width is unlimited, only a single hidden layer is sufficient for UAP. In contrast, when the depth is unlimited, the width for UAP needs to be not less than the critical width $w^*_{\min}=\max(d_x,d_y)$, where $d_x$ and $d_y$ are the dimensions of the input and output, respectively. Recently, \cite{cai2022achieve} shows that a leaky-ReLU NN with this critical width can achieve UAP for $L^p$ functions on a compact domain $K$, \emph{i.e.,} the UAP for $L^p(K,\mathbb{R}^{d_y})$. This paper examines a uniform UAP for the function class $C(K,\mathbb{R}^{d_y})$ and gives the exact minimum width of the leaky-ReLU NN as $w_{\min}=\max(d_x+1,d_y)+1_{d_y=d_x+1}$, which involves the effects of the output dimensions. To obtain this result, we propose a novel lift-flow-discretization approach that shows that the uniform UAP has a deep connection with topological theory.Comment: ICML2023 camera read

DeePMD-kit v2: A software package for Deep Potential models

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials (MLP) known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, Deep Potential - Range Correction (DPRc), Deep Potential Long Range (DPLR), GPU support for customized operators, model compression, non-von Neumann molecular dynamics (NVNMD), and improved usability, including documentation, compiled binary packages, graphical user interfaces (GUI), and application programming interfaces (API). This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, the article benchmarks the accuracy and efficiency of different models and discusses ongoing developments.Comment: 51 pages, 2 figure

Cloning and physical localization of male-biased repetitive DNA sequences in Spinacia oleracea (Amaranthaceae)

Spinach (Spinacia oleracea Linnaeus, 1753) is an ideal material for studying molecular mechanisms of early-stage sex chromosome evolution in dioecious plants. Degenerate oligonucleotide-primed polymerase chain reaction (DOP-PCR) technique facilitates the retrotransposon-relevant studies by enriching specific repetitive DNA sequences from a micro-dissected single chromosome. We conducted genomic subtractive hybridization to screen sex-biased DNA sequences by using the DOP-PCR amplification products of micro-dissected spinach Y chromosome. The screening yielded 55 male-biased DNA sequences with 30 576 bp in length, of which, 32 DNA sequences (12 049 bp) contained repeat DNA sequences, including LTR/Copia, LTR/Gypsy, simple repeats, and DNA/CMC-EnSpm. Among these repetitive DNA sequences, four DNA sequences that contained a fragment of Ty3-gypsy retrotransposons (SP73, SP75, SP76, and SP77) were selected as fluorescence probes to hybridization on male and female spinach karyotypes. Fluorescence in situ hybridization (FISH) signals of SP73 and SP75 were captured mostly on the centromeres and their surrounding area for each homolog. Hybridization signals primarily appeared near the putative centromeres for each homologous chromosome pair by using SP76 and SP77 probes for FISH, and sporadic signals existed on the long arms. Results can be served as a basis to study the function of repetitive DNA sequences in sex chromosome evolution in spinach

Combined toxic effects of nanoplastics and norfloxacin on mussel: Leveraging biochemical parameters and gut microbiota

Antibiotics and nanoplastics (NPs) are among the two most concerned and studied marine emerging contaminants in recent years. Given the large number of different types of antibiotics and NPs, there is a need to apply efficient tools to evaluate their combined toxic effects. Using the thick-shelled mussel (Mytilus coruscus) as a marine ecotoxicological model, we applied a battery of fast enzymatic activity assays and 16S rRNA sequencing to investigate the biochemical and gut microbial response of mussels exposed to antibiotic norfloxacin (NOR) and NPs (80 nm polystyrene beads) alone and in combination at environmentally relevant concentrations. After 15 days of exposure, NPs alone signifi-cantly inhibited superoxide dismutase (SOD) and amylase (AMS) activities, while catalase (CAT) was affected by both NOR and NPs. The changes in lysozyme (LZM) and lipase (LPS) were increased over time during the treatments. Co-exposure to NPs and NOR significantly affected glutathione (GSH) and trypsin (Typ), which might be explained by the increased bioavailable NOR carried by NPs. The richness and diversity of the gut microbiota of mussels were both decreased by exposures to NOR and NPs, and the top functions of gut microbiota that were affected by the exposures were predicted. The data fast generated by enzymatic test and 16S sequencing allowed further variance and correla-tion analysis to understand the plausible driving factors and toxicity mechanisms. Despite the toxic effects of only one type of antibiotics and NPs being evaluated, the validated assays on mussels are readily applicable to other anti-biotics, NPs, and their mixture