Sequencing Errors Research Articles

SARS-CoV-2 evolution during prolonged infection in immunocompromised patients.

SARS-CoV-2 is responsible for a global pandemic, driven in part by the emergence of new viral variants. Where do these new variants come from? One model is that long-term viral persistence in infected individuals allows for viral evolution in response to host pressures, resulting in viruses more likely to replicate efficiently in humans. In this study, we characterize replication in several hospitalized and long-term infected individuals, documenting efficient pathways of viral evolution.

Improved detection of low-frequency within-host variants from deep sequencing: A case study with human papillomavirus.

High-coverage sequencing allows the study of variants occurring at low frequencies within samples, but is susceptible to false-positives caused by sequencing error. Ion Torrent has a very low single nucleotide variant (SNV) error rate and has been employed for the majority of human papillomavirus (HPV) whole genome sequences. However, benchmarking of intrahost SNVs (iSNVs) has been challenging, partly due to limitations imposed by the HPV life cycle. We address this problem by deep sequencing three replicates for each of 31 samples of HPV type 18 (HPV18). Errors, defined as iSNVs observed in only one of three replicates, are dominated by C→T (G→A) changes, independently of trinucleotide context. True iSNVs, defined as those observed in all three replicates, instead show a more diverse SNV type distribution, with particularly elevated C→T rates in CCG context (CCG→CTG; CGG→CAG) and C→A rates in ACG context (ACG→AAG; CGT→CTT). Characterization of true iSNVs allowed us to develop two methods for detecting true variants: (1) VCFgenie, a dynamic binomial filtering tool which uses each variant's allele count and coverage instead of fixed frequency cut-offs; and (2) a machine learning binary classifier which trains eXtreme Gradient Boosting models on variant features such as quality and trinucleotide context. Each approach outperforms fixed-cut-off filtering of iSNVs, and performance is enhanced when both are used together. Our results provide improved methods for identifying true iSNVs in within-host applications across sequencing platforms, specifically using HPV18 as a case study.

Correcting PCR amplification errors in unique molecular identifiers to generate accurate numbers of sequencing molecules

Unique molecular identifiers are random oligonucleotide sequences that remove PCR amplification biases. However, the impact that PCR associated sequencing errors have on the accuracy of generating absolute counts of RNA molecules is underappreciated. We show that PCR errors are a source of inaccuracy in both bulk and single-cell sequencing data, and synthesizing unique molecular identifiers using homotrimeric nucleotide blocks provides an error-correcting solution that allows absolute counting of sequenced molecules.

Comprehensive assessment of 11 de novo HiFi assemblers on complex eukaryotic genomes and metagenomes.

Pacific Biosciences (PacBio) HiFi sequencing technology generates long reads (>10 kbp) with very high accuracy (<0.01% sequencing error). Although several de novo assembly tools are available for HiFi reads, there are no comprehensive studies on the evaluation of these assemblers. We evaluated the performance of 11 de novo HiFi assemblers on (1) real data for three eukaryotic genomes; (2) 34 synthetic data sets with different ploidy, sequencing coverage levels, heterozygosity rates, and sequencing error rates; (3) one real metagenomic data set; and (4) five synthetic metagenomic data sets with different composition abundance and heterozygosity rates. The 11 assemblers were evaluated using quality assessment tool (QUAST) and benchmarking universal single-copy ortholog (BUSCO). We also used several additional criteria, namely, completion rate, single-copy completion rate, duplicated completion rate, average proportion of largest category, average distance difference, quality value, run-time, and memory utilization. Results show that hifiasm and hifiasm-meta should be the first choice for assembling eukaryotic genomes and metagenomes with HiFi data. We performed a comprehensive benchmarking study of commonly used assemblers on complex eukaryotic genomes and metagenomes. Our study will help the research community to choose the most appropriate assembler for their data and identify possible improvements in assembly algorithms.

Deep Learning for Daily 2‐m Temperature Downscaling

AbstractThis study proposes a novel method, which is a U‐shaped convolutional neural network that combines non‐local attention mechanisms, Res2net residual modules, and terrain information (UNR‐Net). The original U‐Net method and the linear regression (LR) method are conducted as benchmarks. Generally, the UNR‐Net has demonstrated promise in performing a 10× downscaling for daily 2‐m temperature over North China with lead times of 1–7 days and shows superiority to the U‐Net and LR methods. To be specific, U‐Net and UNR‐Net demonstrate higher Nash‐Sutcliffe Efficiency coefficient values compared to LR by 0.052 and 0.077, respectively. The corresponding improvements in pattern correlation coefficient are 0.013 and 0.016, while the root mean square error values are higher by 0.22 and 0.338, respectively. Additionally, the structural similarity index metric is higher by 0.033 and lower by 0.015. Furthermore, regions with significant errors are primarily distributed in complex terrain areas such as the Taihang Mountains, where UNR‐Net exhibits noticeable improvements. In addition, the 12 components‐based error decomposition method is proposed to analyze the error source of different models. Generally, the smallest errors are observed during the summer season and the sequence error component is proven to be the main source error of 2‐m temperature forecasts. Furthermore, UNR‐Net consistently demonstrates the lowest errors among all 12 error components. Therefore, combining the numerical weather prediction model and deep learning method is very promising in downscaling temperature forecasts and can be applied to routine forecasting of other atmospheric variables in the future.

Abstract 107: Exploring Non-Human DNA Content in Cerebral Thrombi Using Shotgun Metagenomic Sequencing

Introduction: Prior studies that use 16S rRNA amplicon sequencing to profile bacterial components of cerebral thrombi do not provide species-level taxonomic information or functional gene content, which are critical for the development of subsequent clinical applications. To determine the amount and taxonomic nature of non-human DNA in cerebral thrombi, shotgun metagenomic sequencing was performed on specimens retrieved from ischemic stroke patients. Methods: Thrombi were retrieved during standard of care thrombectomy and preserved in DNA/RNA Shield (Zymo), alongside environmental controls. DNA was extracted per manufacturer instructions, using Zymo kits. Quality control was carried out using Bowtie2 and the bbtools suite. To clump reads, bbmap was applied. Sequencing adapter contamination was removed with bbduk. Data was aligned to the human reference genome (hg38) using Bowtie2. Tadpole (mode=correct, ecc=t, ecco=t) was used to correct sequencing errors. MetaSPAdes was used to assemble quality-controlled sequencing reads into contigs. CAT/BAT was then applied to annotate contigs and their Open Reading Frames (ORF) taxonomically using the Lowest Common Ancestor approach. Results: Of the 41 specimens, N = 31 met quality control. The preponderance of DNA sequencing reads mapped to the human genome. An average of 7,559,292 +/- 1,615,7061 (9.1%) reads per sample did not align (Fig 1A). Contigs resulting from de novo assemblies of these potentially non-human reads contained sequences consistent with bacterial ORFs. The number of these ORFs varied per sample (Fig 1B) and correlated with the number of non-human reads. Proteobacteria and Firmicutes dominated. (Fig 1C). Conclusion: While much work remains to optimize sequencing techniques and controls, the potential to recover near-complete bacterial genomes from thrombus presents an opportunity to further explore the human host-microbiota interactions in acute ischemic stroke.

Hybrid carbon price forecasting using a deep augmented FEDformer model and multimodel optimization piecewise error correction

Accurate and robust carbon price forecasting is crucial for stabilizing the carbon financial market and reducing reliance on fossil resources. This study introduces a novel hybrid model, combining a deep augmented frequency enhanced decomposed transformer (DA-FEDformer), improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), and a multimodel optimization piecewise error correction, for accurate carbon price prediction. To leverage frequency domain information, the proposed DA-FEDformer model enhances the decoder and encoder layers by incorporating a multilayer perceptron layer. A novel improved kernel mean square error loss function is devised for the model, and the evolved sign momentum optimizer is employed for further optimization. To further improve the prediction accuracy, a data postprocessing method is integrated into the model. The DA-FEDformer predicts the carbon price, and the ICEEMDAN method decomposes the error sequence into subsequences. These subsequences are forecasted using five different models. Finally, the DA-FEDformer prediction results and the error correction results are combined to obtain the final carbon price sequence. This hybrid model is systematically evaluated using carbon price data from Hubei, Guangzhou, and Beijing in China. The results demonstrate that the hybrid model achieves favorable performance on three datasets. This innovative approach provides a promising solution for carbon price forecasting in China.

PathMap: a path-based mapping tool for long noisy reads with high sensitivity.

With the rapid development of single-molecule sequencing (SMS) technologies, the output read length is continuously increasing. Mapping such reads onto a reference genome is one of the most fundamental tasks in sequence analysis. Mapping sensitivity is becoming a major concern since high sensitivity can detect more aligned regions on the reference and obtain more aligned bases, which are useful for downstream analysis. In this study, we present pathMap, a novel k-mer graph-based mapper that is specifically designed for mapping SMS reads with high sensitivity. By viewing the alignment chain as a path containing as many anchors as possible in the matched k-mer graph, pathMap treats chaining as a path selection problem in the directed graph. pathMap iteratively searches the longest path in the remaining nodes; more candidate chains with high quality can be effectively detected and aligned. Compared to other state-of-the-art mapping methods such as minimap2 and Winnowmap2, experiment results on simulated and real-life datasets demonstrate that pathMap obtains the number of mapped chains at least 11.50% more than its closest competitor and increases the mapping sensitivity by 17.28% and 13.84% of bases over the next-best mapper for Pacific Biosciences and Oxford Nanopore sequencing data, respectively. In addition, pathMap is more robust to sequence errors and more sensitive to species- and strain-specific identification of pathogens using MinION reads.

BigDEC: A multi-algorithm Big Data tool based on the [formula omitted]-mer spectrum method for scalable short-read error correction

Despite the significant improvements in both throughput and cost provided by modern Next-Generation Sequencing (NGS) platforms, sequencing errors in NGS datasets can still degrade the quality of downstream analysis. Although state-of-the-art correction tools can provide high accuracy to improve such analysis, they are limited to apply a single correction algorithm while also requiring long runtimes when processing large NGS datasets. Furthermore, current parallel correctors generally only provide efficient support for shared-memory systems lacking the ability to scale out across a cluster of multicore nodes, or they require the availability of specific hardware devices or features. In this paper we present a Big Data Error Correction (BigDEC) tool that overcomes all those limitations by: (1) implementing three different error correction algorithms based on the widely extended k-mer spectrum method; (2) providing scalable performance for large datasets by efficiently exploiting the capabilities of Big Data technologies on multicore clusters based on commodity hardware; (3) supporting two different Big Data processing frameworks (Spark and Flink) to provide greater flexibility to end users; (4) including an efficient, stream-based merge operation to ease downstream processing of the corrected datasets; and (5) significantly outperforming existing parallel tools, being up to 79% faster on a 16-node multicore cluster when using the same underlying correction algorithm. BigDEC is publicly available to download at https://github.com/UDC-GAC/BigDEC.

An overlooked phenomenon: complex interactions of potential error sources on the quality of bacterial de novo genome assemblies

BackgroundParameters adversely affecting the contiguity and accuracy of the assemblies from Illumina next-generation sequencing (NGS) are well described. However, past studies generally focused on their additive effects, overlooking their potential interactions possibly exacerbating one another’s effects in a multiplicative manner. To investigate whether or not they act interactively on de novo genome assembly quality, we simulated sequencing data for 13 bacterial reference genomes, with varying levels of error rate, sequencing depth, PCR and optical duplicate ratios.ResultsWe assessed the quality of assemblies from the simulated sequencing data with a number of contiguity and accuracy metrics, which we used to quantify both additive and multiplicative effects of the four parameters. We found that the tested parameters are engaged in complex interactions, exerting multiplicative, rather than additive, effects on assembly quality. Also, the ratio of non-repeated regions and GC% of the original genomes can shape how the four parameters affect assembly quality.ConclusionsWe provide a framework for consideration in future studies using de novo genome assembly of bacterial genomes, e.g. in choosing the optimal sequencing depth, balancing between its positive effect on contiguity and negative effect on accuracy due to its interaction with error rate. Furthermore, the properties of the genomes to be sequenced also should be taken into account, as they might influence the effects of error sources themselves.

GRUPS-rs, a high-performance ancient DNA genetic relatedness estimation software relying on pedigree simulations

Background: The study of fine-grain genetic kinship ties (parents, siblings, cousins, etc.) from ancient remains is now gaining significant interest within the field of paleogenetics, as a means of deciphering the social organization of past societies. However, kinship analyses are in practice often quite difficult to apply within paleogenetic studies, and may carry a high degree of uncertainty in the results they provide, especially when applied on low coverage and/or highly degraded samples, or when studying poorly characterized populations. To overcome these challenges, most of the available kinship estimation methods either refrain from inferring ties beyond the second degree (e.g., half-siblings), and/or rely on the use of a cohort of individuals to obtain a satisfactory statistical significance. Thus, the current state of the art remains intrinsically limited when attempting to estimate kinship on a small number of individuals, or when trying to detect more distant relationships (e.g., cousins). Methods:Here, we present GRUPS-rs:an update and complete reimplementation of GRUPS (Get Relatedness Using Pedigree Simulations), an ancient DNA kinship estimation software based on the methods originally developed in (Martin et al. 2017).GRUPS-rs both computes an estimate of relatedness from randomly sampled pseudo-haploidized variant calls, and leverages high-definition pedigree simulations to bypass the use of a cohort of individuals. Results: We highlight that GRUPS and GRUPS-rs are especially suitable to perform kinship analysis on a restricted number of ancient samples, and can provide a sufficient statistical significance to estimate genetic relatedness past the second degree, while taking into account user-defined contamination and sequencing error estimates. Importantly, GRUPS-rs offers an estimated 14000-fold speed-up in runtime performance compared to its predecessor — allowing the joint estimation of kinship between dozens of individuals in a matter of minutes — and is now bundled with a user-friendly Shiny interface, in which users can interactively visualize their results. Conclusions: The GRUPS kinship estimation method is now fully operational in its "GRUPS-rs" implementation, whose use is particularly recommended when analyzing a restricted number of low coverage DNA samples.

Secure key generation and distribution scheme based on historical fiber channel state information with LSTM.

In this paper, a scheme to realize unclonable physical-layer security key generation and distribution (PL-SKGD) based on historical fiber channel state information (HFCSI) is proposed. PL-SKGD schemes based on channel characteristics for enhancing the physical-layer security of optical networks have been proposed in recent years. However, there are potential disadvantages in these schemes, such as 1) low key generation rate (KGR): the slow frequency of the analog waveform change of the channel characteristic leading to low KGR; 2) incompatibility with existing infrastructure: active scrambling to increase the frequency of channel characteristic changes, or tracking changes of channel characteristics requires additional devices; 3)easy to be cloned: all of the optical channel state information is reflected in the signal transmitted inside the fiber, which makes it easy to reproduce by illegal eavesdropper through features analysis and other methods. In order to solve the above problems, a PL-SKGD scheme is designed which uses the chain structure composed of long short-term memory neural network (LSTM-NN) units to learn and store the unique mapping relationship between historical channel time series and provides unclonability based on the fundamental fact that the eavesdropper Eve can never obtain the full HFCSI. The simulation conducted in a quadrature phase shift keying point-to-point optical link system verified successfully that KGR = 0.82 Gbit/s error-free SKGD. The loss function of LSTM-NN drops sharply in the early stages of training and remains a small value. The security of the SKGD system is analyzed, which effectively improves the unclonability of the system. Finally, it is verified that the optimal fiber channel length for error-free SKGD of the proposed scheme is 150 km considering the error correction capability of information reconciliation and weighing key sequence error rate and valid bit generation rate.

LRTK: a platform agnostic toolkit for linked-read analysis of both human genome and metagenome.

Linked-read sequencing technologies generate high-base quality short reads that contain extrapolative information on long-range DNA connectedness. These advantages of linked-read technologies are well known and have been demonstrated in many human genomic and metagenomic studies. However, existing linked-read analysis pipelines (e.g., Long Ranger) were primarily developed to process sequencing data from the human genome and are not suited for analyzing metagenomic sequencing data. Moreover, linked-read analysis pipelines are typically limited to 1 specific sequencing platform. To address these limitations, we present the Linked-Read ToolKit (LRTK), a unified and versatile toolkit for platform agnostic processing of linked-read sequencing data from both human genome and metagenome. LRTK provides functions to perform linked-read simulation, barcode sequencing error correction, barcode-aware read alignment and metagenome assembly, reconstruction of long DNA fragments, taxonomic classification and quantification, and barcode-assisted genomic variant calling and phasing. LRTK has the ability to process multiple samples automatically and provides users with the option to generate reproducible reports during processing of raw sequencing data and at multiple checkpoints throughout downstream analysis. We applied LRTK on linked reads from simulation, mock community, and real datasets for both human genome and metagenome. We showcased LRTK's ability to generate comparative performance results from preceding benchmark studies and to report these results in publication-ready HTML document plots. LRTK provides comprehensive and flexible modules along with an easy-to-use Python-based workflow for processing linked-read sequencing datasets, thereby filling the current gap in the field caused by platform-centric genome-specific linked-read data analysis tools.

Human complex mixture analysis by "FD Multi-SNP Mixture Kit".

Multiple linked single nucleotide polymorphisms (SNPs) have shown potential in personal identification and mixture detection. However, the limited number of marker and sequencing errors have obstructed accurate DNA typing. To develop more candidate loci, the diversity value (D-value) was introduced as a new parameter for screening the novel polymorphic multiple linked-SNP markers, referred to as multi-SNP. In this study, a "FD Multi-SNP Mixture Kit" comprising 567 multi-SNPs was developed for mixture detection. Additionally, a new computational error correction method was applied as a quality control approach for sequencing data. The results demonstrated higher typing success rates than the conventional CE typing method. For single-source DNA, approximately 70-80 loci were detected with a DNA input of 0.009765625ng. More than 65% of the minor alleles were distinguishable at1 ng DNA with a frequency of 0.5% in 2- to 4-person mixtures. This study offers a polymorphic and high-resolution detection method for DNA genotyping and complex mixture detection, providing an alternative strategy for addressing challenging mixed DNA traces.

AsmMix: an efficient haplotype-resolved hybrid de novo genome assembling pipeline.

Accurate haplotyping facilitates distinguishing allele-specific expression, identifying cis-regulatory elements, and characterizing genomic variations, which enables more precise investigations into the relationship between genotype and phenotype. Recent advances in third-generation single-molecule long read and synthetic co-barcoded read sequencing techniques have harnessed long-range information to simplify the assembly graph and improve assembly genomic sequence. However, it remains methodologically challenging to reconstruct the complete haplotypes due to high sequencing error rates of long reads and limited capturing efficiency of co-barcoded reads. We here present a pipeline, AsmMix, for generating both contiguous and accurate diploid genomes. It first assembles co-barcoded reads to generate accurate haplotype-resolved assemblies that may contain many gaps, while the long-read assembly is contiguous but susceptible to errors. Then two assembly sets are integrated into haplotype-resolved assemblies with reduced misassembles. Through extensive evaluation on multiple synthetic datasets, AsmMix consistently demonstrates high precision and recall rates for haplotyping across diverse sequencing platforms, coverage depths, read lengths, and read accuracies, significantly outperforming other existing tools in the field. Furthermore, we validate the effectiveness of our pipeline using a human whole genome dataset (HG002), and produce highly contiguous, accurate, and haplotype-resolved assemblies. These assemblies are evaluated using the GIAB benchmarks, confirming the accuracy of variant calling. Our results demonstrate that AsmMix offers a straightforward yet highly efficient approach that effectively leverages both long reads and co-barcoded reads for haplotype-resolved assembly.

Human B Cell Receptor Repertoire Sequencing.

Next-generation sequencing has the potential to uncover the complex nature of B cell immunity by revealing the full complexity of B cell receptor (BCR) repertoires in health and disease. However, there are drawbacks which can compromise the validity of the repertoire analysis caused by quantitative bias and accumulation of sequencing errors during the library preparation and sequencing. Here, we provide an optimized protocol designed to minimize bias for reproducible and accurate preparation of human BCR repertoire libraries for high-throughput sequencing.

ESTIMATION OF PROBABILISTIC AND STATISTICAL CHARACTERISTICS OF THE INFORMATIONAL STATE OF A COMMUNICATION CHANNEL

The methods for determining the informational state of a communication channel based on the assessment of probabilistic and statistical characteristics of errors at the channel output are presented. Adaptive information protection methods in digital communication systems, where encoder parameters change depending on the channel state, require the use of network quality control methods based on determining the statistical characteristics of the channel. It is shown that the bit error probability in the channel is constant for the presented error generation process and is independent of the method of dividing information into code blocks. The methods for assessing the statistical characteristics of the channel are based on the topological representation of error generation processes over the length of code blocks. It is demonstrated that, with a fixed code sequence length and a constant bit error probability at the output of the information channel, different error distributions correspond to sets of n-sequences. With a known number of states in the likelihood transition matrix, calculation of observation intervals for counting erroneous blocks is proposed. The presented method of researching statistical characteristics, based on the assumption of error independence, allows for the development of algorithms and procedures for assessing the state of discrete communication channels. The evaluation of potential bounds and statistical characteristics for the decoding error probability enables establishing a connection between the topological characteristics of error sequence partitioning and code parameters. The work confirms that the proposed method allows the synthesis of algorithms for determining code parameters, whose numerical values are determined based on minimizing potential decoding error probabilities.

Automated preparation of nanoscopic structures: Graph-based sequence analysis, mismatch detection, and pH-consistent protonation with uncertainty estimates.

Structure and function in nanoscale atomistic assemblies are tightly coupled, and every atom with its specific position and even every electron will have a decisive effect on the electronic structure, and hence, on the molecular properties. Molecular simulations of nanoscopic atomistic structures therefore require accurately resolved three-dimensional input structures. If extracted from experiment, these structures often suffer from severe uncertainties, of which the lack of information on hydrogen atoms is a prominent example. Hence, experimental structures require careful review and curation, which is a time-consuming and error-prone process. Here, we present a fast and robust protocol for the automated structure analysis and pH-consistent protonation, in short, ASAP. For biomolecules as a target, the ASAP protocol integrates sequence analysis and error assessment of a given input structure. ASAP allows for p prediction from reference data through Gaussian process regression including uncertainty estimation and connects to system-focused atomistic modeling described in Brunken and Reiher (J. Chem. Theory Comput. 16, 2020, 1646). Although focused on biomolecules, ASAP can be extended to other nanoscopic objects, because most of its design elements rely on a general graph-based foundation guaranteeing transferability. The modular character of the underlying pipeline supports different degrees of automation, which allows for (i) efficient feedback loops for human-machine interaction with a low entrance barrier and for (ii) integration into autonomous procedures such as automated force field parametrizations. This facilitates fast switching of the pH-state through on-the-fly system-focused reparametrization during a molecular simulation at virtually no extra computational cost.

Nucleus accumbens and dorsal medial striatal dopamine and neural activity are essential for action sequence performance.

Separable striatal circuits have unique functions in Pavlovian and instrumental behaviors but how these roles relate to performance of sequences of actions with and without associated cues are less clear. Here, we tested whether dopamine transmission and neural activity more generally in three striatal subdomains are necessary for performance of an action chain leading to reward delivery. Male and female Long-Evans rats were trained to press a series of three spatially distinct levers to receive reward. We assessed the contribution of neural activity or dopamine transmission within each striatal subdomain when progression through the action sequence was explicitly cued and in the absence of cues. Behavior in both task variations was substantially impacted following microinfusion of the dopamine antagonist, flupenthixol, into nucleus accumbens core (NAc) or dorsomedial striatum (DMS), with impairments in sequence timing and numbers of rewards earned after NAc flupenthixol. In contrast, after pharmacological inactivation to suppress overall activity, there was minimal impact on total rewards earned. Instead, inactivation of both NAc and DMS impaired sequence timing and led to sequence errors in the uncued, but not cued task. There was no impact of dopamine antagonism or reversible inactivation of dorsolateral striatum on either cued or uncued action sequence completion. These results highlight an essential contribution of NAc and DMS dopamine systems in motivational and performance aspects of chains of actions, whether cued or internally generated, as well as the impact of intact NAc and DMS function for correct sequence performance.

Research on Distributed Virtual Reality Technology Based on VIRTOOLS in the Context of Big Data

Abstract In this paper, virtual reality development software Virtools is used as the main tool for scene rendering in distributed virtual reality systems. The nearest distance-based control strategy is designed to achieve synchronous interaction between nodes by utilizing consistency control and prediction algorithms for nodes in the same cluster. Optimize the virtual scene by using texture mapping, detail level, and dynamic loading techniques. Propose a distributed parallel drawing method based on image plane segmentation to accelerate image drawing. The analysis and testing of the multiuser virtual reality roaming system in this paper is completed from four aspects: offline training model evaluation amount roaming test, lock performance test, and operation sequence error correction test. Among the analyzed data, the average lock time overhead is 123us, which has no obvious connection with the number of nodes, the number of locking times, and the execution of operations. According to each lock overhead of 123us, the number of concurrencies allowed per second is 8563, which fully meets the requirements of the system at this stage.