Fiber chromatic confocal method with a tilt-coupling source module for axial super-resolution.

Current fiber chromatic confocal probes suffer from a low axial resolution. This study proposes a fiber chromatic confocal method with a tilt-coupling source module for axial super-resolution. An annular intensity distribution is generated at the fiber port of the probe by adjusting the tilt-coupling angle between the fiber and source module to reduce the width of the confocal axial response characteristic curve at each wavelength and to enhance the intensity contrast of the spectral signal. Compared with the coaxial coupling state, the developed 21° tilt-coupling state can reduce the FWHM by approximately 17%, and the axial resolution increases by 1.7 times.

Howling Detection and Suppression Based on Segmented Notch Filtering.

The existing adaptive echo cancellation based howling (typically in hearing aids) removal methods have several drawbacks such as insufficient attenuation of the howling component, slow response and nonlinear distortion. To solve these problems, we propose a segmented notch filtering based scheme. Specifically, firstly, it is proved that the attenuation value can reach -330 dB at any detected howling frequency; secondly, the filter coefficients can be readily calculated by a closed-form formula, yielding a fast response to the sudden howling accident; thirdly, the closed-form formula of this filter is theoretically an even function, indicating that this filter possesses a linear transfer characteristic. In combination with proper segmentation and precisely removing these transient samples arising from FIR (Finite Impulsive Response) filtering, nonlinear distortion can be entirely avoided. Experimental results show that our proposed scheme can not only accurately estimate the howling frequency, but can also completely remove it, which yields a high-quality output waveform with a recovery SNR of about 22 dB. Therefore, the proposed segmented notching based scheme possesses vast potential for hearing aid development and other relevant applications.

Multi-Tone Frequency Estimation Based on the All-Phase Discrete Fourier Transform and Chinese Remainder Theorem.

The closed-form robust Chinese Remainder Theorem (CRT) is a powerful approach to achieve single-frequency estimation from noisy undersampled waveforms. However, the difficulty of CRT-based methods' extension into the multi-tone case lies in the fact it is complicated to explore the mapping relationship between an individual tone and its corresponding remainders. This work deals with this intractable issue by means of decomposing the desired multi-tone estimator into several single-tone estimators. Firstly, high-accuracy harmonic remainders are calculated by applying all-phase Discrete Fourier Transform (apDFT) and spectrum correction operations on the undersampled waveforms. Secondly, the aforementioned mapping relationship is built up by a novel frequency classifier which fully captures the amplitude and phase features of remainders. Finally, the frequencies are estimated one by one through directly applying the closed-form robust CRT into these remainder groups. Due to all the components (including closed-form CRT, the apDFT, the spectrum corrector and the remainder classifier) only involving slight computation complexity, the proposed scheme is of high efficiency and consumes low hardware cost. Moreover, numeral results also show that the proposed method possesses high accuracy.

Vital Sign Detection during Large-Scale and Fast Body Movements Based on an Adaptive Noise Cancellation Algorithm Using a Single Doppler Radar Sensor.

The non-contact detection of human vital signs (i.e., respiration rate (RR) and heartbeat rate (HR)) using a continuous-wave (CW) Doppler radar sensor has great potential for intensive care monitoring, home healthcare, etc. However, large-scale and fast random body movement (RBM) has been a bottleneck for vital sign detection using a single CW Doppler radar. To break this dilemma, this study proposed a scheme combining adaptive noise cancellation (ANC) with polynomial fitting, which could retrieve the weak components of both respiration and heartbeat signals that were submerged under serious RBM interference. In addition, the new-type discrete cosine transform (N-DCT) was introduced to improve the detection accuracy. This scheme was first verified using a numerical simulation. Then, experiments utilizing a 10-GHz Doppler radar sensor that was built from general-purpose radio frequency (RF) and communication instruments were also carried out. No extra RF/microwave components and modules were needed, and neither was a printed circuit board nor an integrated-chip design required. The experimental results showed that both the RR and HR could still be extracted during large-scale and fast body movements using only a single Doppler radar sensor because the RBM noises could be greatly eliminated by utilizing the proposed ANC algorithm.

Heterodyne confocal microscopy using symmetrical shifted-focus phase filters.

We propose a heterodyne confocal microscopy technique that uses the symmetry properties of conjugate phase-pupil filters to shift the axial intensity-response curves of two confocal systems symmetrically with respect to the geometric focal plane. A monotonic position-measuring curve is obtained by subtracting the output signals of the two confocal systems collected synchronously, while eliminating the influence of environmental noise. The system's three-dimensional tomographic ability can be improved by optimizing the pupil filter. Theoretical analyses and experiments indicate that the proposed method improves the axial and transverse resolutions of differential confocal microscopy and simplifies system installation and integration.

Non-iterative dartboard phase filter for achieving multifocal arrays by cylindrical vector beams.

We proposed an analytically designed non-iterative dartboard phase filter (DPF) to achieve multifocal arrays by cylindrical vector beams. The DPF is composed of sectors, which is two-dimensionally divided in polar coordinates, along the radial and azimuthal directions. Meanwhile, a modulation factor was first proposed and introduced into the DPF to improve the intensity uniformity of the generated multifocal array. By the proposed DPF, the one-dimensional, two-dimensional and three-dimensional multifocal arrays are generated, which have intensity uniformities larger than 92.5%. The focal position and polarization of these generated multifocal arrays can be controlled, while the transverse sizes of each focal spot are subwavelength. The proposed DPF and the generated multifocal arrays have potential applications in the fields of polarization-multiplexed data storage, polarization-sensitive nanophotonic devices and parallel direct laser writing.

A Novel Instantaneous Phase Detection Approach and Its Application in SSVEP-Based Brain-Computer Interfaces.

This paper proposes a novel phase estimator based on fully-traversed Discrete Fourier Transform (DFT) which takes all possible truncated DFT spectra into account such that it possesses two merits of `direct phase extraction' (namely accurate instantaneous phase information can be extracted without any correction) and suppressing spectral leakage. This paper also proves that the proposed phase estimator complies with the 2-parameter joint estimation model rather than the conventional 3-parameter joint model. Numerical results verify the above two merits and demonstrate that the proposed estimator can extract phase information from noisy multi-tone signals. Finally, real data analysis shows that fully-traversed DFT can achieve a better classification on the phase of steady-state visual evoked potential (SSVEP) brain-computer interface (BCI) than the conventional DFT estimator does. Besides, the proposed phase estimator imposes no restrictions on the relationship between the sampling rates and the stimulus frequencies, thus it is capable of wider applications in phase-coded SSVEP BCIs, when compared with the existing estimators.

Association of Matrix Metalloproteinase-1 and Matrix Metalloproteinase-3 Gene Variants with Ischemic Stroke and Its Subtype.

BACKGROUND: Genetic variations in the genes of matrix metalloproteinases (MMPs) may play an important role in the pathogenesis of ischemic stroke (IS). Here we investigate the association between MMP-1 -1607 1G/2G and MMP-3 -1171 5A/6A genetic polymorphisms and etiological subtypes of IS in the Han Chinese population. METHODS: A total of 640 eligible patients with IS and 637 age- and gender-matched apparently healthy volunteers were enrolled. Subtypes of IS were classified by Trial of Org 10172 in Acute Stroke Treatment criteria. MMP-1 (-1607 1G/2G) and MMP-3 (-1171 5A/6A) polymorphisms were evaluated using polymerase chain reaction-restriction fragment length polymorphism. RESULTS: The frequencies of the 5A/6A + 5A/5A genotypes and 5A allele were significantly higher in patients with IS than in controls (P <.001, P <.001, respectively). No association was found between MMP-1 1G/2G polymorphism and overall IS. In subgroup analyses, MMP-1 1G/2G and 2G/2G genotypes increased the risk of small-artery occlusion (SAO) subtype (multivariate-adjusted, P <.001, P = .002, respectively), and MMP-3 5A/6A + 5A/5A genotypes were related with large-artery atherosclerosis (LAA) subtype (multivariate-adjusted, P <.001). Haplotype analyses indicated that 2G-6A and 1G-5A increased the risk of SAO (multivariate-adjusted, P = .029) and LAA (multivariate-adjusted, P <.001), respectively. CONCLUSIONS: MMP-1 (-1607 1G/2G) and MMP-3 (-1171 5A/6A) polymorphisms may contribute to different subtypes of IS susceptibility.

Impact of 5A/6A polymorphism of matrix metalloproteinase-3 on recurrent atherosclerotic ischemic stroke in Chinese.

Little is known about the impact of the 5A/6A polymorphism of matrix metalloproteinase-3 (MMP-3) on recurrence of atherosclerotic ischemic stroke in Chinese. The aim of this study was to investigate the association of MMP-3 serum level and 5A/6A genetic polymorphism with the recurrence of atherosclerotic ischemic stroke in the Chinese Han population. We analyzed 106 large artery atherosclerosis (LAA) recurrent ischemic stroke patients and 545 LAA first onset ischemic stroke patients from January 2009 to June 2014. Serum MMP-3 concentrations were measured with an enzyme-linked immunosorbent assay. The genotypes of MMP-3 promoter polymorphism (-1171 5A/6A) were determined using polymerase chain reaction-restriction fragment length polymorphism. The frequencies of MMP-3 5A/6A+5A/5A (32.08% vs. 21.47%, p = 0.02) genotype and 5A (16.98% vs. 11.01%, p = 0.01) allele in the recurrent group was significantly higher than those in the first onset group. After adjustment for vascular risk factors, multivariate logistic regression analysis suggested that the MMP-3 5A/6A+5A/5A genotype was an independent risk factor for LAA recurrent ischemic stroke (odds ratio [OR], 1.74; 95% confidence interval [CI], 1.09-2.79, p = 0.021). No significant difference was observed for the MMP-3 serum concentrations between the recurrent group and the first onset group (22.23 ± 8.31 vs. 21.49 ± 7.89 ng/ul, t = 0.88, p = 0.38). The MMP-3 (-1171 5A/6A) polymorphism may contribute to LAA recurrent ischemic stroke susceptibility. Analysis of 5A/6A polymorphism in MMP-3 may identify patients at higher risk for LAA ischemic stroke recurrence, who may be selected for intensive preventive therapy.

Changes in soil microbial community structure with planting years and cultivars of tree peony (Paeonia suffruticosa).

To understand the effects of planting tree peony (Paeonia suffruticosa) on soil microbial community structure, soil samples were collected from the tree peony gardens with three peony cultivars and three planting years, and adjacent wasteland at Luoyang, Henan Province of China. Soil microbial communities were analyzed by the polymerase chain reaction-denaturing gradient gel electrophoresis (PCR-DGGE) of partial 16S rDNA and sequencing methods. With the succeeding development of tree peony garden ecosystems, soil pH, organic C, total P, and available P increased. Soil total N, the cell numbers of bacteria, fungi, and actinomycetes, the Shannon's diversity index (H), richness (S), and Evenness (E(H)) first showed an increasing trend after wasteland was reclaimed and then a decreasing trend became apparent after 5 years of planting. Principal component analysis based on DGGE banding patterns showed that the microbial community structures were influenced by tree peony cultivars and planting years, and the influences of planting years were greater than those of tree peony cultivars. Sequence analysis of the DGGE bands revealed that the dominant bacteria in tree peony garden soils belonged to Proteobacteria, Bacteroidetes, Actinobacteria, Firmicutes, Acidobacteria, Planctomycetes, Euryarchaeota, and Unclassified-bacteria. Moreover, some bacteria closely related to Bradyrhizobium, Sphingopyxis, Novosphingobium, and Sphingomonas, which have been associated with nitrogen fixation and recalcitrant compounds degradation, disappeared with the increasing planting years of tree peony. The bacteria had similarity of 100% compared with Pseudomonas mandelii which was a denitrifying bacteria, and increased gradually with increasing planting years of tree peony.

Analysis of Clinical Characteristics and Influencing Factors of Early Neurological Deterioration in Patients With Mild Stroke by Intravenous Alteplase Therapy.

OBJECTIVES: Thrombolysis treatment for patients with mild stroke is controversial. The aim of our study was to investigate the clinical characteristics and influencing factors of early neurological deterioration (END) in this group of patients. METHODS: A retrospective analysis was performed on ischemic stroke patients with intravenous thrombolysis (IVT) in Wenzhou Central Hospital. Subgroup analyses were performed for the mild stroke group and nonmild stroke group, END group, and non-early neurological deterioration group in mild stroke patients, respectively. RESULTS: A total of 498 patients were included in this study. Compared with the control group, the mild stroke group was younger age, less atrial fibrillation, previous history of stroke and less use of antithrombotic drugs, more dyslipidemia, smoking, and drinking. Small artery occlusion type was more common in mild stroke, cardioembolism and stroke of undetermined etiology type were less. In the mild stroke group, the symptomatic intracerebral hemorrhage (sICH) rate was 2.54%, and the END rate was 16.1%. Predictors of END included systolic blood pressure, blood glucose, cardioembolism subtype, sICH, and large vessel occlusion. In END patients, the sICH rate was 10.53%, and 84.21% of cases started to worsen within 12 hours after IVT. There was no statistically significant difference in the time to exacerbation among different subtypes. CONCLUSIONS: The occurrence of mild stroke in young patients was largely related to unhealthy lifestyles. The incidence of END in mild stroke IVT patients was low, with most occurring within 12 hours of IVT. There were many risk factors for END: large vessel occlusion and hyperglycemia were independent risk factors for END after IVT. sICH was an important but rare risk factor for END.

Hub Gene Screening and Prognostic Modeling of Lung Cancer: An Integrated Bioinformatics Study.

Background: One of the most frequent malignancies is lung carcinoma which poses heavy burden on the global health. The link among differentially expressed genes (DEGs) and lung cancer patients' clinical outcomes was still missing. In this study, we integrated transcriptome data with clinical data to investigate the relationship between them in lung carcinoma patients. Methods: To begin, DEGs were identified using the Gene Expression Omnibus (GEO) gene expression pattern (GSE180347). Then, these DEGs are being searched in the TCGA database using the DEGs collected in the preceding phase. The Kaplan-Meier plotter was then used to assess the predictive value of these DEGs in patients with lung cancer. Results: Our study revealed a total of 45 DEGs, 15 of which were up-regulated and 30 of which were down-regulated. These DEGs were mostly enriched in cytokine receptor binding and cytokine activity, according to GO enrichment analysis. These DEGs were mostly enriched in cytokine-cytokine receptor interaction, according to KEGG enrichment analysis. Based on the PPI network, which comprises of 12 DEGs, a major module was discovered. They are mostly interested in cytotoxicity mediated by natural killer cells. Among all 45 DEGs, the mutations of NCAM1 account for the most cases in TCGA database with a percentage above 15%. Among the 12 DEGs in the significant module, higher expression of FAS, GPR29, HAVCR2, and NCAM1 exhibits longer survival time with hazard ratio and 95% confident interval of 0.79 (0.69-0.89), 0.80 (0.70-0.90), 0.71 (0.60-0.84), and 0.73 (0.62-0.86), respectively. However, higher expression of FCGR3A and IFNG exhibits shorter survival time with hazard ratio and 95% confident interval of 1.50 (1.32-1.71) and 1.15 (1.02-1.31), respectively. Conclusion: Our results demonstrate significant correlation between some DEGs and the survival outcome in lung adenocarcinomas patients, providing a comprehensive bioinformatics study in anticipation of future molecular mechanisms and biomarker studies.

Establishment and validation of a novel immune-related prognostic signature in malignant pleural mesothelioma.

Background: Immune-related genes (IRGs) play an important role in the tumor immune microenvironment and affect tumor prognosis. This study aimed to establish a prognostic signature for malignant pleural mesothelioma (MPM) patients. Methods: We obtained the relevant data of MPM patients in The Cancer Genome Atlas (TCGA), and univariate and multivariate Cox regression were used to construct the prediction signature and verify it with the external validation dataset GSE2549. A nomogram was then constructed, and its predictive ability was evaluated and analyzed the level of immune cell infiltration in different groups in the signature. Results: An IRG-related prognostic signature composed of INHBA, CAT, SORT1, TNFSF13B, and BIRC5 was constructed, with patients divided into high-risk and low-risk groups according to the risk score. The survival time of overall survival (OS), progression-free survival (PFS), disease-free interval (DFI), and relapse-free survival (RFS) in low-risk groups was longer than in high-risk groups. Furthermore, the signature had high predictive performance, and the receiver operating characteristic (ROC) of 1, 2, and 3 years could reach 0.853, 0.881, and 0.914, respectively. The predictive accuracy of the signature was verified by using the independent GSE2549 dataset. The levels of activated CD4 T cells, immature dendritic cells, and type 2 T helper cells were higher in high-risk patients. The gene set enrichment analysis (GSEA) analysis showed that a high concentration and P53 signal pathways were found in high-risk groups. Conclusions: This research developed and verified a new type of immune prognostic signature based on five IRGs, which can predict the prognosis of tumor patients and provide new ideas for individualized treatment.

A Review of Research on the Neurocognition for Timbre Perception.

As one of the basic elements in acoustic events, timbre influences the brain collectively with other factors such as pitch and loudness. Research on timbre perception involve interdisciplinary fields, including physical acoustics, auditory psychology, neurocognitive science and music theory, etc. From the perspectives of psychology and physiology, this article summarizes the features and functions of timbre perception as well as their correlation, among which the multi-dimensional scaling modeling methods to define timbre are the focus; the neurocognition and perception of timbre (including sensitivity, adaptability, memory capability, etc.) are outlined; related experiment findings (by using EEG/ERP, fMRI, etc.) on the deeper level of timbre perception in terms of neural cognition are summarized. In the meantime, potential problems in the process of experiments on timbre perception and future possibilities are also discussed. Thought sorting out the existing research contents, methods and findings of timbre perception, this article aims to provide heuristic guidance for researchers in related fields of timbre perception psychology, physiology and neural mechanism. It is believed that the study of timbre perception will be essential in various fields in the future, including neuroaesthetics, psychological intervention, artistic creation, rehabilitation, etc.

Post-traumatic growth experience of first-line emergency nurses infected with COVID-19 during the epidemic period-A qualitative study in Shanghai, China.

Background: In March 2022, Shanghai, China, was hit by a severe wave of SARS-CoV-2 transmission caused by the Omicron variant strain. The medical staff was greatly infected during this period, which posed a traumatic event for them. Meanwhile, they also experience post-traumatic growth under introspection and positive change. However, the psychological coping and growth after infection with COVID-19 among medical staff have rarely been investigated. Objectives: To explore the process and influencing factors of post-traumatic growth among emergency nurses infected with coronavirus disease (COVID-19) so as to provide a new perspective and theoretical basis for psychological rehabilitation or intervention for medical staff who experienced traumatic events. Methods: The study used a qualitative design based on the phenomenological approach. A purposive sampling method was used to explore the subjective feelings and post-traumatic growth among 13 first-line emergency nurses infected with COVID-19 in Shanghai, China. Semi-structured face-to-face interviews were conducted in June 2022. A Seven-step Colaizzi process was used for data analysis. Results: Themes were described and extracted from the experience and insights at different stages during the fight against the virus. Three main themes, i.e., stress period, adjustment period, and growth period, as well as several sub-themes, were identified. Conclusion: First-line emergency nurses infected with COVID-19 are a sensitive group that should be given more attention. Investigating how they achieve psychological adjustment and growth in the case of severe trauma can provide valuable references for nursing management and education in the future. Society, hospital and nursing managers should pay more attention to the PTG of nurses and establish supportive PTG strategies, which will benefit the retention rate and career development of nurses.

Research on the Variable-Temperature Cracking Mechanism of CRTS I Type Double-Block Ballastless Track on a Bridge.

The CRTS I type double-block ballastless track (CRTS I TDBBT) has the advantages of convenient construction and low cost, but it has low crack resistance and the temperature field distribution of the railway on the bridge is uneven and frequently changes, so it is necessary to study the mechanical properties of the CRTS I TDBBT under the load of a temperature field. The temperature field model of the CRTS I TDBBT on the bridge is established by finite element software, the real-time temperature field of the track bed slab is brought into the coupled model as a load, and the variation laws of the temperature stress of the CRTS I TDBBT under different schemes are compared. The temperature gradient in the CRTS I TDBBT track bed slab has the largest fluctuation range, and the positive and negative temperature gradient range can reach 93.34 °C. For the temperature longitudinal stress around the sleeper block of the track bed slab, the edge is the largest; the temperature longitudinal stress is reduced by at most 5.27% after the anti-cracking diagonal bars are added. When the expansion joint is added, the temperature stress can be reduced by up to 80.29%. The fluctuation range of the temperature gradient of the track bed is basically consistent with the fluctuation range of the local air temperature. The huge temperature difference leads to the occurrence of cracks in the track structure, and cracks are more likely to occur at the corners of the sleeper block. The addition of both anti-crack diagonal bars and expansion joints has an anti-crack effect, but the effect of adding expansion joints is better.

Primary pulmonary choriocarcinoma in male: report a case with genetic testing and review of the literature.

Background: Primary pulmonary choriocarcinoma is an extremely rare malignant trophoblastic tumor with a poor prognosis. Most choriocarcinomas originated from gonads, such as the ovaries and testes. Review the previous literature, only 41 cases were reported. Case Description: We reported that a 65-year-old man found shadows in the lungs when undergoing the X-ray examination. Positron emission tomography (PET) was performed to exclude metastatic disease before surgery. The patient underwent three-dimension uniportal thoracoscopic left upper lung resection and lymph node dissection. The operation was uneventful, and he was discharged on the fourth day postoperatively. Postoperative pathology: malignant trophoblastic tumors (choriocarcinoma). After the operation, the patient has genetically tested, the mutations in tumor protein p53 (TP53), NRAS proto-oncogene (NRAS), and fibroblast growth factor receptor 1 (FGFR1) were found. Conclusions: Primary pulmonary choriocarcinoma is an extremely rare and highly malignant tumor difficult to detect in the early stage. By analyzing the previous literature, the patients with active treatment have more extended survival periods than the patients without treatment (P=0.0051). Patients, including surgery, had better survival than patients without surgery (P=0.027) depending on the different treatment regimens. Hence, once the diagnosis was confirmed, the comprehensive treatment of surgical resection combined with chemotherapy and radiotherapy is of great significance to improve the prognosis of patients.

A Malicious Domain Detection Model Based on Improved Deep Learning.

With the rapid development of the Internet, malicious domain names pose more and more serious threats to many fields, such as network security and social security, and there have been many research results on malicious domain detection. This article proposes a malicious domain name detection model based on improved deep learning, which can combine the advantages of three different network models, convolutional neural network (CNN), temporal convolutional network (TCN), and long short-term memory network (LSTM) in malicious domain name detection, to obtain a better detection effect than that of the original single or two models. Experiments show that the effect of the improved deep learning model proposed in this article is better than that of the combined model of CNN and LSTM or the combined model of CNN and TCN, and the accuracy and regression rates reached 99.76% and 98.81%, respectively.

Research on the longitudinal mechanical behaviours of subway turnouts of large slope under train braking force.

To study subway turnouts' adaptability to steep gradients, a finite element model of a metro No. 9 simple turnout was established. The main works include: (1) The train's most unfavourable loading condition was modelled. (2) The turnout's longitudinal displacement and stress were analysed with different gradients under the train braking load, temperature change load and a combination of the two, to determine the structure's safety and stability under the most unfavourable working conditions. (3) The turnout structure's cumulative longitudinal deformation under reciprocating load was studied. Both a fastener longitudinal resistance-displacement experiment under reciprocating load and a numerical simulation of No. 9 turnout modelled by the finite element modelling software, ANSYS, were carried out to study the gradient's influence on the turnout's longitudinal mechanical characteristics. (1) The turnout's longitudinal displacement and stress increase linearly with an increase in gradient and temperature change, both of which are unfavourable to the turnout structure. As the gradient increases from 0‰ to 30‰, the longitudinal stress and displacement increase by more than 10%. (2) The turnout's rail strength and displacement on a 30‰ slope under the most unfavourable load conditions are within the specification limitations. (3) Under reciprocating load, the fastener longitudinal stiffness decreases and the maximum and residual longitudinal displacement of the switch rail increase; an increased gradient intensifies these effects on the turnout.

Indoor simulation test research on cumulative longitudinal displacement of rail based on force and displacement sensors data collection.

The train sometimes needs to brake frequently on the turnout, although the braking force does not exceed the limit resistance of fastener, cumulative displacement of rail occurs because of the long-term effect of the train brakes, thus, the relationship between the cumulative displacement of rail and the number of train braking actions should be explored. Aiming at the spring bar type III fastener, a 1:1 physical indoor simulation test was carried out, and an electromagnetic relay device was used to simulate the train load, force, and displacement sensors for data collection. Then a single load no more than the maximum resistance of fastener was applied to the rail end to explore the relationship between the number of loads and the rail cumulative deformation. The rail longitudinal cumulative displacement changes linearly in positive correlation with the number of load actions, and increases faster when the number of load actions is small. As the number of repeated loads increases, the above-mentioned relationship approximately and credibly obeys the power function distribution. Repeatedly applying load no more than the maximum longitudinal resistance of fastener to the rail, the existence of the rail cumulative displacement caused by frequent train braking can be demonstrated, and the relationship curve between the rail displacement and the number of loads can be obtained. Applying the fitting formula, the rail displacement after a specific number of loading times can be attained, and then referring to specific codes, we can determine whether it will exceed the safety limit.