Photobiomodulation:a novel approach to promote trans-differentiation of adipose-derived stem cells into neuronal-like cells

Photobiomodulation,originally used red and near-infrared lasers,can alter cellular metabolism.It has been demonstrated that the visible spectrum at 451-540 nm does not necessarily increase cell proliferation,near-infrared light promotes adipose stem cell proliferation and affects adipose stem cell migration,which is necessary for the cells homing to the site of injury.In this in vitro study,we explored the potential of adipose-derived stem cells to differentiate into neurons for future translational regenerative treatments in neurodegenerative disorders and brain injuries.We investigated the effects of various biological and chemical inducers on trans-differentiation and evaluated the impact of photobiomodulation using 825 nm near-infrared and 525 nm green laser light at 5 J/cm2.As adipose-derived stem cells can be used in autologous grafting and photobiomodulation has been shown to have biostimulatory effects.Our findings reveal that adipose-derived stem cells can indeed trans-differentiate into neuronal cells when exposed to inducers,with pre-induced cells exhibiting higher rates of proliferation and trans-differentiation compared with the control group.Interestingly,green laser light stimulation led to notable morphological changes indicative of enhanced trans-differentiation,while near-infrared photobiomodulation notably increased the expression of neuronal markers.Through biochemical analysis and enzyme-linked immunosorbent assays,we observed marked improvements in viability,proliferation,membrane permeability,and mitochondrial membrane potential,as well as increased protein levels of neuron-specific enolase and ciliary neurotrophic factor.Overall,our results demonstrate the efficacy of photobiomodulation in enhancing the trans-differentiation ability of adipose-derived stem cells,offering promising prospects for their use in regenerative medicine for neurodegenerative disorders and brain injuries.

Characteristics of early gastric tumors with different differentiation and predictors of long-term outcomes after endoscopic submucosal dissection

BACKGROUND Gastric cancer is a common malignant tumor of the digestive tract,and endosco-pic submucosal dissection(ESD)is the preferred treatment for early-stage gastric cancer.The analysis of the epidemiological characteristics of gastric mucosal tumors with different differentiation degrees and the influencing factors of long-term ESD efficacy may have certain significance for revealing the development of gastric cancer and ESD.AIM To analyze the features of gastric mucosal tumors at different differentiation levels,and to explore the prognostic factors of ESD.METHODS We retrospectively studied 301 lesions in 285 patients at The Second Affiliated Hospital of Xi'an Jiaotong University from 2014 to 2021,according to the latest Japanese guidelines(sixth edition),and divided them into low-grade intrae-pithelial neoplasia(LGIN),high-grade intraepithelial neoplasia(HGIN),and computed tomography at 3,6 and 12 months after ESD.We compared clinicopathologic characteristics,ESD efficacy,and complications with different degrees of differentiation,and analyzed the related factors associated with ESD.RESULTS HGIN and differentiated carcinoma patients were significantly older compared with LGIN patients(P<0.001)and accounted for more 0-IIc(P<0.001),atrophic gastritis was common(P<0.001),and irregular microvascular patterns(IMVPs)and demarcation lines(DLs)were more obvious(P<0.001).There was more infiltration in the undifferentiated carcinoma tissue(P<0.001),more abnormal folds and poorer mucosal peristalsis(P<0.001),and more obvious IMVPs,irregular microsurface patterns and DLs(P<0.05)than in the LGIN and HGIN tissues.The disease-free survival rates at 2,5,and 8 years after ESD were 95.0%,90.1%,and 86.9%,respectively.Undifferen-tiated lesions(HR 5.066),white moss(HR 7.187),incomplete resection(HR 3.658),and multiple primary cancers(HR 2.462)were significantly associated with poor prognosis.CONCLUSION Differentiations of gastric mucosal tumors have different epidemiological and endoscopic characteristics,which are closely related to the safety and efficacy of ESD.

Novel Investigation of Stochastic Fractional Differential Equations Measles Model via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel

Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.

Remote sensing of air pollution incorporating integrated-path differential-absorption and coherent-Doppler lidar

An innovative complex lidar system deployed on an airborne rotorcraft platform for remote sensing of atmospheric pollution is proposed and demonstrated.The system incorporates integrated-path differential absorption lidar(DIAL) and coherent-doppler lidar(CDL) techniques using a dual tunable TEA CO_(2)laser in the 9—11 μm band and a 1.55 μm fiber laser.By combining the principles of differential absorption detection and pulsed coherent detection,the system enables agile and remote sensing of atmospheric pollution.Extensive static tests validate the system’s real-time detection capabilities,including the measurement of concentration-path-length product(CL),front distance,and path wind speed of air pollution plumes over long distances exceeding 4 km.Flight experiments is conducted with the helicopter.Scanning of the pollutant concentration and the wind field is carried out in an approximately 1 km slant range over scanning angle ranges from 45°to 65°,with a radial resolution of 30 m and10 s.The test results demonstrate the system’s ability to spatially map atmospheric pollution plumes and predict their motion and dispersion patterns,thereby ensuring the protection of public safety.

Spatial-temporal differentiation and influencing factors of rural settlements in mountainous areas: an example of Liangshan Yi Autonomous Prefecture, Southwestern China

Rural settlement is the basic spatial unit for compact communities in rural area. Scientific exploration of spatial-temporal differentiation and its influencing factors is the premise of spatial layout rationalization. Based on land use data of Liangshan Yi Autonomous Prefecture(hereinafter referred to as Liangshan Prefecture) in Sichuan Province, China from 1980 to 2020, compactness index, fractal dimension, imbalance index, location entropy and the optimal parameters-based geographical detector(OPGD) model are used to analyze the spatial-temporal evolution of the morphological characteristics of rural settlements, and to explore the influence of natural geographical factors, socioeconomic factors, and policy factors on the spatial differentiation of rural settlements. The results show that:(1) From 1980 to 2020, the rural settlements area in Liangshan Prefecture increased by 15.96 km^(2). In space, the rural settlements are generally distributed in a local aggregation, dense in the middle and sparse around the periphery. In 2015, the spatial density and expansion index of rural settlements reached the peak.(2) From 1980 to 2020, the compactness index decreased from 0.7636 to 0.7496, the fractal dimension increased from 1.0283 to 1.0314, and the fragmentation index decreased from 0.1183 to 0.1047. The spatial morphological structure of rural settlements tended to be loose, the shape contour tended to be complex, the degree of fragmentation decreased, and the spatial distribution was significantly imbalanced.(3) The results of OPGD detection in 2015 show that the influence of each factor is slope(0.2371) > traffic accessibility(0.2098) > population(0.1403) > regional GDP(0.1325) > elevation(0.0987) > poverty alleviation(0). The results of OPGD detection in 2020 show that the influence of each factor is slope(0.2339) > traffic accessibility(0.2198) > population(0.1432) > regional GDP(0.1219) > poverty alleviation(0.0992) > elevation(0.093). Natural geographical factors(slope and elevation) are the basic factors affecting the spatial distribution of rural settlements, and rural settlements are widely distributed in the river valley plain and the second half mountain area. Socioeconomic factors(traffic accessibility, population, and regional GDP) have a greater impact on the spatial distribution of rural settlements, which is an important factor affecting the spatial distribution of rural settlements. Policy factors such as poverty alleviation relocation have an indispensable impact on the spatial distribution of rural settlements. The research results can provide decisionmaking basis for the spatial arrangement of rural settlements in Liangshan Prefecture, and optimize the implementation of rural revitalization policies.

THE EXACT MEROMORPHIC SOLUTIONS OF SOME NONLINEAR DIFFERENTIAL EQUATIONS

We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Compared with previous results on the equation p(z)f^(3)+q(z)f"=-sinα(z)with polynomial coefficients,our results show that the coefficient of the term f^((k))perturbed by multiplying an exponential function will affect the structure of its solutions.

KSKV:Key-Strategy for Key-Value Data Collection with Local Differential Privacy

In recent years,the research field of data collection under local differential privacy(LDP)has expanded its focus fromelementary data types to includemore complex structural data,such as set-value and graph data.However,our comprehensive review of existing literature reveals that there needs to be more studies that engage with key-value data collection.Such studies would simultaneously collect the frequencies of keys and the mean of values associated with each key.Additionally,the allocation of the privacy budget between the frequencies of keys and the means of values for each key does not yield an optimal utility tradeoff.Recognizing the importance of obtaining accurate key frequencies and mean estimations for key-value data collection,this paper presents a novel framework:the Key-Strategy Framework forKey-ValueDataCollection under LDP.Initially,theKey-StrategyUnary Encoding(KS-UE)strategy is proposed within non-interactive frameworks for the purpose of privacy budget allocation to achieve precise key frequencies;subsequently,the Key-Strategy Generalized Randomized Response(KS-GRR)strategy is introduced for interactive frameworks to enhance the efficiency of collecting frequent keys through group-anditeration methods.Both strategies are adapted for scenarios in which users possess either a single or multiple key-value pairs.Theoretically,we demonstrate that the variance of KS-UE is lower than that of existing methods.These claims are substantiated through extensive experimental evaluation on real-world datasets,confirming the effectiveness and efficiency of the KS-UE and KS-GRR strategies.

A Coupled Thermomechanical Crack Propagation Behavior of Brittle Materials by Peridynamic Differential Operator

This study proposes a comprehensive,coupled thermomechanical model that replaces local spatial derivatives in classical differential thermomechanical equations with nonlocal integral forms derived from the peridynamic differential operator(PDDO),eliminating the need for calibration procedures.The model employs a multi-rate explicit time integration scheme to handle varying time scales in multi-physics systems.Through simulations conducted on granite and ceramic materials,this model demonstrates its effectiveness.It successfully simulates thermal damage behavior in granite arising from incompatible mineral expansion and accurately calculates thermal crack propagation in ceramic slabs during quenching.To account for material heterogeneity,the model utilizes the Shuffle algorithm andWeibull distribution,yielding results that align with numerical simulations and experimental observations.This coupled thermomechanical model shows great promise for analyzing intricate thermomechanical phenomena in brittle materials.

Highly Differentiated Target Detection under Extremely Low-Light Conditions Based on Improved YOLOX Model

This paper expounds upon a novel target detection methodology distinguished by its elevated discriminatory efficacy,specifically tailored for environments characterized by markedly low luminance levels.Conventional methodologies struggle with the challenges posed by luminosity fluctuations,especially in settings characterized by diminished radiance,further exacerbated by the utilization of suboptimal imaging instrumentation.The envisioned approach mandates a departure from the conventional YOLOX model,which exhibits inadequacies in mitigating these challenges.To enhance the efficacy of this approach in low-light conditions,the dehazing algorithm undergoes refinement,effecting a discerning regulation of the transmission rate at the pixel level,reducing it to values below 0.5,thereby resulting in an augmentation of image contrast.Subsequently,the coiflet wavelet transform is employed to discern and isolate high-discriminatory attributes by dismantling low-frequency image attributes and extracting high-frequency attributes across divergent axes.The utilization of CycleGAN serves to elevate the features of low-light imagery across an array of stylistic variances.Advanced computational methodologies are then employed to amalgamate and conflate intricate attributes originating from images characterized by distinct stylistic orientations,thereby augmenting the model’s erudition potential.Empirical validation conducted on the PASCAL VOC and MS COCO 2017 datasets substantiates pronounced advancements.The refined low-light enhancement algorithm yields a discernible 5.9%augmentation in the target detection evaluation index when compared to the original imagery.Mean Average Precision(mAP)undergoes enhancements of 9.45%and 0.052%in low-light visual renditions relative to conventional YOLOX outcomes.The envisaged approach presents a myriad of advantages over prevailing benchmark methodologies in the realm of target detection within environments marked by an acute scarcity of luminosity.

Spin logic devices based on negative differential resistance -enhanced anomalous Hall effect

Owing to rapid developments in spintronics,spin-based logic devices have emerged as promising tools for next-generation computing technologies.This paper provides a comprehensive review of recent advancements in spin logic devices,particularly focusing on fundamental device concepts rooted in nanomagnets,magnetoresistive random access memory,spin–orbit torques,electric-field modu-lation,and magnetic domain walls.The operation principles of these devices are comprehensively analyzed,and recent progress in spin logic devices based on negative differential resistance-enhanced anomalous Hall effect is summarized.These devices exhibit reconfigur-able logic capabilities and integrate nonvolatile data storage and computing functionalities.For current-driven spin logic devices,negative differential resistance elements are employed to nonlinearly enhance anomalous Hall effect signals from magnetic bits,enabling reconfig-urable Boolean logic operations.Besides,voltage-driven spin logic devices employ another type of negative differential resistance ele-ment to achieve logic functionalities with excellent cascading ability.By cascading several elementary logic gates,the logic circuit of a full adder can be obtained,and the potential of voltage-driven spin logic devices for implementing complex logic functions can be veri-fied.This review contributes to the understanding of the evolving landscape of spin logic devices and underscores the promising pro-spects they offer for the future of emerging computing schemes.

Continuous-Time Channel Prediction Based on Tensor Neural Ordinary Differential Equation

Channel prediction is critical to address the channel aging issue in mobile scenarios.Existing channel prediction techniques are mainly designed for discrete channel prediction,which can only predict the future channel in a fixed time slot per frame,while the other intra-frame channels are usually recovered by interpolation.However,these approaches suffer from a serious interpolation loss,especially for mobile millimeter-wave communications.To solve this challenging problem,we propose a tensor neural ordinary differential equation(TN-ODE)based continuous-time channel prediction scheme to realize the direct prediction of intra-frame channels.Specifically,inspired by the recently developed continuous mapping model named neural ODE in the field of machine learning,we first utilize the neural ODE model to predict future continuous-time channels.To improve the channel prediction accuracy and reduce computational complexity,we then propose the TN-ODE scheme to learn the structural characteristics of the high-dimensional channel by low-dimensional learnable transform.Simulation results show that the proposed scheme is able to achieve higher intra-frame channel prediction accuracy than existing schemes.

Deep Structure Optimization for Incremental Hierarchical Fuzzy Systems Using Improved Differential Evolution Algorithm

The optimization of the rule base of a fuzzy logic system (FLS) based on evolutionary algorithm has achievednotable results. However, due to the diversity of the deep structure in the hierarchical fuzzy system (HFS) and thecorrelation of each sub fuzzy system, the uncertainty of the HFS’s deep structure increases. For the HFS, a largenumber of studies mainly use fixed structures, which cannot be selected automatically. To solve this problem, thispaper proposes a novel approach for constructing the incremental HFS. During system design, the deep structureand the rule base of the HFS are encoded separately. Subsequently, the deep structure is adaptively mutated basedon the fitness value, so as to realize the diversity of deep structures while ensuring reasonable competition amongthe structures. Finally, the differential evolution (DE) is used to optimize the deep structure of HFS and theparameters of antecedent and consequent simultaneously. The simulation results confirm the effectiveness of themodel. Specifically, the root mean square errors in the Laser dataset and Friedman dataset are 0.0395 and 0.0725,respectively with rule counts of rules is 8 and 12, respectively.When compared to alternative methods, the resultsindicate that the proposed method offers improvements in accuracy and rule counts.

A Differential Privacy Federated Learning Scheme Based on Adaptive Gaussian Noise

As a distributed machine learning method,federated learning(FL)has the advantage of naturally protecting data privacy.It keeps data locally and trains local models through local data to protect the privacy of local data.The federated learning method effectively solves the problem of artificial Smart data islands and privacy protection issues.However,existing research shows that attackersmay still steal user information by analyzing the parameters in the federated learning training process and the aggregation parameters on the server side.To solve this problem,differential privacy(DP)techniques are widely used for privacy protection in federated learning.However,adding Gaussian noise perturbations to the data degrades the model learning performance.To address these issues,this paper proposes a differential privacy federated learning scheme based on adaptive Gaussian noise(DPFL-AGN).To protect the data privacy and security of the federated learning training process,adaptive Gaussian noise is specifically added in the training process to hide the real parameters uploaded by the client.In addition,this paper proposes an adaptive noise reduction method.With the convergence of the model,the Gaussian noise in the later stage of the federated learning training process is reduced adaptively.This paper conducts a series of simulation experiments on realMNIST and CIFAR-10 datasets,and the results show that the DPFL-AGN algorithmperforms better compared to the other algorithms.

Value Iteration-Based Cooperative Adaptive Optimal Control for Multi-Player Differential Games With Incomplete Information

This paper presents a novel cooperative value iteration(VI)-based adaptive dynamic programming method for multi-player differential game models with a convergence proof.The players are divided into two groups in the learning process and adapt their policies sequentially.Our method removes the dependence of admissible initial policies,which is one of the main drawbacks of the PI-based frameworks.Furthermore,this algorithm enables the players to adapt their control policies without full knowledge of others’ system parameters or control laws.The efficacy of our method is illustrated by three examples.

Differentially Private Support Vector Machines with Knowledge Aggregation

With the widespread data collection and processing,privacy-preserving machine learning has become increasingly important in addressing privacy risks related to individuals.Support vector machine(SVM)is one of the most elementary learning models of machine learning.Privacy issues surrounding SVM classifier training have attracted increasing attention.In this paper,we investigate Differential Privacy-compliant Federated Machine Learning with Dimensionality Reduction,called FedDPDR-DPML,which greatly improves data utility while providing strong privacy guarantees.Considering in distributed learning scenarios,multiple participants usually hold unbalanced or small amounts of data.Therefore,FedDPDR-DPML enables multiple participants to collaboratively learn a global model based on weighted model averaging and knowledge aggregation and then the server distributes the global model to each participant to improve local data utility.Aiming at high-dimensional data,we adopt differential privacy in both the principal component analysis(PCA)-based dimensionality reduction phase and SVM classifiers training phase,which improves model accuracy while achieving strict differential privacy protection.Besides,we train Differential privacy(DP)-compliant SVM classifiers by adding noise to the objective function itself,thus leading to better data utility.Extensive experiments on three high-dimensional datasets demonstrate that FedDPDR-DPML can achieve high accuracy while ensuring strong privacy protection.

Multiple factors to assist human-derived induced pluripotent stem cells to efficiently differentiate into midbrain dopaminergic neurons

Midbrain dopaminergic neurons play an important role in the etiology of neurodevelopmental and neurodegenerative diseases.They also represent a potential source of transplanted cells for therapeutic applications.In vitro differentiation of functional midbrain dopaminergic neurons provides an accessible platform to study midbrain neuronal dysfunction and can be used to examine obstacles to dopaminergic neuronal development.Emerging evidence and impressive advances in human induced pluripotent stem cells,with tuned neural induction and differentiation protocols,makes the production of induced pluripotent stem cell-derived dopaminergic neurons feasible.Using SB431542 and dorsomorphin dual inhibitor in an induced pluripotent stem cell-derived neural induction protocol,we obtained multiple subtypes of neurons,including 20%tyrosine hydroxylase-positive dopaminergic neurons.To obtain more dopaminergic neurons,we next added sonic hedgehog(SHH)and fibroblast growth factor 8(FGF8)on day 8 of induction.This increased the proportion of dopaminergic neurons,up to 75%tyrosine hydroxylase-positive neurons,with 15%tyrosine hydroxylase and forkhead box protein A2(FOXA2)co-expressing neurons.We further optimized the induction protocol by applying the small molecule inhibitor,CHIR99021(CHIR).This helped facilitate the generation of midbrain dopaminergic neurons,and we obtained 31-74%midbrain dopaminergic neurons based on tyrosine hydroxylase and FOXA2 staining.Thus,we have established three induction protocols for dopaminergic neurons.Based on tyrosine hydroxylase and FOXA2 immunostaining analysis,the CHIR,SHH,and FGF8 combined protocol produces a much higher proportion of midbrain dopaminergic neurons,which could be an ideal resource for tackling midbrain-related diseases.

Risk stratification for radioactive iodine refractoriness using molecular alterations in distant metastatic differentiated thyroid cancer

Objective: Patients with radioactive iodine-refractory differentiated thyroid cancer(RAIR-DTC) are often diagnosed with delay and constrained to limited treatment options. The correlation between RAI refractoriness and the underlying genetic characteristics has not been extensively studied.Methods: Adult patients with distant metastatic DTC were enrolled and assigned to undergo next-generation sequencing of a customized 26-gene panel(Thyro Lead). Patients were classified into RAIR-DTC or non-RAIR groups to determine the differences in clinicopathological and molecular characteristics. Molecular risk stratification(MRS) was constructed based on the association between molecular alterations identified and RAI refractoriness, and the results were classified as high, intermediate or low MRS.Results: A total of 220 patients with distant metastases were included, 63.2% of whom were identified as RAIRDTC. Genetic alterations were identified in 90% of all the patients, with BRAF(59.7% vs. 17.3%), TERT promoter(43.9% vs. 7.4%), and TP53 mutations(11.5% vs. 3.7%) being more prevalent in the RAIR-DTC group than in the non-RAIR group, except for RET fusions(15.8% vs. 39.5%), which had the opposite pattern. BRAF and TERT promoter are independent predictors of RAIR-DTC, accounting for 67.6% of patients with RAIR-DTC. MRS was strongly associated with RAI refractoriness(P<0.001), with an odds ratio(OR) of high to low MRS of 7.52 [95%confidence interval(95% CI), 3.96-14.28;P<0.001] and an OR of intermediate to low MRS of 3.20(95% CI,1.01-10.14;P=0.041).Conclusions: Molecular alterations were associated with RAI refractoriness, with BRAF and TERT promoter mutations being the predominant contributors, followed by TP53 and DICER1 mutations. MRS might serve as a valuable tool for both prognosticating clinical outcomes and directing precision-based therapeutic interventions.

Differentially private SGD with random features

In the realm of large-scale machine learning,it is crucial to explore methods for reducing computational complexity and memory demands while maintaining generalization performance.Additionally,since the collected data may contain some sensitive information,it is also of great significance to study privacy-preserving machine learning algorithms.This paper focuses on the performance of the differentially private stochastic gradient descent(SGD)algorithm based on random features.To begin,the algorithm maps the original data into a lowdimensional space,thereby avoiding the traditional kernel method for large-scale data storage requirement.Subsequently,the algorithm iteratively optimizes parameters using the stochastic gradient descent approach.Lastly,the output perturbation mechanism is employed to introduce random noise,ensuring algorithmic privacy.We prove that the proposed algorithm satisfies the differential privacy while achieving fast convergence rates under some mild conditions.

Identifying Brand Consistency by Product Differentiation Using CNN

This paper presents a new method of using a convolutional neural network(CNN)in machine learning to identify brand consistency by product appearance variation.In Experiment 1,we collected fifty mouse devices from the past thirty-five years from a renowned company to build a dataset consisting of product pictures with pre-defined design features of their appearance and functions.Results show that it is a challenge to distinguish periods for the subtle evolution of themouse devices with such traditionalmethods as time series analysis and principal component analysis(PCA).In Experiment 2,we applied deep learning to predict the extent to which the product appearance variation ofmouse devices of various brands.The investigation collected 6,042 images ofmouse devices and divided theminto the Early Stage and the Late Stage.Results show the highest accuracy of 81.4%with the CNNmodel,and the evaluation score of brand style consistency is 0.36,implying that the brand consistency score converted by the CNN accuracy rate is not always perfect in the real world.The relationship between product appearance variation,brand style consistency,and evaluation score is beneficial for predicting new product styles and future product style roadmaps.In addition,the CNN heat maps highlight the critical areas of design features of different styles,providing alternative clues related to the blurred boundary.The study provides insights into practical problems for designers,manufacturers,and marketers in product design.It not only contributes to the scientific understanding of design development,but also provides industry professionals with practical tools and methods to improve the design process and maintain brand consistency.Designers can use these techniques to find features that influence brand style.Then,capture these features as innovative design elements and maintain core brand values.

Dynamic Characteristics of Functionally Graded Timoshenko Beams by Improved Differential Quadrature Method

This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method(DQM)for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution.Firstly,based on the first-order shear deformation theory,the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement,transverse displacement,and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section.Then,ignoring the shear deformation of the beam section and only considering the effect of the rotational inertia of the section,the governing equation of the beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam transverse displacement.Based on the differential quadrature method theory,the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of standard generalized algebraic equations.Finally,the first several natural frequencies of the beam can be calculated.The feasibility and accuracy of the improved DQM are verified using the finite element method(FEM)and combined with the results of relevant literature.