To understand whether sets of genomic loci are enriched at the regulatory loci of one or more cell types, we developed the gaiaAssociation package to perform Regulatory Landscape Enrichment Analysis (RLEA). RLEA is a novel analytical process that tests for enrichment of sets of loci in cell type-specific open chromatin regions (OCRs) in the genome.We demonstrate that the application of RLEA to genome-wide association study (GWAS) data reveals cell types likely to be mediating the phenotype studied, and clusters OCRs based on their shared regulatory profiles. GaiaAssociation is Python code that is freely available for use in functional genomics studies.https://pypi.org/project/gaiaAssociation/0.6.0/#description) for pip download and use on the command line or as an inline Python package. Gaia Association can also be installed from GitHub at https://github.com/GreallyLab/gaiaAssociation.Gaia Association is available on PyPi ( Despite the immense number of genome-wide association studies (GWAS) performed to study human diseases and traits, prioritizing the resulting variants for functional characterization remains a difficult task. Most DNA sequence variants implicated in GWAS occur in the non-coding majority of the human genome, and have been explored with functional genomic approaches to identify those variants with effects on gene expression or transcriptional regulatory processes . This method reveals candidate cell types mediating the effects of genetic variants on the phenotype, a valuable post-GWAS insight, while clustering cell types by their OCR enrichment profiles.To test for enrichment of sets of loci in the regulatory elements of different cell types, we developed the gaiaAssociation package to perform Regulatory Landscape Enrichment Analysis (RLEA). The implementation of RLEA partitions the genome into equally sized windows and then models the number of overlaps between single nucleotide variants (SNVs) or small indels and ATAC-seq peaks in each window as a binomial random variable. For the entire genome, the number of overlaps is modeled as a sum of independent binomial random variables, which can be estimated using saddlepoint approximation  a folder containing the chromatin regulatory region data of interest in bed text (.txt) format, 2) a folder containing the genomic loci of interest in tab-separated values (.tsv) or comma-separated values (.csv) format, 3) a .csv file containing the chromosome sizes of the desired genome build, and 4) a folder for the output of gaiaAssociation analyses.2.3The most straightforward example of the use of gaiaAssociation is represented by the input of a list of loci to test for overlap with OCRs from multiple cell types. The package supports SNVs and small indels, not larger copy number variants, with the primary goal of supporting data typical of GWAS results. When entering multiple sets of genomic loci, the user can define cutoff values to filter for a minimum size requirement for a dataset, for example. We used a minimum cutoff of 200 genomic loci as a conservative threshold.GaiaAssociation also permits the user to incorporate their own ATAC-seq loci or regulatory loci defined by other genome-wide assays. The software tests the relatedness of the loaded ATAC-seq profiles as a pre-processing step. The relationship between each pair of cell types is defined by calculating a weight, using the following formula:This weight matrix can be used to generate a dendrogram, based on the Euclidean distance metric and hierarchical clustering, using the SciPy8 algorithm , allowing the query set to be tested for enrichment, given the observed number of overlaps. For each window, the proportion that is occupied by OCRs is calculated for each cell type, and the total number of loci within that window is found. In the case of loci that overlap the OCR and have a length greater than one base pair, the size of each OCR in the window is extended to include the length of these extended loci. This is a slight adjustment to the more conventional single base pair loci calculation which is made to account for the possibility that an indel could land outside the OCR region but still overlap with it. This proportion of OCR coverage and the count of loci that overlap OCRs within that window, along with the total number of loci that overlap OCRs genome-wide, are used to calculate a p-value for global enrichment using the sinib package , which has been translated from R to Python and included with gaiaAssociation. This p-value is calculated for each cell type  and loci dataset  combination, to create an n x m matrix which describes the relative enrichment of these loci in each cell type.To calculate the sum of independent but non-identical binomial random variables, RLEA takes the user-provided chromosome size file and divides the chromosomes into windows of equal length, as close to the user-defined window size as possible. For each window in which there is at least one query loci /SNP, the number of overlaps between the query set and the subject regions in the absence of enrichment is modeled as a binomial random variable. This binomial random variable is determined by OCR overlap percentage and loci count. Thus, for the entire genome, the number of overlaps is modeled as a sum of independent binomial random variables. This distribution is estimated using saddlepoint approximation  through which they affect a trait or disease, and a clue to the identity of the regulatory elements that should be the focus of studies of non-coding sequence variation. We have provided a novel and efficient analytical resource for RLEA analysis that is freely-available and a useful part of the toolkit for understanding non-coding variants in human traits and diseases.Understanding the distribution of associated variants across the Supplement 12


Women who received a diagnosis of breast cancer often report impairments in physical and psychological wellbeing, even some years after treatments. Individual awareness about physical changes, body image, and current sensations related to their body is important to maintain a psycho-emotional balance. Virtual reality, as an advanced human–computer interface, can be an effective tool to improve breast cancer survivors' abilities to know and manage their current sensations related to their bodies. The present study protocol proposes a virtual reality intervention aiming at promoting interoception and emotional wellbeing, fear of cancer recurrence, and body perception in breast cancer survivors, according to the three data collection times. Repeated-measure analysis of variance (ANOVA) with between–within interaction will be performed. Expected results include participants' awareness of their internal feelings, the reduction of negative emotions, and the management of symptoms related to the body, clarifying characteristics for the effective implementation of VR psychological intervention in the future. Body image (BI) is defined as the internal representation of one's outward appearance , is generally involved in promoting body awareness and regulation of emotional wellbeing, especially in the eating disorder fields  that occupies a specific space (self-location) and its related internal sensations , as a tool that allows users to experience a sense of belonging with a body in a virtual world  through VR;- A VR intervention on body awareness and negative body sensations following illness, addressing interoceptive sensations related to the body.We expect that the present study focusing on VR intervention may help women with a history of breast cancer to improve their psychological wellbeing and awareness of inner sensations, promoting better emotional regulation.Women who have experienced breast cancer in the past and that have completed cancer treatments will be included in this study. Specifically, inclusion criteria are as follows: (a) adult women (18 years and older); (b) women who have previously received a diagnosis of breast cancer (stage I and II); (c) women who have received cancer treatment  in the past. Contrarily, exclusion criteria include people with a diagnosis of metastatic cancer and women who are unable to sign an informed consent and/or have poor knowledge of the Italian language. A sample size of at least 40 participants  is estimated to be involved.The study duration will be ~12 months, from recruitment until the conclusion of T2. Researchers will contact various breast cancer patient associations to share the current project and promote contact with interested people. Women interested in participating in the present research project can contact the researchers by writing to the email address provided by the association. The study will also be publicized through social networks , inviting interested women to contact the researchers through the email indicated in the study announcement. No monetary compensation will be provided, and mandatory adherence to the study will be requested as informed consent before administering the questionnaires. It will be made clear that participation in the research is completely free, voluntary, and free of charge. All participants will have the option to discontinue the research at any time without providing any explanation. At the end of the VR intervention, participants will be asked for their willingness to provide a personal contact that will be exclusively used to send them the follow-up questionnaires after 1 month (T2). Regarding the questionnaires, a code will be assigned to make the collected data pseudonymized.The study will be conducted following the Declaration of Helsinki principle and informed written consent will be collected from all participants. The study protocol has been revised and approved by the Ethical Committee of the University of Milan.Before VR intervention, participants will be randomized into the two research groups through Excel software (RAND function). Women in the experimental group will be invited to wear a 3D oculus and follow specific steps of the present intervention. Specifically, women will be shown a female avatar. The proposed virtual environment will be located in a neutral room, and the avatar will have an average body size compared to the general population. Women will be able to see the avatar's entire body looking straight ahead through the use of a 3D oculus. Then, visual and auditory stimuli will allow for an increased sense of belonging with respect to the virtual body, as described by Slater et al. . To sum More specifically, the proposed intervention will be structured as follows:Following the presentation of the study and the signing of the informed consent, participants will be asked to fill out the socio-demographic data, the clinical history of illness, any ongoing psychological support course, and a series of questionnaires aimed to explore some psychological aspects. Specifically, the following questionnaire will be administered:The multidimensional assessment of interoceptive awareness , the tendency to ignore uncomfortable bodily sensations , the ability to have emotional reactions following negative sensations , the ability to adjust attention regarding multiple sensations , the ability to be aware of the relationship between body states and affective states , the ability to pay attention to body states to regulate psychological distress , the ability to feel one's bodily sensations to make decisions , and the experience of one's body as safe and trustworthy . Some subscales measure direct experience with the body, and others are associated with the assessment of cognitive processes, such as self-regulation  In the past 7 days, how often have you checked your breasts for lumps? (b) In the past 7 days, have you felt anxious? and (c) How many times have you told your family members about your fears related to the disease in the past 7 days?- The duration of T0 will be about 20 min.Subsequently, participants will be randomly divided into the experimental and control groups. Participants in the experimental group will be asked to sit on a chair and place their open palms on the table without crossing their legs and keeping their backs straight. Wearing 3D oculus and donning the sensor, the participants will be immersed in VR where they will see the virtual body of an avatar positioned in the same position as them. The experiment will begin with an initial warm-up phase in which participants will be allowed to stand in the virtual environment without receiving additional stimuli (2 min). In this first phase, psycho-physiological indices (heart rate and heart rate variability) will be measured using wearable sensors at the wrist so as not to interfere with the session. Next, the experimental group will observe via VR visual stimulation on different parts of the virtual body  and listen to vocal stimulation, in a consecutive and randomized manner among the group participants. Specifically, this intervention will be structured as follows: The participants will see a light on their virtual body that, starting from an iridescent red color, will fade slowly, becoming white. At the same time, an external voice will guide the participants toward a gradual decrease in sensations of discomfort and itching, in a combination of the visual stimuli. This treatment will initially be proposed for a total of 5 min, considering that 90 s is sufficient to induce body illusion. This process will be proposed in the same mode  for the body parts of interest of the same , with a 2-min break between stimulations. During the breaks, participants will remain immersed in VR, without additional stimulation. In contrast, participants assigned to the control group, once immersed in a VR depicting a natural environment, will hear only a guiding voice reading a script aimed at relaxation. Once the experiment is over, all participants will fill out the battery of post-intervention questionnaires, which includes the following:The multidimensional assessment of interoceptive awareness (MAIA);- Measures regarding satisfaction related to the intervention: participants will answer some ad hoc questions designed to measure their satisfaction with the intervention;- ITC-Sense of Presence Inventory  Involvement: how much users perceive the content proposed by the virtual environment; (3) Ecological Validity: the level of realism and naturalness of the virtual environment; and (4) Negative Effects: the disruptive effects on the physical plane, such as nausea and eye discomfort, that users might experience while immersed in the virtual environment.- Multidimensional Assessment of Interoceptive Awareness (MAIA), the State-Trait Anxiety Inventory (STAI-Y1), the Self-Assessment Manikin (SAM), and the Checking behaviors, the Cancer Worry Scale (CWS) will be administered to participants , the required sample size is 40 . The type-I error rate (α) was set at 0.05 (two-sided), and the power (1 – β) was set at 0.90. The collected data could be analyzed using a statistical analysis software, the Statistical Package for Social Science .An This study could help people with a history of breast cancer to become more aware of their internal feelings, promoting the reduction of negative emotions  in the long term. Additionally, VR intervention focused on inners sensation awareness and emotional wellbeing may improve the control of possible symptoms , reducing anxiety and shame to foster better social relationships (Savioni et al., A possible study limitation could be the lack of a state-emotional assessment of breast cancer survivors. Future research needs to assess the state shame and guilt related to the worst memory focused on BI (i.e., State Shame and Guilt Scale—SSGS-8; Cavalera et al., In conclusion, in this study, there are no anticipated discomforts or undesirable effects for participants. It will be the researchers' responsibility to inform of the possibility for participants to discontinue participation in the research at any time, without giving any explanation and without incurring any possible negative consequences.The Ethics Committee of University of Milan approved the study and all participants signed the informed consent form. This study followed the Declaration of Helsinki.VS, ID, MS, and SP designed the study and wrote the protocol. KM and GP revised the draft of the paper. All authors contributed to the article and approved the submitted version.


This study proposes a remaining useful life (RUL) prediction method using limited degradation data with an unknown degradation model for hydraulic pumps with long service lives and no failure data in turbine control systems. The volumetric efficiency is calculated based on real-time monitoring signal data, and it is used as the degradation indicator. The optimal degradation curve is established using the degradation trajectory model, and the optimal probability distribution model is selected via the K-S test. The above process was repeated to optimize the degradation model and update parameters in different performance degradation stages of the hydraulic pump, providing quantification of the prediction uncertainty and enabling accurate online prediction of the hydraulic pump’s RUL. Finally, an RUL test bench for hydraulic pumps is built for verification. The results show that the proposed method is convenient, efficient, and has low model complexity. The method enables online accurate prediction of the RUL of hydraulic pumps using only limited degradation data, with a prediction accuracy of over 85%, which meets practical application requirements. As industrial systems become increasingly complex, the maintenance and management of large hydraulic pumps in steam turbine control systems present significant challenges . A faultCurrently, research on methods for predicting RUL can be broadly categorized into three principal approaches: physical model-based methods, data-driven methods, and hybrid methods that combine elements of both. There exist several prediction methods based on physical failure models ,5,6,7,8,The commonly used stochastic models in statistical data-driven methods for predicting the remaining lifespan include stochastic coefficient regression models, Wiener processes, Gamma processes, inverse Gaussian processes, and so on . The WieBased on the literature analysis above, it can be observed that there has been a considerable amount of research on degradation modeling and remaining lifespan prediction for randomly degrading equipment, especially in the area of statistical data-driven methods. However, it should be noted that the existing research mainly focuses on modeling the evolution trajectory of equipment performance degradation variables that have a certain trend and generally adopts a fixed degradation model function form. In practice, the selection of the degradation model function form itself is a challenge, especially when the chosen model function form is not suitable. It is difficult to achieve effective calibration of the degradation model solely through updating the model parameters, which can affect the accuracy of remaining lifespan prediction. Hydraulic pump is a kind of special equipment with long service life and a lack of full life cycle operation data. Although there are failure data obtained through historical fault data and accelerated experiments, considering the cost and test cycle, there is a lack of complete degradation cycles of the sample. Therefore, the early calibrated model is often difficult to adapt to the accurate prediction of the remaining service life of the hydraulic pump in the later period of service. Therefore, in order to meet the actual demand of residual service life prediction for randomly degraded equipment, it is necessary to develop a method that accurately predicts the residual service life by using the dynamic degradation distribution model and its parameters based on the previous limited degradation data.This paper proposes an RUL prediction method for hydraulic pumps based on limited degradation data. The method utilizes only a small amount of real-time monitoring data to construct a limited dataset, with volumetric efficiency as the degradation indicator. The optimal degradation curve is established using the degradation trajectory model, and the optimal probability distribution model is selected via K-S test. The above process is repeated to optimize the degradation model and update parameters in different performance degradation stages of the hydraulic pump, providing quantification of the prediction uncertainty and enabling accurate online prediction of the hydraulic pump’s RUL.This study focuses on the PVH74QIC-RSM-IS-10-C25-31 swash plate variable piston pump as the research object, using volumetric efficiency as the criterion to evaluate the pump’s operational status. According to 6.2.2 of JB/T7043-2006, as shown in The volumetric efficiency of the pump represents the ratio of actual flow to theoretical flow. In JB/T7043-2006, the calculation formula for the volumetric efficiency of an axial piston pump is given by Equation (1):Equation (1) shows that the volumetric efficiency is calculated using online monitoring parameters such as flow rate and rotational speed, and it is used as the degradation data In the case of degradation data (volumetric efficiency), selecting an appropriate degradation trajectory is crucial. Curve fitting is utilized to investigate the relationship between degradation and RUL, making it easier to reveal the degradation behavior of equipment. As the degradation model is unknown, this paper performs curve fitting using exponential, Fourier, linear, and quadratic models. The formula for curve fitting is given by Equation (3):(1)Residual sum of squares (SSE): SSE represents the error between the curve fitting value and the test value, indicating the degree of model fitting. A smaller SSE value indicates better model fitting, as it reflects a closer match between the fitting method and the real test result. This leads to more successful data prediction.(2)Root Mean Square Error (RMSE): RMSE represents the standard deviation between the fitting value and the test value. A smaller RMSE value indicates a better fitting effect, as it reflects a closer match between the fitting result and the test value. When the RMSE is closer to 0, it means that the fitting result is closer to the test value, indicating a better fitting effect.(3)R-square : R-squared is a statistical measure that represents the square of the correlation coefficient between the measured data  and the fitted value. Its value ranges from 0 to 1. A value closer to 1 indicates a better fitting effect, implying that the curve fitting method is more accurate. In other words, R-squared measures the proportion of the variation in the dependent variable  that is explained by the independent variable .The merits and demerits of curve fitting are evaluated using the following three indicators to determine the optimal degradation curve:In this study, the Weibull distribution model, extreme value distribution model, and lognormal distribution model were selected as probability distribution model candidates for random effects. The best probability distribution model, which is most consistent with random effects, was determined using the Kolmogorov-Smirnov (K-S) test.The Weibull distribution is a theoretical basis for reliability analysis and life testing . It has The extreme value distribution is a probability distribution that describes the distribution of the maximum (or minimum) value in probability theory. It represents the probability density distribution that each maximum value selected from many independent values should follow . The proThe lognormal distribution is a probability distribution that describes a random variable whose logarithm follows a normal distribution . In the The K-S test is a commonly used method to assess whether an empirical distribution follows a theoretical distribution or to compare whether two empirical distributions have significant differences . The K-Sp, where D is an indicator variable: accepting the null hypothesis that the data follow the theoretical distribution  or rejecting the null hypothesis that the data do not follow the theoretical distribution . p is the significance probability, usually set at 0.05, which determines whether to accept or reject the null hypothesis. The greater the p-value, the better the probability distribution model, and the closer it is to the reality.The key test parameters of the K-S test are D and The reliability A hydraulic pump volume efficiency reduction to 88% is considered to indicate that the end of its working life has been reached. In other words, when the degradation curve The reliability function can be expressed as Equation (9):In (1)Determining the failure criteria of hydraulic pumps and investigating the degradation laws of degradation data over time.(2)Fitting the degradation curve, calculating the residual data, and eliminating outliers.(3)To achieve this, different fitting methods such as exponential fitting and linear fitting are used to characterize the optimal function that matches the degradation data over time. The best fitting method is selected through evaluation index. Additionally, a random variable is determined to characterize the random fluctuations of the degradation data around the degradation curve.(4)Based on the theory of probability and statistical analysis, the parameter identification of random variables in different probability distribution models is performed. The optimal probability distribution model is determined using the K-S test to quantify the uncertainty.(5)The failure time of the hydraulic pump is calculated by determining the given reliability probability of a given time The RUL prediction method for hydraulic pumps based on degradation data proposed in this study is as follows:The prediction process is illustrated in Based on the data required in Equation (1), a remaining life test bench for the plunger pump is constructed as shown in The basic principle of the test bench is illustrated in During the test, the automatic circulating cooling system ensures that the test oil temperature remains within the working oil temperature range of the equipment, which is 40~55 °C. The pump to be tested is shown in The displacement, speed, and flow data were collected through the online arrangement of sensors, and the collected data was processed and calculated to obtain volumetric efficiency. The data were recorded once per minute. Due to the large amount of data, the table only lists the average volume efficiency calculated every four days. The data for the first 120 days is shown in Based on the data in During the experiment, external factors may cause anomalies in the data, which can introduce errors in subsequent analysis results. These anomalous data points are referred to as data anomalies. To ensure the accuracy of the results, it is necessary to perform residual analysis on the data to eliminate any data anomaly points. The difference between the observed value and the predicted value  is known as the residual. By analyzing the information concealed within the residual, residual analysis can be employed to determine the reliability of the data. In regression analysis, standardized residuals of the test data points that fall outside the  interval can be classified as data outliers at a 95% confidence level and should be directly eliminated. The results of the residual analysis are presented in The expression for the fitting curve after eliminating the abnormal data points is given by Equation (10).The degradation curve, after the elimination of outliers, is illustrated in The random effect primarily accounts for the random fluctuations observed in the degradation data around the degradation curve, denoted by The data presented in h values of the three models are 0, indicating that they are in line with the data. The p value of the lognormal distribution model in the three models is closer to 1, indicating a higher consistency. Therefore, the most consistent probability distribution model is the lognormal distribution.The K-S test results are shown in The probability distribution curve is shifted along the direction of the fitting curve until the area above the failure reference line corresponds to a given probability of 90%. At this point, the probability distribution curve stops moving, and the corresponding abscissa on the curve is 236.0443 days, as shown in The trend of the RUL with the change of reliability probability can be obtained from the diagram, which fully demonstrates the intuition of the proposed method and the accuracy of relying on probability and statistics theory. As the amount of monitoring data continues to increase, the prediction accuracy also improves.As the hydraulic pump life test has a long duration, it may not reach the failure state during the test, making it difficult to verify the accuracy of the prediction results. To address the challenge of obtaining long-term and complete prior sample data, this study proposes a method of changing the failure reference value to verify the accuracy of the proposed method.Using the available 120 day test data as a basis, the failure reference value is set as the volumetric efficiency observed on the 120th day, at which point the hydraulic pump is considered to have failed. Five observation points are selected at the 20th, 40th, 60th, 80th, and 100th days. The proposed method is used to predict the RUL at each of these observation points, and the accuracy of the method is verified by comparing the deviation between the predicted results and the actual results.The deviation between the predicted RUL and the actual value is denoted as Based on the comparative analysis presented above, it can be inferred that the method proposed in this paper achieves high prediction accuracy and low computational complexity while using only limited degradation data. This method enables accurate online prediction of hydraulic pumps.(1)The RUL method proposed in this study constructs a degradation trajectory model using volumetric efficiency as the performance degradation indicator. The method achieves a prediction accuracy of over 85% while only using limited degradation data. Compared with traditional AdaBoost, Random Forest, and FCM-HSMM, the prediction error of the proposed method shows a monotonically decreasing trend, and the prediction fluctuation gradually decreases. Additionally, the computational complexity is low, ensuring both the accuracy and real-time performance of the prediction.(2)This study proposes an evaluation method for curve fitting and probability distribution models for unknown degradation models. The method selects the best degradation curve and probability distribution model, effectively revealing the degradation law of hydraulic pumps and quantifying the uncertainty of random effect.(3)This study proposes a verification method based on changing failure threshold, which enables the test verification of hydraulic pumps with long service lives and no failure data by assuming a failure threshold.In this study, we propose a method for predicting the RUL of hydraulic pumps based on limited degradation data, which enables accurate online prediction of hydraulic pumps that have long service lives, are difficult to shut down, and have no failure data. The main conclusions of this study are as follows:


The inverse kinematics plays a vital role in the planning and execution of robot motions. In the design of robotic motion control for NAO robot arms, it is necessary to find the proper inverse kinematics model. Neural networks are such a data-driven modeling technique that they are so flexible for modeling the inverse kinematics. This inverse kinematics model can be obtained by means of training neural networks with the dataset. This training process cannot be achieved without the presence of the dataset. Therefore, the contribution of this research is to provide the dataset to develop neural networks-based inverse kinematics model for NAO robot arms. The dataset that we created in this paper is named ARKOMA. ARKOMA is an acronym for ARif eKO MAuridhi, all of whom are the creators of this dataset. This dataset contains 10000 input-output data pairs in which the end-effector position and orientation are the input data and a set of joint angular positions are the output data. For further application, this dataset was split into three subsets: training dataset, validation dataset, and testing dataset. From a set of 10000 data, 60 % of data was allocated for the training dataset, 20 % of data for the validation dataset, and the remaining 20 % of data for the testing dataset. The dataset that we provided in this paper can be applied for NAO H25 v3.3 or later. Specifications Table1•In the design of the robotic motion control for NAO robot arms, it is required to obtain the proper inverse kinematics model. Inverse kinematics is such a highly nonlinear problem that it is frequently difficult to solve analytically. This problem can be overcome by neural networks. The dataset provided in this paper can be utilized by NAO robot developers to develop the inverse kinematics model based on neural networks.•This dataset contains the input-output data pairs, so this is suitably addressed on supervised learning. Supervised learning is a paradigm where the neural networks are trained by using labeled data. Labeled data means that each input has its corresponding output or desired target. In other words, labeled data is the dataset that comprises the input-output data pairs. In supervised learning, there are different neural network architectures, such as multi-layer perceptron neural networks (MLPNN), convolutional neural networks (CNN), radial basis function neural networks (RBFNN), and so on. By using the dataset, NAO robot developers can develop different neural network architectures to obtain the inverse kinematics model.•This dataset was divided into three subsets: training dataset, validation dataset, and testing dataset. The training dataset is used to train neural networks. The validation dataset is then utilized to validate the performance of neural networks during the training process, while the testing dataset is employed after the training process to test the performance of the trained neural networks. Therefore, the dataset that we provided in this paper can be applied to not only train neural networks but also validate and test the performance of the trained neural networks-based inverse kinematics model for NAO robot arms.2Inverse kinematics plays a significant role in various applications related to robot motions. This is because the planning and execution of appropriate robot motions are inexorable from the inverse kinematics role. It is important to note that most tasks to be performed by the robotic arm are defined in the cartesian space. To perform manipulation tasks such as grasping objects, pick-and-place objects, and path tracking, the control inputs are given in terms of the desired position and orientation of the robot end-effector in the cartesian space. The manipulation tasks in industrial manufacturing for the welding robot, painting robot, and assembling robot are also determined in the cartesian space. However, what we can directly control from the robotic arm to perform the given tasks is its joint actuators that operate in the joint space. Therefore, the only way to solve this problem is through the inverse kinematics. The inverse kinematics deals with the mapping from the robot end-effector operational space, which is the cartesian space, to the robot joint space. The inverse kinematics is specifically used to find a set of joint angular positions based on the given position and orientation of the robot end-effector. The joint angular positions obtained from the inverse kinematics are required to control the joint actuators so that the robot end-effector can be driven to the desired targets in the cartesian space Due to its nonlinearity, solving the inverse kinematics becomes a complex and challenging task. In general, the inverse kinematics can be solved by using analytical and computational methods. The analytical methods highly depend on the robot kinematics structure, so they are applicable to only a certain robot structure. In the case of robotic arms, Pieper's criterion stated that the inverse kinematics can be possibly solved by the analytical methods when the robotic arms contain a spherical wrist whose three revolute joint axes intersect at a common point Neural networks are such a data-driven modeling technique that they require the dataset to create the inverse kinematics model. The presence of the dataset is a fundamental requirement in neural networks. It means that the presence of the dataset becomes a prerequisite in the use of neural networks. For that reason, we are motivated to create the dataset and disseminate this dataset through this paper. The dataset that we provided in this paper can be widely used by the NAO robot developers to build the neural networks-based inverse kinematics model for NAO robot arms. It can be only achievable with the presence of the dataset. Through this dataset, neural networks can learn from the patterns of the data to find the relationship model between the inputs and outputs in the dataset. In this dataset, the inputs are the robot end-effector position and orientation, whereas the outputs are a set of joint angular positions. This relationship model resulted from neural networks is so-called the neural networks-based inverse kinematics model.Based on the number of the input and output parameters in the dataset, the neural networks-based inverse kinematics model will have six neurons in the input layer and five neurons in the output layer, as shown in 3The dataset that we published in this data repository ,8 contaiMeanwhile, for the output data, there are five output parameters. The number of the output parameters for the inverse kinematics is equal to the number of joints. Physically, the NAO robot has five revolute joints for each arm. These revolute joints are the shoulder pitch . In total, the NAO H21 has 21 DOF, while the NAO H25 has 25 DOF distributed on its head, two arms, and two legs. The main difference between these two models lies in the number of joints and the type of end-effector on their arms. Meanwhile, for the other parts of the body, the number of joints and the type of end-effector are the same. For this reason, our discussion will be more focused on the robotic arms of the NAO H25. The NAO robot version that we used for the data acquisition is the NAO H25 v3.3.The NAO robot arms kinematically contain a series of rigid links connected by revolute joints. The assembly of rigid links connected by the revolute joints forms the kinematic chain 5.2From the data acquisition, we obtained 10000 robotic arm poses. As previously mentioned, the robotic arm poses are created from various joint configurations. Therefore, by extracting the robotic arm poses, we can obtain the data containing a set of joint angular positions of the NAO robot arms. The data samples for the joint angular positions are presented in 66.1Forward kinematics is concerned with the mapping from the joint space to the end-effector operational space, which is the cartesian space. The forward kinematics is also referred to as direct kinematics. The forward kinematics has a specific function to calculate the end-effector position and orientation in the cartesian space based on a given set of joint angular positions. Because of its important role, the forward kinematics must be formulated correctly. The way to formulate the forward kinematics of the NAO robot arms has been entirely explained in our previous research 6.2As mentioned in 6.3From the matrix decomposition, we obtained the translation matrix and rotation matrix. The translation matrix has three elements, each of which denotes the end-effector position in the three-dimensional cartesian space. Meanwhile, the rotation matrix contains nine elements. However, only three elements of them are independent Alternatively, to make the transformation from the rotation matrix to the rotation vectors easier, we can use SciPy library 6.4The end-effector position in the three-dimensional cartesian space is denoted by using three parameters [77.1The experiment has been conducted to create the dataset. From the data acquisition that we explained in the previous section, we obtained data composed of a set of joint angular positions. Besides, we also require the end-effector position and orientation data. By using the forward kinematics, we can generate the data containing the end-effector position and orientation. It can be conducted by feeding a set of joint angular positions into the forward kinematics 7.2The dataset to build neural networks-based inverse kinematics model for NAO robot arms consists of 10000 input-output data pairs, where the input data is the end-effector position and orientation and the output data is a set of joint angular positions. This dataset should be then split into three partitions: the training dataset, validation dataset, and testing dataset Meanwhile, the result of data allocation for the NAO's right arm can be seen in The dataset that we generated in this research is entirely in CSV format. CSV stands for Comma Separated Values. This file format has been widely used for saving data. A CSV file is generally tabular data that is saved as plain text. This file uses commas to separate values in tabular data. It should be noted that the kind of dataset in this paper is tabular data. As mentioned earlier, this dataset contains the input-output data pairs. For further applications, this dataset is divided into three partitions: training dataset, validation dataset, and testing dataset. This dataset is entirely stored in CSV format whose file names can be seen in This dataset consists of input and output data pairs, so this dataset is specifically addressed on supervised learning. Supervised learning is such a paradigm where the neural networks are trained by a set of labeled data. Labeled data means that each input has its corresponding output or desired target. In supervised learning, the objective is to find the relationship model between the inputs and outputs. In this dataset, the inputs are the end-effector position and orientation in three-dimensional cartesian space, and the outputs are a set of joint angular positions in the joint space. The relationship model resulted from this learning is called the neural networks-based inverse kinematics model. The number of data provided in this paper is sufficient to build the neural networks-based inverse kinematics model for NAO robot arms. In supervised learning, where the dataset contains input and output data pairs, the number of required data is typically not as many as in unsupervised learning. This is because the labeled data in supervised learning provides guidance in the learning process. This guidance reduces the ambiguity in the learning process, thereby making it possible to achieve good performance with a smaller number of data compared to unsupervised learning. Different from supervised learning, unsupervised learning typically requires more data to achieve good results because it has to learn from unlabeled data.The dataset that we provided in this paper is compatible with the NAO H25 v3.3 or later. However, this dataset is incompatible with the previous version.The authors declare that our dataset meets the ethical requirements for publication in Data in Brief and our work does not involve human subjects, animal experiments, or any data collected from social media platforms.Arif Nugroho: Conceptualization, Methodology, Formal analysis, Visualization, Data curation, Software, Writing – original draft, Writing – review & editing. Eko Mulyanto Yuniarno: Methodology, Formal analysis, Validation, Investigation, Writing – review & editing. Mauridhi Hery Purnomo: Conceptualization, Supervision, Validation, Writing – review & editing.


The availability of a wearable artificial liver that facilitates extracorporeal dialysis outside of medical facilities would represent a significant advancement for patients requiring dialysis. The objective of this preliminary investigation is to explore, using validated mathematical models based on in vitro data, the feasibility of developing a novel, cost-effective, and highly compact extracorporeal liver support device that can be employed as a transitional therapy to transplantation outside of clinical settings. Such an innovation would offer substantial cost savings to the national healthcare system while significantly improving the patient’s quality of life. The experimental components consisted of replacing traditional adsorbent materials with albumin-functionalized silica microspheres due to their capacity to adsorb bilirubin, one of the toxins responsible for liver failure. Two configurations of the dialysis module were tested: one involved dispersing the adsorbent particles in dialysis fluid, while the other did not require dialysis fluid. The results demonstrate the superior performance of the first configuration compared to the second. Although the clinical applicability of these models remains distant from the current stage, further studies will focus on optimizing these models to develop a more compact and wearable device. The liver is a complex organ responsible for carrying out multiple functions, such as the control of metabolic processes, the synthesis of plasma proteins, and the purification of blood from endogenous and xenobiotic substances . Replaci–108 M−1 . In ordeBovine serum albumin  and bilirubin (mixed isomers) were utilized in their original form without any additional purification steps. The 3-Aminopropyl-functionalized silica gel (40–63 µm), a white powder consisting of silica microparticles with a pore diameter of 60 Å, was chosen as the solid support to adsorb bilirubin, using albumin as a host. To aid in the functionalization (chemisorption) of the silica particles with albumin , promoters such as MES hemisodium salt, N-(3dimethylaminopropyl)-N′-etilcarbodiimmide (EDC) and N-Hydroxysuccinimide (NHS) were utilized. Sigma Aldrich was the source of all the materials and chemicals used, which were of reagent-grade quality. In this work, the experimental activity was conducted in two different setups (described later), employing hollow fiber membrane modules. In both configurations, we used two small hollow fiber modules obtained from a renal dialysis device, the Revaclear Capillary Dialyzer 300 . Such fibers were characterized by a porous membrane in polyarylethylsulfone (PAES) and polyvinylpyrrolidone (PVP). The latter polymers were selected for their excellent mechanical and thermal properties. Furthermore, their biocompatibility minimizes the possibility of thrombotic phenomena or non-physiological alterations of the hemodynamic. An overview of the main characteristics of the Revaclear Capillary Dialyzer 300 is provided in The artificial blood utilized in this study consisted exclusively of albumin and bilirubin. Bilirubin, which exhibits low solubility in water, was incorporated into the solution by initially dissolving it in a 20 mM aqueous NaOH solution. Subsequently, the albumin solution was added, which had been prepared in a 0.15 M phosphate buffer (PBS) at a pH of 7.4. The concentration of bilirubin was determined by performing spectrophotometric analysis at a wavelength of 458 nm using an Infinite M200 PRO Tecan microplate spectrophotometer . In the subsequent sections, a detailed description of the two experimental setups will be provided.The first configuration simulates a classic module of dialysis with dialysis fluid containing albumin. More precisely, this setup involves the immersion of the hollow fiber module inside a beaker containing 65 mL of dialysis fluid rich in albumin and the suspended silica microspheres. The dialysis fluid was obtained from an albumin solution prepared with a 0.1 g albumin weight dissolved in a phosphate buffer (PBS) of 0.15 M at a pH of 7.4. The rescaled hollow fiber module was inserted into the beaker by the presence of two holes drilled into it. Then, a biphasic resin was used to anchor the module to the beaker walls, avoiding leakages. Finally, the beaker was filled with the albumin-rich dialysis fluid, in which the adsorbent silica microspheres were suspended, as shown in The artificial blood containing albumin and bilirubin was continuously pumped inside the fibers using a 4020 single syringe pump . The concentration of blood entering the fibers was constant and equal to (a)Membrane functionalization by physical adsorption of the silica microspheres;(b)Membrane functionalization by chemical bonds with the silica microspheres.Given the considerable adsorption capacity of the silica microspheres used , it was Since the albumin–bilirubin bond is fluorescent, the fluorescence intensity was observed with a Nikon A1+R confocal microscope. The sample immersion in a sodium–hydroxide solution and the subsequent immersion in a HCl solution were performed in the last selected procedure. The hydrolysis of the double bonds of the carbon and the oxygen of the polymer followed, with the subsequent formation of the COOH carboxylic groups. In this way, the amino group’s functionalized silica microspheres were bound to the membrane. Recalling that the microspheres were, in turn, functionalized with albumin, the proposed module is suitable to be used as a stand-alone regenerative albumin dialysis module. To sum up, the two configurations involved are graphically represented in The experimental data collected for the two described configurations were elaborated, and two mathematical models were developed, starting from both experimental setups. The unknown parameters  were estimated from the following mathematical models.-Mass transfer across the membrane to the external compartment containing the dialysis fluid, which is assumed to be perfectly mixed;-Adsorption on silica microspheres.Two main steps are involved in the bilirubin  removal from the artificial blood:The experimental setup schematically described in Equation (3) is the bilirubin mass balance in the dialysate with its boundary condition:Equation (5) shows the bilirubin mass balance on the silica’s adsorbent microspheres with the linear isotherm, Equation (6), and its boundary condition, Equation (7):Being isotherm , and thei et al. . The bilAssuming that In both cases:In the second configuration, we considered a microscopic mass balance for the solid phase since the spheres are chemically bound to the outer surface of the fibers. In this case, the global material transfer coefficient includes resistance to transport relative to the liquid film on the artificial blood side and resistance relative to the membrane and transport on the microspheres. -Mass transfer across the membrane;-Adsorbed-on-silica microspheres linked to the membrane surface.Furthermore, in this case, two main steps are involved in the bilirubin  removal from the artificial blood:The experimental setup described has been modeled by the following set of finite difference equations. Equation (14) represents the bilirubin mass balance in the blood compartment with the boundary conditions in Equation (15):As shown in Equation (15), the initial condition is different from the previous Equation (2). In this case, at the beginning of the test, the bilirubin concentration in the blood is at a maximum since the fibers are initially full of blood. This full-fiber modeling was carried out to make the analysis more accurate in order to obtain a decreasing monotonic trend caused by the saturation behavior of the solid particles. In Equation (16), the bilirubin mass balance on the silica’s adsorbent microspheres is provided together with the linear isotherm, Equation (17), and its boundary condition, Equation (18):δ being the adsorbent solid layer thickness, and The increase in the particle adsorbent weight in the dialysis fluid was tested in the first configuration. The increased removal of bilirubin from the artificial blood can be observed due to the increased number of adsorbent particles in the dialysis fluid during the time of the experimental simulation (720 min), as shown in In order to obtain the simulated curve of the first configuration, the set of differential Equations (1)–(7), was integrated numerically with the gProms package , using a first-order backward finite difference method. The same software was used to perform data fitting, using The model simulation follows the trend correctly with respect to the experimental data, especially from 100 min to 500 min. The trend shows a zero-toxin concentration in the blood initially because the fibers are empty. While the fiber fills up, the concentration rises sharply due to the maximum driving force between the artificial blood and the dialysate fluid. Then, the removed toxin concentration in the blood decreases, which is caused by an active site saturation between the bilirubin and the solid adsorbent in the dialysate.Eliminating the need for dialysis fluid in such a blood purification device would make it less heavy and bulky, as well as easier to transport. This was investigated in the second configuration. In this new configuration, the set of differential Equations (14)–(18), was integrated numerically with the gProms package. The same software was used to perform data fitting, using rameters  and follComparing the values of the parameters estimated from the first and second configurations, it is possible to note the reduction of both the -Extended time for toxin removal from the blood;-Lower efficiency.In the second configuration, the toxin removal from the blood reaches only 50% within 0 to 100 min, whereas in the first configuration, it averages around 78%. Generally, the first configuration exhibits higher efficiency (averaging 70%) compared to the second configuration (averaging 55%). Based on these observations, it can be concluded that the performance of the first modeled device is superior to that of the second configuration.Two configurations of small hollow fiber modules were investigated in this study. The first configuration involved immersing the hollow fibers in a dialysis fluid containing dispersed albumin-functionalized silica adsorbent particles. In the second configuration, the membrane of the fibers was chemically bound to the silica microspheres for functionalization. Mathematical models were developed for each experimental setup to describe the relevant phenomena occurring in the different configurations. The experimental data were utilized to determine the parameters for the model fitting, enabling a comparison between the simulated models and the actual experimental data. The results indicated that the simulated model accurately represented the trends observed in the experimental data for both configurations. Although the first configuration demonstrated better performance than the second one, further studies will focus on the latter configuration. The goal is to develop a compact and wearable device that can be utilized by patients, with liver disease, outside of hospital and home environments. The models shown in this study are validated by the experimental data. The mathematical model developed in this work is based on a preliminary study carried out by using bilirubin as the key toxin of the performance device. Further studies will be devoted to assessing device clearance in relation to several other toxins involved in liver failure, such as tryptophan, mercaptans, and bile acids. It is worth noting that the proposed device was tested using artificial solutions far from having the same characteristics as human blood. Therefore, the definitive application of this experimental setup in patients will require much additional research also aimed at avoiding certain possible side effects .


When the initial size of an atom cloud in a cold atom interferometer is negligible compared to its size after free expansion, the interferometer is approximated to a point-source interferometer and is sensitive to rotational movements by introducing an additional phase shear in the interference sequence. This sensitivity on rotation enables a vertical atom-fountain interferometer to measure angular velocity in addition to gravitational acceleration, which it is conventionally used to measure. The accuracy and precision of the angular velocity measurement depends on proper extraction of frequency and phase from spatial interference patterns detected via the imaging of the atom cloud, which is usually affected by various systematic biases and noise. To improve the measurement, a pre-fitting process based on principal component analysis is applied to the recorded raw images. The contrast of interference patterns are enhanced by 7–12 dB when the processing is present, which leads to an enhancement in the precision of angular velocity measurements from 6.3 μrad/s to 3.3 μrad/s. This technique is applicable in various instruments that involve precise extraction of frequency and phase from a spatial interference pattern. Analogous to optical interference, wave-particle duality allows for interference of microscopic particles. Unlike neutrons and electrons, atoms possess distinctive internal energy-level structures and properties such as discrete mass, magnetic moments, and polarizations, making atomic interference capable of revealing information on physical fields in detail. Atomic interferometry holds significant importance in the domain of precision measurements. Additionally, atom interferometers have been successfully utilized for measuring gravitational acceleration ,2, fine An atom point-source interferometer (APSI) is a new type of atomic inertial sensor capable of measuring both gravitational acceleration and angular velocity . These iFollowing the point-source model , the spaTo accurately extract the spatial frequency of the interference patterns of an atom cloud in such an interferometer, we have applied specific methods based on principal component analysis (PCA)  in proceIn an atom interferometer, the interference phase shift rising from the gravitational acceleration In point-source approximation, the atom cloud in the interferometer is focused to a size much smaller compared with its final size after free expansion. When the initial cloud before expansion is regarded as a volume-less point with a certain velocity distribution, the influence of an atom’s initial position on its final displacement is neglected and its displacement The displacement–velocity coupling in the point-source model makes the APSI sensitive to rotations, even in a single axis interferometer that is conventionally used in gravitational acceleration measurements. Here is demonstrated the measurement of angular velocity The APSI works in a way similar to its optical counterpart of a shear interferometer. It is the phase shear added to the interferometer that reveals rich details in the total phase shift in an APSI. As is shown in When point-source approximation  was applied prior to fringe extraction.The PCA algorithm is a classic data processing method that is commonly used in dimensionality reduction and feature extraction of multidimensional data sets . With thThe process of carrying out PCA is essentially a process of dimensionality reduction and noise reduction. Firstly, the covariance matrix is optimized to obtain its eigenvectors and eigenvalues, which, respectively, represent the PCs and their corresponding variances. Then, different components of the original data set can be obtained using basis transformation. The optimization of the covariance matrix follows two principles. The off-diagonal elements of the covariance matrix are supposed to be as small as possible, because they indicate the correlation between different dimensions. On the contrary, the diagonal elements are supposed to be as large as possible, because they indicate the variance of the corresponding basis vector. Larger variances on most significant PCs would lead to lower residue noise, interfering with the detection.87Rb atoms for the fountain. Cooling laser beams are then red-detuned by 12 MHz from the D-line resonance of 87Rb atoms are trapped and cooled for the following fountain process.The ASPI-type inertia sensor was implemented in an atomic fountain interferometer, as is shown schematically in When the loading process is finished, the magnetic fields of both 2-D and 3-D MOTs are switched off and atoms are then launched into the interferometer chamber vertically using the moving molasses technique. The 2 pairs of upward and downward cooling laser beams are differentially detuned by The atoms are further cooled down when they are in ballistic launch using the polarization gradient cooling technique, where cooling laser beams are detuned far, to T = 140 ms. To reduce the influences of non-uniformity of the Raman laser, the light out of a single mode fiber is expanded to diameter of 60 mm, collimated, and then truncated with a 25 mm round diaphragm to match the 25 mm diameter of the vacuum fountain tube. The collimator and diaphragm are mounted on top of the whole instrument and shoot the Raman pulse downward to the bottom, where a mirror is mounted on an electrically controlled tilt stage to reflect it back to top. The phase shear in the APSI setup can then be applied by manipulating the rotation angle or the asymmetrical timing of Raman pulses to induce horizontal or vertical interference fringes.When the 3-pulse interferometer sequence is finished 0.6 s after fountain launching, a short detection pulse resonant with x. In the measurement, 3 separate tilting steps are applied to the reflecting mirror to achieve the compensation of Earth’s rotation. The tilting angles were set at t is set to 0 at the first Raman pulse for calculation convenience.It is necessary to compensate for the rotation of the Earth After rough compensation, an extra tilt When the Earth’s rotation has been properly compensated, it is also possible to obtain vertical interference fringes by introducing a small asymmetrical timing difference The measurement of angular velocity on an APSI relies on the accurate derivation of spatial frequency of the interference fringes captured by the imaging sensor. However, fitting the raw images directly to the theoretical model is far from accurate because of multiple imperfections of the instrument. For example, uneven distribution of atoms’ velocity and, consequently, their displacement from the center of the cloud is always superposed on the spatial fringes supposed to be measured. Thermal noise of the imaging sensor, residue stray light from detection laser pulses, and reflections from the inside of the vacuum chamber also disturb the detection in a way that is difficult to model and predict. To fulfill the measurement, a PCA-based pre-fitting procedure was applied to the detected raw image signals. The PCA-based procedure acts on the detected raw images much like an image filter separating the desired interference patterns from unwanted background bias and noise. As an unsupervised machine learning algorithm, PCA requires multiple raw images as a training set to derive the eigenvectors in subspace. In the experiment, a training set comprises 100 images from consecutive detection with identical phase shear settings. In PCA, the corresponding eigenvalue of a specific principal component reflects the proportion of information it contains in the original signal, and the component with a larger eigenvalue is more related to lower-frequency changes in the image . Among tWhen the intensity variance of the detection beam is not taken into account, the ideal spatial distribution of atoms after beam-tilt phase shear should be a superposition of horizontal fringes and a Gaussian number density distribution. The position-dependent probability of finding an atom on To find the spatial frequency For a comparison of the accuracy and reliability of raw fitting and PCA, both the averaged raw image and the second principal component derived from PCA were integrated along the direction perpendicular to the fringes and subject to parameter fitting according to Formula (7). As the PCA-based pre-fitting processing significantly screened out influences via unwanted systematic bias and noises, the characteristics of the interference pattern were significantly enhanced, and the contrast of the fringe as improved by 7–12 dB, resulting in a more reliable recovery of the spatial frequency and phase from atomic interference fringes. The enhancement is effective in both the vertical and horizontal fringe detection schemes. When the rotation angle in the beam-tilt phase shear scheme or asymmetry time in timing-asymmetry scheme is scanned, spatial frequency extraction with PCA from any image set proves more reliable than that from simple stacking and averaging the images in the set. The comparison is shown in When compared with the theoretical predictions, the improvement by PCA-based fringe enhancement is obvious. In In angular velocity measurements with the fountain-type APSI inertia sensor, the precision of the measurement is evaluated by calculating the variation of measured spatial frequency and converting back into rotation velocity following Equation (3). The evaluation gives a precision of 6.3 μrad/s without PCA-based enhancement and 3.3 μrad/s with enhancement from results of the same measurement.As for the measurement of very small angular velocity or timing asymmetry where the spatial frequency is too low to be precisely recovered from an image in the limited space within the detection chamber, differential measurement by adding an extra rotation angle or timing difference in opposite directions solves the problem, because the small frequency to be measured is transferred to larger frequencies while maintaining the mean value. The PCA-based processing technique is still appliable and works equally well in such differential measurements. However, because these measurements are not as reliable as those of relatively high frequencies in the same measurement scheme, these inaccurate results are ruled out in the evaluation of the enhancement.By implementing PCA-based image processing techniques, measurement of angular velocity on an APSI-type inertial sensor is enhanced. A comparison of measurement results with and without the PCA procedure, and the theoretical predictions according to the dependency of the spatial frequency of interference fringes on angular velocity proves the PCA-based technique capable of improving both the accuracy and precision of measurements. The technique is versatile in various applications of atomic interferometers where the detection is carried out via the imaging of fluorescence from stimulated atoms.


To improve the prediction accuracy of traffic flow under the influence of nearby time traffic flow disturbance, a dynamic spatiotemporal graph attention network traffic flow prediction model based on the attention mechanism was proposed. Considering the macroscopic periodic characteristics of traffic flow, the spatiotemporal features are extracted by constructing spatiotemporal blocks with an adjacent period, daily period, and weekly period respectively. The spatiotemporal block is mainly composed of a two-layer graph attention network and a gated recurrent unit to capture the hidden features of space and time. In space, based on considering adjacent road segments, the Pearson correlation coefficient is used to capture the hidden correlation characteristics between non-adjacent road segments according to a certain time step. In terms of time, due to the random disturbance of traffic flow at the micro level, the attention mechanism is introduced to use the adjacent time as the query matrix to weight the output characteristics of daily cycle and weekly cycle, and the three are connected in series to output the prediction results through the linear layer. Finally, the experimental results on the public data sets show that the proposed model is superior to the six baseline models. As an important basis for traffic planning, traffic management, and control, traffic flow prediction is one of the most critical problems in intelligent transportation system research. With the widespread deployment of intelligent data acquisition terminals such as Radar and GPS devices, a large amount of data reflecting the state of the road network has been accumulated, and massive traffic data provides a good foundation for traffic flow prediction. Therefore, how to improve prediction efficiency and accuracy by optimizing the prediction method has become a key issue.1. For this reason, the early effort to predict mostly predict based on time series prediction models, such as Xingwei et al.2, which compared ARIMA and LSTM for traffic flow prediction. Kumar et al.3 proposed a short-term traffic flow prediction method based on SARIMA to overcome the availability problem. Since the traffic flow is affected by many factors, the general parameter method cannot adapt to the complex random characteristics of traffic flow. Therefore, some machine learning methods have been applied to traffic flow prediction. For example, Castro-Neto et al.4 proposed an online regression support vector machine model (OL-SVR) for highways under typical and atypical conditions, and the research results show that the model has better performance under atypical traffic conditions. Wang et al.5 assume that in an expected interval, the traffic flow is related to the traffic flow in previous intervals, and propose a new Bayesian method for traffic flow prediction based on the grey relational analysis method of entropy.Traffic flow prediction is mainly to predict the traffic flow parameters of a certain region in a future period based on historical traffic data8, Recurrent Neural Networks (RNN)10, and Generative Adversarial Networks (GAN)13 have powerful feature processing capabilities, so they have good prediction effects in traffic prediction tasks. In addition, variants of recurrent neural networks such as Long Short-Term Memory (LSTM)14 and Gated Recurrent Unit (GRU)16 are also widely used due to their powerful time series data processing ability. To better extract data features and give full play to the advantages of each model, researchers enhance the performance of the model by stacking different networks. For example, Ma et al.17 proposed to use Convolutional Neural Network (CNN) to extract daytime and intra-day traffic flow patterns. Then, the extracted features were input into the Long Short-Term Memory (LSTM) unit to learn the intra-day time evolution process of traffic flow. This method captures the temporal correlation of traffic flow well, but ignores the spatial correlation of traffic flow. Fang et al.18 proposed a long short-term memory network attention mechanism considering the long-term dependence of traffic flow evolution. Experiments have proved the effectiveness of the model in capturing subtle fluctuations of traffic flow, but there are still shortcomings in capturing long-term dependence. Attention mechanism19 helps the network model to focus on key information and ignore small fluctuations. Jian-xi et al.20 used multi-scale convolution kernel to capture multi-factor nonlinear correlation and spatial correlation of road network nodes, extracted time features through gated recurrent unit, and proposed a multi-periodic component spatiotemporal neural network model, which considered the periodic characteristics of traffic flow. Wang et al.21 considered road traffic flow data and weather conditions, introduced an attention mechanism to enable the model to focus on learning more important data features, and proposed a short-term traffic flow prediction model based on the attention mechanism of 1DCNN-LSTM network. Experiments show that the introduction of multiple traffic environment parameters plays an important role in improving the performance of the model. Jia et al.22 proposed a grouping residual network model based on self-attention mechanism to predict urban traffic flow, and the experiment shows that the prediction effect of the model is good. Using CNN can extract spatial relationships in Euclidean space, however, there are certain limitations in feature extraction in non-Euclidean space. In recent years, graph neural networks have been widely used in spatial information extraction of road networks due to their powerful performance in capturing the structural features of graph networks23. Guo et al.24 proposed a new Attention-based Spatiotemporal graph Convolutional Network (ASTGCN) model to solve the traffic flow prediction problem based on the three time characteristics of traffic flow, namely recent, daily and weekly cycle dependencies. Experiments show that the model can well capture the spatiotemporal correlation characteristics of traffic flow, but it only considers the direct links between road segments and ignores the indirect links, that is, ignores the correlation of upstream road segments. Li et al.25 effectively learned the hidden spatiotemporal dependencies on the basis of the temporal graph and proposed a spatiotemporal fusion graph neural network (STFGNN) for traffic flow prediction. Wang et al.26 constructed an attention-based Spatiotemporal Graph attention network (ASTGAT) model by using an attention mechanism, dilated gated convolution, and graph attention network. The results proves that the model can effectively extract in-depth spatiotemporal information, and the prediction effect is significant excelled other algorithms.With the acquisition of high-fine-grained spatiotemporal data of road traffic flow becoming more and more convenient, traditional machine learning methods perform poorly in dealing with high-dimensional and complex spatiotemporal data. Deep learning has certain advantages in mining high-dimensional features of data. Many deep learning models such as Convolutional Neural Networks (CNN)The existing research has achieved abundant achievements, but there are still the following shortcomings: (1) The traffic flow prediction task is simply regarded as a time series prediction task, ignoring the spatial correlation characteristics, and cannot make good use of the traffic information of upstream and downstream traffic flows; (2)Simply defining the neighbor matrix based on the geographical location distance of nodes cannot describe the spatial correlation of non-adjacent sections, and some potential similar traffic flows are ignored; (3) Feature extraction of time series is mostly based on the data of the same location at different times, and the impact research on the current prediction period is insufficient, neglecting the feature extraction under the influence of unexpected traffic incidents; (4) GCN is suitable for processing static undirected graphs, while traffic flow is time-varying, and it is usually difficult to deal with a dynamic adjacency matrix.A traffic flow prediction model based on Dynamic Spatiotemporal Graph Attention Network (DSTGAT) is proposed. Experiments show that the prediction accuracy of the model is high.Considering the indirect links of non-adjacent sections, the Pearson correlation coefficient is used to extract the correlation features of the traffic sequence of non-adjacent nodes.DSTGAT is used to effectively learn the hidden spatiotemporal relationship of traffic flow.The attention mechanism is introduced to enhance the performance of the model to capture the impact of microscopic traffic incidents according to the traffic flow fluctuation characteristics in the adjacent period, and the prediction effect of the model is improved.The main contributions of this paper are as follows:The rest of this paper is organized as follows: “N represents the number of nodes. i and node j.Traffic flow prediction is the process of forecasting traffic conditions for a future period based on historical traffic information. We define a road network graph, denoted as a graph In the road network, it is not necessarily the adjacent road section that is associated with the target road section. At the same time step, different road sections show similar flow characteristics. Considering the linkage characteristics of traffic flow, this paper uses the Pearson correlation coefficient of the same time step between different sections to explore the spatial correlation of non-adjacent sections. Due to the excessive connection relationship and more calculation parameters, we define that when the Pearson correlation coefficient of two road segments is greater than the threshold, there is an implicit connection relationship between two road segments. In this paper, the threshold is set to 0.9 according to the data experiment, and the spatiotemporal adjacency matrix fusing the implicit connection relationship can be expressed as shown in Eq. .2\documef predicts the flow at time T in the future by using the direct and indirect association relationship The feature matrix n in Eq. .3\documeThe architecture of the DSTGAT model proposed in this paper is shown in Fig. 27. Graph Attention Network(GAT)28 is a spatial domain convolutional network, which uses a self-attention mechanism to learn neighbors' relative weights and aggregate neighbors' spatial features. The attention weights change with the change of data, adding dynamic spatial correlation to the network. The model structure is shown in Fig. i, the softmax function is used to normalize the attention weight, as shown in Eq.  in that both use a gating mechanism to control input and memory. Compared with LSTM, GRU uses fewer parameters, has a simpler network structure, and is more efficient. LSTM has three gates, namely the input door, the forgotten door, and the output door, while GRU has only two gates, namely the updated door and the reset door. The update door is used to control how much the hidden layer state of the previous moment has been updated to the current hidden layer state. The reset gate is used to control how much the hidden layer state of the previous moment is updated to the current candidate hidden layer state. The model structure diagram is shown in Fig. At present, the recurrent neural network is the most widely used in processing sequence data, but the traditional recurrent neural network has the defect of gradient explosion and gradient disappearance due to the influence of prediction length. Therefore, to solve the above problems, this paper adopts a gated recurrent unit to extract the time feature. The gated recurrent unit (GRU)i adjacent time series, daily periodic time series, and weekly periodic time series are input into GRU to extract time features. In order to reduce the influence of redundant information on the prediction results, the adaptability of the model to the neighboring time affected by traffic incidents is increased. Therefore, the attention mechanism30 is introduced to capture the importance of different periodic time series data by taking the nearby time traffic flow as the main reference. The model uses the nearby time as the query matrix and the cycle time as the key matrix. The model uses the adjacent time as the query matrix and the cycle time as the key matrix. The score function of the model is shown in Eq.  is used to prevent the model from overfitting, and L2Loss is used as the loss function of the model. Other baseline model parameters are shown in Table We implemented the DSTGAT model based on the pytorch framework. The prediction step mentclass2pt{minimm represents the number of nodes in the graph G;In this paper, Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage error (MAPE) are selected to evaluate the effectiveness of the model. The calculation process is as follows:The proposed model and the baseline model are used to predict the traffic of the next hour on the data set, and the performance pairs are shown in Table In order to verify the prediction performance of the proposed model at different time lengths, four models of the baseline model, GRU, STGCN, ASTGCN and the proposed model, are selected to predict the traffic flow in the next 15 min, 30 min, 45 min and 60 min, and the results are shown in Fig. A) of adjacent road segments on the original model, and considered adjacency matrix (Ap) of non-adjacent road segments at the same time, added attention mechanism (TA) in capturing temporal correlation features, and determined Pearson coefficient p = 0.9 for indirect correlation features. As can be seen from the table, each component of the model contributes to the model performance. Among them, the introduction of the attention mechanism reduces the mean absolute error of the model by 7.56% and the mean absolute percentage error by 8.56%, indicating that this component has a significant effect on improving the accuracy of the model. The choice of correlation coefficient shows that the model does not improve the prediction accuracy with higher correlation coefficient. Of course, the model will not improve the efficiency of the model because of the small correlation coefficient and the inclusion of more data node information.We verified the impact of the proposed model components on the prediction accuracy, and the results are shown in Table The upstream and downstream traffic flow has an important influence on the road section and has a certain correlation, but not all adjacent road sections are related to the traffic flow of the target road section, and affected by geographical location or other factors, non-adjacent road sections are not necessarily unrelated to the target road section. Therefore, this paper uses the Pearson correlation coefficient to evaluate the similarity of traffic flow series under a certain time granularity and constructs the adjacency matrix accordingly. Ablation experimental results show that discussing the indirect correlation of non-adjacent sections has a certain effect on improving the accuracy of the model.The traffic flow has periodic characteristics, that is, the macroscopic fluctuation of traffic flow is not large, but due to the influence of microcosmic traffic events, the short-term traffic flow is extremely vulnerable to being affected and fluctuated, so the features extracted by periodic historical data cannot adapt to the fluctuation of current traffic flow caused by traffic events. Therefore, this paper introduces the attention mechanism to assign weights to periodic data concerning the current neighboring time. Experiments show that micro fluctuations have an important impact on the prediction effect.The prediction accuracy of the model is affected by the prediction step size, the longer the prediction step size is, the lower the accuracy is. This paper uses the periodic characteristics of traffic flow modeling and combines the GRU model based on historical periodic data, which can better capture the long-term dependence characteristics of traffic flow. The experimental results show that the model has better benefits in the medium-long step size prediction.The experimental results show that according to the traffic flow data in the near time, the spatiotemporal similarity link is constructed, the daily cycle time and weekly cycle time traffic data are combined, the influence of traffic events in the near time on traffic flow is fully considered, and the evaluation effect of the model is enhanced.Aiming at the problem of traffic flow prediction, a dynamic spatiotemporal graph attention network traffic flow prediction model based on the attention mechanism was proposed. PeMSD4 was used for experimental verification and comparison analysis with multiple baseline models, and the following conclusions were obtained:37, holidays38, and regional POI features39, to enhance the capture ability of geospatial semantic information of the model. At the same time, new arriving data are processed in real-time, and a more effective prediction system is explored in the field of dynamic training40, to further optimize the design of the traffic flow prediction model and improve its generalization ability.Based on the existing research results, in the future, we plan to enrich and expand the traffic flow prediction framework by integrating multi-source external data, such as weather