Gastric cancer is one of the leading causes of death worldwide. Screening for gastric cancer greatly relies on endoscopy and pathology biopsy, which are invasive and pose financial burdens. Thus, the prevention of the disease by modifying lifestyle-related behaviors and dietary habits or even the prevention of risk factor formation is of great importance. This study aimed to construct an inexpensive, non-invasive, fast, and high-precision diagnostic model using six machine learning (ML) algorithms to classify patients at high or low risk of developing gastric cancer by analyzing individual lifestyle factors.This retrospective study used the data of 2029 individuals from the gastric cancer database of Ayatollah Taleghani Hospital in Abadan City, Iran. The data were randomly separated into training and test sets (ratio 0.7:0.3). Six  ML methods, including multilayer perceptron (MLP), support vector machine (SVM) (linear kernel), SVM (RBF kernel), k-nearest neighbors (KNN) , random forest (RF), and eXtreme Gradient Boosting (XGBoost), were trained to construct prognostic models before and after performing the relief feature selection method. Finally, to evaluate the models’ performance, the metrics derived from the confusion matrix were calculated via a test split and cross-validation.This study found 11 important influence factors for the risk of gastric cancer, such as Helicobacter pylori infection, high salt intake, and chronic atrophic gastritis, among other factors. Comparisons indicated that the XGBoost had the best performance for the risk prediction of gastric cancer.The results suggest that based on simple baseline patient data, the ML techniques have the potential to start the prescreening of gastric cancer and identify high-risk individuals who should proceed with invasive examinations. Our model could also considerably lessen the number of cases that need endoscopic surveillance. Future studies are required to validate the efficacy of the models in a larger and multicenter population. Gastric cancer  is the fourth most prevalent neoplastic disease and the second leading cause of cancer-related deaths worldwide . GastricEndoscopy along with pathology biopsy is the current gold standard in the screening and detection of gastric cancer . HoweverThus far, no non-invasive measures have been taken to diagnose gastric cancer with high sensitivity and specificity. Early diagnosis of gastric cancer and the subsequent early treatment are crucial to improve survival and reduce mortality from this cancer. Therefore, due to the complexity and interlinking factors that are causally related to gastric cancer, it is increasingly urgent to adopt non-invasive and time-saving diagnostic methods with high accuracy to minimize imprecision and uncertainty in the diagnosis of gastric cancer.The adoption of artificial intelligence (AI)-based solutions, such as machine learning (ML), can overcome the restrictions of invasive diagnostic procedures in the screening and diagnosis of gastric cancer due to their computational capacity. ML techniques are well-known tools for developing predictive and data analysis models and can implicitly extract useful information from raw datasets . ML can Many studies have used ML techniques to predict gastric cancer up until now. Liu et al. used ML to predict gastric cancer with an accuracy of 77% . Cai et The structure of the manuscript is as follows: First, the dataset is presented. The ML techniques used in this paper are then described in detail. After that, the results of comparing ML techniques are shown. In the next stage, the most accurate model for predicting gastric cancer based on the results of performance evaluation metrics is reported.This is a retrospective, single-center study that was conducted in 2022. A dataset was collected from the Ayatollah Taleghani database affiliated with Abadan University of Medical Sciences, Abadan City, Iran. Six ML-based models were developed for the prediction of gastric cancer using lifestyle-related factors. This study was conducted based on the cross-industry standard process for data mining (CRISP-DM). The prediction models were developed using Python programming language in five main CRISP stages including data understanding, pre-processing, feature selection, model training, and evaluation, as shown in the block diagram below Fig. .Fig. 1BlThe dataset used in this study was obtained from the gastric cases referred to the internal clinic of Ayatollah Taleghani Hospital in Abadan, Iran, during 2015–2021. The patients’ information was reviewed and extracted by a health information management expert. The patients who were referred to the clinic for the screening, diagnosis, and treatment of gastric cancer were included in this study. A total of 2029 individuals  participated in the study. The analyzed dataset contained descriptive information about the respondents (28 features) and the outcome of the gastric cancer risk (one feature), which can be viewed as the dependent variable (Table synthetic minority oversampling technique (SMOTE) was applied to the resampling process. The SMOTE method is the most common and effective oversampling method, which is applied in various fields to balance the datasets [Data preprocessing is an essential step in the CRISP-DM method, and it has a significant impact on the performance of data mining techniques. The objectives of data preprocessing are to cleanse the outlier, remove the noisy data, impute missing values, and convert the data into a suitable format for more reliable and accurate data analysis. In the first phase of preprocessing steps, we employed the interquartile range rule to detect outliers and normalize the dataset by using the min–max method. To impute missing values, mean and regression-based methods were applied. We also deleted the rows with more than 70% missing values. The Z-score standardization method was used as a data distribution-based data scaling, and for data range-based scaling, the min–max method was employed. In the preprocessing phase, 240 records of the dataset were deleted, and after removing these records, the number of the cases of the dataset was reduced to 2029 records. Since group distribution in the dataset used for this study is imbalanced, one of the groups contains 1780 samples  while the other has 429 samples (patients). Therefore, we created a new dataset by approximating the group with fewer samples (patient group = 429) to the group with a larger number of samples , such that the samples of the group with fewer cases in the dataset are randomly reproduced. In this study, the datasets , 35.One of the fundamental issues with many data mining tasks is to determine and specify relationships between attributes in the dataset and outcome. Feature selection is one of the main phases of a successful data mining process, especially in problems with a large number of dimensions or variables in the dataset. Feature selection is defined as the process of determining relevant variables and removing irrelevant ones . In the In order to develop an early prediction model for gastric cancer risk, a total of six ML algorithms were used: MLP, SVM (linear kernel), SVM (RBF kernel), KNN , RF, and XGBoost. To implement these models, we experimentally tuned the hyperparameters on the training split of the dataset based on the cross-validation (CV) method. The performance of the ML algorithms was evaluated using the holdout technique, a method for out-of-sample assessment where the dataset was split into two parts (70% training and 30% test). The ML models were then trained on the first split of the dataset and tested on the other part. In addition, the K-fold CV method (K = 10) was applied to evaluate the performance of the best algorithms to overcome a feasible biased error estimate. Five performance evaluation metrics were selected and reported for each ML technique to compare the performance of classifiers, which is common in medical prediction studies. The performance evaluation metrics of the classifiers are listed below, along with their definitions:This study was approved by the ethics committee board of Abadan University of Medical Sciences (Ethics code: IR.ABADANUMS.REC.1401.013). To protect the privacy and confidentiality of patients, we concealed the unique identification information of all patients in the process of data collection and presentation. The present study adhered to the principles expressed in the Declaration of Helsinki.After applying the exclusion criteria and conducting a quantitative analysis of patients’ records, 2029 patients were found to be eligible. Of the 2029 participants in the study, 1094 (54%) were male and 1015 (46%) were female, and the age of the participants was between 18 and 94. In total, 1780 (88%) of the study subjects were healthy controls, and 429 (22%) were patients. The descriptive statistics for the 2029 samples in this dataset are shown in Table A total of 11 features were selected due to their positive correlation with gastric cancer by performing the Relief feature selection algorithm. These features are Helicobacter pylori infection, high salt intake, chronic atrophic gastritis, consumption of fruits, stomach or duodenal ulcers, weight loss, consumption of high-fat foods, educational level, smoking, stress status, and weight. The key features selected by the Relief feature selection algorithm and their scores are presented in Table Based on the results of the Relief feature selection algorithm Table , HelicobIn order to improve the performance of ML techniques, many methods can be used to tune hyperparameters. In this study, the randomized search CV method was employed for the tuning of parameters and the optimization of ML techniques. Table In the present study, full features and features selected by the Relief feature selection algorithm were tested on six classification algorithms using the 10-fold CV methods. In the tenfold CV method, 90% of the dataset was used for training the algorithms and only 10% was tested. The mean metrics of tenfold methods were measured. Additionally, different metrics values were passed through classification algorithms. At first, we trained and tested the data mining algorithms with all the dataset features. Then we fed 11 features into the selected classifiers. To better represent the performance of classifiers, some figures were created for classification accuracy, sensitivity, specificity, AUC, and the H-score metric. The performance of the ML algorithms on all features and selected features using the tenfold CV method is displayed in Table According to the results presented in Table According to Fig. It is important to provide accurate and rapid screening for gastric cancer since this malignancy is very treatable when diagnosed in early phases. Therefore, implementing procedures for the screening and diagnosis of gastric cancer is highly beneficial. In this regard, a timely and reliable screening method enables rapid detection of the disease, and the subsequent timely interventions can help boost the likelihood of patient survival . In this study, we developed non-invasive and cost-effective predictive models using six ML algorithms for gastric cancer risk assessment to distinguish high-risk patients with gastric cancer from the general population. Due to the fact that gastric cancer has multiple features with many potentially important confounders, it is a great challenge for clinicians to consider and analyze all the engaging features and decide on the patient's condition. It also raises the likelihood of a physician error during the decision-making process of disease diagnosis . Thus, iSeveral studies have been conducted with the aim of improving the early screening accuracy of gastric cancer through the use of ML. The predictive models in previous studies were developed based on diagnostic, laboratory, pathology, and imaging data and were not related to lifestyle data and individual habits and behaviors. Therefore, the advantage that distinguishes our study was that we obtained relatively significant results by applying ML methods based on data on the lifestyle features and behavior of individuals. Moreover, our study used feature selection to select the most significant lifestyle-based variables in order to maximize the capability of the models when compared to the analysis of all variables in the dataset. Feature selection enhances the accuracy, specificity, and sensitivity of the classifiers and decreases the running time of the predictive system. In this study, we used the ML algorithms due to the fact that these methods resulted in better predictions than the conventional statistical techniques when dealing with a large number of features with complicated relationships , 40. AltThe main advantage of our study was that it estimated the risk of gastric cancer based on lifestyle-related factors. Some researchers have incessantly focused on medical equipment and detection reagents to improve the screening of gastric cancer, and the results of their studies were applied to clinical gastroscopy and biopsy , 44. A fNevertheless, this study also had some limitations. First, the participants in the study included patients from a single care center, which limits the generalizability of the results to larger populations. Second, there was some subjective bias in selecting variables and examining lifestyle behavior that may affect the predictive results. Another limitation of this study was a retrospective analysis using registered data, which reduces the external validity of the results. Thus, future testing in a larger population is recommended.This study utilized the routine available non-invasive features to implement six models for screening the risk of gastric cancer. The XGBoost model demonstrated better performance than the other ML models and can be applied to assist clinicians in the screening of gastric cancer risk in accordance with the Iranian health referral system and hierarchical leveling of healthcare services, which will improve the early screening of gastric cancer on a large scale. The ML models may identify high-risk patients with gastric cancer early, which draws the attention of clinicians and patients, and appropriate and timely interventions will be implemented to improve the patients’ survival chance and quality of life. This study can also aid clinical researchers in choosing and implementing the optimal prediction models and evaluating the main influencing features.


Piezo-actuated flexure-based systems are widely used in applications with high accuracy requirements, but the intrinsic hysteresis has a detrimental effect on the performance which should be compensated. Conventional models were presented to model this undesired effect using additional dead-zone operators. This paper presents a new approach using two sets of operators with a distributed compensator to model and compensate for the asymmetric system hysteresis based on inversion calculation with a simplified digitized representation. The experimental results validate the effectiveness of the proposed model in modeling and compensating the asymmetric system hysteresis. Piezoelectric actuators are ideal for micromanipulation due to their fast response with high repeatability, but they often have a limited stroke. The flexure mechanism are often used together with the piezoelectric actuators to amplify their stroke with no backlash. The piezo-actuated flexure-based systems are used in precise fabrication ,2,3, autHysteresis is a very complex phenomenon with different possible causes. Hysteresis may arise from material properties ,14, mechVarious models were proposed to describe the hysteresis. The phenomenology-based models are classified into roughly three groups : differeThe construction of the operator-based models are often easier, among the various operator-based models the Prandtl–Ishlinskii (PI)  model isIn this paper, a dual-operators-based modified Prandtl–Ishlinskii (DPI) model is proposed to describe and compensate for the asymmetric system hysteresis, which is an extension of our previous work , where tThe rest of this paper is organized as follows. This section describes a digitized representation and the proposed DPI model. The inverse DPI model and the link between the classical and the digitized representation are also described.N operators is represented by a binary number B with N digits, as shown in following equation:B are represented with Here, we adopt the similar digitized representation of the classical Prandtl–Ishlinskii model in . The staH as:Each fundamental operator, The change of operator The binary state of a fundamental operator When the binary state of a fundamental operator A simple example with 3 operators can be shown in The classical PI model requires the hysteresis behavior to be symmetric, this limitation is mainly due to the one-paired property of the play operator for modeling the expansion curve and the contraction curve. In this section, the DPI model for modeling and compensating the asymmetric system hysteresis is presented. The proposed DPI model applies two sets of operators for modeling the expansion curve and the contraction curve respectively with a similar digitized representation.N fundamental operators.We used the same representation as  to repreN elementary operators are expressed in the following equations:Compared to the previous one, each digit bi in  has two Similarly, the change of the system input and output will change according to its paired properties using the following equations:The sum of the expansion operators may not equal to the sum of the contraction operators, and this may lead to drifting of the proposed model in some cases. With a repetitive input, the drifting will accumulate and the output of the model may reach infinity, which may lead to the failure of the proposed model. For example, when The expansion and contraction properties may not equal:a, i.e., We denote The contraction paired properties are then updated at the turning point:Similarly, a compensator The expansion paired properties are then updated at the turning point:At turning points, the value of operators are updated with an addition of a distributed compensator to avoid drifting. An equal weight distribution is chosen so that the value of each operator is not modified too much. When the proposed method is applied to other systems with hysteresis, different distribution strategies can be chosen subject to the observations of the hysteresis behavior. An assumption is also made that Similar to the previous work in , the invThe process of calculation in the system identification is simplified with the proposed method. The order of computation complexity can be reduced greatly to The inverse model quations :(24)ΔXi′The inverse model parameters lculated  by:(26)rFrom , we can The inverse model parameters lculated  by:(30)wAlternatively, we can calculate the The equations above show that the inverse model parameters are the same using the digitized and the classical representation. Moreover, the calculation complexity can be reduced with the proposed digitized representation.In this section, the same 16-bit D/A card, actuator, amplifier, sensor, 16-bit A/D card used in  is choseIn this section, the system hysteresis behavior is modeled using the PI, modified PI model with dead zone operators (MPI), and the DPI model, respectively. The inverse model is then identified to compensate for the system hysteresis under fixed amplitude and changing amplitude using the PI, MPI, and DPI model, respectively. A brief description of the experimental setup is first given.The asymmetric system hysteresis behavior at To test the performance of the feedforward controller deploying the inverse model, a 1 Hz sinusoidal signal with fixed amplitude To further test the performance of the feedforward controller with different magnitudes deploying the inverse model, a 1 Hz sinusoidal signal with gradually changing amplitudes ed using . The comThe compensation results at fixed and varying amplitudes using the PI, MPI, and DPI models are summarized in The DPI model also performs the best of the three for compensation of the asymmetric system hysteresis at a changing amplitude, using the DPI model the RMSE is 1.75 The classical PI model has considerable error for modeling and compensation of asymmetric hysteresis. The dead zone operators are proposed to extend the classical PI model, but the MPI model still has the potential to be improved while modeling the asymmetric system hysteresis. The DPI model is thus proposed to capture the details of the asymmetric system hysteresis by modeling the expansion and the contraction curve respectively. Validation experiments show that the DPI model performs better than the classical PI model and the MPI model, and this proves that the proposed DPI model is effective in modeling and compensating for the asymmetric system hysteresis. The proposed DPI model can reduce the RMSE by around A similar digitized representation of the MPI model as described in  is also While implementing the DPI model, the error in percentage at changing amplitudes is slightly bigger than the fixed amplitude, this may be due to the model being sensitive to the rate-dependent hysteresis behavior. Another possible reason is that the distribution used in this paper is a weighted average distribution and a better-weighted strategy may be applied. A training model using the neural networks may also be applied in the future.The aim of this paper is to propose a generalized model to describe the asymmetric system hysteresis behavior. The DPI model can be further modified for different scenarios, and the backlash can also be included in the model for some applications. The weighted distribution of the observer for updating the fundamental operators may also be further modified to fit different hysteresis behavior.A dual-operators based modified Prandtl–Ishlinskii hysteresis model is presented to model and compensate for the asymmetric hysteresis behavior of the piezo-actuated flexure-based system. With a similar digitized representation, the inverse calculation can be greatly simplified. Compared with the MPI model and the PI model, our model yields significantly better experimental results.


The submicroscopic level focuses on particles. The representative level includes pictorial and symbolic representations to visualize substance in its nature. Students often have problems separating these levels and conceptually transfer each of the three levels to the other. Therefore, teachers need to use chemical terminology correctly when teaching the substance-particle concept. Augmented reality (AR) connects the real and virtual worlds. The observer physically moves in a real environment that integrates virtual elements. This can be effective for learning when chemical processes that are invisible are made visible. The simultaneous presentation should avoid split attention and offers new possibilities to interactively deal with multiple external representations ((M)ER). The question arises whether AR has a positive effect on the use of technical language. With an AR app on the tablet and on the hololens, chemical processes of a real experiment are represented by AR visualizations. In this study, the chemistry terminology of chemistry teachers (N = 30) was captured using a pre-post survey. Each test includes five tasks elaborated by thinking aloud. Therefore, the AR app was piloted. The thinking-aloud protocols to acquire the use of the chemical terminology are evaluated in MAXQDA.Chemistry as a whole is divided into three levels. The  According to This study focuses on the learning effectiveness of an AR learning environment (on tablet or hololens) to promote the use of chemical terminology, i.e., dealing with (M)ER. Therefore, a learning environment was designed that is aimed at teachers to expand their professional knowledge. The target is to be able to use innovative digital technologies in the subject lessons with students in a perspective and didactically reflected way. The following questions will be investigated in the research project:(1) Can the AR learning environment be used to promote reflective use of technical language at the substance and particle level from a teaching perspective among chemistry teachers?It is hypothesized that the use of AR learning environment promotes the integration of the representation level when observing a real experiment and improves in this context the substance-particle concept understanding.(2) Can the interactive use of augmented representational forms in the learning environment, with regard to the use of tablet or hololens, describe different elaboration profiles?It is hypothesized that the use of the AR learning environment on a tablet has a positive effect on the use of chemical terminology. The simultaneous linking of AR representations with the content of the real experimental environment is expected to initiate cognitive processing. In comparison, the use of the simulation should disrupt cognitive processing and improve chemical terminology to a much lesser extent. By avoiding split attention, AR is expected to support the construction of mental models and thus largely shape elaboration behavior.or hololens.Besides this, (M)ER can be controlled in a self-regulated way. Different elaboration profiles are expected when interacting with augmented (M)ER on the tablet N = 30). Experimental group 1 consists of 10 subjects working with AR learning environment on the tablet. Furthermore, experimental group 2 works with the same AR learning environment on a hololens. The control group consists of 10 other subjects working with a content equivalent simulation-based learning environment on the tablet.The subjects are teachers from German secondary schools who teach chemistry ER. The tasks refer to the donor-acceptor principle. They always focus on the construction, interpretation, and translation of (M)ER. In order to analyze the effect of AR on technical language and the related construction of mental models about redox reactions, the method of thinking aloud is used. For this purpose, subjects’ utterances are recorded during the processing of the tasks and the AR learning environment.In order to investigate technical language via the elaboration behavior of virtual representations in the AR environment among chemistry teachers , all subjects in the study participate in a pre-post survey: Before starting the learning environments, subjects are informed about what they need to pay attention to when completing the tests and thinking aloud. This is followed by the completion of the pre-test. Teachers are then briefly instructed on how to use the digital device (AR or simulation-based technology) on the tablet/hololens. Afterward, the experimental group 1 resp. 2 works on the AR learning environment on the tablet resp. hololens and the control group on the simulation-based learning environment. The simulation-based learning environment is designed to be similar in content to the AR environment but has—compared to the AR app—on the tablet a detrimental split attention effect from a cognitive psychology perspective . During The thinking-aloud protocols of processing the test tasks will be analyzed with qualitative content analysis according to If AR is to be applied in the classroom, the teaching and learning offer must be accepted by the teachers . AcceptaN = 18). Natural scientists, (prospective) chemistry teachers, science educators, and software developers were interviewed, all of whom use digital media regularly. Half of the subjects consisted of teachers.In March 2021, the review of the AR learning environment (acceptance/usability) took place  had not been completed. Help buttons were missing and particle modeling was undeveloped.All subjects processed the AR learning environment using a tablet. During the interaction with the AR learning environment, the participants had to explain the processes on the particle level with different representations. Subsequently, the questionnaire on the acceptance and usability of the AR learning environment was completed by the subjects.During the piloting of the AR learning environment, scales according to A reliability analysis of the AR learning environment provided predominantly good to excellent internal consistency values:I would use the AR learning environment in my own chemistry classes.”) with a total of 7 items has a Cronbach’s alpha of 0.73. The eight Usability scales  with 4–17 items per scale also show a Cronbach’s alpha between 0.668 and 0.904. Furthermore, all scales on the characteristics of the learning environment have mean values above the mean scale level  to be used in the main study.The original contributions presented in this study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.The studies involving human participants were reviewed and approved by the Ethics Committee of the Technical University of Munich. The patients/participants provided their written informed consent to participate in this study.MR was a Ph. D. student under the supervision of CN at TUM. In the context of the doctoral project, the presented study was carried out. Both authors contributed to the article and approved the submitted version.


This study aims at the problem of reconstruction the unknown links in debt networks among enterprises. We use the topological matrix of the enterprise debt network as the object of reconstruction and use the time series data of accounts receivable and payable as input and output information in the debt network to establish an underdetermined linear system about the topological matrix of the debt network. We establish an iteratively reweighted least-squares algorithm, which is an algorithm in compressed sensing. This algorithm uses reweighted  Against the background of increasingly detailed enterprise operations, the connection between enterprises is closer, and the impact caused by emergencies is more likely to spread among enterprises, resulting in systemic risks in the market. It can be seen that financial risks have the characteristics of potential, systematicness and complexity. Once they break out, they are quickly transmitted among different markets and difficult to control, making the financial system the most vulnerable link in the modern economy2.Risk contagion refers to the phenomenon in which an emergency affects the business of related enterprises and then spreads to other enterprises or markets, and it may result in a deepening of risk hazardsTo analyze the contagion process of default risk in enterprise debt networks, we must first have a clear understanding of the enterprise debt network. A debt network with full links and information is convenient for analyzing the contagion process of default risk. However, owing to the lack of information about debt relationships among enterprises, the topological structure of the debt network of enterprises is incomplete and some links may be missing in the network. This study reconstructs the topological structure of the debt network of enterprises and discover the unknown link of the debt network using a mathematical method based on compressed sensing.Our main contribution in this study is that we provide a link reconstruction method based on compressed sensing for complex debt networks among companies. This method uses accounts receivable and accounts payable to establish underdetermined linear systems and solves them with an iteratively reweighted least-squares algorithm. The results showed excellent performance.s-sparse vector s nonzero components, and the other components are zero. s-sparse vectors. Given matrix s, sth largest element of the set Notations: An 4 to construct a complex network of stock financial markets and characterized its properties with the characteristic parameters of the complex network. The threshold method is a relatively simple method for constructing complex networks, and it is also commonly used in many empirical analyses. However, the threshold method relies heavily on the experience of researchers, and subjective factors significantly influence its performance. Other scholars6 used the minimum spanning tree method to construct a complex network of stock associations. This type of complex network can analyze the association between different stocks much better and reflect the asset-liability relationship of enterprises to some extent, but ignores known information such as accounts receivable and accounts payable. The threshold and minimum spanning tree method construct the enterprise correlation network through the correlation coefficients of logarithmic return rate of stock prices, and the constructed network can analyze the enterprise risk contagion. However, the enterprise correlation network cannot directly reflect the debt relationship between enterprises. In contrast to correlations based on the stock return rate, some studies build complex networks based on the sparseness of complex network topologies. The essence of complex network reconstruction is to predict the unknown links in complex networks. Wang et al.7 proposed a link prediction model that considers the power law distribution of the node degrees. The principle of this model to build a network was to make use of the sparseness of the network topology and to predict network links through node clustering coefficients. Mishchenko et al.8 applied a Bayesian framework to reveal the structure of a neural network, constructed the least absolute shrinkage and selection operator (LASSO) problem according to the sparseness of the neural network, and solved it using compressed sensing according to the relationship between the LASSO problem and the compressed sensing problem. However, the application of the Bayesian framework requires some prior information; otherwise, this method cannot be applied. Some scholars12 revealed the network topology by using the sparsity and power law distribution of network links, proposed to reconstruct the unknown links of the network using compressed sensing, and constructed the network topology identification problem as the sparse solution problem of linear systems. Compressive sensing methods are often used to reconstruct complex network topologies with high accuracy, but current research mainly focuses on the link prediction of physical networks, and the effect of link prediction of complex networks of enterprise debt is unknown.At present, research on the construction of financial market networks is mostly based on the correlation of stock returns. Some scholars used the threshold methodIn addition to signal and image processing, compressed sensing can also be applied to complex network reconstruction of the financial market. By fully considering accounts receivable and accounts payable, the compressed sensing method objectively and accurately reconstructs the debt network of enterprises.13. Si et al. used compressed sensing to construct a complex financial network and improved the reconstruction accuracy15. The debt relationships among enterprises can be expressed through a network. Assuming that there are n enterprises, the topology structure of the debt network can be expressed as a matrix 17. When the number n of enterprises is sufficiently large, the network structure will show complex network properties, such as self-organization, self-similarity and small world. As a complex network, this network has a cluster effect; that is, only some nodes have a high degree, whereas most nodes have a small degree. In the network topology matrix, the cluster effect is characteristic of the sparsity of its column vector. Therefore, compressed sensing can be used to reconstruct the network topology matrix, and we can accurately reconstruct the complete information of the debt complex network using only underdetermined information18. According to the reconstructed debt network, we can accurately analyze the contagion process theory of enterprises’ debt defaults.To analyze the risk contagion and default compensation of companies, it is necessary to accurately construct a debt network among these enterprises. Because of the incompleteness of the information released by these enterprises, it is theoretically difficult to construct a high-precision debt network among these enterprises. In a corporate debt network, an enterprise usually only has debt relationships with a few other enterprises, and the column vectors of the link matrix are sparse, which provides possibility for the debt network reconstruction by compressed sensingn enterprises in the network at time t. In a linear network system, the derivative Suppose that p experiments at time To reconstruct the network topology, we take Let matrices kth column of kth column of The sparsity of the column vector is expressed in the topology matrix of the network owing to the clustering effect of the network. In other words, the column vector of 19.This is an underdetermined linear system, and compressed sensing has a positive effect on solving the sparse solution of this type of underdetermined linear systemCompressed sensing is a method for recovering sparse signals from an underdetermined linear system. A precondition is that the signal is sparse. As the column vector r system . Assuminr system , the pro21, which is NP-hard: when the dimension of the column vector Problem  is a commization . The solr system , the con23,Donoho24, Romberg25, Tao22, Gribonval26 and others successively proposed the null space property (NSP)24 and the restricted isometry property (RIP)22. Gribonval26 proved that any s-sparse signal can be accurately recovered by s order. Candès and Tao22 proved that if the measurement matrix 23 proved that if the measurement matrix 25 obtained that if the measurement matrix The natural question to ask is whether the solution Reconstruction of enterprise debt network is an  problem , and we mization . Restricmization  is the smization . Meanwhis if there exists a constant s.Matrix The definition of the restricted isometry property of matrix r is observed by the measured vector The low-rank approximation of the matrix is used to find the rank-lowest matrix from a linear measurement, which is also called low-rank matrix recovery. The problem of matrix low-rank approximation can be described as follow. A matrix Similar to the  problem  is NP-ha problem  to the kSimilar to compressed sensing, the low-rank matrix recovery problem has a restricted isometry property. Its function is to determine the relationship between the minimum solutions of the kernel norm minimization and rank minimization.r, if there exists r, the inequalityFor a linear mapping Using low-rank matrix recovery to reconstruct the network topology matrix is also a method of network link prediction, but this area requires further research.The restricted isometric property shows that the  problem  for the mization . To solv problem , we provThe algorithm is as follows.29, and the results showed that the algorithm has good convergence and robustness. Moreover, its convergence rate is high. Iteratively reweighted least-squares algorithm can realize the fast and high-precision reconstruction of enterprise debt network. When this algorithm is applied to solve the We studied the convergence and robustness of the algorithm problem , it is ot, t, and We considered a debt network with 50 enterprise nodes,and conducted 30 simulation experiments,i.e. mentclass2pt{minimTo analyze the characteristics of the network before and after reconstruction, we imported these two debt networks into Gephi software for data analysis and obtained the network topology characteristics, including the average degree (AD), average weighting degree (AWD), graph density (GD), average clustering coefficient of each node (ACC), and average path length (APL), as shown in Table To reconstruct the enterprise debt network to determine its hidden links, we establish Supplementary Information.


Introduction: Chest deformation has been proposed as the best predictor of thoracic injury risk in frontal impacts. Finite Element Human Body Models (FE-HBM) can enhance the results obtained in physical crash tests with Anthropometric Test Devices (ATD) since they can be exposed to omnidirectional impacts and their geometry can be modified to reflect specific population groups. This study aims to assess the sensitivity of two thoracic injury risk criteria (PC Score and Cmax) to several personalization techniques of FE-HBMs.Methods: Three 30° nearside oblique sled tests were reproduced using the SAFER HBM v8 and three personalization techniques were applied to this model to evaluate the influence on the risk of thoracic injuries. First, the overall mass of the model was adjusted to represent the weight of the subjects. Second, the model anthropometry and mass were modified to represent the characteristics of the post-mortem human subjects (PMHS). Finally, the spine alignment of the model was adapted to the PMHS posture at t = 0 ms, to conform to the angles between spinal landmarks measured in the PMHS. The following two metrics were used to predict three or more fractured ribs (AIS3+) of the SAFER HBM v8 and the effect of personalization techniques: the maximum posterior displacement of any studied chest point (Cmax), and the sum of the upper and lower deformation of selected rib points (PC score).Results: Despite having led to statistically significant differences in the probability of AIS3+ calculations, the mass-scaled and morphed version provided, in general, lower values for injury risk than the baseline model and the postured version being the latter, which exhibited the better approximation to the PMHS tests in terms of probability of injury. Additionally, this study found that the prediction of AIS3+ chest injuries based on PC Score resulted in higher probability values than the prediction based on Cmax for the loading conditions and personalization techniques analyzed within this study.Discussion: This study could demonstrate that the personalization techniques do not lead to linear trends when they are used in combination. Furthermore, the results included here suggest that these two criteria will result in significantly different predictions if the chest is loaded more asymmetrically. Anthropometric Test Devices (ATD), also known as crash test dummies, are commonly used in regulatory procedures and consumer testing programs in the assessment of the potential injury risks of car occupants . This asStudies focusing on oblique impacts have suggested that oblique loading can cause larger chest deformations than frontal loading . HoweverThus, in parallel to strain-based thoracic injury criteria, several studies have used HBM chest deformations as a potential predictor of thoracic injuries, similar to what is done with ATD. For instance, One of the advantages of FE-HBM is the possibility of modifying the geometry of the model to represent specific groups of people within the population. This possibility has resulted in the development of parametric models capable of reproducing subject-specific characteristics . AnotherThus, the assessment of the effect of the personalization techniques on the injury risk prediction of FE-HBM requires additional research. This study aims to assess the sensitivity of two multi-point deflection metrics commonly used with FE-HBM to estimate the risk of thoracic injuries  to several personalization techniques in nearside oblique impacts.In order to assess the sensitivity of the PC Score and Cmax metrics under oblique loading, three 30° nearside oblique PMHS sled tests  Baseline model: the SAFER HBM v8 model remains unmodified representing a 50th percentile male occupant.(2) Baseline postured model: The spine alignment of the baseline model was adjusted to the PMHS initial position.(3) Scaled mass model: The density of the outer flesh parts was adjusted until the full model mass reached the overall weight of the subject.(4) Scaled mass postured model: In this version, the spine of the scaled mass model was adapted to the initial posture of the PMHS.(5) Morphed model: The geometry and the mass of the baseline SAFER HBM v8 model were modified to represent the PMHS anthropometry using the PIPER software.(6) Morphed postured model: The mass, the geometry, and the posture were modified to represent the characteristics of the subject.The targeted mass, anthropometry, and spine alignment have been calculated considering the subjects tested with each RSv. The anthropometry of PMHS A and PMHS B was averaged to develop a single personalized HBM. This was decided due to the large similarities in anthropometry see  and initth and 8th ribs bilaterally . The deflection was calculated as the change in length of a vector joining the location of a marker cluster that was used to define a local coordinate system (LCS) rigidly attached to the rib points mentioned above and the origin of an LCS attached to the eighth thoracic vertebra (T8)  resulting in 18 comparisons . Two main predictors based on multi-point chest deformation measurements were considered: Cmax and PC Score. Cmax computes the maximum posterior resultant displacement of any studied rib point of the chest, independently of the displacement of the rest of the rib points. For instance, as shown in In order to consistently compare the results obtained from both injury criteria, the probability of sustaining an AIS3+ injury to the chest  was calcFirst, the equivalence of using Cmax or PC Score for the p (AIS3+) calculation was assessed. Due to the reduced number of samples, a non-normal distribution has been assumed. Thus, a non-parametric Wilcoxon signed-rank test for paired samples was carried out for the analysis. The results of p (AIS3+) calculated based on Cmax for all the model versions were compared with those calculated based on PC Score, establishing equal medians as a null hypothesis (H). Second, the influence of the three personalization techniques  on the p (AIS3+) was analyzed by comparing the results of the different model versions. The simulation results were separated into two groups for each personalization technique: Group one (reference group), in which the model did not include the monitored personalization technique, and group two, with the models that had been modified including that technique .Then, the results of p (AIS3+) were compared using a non-parametric Mann-Whitney p-value of <0.05.In both analyses, the significance level of the statistical tests was established at a The maximum deflection results from the PMHS tests were extracted from The results of p (AIS3+) computed using Cmax and PC Score obtained for each HBM version are shown in According to the data observed in According to the data, the p (AIS3+) calculated based on the PC Score resulted in higher probability values than those based on the Cmax metric, as can be seen in p-value of 0.0007, and even when each RS was analyzed separately, obtaining a p-value of 0.005 for RSv1 and a p-value of 0.03 for Rsv2. However, these differences were found to be higher for the RSv1 than for the RSv2.This hypothesis was confirmed by the Wilcoxon test, obtaining a p-values for the Mann-Whitney U tests are shown in In order to evaluate the effect of each technique, the results shown in This analysis revealed that the mass scaling and morphing of the HBM significantly influenced the prediction of AIS3+ while the posturing did not show statistically significant differences in the results, regardless of the injury metric used.In the present work, the ATD deformation-based criteria, PC Score and Cmax, have been applied to the SAFER HBM v8 under nearside oblique impacts to evaluate the influence of several proposed personalization techniques.p < 0.05) than those based on the Cmax metric. These results suggest that these two formulations can result in a different risk estimation in impact configurations that cause a more asymmetric deformation of the chest, such as in the case of the oblique impacts considered here. The formulation of the PC Score includes weighting coefficients assigned to the terms in the formula . The UPdif and LOWdif components resulted in the highest weighting coefficients in the formulation. Thus, the more influential parameters on the PC Score calculation are strongly related to the differential deformations as a relevant injury mechanism. Oblique loading has been shown to produce larger chest deformations than frontal impacts , this last version being close to the reference PMHS sled tests that sustained 15, 5, and 10 fractured ribs respectively. Posturing did not show any statistically significant influence on injury prediction and showed a lower p (AIS3+) when it was combined with the other personalization techniques (versions 4 and 6). This could demonstrate that the separate personalization techniques do not lead to linear trends when they are used in combination. Additionally, those models in which the posturing was performed  successfully predicted that the lower right chest landmark suffered the maximum deformation, while the non-postured model predicted that this deformation would happen at the upper left landmark see .It has to be noted that the results from the PMHS tests were used so that the HBM could be simulated under realistic impact conditions. It would be reasonable to expect that increased levels of personalization would result in improved predictions of risk. However, it is difficult to establish a direct comparison between the risk predicted by the HBM and the risk observed in the PMHS tests. First, even if the three experimental tests resulted in AIS3+ injuries, an exact calculation of the risk of AIS3+ injuries in the experimental loading conditions is not feasible with such a limited sample of PMHS tests. In addition, the definition of the AIS level based on rib fractures encompasses very different injury patterns (i.e. different numbers of rib fractures would result in the same AIS3 score depending on their location in the rib cage). This is why this study does not intend to highlight which personalization technique results in more biofidelic predictions, but rather how sensitive the injury criteria used with HBM are to the personalization of the models. From a more general perspective, if a criterion is not sensitive enough to change when the model is personalized, then there is not really a reason for not using the normalized, standard HBM.This study is subject to some limitations. First, only three PMHS sled tests were taken as a reference for the comparison with the different model versions of the thoracic injury risk under oblique impact. Thus, more experimental data are required covering different impact angles, subject ages, sex, and anthropometrical characteristics for supporting the conclusions of this study. In terms of methodology, the morphing personalization technique was implemented attending to the external anthropometry, thus internal subject-specific geometry was not personalized. Since the scope of this study was to evaluate the influence of the subject-specific posture, mass, and anthropometry only, soft and hard tissue material properties remained unmodified in the SAFER HBM model. It should be noted that the anthropometry of PMHS A and PMHS B was averaged to develop a single personalized HBM. This was decided due to the large similarities in anthropometry and initial posture of the two subjects that would have resulted in minimal differences in the corresponding HBM.This study analyzed the influence of different personalization techniques on the probability of chest injury predictions of HBM. Despite having led to statistically significant differences in the probability of AIS3+ calculations, mass-scaled and morphed model versions provided, in general, lower values of injury risk than the baseline model and the postured version (1 and 2). The postured model version (2) exhibited the highest values of probability of injury and resulted in predictions that closer resembled the injuries observed in the reference PMHS tests. Furthermore, the models in which the posturing was performed  successfully predicted that the lower right chest landmark suffered the maximum deformation as occurred in the PMHS tests. Additionally, this study found that PC Score-based prediction showed higher values of p (AIS3+) than the prediction based on Cmax for the loading conditions and personalization techniques analyzed. Previous studies have suggested only minor differences between the two criteria, but the results included here suggest that these two criteria will result in significantly different predictions if the chest is loaded more asymmetrically.


This paper investigates the problem of distributed ellipsoidal intersection (DEI) fusion estimation for linear time-varying multi-sensor complex systems with unknown input disturbances and measurement data transmission delays. For the problem with external unknown input disturbance signals, a non-informative prior distribution is used to model the problem. A set of independent random variables obeying Bernoulli distribution is also used to describe the situation of measurement data transmission delay caused by network channel congestion, and appropriate buffer areas are added at the link nodes to retrieve the delayed transmission data values. For multi-sensor systems with complex situations, a minimum mean square error (MMSE) local estimator is designed in a Bayesian framework based on the maximum a posteriori (MAP) estimation criterion. In order to deal with the unknown correlations among the local estimators and to select the fusion estimator with lower computational complexity, the fusion estimator is designed using ellipsoidal intersection (EI) fusion technique, and the consistency of the estimator is demonstrated. In this paper, the difference between DEI fusion and distributed covariance intersection (DCI) fusion and centralized fusion estimation is analyzed by a numerical example, and the superiority of the DEI fusion method is demonstrated. In recent years, multi-sensor systems have been widely used in sensor networks, artificial intelligence, combinatorial navigation, and industrial control. Since multi-sensor systems can provide more information for more accurate control of the system, it makes the information fusion estimation techniques of multi-sensor systems receive wide attention and have important research significance ,4,5,6,7.The centralized fusion estimator can provide the best estimation accuracy when all sensors are working properly. However, if the sensors fail in operation, the centralized fusion estimator cannot detect and discard the faulty sensors in time, leading to a decrease in the reliability of the fusion estimation results and an increase in the error. A suboptimal distributed estimator with a parallel structure can solve this problem well. The presence of a parallel structure makes it easy to detect and isolate the faulty sensors, so the distributed estimator has good reliability and flexibility ,11,12. AIn a multi-sensor complex system, the system is affected by some network-induced phenomena due to the uncertainty of the network heterogeneous model and the occurrence of sensor failures. For example, unknown external information disturbances, random delays in measurement data, and packet loss. For systems with unknown inputs or disturbances, these disturbances may be invariant, time-varying, or random ,15. In , the proMeanwhile, network congestion occurs due to limited communication bandwidths in sensor networks. Random delays are inevitable when transmitting measurement data. The delay phenomenon is inevitably accompanied by packet loss, which significantly affects the performance of the network system . When deFacing the problem of computational resource limitations and system uncertainty in complex systems with multiple sensors, a distributed fusion estimator is used to estimate the system. Despite the rapid rise of the distributed fusion estimation in recent years, it is often plagued by unknown correlation information in sensor networks, which prevents the design of fusion estimators with high accuracy . CurrentIn this paper, we study the problem of data fusion estimation for a linear time-varying multi-sensor complex system with two network-induced phenomena of both unknown input disturbances and measurement transmission delays. In order to obtain a fusion estimator with high accuracy and low computational cost, distributed fusion estimation is used in this paper for the system estimation. In this case, the information of unknown input perturbations is modeled by a non-informative prior distribution. All possible values are described by using a probability density function. The randomness of the measured data transmission delay is described by a set of independent random variables obeying Bernoulli distribution, and a buffer of finite length is added at the link node to obtain the data set for the delay measurement. For the design of the system local estimator, the MMSE local estimator is designed in a Bayesian framework based on the nature of the state-conditional distribution and the maximum a posteriori (MAP) estimation criterion. When fusion processing is performed on the local estimates, the correlation between the local estimates is unknown due to the randomness of the measurement data delay, which makes it difficult to obtain fusion results with high accuracy. To solve the problem of fusion estimation with unknown correlations between local estimates, a distributed ellipsoidal intersection (DEI) fusion estimator is designed by analyzing the distributed fusion algorithms. Compared with the distributed covariance intersection (DCI) fusion estimation, the problem of overly conservative estimation results is solved, and the estimation accuracy is improved. The parallel structure makes the designed estimator less computationally expensive and reduces the computational complexity than the centralized fusion estimator.The structure of this paper is as follows. In k, ith network transmission channel with the total number of sensors L. Let us consider a multi-sensor linear time-varying system disturbed by unknown input information:For the problem of data fusion estimation of a multi-sensor linear time-varying system with unknown input disturbances and measurement data transmission delays, the flow structure of the system is shown in Since the external input vector ased. In , an assuribution . The proInspired by ,19, for kth moment and the ith buffer is defined as:When the measurement information is transmitted through the network channel, the measurement delay occurs randomly, because the limited bandwidth of the network channel causes the channel congestion phenomenon. During transmission, if the measurement information is not received by the link node within a given time interval, packet loss occurs, so the packet loss phenomenon also exists at the same time . Since te buffer . Here, wkth moment or before. When the delay time is equal to or greater than ith buffer at the kth moment by defining The receipt of the measurement In this section, in order to solve the problem of estimating the state To ensure that the local estimator design is error-free, we have to verify that the coefficient matrix atrix Dk . The aboFor systems that satisfy the condition of ith link node, the posterior probability distribution of the state The set of measurements The prior probability distribution Converting Equation (9) to the Gaussian distribution form yieldsAccording to the nature of the marginal distribution of the multivariate Gaussian distribution, Equation (10) is organized to obtain:Based on Equation (11), it is known that the prior probability Under the condition that the prior probability distribution Based on the measurement set The maximized posterior probability distribution function is:Substituting Equations (11) and (13) into (14), we obtain the posterior probability distribution Since the prior probability distribution and the measurement noise obey Gaussian distribution, i.e.,Thus, we obtain a local estimator of the Gaussian distribution of state Our goal is to fuse the obtained local estimates at the fusion center to obtain estimation results with high accuracy.In this section, in order to solve the fusion problem of multi-sensor local estimation, a distributed fusion estimation algorithm suitable for linear multi-sensor time-varying discrete systems with unknown input disturbances and measurement transmission delays is selected. When we fuse the local estimates, we first consider the optimal matrix-weighted distributed fusion method for fusion estimation with the following fusion equation:obtained . An unknCurrently, a commonly used method in dealing with fusion estimation of unknown correlations is the CI fusion technique, which parameterizes the fusion formula and avoids the determination of the expression for the mutual correlation covariance covxi,xj . Althougcovxi,xj . Based ocovxi,xj .Next, we analyze the EI fusion method. First, we consider two random vectors: Our goal is to fuse the two prior estimates into a new estimate It is also important to ensure that the fusion results of these two prior estimates satisfy the consistency of the fusion estimates, i.e., To characterize the unknown correlation, the EI fusion technique is performed by introducing three new two–two independent random vectors According to the relationship between the random vectors Since the correlation is unknown, to obtain a description of an arbitrary correlation, the information of the mutual correlation covariance For random vectors Since the prior estimates can be described by the introduced random variables, the fusion of the prior estimates is equivalent to the fusion of the introduced random variables, and by conditioning the function of Substituting Equation (21) and the variable information into Equation (24), it is obtained thatIn order to pursue a computationally inexpensive fusion algorithm, the mean estimate , i.e.,, the first fusion result of According to (27) and (28), we obtainThe following conclusions can be drawn from the collation.L − 1 times of the fusion process, based on mathematical induction, it is obtained thatIn the In summary, the distributed ellipsoid (DEI) fusion estimator designed in the paper has good consistency, and the fusion estimator outperforms the individual local estimators.In this section, the proposed DEI fusion is validated by a numerical example in order to intuitively obtain a fusion estimation problem consistent with being able to solve the unknown correlation in a complex multi-sensor system with unknown input disturbances and measurement data transmission delays. First, consider a complex multi-sensor linear time-varying system with unknown external inputs and measurement data transmission delays with the expression:The expression for each element in the state matrix is:The respective measurement matrices of the three sensors are as follows:The unknown input coefficient matrix is milar to , the timThe mean value of the Poisson distribution obeyed by each channel delay time is Based on the property that any Gaussian distribution can be described by the sublevel set ormances .L is a positive integer greater than 1, Next, let us discuss the computational cost of the designed DEI fusion estimator and compare the computational complexity of the centralized estimator with that of the DEI fusion estimator. First, we unify the dimensions of the different measurement equations, i.e., In the centralized fusion estimation, the state estimation is handled using the state augmentation method, and the state transfer matrix is an invertible, sparse matrix. According to the nature of a computational complexity analysis, the computational order of magnitude of the centralized fusion estimator is obtained as From the analysis of the above results, it can be concluded that the designed DEI fusion estimator solves the problem of low computational cost that centralized fusion does not have and the problem that DCI fusion estimation is too conservative and verifies the superiority of the designed fusion algorithm. Although the distributed fusion algorithm is suboptimal, the proposed DEI fusion estimator with good accuracy and low computational cost is preferred for the estimation of multi-sensor complex systems.In this paper, we studied the problem of data fusion estimation for a complex multi-sensor system with two network-induced phenomena of both unknown input disturbances and measurement transmission delays. By treating the unknown input disturbance as a non-informative prior distribution, the measured data transmission delay was represented by a set of independent stochastic Bernoulli processes, and a finite length buffer was added at the link nodes to retrieve the delayed data set. In analyzing the data fusion estimation problem, the MMSE local estimator was designed with a Bayesian framework for a multi-sensor complex system. For the problem of an unknown correlation between local estimates, a DEI fusion estimator that could solve arbitrary correlation was designed, and the consistency of the fusion estimator was demonstrated. In the paper, the superior tracking performance of the designed DEI fusion estimator was analyzed by simulation examples, and the problems of conservative estimation in DCI fusion estimations and high computational costs in centralized fusion were solved. Although information fusion is developing rapidly in this era of rapid development, the research on information fusion estimation needs further efforts.


The disruption caused by the Covid-19 pandemic generated an unprecedented situation, in which digital learning, in the form of Emergency Remote Teaching, was the only possible form of schooling. Italy soon decided to close schools as a measure to counter the spread of the virus. Although the Ministry of Education suggested general guidelines, school principals and teachers were autonomous in deciding how to best organise their educational activities. The first objective of our study is to identify subgroups of teachers, based on the use of digital tools during the Covid-19 emergency. Secondly, we explore how subgroups differ in terms of teachers’ satisfaction and students’ performance. To this end, we integrate information from an ad hoc survey completed by 1,407 primary and lower secondary teachers in Italy, with the students’ standardised test scores provided by INVALSI. Data have been analysed through a 3-step latent class analysis. The findings reveal that one third of the teachers showed resistance to the use of digital technologies and focused mainly on asynchronous teaching. Teachers that used a broader set of digital instruments, instead, were more satisfied with their teaching practices. A more articulated use of technology for teaching activities was also positively associated with higher students’ performance in 2021. The disruption caused by the Covid-19 pandemic generated an unprecedented situation, in which emergency remote education was adopted globally to ensure educational continuity for 1.5 billion students and 63 million teachers . The teaRecent studies focused their attention on students’ learning conditions during the Covid-19 outbreak, trying to highlight the difficulties and disadvantages of distance learning in lockdown , 5, 6. EThe context of application is the Italian scenario where the shutdown was enforced in late February 2020 and lasted until September, making Italy one of the countries affected by the longest school closure in the world . Althougad hoc survey designed in partnership with the National Evaluation Committee for Education (INVALSI) and handed out to a nationally representative sample of primary and middle schools. The survey was carried out between July and September 2020, covering information about the use of ICT during the first wave of school closures (March-June 2020). Besides the survey data, we use information on INVALSI standardised test scores in 2021 to investigate the effect of digital tools used by teachers on students’ performance. To the best of our knowledge, this is the first academic paper that combines these two levels of investigation.To pursue our objectives, a 3-step Latent Class Analysis (LCA) is employed to identify latent groups of teachers with similar digital behaviours during Covid-19 school closure. Besides, latent classes are characterised by means of teachers’ and contextual characteristics. Finally, we test the difference of two outcomes (i.e. teachers’ satisfaction and students’ performance) across latent classes. Data are collected through an In the past two decades, several scholars addressed the use of ICT for teaching, underlining facilitators and barriers of the use of digital technologies –15. InstFocusing specifically on teachers’ satisfaction during the Covid-19 pandemic, the literature provides interesting results. In general, the teachers’ well-being was negatively affected by the school closure imposed by the pandemic. During those months, teachers had to face disruptive and structural changes on short notice. Analysing the satisfaction of Portuguese teachers during the Covid-19 pandemic, , 20, 21.We contribute to this strand of research by exploring the relationship between the teachers’ use of digital tools and their satisfaction with teaching activities during the emergency. In this context, we use teachers’ satisfaction as a proxy, albeit subjective, for the quality of teaching carried out in ERT . This isResearch on how digital tools influence students’ outcomes is part of a relevant and growing stream of academic literature. The possibilities offered by technology in the educational setting are multiple: game-based activities , virtualThe impact of educational technology in the classroom is highly debated among researchers and practitioners. Particularly, the link between the use of educational technology and students’ achievement is still unclear . HoweverThis paper aims at filling this gap in the literature by linking teachers’ practices during the first months of Covid-19 emergency and students’ performance in standardised test scores collected in May 2021, focusing on the Italian educational system. Despite Italy was one of the European countries mostly affected by the Covid-19 emergency , 35. TheThe empirical analyses rely on a framework that models the digital practices implemented by teachers during ERT. In the literature, we observe two dimensions for classifying digital technologies for teaching , 37: (1)The second dimension distinguishes between synchronous and asynchronous technologies. Synchronous digital tools involve real-time interaction between teachers and students, while asynchronous activities take place in delayed time and do not allow teachers to have simultaneous feedbacks on the learning outcomes . The litBased on the evidence here presented, we classified digital tools into three main categories: (i) tools for synchronous teaching, (ii) tools for asynchronous teaching, and (iii) tools for communication with students and families.The methodology used to explore the heterogeneity across teachers’ practices during ERT is a 3-step LCA, a mixture modelling technique increasingly used to identify latent subgroups within a population . By lateMore specifically, in Step 1, the latent classes are defined based on 12 indicators related to the three categories defined in the digital practices’ framework (see previous section): (i) synchronous teaching, (ii) asynchronous teaching and (iii) communication with students and families. The indicators are based on questions collected through an ad-hoc survey. All the Likert-scale indicators have been dichotomised to fit the LCA algorithm, meaning that a value equal to 1 represents a frequent use of the technology , while a value equal to 0 means that the technology was rarely or never used . As a result of the first step, each observation is assigned to the group for which the probability of class membership is the highest.In Step 2, multinomial regressions are run to characterise the groups by means of personal and career-related factors. Class assignment is regressed against a set of personal and career-related covariates to provide a useful characterisation of the latent groups. In this multinomial logistic regression, one class is used as the reference group, according to which odds ratios are provided to estimate the likelihood that a certain characteristic recurs in relation to the reference group.Step 3 makes it possible to verify whether the distal outcomes vary across groups, testing whether groups with different use of technologies report differences in teachers’ satisfaction and students’ performance . In this step, we compute a Pearson chi-square test to detect significant differences across groups (latent classes) obtained in Step 1 .The analysis was run using Mplus version 7.4, and we followed the literature on the topic to determine the number of latent groups . In thisprivacy@polimi.it). The survey collection started in July 2020 and was concluded at the beginning of the new school year (September 2020). Teachers were asked to answer making reference to the period of school closure lasting from February to June 2020. To guarantee comparability within grades, the questionnaires were sent out to grade 4 (primary school) and grade 7 (lower secondary school) teachers of Reading, Mathematics and English. This way, we were able to monitor the performance of the same students through the INVALSI tests in 2021, in grades 5 and 8 . The survey was created with the support of the National Evaluation Committee for Education (INVALSI), which selected a nationally representative sample of schools across the country. We obtained answers from 1,407 teachers, with a response rate ranging between 24% (grade 4) and 31% (grade 7) of the national sample. The moderate response rate does not affect the validity of the results since our objective is not to be representative at national level, but to identify underlying patterns in the use of digital tools during the Covid-19 emergency. Indeed, data are analysed by means of a combination of statistical descriptive methods to build a picture of the use of digital tools during the pandemic and its relationship with teachers’ satisfaction and students’ results. Nevertheless, we also analysed the differences between the group of teachers answering the survey and those who did not, to identify any potential self-selection bias. The results, reported in Supplemental information Section , their previous training on technologies for teaching, their level of readiness for guaranteeing learning continuity , their relationships with colleagues, and their working environment . The inThe second distal outcome considered in the third Step of LCA is students’ results in standardised test scores, as collected by INVALSI with reference to Reading, Mathematics and English. Teacher-level information, gathered through the survey, has been associated with the class average score in the specific subject taught by the teacher. Due to the emergency, INVALSI suspended standardised tests in 2020; therefore, we employed the students’ scores collected in May 2021. These data represent the first available information on standardised test scores of Italian students after the Covid-19 emergency. In this sense, this indicator does not capture the short-term effect of ERT on students’ performance, but it provides rather indications of a medium-term outcome.The complete descriptive statistics of the variables collected through the survey and adopted in the Step 2 of LCA are reported in the S5 Table in Regarding the reaction to ERT, only less than one-third of the teachers started synchronous lessons within two weeks after school closure. Other important aspects relate to teachers’ working conditions and social environment. The majority of teachers have a quiet place of work and a personal laptop . They also report having had stimulating discussions with colleagues and, in most cases, they received clear guidelines from school principals on their teaching activity. On the use of digital tools, Concerning the outcome measures of this study, Figs As a result of the application of the 3-step LCA to the 12 indicators related to the digital technologies used by teachers, the model fit statistics are presented in The profile of the four classes of teachers is presented in all-round digital (9% of the observations) and the resistant to digital (33%) groups. The first class is made up of teachers who used a wide range of digital tools, ranging from teaching games  to teaching apps . Still, this group used instant surveys and quizzes, phone calls and text messages to a very limited extent.By analysing the profile of the four latent classes, the following subgroups emerge . The two classes at opposite poles are the resistant to digital teachers, comprising one third of the total observations. This group used all the digital technologies to a very limited extent, thus showing some sort of resistance to digital teaching. Remarkably, only half of them shared texts or videos with students to support asynchronous teaching. All the other digital tools were used by less than 25% of the teachers. The fact that this group makes up one third of the overall number of observations is an important point to consider, as it implies that one third of the student population was stimulated very poorly by their teachers and mainly through asynchronous teaching.The opposite group is made up of integrated digital teaching, which makes up 38% of the observations. This group of teachers used a wide range of digital tools and was particularly keen on using them to support the teaching activity. On the one hand, they did not use communication tools, a fact that underlines the attention specifically devoted by this group to the main task of a teacher, which is to support student learning through the teaching activity. On the other hand, this group of teachers did not pay particular attention to the communication aspects, although this was a particularly relevant matter during school closure.The third and largest class is that of asynchronous chat-based (20% of the observations), which has a peculiar profile related to the fact that these teachers mainly used asynchronous digital tools, either for teaching or for communicating. Indeed, to a large extent, they used asynchronous tools for teaching and WhatsApp groups to communicate with students and families. It may also be the case that these teachers used a mobile app, like WhatsApp, to assign asynchronous tasks to students, thus using a non-teaching-related digital tool for teaching activities.The fourth and final class is resistant to digital group is used as the reference group. Looking at the comparison between integrated digital teaching and resistant to digital groups, the teaching experience has a significant impact on the likelihood of resisting. Indeed, the negative coefficient states that being a more experienced teacher reduces the probability of belonging to the integrated digital teaching class relative to the resistant to digital group. In this respect, this effect may represent a propensity to use digital tools for teaching that decreases with a teacher’s experience. This finding highlights the relevance of digital competence and confidence in managing a larger use of technologies. Moreover, teachers who received training on digital technologies for teaching in the previous two years are 1.69 times more likely to conduct integrated digital teaching rather than being resistant to digital, stressing the importance of training on digital tools [The second step of the LCA aims to characterise the classes defined above through demographic, career-related and school-related information. al tools .all-round digital to the resistant to digital group. In this comparison is worth stressing the relevance of supplementary personal information about the teacher. First, female teachers are 7.22 times more likely to be all-round rather than resistant to digital. However, in interpreting this result, we should keep in mind that 98% of the respondents are women  to be all-round rather than resistant to digital. This finding holds true for the asynchronous chat-based class as well, and leads us to think that teachers resistant to digital are more likely to be in northern regions. However, this finding may also suggest a larger self-selection of teachers responding to the survey in southern rather than in northern regions.Similar findings emerge when comparing omen see . Moreoveresistant to digital and asynchronous chat-based groups is statistically lower than that of the integrated digital teaching and all-round digital classes. Thus, the results show that teachers using digital tools to a larger extent, are also more satisfied with their teaching activities. When looking at students’ results, the differences in student test scores are significant only when comparing integrated digital teaching with the other groups. This class reports significantly higher student performance, meaning that the use of a wide range of digital tools is positively associated with students’ test scores. It is worth to stress that only digital tools for teaching seems to matter, given that teachers who used digital tools also for communication  do not report significantly different student performance.Step 3 of the LCA allows to assess whether latent classes are statistically different in terms of distal outcomes, highlighting a statistically significant difference in teachers’ satisfaction and in student test scores among latent classes. In particular, the Chi-Square tests reported in integrated digital teaching group reports the highest student performance also when jointly controlling for the geographical regions, and that this difference is still statistically significant.Given the relevance of the geographical factor in affecting our results (as emerged in Step 2) and given the structural differences in terms of student achievement between the high-performing Northern regions and low-performing Southern regions of Italy , we run Our findings contribute to the recently growing debate about teachers’ practices during the Covid-19 crisis , 6, 58. resistant to digital teachers should be interpreted as a lower-bound estimate—especially in the southern and central regions, in which there is the lowest share of respondents. Asynchronous chat-based class is, instead, associated with one-quarter of the teachers, who are characterised by an intensive use of asynchronous digital tools for teaching and communication finalities. Finally, our findings reveal that less than 10% of the teachers used a wide range of digital tools in all their job activities .Results provide new insights into how teachers addressed the online transition during the pandemic, revealing a high heterogeneity of approaches to ERT by teachers. Our findings suggest the existence of four latent classes of remote teaching behaviours during school closure. These typologies are in line with pre-Covid evidence on digital practices of teachers available in the literature . More spTo answer the second research question, we investigate the link between the four classes of teachers’ digital behaviours and learning outcomes. The results reveal that a larger use of digital tools specifically for teaching activities is associated with both higher teachers’ satisfaction and students’ standardised test scores. This result is likely to capture the educational effects associated with teachers being mainly focused on teaching activity, rather than devoting their time to organisational and communication tasks. These teachers might have spent more time to develop learning content and have produced, therefore, a positive effect on students’ achievement. Besides, in some cases, live chat software could distract the students since creates a new communication environment with all the kids in the class . On the Overall, our findings suggest that the employment of digital tools to support remote teaching activities can play a relevant role in positively influencing student learning. From this perspective, the high presence of resistant to digital teachers represents a critical issue that should be considered in the development of teachers’ training in a post-Covid situation. Indeed, our results indicate that previous experience with digital and training on digital tools reduce the likelihood of resistance to digital technologies for teaching. This is a relevant finding to support policymakers in developing plans for teachers’ training on digital technologies and adds up to the current evidence on the relevance of teachers’ digital competence to carry out high-quality ICT-mediated teaching , 15.resistant to digital teachers.The study has some limitations, especially in relation to the possible self-selection of teachers in the survey, affecting the external validity of results. This happened more consistently in southern regions and may affect some of the geographical-related results emerging from Step 2 of the analysis. As a potential consequence of this bias, we must interpret our finding as the optimistic picture of ERT, as we could be underestimating the number of The results presented in the paper open the avenue for future research, which may study longitudinal data to investigate the long-term effects of ERT behaviours and monitor the evolution of teachers’ digital skills. Forthcoming studies could also enlarge the context of the analysis by investigating similar research questions from an international perspective to compare the findings across countries.S1 Fig(PNG)Click here for additional data file.S1 File(DOCX)Click here for additional data file.