The recognition of Activities of Daily Living (ADL) has been a widely debated topic, with applications in a vast range of fields. ADL recognition can be accomplished by processing data from wearable sensors, specially located at the lower trunk, which appears to be a suitable option in uncontrolled environments. Several authors have addressed ADL recognition using Artificial Intelligence (AI)-based algorithms, obtaining encouraging results. However, the number of ADL recognized by these algorithms is still limited, rarely focusing on transitional activities, and without addressing falls. Furthermore, the small amount of data used and the lack of information regarding validation processes are other drawbacks found in the literature. To overcome these drawbacks, a total of nine public and private datasets were merged in order to gather a large amount of data to improve the robustness of several ADL recognition algorithms. Furthermore, an AI-based framework was developed in this manuscript to perform a comparative analysis of several ADL Machine Learning (ML)-based classifiers. Feature selection algorithms were used to extract only the relevant features from the dataset’s lower trunk inertial data. For the recognition of 20 different ADL and falls, results have shown that the best performance was obtained with the K-NN classifier with the first 85 features ranked by Relief-F (98.22% accuracy). However, Ensemble Learning classifier with the first 65 features ranked by Principal Component Analysis (PCA) presented 96.53% overall accuracy while maintaining a lower classification time per window (0.039 ms), showing a higher potential for its usage in real-time scenarios in the future. Deep Learning algorithms were also tested. Despite its outcomes not being as good as in the prior procedure, their potential was also demonstrated  Neural Network), indicating that they could be a valid option in the future. The recognition of Activities of Daily Living (ADL) has been a widely debated topic of study for the past several years with applications in a vast range of fields, from medicine to supervision of a persons’ driving style, and even to sports training analysis, passing through surveillance ,2. SeverThe identification of human activities can be accomplished by processing signals or image sequences gathered from one or more sensors, such as examining videos and photos from cameras or motion data from inertial sensors . When coOffline activity recognition is the most basic method of activity recognition . SensorsMoreover, on several benchmark datasets used by ML-based solutions, conventional (CNN and LSTM) and hybrid (CNN-LSTM) Deep Learning (DL) models have lately shown improved and promising performances, cutting down the time spent on data processing and feature extraction ,14. ExpeFor the most part, the results achieved by Artificial Intelligence (AI)-based algorithms for ADL recognition are highly satisfactory. However, the number of activities recognized is still generally small, with the analyzed state-of-the-art detecting a maximum of 14 ADL  , and theThis manuscript addresses the aforementioned drawbacks and, in addition, addresses a higher number of ADL than any other of the works analyzed before, recognizing a total of 20 classes, including transitional activities  and falls . Furthermore, this manuscript aims to answer the following research questions concerning recognition/classification of 16 ADL and four types of fall events from data collected from waist-located inertial sensors: (i) Which is the most suitable classifier and what are the most relevant features? and (ii) Which approach, ML or DL-based models, presents better performance?With these objectives in mind, an AI-based framework was developed that allows for the benchmarking of several classifiers, including Discriminant Analysis (DA), K-NN, Ensemble Learning, DTs, SVM, CNN, mono and bidirectional LSTM, and CNN-LSTM neural networks. Simultaneously, feature selection algorithms are used to extract only the relevant features from the dataset’s lower trunk inertial data. Furthermore, a dataset fusion and normalization procedure is applied in order to gather a large amount of data to improve the robustness of the suggested algorithms during the several validation steps.The remainder of this paper is organized as follows. The proposed algorithm makes use of a large number of publicly available datasets to validate activity recognition models based on inertial data collected from the participants’ waists. Thus, a vast dataset was built from the fusion and normalization of several ADL public datasets. This process, to the best of our knowledge, has not been carried out before in any other works of the kind, despite its importance being highlighted multiple times ,28. DataSisfall : Data acFallAllD : Data acFARSEEING : Large-sUCI HAR : DatasetCotechini et al. : DatasetUMAFall : A datasThe used team-owned datasets were as follows.+Sense : DatasetSafeWalk : DatasetInertialLab : DatasetThe fusion of these various datasets, which include information from both adult and elderly subjects, as well as healthy and unhealthy individuals, served two purposes. First, to create a large and diverse dataset suitable for training ML models. The second goal was to develop AI-based models capable of recognizing ADL regardless of the subject’s age and health condition.A global dataset containing 6702 files covering a total of 20 ADL and falls conducted by 180 subjects  was generated. This vast amount of data is crucial for validation purposes since it is far larger than any other dataset used in the AI-based ADL recognition research carried out. Furthermore, the global dataset presents a balanced distribution regarding the subject’s gender , also containing data from both young adults and elderly people. However, despite the presence of elderly data, the average and standard deviation values show that the global dataset is still made up mostly of young adults, with the percentage of people over 65 years old being just over 20% of the total dataset (37/180 subjects).Due to the great variability found between datasets, it was necessary to normalize the data from all datasets, according to the normalization procedure depicted in The datasets, whether public or private, contain the great majority of ADL used for activity recognition in the literature. Therefore, a total of 20 labels, including periodic activities, static postures, transitions between postures and falls, were used in order to cover all ADL listed in every dataset. It should be noted that some activities whose labels in public datasets were considered different were recognized as the same activity in this work, since their basic body movement is similar, e.g., the cases of Sisfall’s activity of sitting in high chairs or low chairs were included in the “Stand to Sit” class; or even cases of standing in different places, such as in the room and in the elevator, were all included in the “Standing” class. A study carried out on how the ADL were distributed showed that the global dataset is unbalanced, with a greater tendency toward cyclical activities, such as walking or lying , with only a small percentage of transitions between activities and fall events, such as the fall by syncope, which is the activity with the least amount of data in the constructed dataset (0.27%). ® GeForce® GTX 1650; memory—8 GB DDR4 at 2666 MHz and SSD PCIe of 512 GB.We performed a comparative analysis, whose strategy is illustrated in Feature extraction was achieved through the sliding window method, where a signal is segmented into several windows of equal size, on which different features can be calculated. The most used sliding windows’ size corresponded to approximately 1 s for this type of activity classification, and the overlap between consecutive windows can vary from 50% to 87% . Within Thus, for each window, several features, such as the averages, maximums, minimums, and standard deviations of each of the acceleration and angular velocity signals, among other metrics, were extracted, making a total of 199 features calculated. A summary of the extracted features can be seen in After the aforementioned extraction, min–max scaling  was carried out to ensure a low computational cost when building the models . Since eIn order to understand what kind of improvements this feature selection process can bring, nine Feature Selection Methods (FSM) with diverse types of selection  were applied to the extracted features ,39. CoveFeature selection was also performed by the Principal Component Analysis (PCA), as shown in 199 by 2 ,48. As aWe compared the following five ML classifiers by using a set of procedures depicted in Initially, we performed the hold-out (HO) method to split 70% of the created dataset’s data for training and 30% for testing. The mentioned classifiers were used to obtain the subset of the most relevant features by performing an initial five-fold cross-validation (CV) with one repetition and using only training data. Once we determined the subset of the most relevant features, we performed a five-fold CV with ten repetitions to the four best classifiers from the previous step in order to evaluate the generalization capabilities of each model. The two best classifiers from this step were chosen, and its hyperparameters were optimized through a gridsearch process. The optimized ML classifiers and the neural networks architectures were further trained with all training data and tested with the test data from the HO method and the final performance of each classifier was compared in order to choose the best AI-based classification models.In order to understand if these can be a viable alternative to ML methods, the classification of ADL and fall events was also carried out using the four Neural Networks architectures presented in The last study evaluates which of the chosen window sizes provides better performance results to the selected classifiers. Due to the great diversity in the classes to be classified  and their duration, this study became imperative, in order to find the size that best fits the activities to be classified. Furthermore, the time required to perform the training and testing of the K-NN and Ensemble Learning classifiers for each of the window sizes was also computed. This exercise had the objective of investigating the possibility of using one of the algorithms that presented better performance in real-time situations.The key performance indicators in the developed work were the Mathew’s correlation coefficient (MCC) and the accuracy (ACC). The first evaluation metric exhibits good representational features of unbalanced classes, as occurs in this study . We usedWe determined that 11 PCs were necessary for a cumulative percent explained greater than 70%. Furthermore, the resulting PC demonstrated that there were 55 features with PC values greater than 1/199. After performing the PCA, we reduced the number of features to lower the computational cost of the comparative analysis ; i.e., iThe results attained from the five-fold CV with one repetition disclosed the Ensemble Learning classifier as the one that presented the best performance among the used classifiers  when using the first 65 features ranked by the PCA method . With thWhen using test data from the HO data split method, the two best classifiers presented slight improvements in their performance in comparison to the results shown in The BiLSTM stood out among the neural networks in both case studies, using the first 85 features ranked by the Relief-F method  and the first 65 features ranked by PCA . However, in both cases, it presented lower results when compared to Ensemble Learning and K-NN. On the contrary, CNN presented the lowest performance results for both case studies, using the first 85 features ranked by the Relief-F method  and the first 65 features ranked by PCA . Thus, the ML-based methods, K-NN and Ensemble Learning, were considered the classifiers with better performance for ADL and fall events recognition, among all tested classifiers, being selected for the window size study and classification time analysis. The results attained in this last analysis, for the optimized K-NN and Ensemble Learning classifiers, are depicted in In addition to the results obtained regarding performance metrics, the time required to perform the training and testing of the K-NN and Ensemble Learning classifiers for each of the window sizes used in this last study was also computed. This exercise has the objective of studying the possibility of using one of the combinations which presented better performance results in real-time situations. Through direct observation of The ML-based classification was established with a combination of different classifiers and feature selection methods, and it proved to be an accurate strategy. This process allowed the most relevant features to be found for the classification of 20 distinct activities and fall classes , which sThe success achieved regarding the performance of the classification models through different validation methods, namely hold-out and cross-validation, shows the robustness of the applied processes. The creation of a vast dataset also positively influenced the performance results obtained. According to the results presented in According to the literature, windows with a larger size have the tendency to perform worst in the recognition of shorter activities or transitions and better in the classification of cyclical or static activities, which are maintained for longer periods of time. Furthermore, as the window size increases, the model’s capability to recognize ADL in real time decreases ,36. As sA direct comparison between the two best results obtained in tests performed with Neural Networks  and the Thus, this initial study of the behavior of several neural networks showed that despite positive results in some of the cases tested, it did not reach the desired potential when compared to the results obtained with the ML classifiers. This fact raises the need to carry out several studies and some changes in the future in order to obtain performance results higher than those found in the literature. The architectures used must be improved in the search for better results in order to be comparable with the studies currently carried out in the literature. Finally, and as mentioned in most of the works analyzed in the literature, new tests should be carried out in the future with windows segmented from raw inertial data as inputs rather than features, given the ability of neural networks to carry out a process extraction of features .An algorithm to recognize sixteen ADL and four different types of fall  from several AI-based classification models and feature selection models was built in order to find the combination that presents better performance in this type of classification. The performance of the different combinations was evaluated using the following parameters: (i) performance evaluation metrics, (ii) subset of features used, and (iii) classification time per window of the models.Two different approaches (ML and DL) were investigated and compared: when performing one waist-located inertial sensor-based ADL and fall events recognition. Furthermore, a new procedure of fusion and normalization of public datasets was carried out in order to generate a big enough dataset to validate the activity classification models in order to battle concerns observed in the literature. Our long-term objective is to evaluate these techniques on elderly waistband users to evaluate whether the results of this study translate to identical outcomes in continuous real-life usage.Taking into account the performance values as well as the classification times found in this work for the machine used, it is concluded that the most effective AI-based classifier was the Ensemble Learning classifier with the first 65 features ranked by the PCA feature selection method. Moreover, the classification time per window in this combination was lower than the window advance time in every window tested, which represents an encouraging result for the application of this algorithm in real time in the future. The DL outcomes were not as good as in the prior procedure; however, their potential was demonstrated, indicating that they could be a good option in the future with the appropriate future work regarding the input data used and its architectures. Although the established methodology allows for a reduction in computing cost, we recommend using a sufficient processor so that all classifiers respond rapidly.The constructed dataset contains a large amount of successfully normalized data for the validation of activity recognition algorithms. Different steps can still be applied for its continuous improvement, such as the addition of more senior subjects’ data and data-balancing techniques, such as data augmentation, to balance the amount of samples of ADL represented on a smaller scale. However, the choice between using balanced data or preserving the overall distribution of activities should be backed by a critical analysis of the results obtained through a validation with data collected in day-to-day circumstances over long periods of time. Data fusion from other sensors, such as magnetometers or barometers, as well as the addition of other devices for data collection , may aid in the differentiation of activities with similar movement patterns. Improved data-splitting methods must be verified in the future to guarantee that the results attained were not due to the usage of comparable data during the train and test stages of the model. Despite attaining performance results comparable with the literature for bidirectional LSTM, considering the higher number of classes classified, continued development of the tested neural networks is needed. New and improved architectures, as well as ablation studies, should also be conducted to determine the impact of the various settings and stages of each architecture on ADL and fall events recognition. Furthermore, the constructed classifiers should be trained and tested on the various public datasets independently in order to make a more direct comparison between the methods covered in this study and those listed in the literature that use the same datasets for evaluation.This study contributes to the state-of-the-art with two versatile ADL and fall events detection methods, which are capable of discriminating 20 classes of events. There is also evidence that dataset fusion and normalization is imperative to guarantee a vast and diverse amount of data for ADL recognition algorithms’ validation. Furthermore, it may lead to the incorporation of these tools on instrumented waistbands or other devices for real-time fall risk assessment in the future .


Sport injuries have been common among athletes across the globe for decades and have the potential to disrupt athletic careers, performance, and psyche. Many health professionals and organizations have undertaken injury mitigation strategies to prevent sport injuries through protective equipment, training protocols, and a host of other evidence-based practices. Many of these specialized training methods were disrupted due to protocols to mitigate the spread of COVID-19. This research examines the effects of the COVID-19 pandemic in relation to the prevalence of athletic injuries in the National Football League (NFL).During the COVID-19 pandemic, NFL teams and athletes across all levels of sport were reported to have reduced training in preparation for their seasons due to protocols to mitigate the spread of COVID-19. This study compares the prevalence of injury during the 2018, 2019, and 2020 NFL seasons, with the aim to determine the potential causes of the differences in injury prevalence.Official injury reports from each team were counted during the 17-week regular season of each year . The data were analyzed using an unpaired t test to compare the injury prevalence between each of the three seasons.P<.001); comparison of the 2020 season to the 2018 season found a statistically significant difference (P<.001); and comparison between the 2019 and the 2018 seasons found a statistically significant difference (P=.03).The 2018 season produced a total of 1561 injuries and a mean of 48.8 injuries per team. The 2019 season produced a total of 1897 injuries and a mean of 59.3 injuries per team, while the 2020 season produced a total of 2484 injuries and a mean of 77.6 injuries per team. An unpaired t test was performed using the data to compare the mean number of injuries per team during each of the seasons. Comparison of the 2020 season against the 2019 season showed a statistically significant difference (P=.03), this difference is not as large when we compare the 2020 seasons versus the 2019 (P<.001) and 2018 (P<.001) seasons. The astronomical increase in injury prevalence during the 2020 season over the previous years raises the possibility that there was a reduced physiological adaptation to stress, due to the limited amount of training as a result of the closure of practice facilities in order to slow the spread of COVID-19.Although the 2019 and 2018 seasons showed a statistically significant difference ( The National Football League (NFL) is a professional American football league composed of 32 teams. The NFL is composed of high-level, elite athletes who are able to train rigorously and consistently at state-of-the-art facilities, with the assistance of some of the best trainers and medical professionals in the world. As the COVID-19 pandemic spread across the world, many professional, collegiate, and amateur sports were brought to a halt . It has American football is a contact sport, with at least some level of contact occurring on every play. Given that American football is a contact sport, it comes with nonmodifiable risks of injury . In ordeResistance exercise is a method of conditioning in which an individual works against resistive loads such as free weights, resistance bands, or body weight in order to increase sport performance or overall health and strength . ResistaIn this study, we aimed to determine if there is a change in injury prevalence during the COVID-19 season (2020). We hypothesize that there will be an increase in overall number of injuries and an increase in the mean number of injuries per team during the COVID-19 season (2020). If true, we further hypothesize that this increase in injuries may be due to reduced physiological adaptations of training due to lack of access to sufficient training facilities and training stimuli, stemming from COVID-19 health precautions.t test.The number of injuries for each team was tallied during the 17-week long NFL regular season using the weekly medical data injury reports that are published publicly by each team. If an official team report was not available through the individual team, deferment was made to the injury report on the official NFL website. Athletes on the injury reports for the same injury for consecutive weeks were only counted once; however, athletes were counted again if they presented with a new injury to a different anatomical region. Illnesses, COVID-19–positive cases, holidays, and nonmedical days off were not included in the total tally. Illnesses were not included in the final tally because they are not within the scope of this research. An injury has been defined as a physical complaint during a match or training that affects performance; therefore, illnesses should be reported separately from the incidence of physical complaints . The tott test was performed on the data set to compare the mean number of injuries per team per season to each of the three seasons. A data analysis was conducted by comparing the three different seasons. An unpaired t test was performed to compare the mean number of injuries per team of each season. Comparison of the 2020 season against the 2019 season showed a statistically significant difference (P<.001). Comparison of the 2020 season to the 2018 season also showed a statistically significant difference (P<.001). Comparison between the 2019 and the 2018 seasons showed a statistically significant difference (P=.03) as well. After tallying the injuries, the 2020 season produced a total of 2484 injuries with a mean number of 77.6 injuries per team. The 2019 season produced a total of 1897 injuries with a mean number of 59.3 injuries per team. The 2018 season produced 1561 injuries with a mean number of 48.8 injuries per team. An unpaired P=.03) and the 2020 season (P<.001) when compared to the 2018 season. The 2020 season also demonstrated a statistically significant (P<.001) increase in the mean number of injuries per team when compared to the 2019 season. There could be several possible factors that play into the injury prevalence between the three NFL seasons. However, we believe that a decrease in physiological adaptation, due to reduced access to training facilities during the COVID-19 pandemic, contributed to the difference in injury prevalence during the 2020 NFL season when compared to the 2018 and 2019 seasons.The results of this study demonstrated an increased number of overall injuries in the 2019 season and 2020 season when compared to the 2018 season. The results of the study also demonstrated an increased mean number of injuries per team during the 2019 season (We acknowledge that there may be limitations to the study in that it may not have accounted for other injuries, such as injuries sustained during the preseason of the 2018 and 2019 seasons, injured reserve players, and unreported injuries. We also admit that there is a limitation due to an inability to calculate the exact hours of training per season. This calculation would be significantly hindered, as we used a public data set and do not have access to the individuals’ training regimens within the data set. Furthermore, even if training hours could be gathered, there would be a potential for significant recall bias in any survey that attempted to calculate these hours, as the data go several years into the past. While we admit this is a limitation, we have created the best possible scenario by showing there was closure of the NFL training facilities between March 25, 2020, and May 19, 2020 , and demTraining is important for athletes as it can induce advantageous physiological adaptations to bone, muscles, and tendons when provided with an adequate stimulus -15. TraiThe demonstration of increased injury prevalence during the 2020 NFL season could be impactful to athletic programs around the world and allow organizations to focus on strategies to mitigate injuries in the future. This information may also be useful for understanding sport preparation and rehabilitation protocols. There should be more work carried out, at both the professional and amateur levels, to determine the training intensity necessary for physiological adaptation to occur that will reduce injuries. There must also be further follow-up to see if there was also a rise in injuries at the collegiate and amateur levels of sport.Potential follow-up studies could include analyzing the prevalence of injuries for individual teams with severe COVID-19 outbreaks, examining the relationship between geographic COVID-19 hotspots and number of athletic injuries, and examining injury prevalence at the collegiate and amateur levels of sport. We invite other researchers to continue researching the number of injuries in athletes before and after the COVID-19 lockdown measures.


Current methods for extracting information from user resumes do not work well with unstructured user resumes in economic announcements, and they do not work well with documents that have the same users in them. Unstructured user information is turned into structured user information templates in this study. It also proposes a way to build person relationship graphs in the field of economics. First, the lightweight blockchain-based BERT model (B-BERT) is trained. The learned B-BERT pretraining model is then utilized to get the event instance vector, categorize it appropriately, and populate the hierarchical user information templates with accurate user characteristics. The aim of this research is that it has investigated the approach of creating character connection graphs in the Chinese financial system and suggests a framework for doing so in the economic sector. Furthermore, the relationship between users is found through the filled-in user information template, and a graph of user relationships is made. This is how it works: finally, the experiment is checked by filling in a manually annotated dataset. In tests, the method can be used to get text information from unstructured economic user resumes and build a relationship map of people in the financial field. The experimental results show that the proposed approach is capable of efficiently retrieving information from unstructured financial personnel resume text and generating a character relationship graph in the economic sphere. In the information age, companies and regulatory agencies in the financial industry publish many announcements on the internet every day, extract the personnel entities and related attributes in the reports, discover the implicit relationship between personnel, and describe the form in a structured way. Concepts, entities, and their relationships related to people in the financial industry build a relationship map of people in the economic field, conduct an in-depth analysis of financial activities, help financial practitioners make vital decisions such as partner selection and personnel appointment, and promote financial activities. It is essential to smoothly do it. In addition, with the rapid development of our country's economy, financial activities are becoming more and more frequent, and economic crimes are more and more difficult to detect and supervise. By constructing a relationship graph of people in the financial industry, social relationships such as alumni and colleagues of financial practitioners can be found, and early warnings can be provided. Potential financial activity risks and the fight against economic crime are also significant. The key to building a personnel relationship graph in the financial sector is extracting personnel-related entities, attributes, and events from unstructured economic announcements, which entails tasks such as named entity recognition , 2, relaNamed Entity Recognition Effects: In this approach, the neural network-based technique builds a multilayer neural network model from the text, representing words or characters as word vectors and employing them as model input to classify words or characters using neural networks. Author  uses dilThey cannot find the link between people across documents in financial announcements. A person as an entity often contains several entity attributes (such as date of birth and gender) . CharactUnstructured personnel resume text usually contains multiple employment events and education events. Accurately extracting numerous employment events and educational events of personnel resumes without trigger words is a problem worthy of study. The CRFs are a type of statistical modeling tool used for organized prediction in object detection and recognition. Comparative investigations demonstrate that the bidirectional LSTM-connected conditional random field (CRF) model outperforms the LSTM-connected conditional random field (CRF) model. Existing event extraction methods , 17, usuAiming at the unique situation of unstructured personnel resumes, this study studies how to fill hierarchical personnel information templates that extracts the relationship between personnel across documents. It removes multiple positions in the unstructured personnel resume text without relying on trigger words. Furthermore, experience and educational experience events, a BERT-based framework for constructing a relationship graph of Chinese characters in the financial field, are proposed. Experiments demonstrate that the suggested technique is capable of efficiently resolving the problem of extracting information from unstructured financial personnel resume text and constructing a relationship graph of characters in the economic area.This study has been planned into various sections. F denotes the word that corresponds to each word in the input sentence. The vector, Trm, denotes the transformer encoder, and T is the output word vector for each word in the input phrase.The BERT is a Google-developed pretrained language model that got the top results in 11 natural language processing tasks. It represents one of the most important improvements in natural language processing in recent years. The masked language model masks some words at irregular intervals by uniformly substituting some words with identifiers and afterward assumes these masked words using the context information of the masked terms, allowing the vector representation of every word to relate to relevant information in a clear and concise manner. BERT is a paradigm for deep bidirectional language representation based on transformer . The traThe input word vector of the BERT model is obtained by adding three parts: token embedding, segment embedding, and position embedding. The word representation represents the initial word vector of the current word, which is usually obtained by looking up a table; the segment representation represents which sentence the present word belongs to; the position representation represents the position index of the current term in the sentence. In addition, the original input of the sentence needs to add (CLS) and (SEP) tags; (CLS) is added at the beginning, which can be used to represent the entire sentence; the (SEP) tag is used to separate two sentences, indicating the end of the sentence.The BERT pretraining process consists of two different pretraining tasks, the masked language model and the following sentence prediction task. First, the masking language model randomly masks some words by uniformly replacing some words with identifiers (MASK) and then predicts these masked words by the context information of the masked terms so that the vector representation of each word can comprehensively refer to contextual information . Next seAfter the pretraining of the BERT model is completed, the model parameters in the pretraining process are adjusted by fine-tuning and retraining so that the model is more suitable for downstream tasks to obtain better results. The event instance vector is obtained using the learned B-BERT pretraining model, which is then suitably classified and used to populate the hierarchical user information templates with accurate user attributes. The B-BERT pretraining model is used to classify event instance vectors, construct a hierarchical personnel information template, and solve the problem of personnel attribute association.For example, for sentence-level classification tasks, the output vector representation of the first label (CLS) is taken as the sentence representation; for character-level classification tasks, the output of the last layer transformer of all characters is taken and sent to the softmax layer for classification.The BERT pretrained language model is used to build a personal relationship graph in the financial field, and the personal relationship graph is used to create a framework. The BERT-Template technique is used to fill the personnel template, which solves the problem of personnel attribute association. The personnel attribute entity is extracted from the unstructured personnel resume text using the prediction findings. The framework is divided into three parts: the first part is personnel attribute entity extraction, which uses the BERT model to extract personnel attribute entities such as the birth date and employer from the resume text of financial personnel; the second part is personnel attribute association, which is defined and analyzed by fill in the personnel template, associates the personnel attribute name with the personnel attribute value, and associates the relevant personnel attribute value to form a job event or education event; the third part is the construction of the personal relationship graph, which uses the personnel template to discover the relationship between personnel. Finally, the character relationship graph storage model is defined and the graph database is used to store the character relationship graph.The model consists of an input layer and 24 hidden layers. The output of the last hidden layer is the vector representation of each character corresponding to each character . The vecClassification of entities inputs the vector encoding of the character into the linear classifier, and then, the softmax operation is gone through to obtain the probability distribution of each symbol corresponding to each personnel attribute label, and the personnel attribute label corresponding to the maximum probability value as the final personnel attribute label of the current character classification is selected . After oThe personnel attributes  extracted from the BERT model may have multiple candidate values. Therefore, it is necessary to determine the personnel attribute values that uniquely correspond to some personnel attribute names to associate them with the personnel attribute values associated. In addition, there is an association relationship between some personnel attribute values, and the personnel attribute values with the association relationship constitute an event instance.For example, attribute values such as tenure time, resignation time, tenure unit, tenure department, and position form a tenure event instance. Therefore, it is necessary to correctly associate and combine relevant attribute values to identify and filter out the correct event instance . The perThe key of the personnel template is used to identify the attribute of the personnel, which is usually represented by a string; the value of the personnel template corresponds to a specific key, which can be an array or a particular value. A legend whose value is an array is called a multivalued attribute of the person template, and a key whose value is not an array is called a single-valued attribute of the person template . The sinThe core of completing the task of personnel attribute association is to establish the association between the multivalued attribute entities of personnel. The multivalued attributes of the personnel template are filled in through the BERT-Template method to complete the association between the multivalued attribute entities of the personnel , 28. ThiQ represents the final event instance vector, Vi represents the character attribute entity vector, fwi represents the feature vector group of the character attribute entity, MaxPooling represents the maximum pooling operation, and ⊕ represents the vector splicing operation. First, the ultimate pooling operation (MaxPooling) is performed on the feature vector group of the person attribute entity to obtain the maximum value of each dimension of the vector in the vector group, and then, the total value of each size is combined into a new vector as the person attribute entity vector, the record is Wi; the maximum pooling operation is performed on the character vector group of all personnel attribute entities of the current event instance, all personnel attribute entity vectors {W1, W2,…, Wi,…, Wn} of the current event instance are obtained, and all personnel attributes are spliced. The entity vector gets the final event instance vector Q. The last is the output layer of the model. The event instance vector is sent to a fully connected network for classification at the output layer to determine whether it is an actual event instance.In the formula, f1, f2,…fi,…, fn|n ≥ 0}, where fi represents the multivalued attribute of personnel, denoted as fi={u1, u2,…, ui,…um|m ≥ 2}, where ui is the attribute value of the person. The same multivalued attributes in personnel template B and personnel template C are denoted as attr_B and attr_C. A certain personnel attribute entity in personnel templates B and C is denoted as uB and uC, respectively. If {uB=uC|(uB ∈ fi ∈ attr_B)∧(tC ∈ fi ∈ attr_C)} ≠ ∅, it can be considered that personnel template B and personnel template C have the assignment attribute fi of co-occurrence relation personnel in multiple dimensions, namely, person B and person C have a certain relationship. When fi is a graduate school, B and C are considered to have alumni; when fi is a work unit, B and C are considered colleagues.A person template contains a list of event instances consisting of single-valued person attributes and multivalued person attributes. Hierarchical people templates can be used to discover relationships between people entities. A certain multivalued attribute of the personnel template can be denoted as attr =  {The person entity is mapped to the person node in the Neo4j graph database, the single-valued attribute of a person and its corresponding person attribute entity are mapped to the attribute key-value pair of the person node in the Neo4j graph database, the colleague relationship is mapped, and alumni relations in the Neo4j graph database are mapped as an edge.After defining the data model of the personal relationship graph in the graph database, the information in the person template and the personal relationships is stored that is found in There is no public resume text dataset in the Chinese financial field. Therefore, this study crawled the annual reports, prospectuses, and documents on the official website of listed companies from the internet and obtained the unstructured personnel resume text information in the financial announcements. The unstructured personnel resume text information is labeled with BIO  related to personnel attribute entities through manual annotation. The basic knowledge of the personnel attribute entity annotation dataset is shown in A hierarchical personnel template is manually constructed, and several experts in the financial field are invited to proofread and modify the generated dataset to ensure the accuracy of the dataset. The basic information of the artificially constructed hierarchical personnel template dataset is shown in This study uses albert_large_zh as the basic model, consisting of 24 transformer encoders, each transformer encoder contains 16 attention heads, and the dimension of the word vector is 1,024. In the fine-tuning training phase, the batch size is set to 32, the corresponding learning rate is set to 2E-5, the warm-up rate is set to 0.1, the maximum sentence length is set to 128, the dataset is iterated six times, and Adam is used for optimization on a RTX2080Ti machine training.F1 value as evaluation indicators for entity extraction of personnel attributes. They are compared with the method based on heuristic rules and the classic BiLSTM-CRF [This study uses precision, recall, and LSTM-CRF  method. F1 value. However, the heuristic rule method relies on manual regulations, and it is difficult for the authorities to cover all cases. Therefore, the precision and recall are the worst compared with the F1 value and the other two methods.It can be seen from After extracting the personnel attribute entity from the unstructured text, a hierarchical personnel template is constructed through the BERT-Template method to complete the personnel attribute association. The training data are divided into a training set and a test set according to the ratio of 9 : 1, and the training set is used for 8 000 iterations of training. The test set is used to test the model during the training process. The BERT model replaced the BiLSTM-CRF model as a comparative experiment.The evaluation indicators of the final classification of educational experience event instances and employment experience event instances are shown in The F1 value of the BERT-Template method is 0.03 and 0.03 higher than that of the BiLSTM-CRF form in the classification of job experience and education experience events, respectively. Overall, the BERT-Template process is better. The event classification results on work experience and educational experience is shown in Figures After obtaining the hierarchical personnel templates, the colleague and alumni relationships between the personnel templates are discovered and extracted. The removed personnel relationship and personnel template information are used to build a knowledge graph and store it in the Neo4j graph database. The hierarchical personnel templates constructed by artificial heuristic rules, BERT-Template method, and BiLSTM-CRF method are used to discover and extract personal relationships, and the artificially created accurate hierarchical personnel templates for personnel relationship discovery and extraction are carried out and compared. The comparison results are shown in F1 value on the basis of their results, we find that the precision rate increased by 0.07 and 0.23, respectively, and the F1 value increased by 0.07 and 0.22, respectively. The precision value is more accurate than F1 value. Compared with the BiLSTM-CRF process, the relationship between colleagues and alumni is accurate compared with the heuristic rule method, in terms of colleague and alumni relations, the precision rate increased by 0.07 and 0.23, respectively, and the F1 value increased by 0.07 and 0.22, respectively. Overall, the BERT-Template method can achieve better results.In This study studies the construction method of character relationship graphs in the Chinese financial field and proposes a framework for constructing a character relationship graph in the economic area: person attribute extraction and association problem in unstructured personnel resume text. The current approaches for obtaining information from user resumes do not function well with unorganized user descriptions seen in economic announcements, nor do they work well with papers containing the same users. The BERT model is used to accurately extract personnel attribute entities, the fine-tuned trained BERT model is used to classify event instance vectors, a hierarchical personnel information template is constructed, and the problem of personnel attribute association is solved. Finally, the filled personnel information template is more convenient and accurate. The relationship between people is extracted, and a relationship map of people is built. Experiments show the framework's effectiveness for constructing person relationship graphs in the financial field. The future scope of this research is that the proposed BERT-based framework for constructing a relationship graph of Chinese characters in the financial field is proposed.This framework relies on manually annotated datasets. The next step is to consider using weakly supervised learning methods to expand the dataset further and reduce manually constructing datasets.


Although seemingly effortless, the control of the human hand is backed by an elaborate neuro-muscular mechanism. The end result is typically a smooth action with the precise positioning of the joints of the hand and an exerted force that can be modulated to enable precise interaction with the surroundings. Unfortunately, even the most sophisticated technology cannot replace such a comprehensive role but can offer only basic hand functionalities. This issue arises from the drawbacks of the prosthetic hand control strategies that commonly rely on surface EMG signals that contain a high level of noise, thus limiting accurate and robust multi-joint movement estimation. The use of intramuscular EMG results in higher quality signals which, in turn, lead to an improvement in prosthetic control performance. Here, we present the evaluation of fourteen common/well-known algorithms  for the direct and proportional control of a prosthetic hand. The method involves the estimation of the forces generated in the hand by using different algorithms applied to iEMG signals from our recently published database, and comparing them to the measured forces (ground truth). The results presented in this paper are intended to be used as a baseline performance metric for more advanced algorithms that will be made and tested using the same database. The anatomy concerning the muscles controlling the human hand demonstrates the complexity of the system responsible for the control of voluntary movement. The majority of muscles controlling hand and finger movements are located in the forearm, and they have long, sometimes multiple tendons crossing several joints, sometimes acting on several fingers. Thus, the control of hand and individual finger movements involves a complex pattern of neural activation and the inhibition of several muscles, ultimately resulting in a smooth action with the precise positioning of the joints with a force that is gradually adapted to interact with the surroundings .The underlying mechanics and mechatronics in hand prostheses have been significantly improved in recent decades ,3 and prThe real bottleneck preventing the optimal use of a prosthetic hand in a dexterous manner is the control part. More precisely, the methods for decoding velocities and forces of individual digits and the wrist, while interpreting the desire to move the joints of a prosthetic hand by a user, are still far from being intuitive and robust . In mostSome of the control solutions that provide a higher level of functionality for prosthetic hands are oriented towards improving the quality of the signals used for control. To do so, it is necessary to obtain EMG signals close to their source, thus avoiding distortion and the loss of information that occurs due to mixing with signals from other muscles and attenuation in biological tissue. Acquiring the EMG signal close to the desired muscle has proven to yield superior results using fully implantable devices that record EMG signals directly from the surfaces of multiple muscles , includiTo contribute to the body of knowledge within the field of prosthetic control, our previous effort was directed towards obtaining and disseminating a database of iEMG signals  that couFourteen male able-bodied volunteers aged between 25 and 57 years (mean 39 years) participated in the study which was divided into two protocols. As the volunteers were equally divided between protocols and two of the volunteers were included in both protocols, the final database contained sixteen files, eight for each protocol. All the volunteers signed an informed consent, and the study was approved by the Regional Ethical Review Board in Lund, Sweden (Dnr 2017-297).The signals database  was recoThe short residual limb (SRL) protocol targeted the following muscles: flexor carpi radialis (FCR), extensor carpi radialis (ECR), pronator teres (PT), flexor digitorum profundus (FDP), extensor digitorum communis (EDC), and abductor pollicis longus (APL);The long residual limb (LRL) targeted the following muscles: flexor digitorum profundus (FDP), extensor digitorum communis (EDC), abductor pollicis longus (APL), flexor pollicis longus (FPL), extensor pollicis longus (EPL) and extensor indicis proprius (EIP).The iEMG signals were recorded from 9 forearm muscles divided into 2 groups which were associated with the 2 levels of amputation:11 Ω on the entire bandwidth, and a noise level lower than 1 µVRMS. To reduce the interferences induced in the leads between the fine wires and the amplifier, shielded differential preamplifiers were used in close proximity to the fine-wire skin entry points. In parallel with the iEMG recordings, forces resulting from hand muscles contractions were also recorded using the measurement device which kept the hand stationary during the procedure. In total, 9 force gauges picked up the resulting hand forces: one per finger (D2 (index finger)–D5 (little finger)), two for the thumb, and three for the wrist. The recording protocol was guided by an automated graphical user interface which, in a strictly timed manner, displayed commands and cues to the volunteer. It also provided feedback on the exerted force which was crucial for force matching/tracking tasks. An example of this functionality is the sine wave tracking task which started by instructing the volunteer to perform maximal voluntary flexion and the extension of a finger, thumb or the wrist, the adduction–abduction of the thumb, or the pronation–supination of the wrist. Although the inserted electrodes targeted only a subset of the muscles involved in the abovementioned hand movements, the protocol was consistent for all volunteers and all electrode placements. This way, it was possible to compare muscle synergies and crosstalk between iEMG channels, which is not in the focus of this study, but might be of interest for other studies that use the database. Then, the software generated a low-frequency sine wave with an amplitude equal to 20% of the maximal voluntary flexion/extension and a frequency of 0.1 Hz and displayed it in the same graph with the finger or wrist force that the volunteer produced  were amplified and digitalized using the Quattrocento biomedical amplifier system from OT Bioelettronica, Torino, Italia. The amplifier had a common mode rejection ratio (CMMR) higher than 95 dB, an input resistance higher than 10uced see . The ideAlthough the measurement protocol included various hand gestures, for the scope of this paper, only the sine tracking data were used because the aim of this paper is to produce the direct and proportional control of a multi-joint prosthetic hand.https://figshare.com/s/06f113bd74ecf6384729 (accessed on 2 June 2022)).As the iEMG was recorded at 10 kHz, the force data were up-sampled for easier manipulation. In addition, the commands and cues presented to the volunteers were recorded for the offline segmentation of the measurements into individual finger/wrist movements. The Matlab data container files (*.mat) can be found here: (0f) and its harmonics , which also exceeded iEMG signal amplitude, a band-stop comb filter comprising third-order Butterworth notch filters (0f = 50 Hz and Δf = ± 2 Hz) was applied to the recorded signals [As the methods presented in this paper are intended for online implementation, the recorded signals were minimally pre-processed. Namely, the powerline noise was superimposed with the iEMG signal, which was relatively weak compared to the sEMG. To remove the powerline base frequency  and refined based on the minimal root mean square error (RMSE) between a normalized force gauge output and the estimated force using the MAV algorithm.The algorithm evaluation procedure was designed with a specific prosthesis-use scenario. The performance of the algorithms was tested in a similar fashion as that shown in The testing of the iEMG algorithms for extracting signal features was also performed in a manner that corresponded to the real-time application. To achieve this requirement, all algorithms were implemented within the moving/sliding windows of different widths where the computed value was adjoined with the last (newest) sample from the window. This scenario corresponds to the direct control of a prosthesis degree of freedom in real-time using a single muscle.The algorithms selected for evaluation are already well-known from numerous publications in the field of prosthetics ,31,32. D1.Mean Absolute ValueMean absolute value (MAV) is the favored EMG feature in many myoelectric control applications ,34. It i2.VarianceVariance (Var) is the mean value of the square of the deviation of the signal . As the 3.Slope Sign ChangeSlope sign change (SSC) is a time-domain method used to estimate the frequency feature of the iEMG signal . The cal4.Zero CrossingZero crossing (ZC) is the function that counts the number of consecutive EMG samples that change signs within the sliding window . Similar5.Willison AmplitudeWillison amplitude (WA) is a measure related to the superimposed action potentials that make the EMG signal . The WA 6.Waveform LengthWaveform length (WL) is the cumulative length of the waveform over the time window .7.EnvelopeThe signal envelope (ENV) is calculated as the root mean square over the time window.8.Total signal energyThe total signal energy (Etot) is defined as the sum of spectral amplitudes calculated using fast Fourier transformation.9.Teager energy in time domainThe Teager energy operator is a non-linear operator that can track the energy and identify the instantaneous frequencies and instantaneous amplitudes of signals at any instant. It strongly correlates with the nature of the iEMG signal which comprises individual action potentials ,40,41. T10.Teager energy in frequency domainAnother implementation of the Teager energy operator is in the frequency domain (Tf) using fast Fourier transformation .11.Modified Teager energyThe modified Teager energy (Tf_mod) is similar to the Teager energy operator in the frequency domain (Tf) with the only difference being that the frequencies are not squared.12.Mean of signal frequenciesMean of signal frequencies (MNF) is calculated from the windowed iEMG power spectrum as the average frequency .13.Median of signal frequenciesMedian of signal frequencies (MDF) is calculated as the frequency at which the power spectrum is divided into two regions with equal power .14.Firing rateThe calculation for the firing rate (FR) iEMG signal feature is performed by implementing the algorithm presented in . The algThe mathematical formulas used to compute algorithms are given in To provide greater insight into the iEMG signal properties, the abovementioned computational methods were optimized to provide the lowest discrepancies between measured and estimated forces. The optimization (parameter exploration) was performed in a brute-force manner by testing all combinations of parameters within defined ranges. The rationale behind this method is to provide outputs for the incrementally increasing parameters in order to obtain the gradual evolution of error between measured and estimated force. The main reason for having such data is to identify trade-offs between force estimation error and computational complexity.PC with Intel i7-6700K, 64-bit processor at 4 GHz;Teensy 4.0 with Cortex-M7, 32-bit processor at 600 MHz;Teensy 3.6 with Cortex-M4, 32-bit processor at 180 MHz;BLE-Nano with Cortex-M0 (NRF51822), 32-bit processor at 16 MHz;Arduino-Nano with ATmega328, 8-bit processor at 16 MHz.The computational complexity of individual algorithms is estimated theoretically and practically. For the theoretical computational complexity, which is completed in big O notation, the algorithms were analyzed down to the basic arithmetic operations. The results for theoretical computational complexity are given in The implementation on the PC platform was performed with Matlab 2018b  scripts where the timing was an average of all sliding window computations within the whole signal. It should be noted that the execution time of algorithms on the PC platform was not deterministic nor constant, as the operating system  was not in real time. To minimize the variability of the execution time required for single window processing, the results were based on the averaged values for all signals and all subjects. Thus, the execution times on the PC platform are given only for inter-algorithm comparison. The implementations on other real-time platforms were written and compiled in the Arduino IDE environment using a single-precision floating-point format (float32) which guarantees the same conditions for all three processors. All functions, except for fast Fourier transformation (FFT), were written using basic mathematical operations. The Arduino library (github.com/kosme/arduinoFFT (accessed on 18 February 2022)) was modified for single precision and used as an FFT function in Arduino IDE. The exact duration of individual algorithm executions was measured by pulling a single digital output port during the computations. Furthermore, for the processors based on the Cortex-M4 or M7 architecture, some of the algorithms were implemented using CMSIS-DSP functions that are highly optimized for these types of operations.The parameter included in all the algorithms that was varied was window size. An additional parameter present in some of the algorithms was the threshold  which was also varied together with the window size. The list of varied parameters is shown in The range of window sizes tested within this study was 50–1050 ms, which is wider than that of the state of the art ,44,45,46The outputs of the algorithms were evaluated with respect to the elicited force which served as the ground truth. As previously stated, both estimated and measured forces were normalized using only the first two full periods of the sine tracking task. The metrics selected for the evaluation of the algorithms included root mean square error (RMSE) and cross-correlation (Pearson), as in . As the A sample of the measured and estimated forces is shown in In addition to the theoretically calculated computational complexity of each algorithm, the first performance parameter of the tested algorithms was the execution time across different platforms. These results are presented in As the aim of this paper is to evaluate the possibility of direct force tracking using only iEMG signals, the most appropriate performance evaluation metric was the root mean square error (RMSE) between the measured and the estimated force signals. This was also the most rigorous metric, as it showed sample-to-sample difference without any time-lag compensation between the measured and estimated joint forces. The RMSE results for each finger movement and each subject (6 iEMG channels × 16 datasets) were aggregated to enable stronger statistical analysis see .p < 10−6) between the mean ranks of MNF, MDF and FR and the rest of the algorithms. In addition, other statistical differences could also be found between some of the other algorithms, as shown in As the cumulative RMSE data did not follow a normal distribution, the Friedman test with Bonferroni correction for multiple comparisons was used to assess the differences between the algorithms. The results of the statistical analysis are summarized in The cross-correlations between the measured and estimated forces are provided in In addition to comparing different algorithms, this paper shows the impact of parameters associated with individual algorithms on the RMSE and cross-correlation metrics. For all the algorithms, the computational sliding window size was used as a variable parameter. The range for this parameter was broader than in other relevant publications —between In the case of two-parameter algorithms , the second parameter is the threshold. SSC and ZC use a threshold to exclude events within a dead zone, while FR relies on the signal amplitude percentile-based threshold to detect motor units firing above it (above the noise level). The central part of the paper is the database of iEMG signals that we have recently published  that areAn analysis of the RMSE metric of different algorithms showed statistically significant differences between FR and all other algorithms. This clear advantage of FR is somewhat unexpected, as some of the other algorithms are commonly used, and preferred, for prosthetic control, especially in commercially available systems . We hypoIn addition, the optimal window size for different algorithms was also investigated in the current study. A wide range of window sizes (50–1050 ms) was used to assess the performance of the algorithms. The results indicating the best tradeoff between RMSE, correlation, and the controller delay (due to the window size) for the MAV algorithm are presented in The results of applying simple computational algorithms with this database could also be compared to other studies. For example, Kamavuako et al. , in theiIn terms of computational complexity, the approach of using simple feature extraction algorithms as the main force regression method significantly reduces the necessary processing power, which is an important step in the development of an embedded real-time prosthetic hand controller. Preferably, the controller should provide an immediate joint force output response to the user command to enhance the sense of agency of the prosthetic hand. Due to the latencies of the motorized actuator system, the computational aspect of the prosthesis control chain should have a delay below 125 ms  so that In the context of the iEMG used within the scope of this paper, which was sampled at 10 kHz, the embedded implementations of MAV, Var, WA, WL, Env, and Ttd were able to perform real-time control for the window sizes found to be optimal. In other words, with window sizes up to 450 ms (4626 samples), the listed algorithms would execute computations under 0.1 ms (running on a Cortex-M7), ensuring a window increment of only a single sample. In the case of other time-domain algorithms , the increment should be more than two samples (>0.2 ms), which still fulfils the commonly used computational delay requirement  by far. A strong point regarding the methodology presented in this paper is the calibration phase, which tunes the output of individual algorithms to match the level of the desired joint force. This phase comprises only two repetitions of slowly increasing/decreasing self-perceived muscle contractions in the case of amputees, or isometric muscle force in the case of the signals used within this paper. Thus, the transfer function between iEMG and the force of an actuated prosthetic hand joint is governed by self-selected maximal muscle activity level. Although this method is intended for the recording/testing protocols associated with this iEMG database , there are also implications for real-world prosthetic control strategies. Specifically, based on our findings, by executing one or two slow muscle contractions per controllable degree of freedom while recording iEMG, it should be possible to establish direct muscle control. Therefore, the initial calibration process could be relatively quick when compared with the machine learning methods that usually require a large number of repetitions to build an accurate movement model.A limitation of the results presented here is related to the dataset of iEMG signals that was recorded and made publicly available . Some ofThe methods presented in this study were devised in line with recent trends in prosthetic technology, namely, osseointegration , targete


We consider the model of two coupled oscillators with Kerr nonlinearities in the rotating-wave approximation. We demonstrate that for a certain set of parameters of the model, the multi-photon transitions occur between many pairs of the oscillator states simultaneously. Also, the position of the multi-photon resonances does not depend on the coupling strength between two oscillators. We prove rigorously that this is a consequence of a certain symmetry of the perturbation theory series for the model. In addition, we analyse the model in the quasi-classical limit by considering the dynamics of the pseudo-angular momentum. We identify the multi-photon transitions with the tunnelling transitions between the degenerate classical trajectories on the Bloch sphere. Nonlinear oscillator networks were suggested as a framework for universal quantum computation5, and also quantum nonlinear oscillators were suggested as a tool for non-classical states creation such as squeezed states6, entangled states8 and cat states9. Also, such models are a fundamental tool to study quantum-classical correspondence10.For decades, the models consisting of interacting nonlinear oscillator modes attract much attention because of their importance for various fundamental concepts of quantum physics, quantum information and nonlinear dynamics. The phenomena present in such models include quantum chaos11, trapped ions12 and superconducting circuits13. The presence of a dynamical bifurcation point was experimentally demonstrated in RF-driven Josephson junctions14 and transitions between two basins of attraction were observed in a nano-mechanical resonator. Also, non-degenerate parametric amplifiers were created based on the Josephson junction arrays13.The models of interacting nonlinear oscillators can be realised in various experimental setups including optomechanical systems15. In this regime, it is possible to use the quasi-classical approximation, but the quantum effects are important as well. The interplay of complex classical dynamics and quantum effects such as quantum tunnelling leads to new interesting phenomena. For example, it was shown that in the model of a single oscillator mode with Kerr nonlinearity, tunnelling affects the switching rate between the stable states16.Lots of efforts are devoted to studying the nonlinear oscillator systems in the mesoscopic regime4. Also, the interconnection between tunnelling and multi-photon transitions was established in many systems20. In particular, for a single nonlinear oscillator with Kerr nonlinearity, tunnelling between different regions of the phase space is equivalent to simultaneous absorption or emission of many oscillator quanta in the quasi-classical limit.The specifics of tunnelling in such systems are determined by the complex structure of the phase space. For the models exhibiting bi- or multi-stability, there exist several different classical trajectories with the same energies. This opens way for tunnelling transitions between the corresponding quantum states. However, as the tunnelling transition amplitudes are exponentially small, the certain resonant condition should be usually satisfied in order to achieve a non-vanishing tunnelling probability21. The classical limit of this model can be described as the dynamics of the pseudo-angular momentum on a two-dimensional sphere. Among the classical trajectories, there exist ones with equal energies, which makes tunnelling transitions between them possible. We show that tunnelling between such trajectories can be described with the perturbation theory in the coupling constant, and tunnelling transition is equivalent to the exchange by many quanta between the oscillators. We use high-order perturbation theory to study these processes and account for both resonant and non-resonant contributions. We identify the resonant condition for tunnelling between different classical trajectories and we prove rigorously that this resonant condition is satisfied simultaneously for many pairs of the oscillator states. Also, it is independent of the value of the coupling constant between oscillators, in contrast with many systems demonstrating similar behaviour (such as22). This fact is a consequence of an internal symmetry of the system Hamiltonian which we establish in all orders of the perturbation theory series. Also, we discuss how the presence of such symmetry modifies the energy spectrum and the structure of the eigenstates.In this work, we consider the model of two coupled nonlinear oscillators in the rotating-wave approximation (RWA)24 of dissipative time crystals (DTC)26. The results of this work could be useful to study the quantum effects in the DTC. In addition, the discovered symmetry extends the range of known symmetries in quantum–optical systems30.These results could have applications for quantum information processing and quantum state manipulation, in particular, the generation of the entangled states of two modes. We believe that the predicted features can be observed in systems with high-quality oscillator modes with a pronounced Kerr nonlinearity, such as the plasmon modes of Josephson junction arrays or the phonon modes of trapped ion ensembles. Both mentioned systems represent a natural realization of a system of coupled quantum nonlinear oscillators well isolated from the environment Also, the considered model is closely related to some models21, and the model Hamiltonian readsg is the coupling constant between the oscillators. As the counter-rotating terms are not present in (N). Therefore, the total Hilbert space N quanta in the oscillators: a and b respectively), andWe consider the model of two oscillators with linear coupling and Kerr nonlinearities. Let the frequencies of the oscillators be mentclass2pt{minimmentclass2pt{minim31 in the classical external field. Namely, in the limit The model  is closeentclass1pt{minimag as a theoretical tool. Because of that, let us first consider the model without perturbation. In this case, the Hamiltonian  perturbation of the Fock states of the system: the eigenstates remain close to Fock states. This is not the case when the multi-photon resonance condition is satisfied. Due to the reasons indicated above, even at small couplings the structure of the Hamiltonian eigenstates and the temporal dynamics of the system wave function for integer In the absence of degeneracy in the unperturbed model ,,6), for n. This result is in agreement with Eq.  of the presence of many simultaneous anti-crossings at mentclass2pt{minimLet us consider the coupling term between the oscillators as a perturbation. As commented above, at integer g for the system energies. However, at non-integer n-th Fock state Because of the degeneracies, one can not use directly the non-degenerate perturbation theory series in n and To some extent, this expansion is valid for xpansion  up to thSurprisingly, the following identity is valid for the perturbation theory corrections at n and n and Strictly speaking, the identity  makes sen can be made in a natural way for all k. For that, the whole energy spectrum n. To do this, let us assume that the Hamiltonian :15\docuequality  valid fo33 for several lowest orders, and the sketch of the proof was given previously34.We should note that the analogous properties hold for the model of a single nonlinear mode with Kerr nonlinearity driven by the classical external field  exp exp23) eg to Eq.   emerges which divides the phase portrait into three regions with a stable point inside each one (denoted as g, only two stable points remain. Depending on the value of the ratio Let us discuss the structure of the phase portrait in detail. At 37.The value of iltonian  as a funX-Y plane.The dependence of the positions of the stable states on the dimensionless coupling strength g, the classical trajectories are close to the circles in the X-Y plane (see Fig. X-Y plane. However, we state that the condition for resonant tunnelling remains the same for all values of g. In addition, the numerical diagonalization of the Hamiltonian (Now let us discuss how tunnelling modifies the classical picture and establish the relation between tunnelling and multi-photon transitions. Tunnelling transitions are possible providing that there exist classical trajectories with the same energies. Because of the structure of the classical phase portrait, this holds for mentclass2pt{minimFor the model of two coupled quantum oscillators with Kerr nonlinearities and linear coupling, we studied the multi-photon transitions between the oscillators. We showed that for certain parameters of the model, the resonant condition for multi-photon transitions is simultaneously satisfied for many pairs of the oscillator Fock states. This holds even for the moderate coupling strength between oscillators, and this is the consequence of a special symmetry of the oscillators Hamiltonian.The latter is related to the structure of the perturbation series of the model eigenenergies and was proven with help of analytical continuation of the Hamiltonian for non-integer numbers of quanta.Also, in the quasi-classical limit, the phase space of the two coupled oscillators can be mapped on a sphere, and the multi-photon transitions can be interpreted as tunnelling transitions between the trajectories lying in different regions of the classical phase space. Thus, when the resonant condition is satisfied, tunnel transitions affect the whole region of the classical phase space.We believe that the results obtained in this work could be relevant for the experiments involving high-quality oscillator modes with low occupation numbers, such as the plasmon modes of the Josephson junction arrays or phonon modes of trapped ions ensembles. In particular, the independence of the multi-photon resonances positions could be used for the measurements of the Kerr coefficients of the modes. Also, the multi-photon transitions provide a way to create the entangled states of two oscillators. In addition, the obtained results could be used for certain models of dissipative time crystals in the quantum regime, and the symmetry discovered in the considered model may allow obtaining new exact results in quantum-optical systems.Supplementary Information.


This paper presents a formulation of a preview optimal control strategy for a half-car model equipped with active aerodynamic surfaces. The designed control strategy consists of two parts: a feed-forward controller to deal with the future road disturbances and a feedback controller to deal with tracking error. An anti-jerk functionality is employed in the design of preview control strategy that can reliably reduce the jerk of control inputs to improve the performance of active aerodynamic surfaces and reduce vehicle body jerk to enhance the ride comfort without degrading road holding capability. The proposed control scheme determines proactive control action against oncoming potential road disturbances to mitigate the effect of deterministically known road disturbances. The performance of proposed anti-jerk optimal control strategy is compared with that of optimal control without considering jerk. Simulation results considering frequency and time domain characteristics are carried out using MATLAB to demonstrate the effectiveness of the proposed scheme. The frequency domain characteristics are discussed only for the roll inputs, while time domain characteristics are discussed for the corresponding ground velocity inputs of bump and asphalt road, respectively. The results show that using anti-jerk optimal preview control strategy improves the performance of vehicle dynamics by reducing jerk of aerodynamic surfaces and vehicle body jerk simultaneously. During the past few decades, the significant advancement in the design of automobiles employing active suspension components has resulted in an improvement in ride comfort and road holding. Even though the ride comfort in the vehicle ride has vastly improved, driving on uneven roads is still a serious concern for automotive engineers . The ridControl system theory plays an essential role in increasing vehicle performance by adjusting the power input required by the actuators. Researchers in the automobile industry have utilized various dynamical models with different control strategies to evaluate vehicle performance in terms of ride comfort and road holding capabilities. In ,11,12,13With the advent of high-speed vehicles, aerodynamics has become increasingly important in terms of improving ride comfort and ride holding capability. The vehicle outfitted with Active Aerodynamic Surfaces (AAS) significantly increases negative lift force with vehicle speed, improving ride comfort and road holding capabilities. However, this complicates the dynamics of the vehicle models, necessitating the use of a sophisticated control strategy to handle such complicated dynamics. Various control approaches for the control of vehicles equipped with AAS exist in the literature, resulting in considerable improvements in ride comfort and road holding capabilities. The preliminary research work for the control of vehicles equipped with aerodynamic surfaces has been reported in ,24,25 utPreview control scheme is considered to be an impressive control strategy for the vehicle performance against future information about road disturbances. These disturbances can be detected using a look-ahead sensors, installed in the front of the vehicle. The look-ahead sensor is used by many researchers ,39,40 toA comprehensive case study for the control of half-car model equipped with active aerodynamics surfaces is presented.We consider an anticipation of future values of deterministically known road disturbances in the design problem.To reduce the effect of jerk related to the ride comfort of a vehicle, a weighted norm of jerk control input is included in the pre-specified performance index. The minimization of the performance index accounts for improvisation of ride comfort and road holding capability.The feed-forward controller is designed based on the formulation for the preview control subjected to oncoming measured road disturbances.Simulations were carried using MATLAB that demonstrates the effectiveness of the proposed scheme in terms of minimizing control jerk, and assuring ride comfort and road holding capabilities. It was also demonstrated that the designed control algorithm has a proclivity to anticipate future measured disturbances and to take remedial action accordingly ahead of the occurrence of disturbances.Motivated by these observations, in this manuscript we consider a four-degree-of-freedom half-car model equipped with active aerodynamic surfaces that accounts vertical acceleration of the vehicle body. The aim is to formulate an anti-jerk preview control (AJPC) strategy based on the feedback and feed-forward control that can reliably reduce the jerk of AAS to improve its performance, and reduce the vehicle body jerk and other outputs to improve the ride comfort while maintaining the road holding capabilities. The distinguishing features of this work are given as follows.The rest of paper is organized as follows. a and b are the distances between the mounting points of suspension system and C.M. In this paper, a four degree-of-freedom half-car model with active aerodynamic surfaces is used to investigate its performance in the presence of detected oncoming road disturbances. M is the sprung mass, I is the moment of inertia of the vehicle. Equations fr=kEquation  represenquations  and 6)  1)Mz¨c=Mz¨c=(1)Mquation (Iθ¨=(fr+untiating  and 8)  (1)Mz¨c=v is the speed of the vehicle, S is the surface area of the airfoil, and The main goal of this research is to adopt an anti-jerk optimum control method based on active aerodynamics to increase AAS performance and ride quality. The installation of AAS on sprung mass produces the required control forces to affect the vertical motion of the vehicle body. These forces can modify the sprung mass system’s vertical load, which in turn affects the acceleration of pitching and heaving, tyre deflection, and suspension deflection. The aerodynamic surfaces forces, This, study consists of the measurement of road profile from the sensor data, and to utilize it to design an active aerodynamic based preview control strategy. In order to evaluate the performance of the proposed controller with respect to the vehicle suspension performance characteristics, two types of disturbance inputs, a bump velocity input an asphalt road disturbances given to the right are considered. As shown in V represents the vehicle speed of 20 m/s.The following equation represent the corresponding ground velocity input.ous work , the co-The corresponding performance index that need to be minimized by suitable control law, and can be expressed in terms of heaving acceleration, roll acceleration, suspension deflection, roll angle, tyre deflection and jerk control input is given byThe weighting constants Consider a half car whose dynamics can be represented by the following continuous-time state-space model.Assumption A1.It is assumed that all the states of the system under consideration are measurable and available for feedback.Assumption A2.The tire damping coefficient can be ignored because it is much smaller than tire stiffness, and it is assumed that the wheel is always in contact with the ground.Assumption A3.The drag forces generated by active aerodynamics surfaces and vehicle’s body are ignored, and the actual dynamics of the AAS are beyond the scope of this study. Therefore, only the control jerk caused by the AAS is taken into account.The control law Equation  can be cquation (v(t)=fx   isSubstituting Equation  in 14),,14), theEquation  and vectEquation .28)r(tr(t(27)x˙In this section, simulation results for a four-degree-of-freedom half-car model with active aerodynamic surfaces traveling at 20 m/s are carried out using MATLAB. The results are discussed using various weighting factors for jerk control inputs. The efficiency of the proposed anti-jerk preview control approach is evaluated via two types of characteristics. In the first type, the proposed AJPC and OPC strategy without jerk are compared to evaluate simulation results for frequency domain characteristics. In the frequency domain, opposite-phase roll inputs are evaluated, and simulation results show that, when compared to the OPC strategy without jerk, the proposed AJPC approach successfully enhances vehicle performance. The second type of characteristics is time domain characteristics, which are discussed in two separate scenarios for a bump input and an asphalt road, respectively. Comparing AJPC and OPC strategy without jerk, the results indicate that the proposed control strategy successfully enhances the performance of active aerodynamic surfaces, allowing the AAS to run more smoothly to efficiently manage the control jerk, and reduces the vehicle body jerk to enhance ride comfort.Frequency domain characteristics are one of the most significant characteristics of a vehicle suspension control system to evaluate its performance in the presence of various disturbances. In frequency domain analysis the amplitude ratio between the steady state output and disturbance input is described by the magnitude of the frequency response function. Frequency response provides a great deal of information about just how your system responds to disturbances in different frequency bands. In this paper, the half-car model, which can be excited by two kind excitation inputs i.e., heaving input or rolling input to investigate the performance of the proposed AJPC strategy. Therefore, a harmonic disturbance with appropriate phasing is used to induce roll motion to acquire a better understanding of the performance of closed loop systems in the frequency domain. For AJPC and OPC strategy without jerk, the frequency domain properties of roll acceleration, suspension, and tyre deflection are compared.The frequency domain characteristics are determined using Fourier transform of the closed loop system and Equation  as:(29)XThe amplitude ratio between body motions and disturbance inputs can be determined using the aforementioned equations without taking body forces into account. To derive frequency domain characteristics, only roll inputs that are opposite in phase as In this section, the simulation results are discussed for time domain characteristics, which are very insightful for the transient as well steady-state response of the system. Therefore, the simulation results are carried out for the jerk of active aerodynamic surfaces, vehicle body jerk, vehicle body acceleration, tyre deflection, suspension deflection, and roll angle. The results demonstrate that in the presence of disturbances, the proposed AJPC strategy assists the vehicle better than the OPC strategy without jerk in achieving optimum control jerk, reducing vehicle body jerk and acceleration to improve the ride comfort, and tire deflection to maintain the road holding capability.The performance of vehicle is evaluated for two different scenarios: a bump velocity input and an asphalt velocity road disturbances.This guarantees that aerodynamic surfaces operate smoothly and assist the vehicle in enhancing ride comfort and road holding capability. The simulation results for suspension deflection shows that for the proposed AJPC strategy, suspension deflection is within the allowable space 0.08 m range, as defined by . MoreoveThe simulation results for an asphalt road disturbance defined in  and its The simulation results for the jerk control inputs AJPC and OPC strategy without jerk are shown in AJPC results in 14% decrease in heaving acceleration and a 2% decrease in rolling acceleration. Hence, by reducing both jerk and acceleration in attitude motion of the vehicle body, the proposed AJPC strategy successfully enhances the ride comfort. The rms values in Remark 1.The challenge of how to put the recommended strategy into practice arises since it is preferable to utilize a control force due to the availability of the force actuator. However, a discrete time formulation of their derivative using the change in actuator force In this paper, an anti-jerk preview control scheme is designed for a half car equipped with active aerodynamic surfaces to improve the performance of AAS and enhance ride comfort and road holding capability of the vehicle. The proposed control approach consists of feed-forward part using future road disturbances and feedback part to deal with the tracking error. To validate the performance of the suggested approach, the vehicle is subjected to two types of road disturbances a bump input and an asphalt road. The efficient performance of the proposed control strategy is analyzed by frequency and time domain characteristics. Frequency domain characteristics are discussed for the ride comfort and road holding capability only, while the time domain characteristics are discussed for the performance of AAS, ride comfort, and road holding.The main objective of this work is to avoid abrupt moment of AAS, which has a direct impact on the ride comfort. The simulation results show that the proposed AJPC strategy has successfully reduced the control jerk to improve the performance of AAS, and reduced heaving and rolling jerk, heaving and rolling acceleration to enhance ride comfort without degrading road holding capability. The simulation results are displayed in MATLAB, demonstrating the superiority of the proposed AJPC scheme over the OPC strategy without jerk.The current research work can be envisaged in the near future to design the proposed control strategy by considering the following recommendations.The proposed control strategy can be investigated considering the actual model of active aerodynamic surfaces with experimental implementations or with some commercial software such as CarSim or CarMaker.More advanced robust, and intelligent control algorithms can be considered in the future to tackle both road as well as air disturbances.