Therapeutic antibodies can elicit unwanted immune responses in a subset of patients, which leads to the production of anti-drug antibodies (ADA). Some of these ADAs have been reported to effect the pharmacokinetics, efficacy and/or safety of the therapeutic antibodies. The sequence diversity of antibodies are generated by VDJ recombination and mutagenesis. While the antibody generation process can create a large candidate pool for identifying high-affinity antibodies, it also could produce sequences that are foreign to the human immune system. However, it is not clear how VDJ recombination and mutagenesis impact the clinical ADA rate of therapeutic antibodies. In this study, we identified a positive correlation between the clinical ADA rate and the number of introduced mutations in the antibody sequences. We also found that the use of rare V alleles in human-origin antibody therapeutics is associated with higher risk of immunogenicity. The results suggest that antibody engineering projects should start with frameworks that contain commonly used V alleles and prioritize antibody candidates with low number of mutations to reduce the risk of immunogenicity. Antibody-based therapeutics have been developed and used to treat a variety of diseases, including cancer, autoimmune diseases, allergy, infectious disease and many more . As of DWith modern antibody engineering technology, it is now a routine practice to humanize the candidate antibodies or develop human-origin monoclonal antibodies. Compared to animal-origin antibodies and chimeric antibodies, human and humanized antibodies show significantly lower immunogenicity , 15. HowADA can be generated by T-cell dependent or independent B cell activation pathways . In the in vivo and the experimentally induced mutation that happens in vitro. Among the diverse sequences generated, many are foreign to the human immune system and can elicit ADA responses. A previous study has shown that the unique sequences in the CDR regions of human or humanized antibodies can induce the activation of CD4+ helper T cells  as of Oct 05 2022 . We filtThe amino acid level sequences of the 93 therapeutic antibodies were obtained from the IMGT monoclonal antibody database (mAb-DB) . The cliFor the OAS dataset, the V and J alleles were identified by the OAS team based on previously published workflow and were included as part of the OAS dataset . BrieflyThe allele usage of V and J segments were measured by dividing the number of sequences that use the V or J allele by the total number of sequences in the B cell repertoire sequencing dataset. The allele usage was first measured in the B cell repertoire of each individual. The median percentage of the V and J alleles was used to represent the allele usage in the OAS dataset. For therapeutic antibodies whose sequence only has one closest allele, the usage of the allele was used to correlate with the immunogenicity. For therapeutic antibodies whose sequence has more than one closest allele with the same number of mismatches, the percentages of the alleles were summed up.The gene usage of V and J segments were measured by dividing the number of sequences that use the V or J gene by the total number of sequences in the B cell repertoire sequencing dataset. The gene usage was first measured in the B cell repertoire of each individual. The median percentage of the V and J gene was used to represent the allele usage in the OAS dataset. For therapeutic antibodies whose sequence only has one closest gene, the usage of the gene was used to correlate with the immunogenicity. For therapeutic antibodies whose sequence has more than one closest gene with the same number of mismatches, the percentages of the genes were summed up.The deletion of V genes are detected using a previously published criteria . BrieflyFor each non-deleted-gene, an individual can either have one (homozygous) or two (heterozygous) alleles of the gene. However, because of the introduced random mutations, a sequence in B cell repertoire has a low but non-zero probability to be mapped to an allele even if the allele is not present in the genome. We reason that, despite the existence of mutations, the majority of BCR sequences will be matched to its originating alleles. For a given gene, we first calculate the abundance of the alleles by dividing the number of sequences with a certain allele by the number of sequences with the gene that the allele belongs to. The allele is set as the candidate allele if its abundance is greater than 20%. For each individual, If there is only one candidate allele, the person is annotated as homozygous. If two or more alleles are set as candidates, the individual is annotated as heterozygous of the top two alleles. The frequency of the allele is measured as the number of individuals with a certain allele divided by the total number of individuals who carry the gene in the OAS dataset.Spearman correlation was used to measure the association between clinical ADA rate and variables of interest, including the number of mismatches, the allele usage, gene usage, gene deletion frequencies, and allele frequencies. Spearman correlation was used to measure the correlation of allele usage between different disease cohorts. T-test was used to compare the differences of mismatch numbers between human and humanized antibodies. As a rank-based correlation metrics, spearman correlation does not require data transformation to reduce the effect of outliers. However, we used log transformation to variables that are not normally distributed for data visualization purposes. For data that contain zeros, pseudo counts are added to allow log transformation.Multivariable linear regression was used to test the association between ADA rate and V gene usage among human-origin antibodies while controlling for other factors that could impact the immunogenicity, including the class of drug target, the disease category (based on drug’s first approved indication) and the year of drug’s first approval. The V gene usage was measured as the log2(percent of sequences with light chain V * percent of sequences with heavy chain V). The purpose of the log transformation was to reduce the effect of outliers and make the data normally distributed.R (version R-4.1.1) was used for all statistical analysis .It has been long known that the usages of different V and J genes in the B cell receptor (BCR) repertoire are not equal , 29. SomWe leveraged the BCR repertoire sequencing data from the observed antibody space (OAS) database to quantify the usage of different V and J alleles in the BCR repertoires of 199 individuals . We idenThe OAS dataset includes not only samples from healthy donors but also samples from patients with different diseases, including COVID-19, POEMS syndrome, celiac disease, HIV infection, Light Chain Amyloidosis and Myasthenia Gravis. Our analysis shows that the usage of V and J genes are largely conserved across different disease cohorts . The seWe examined the relationship between the usage of V/J alleles and the immunogenicity of the therapeutic antibodies. We found that the clinical ADA rate is positively correlated with the usage  of V alleles in both light chain and heavy chains of the therapeutic antibody  and the year of drug’s first approval. The result of the multivariable regression again shows a significant association between V gene usage and clinical ADA rate .To summarize, our analysis showed that V alleles are associated with ADA in human-origin antibodies, but not in humanized antibodies. J alleles are not associated with ADA of human-origin and humanized antibodies.The usage of V alleles in a patient population is determined by both its availability in the genomes and the gene-level usage in the BCR repertoires. Specifically, the usage of V alleles can be decomposed into three factors: allele variation , gene deWe used the OAS dataset to estimate the usage of the different V genes in BCR repertoires, the frequency of specific alleles of each V gene, and the frequency of deletions of the V genes  and in vivo animal models (rat and non-human primates) (Therapeutic antibodies are a class of protein-based therapeutics that can elicit unwanted immune responses in patients . ADAs harimates) –40. MoleThe result of our study shows that the usage of V alleles is associated with the ADA rate of the human-origin therapeutic antibodies. The results suggest that antibody engineering efforts should start with antibody frameworks that use popular v alleles to reduce the risk of immunogenicity. Our analysis also identified a significant correlation between immunogenicity and the number of mismatches between the antibody sequence and somatic sequences. The result suggests that mismatch number should be considered as a factor in prioritizing antibody candidates during the drug development process.Our analysis shows that the V allele usage is correlated with the immunogenicity of human-origin antibodies, but not with the immunogenicity of humanized antibodies. This may be due to the fact that there is a large number of mismatches between humanized antibodies and the somatic sequence. Because the V chain has been heavily modified, the usage of the originating V chain may not play a major role in the immunogenicity of the humanized antibody. In addition, the mismatch makes it difficult to reliably identify the originating V chain of the humanized antibody. In fact, a portion of the humanized antibodies are derived from animals, especially in the CDR regions. Furthermore, some of the humanized antibodies used consensus sequences of multiple human V genes rather than any individual human V gene , 42. TheThe study is an observational study. Further studies are needed to establish the causal relationship between V allele usage and immunogenicity. However, existing understanding on the mechanism of immunogenicity suggests that the V allele usage contributes to the immunogenicity. Due to the variation between alleles, antibodies that use rare V alleles are more likely to be seen as foreign antigen in patients that do not carry the allele. The foreign sequence could serve as both T cell and B cell epitope that leads to the development of ADA.The current study analyzed the immunogenicity data at the drug level. In future studies, the patient-level data from clinical trials will be valuable to further understand the relationship between V gene usage and immunogenicity. If there is a causal relationship between V allele variation and immunogenicity, we expect the ADA risk to be lower in patients who carry the same allele used by the antibody drug and higher in patients who don’t carry the allele. Results from the patient level study will help us better understand the personalized ADA risk of patients.https://figshare.com/articles/dataset/Mab_VJ_datasets/22796135.The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found below: Conceptualization: ZH and SS. Methodology: ZH. Data collection: ZH and SC. Data analysis: ZH. Writing – Original Draft Preparation: ZH. Writing – Review & Editing: ZH, SS and SC. Visualization: ZH. Supervision: SS. All authors contributed to the article and approved the submitted version.


The results showed that Gradient Boosting and Extra Trees models had high accuracy, with R2 values above 0.96 and low MAPE and Max Error values for both solubility and density output. The Random Forest model was less accurate than the other two models. These findings demonstrate the effectiveness of tree-based models for predicting the solubility and density of chemical compounds and have potential applications in determination of drug solubility prior to process design by correlation of solubility and density to input parameters including pressure and temperature.This work presents the results of using tree-based models, including Gradient Boosting, Extra Trees, and Random Forest, to model the solubility of hyoscine drug and solvent density based on pressure and temperature as inputs. The models were trained on a dataset of hyoscine drug with known solubility and density values, optimized with WCA algorithm, and their accuracy was evaluated using R Either physical or chemical methods can be used for increasing the solubility of drugs in aqueous media, however the method of nanonization based on physical methods has attracted much attention recently for preparation of drug nanoparticles. One of the physical methods for drug nanonization is supercritical processing which can be used to prepare drug particles at nano size for enhanced aqueous solubility2. For developing this new technique, drug solubility in the supercritical solvent must be known prior to process design and development.The poor water solubility of newly discovered medicines has been a major issue for pharmaceutical industry, and various techniques have been explored and developed to enhance the solubility of drugs in aqueous solutions2 has been reported by different methods such as thermodynamics and data-driven models3. The main inputs for the modeling have been considered to be pressure and temperature as these factors showed the most important effects on the drug solubility change7. It is a crucial step to measure and correlate drug solubility to prepare drugs with nanosized and better bioavailability. The process of supercritical for solid-dosage drugs is also considered as green technology because CO2 gas is usually employed for the drug treatment, and no organic solvent is used for the process10.Estimating pharmaceutical solubility in supercritical solvents such as CO10. The method of supercritical processing can be also developed for continuous processing thereby a hybrid process can be developed using this novel technology. For solubility estimation of pharmaceuticals, basically two main approaches are utilized including thermodynamics and data-driven models. The methods of thermodynamics estimate the drug solubility based on solid–liquid equilibrium, and the computations are performed to find the amount of dissolved drug (solid phase) in the solvent as function of pressure and temperature13. On the other hand, data-driven models estimate the solubility based on the available measured data via training appropriate algorithms. Despite the acceptance of thermodynamic models for pharmaceutical solubility, these models are not straightforward to develop for a variety of drug substances. The method of machine learning which is data-driven model has indicated greater performance in terms of fitting accuracy for estimating different drugs solubility in supercritical solvents16.Other approaches have been studied for enhancing drug solubility in water, however nanonization is a facile and effective process specifically mechanical approaches which do not use chemical agents for preparation of nanomedicines3. However, other methods based on machine learning can be developed and tested for correlation of Hyoscine solubility in supercritical CO2 solvent.Therefore, it is crucial in drug development and pharmaceutical industry to determine solubility as well as density of supercritical solvent, which can have a significant impact on its bioavailability and efficacy. Therefore, accurate prediction of these properties is essential for the success of drug development. The methods of machine learning can be employed for both solubility prediction and solvent density, as the solvent is considered to be compressible in this process. Begum used several methods including SVM, KNN, and linear regression (LR) to predict the solubility of Hyoscine and density of solvent in supercritical processing, and the results were promising17. In this study, we explore the performance of three popular machine learning algorithms, Extra Trees (ET), Random Forest (RF), and Gradient Boosting (GB), in predicting the solubility of Hyoscine drug and density of the solvent as function of pressure and temperature. Furthermore, we use the Water Cycle Algorithm (WCA) to tune the hyperparameters of the models to improve their performance.Machine learning algorithms have shown great potential in predicting the solubility and density of drugs, thereby reducing the cost and time required for drug development21.RF works by building several decision trees, each with a subset of the features and training data, and then combining their results to make a final prediction. ET is similar to RF, but it uses random thresholds to split nodes in the decision trees and randomly selects features for each tree. Both RF and ET have a low risk of overfitting and are robust to noisy data, making them popular choices for high-dimensional datasets22.GB, on the other hand, combines multiple weak decision trees to create a strong predictor. It starts with a simple tree and then iteratively improves the model by adding more trees that predict the residual error of the previous trees. GB has shown to be effective for tasks where the output variable is continuous, such as in regression tasks. However, GB can be sensitive to overfitting and is computationally more expensive than RF and ET-3)3. The dataset was preprocessed using min–max scaling to normalize the input variables. The key aim of this research is to evaluate the RF, ET, and GB models in predicting the solubility and density and to determine the optimal hyperparameters for these models using the WCA algorithm.The dataset used in this study contains 45 observations of Hyoscine solubility and density of the solvent at various combinations of temperature and pressure. The input variables are temperature (in K) and pressure (in bar), while the output variables are solubility (mole fraction) and density  can be mathematically expressed as27:In this subsection, we will introduce three ensemble methods based on decision trees that are employed in this study. Random Forest (RF) is a widely-used ensemble model that is designed to overcome the shortcomings of the conventional Decision Tree algorithm. The RF technique involves training numerous decision tree learners concurrently to minimize model bias and variance. The construction of a random forest model involves randomly selecting N bootstrap samples from the original dataset, and for each sample, an unpruned regression tree is trained. Instead of using every possible predictor, K randomly selected predictors are used as potential splitsx, and produces an output by combining the predictions of C decision trees, where Ti(x) represents a single regression tree generated using a subset of input variables and bootstrapped samples24. The RF method has the potential benefit of performing out-of-bag error estimation during forest construction by reusing training instances that were not used to build individual trees. The out-of-bag subset is a random subset of samples used to estimate the generalization error without consulting an external validation dataset24.The random forest regression predictor takes a vectored input variable 29.RF can determine the importance of input features, helping to enhance model performance on high-dimensional datasets. It involves measuring the mean decrease in prediction accuracy by changing one input variable while keeping others constant. This assigns a relative importance score to each variable and guides the selection of the most influential features for the final model20. This method is a relatively new approach in the field of machine learning and can be seen as an expansion of the widely-used random forest algorithm. It is designed to be less prone to overfitting20. Similar to the random forest, the extra trees algorithm (ET) works by training each base estimator with a random subset of features. In contrast to random forest, it does not randomly choose a feature and its corresponding value to use in node splitting30.One other tree-based ensemble similar to Random Forest is Extremely Randomized Tress or Extra TreesRandom Forest (RF) and Extremely Randomized Trees (ET) are both ensemble learning algorithms that combine multiple DT to create a more robust model. The main difference between the two algorithms is in the way they select the features used in each decision tree. In RF, a random subset of features is selected for each tree, and the best feature is chosen for each node split. In contrast, ET uses a random subset of features for each tree and selects a random threshold value for each feature to split the node. This makes ET even more random than RF, as it completely eliminates the bias that comes from choosing the best feature. ET is therefore less likely to overfit a dataset, but may have slightly higher bias than RF. Overall, both algorithms are highly effective for high-dimensional datasets with many features, and the choice between the two will depend on the specific characteristics of the data and the trade-off between bias and variance.31.As the last one, Gradient Boosting Regression (GBR) is a regression technique that involves combining a set of simple decision trees to form a strong predictor. The technique entails adding decision trees to a model iteratively in order to correct errors made by previous trees. The model learns the difference between the previous model’s predictions and the actual values of the target variable at each iterationThe GBR algorithm uses a loss function to examine the accuracy of the model at each iteration. The objective function measures the discrepancy between the target variable's predicted and actual values. In GBR, the widely adopted loss function is the mean squared error (MSE) function.31:The GBR model is formulated as followsf(x) is the predicted target variable, m-th decision tree, m-th decision tree for input x, and M stands for the quantity of trees in the model.Here, The decision trees used in GBR are typically shallow, with only a few levels of branching. In order to define the tree structure, the input space is partitioned into regions according to the values of the input features. The principle for selecting splits is to maximize the reduction in the MSE of the target variable.The GBR algorithm uses gradient descent to update the weights of the decision trees at each iteration. The gradient of the loss function in relation to the predicted target variable is calculated, and the decision tree is trained to predict the negative gradient. The weight of the tree is then updated to minimize the loss function.32.The Water Cycle Algorithm (WCA) is an optimization algorithm based on population that is inspired by the natural water cycle process. The algorithm is based on the concept of the water cycle, which involves water evaporation from the earth's surface, cloud formation, and precipitation back onto the earth's surface. In its search for optimal solutions, the WCA follows a similar pattern. Initialization, evaporation, precipitation, and river formation are all steps in the algorithm33.During the initialization step, a random population of candidate solutions is generated. Each solution is characterized by a set of parameters that describe the issue at hand. In a function optimization problem, for example, the parameters could be the values of the input variables34.The fitness values of the solutions are evaluated during the evaporation step. A solution's fitness is a measure of how good it is, with higher fitness values indicating better solutions. The fitness values are used to calculate the evaporation rate, which is used to determine how much water evaporates from each solution35.The evaporated water is transformed into clouds in the precipitation step, which are then randomly distributed across the population of solutions. Each cloud represents a potential solution improvement. The cloud fitness values are compared, and the best one is chosenThe selected cloud is used in the river formation step to create a river that flows from the current solution to the selected cloud. The river is represented as a set of solution parameter changes. The differences between the current solution and the chosen cloud determine the changes.36.Evaporation, precipitation, and river formation are all repeated until a stopping criterion is reached. A maximum number of iterations, a minimum fitness value, or a maximum computational time could be used as the stopping criterion36.The WCA's ability to handle multiple objectives is one of its strengths. The goal of multi-objective optimization is to determine a set of solutions that are optimal in terms of several competing objectives. The WCA can be extended to handle multiple objectives by employing the dominance concept. A solution is said to dominate another solution if it outperforms it in at least one objective while failing in none. The WCA can be used to find a set of solutions that are not dominated by any other solution2) at different combinations of temperature and pressure using machine learning models. We utilized three models, Random Forest (RF), Extra Trees (ET), and Gradient Boosting (GB), and fine-tuned their hyperparameters using the Water Cycle Algorithm (WCA). The dataset was preprocessed using the Min–Max scaler to normalize the input features. The methodology can be visualized through the flowchart in Fig. In this work, we aimed to predict the solubility of Hyoscine drug as well as density of solvent (supercritical CO3. The entire data set is displayed in Table 37. The ρscCO2 stand for the density of solvent and y is the solubility in this table. Also, in Fig. The given dataset comprises of 45 instances that represent the solubility of the Hyoscine drug at distinct combinations of temperature and pressure. The input variables considered for the dataset are temperature in Kelvin and pressure in bar, whereas the output variables are density and solubilityIn order to implement the models in this study, we used Python 3.9, along with several libraries and frameworks for machine learning and data analysis including NumPy, Pandas, Scikit-learn, and Matplotlib. Based on the tree-based models used in the work, the results for solubility and density output are summarized in the Table 2 values of above 0.96. Nevertheless, the Random Forest model was less accurate than the other two models. The MAPE values for all models were below 0.04, indicating that the models had a low average percentage error. Max Error values indicate the maximum deviation from the true value, and the models had a relatively low maximum error for both solubility and density output. The comparison of estimated and observed values of solubility and density are visualized in Figs. As shown in the table, Gradient Boosting and Extra Trees models have achieved high accuracy for both solubility and density output, with RVariations of both responses, i.e., drug solubility and solvent density as 3D and 2D representations are indicated in Figs. 2, MSE, MAPE, and Max Error metrics. Our results demonstrated that both Gradient Boosting and Extra Trees models were highly accurate in predicting the solubility and density values of the hyoscine drug. The models had R2 values above 0.96, and their MAPE and Max Error values were relatively low, indicating a low average percentage error and maximum deviation from the true value. These findings suggest that tree-based models, particularly Gradient Boosting and Extra Trees, could be effective in predicting the solubility and density values of the hyoscine drug. This could have significant implications in drug discovery and other chemical industries, where the ability to accurately predict solubility and density values could aid in the development of new drugs or chemical products.In this work, we investigated the effectiveness of tree-based models in predicting the solubility of hyoscine drug and density values of the solvent in supercritical processing of drugs. We utilized Gradient Boosting, Extra Trees, and Random Forest models alongside with WCA as model optimizer to evaluate their performance in predicting the solubility and density of the hyoscine drug, and their accuracy was evaluated using R


Multifocal glasses are a new type of lens that can fit both nearsighted and farsighted vision on the same lens. This property allows the glass to have various curvatures in distinct regions within the glass during the grinding process. However, when the curvature varies irregularly, the glass is prone to optical deformation during imaging. Most of the previous studies on imaging deformation focus on the deformation correction of optical lenses. Consequently, this research uses an automatic deformation defect detection system for multifocal glasses to replace professional assessors. To quantify the grade of deformation of curved multifocal glasses, we first digitally imaged a pattern of concentric circles through a test glass to generate an imaged image of the glass. Second, we preprocess the image to enhance the clarity of the concentric circles’ appearance. A centroid-radius model is used to represent the form variation properties of every circle in the processed image. Third, the deviation of the centroid radius for detecting deformation defects is found by a slight deviation control scheme, and we gain a difference image indicating the detected deformed regions after comparing it with the norm pattern. Fourth, based on the deformation measure and occurrence location of multifocal glasses, we build fuzzy membership functions and inference regulations to quantify the deformation’s severity. Finally, a mixed model incorporating a network-based fuzzy inference and a genetic algorithm is applied to determine a quality grade for the deformation severity of detected defects. Testing outcomes show that the proposed methods attain a 94% accuracy rate of the quality levels for deformation severity, an 81% recall rate of deformation defects, and an 11% false positive rate for multifocal glass detection. This research contributes solutions to the problems of imaging deformation inspection and provides computer-aided systems for determining quality levels that meet the demands of inspection and quality control. Curved components can often meet a wide range of structural requirements because they allow greater geometric freedom in design. They can establish the general look and feel of the design . ComponeMultifocal glasses are a new type of lens that can fit both nearsighted and farsighted vision on the same lens. This property allows the glass to have various curvatures in distinct regions within the glass during the grinding process. However, the disadvantage of multifocal glasses is that when the curvature changes abnormally, the glasses are prone to optical deformation during imaging. Because the glasses are utilized to directly envelop the eyes of the user, the deformation of the glass will cause imaging errors, which will bring trouble or even danger to the daily activities of the user. For example, dizziness may occur when going downstairs, or the inability to correctly decide the location between steps may be hazardous for the person. Progressive multifocal glasses allow people with myopia and presbyopia to easily and effectively improve their vision ,5. The pAlthough the blind spot location is usually not larger than in the other areas, the use of this area is very important and requires special inspection. At present, the degree of deformation of the blind area is inspected by inspectors operating manual instruments. Since imaging deformation has no regular form and clear borders, it is frequently difficult to identify and quantify, particularly on curved multifocal glasses. Furthermore, outwardly curved glasses tend to hinder the identification of deformation defects in multifocal glasses due to their high transmittance and reflectivity. This study develops an optical inspection system to quickly inspect and classify deformation defects in multifocal glasses to replace professional assessors.The rest of the article is composed as follows. First, we review the articles on the current techniques used by visual inspection systems for transparent products. Second, we describe the proposed image procedures to detect imaging deformation defects and determine the quality level of multifocal glasses. Third, we conduct tests and assess the performance of the suggested approach and traditional techniques. Finally, we conclude the contributions and indicate further directions.Automated visual inspection (AVI) is a crucial step in quality assessment for production processes as it assures high quality and enhances productivity by rigorously examining and evaluating all products in an industrial process ,7. The AImage deformation caused by perspective requires image correction before further image processing . In prevTransmission deformation refers to the image quality degradation of an observed object due to refractive media. Previous studies on deformation detection via the transmission of industrial components include Dixon  who desiGlasses are wearable products that are closely related to human daily activities and require strict testing and verification. If the eyeglass lenses have excessive defects, the user’s safety will be compromised. Wang et al.  performeCurrently, most optical inspection systems for transparent glass products mainly detect surface defects and do not identify imaging deformation defects. The imaging deformation defects in curved glass surfaces are highly transmissive and reflective and are difficult to accurately detect . Most ofThis study presents an optical inspection system with familiar norm patterns of image capture and employs a slight deviation control scheme to check for deformation defects, and a mixed intelligent model incorporating a genetic algorithm and a network-based fuzzy inference system to decide the grade of deformation severity of the multifocal glasses. To measure the grade of deformation of a multifocal glass, we first digitally imaged a pattern of concentric circles through a test glass to generate an imaged image of the glass deformation. This deformation image is examined to investigate the deformation’s presence and the defects’ location. Secondly, the imaged image is preprocessed to enhance the clarity of the concentric circles’ appearance. A centroid-radius model is adopted to represent the form variation properties of every concentric circle in the processed image. Thirdly, by looking for small changes in characteristic distance deviations to detect deformation defects through a slight deviation control scheme, a difference image showing the detected deformation defects can be obtained. Fourthly, according to the deformation measurements and locations that occurred during the training phase, the deformation’s fuzzy membership functions and inference rule sets are established. Finally, a mixed model incorporating a genetic algorithm and a fuzzy inference model is adopted to judge the grade in the deformation severity of the detected deformation defects. The adopted test samples are 6.0 mm thick and 48.4 mm in diameter and are arbitrarily drawn from the production line of a multifocal glass producer. In order to capture digital imaging images of norm patterns by testing samples to create imaging deformation maps of samples, this work suggests an imaging acquisition device using a concentric circular pattern for imaging image extraction. When using coordinates for image feature processing, some problems arise. When the image is translated, zoomed, or rotated, the judgment result will be erroneous due to the coordinate changes. Hence, it should be depicted by geometric properties. We use the centroid-radius model  to repre0, y0) and the s-th boundary point . The distances to the u-th circle in the concentric circular pattern are:We use the commonly used concentric circular pattern, which consists of eight concentric circles. The centroid radius u-th concentric circle can yield a distance vector For this pattern of concentric circles, many centroid radii of the Due to scale and rotation invariance, we normalize the distance vector u-th circle to the circle’s centroid and normalizing it to a vector When calculating the distances of centroid radii from the The distance feature vectors of all complete concentric circles in a test image are contrasted with those of the defect-free image, and the distance deviations of the respective edge points are measured to locate potential deformations in the test image. To detect slight deviations in distance variations, we propose a slight deviation control scheme, the exponentially weighted moving average (EWMA) scheme, which is usually applied in statistical process control ,32. We as-th sample point is defined as:UCL) and the control limit of lower bound (LCL) for the EWMA scheme are expressed as [The EWMA scheme is also a good option to detect slight drifts ,34. The essed as :(5)UCLs=L) and the value of constant weight The parameter designs of the chart are the multiple of the standard deviation e schema ,36. FiguThis research applies a fuzzy-related model to automatically detect changes in deformation severity . The genx, y) coordinates of the s-th edge point in a test image, x, y) coordinates of the s-th edge point in the concentric circular pattern image.By contrasting the detected deformation defect image with the concentric circular pattern image, σ is the standard deviation and c is the center point of the Gaussian membership function.The main purpose of the FIS model is not only to transform the measured values into fuzzy membership functions but also to set up fuzzy inference regulations and modes ,39. Its 1, U2, and U3, are the deformation levels of the zones A, B, and C, respectively, and the outputs are deformation levels. For example, while the deformation measure U1 of zone A is small (A1) and the deformation measure U2 of zone B is small (B1) and the deformation measure U3 of zone C is small (C1), the severity of the output Y is a slight distortion (Y1). A fuzzy regulation base containing eighteen regulations is created in this experiment.When the fuzzy membership functions have been set up, the fuzzy regulation base could be created based on the allowance of the deformation level of the multifocal glass. The closer the deformation defect occurs to the middle of the glass, the smaller the allowed allowance is, and the degree of deformation is severe. The closer the deformation flaw region is to the glass boundary, the higher the tolerance is allowed and is then categorized as slight on the deformation level. The fuzzy regulations are created according to the empirical regulations of experts. Three inputs, UWe use the TSK (Takagi–Sugeno–Kang) fuzzy model  as an inANFIS model is mostly a network-based fuzzy inference model set up by merging the concepts of fuzzy theory and neural networks ,41. It iGenetic algorithm mostly uses the procedure of reproduction and inheritance of organisms by means of mutation and crossover of chromosomes. Firstly, the original population of the GA is established by using the membership function parameters of the deformation measures, and the fitness values of each parameter combination are evaluated. The parameters of every parameter combination are then uniformly crossed and mutated, resulting in more diverse parameter values. The merit of this arithmetic is that it could be upgraded from a local optimal answer to a globally optimal solution by a mutation function.When a fuzzy inference system is created, it consists of membership functions of the three zones of deformations, the regulation set, and the inference module. The GA-based ANFIS method primarily optimizes the arithmetic in two stages ,43. The To confirm the capabilities of the proposed approach using concentric circular patterns, the performances of these recommended techniques are assessed on 550 sample images (350 training images and 200 test images) with different degrees of deformation. Each captured image has a size of 256 × 256 pixels, and each pixel contains 8 bits of gray scale. The algorithm of the realized deformation defect detection system is edited on the MATLAB application software platform, and implemented on the MATLAB R2013 version on the desktop . In this study, experimentally detected images are compared for correctness with manually labeled images. In terms of checking deformation defects, recall, precision, and accuracy are adopted as performance evaluation metrics for the proposed models. When the above performance indices are higher, the inspection performance is better. The recall rate is the regions of correctly identified true defects  divided by the regions of correctly identified true defects (TP) plus the regions of true defects incorrectly labeled as non-defects . It can be thought of as the fraction of true defects that are correctly identified in the set of all real defects. The precision rate is the regions of exactly identified true defects (TP) divided by the regions of correctly identified true defects (TP) plus the regions of non-defects incorrectly labeled as defects . It can be thought of as the fraction of these detected defects that are real defects. The accuracy rate is the regions of exactly identified true defects (TP) and the regions of correctly labeled true non-defects (TN) divided by the total regions of a testing instance (TP + TN + FP + FN). It represents the rate of correctly identified defects and non-defects over the total region of a testing image. If the dataset is imbalanced (both defect and non-defect classes have significantly different regions of testing images), the accuracy rate is not a good metric ,45.In terms of determining the deformation quality level, the accuracy rate is modified from individual deformation defects to a performance evaluation index with individual images as the basic unit. The detected deformations in an image are judged combinedly into three categories  by the GA-based ANFIS model and they are checked that each class is correctly classified. The accuracy rate is the number of test images categorized into the exact level class divided by the total number of test images.The size in pixel units of the line thickness of each circle on the concentric standard patterns influences the detection efficiency of the suggested approach for deformation defects. Smaller deformation defects will be more completely identified if an appropriate line thickness pixel size is chosen in the concentric standard pattern. We use a computer program to generate standard concentric patterns with different line thicknesses and then use these standard patterns with different line widths together with test samples to capture test images. We examine concentric circular patterns with line widths from 1 to 6 pixels in concentric circles by the suggested approach. In order to evaluate the inspection performance of multifocal glass deformation defects, To assess the performance of the classification of deformation defect severity in multifocal glasses, three classification models BPN , ANFIS, Using the method based on the Hough transform , two conThis study uses different parameter settings of the capture-related devices to take various test image sets and then select the test image set with the best defect detection effect. The parameter settings of this selected test image set are used as the standard for subsequent image acquisition. During the image acquisition process, the brightness of the acquired image is easily affected by the intensity of ambient light, which in turn affects the detection results. We investigate whether the detection results of the proposed method are susceptible to certain changes in image brightness to test the robustness of the method. In this study, the EWMA control scheme is applied to detect deformation defects, and the GA-based ANFIS method is adopted to categorize the severity of deformation defects. The performance evaluation results using different brightness variations are shown in The proposed concentric circular pattern outperforms the other two norm patterns in detecting slight to average deformations and small to medium area deformations. Therefore, the use of concentric circular patterns is more suitable for detecting deformation defects with less deformation in multifocal glasses. The main merit of this research method is to use the centroid radius descriptor to understand the deformation state of each edge point and use the EWMA control scheme to detect small deformations. In addition, using the GA-based ANFIS classifier model, the parameters that only converge in the local domain are extended to the global domain, which improves the classification effect.Since the proposed method is mainly established on extracting features from geometric properties for deformation detection, it is moderately sensitive to changes in illumination intensity. If the brightness variation range is within (μ ± 1σ) as a whole, it will have little effect on the detection results of this study. However, large changes in illumination can significantly increase grayscale variation, which in turn can significantly affect defect detection. To conquer the restrictions of the proposed method, it is suggested to update the statistics (mean and standard deviation) of the intensity in the training samples when the illumination changes significantly.This research presents a mixed approach constructed using computer vision and fuzzy theory techniques to detect deformation defects and decide the deformation level of multifocal glasses. It investigates the detection of imaging deformation defects in multifocal glass images and the classification of deformation severity. In this study, a vision system using concentric circular patterns for imaging is first developed to obtain test images showing imaging deformed areas and binarize and refine the circle edges in the image. If the boundary point-to-centroid distance value of the concentric circle goes beyond the upper or lower limit of the suggested EWMA scheme, it indicates that there is a deformation defect in this boundary point area. Then, through comparing the discovered defect image, the norm pattern is used to measure the amount of deformation. By partitioning the probable locations of defects into three zones of slight, average, and severe deformation, we summarize the individual deformation measures of the three zones. Finally, a GA-based ANFIS model is suggested to categorize the severity of multifocal glass deformation. The suggested approach is effective and efficient in detecting deformation defects and classifying the severity of deformed regions on multifocal glass images. Testing outcomes show that the proposed methods attain a 94% accuracy rate of deformation severity quality grades, an 81% recall rate of deformation defects, and an 11% false positive rate in multifocal glass deformation detection. Further studies can extend the proposed method to the problem of imaging deformation defect inspection of curved glass-related products, for example, the distortion detection of automobile windshields and the deformation detection of automobile rearview mirrors.


We investigate the life cycle of the large amplitude Higgs mode in strongly interacting superfluid Fermi gas. Through numerical simulations with time-dependent density functional theory and the technique of the interaction quench, we verify the previous theoretical predictions on the mode’s frequency. Next, we demonstrate that the mode is dynamically unstable against external perturbation and qualitatively examine the emerging state after the mode decays. The post-decay state is characterized by spatial fluctuations of the order parameter and density at scales comparable to the superfluid coherence length scale. We identify similarities with FFLO states, which become more prominent at higher dimensionalities and nonzero spin imbalances. In recent years, advances in cooling techniques also allowed investigating this phenomenon in highly controllable environments of ultracold atoms3, as well as developments in THz spectroscopy for superconductors9. Simultaneously, many theoretical considerations have been presented concerning the Higgs mode in ultracold atomic systems: properties of small and large amplitude oscillations14, impact of the trapping potential on the mode characteristics17, angle-resolved photoemission spectroscopy (ARPES)20 and various other ways to induce collective modes24. Moreover, many analytical results have been derived in the weak-coupling limit28. The most well-known property is that the frequency of small-amplitude oscillations is related to the equilibrium value of the pairing gap by 29.Spontaneous breaking of continuous symmetries inevitably leads to the appearance of associated collective modes of a physical system. In the case of a U(1) symmetry these are either gapless Goldstone mode, associated with oscillation of the phase of the order parameter, or the Higgs mode, which is associated with oscillations of the amplitude . The Mexican-hat-like potential is typically drawn to visualize these modes. The Goldstone mode corresponds to motion around the hat in the minimum energy valley; in contrast, the Higgs mode is related to oscillations around the minimum in the perpendicular direction and consequently has much higher energy. Many studies related to the Higgs mode have been conducted in condensed matter  depends on the interaction strength, which is typically characterized by the dimensionless value a is the scattering length and n. Thus, by preparing the system in the ground state for a selected initial interaction strength The most widely discussed method of generation of the amplitude mode, in ultracold atomic systems, is through the interaction quench37. The mode decays into a new state with spatially nonuniform order parameter. Numerical simulations performed for the attractive Fermi–Hubbard model38 indicated that the mode is indeed dynamically unstable, which was consistent with the theoretical predictions.A separate aspect concerns the stability of the amplitude (Higgs) mode. In the case of weak couplings and small amplitude oscillations, Dzero, Yuzbashyan, and Altshuler demonstrated by utilizing linear response theory that the mode is unstable39 or Fulde–Ferrel (FF)40 type oscillations. Upon introducing another degree of freedom to the problem in the form of spin imbalance, the post-decay state indeed acquires properties as predicted for spin-imbalanced systems44, although the final state corresponds to an excited state.The purpose of the presented article is twofold. First, we examine the stability of the Higgs mode in strongly interacting Fermi gases—the systems that are of particular experimental interest. By means of time-dependent density functional theory, we simulate the whole process: from the generation of the Higgs mode via the interaction quench, through the decay dynamics until the equilibration of the final (post-decay) state. Secondly, we investigate the properties of the post-decay state. We show that it is characterized by spatially inhomogeneous order parameter, bearing similarities to Larkin–Ovchinnikov (LO)46. It is a microscopic theory where the system is described in terms of fermionic quasi-particles, defined through Bogoliubov amplitudes: n-th state to be occupied by a particle and a hole with spin projection Normal densities Kinetic densities Current densities Anomalous density The Fermi–Dirac distribution function T (47. The minimization yields static equations for the quasi-particle amplitudes (hereafter we use units where 48).We employ the Density Functional Theory (DFT) formalism to study the properties of the amplitude mode. Many variants of DFT methods exist; here we utilize the one known as Superfluid Local Density Approximation (SLDA), which has been specifically designed to simulate fermionic superfluid systems where interparticle interactions have short range49, which has the generic formA, B and C are constructed in such a way to ensure the correct reproduction of thermodynamics quantities for a uniform system  over the entire interaction regime from weak (BCS regime) to strong (unitary Fermi gas regime). Their explicit forms are given in paper49. The SLDAE functional has been designed to provide accurate results for spin-symmetric systems  and the first derivative The initial state is driven adiabatically towards the new interaction strength Higgs oscillations:  is the amplitude, which in general may depend on time26. Moreover, for the small amplitude Higgs mode, the oscillation frequency is related to the equilibrium value of the pairing gap k is related to maximum and minimum values of the paring field during the oscillations:We start by examining the properties of the amplitude mode. The aim of this section is to demonstrate that the interaction quench method induces the Higgs mode, having the well known properties. The mode is typically regarded as as oscillating system in the effective potential in the form of a Mexican hat:26.In Fig.  see Eq. . In bothying Eq.  . These k (resonance) that triggers the instability almost immediately. The location of the optimal value depends on the interaction strength quench. For tested cases it is located around The Higgs mode is attributed to oscillations of the amplitude of the order parameter, while the density of the system remains unchanged. Indeed, when the mode is induced in a uniform system, Instead of using a perturbation with well defined wave length The results obtained for the 37 demonstrated that the small amplitude Higgs mode is unstable. Their result has been obtained within mean-field (BdG) treatment, which is valid for weakly interacting superfluid Fermi gases. In such case, the presence of dynamical instability was demonstrated analytically within the framework of the linear response theory. In the present study, we have released these constraints by considering large amplitude and strongly interacting regime and we have demonstrated the instability of the mode. Namely, we have shown that similarly to the small amplitude regime, the mode decays predominantly into a state where the spatial modulation of the pairing field is given by A(t) is the amplitude of the perturbation which grows rapidly in time. Consequently, this implies that after the decay the order parameter exhibits fluctuations of the type 39, if they emerge in spin-imbalanced system in a ground state. None of these requirements is satisfied in the cases discussed so far. However, it is interesting to note that the state emerging from the decay process shares similarities with the exotic type of superfluidity. This issue will be discussed in more detail in next section.Dzero et al.We now consider the properties of the state after the decay. To better visualize the typical characteristics of the post-decay state, we switch to a quasi-2D geometry, ansatz . The cal43. The main difference is that if the imbalance is present  focus on the stabilization of this mode. Here, and also in37, we demonstrate that the nonuniform state emerging from the decay of the mode can provide access to new class of states with order parameter that is periodically modulated in space. Such states are frequently associated with exotic types of superfluidity, generically related to FFLO phase—a state that is routinely discussed in the context of spin-imbalanced systems. Indeed, when introducing a spin-imbalance to the configuration, the states emerging from the decay consist of many spin-polarized droplets42. Surprisingly, experiments devoted to Higgs modes in strongly interacting Fermi gases may contribute to deeper understanding of exotic states emerging in superfluids.The relation between frequency of the small amplitude Higgs mode and strength of the pairing correlations (65. Such setups have already demonstrated their high capabilities for detecting the system’s nonuniformities. For example, there were successfully used to visualize density modulations due to the propagation of sound waves up to wavelengths of the order 0.1 66—the resolution that should be sufficient to detect predicted here inhomogeneities in the post-decayed state.Tunable ultracold atomic gases confined in box traps can be potentially used to verify the findings of this workSupplementary Information 1.Supplementary Information 2.Supplementary Information 3.Supplementary Information 4.Supplementary Information 5.


The innate immune system in our bodies responds to pathogenic infections and cellular damage by inducing pyroptosis through the assembly of inflammasome complexes. The apoptosis-associated speck-like protein containing a CARD (ASC) serves as an adapter, recognizing pattern recognition receptors (PRRs) and procaspase-1 based on the homotypic interactions of the pyrin domains (PYD) and the caspase recruitment domains (CARD) within the inflammasome complexes. The structural diversity of ASC and the role of the semi-flexible linker in structural transitions are critical in understanding the biological functions of ASC. This study employs molecular dynamics simulations to explore the structural dynamics of ASC and to analyze the potential relationship between interdomain dynamics and the biological roles of ASC as an adapter. The findings suggest that ASC dynamics partially originate from the movement of the linker and that the type I interaction surface on PYD is generally exposed and inaccessible to the CARD domain. These insights are consistent with experimental results and shed light on the function-related dynamic behaviors of ASC.The canonical ASC domains, PYD and CARD, are interconnected by a lengthy, semi-flexible linker. The molecular basis and purpose of ASC’s highly dynamic feature remain elusive. In this study, all-atom molecular dynamics simulations were utilized to examine the role of the linker and the interdomain dynamics of the ASC monomer. As revealed in the principal component analysis (PCA), the flexible linker enables interdomain dynamics and rotation. The stumbling between domains is partially attributed to the helical portion of N-terminal residues in the linker. Additionally, the linker exhibits a certain structural preference due to the turn-type structural inclination of the N-terminal and the presence of several prolines on the linker. Such structural preferences lead to the unavailability of regions for PYD type I interactions to CARDs, as evidenced by the CARD spatial restraint analysis. In conclusion, the semi-flexible linker introduces functionally relevant interdomain dynamics, potentially enhancing PYD self-assembly and the subsequent assembly of the inflammasome complex. The immune system can rapidly recognize and respond to damage- or pathogen-associated molecular patterns (DAMPs and PAMPs) in order to maintain homeostasis and promote health. These DAMPs and PAMPs can be detected by host pattern recognition receptors (PRRs), such as NOD-like receptors (NLRs) and absent in melanoma 2 (AIM2), via inflammatory pathways ,2,3. PRRHuman ASC is a protein comprised of 195 amino acids . The solAtomic resolution information on structure and dynamics is pivotal for understanding the fundamental physicochemical properties of the multi-talented ASC. Previous NMR experimental studies have shown that the ASC linker governs its interdomain dynamics by partially restricting the accessible conformational space of each domain relative to the other . In this+ or Cl−) to neutralize the whole system at 300 K. Long-range electrostatics were calculated using the particle-mesh Ewald (PME) algorithm [Two systems were simulated: the ASC full-length monomer (195 residues), as shown in lgorithm ,35. Perilgorithm ,37, whiclgorithm , using tlgorithm ,37 was uThe hierarchical cluster analysis was performed using Ward’s minimum variance method . It is bDistance and angle analyses were performed using the GROMACS package . The cenAs observed from the ASC monomer simulations, there is no stable packing structure between PYD and CARD. As shown in To delve deeper into the interdomain dynamics, a thorough analysis of the ASC monomer was conducted, employing time-resolved force distribution analysis (TRFDA) and correlation plots. TRFDA is a useful tool for detecting residues under significant punctual stress, which are integral to maintaining the protein’s structural integrity and contribute to the ASC interdomain dynamics. Here, TRFDA was applied to evaluate the interaction between PYD and CARD using six 1 µs trajectories. The punctual stress was averaged over the six trajectories. The ASC monomer is highly dynamic, with its PYD and CARD domains arranged differently in terms of spatial positions and orientations. The loop regions in the two domains and the linker demonstrate significantly more fluctuation compared to other regions. One domain interacts with varying surfaces of the other domain across different clusters. TRFDA results suggest some weak interactions between PYD and CARD, with the motion of these two domains showing correlation in certain segments. In order to further understand the dynamics of the ASC monomer, we have isolated the linker from the simulation for a detailed analysis, which we will present in the following section.13Cα secondary chemical shifts, implying the possible adoption of turn-type conformations. In contrast, residues 95–112 had primarily negative 13Cα chemical shifts, indicating the formation of sparsely populated extended structures. We utilized the DSSP program [The linker, as observed in the TRFDA results  and corr program ,46 to asThough the linker exhibits some structural preference, its probability is relatively low. Consequently, a more in-depth analysis of the linker’s flexibility is required. As demonstrated in The linker is highly dynamic, but we do observe the low-populated structures with a turn-type structure transiently formed at its N-terminus, especially in the monomer. In combination with the presence of prolines, the linker is not fully flexible but displays a structural preference to some extent.To study the interdomain dynamics, it is essential to conduct principal component analysis (PCA). In Moving on to the ASC monomer, the linker region has a very similar movement to the one described above, albeit with some distortion in shape. It is important to analyze how the movement of the linker is coupled with changes in rotation and orientation of the PYD and CARD domains. As shown in While observing these varied movements, it is important to emphasize that the interfaces formed by H1–H4 and H2–H3 of PYD (Type I interaction) are consistently maintained at a distance from CARD. Previous NMR work  proposedThe interdomain movement was further evaluated by analyzing the torsional angle illustrated in PCA results on the isolated linker and ASC monomer reveal that the interdomain dynamics of ASC originate from the linker. Moreover, interdomain dynamics are accompanied by interdomain rotation. We characterize the interdomain rotation using a torsional angle, as shown in De Alba previously proposed that the ASC interdomain topological organization aids binding by avoiding steric interference between the two interacting regions of both domains and by favoring a specific protein binding orientation . AlthougWe utilized the acquired frames to cluster the structures and calculate the probability of each spatial arrangement of CARD . This shThe spatial distribution of CARD around PYD implies that the ASC dynamics contribute to its function as an adapter in the inflammasome. In general, the Type I interaction on the surface of PYD, which is responsible for ASC self-assembly, is not blocked by CARD. Consequently, the preferred dynamics have evolved over time to serve the function.The loop regions in PYD and CARD and the central linker are the regions with the largest fluctuation. The interdomain bending angle (defined by the Cα atoms of residues 49–69–163) varied from 30° to 160°, and the COM distance distribution between PYD and CARD ranges from 2 to 8 nm, indicating that ASC is relatively flexible. The structure with the greatest COM distance seems to be the inter-conversion state of various compact structures. The representative structures from the cluster analysis of the ASC monomer demonstrate the interdomain flexibility and varied contact interfaces between PYD and CARD.The structural features of the linker were characterized to study the origin of ASC interdomain dynamics. It is worth noting that the N-terminus of the linker prefers the helical structure in the ASC monomer, as shown in Subsequently, we conducted an in-depth study on the potential role of interdomain dynamics in ASC assembly. PCA results show that CARD can rotate relative to PYD. This is important because several adjacent CARDs can rotate their binding interfaces to form homotypic interactions after PYD nucleation and assembly. Furthermore, the torsional angle between PYD and CARD (defined by Cα of residues 81–69–163–177), employed to describe the relative stumbling of PYD and CARD, is widely distributed in the range of −180–180°. The time evolution of the above-mentioned torsional angle shows that the angle sometimes oscillates frequently between −180° and 180°, indicating the interdomain stumbling of the ASC monomer, which is consistent with the PCA results. The rotation may be related to the transient contacts involving the linker and domains. Some interactions were observed in one conformation, while others were observed in other conformations. In other words, these transient interactions were not strong enough to stabilize ASC in one single structure during the entire simulation, yielding structural transitions. In addition, the interdomain rotation appears to be correlated with the dynamic variation of helical probability of residues 90–94 in the linker. Given the flexibility of the linker, CARD can access many regions around PYD. However, the helices involved in the Type I interactions in PYD, namely H1–H4, are inaccessible to CARD. The interdomain spatial restrain is highly related to the properties of the linker, which is flexible but also has structural preferences, such as the turn-type structural preference in the N-terminal region of the linker and geometry limitation of prolines in the linker. Taken together, the structural features of the linker and the weak interdomain interplays lead to the ASC monomer favoring interdomain dynamics that seem to benefit ASC assembly and ultimately the assembly of the inflammasome complex.With the MD simulation on the ASC monomer and the isolated linker, we analyzed the origin of the interdomain dynamics of ASC. According to the PCA results, the interdomain dynamics stem from the semi-flexible linker since the ASC monomer showed similar motions as the linker. Additionally, the residues at the N-terminus of the linker show a weak tendency to form a turn-type structure, one possible factor driving the interdomain rotation. ASC is observed to show evident interdomain dynamics, but the dynamics are not entirely free to adopt diverse organizations for the two domains. Analysis of the spatial restraint of CARD suggested that it is likely to populate in certain positions with the Type I interface of PYD being exposed. Therefore, such positions contribute to the subsequent assembly of inflammasome complexes. These findings can be verified by further assembly simulations of more complex systems. With more information on the dynamic behaviors of ASC, we will be able to reveal the activation mechanism of the inflammatory signaling pathway and target ASC to regulate the immune response in inflammasome-related disorders.


In cases where a client suffers from completely unlabeled data, unsupervised learning has difficulty achieving an accurate fault diagnosis. Semi-supervised federated learning with the ability for interaction between a labeled client and an unlabeled client has been developed to overcome this difficulty. However, the existing semi-supervised federated learning methods may lead to a negative transfer problem since they fail to filter out unreliable model information from the unlabeled client. Therefore, in this study, a dynamic semi-supervised federated learning fault diagnosis method with an attention mechanism (SSFL-ATT) is proposed to prevent the federation model from experiencing negative transfer. A federation strategy driven by an attention mechanism was designed to filter out the unreliable information hidden in the local model. SSFL-ATT can ensure the federation model’s performance as well as render the unlabeled client capable of fault classification. In cases where there is an unlabeled client, compared to the existing semi-supervised federated learning methods, SSFL-ATT can achieve increments of 9.06% and 12.53% in fault diagnosis accuracy when datasets provided by Case Western Reserve University and Shanghai Maritime University, respectively, are used for verification. As an important part of modern industrial systems, the fault diagnosis of a rolling bearing is crucial ,2,3. DatThe existing semi-supervised federated learning methods are constrained by unreliable information hidden in the corresponding local model and struggle to optimize the performance of the federation model. Therefore, it is important to design a reliable screening mechanism for the local model and guide the federated learning process. This paper starts from the perspective of a reliable information-screening mechanism for the corresponding local model. Then, a dynamic semi-supervised federated learning method based on an attention mechanism is proposed, aiming to solve the problem of negative migration for federated learning due to unreliable information from a low-quality local model and improve the classification ability of clients without labeled data.A dynamic semi-supervised federated learning fault diagnosis method based on an attention mechanism is proposed to solve the problem of negative transfer due to unreliable information hidden in a local model. This guarantees the performance of the federation model and enhances the classification ability of clients without labeled data.A federation strategy driven by an attention mechanism is designed to filter out unreliable information so that the federation model can incorporate useful information from an unreliable local model. A new loss function related to supervised classification, unsupervised feature reconstruction, and the reliability of the local model is designed to train the federation model. According to the reliability of the federation model, the local model can be optimized by dynamically adjusting how the unlabeled data are utilized and the extent to which they can contribute.In cases where there are certain clients without labeled data, the method proposed in this study can still ensure the performance of the federation model and render it capable of fault classification for local clients without labeled data. The main contributions of this work are as follows: Semi-supervised deep-learning methods can achieve the full utilization of massive collections of unlabeled data to optimize fault diagnosis models built with a small quantity of labeled data . The exiIn generative semi-supervised methods, it is assumed that all samples are from the same latent model, and unlabeled data are treated as missing parameters of the potential model. An expectation maximization algorithm (EM) is usually used to determine the parameters ,17. SemiCompared to the above semi-supervised deep-learning methods, the process of the semi-supervised learning method based on pseudo-label self-training is simpler and more effective . Model pSemi-supervised federated learning is a method that combines semi-supervised learning and federated learning  to addreWhen there are certain clients without labeled data, existing semi-supervised federated learning methods can suffer from performance degradation due to an inability to screen for unreliable information. To ensure the performance of a federation model, a federation aggregation strategy based on an information reliability screening mechanism is necessary. This paper proposes a dynamic semi-supervised federated learning method for fault diagnosis based on an attention mechanism, whose main processes include a dynamic local training mechanism based on model performance, with the aim of dynamically adjusting the way and degree to which unlabeled data are used according to the performance of the federated model. On the other hand, local model optimization is achieved through supervised and unsupervised loss. An optimal federation aggregation strategy driven by reliable information screening is designed to filter reliable information by measuring the difference between the local model and the federated model through the attention mechanism and reflecting the contribution of each client using the attention score. The aim of this process is to filter out unreliable information through the attention mechanism and thus ensure the federated model’s performance. The block diagram of the dynamic semi-supervised federated learning fault diagnosis method based on an attention mechanism is shown in In this section, a dynamic unlabeled data utilization strategy is designed to dynamically adjust the way and the extent to which unlabeled data are used based on the performance of the federation model. The specific steps are as follows.Step 1: When the federation model is unreliable, the recursive optimization of the local model is achieved using unlabeled data.After receiving model parameters from the federation center, they are used as the initialization parameters of the local model, as shown in Equation (1).Client Step 2: Dynamic local semi-supervised training based on the degree of pseudo-label utilization.In the Above, The local loss function is constructed using the classification loss of the labeled data and that of the unlabeled data with a pseudo-label, as shown in Equation (7):In this study, the number of communication rounds was used as a measure of federation model performance, and In this step, the local model parameters are updated, as shown in Equation (9).The above steps enable the utilization of labeled and unlabeled data in a supervised learning manner, and the differential utilization of unlabeled data can achieve the goal of the full use of large collections of unlabeled data from each client for model optimization.Unreliable information is hidden in the local model because it is difficult to achieve high-quality model building for clients without labeled data. Therefore, at this stage, a semi-supervised federation aggregation strategy based on an attention mechanism is designed. The specific steps are as follows.Step 1: Semi-supervised federation model aggregation.After receiving the local model uploaded by all clients, the federation center aggregates all local models using the initialized federation aggregation parameters, as shown in Equation (10).Above, Step 2: Establish model reliability metrics based on the degree of consistency.The local model parameters are used as query values to query the attention distribution between each local model and federation model in turn, and the attention score is scaled to between 0 and 1. The contribution degree of the local model Step 3: The federation aggregation process is driven by the performance of the federation model and the reliability of the local model.The loss function of the dynamic semi-supervised federation aggregation process is designed by integrating federation model performance and the local model reliability of the clients, as shown in Equation (13):Step 4: Joint optimization of local model parameters and federation aggregation weights.The joint optimization of local model parameters and federation aggregation weights based on the loss function of the federation center can further improve the fault diagnosis performance of the federation model by improving the reliability of the local model. The gradients of the local model parameters and the federation aggregation weights are calculated as shown in Equations (17) and (18), respectively.The joint optimization process can dynamically update the federation aggregation weights and local model parameters, which improves the reliability of local models and thus reduces the impact of unreliable local models on the performance of the federation model. This section highlights the detailed steps of the SSFL-ATT fault diagnosis method proposed to solve the problem of reliable information screening for local models.Algorithm 1: Fault diagnosis based on SSFL-ATTServer executes: Initializing federation model Step1: Model training for semi-supervised federated learningDynamic local training mechanism based on federation model performanceClients dynamically adjust how to use local unlabeled data based on federation model performance.Federation aggregation strategy driven by reliable information screeningReliable information can be screened from local models based on attention mechanismsThe loss function can be designed by combining performance of federation model and reliability of local modelJoint optimization of local model parameters and federation aggregation weights.Joint optimization of local model parameters and coalition aggregation weights can be achieved based on loss function of federation center,Step2: Fault diagnosis for each clientEach client uses well-trained federation model Require: local data A flowchart of the dynamic semi-supervised federated learning algorithm based on the attention mechanism is shown in Using the benchmark dataset of Case Western Reserve University (CWRU) for experimental verification, this section validates the effectiveness of the proposed method through specific experimental analysis.The Case Western Reserve University bearing dataset is widely used in fault diagnosis. The experimental platform is shown in In this section of the experiment, the monitoring signal of the accelerometer at the drive end was selected. The motor load was 0 HP, the speed was 1797 rpm, and the sampling frequency was 48 KHz. The four operation states of the rolling bearing comprise the normal operation state and the fault states of the inner ring, ball, and outer ring measured at a fault inch of 0.021. The detailed composition of the dataset is shown in To verify the superiority of the proposed method, it was compared with various existing models of semi-supervised federated learning. An experimental scenario of semi-supervised federated learning was designed by changing the data of the clients. The dataset was obtained by intercepting the vibration data through a sliding window with a window size of 400 and a step size of 30, and the number of samples in the test set is 4 × 300. Experiments 1–3 are designed to verify the effectiveness and superiority of SSFL-ATT when clients have different quantities of labeled data. The fault diagnosis results are shown in As can be seen in Columns 3 and 4 of To further validate the effectiveness of the proposed method, the confusion matrices of each fault diagnosis method shown in Experiment 2 are given in Upon comparing the confusion matrices of Pk, and attention scores, Att, in Experiment 2. As shown in Pk is a matrix, we determined the mean value of Pk and then plotted its evolutionary trend; as shown in Pk is like that of Att, which further shows that the method proposed in this paper can filter reliable information and improve the performance of the federation model.This section analyzes the evolution of the aggregation weights, Experiments 4–6 were designed to verify the improvement induced by SSFL-ATT on the performance of the fault diagnosis model when clients have different quantities of unlabeled data. The experimental results are shown in Compare Columns 3–8 and 9 of Experiment 3 and Experiments 4–6. This comparison reveals that when the quantity of the labeled data is fixed, the fault diagnosis accuracy of all the methods decreases as the quantity of unlabeled data decreases. However, SSFL-ATT still achieved high classification accuracy, which indicates that SSFL-ATT was better able to extract reliable information from unreliable local models for clients without labeled data, thus achieving the aim of reducing the perturbation caused by unreliable pseudo-label information sent to the local model.Using the Shanghai Maritime University motor dataset for experimental validation, this section verifies the effectiveness of the proposed method through specific experimental analysis.The Shanghai Maritime University motor fault simulation experiment bench is shown in During the experimental validation, DNN was used as the base network model, with the number of neurons in each layer set to 7/200/90/30/10 and a learning rate of 0.005 applied, and model optimization was performed using the Adam optimizer. The number of samples in the test set was 10 × 1000. The detailed design of the experiment is in In order to verify the effectiveness of SSFL-ATT with multi-channel signals, the results of Experiments 1–3 are shown in As can be seen in SSFL-ATT was still superior to the other methods in the above two experimental scenarios. From the experimental results in To illustrate the superiority of SSFL-ATT more intuitively in different experimental scenarios with two datasets, In semi-supervised federated learning for fault diagnosis, when there are certain clients without labeled data, existing semi-supervised federated learning methods can lead to a negative transfer problem due to unreliable information hidden in these clients’ local models. This paper proposes a dynamic semi-supervised federated learning fault diagnosis method based on an attention mechanism for designing an optimal federation aggregation strategy. The federation aggregation strategy was dynamically optimized based on reliable information screened in the local model.First, to ensure the effectiveness of its utilization for local unlabeled data, clients can dynamically adjust the way and extent to which unlabeled data are used according to the performance of the federation model. The aim is to fully utilize unlabeled data for model optimization while reducing the perturbation of the local training process with low-quality pseudo-labels. Then, in the process of federation aggregation, the occurrence of negative transfer in federated learning due to unreliable model information can be avoided by establishing reliability evaluation metrics based on the attention mechanism. At the same time, the feedback information from clients on the performance of the federation model can be combined to drive the federation aggregation process and achieve the joint optimization of aggregation weights and local model parameters. The experimental results show that SSFL-ATT can utilize an attention mechanism to filter out unreliable information to avoid negative transfer caused by unreliable information, and it can also effectively improve the classification ability of unlabeled clients. Compared to existing semi-supervised federal learning methods , these results indicate that SSFL-ATT is superior and more applicable.