Social insurance is an essential component of a contemporary social security system since it protects people’s fundamental well-being, but it also incurs a heavy cost for businesses. If social security costs are excessively high, business profitability will suffer, and innovation will be discouraged. The most affected companies would be those in labor-intensive industries and medium-sized enterprises. Chinese businesses have suffered severe losses as a result of the COVID-19 outbreak. Given the circumstance, China enacted additional tax cuts and preferential social insurance premium plans. This article suggests a lower ratio of contribution as a strategy to cut the cost of social insurance premiums for businesses, given the growth of the social security fund in recent years and the proportion of participants to recipients in pension funds. It would be possible to increase firm profitability and lessen the impact of COVID-19 on industries by minimizing this operation burden. In order to compare the financial performance of state-owned manufacturers (SOMs) to that of their non-state-owned peers, who have a lower ratio of contribution, this study uses a multiple regression model. The ratio of contributions was inversely correlated with an enterprise’s financial performance. In other words, financial performance will improve as the ratio of contribution lowers; nevertheless, this effect is more pronounced in SOMs. The final section of this study proposed optimized approaches for social insurance premiums reform. Public insurance is an essential component of a contemporary social security system. Compared with developed economies, China’s social insurance system has a shorter history, with its beginning marked by the implementation of the Regulations of the People’s Republic of China on Labor Insurance in 1951, a milestone in China’s exploration of social insurance reform. 2011 saw the introduction of the Social Insurance Law of the People’s Republic of China, which was a remarkable event in the legalization of the social insurance system in China. Zhao et al. [Li et al.  pointed The National Bureau of Statistics reports that since 2000, the income, expenses, and accrued balance of China’s social security fund have all increased. This information is displayed in Main contributions of this thesis is discovered that COVID-19 led to an increasing number of enterprises suffering losses in China, so a lower ratio of social security contributions without guaranteed benefits for the normal operation of social security funds could reduce the labor cost of enterprises, increase cash flow and profits, and restore the vitality of enterprise production. This thesis conducts an empirical study on the impact of a lower ratio of social security contributions on the financial performance of state-owned manufacturers (SOM) and non-state-owned ones, respectively. Research shows that a lower ratio of contribution would improve the financial performance, and such effects are more profound and apparent in SOMs. This thesis provides a reference for the recovery of SOMs and non-SOMs in the post-COVID era.China’s social insurance fund has three contributors: the employee, the employer, and the official authority. The ratios of contributions applied to employees and employers are different, while the remaining subsidies are attributable to the national budget. The ratio of contribution for enterprises is formulated in the national social insurance policy, affecting a company’s profitability. There are two major viewpoints about the impact of social insurance contributions: "incentive theory" and "cost theory".Yuan and Luo  pointed Zhang et al.  pointed Foreign scholar Griliches  found thFor the sustainability of business operations, the increased investment in social insurance for employees could indirectly force enterprises to improve their R&D efforts and optimize the management structure, while social insurance as a kind of staff welfare, can motivate employees and improve productivity –15. HoweSocial insurance premiums are recorded as corporate tax burdens. China has adopted quite a high ratio of social insurance contributions, compromising five components: pension, healthcare, work injury, maternity, and unemployment. A total rate of 40% is also at a fairly high level compared with other countries. However, the actual social insurance contribution is lower than the nominal ratio due to regional policy differences, and a huge number of companies pay the social insurance based on the basic salary instead of the actual salary for employees to save on labor costs –21. AccoHypothese 1: Reducing the actual social security contribution rate of enterprises is beneficial for promoting their financial performance.Gong et al.  found thHypothese 2: The reduction in the actual social security contribution rate of SOMs has a more significant promoting effect on their financial performance than non-SOMs.In summary, the ever-changing connection between social insurance premiums and enterprise performance has been widely studied. Despite variations in the study subjects and research methodologies, the studies have arrived at a consensus that the ratio of social insurance contributions has an impact on the input of production factors in enterprises. Furthermore, national policies that involve tax cuts and fee reductions have been found to effectively reduce enterprise costs. China has implemented several policies pertaining to social insurance premiums in response to the effects of COVID-19. These policies aim to alleviate the financial burden experienced by enterprises and facilitate economic recovery. Notwithstanding the aforementioned conclusion, there is an absence of empirical research on the potential effects of a reduced ratio of social security contributions on the financial performance of both SOMs and non-SOMs. This study employs a regression model to conduct an empirical comparative analysis of the financial performance implications of a reduced contribution ratio for SOMs and non-SOMs. The study provides recommendations for the improvement and streamlining of the social insurance system.Gong et al.  and ZhanThe data used in the empirical analysis are cited from the Guotaian CSMAR database and the WIND database. The data for all financial statements was cited from the public documents of A-share-listed SOMs and non-SOMs from 2011 to 2020. The sample collection mainly selected labor-intensive manufacturers in China, whose labor expenses make up a larger portion of operating costs, so they are more sensitive to changes in the ratio of social insurance contributions. In order to improve the real validity of the sample data, companies with suspensions or delistings, or ST companies, during 2011–2020 were excluded, so were companies with zero social insurance contributions. Based on the above conditions, this thesis selected a total of 3,691 listed companies with 15,937 observations in the non-SOMs and 483 listed companies with 3,451 observations in the SOMs.The explanatory variable in this thesis is the ratio of social insurance contributions paid by enterprises. There are two types of explanations of the ratio of contribution: nominal and real. When the enterprise pays social insurance strictly according to the statutory standard formulated by the national policy, the ratio of social insurance contributions to total costs is called the nominal ratio. The nominal ratio is more of an ideal situation, but research shows that some enterprises do not fully pay the social insurance fees in line with the requirements of laws and regulations, so the nominal ratio is more often higher than the actual ratio. In this thesis, the “ratio of social insurance contribution” refers to the actual ratio adopted by enterprises, measured by: social insurance premiums/employee compensation payable × 100%.In this thesis, Chen and Wang  were refTo mitigate endogeneity concerns and enhance the precision of the model, this study has incorporated control variables. The primary themes explored in the earlier research and pertinent literature have both influenced the choice of these variables. The chosen control variables encompass corporate growth (Growth), debt level (Lev), independent director ratio (Bind), equity checks and balances (CS), corporate age (AGE), corporate size (Size), board size (Bsize), and year (Year). The explanatory variable, explained variable, and control variable data utilized in this study were obtained from the CSMAR and WIND databases. In In this thesis, the following fixed effect regression model is constructed to further investigate the impact of a lower ratio of social security contribution on firms’ financial performance.In In this thesis, descriptive statistics of selected SOM and non-SOM variables are shown in Tables In conclusion, non-SOMs made a higher actual paid ratio of social security than SOMs did, while SOMs performed better operationally than non-SOMs did.Tables This thesis carries out regression analysis on the relationship between the actual ratio of social security contribution and the financial performance of the SOMs and non-SOMs by citing the short panel data from 2011 to 2020. The analysis was based on the time fixed effect model with the results shown in In conclusion, both SOMs and non-SOMs can improve their own financial performance by reducing the actual ratio of social security contribution and asset-liability ratio, increasing the growth rate of operating revenue and the shareholding proportion of the largest shareholder in the post-pandemic era, leading to a faster recovery of economy and business, moreover, the effect of reducing the social security contribution rate of SOMs on promoting financial performance is more significant than that of non-SOMs. Therefore, the previous research hypothese 1 and research hypothese 2 are valid.In order to test the overall significance of the fixed effect model, the variance analysis method is employed. In order to achieve the purpose of assessing whether the influence of explanatory variables on explained variables is significant, it is necessary to test the significance of the fixed effects model, which is generally measured by F value and P value. In this thesis, the overall significance test of the two models for non-SOMs and SOMs is shown in Tables P<0.005), indicating that the F-test is significant. The model was set reasonably through the test, and the explanatory variables could well explain the explained variables. The F-tests for the other variables Rate, Growth, Lev, Bind, CS, AGE, Size and Bsize are also all positively significant at the 1% level, indicating that each variable has an impact on the differences in ROA.According to P<0.005), indicating that the F test was significant. Through the test, the model was set reasonably, and the explanatory variables could well explain the explained variables. The F-tests for the other variables Rate, Growth, Lev, CS, AGE and Bsize are also all positively significant at the 5% level, indicating that each variable has an impact on the differences in ROA.According to The variance inflation factor (VIF) evaluates the model’s multicollinearity problem. The VIF test’s results of non-SOMs and SOMs are shown in To test the robustness of the results of the empirical analysis, this thesis replaces the explanatory variables to test the results of the previous regression analysis. Since the ROE and ROA are both important indicators in the measurement of business financial performance, the regression analysis is conducted after replacing the original explanatory variable, corporate performance (ROA), with return on net assets (ROE) in the robustness test. The regression results upon the variable replacement are shown in This thesis analyzes the relationship between the actual ratio of social security contribution and the financial performance of SOMs and non-SOMs by establishing a fixed-effects regression model. It is found that the actual ratio of social security contribution and the total average ROA in SOMs are higher than those of non-SOMs. When the actual ratio of contribution is equal, the gap between the maximum and minimal ROA in SOMs is huge and unevenly distributed. Some S0OMs have better management, so the actual ratio of contribution is higher, while some non-SOMs poor operation leads to a lower actual ratio of contribution. In summary, the ratios of contribution adopted by SOMs and non-SOMs are polarized. In addition, the actual ratio of contribution and the ROA were significantly negatively correlated in both SOMs and non-SOMs. To be specific, a lower ratio of contribution can improve an enterprise’s financial performance, but the absolute value of the correlation coefficient between the actual ratio of contribution and ROA in non-SOMs is greater than in SOMs. Indeed, a lower ratio of contributions for SOMs would boost their financial performance.(1) Implement tax and premium reduction policies. The general ratio of social insurance contributions implemented in China is higher than the international average level, which could translate into a heavy burden shouldered by enterprises. Pension insurance premiums account for the largest part of the social security package. Facing the dilemma of an increasing aging population and high pension insurance premium rates, the government should reduce the burden for enterprises based on the actual situation while balancing a lower ratio of pension contribution with guaranteed pension payment mechanisms by effectively coordinating with enterprises. In addition, when formulating specific social insurance policies, local governments should take the particular operating conditions of different companies into full consideration, managing to find the balance between social welfare and financial performance. Many enterprises suffered financial crises due to the outbreak of COVID-19, and social insurance contributions have become a heavy burden for enterprises that are losing growth momentum. To motivate business development, the Chinese government should try to find solutions with a lower ratio of social insurance contributions. According to the above empirical study, a lower ratio of social security could play a more positive role in non-SOMs’ financial performance. That is to say, how to reduce the actual ratio of social security contributions for SOMs should be the new focus for the Chinese government.(2) Implement a differentiated social insurance contribution policy. The ratio of social insurance contributions applied to enterprises in different industries varies. Therefore, local governments should also take into account the differences among enterprises when determining the ratio of contribution and formulating relevant policies accordingly. It is important to ensure that enterprises are subject to a fair and just ratio of contribution that adapts to individual conditions. At the same time, regions with better conditions may promote commercial insurance as a supplement to the social security system.(3) Strengthen the supervision of social insurance contributions. At present, the actual ratio of social insurance contributions is lower than the nominal ratio, and some enterprises do not pay social insurance in full and on time as required. Those who violate relevant regulations and policies bear lower labor costs than compliant ones, which will translate into unfair market competition, hurting the sustainability of a healthy business environment. To build a level playing field, the government should leverage the measures of tax and premium reduction to maintain a fair and just market with enhanced management, thus stimulating the enthusiasm of enterprises to contribute to the social insurance fund. In this way, we could maintain a healthy and sustainable operation of the social insurance system.S1 File(ZIP)Click here for additional data file.


To address the problems of complex background interference, difficult detection of tiny targets and biased detection of prediction boxes that exist in standard detectors, in this paper, we constructed a tiny target dataset TTALDD-4 containing four types of diseases, which include Alternaria leaf spot, Frogeye leaf spot, Grey spot and Rust, and proposed the HSSNet detector based on the YOLOv7-tiny benchmark for professional detection of apple leaf disease tiny targets. Firstly, the H-SimAM attention mechanism is proposed to focus on the foreground lesions in the complex background of the image. Secondly, SP-BiFormer Block is proposed to enhance the ability of the model to perceive tiny targets of leaf diseases. Finally, we use the SIOU loss to improve the case of prediction box bias. The experimental results show that HSSNet achieves 85.04% mAP (mean average precision), 67.53% AR , and 83 FPS (frames per second). Compared with other standard detectors, HSSNet maintains high real-time detection speed with higher detection accuracy. This provides a reference for the automated control of apple leaf diseases.Apple leaf diseases are one of the most important factors that reduce apple quality and yield. The object detection technology based on deep learning can detect diseases in a timely manner and help automate disease control, thereby reducing economic losses. In the natural environment, tiny apple leaf disease targets (a resolution is less than 32 × 32 pixel Apples have been widely grown worldwide because of their ecological adaptability, high nutritional content and economic profit. Influenced by natural environmental factors, apple leaves are susceptible to infection by a variety of diseases. These diseases seriously impede the normal metabolic process of apples , causing leaf decay and even leaf loss, which leads to a decrease in fruit quality and yield ,2. ThereCurrently, in apple leaf disease detection research, traditional machine vision methods based on machine learning and pattern recognition have achieved certain results under restricted situations. For example, certain detection and recognition results can be achieved in a laboratory environment (uniform illumination and simple background environment) ,7,8. HowRecently, deep learning-based methods have begun to be widely discussed and studied in crop disease identification ,10. DeepFollowing an existing survey ,18,19, YThe aforementioned studies achieved good results and demonstrated the viability of the YOLO family of algorithms for leaf disease detection tasks. However, these studies mainly focused on issues such as improving model inference speed, reducing the number of model parameters, and not using the state-of-the-art YOLO detector. The influence of tiny target characteristics of the disease and the complex background of natural environments on detection models needs to be thoroughly explored. For this reason, we chose the latest YOLOv7 as the benchmark network to carry out related research. To this end, we chose the latest YOLOv7-tiny as a benchmark network to carry out related work to explore the possibility of deep learning to optimize apple leaf disease detection. This paper focuses on four types of apple leaf diseases, Alternaria leaf spot, Frogeye leaf spot, Grey spot and Rust disease. Their detailed properties and negative effects will be presented in In the current apple leaf disease detection process e.g., , there a(a) Complex image background. Apple leaf images in real environments have complex background environments, natural illumination conditions, or shadow occlusion. The chromaticity and appearance of the background environment may be similar to the foreground features of the disease. This can interfere with the feature parameters of the network, interfere with the supervised learning process, and pose a great challenge to the detection network.(b) Tiny disease targets. The spot texture of tiny target diseases occupies a small area on the leaf and is sparsely distributed. The feature information domain is limited and difficult for the network to capture accurately. The existing standard detectors do not guide the model to focus on these features and are prone to missed detection.(c) Prediction box detection bias. When some tiny target diseases are clustered, the YOLO object detection algorithm tends to generate more dense redundant frames in the prediction process, and the loss function does not consider the mismatch direction between the real frame and the predicted frame. This can lead to difficulty in quickly calibrating the exact location of tiny target diseases, slowing down the training speed and impairing the detection precision.For the problem of complex background, the traditional concept uses filters with hand-constructed operators to reduce background noise ,24 in or2. To address the problem of tiny object detection, some researches increase the network’s ability to fit tiny object features by training strategies such as oversampling and data augmentation [In the existing studies, the most general definition of tiny targets comes from MS COCO, a common dataset in the field of object detection . It defientation ; some reentation ; others entation . The Traentation  with dynentation  with a sTo address the problem of more redundant boxes in the prediction process for tiny targets of disease, the classical IOU loss cannot measure the overlap between the predicted and real boxes well, so it is more biased towards objects of larger size in the training process. GIOU  introducTo address the foregoing issues, in this paper, we propose a novel object detection network, HSSNet, focusing on the detection of tiny target apple leaf diseases, using YOLOv7-tiny as a benchmark.(1) We construct an image dataset of the tiny target apple leaf diseases for detection (TTALDD-4), which contains Alternaria leaf spot, Frogeye leaf spot, Grey spot and Rust four categories of apple leaf diseases, and 6482 images in total. Among them, 5998 images contained complex backgrounds, accounting for 92.55% of all disease areas in TTALDD-4, were accurately labeled with location boxes and corresponding disease category labels. There was a total of 31,914 target boxes and 22,506 small target boxes, accounting for 70.52% of all disease areas.(2) The main improvements of HSSNet are as follows:(a) For the problem of complex apple leaf disease background, we propose the H-SimAM attention mechanism. It enhances the expression of neural signals that are highly correlated with disease targets, and suppresses interfering signals. H-SimAM improves the ability of YOLOv7-tiny to focus on foreground leaf lesions in complex backgrounds.(b) For the problem of disease tiny object detection, we propose the SP-BiFormer Block. This block is based on the BRA module with dynamic sensing queries and SoftPool, which enhances the ability of YOLOv7-tiny to capture the sparse distribution of tiny targets of leaf diseases.(c) To address the problem of biased prediction frame detection, we use the SIOU loss function to optimize the training process. This loss function takes into account the mismatch direction between the prediction frame and the real frame to make the training process fit better with the dense distribution characteristics of tiny targets of apple leaf diseases.(3) The experimental results show that the detection accuracy of HSSNet is significantly improved compared with the baseline network YOLOv7-tiny. The proposed model achieves a good tradeoff between accuracy, detection speed, and parameters.Suitable image datasets are required to train the object detection network. The AppleLeaf9 dataset  provides2) are 22,506, accounting for 70.52%. In addition, during the labeling process, we removed the very blurred images to facilitate the effective training of the network, and the number of images and labels obtained are statistically shown in Supervised learning for object detection training requires not only the category labels but also the localization labels of the diseases. Therefore, we used the Labelimg software (v1.8.1) to accurately label disease areas under the guidance of Yahui Hu  from theIn order to improve the expertise of the detector in detecting phenotypic characteristics of tiny target diseases of apple leaves, we analyzed the four categories of diseases mentioned above. Healthy apple leaves are overall ovate or oval in shape, with serrated leaf margins, well-defined vein textures, and are usually soft or dark green in color. Alternaria leaf spot disease of apples caused by Streptomyces infection is a devastating disease for apple production. Infected leaves show dark brown or black leaf spots, and these cells rapidly spread and accumulate into necrotic lesions that eventually cause leaf abscission . FrogeyeAll four types of diseases have tiny areas of incidence and lesion traits that are more easily confused with the leaf background. All these problems make the standard detector performance low. Failure to detect diseases in a timely manner will seriously affect apple production and make economic benefits significantly impaired. Therefore, the research of these representative apple leaf disease tiny targets has practical application value for apple leaf pest control.In this paper, a more specialized detection model, HSSNet, is proposed for the characteristic of tiny target diseases of apple leaves. Its network architecture is shown in In the natural environment, the precise location of apple leaf disease is difficult to capture directly by sensing devices. Areas of lesions under natural lighting are not well distinguished and can easily be confused with similar backgrounds, leading to missed detections. In addition, the color of certain diseases is not well differentiated from the planting background or the leaves themselves, and the features abstracted by convolutional networks are easily disturbed by background noise. These complex natural environments place high demands on the model to accurately focus on disease features. The attention module in machine vision can be understood as focusing on the part of the input that is expected to be attended to and suppressing the unimportant interference signals.As mentioned in the introduction, the SE Attention Module is a classical attention mechanism for channel dimension. It first performs the global average pooling operation on the input feature map to compress the global feature volume, and then obtains the importance of each channel of the feature map through the excitation operation, so that the neural network can focus on certain feature channels. It consists of two submodules: the CAM (channel attention module) and the SAM . The CAM module compresses the information in the spatial dimension and focuses more on the information in the input image that is meaningful to the task. SAM compresses the information in the channel dimension and the module focuses on the location information of the target. The above attention modules do not pay differential attention to different feature maps or neurons in spatial locations, which may limit their expressive power. In addition, these attention modules inevitably increase the parameters and computational complexity while improving network detection.For this purpose, we propose a parameterization-free attention module, H-SimAM, as shown in To select the more important feature signals, SimAM estimates the importance of individual neurons  by means of an energy function:Through minimizing the above equations, the linear differentiability of Assume that the values in the same channel have the same distribution pattern. Given this assumption, the minimum energy of the input features in both equation :(3)etminThe use of the Finally, the whole process can be expressed as follows:In the real environment, apple leaf disease targets have low resolution, limited pixel area, and are characterized by tiny targets. In addition, some of these diseases are sparsely distributed on the leaves or have a tendency to cluster. In the prediction phase of the YOLOv7 model, the anchor frames generated by the prediction rely on NMS (non-maximum suppression) to filter out a large number of low-confidence borders, which tends to miss the tiny targets. Transformer self-attention is a type of attention mechanism. The design idea is to reduce the dependence on external information and to use the original feature information to encode the association information at different locations as much as possible to achieve attention focusing.To this end, we propose the SP-BiFormer Block to optimize the ability of YOLOv7-tiny to focus on tiny targets, as in According to reference , we giveNext, we will introduce the three parts of BRA; the first is the “Region partition and input projection” part. The input feature map The second part of BRA, “Region-to-region routing with directed graph”, is presented next. This part calculates the regions that should be focused on by constructing a weighted directed graph from the input feature map To reduce the interaction times of each region with other regions, BRA keeps the Compared with the conventional transformer, this operation can effectively reduce the amount of computation.In the third part of BRA, “Token-to-token attention”, the key and value vectors are integrated for GPU (graphics processing unit) operations :(11)Kg=gTherefore, we can represent BRA according to the transformer self-attentiveness defined by Equation (7):networks .In order to provide sufficient information about small objects, we constructed the SP-Biformer Block based on BRA, which can utilize higher-level abstract features as the context of small targets and query contextual association information from the surrounding pixels of small objects. In BRA, average pooling for region-to-region routing is used to find the most relevant token regions. In SP-Biformer Block, we use SoftPool pooling instead of average pooling in the original BRA to reduce the redundancy of features. The SoftPool operation can retain. The output feature map of SoftPool is calculated by weighing the sum of all signal values in the candidate region In supervised learning, the loss function as a penalty is the key to guide the model parameters to update correctly. The accuracy of prediction localization is measured in the YOLO algorithm by calculating the IOU (intersection and concurrency ratio) loss between the prediction frame and the ground truth. Existing methods rarely consider the direction of mismatch between the ground truth and the prediction box. This drawback often leads to slow convergence and reduced efficiency of the model. Tiny apple disease targets are difficult to be quickly calibrated in the final prediction process, and the presence of more perceptual regions leads to a larger number of redundant feature frames. In this paper, we use SIOU as a loss function to accelerate the tiny target matching of apple leaf diseases.In particular, SIOU is defined as follows:The distance cost is defined as follows:The shape cost is defined as follows:s 2 to 6 .P (precision), R , mAP, AR, FPS, and parameter size to evaluate the performance of the model.Herein, we use the classic P (precision) and R . P represents the probability that the predicted category is correct; R represents the proportion of the number of samples correctly predicted to be positive to the total number that actually turned out to be positive. The relevant formulas are defined as follows:We first define the basic metrics P–R curve is formed by P and R, and its area is AP (average precision), reflecting the accuracy of a single class. mAP is an average of AP values for multiple prediction categories and is commonly used to measure the performance of models containing multiple categories in object detection. In this paper, the model is tested using an mAP value with an IOU threshold of 0.5. The calculation formula is as follows:The n is the number of image frames detected.The AR  is mainly used to measure the degree of model inspection failure. AR is calculated as follows:t is the time required to process each image from input to output.FPS (frames per second) is an important measurement of detection speed. In this paper, it represents the average number of images detected per second. The formula for calculating FPS is as follows:−9) floating point operations per second.In addition, we use Params and GFLOPs to measure model size and computational complexity. Where FLOPs stands for floating point of operations, and one GFLOP is equal to one billion , validation set (648), and test set (648) using common ten-fold cross-validation . And theIn addition, in real-world environments, the incidence of a fewer number of categories is lower and sample collection is difficult. If extensive digital enhancement is performed directly, the resulting image is very similar to the original image in terms of disease characteristics. For example, the affine transformation leaves the disease values essentially unchanged, with only a displacement of the disease region. This causes the network to be trained multiple times with the same disease features, falling into local optimization and producing overfitting. In order to ensure the generalization performance of the detector over these classes, we did not carry out further data enhancement strategies.−3 to 1 × 10−5 and the decay rate is 5 × 10−4. We followed PyTorch’s default settings [Considering the hardware resource limitation, we set the Batch size to 32  and Epochs to 150  and the true label encodings as two independent variables, and then performed a differentiation analysis on these two variables. Considering that disease location and category do not present a certain regular distribution on the images, we use the Wilcoxon Signed-Rank method  to carryp < 0.05), it indicates that the gap between the model prediction results and the accurate labeled boxes is large, and the model prediction effect is poor; Cohen’s d value can measure the volatility of the detection, and the lower the value, the more stable the detection effect is. From the table, it can be seen that HSSNet is not only smaller than YOLOv7-tiny in detection error, but also the detection results are more stable, with better robustness and stability.In the Wilcoxon Signed-Rank hypothesis test results, the P value represents whether the error between the detector prediction and the manual labeling of the frames shows significance. If it presents significance  to tiny disease targets.To optimize bounding box regression of tiny disease targets in training, we use the SIOU loss function. In order to verify the necessity of various improved algorithms for YOLOv7-tiny, we conducted ablation experiments on HSSNet, as shown in As shown in Comparing the A, C, E, and G experiments, it was found that SP-BiFormer decreased in FPS and improved the number of parameters and GFLOPs. However, its improvement in recall and precision is very significant, effectively distinguishing different categories of disease features and improving detection precision. Such a trade-off is very meaningful and worthwhile for small-target detection. Therefore, the embedding of this module is necessary for the detection of sparse tiny target diseases.Comparing group A, D, F, and G, SIOU optimizes the detection training process and improves the detection precision of the model. In addition, the inclusion of the angle loss metric is beneficial for the inference speed of the model.In summary, H-SimAM inhibits unsupervised signals and improves the model’s effective focus on disease targets. SP-BiFormer is based on sparse perceptual query ability, which greatly promotes the ability of the model to detect tiny targets. SIOU considers the direction of the mismatch between the predicted box and the real box, and weighs the distance loss and angle loss in the design, which improves the model accuracy and improves the model’s training efficiency.We compared the performance effects of the baseline network YOLOv7-tiny and HSSNet in the typical scenarios under four categories, and the results are shown in In In In In In addition, we also compare the performance of different models to explore the adaptability of HSSNet in tiny target apples. In order to explore the scalability of the larger scale YOLOv7 detector on the dataset of this paper, we conducted related experiments using both the standard and X versions. The results show that the detection speed, precision, and recall decrease drastically as the model size increases. This suggests that the YOLOv7 version with a larger number of parameters suffers from severe overfitting and the model falls into some simple disease targets. Therefore, the YOLOv7-tiny model is a better fit for the application scenario of this task.In addition, we compared other series of detectors of the same era as YOLOv7. In order to avoid the overfitting of detectors, we chose detectors that are similar to the tiny version in terms of model size and number of parameters. The experimental results show that RTMDet-S improves the backbone and neck network of the YOLO series and performs better in detection accuracy. However, it shows a severe decrease in FPS and an increase in the number of parameters and GFLOPs. Compared to the YOLOv7-tiny benchmark, it does not have an advantage in terms of overall performance. We also compare the lightweight detectors GhostNetV2 and MobileViT-S. Among others, GhostNetV2 has a great advantage in speed and the extreme lightness of the model makes the GFLOPs very small. However, this also loses the feature expression ability of the model, and thus the detection accuracy is poor. MobileViT-S, based on the transformer architecture, has better long-range modeling capability and is close to YOLOv7-tiny in small-target disease detection. However, the model loses serious inference speed as the current hardware does not have a dedicated transformer accelerator.The YOLOv7-tiny lightweight baseline network can rapidly detect apple leaf diseases with a certain accuracy. Based on this, we propose HSSNet to improve the detection precision of YOLOv7-tiny for apple leaf diseases with complex background features and tiny target features in natural environments, while ensuring high real-time detection speed.We selected some typical scenarios in the detection process to discuss the comprehensive performance of the model, as shown in (a) When the lighting conditions changed, HSSNet still maintained robustness and detected tiny targets with high confidence;(b) HSSNet missed or judged the location and type of disease with low precision when there was a certain angle between the front surface of the leaf disease and the front surface of the camera;(c) HSSNet had difficulty in distinguishing the leaf disease with a deep distance when the foci of the leaf disease varied in spatial distance from the camera.Although HSSNet achieved a high detection precision in the four types of apple leaf disease detection mentioned in this paper, it still has some limitations. In our detection example, there is a lack of datasets with multi-directional shooting views involved in the training and testing process, and the model robustness needs to be further optimized. In addition, the robustness of HSSNet in detection scenarios with multiple apple leaves and overlapping occlusions still needs to be verified. In view of the limited hardware resource budget in practical application environments, a more lightweight real-time detection network needs to be investigated.Herein, to explore the optimization of apple leaf disease detection using deep learning object detection algorithms, we propose an improved HSSNet based on the baseline YOLOv7-tiny model. First, we constructed a precisely labeled image dataset, TTALDD-4, with four categories of apple leaf diseases by ourselves. For the complex background of apple leaf diseases, we propose that the H-SimAM zero-parameter attention module optimizes the ability of YOLOv7-tiny to focus on foreground targets. The structure can suppress the expression of unsupervised signals and prompt the network to focus on disease information more efficiently. For the characteristics of apple leaf disease mini-targets, we propose the BRA module-based SP-BiFormer Block to optimize the ability of YOLOv7-tiny to capture tiny-target disease information. This module aids in inferring small targets through associating context-aware features of disease small targets and using a wider range of features in the scene. Furthermore, with these implementations, we address the problem that it is difficult to quickly calibrate the true location of apple leaf disease tiny targets resulting in reduced training efficiency and detection accuracy. We use the SIOU loss function to optimize the model training. SIOU better fits the dense distribution features of apple leaf diseases in the training process and accelerates the inference process. The experimental results show that HSSNet achieves 85.04 (+4.67) in mAP and 67.53 (+7.68) in AR, and effectively reduces the cases of YOLOv7-tiny false detection and missed detection of small-target diseases. It must be noted that we have not incorporated variety-specific a priori knowledge into the optimization of the detector because different apple varieties were not taken into account. Nevertheless, HSSNet was able to perform well in the detection of small targets in apple leaves of mixed varieties.In summary, HSSNet significantly improved the precision of the YOLOv7-tiny model in the field of apple leaf disease detection, while maintaining a balance between model parameters and detection speed. This research can assist apple growers to accurately apply pesticides based on the detection results. This provides a fresh reference for deep learning in ensuring modern pest control planting in the apple growing industry with practical applications.


The Health Poverty Alleviation Project (HPAP) has received widespread attention as a primary means of preventing poverty caused by illness. However, further evidence is required to confirm the effects of HPAP.This study examines the effectiveness and mechanisms of action of HPAP using data from a special survey conducted in five Chinese prefectures in 2018–2019.This study uses a three-step feasible generalised least-squares method to measure the farm households’ vulnerability to poverty. Hierarchical linear regression and propensity score matching were employed to assess the poverty-reduction effects of HPAP. A mediating effects model was used to test how these policies alleviated poverty.The mean vulnerability to poverty among farm households was 0.367, with 11.89% experiencing both poverty and vulnerability, particularly in areas of deep poverty. This study has found that HPAP significantly reduces poverty and is more effective in reducing the vulnerability of non-poor farm households than poor farm households. Additionally, the results suggest that improving human capital stock and reducing medical expenditure are the two pathways through which HPAP can alleviate farm households’ vulnerability to poverty.This study suggests that the vulnerability to poverty perspective should be incorporated into poverty alleviation policy formulation. HPAP enhances differentiation and precision. Thus, a long-term mechanism of HPAP should be developed. The primary goal of the United Nations 2030 Agenda for Sustainable Development is to eradicate poverty , and ChiPoverty is defined as a state in which income or consumption falls below a certain level . The limHealth shocks have become the most important cause of vulnerability to poverty . The essTo end the cycle of illness and poverty, China has implemented the Health Poverty Alleviation Project (HPAP) since 2016. HPAP includes a series of policies aimed at implementing medical assistance and improving medical conditions . The polIn addition to China, numerous other governments worldwide have their own HPAP. Researchers have studied the relationship between these policies and individuals’ susceptibility to poverty. For example, Atake’s study in sub-Saharan Africa found that reducing healthcare costs or increasing medical insurance coverage could effectively improve vulnerability to poverty , and Vo Despite the abundance of research on this topic, several gaps remain in our understanding of HPAP and its impact on farmers’ vulnerability to poverty. Specifically, there is a lack of research evaluating HPAP performance and the mechanisms through which these policies contribute to poverty reduction. Additionally, previous studies have often neglected the role of village-level or community variables in vulnerability to poverty. This study aims to address these shortcomings using special survey data to explore the relationship between HPAP and vulnerability to poverty and the pathways through which these policies impact poverty reduction.The dependent variable in this study is vulnerability to poverty, which is measured using the three-stage feasible generalised least squares (FGLS) method by calculating the log of income and the variance of the log of income. This measure represents the probability that a farm household will fall into poverty in the future and ranges from 0 to 1. The independent variable is whether a household is eligible for HPAP, which is indicated by a binary variable with a value of 1 for eligible households and 0 for ineligible households. The control variables include the characteristics of the household head , characteristics of the household , and characteristics of the village . Ecological fragility refers to whether the village is located within an ecologically fragile area. The government designates the ecologically fragile areas accounting for more than 55% of China’s land . The eco121 mu = 666.67 m At the village level, the average coverage distance to the clinic was 2–4 km, and 27% of the farm households were located in ecologically fragile areas.The characteristics of the variables used in this study are summarised in The data for this study were collected during a special survey on ‘precise HPAP and population development’ founded by the National Social Science Foundation of China from December 2018 to February 2019. The survey targeted areas of deep poverty and key HPAP regions designated by the government. The study sites were selected from Liangshan Prefecture in Sichuan Province, Linxia Prefecture in Gansu Province, Anqing City in Anhui Province, Enshi Prefecture in Hubei Province, and Shangluo City in Shaanxi Province . These fThe survey was conducted by recruiting local college students with rural household registrations as investigators, who were trained and supervised by the subject team or coordinating teachers. Investigators returned to their hometowns to conduct the survey during the winter vacation, using a stratified sampling approach based on the registration forms of voluntarily enrolled students to cover as many regions as possible. A total of 252 college students from rural areas participated in the survey. The subject team followed up with some respondents and reviewed the returned questionnaires to ensure data quality. The survey included questionnaires on both household and village. The questionnaire on household covered five areas: basic family information and social support, family member information, health status and social support, satisfaction with medical services, and perception of HPAP. The questionnaire on village covered four areas: basic personal information of village officials, basic village information, living conditions, regional environment, and rural clinic hygiene. The survey first randomly extracted poor households defined by national rural poverty alleviation standards in each province and then extracted a random sample of non-poor households from the same villages. The sample size of poor households is the same as that of non-poor households. The final valid sample size was 2102. Based on the missing data, a final sample of 1295 farm households and 148 villages were analysed. A comparison of the survey data with data from the Sixth National Health Service Survey revealed good consistency . The SixThis study employed the VEP method, which was further refined by Bronfman et al., to measure vulnerability to poverty among farm households . To contrty line .(1)LnincIn the above equations, e at 0.5 . This vuTo assess the impact of the HPAP on vulnerability to poverty and to consider the influence of both individual- and village-level covariates on the farm households’ vulnerability to poverty, this study used a hierarchical linear regression model implemented using HLM 8 software. Given that the future welfare status of farm households is affected by household- and village-level factors, each farm household can be nested within its corresponding village. The hierarchical linear model used to analyse the factors influencing the farm households’ vulnerability to poverty is as follows:From the perspective of poverty dynamics, this study examined the effect of a farm household’s enjoyment of HPAP on its vulnerability to poverty to assess the impact of HPAP on poverty reduction. Since it is impossible to observe the state of enjoying HPAP and not enjoying it simultaneously, this study used a counterfactual causality approach for the analysis. The main idea of the Propensity Score Matching (PSM) method is to identify a control group through feature matching and thereafter make the experimental and control groups highly similar in characteristics through PSM. Thus, the difference in vulnerability to poverty after matching can be attributed to the impact of the HPAP, and the balancing and common support hypotheses are satisfied before matching. Logit regression models were used with Stata to estimate the probability of eligibility for HPAP, and the Average Treatment Effect (ATT) was calculated.In This study used a mediating effect model to empirically test the mediating effects and mechanisms of the increment in human capital and out-of-pocket medical costs on the relationship between HPAP and vulnerability to poverty among farm households, based on the theoretical mechanisms of ‘HPAP improving human capital and reducing vulnerability to poverty’ and ‘HPAP reducing out-of-pocket medical costs and reducing vulnerability to poverty’. The mediating effect of the increment in human capital is measured using responses to the question ‘Health poverty reduction improves the quality of family labour’ in the household questionnaire. The proportion of out-of-pocket medical expenses among farm households is calculated as the proportion of out-of-pocket medical expenses to total household expenses.The above three equations were used to test these mediating effects and mechanisms, where The results for vulnerability to poverty and the distribution of the five municipalities are presented in Before applying propensity score matching to obtain the ATT, it is necessary to conduct common support and balancing assumption tests. A common support test was performed on the sample to ensure that most of the treatment groups had matches in the control group. The kernel density curves of the treatment and control groups almost overlapped, satisfying the common support assumption of PSM. In other words, that means there are pairs of samples with almost characteristics of covariates, and the HPAP is the critical difference between the pairs. The balancing assumption requires that all covariates are balanced between the treatment and control groups with no significant differences, under the assumption of conditional exogeneity. The p-values of the post-matching t-tests were all greater than 0.1, and the deviations of all covariates after matching were less than 10%, satisfying the balancing assumption. The result of the balancing test means the pairs of samples mainly cover the treatment and control groups.To eliminate the problem of self-selection bias, PSM was used to test the causal relationship between HPAP and vulnerability to poverty. In addition, the results of the vulnerability to poverty measure to determine whether the farmers are poor may have an impact on the above results, a sub-sample test was conducted using whether the farmers are poor as the basis for sub-sample division. Exploring the internal logic between HPAP and vulnerability to poverty is helpful for better understanding the relationship between the two, i.e. the ways in which HPAP reduces vulnerability to poverty. Based on the availability of data, a mediating effect test model of HPAP on farm households’ vulnerability to poverty was constructed using human capital increment and out-of-pocket medical ratio as mediating variables to further test the mechanism of the effect of HPAP on poverty reduction. In accordance with the steps of the mediating effect test model introduced in the previous section, For the human capital increment effect in Group 1, Models 1 and 3 are tobit regressions with vulnerability to poverty as the explanatory variable and Model 2 is a multiple linear regression with human capital increment as the explanatory variable. The control variables are related variables such as the marital status of the household head, education level of the household head, land area per capita, and work outside the household. The results reveal that HPAP is negatively correlated with vulnerability to poverty among farming households in Model 1. In Model 2, HPAP is found to have a significant positive effect on human capital growth. In Model 3, HPAP and human capital increment negatively impact vulnerability to poverty among farming households. These findings suggest that efforts to address health poverty can reduce vulnerability to poverty among farming households and that increasing human capital through HPAP is also effective in reducing vulnerability to poverty. In summary, HPAP reduces farm households’ vulnerability to poverty by increasing their human capital.To assess the effect of the out-of-pocket medical ratio in Group 2, Model 4 and Model 6 are tobit regression with vulnerability to poverty as the explanatory variable, and Model 5 is a multiple linear regression with the out-of-pocket medical ratio as the explanatory variable. The control variables were related variables, such as the health status of the household head, prevalence of severe or chronic illness, and the farthest distance covered by rural clinics. The results reveal that HPAP is negatively correlated with vulnerability to poverty among farmers in Model 4. In Model 5, HPAP is found to have a significant positive effect on the proportion of out-of-pocket medical expenses incurred by farmers. In Model 6, HPAP and the out-of-pocket ratio of medical expenses were found to significantly impact vulnerability to poverty among farmers. In summary, the mechanism by which the HPAP can alleviate vulnerability to poverty in farm households by reducing medical expenses was verified.This study first measured vulnerability to poverty; thereafter, it evaluated the factors influencing vulnerability to poverty and the poverty-reduction effect of HPAP and finally explored the mechanism of the health poverty-reduction effect. The results reveal that HPAP significantly reduces households’ vulnerability to poverty in two ways: by improving human capital stock and by reducing medical expenditures.The survey results demonstrate that some non-poor farm households also belong to the vulnerable group. Of the farm households, 8.26% were in a non-poor status, however, in a poverty-vulnerable state. The results of this study suggest that it is vital to consider both poor and non-poor farming households that are vulnerable, for poverty-reduction efforts. Of the poor farm households, 23.09% may come out of poverty stably, indicating that the poverty alleviation policy has achieved specific results; 11.89% of the farm households are not only poor at present but also face poverty in the future, and it is more difficult for these farmers to escape poverty, indicating that high vulnerability is accompanied by poverty.Consistent with previous studies , this stBased on the results of this study, initiatives focused on improving health and reducing poverty have a more notable effect on reducing vulnerability to poverty among households that are not currently impoverished as opposed to those that are already poor. This conclusion differs from previous research, suggesting that medical aid can significantly decrease vulnerability to poverty among low-income households . This maThis study had certain limitations. First, this study should have considered differences in the prevalence of chronic and acute diseases. Some studies have revealed that HPAP may have different effects on VEP in patients with chronic or severe diseases . Second,This study used special survey data from five provinces in China to quantitatively examine the poverty-reduction effect of HPAP in poverty-stricken areas from the perspective of vulnerability to poverty and reached the following conclusions:First, from the perspective of vulnerability to poverty, the stability of poverty alleviation in rural areas remains less optimistic, and there are noticeable regional differences. Deeply impoverished areas are primarily located along borders and in ethnic minority areas. The main characteristics include ecological fragility, frequent natural disasters, insufficient medical resources, and poor infrastructure. Farm households are more vulnerable to risks and have insufficient ability to resist shocks, which could easily lead to them becoming trapped in the ‘poverty trap’ cycle .Second, HPAP has a significant poverty-reduction effect, which can effectively reduce the risk of farm households falling into poverty in the future and significantly reduce the vulnerability of non-poor farm households.Third, increasing the stock of household human capital and reducing medical expenditures are two ways to effectively alleviate farm households’ vulnerability to poverty. Policies aimed at alleviating poverty in rural areas can have several positive impacts, including improving the overall health of residents, strengthening the public health system, increasing household labour productivity, and reducing farm households’ vulnerability to poverty . Additio


In this paper, we provide geometric insights with visualization into the multivariate Gaussian distribution and its entropy and mutual information. In order to develop the multivariate Gaussian distribution with entropy and mutual information, several significant methodologies are presented through the discussion, supported by illustrations, both technically and statistically. The paper examines broad measurements of structure for the Gaussian distributions, which show that they can be described in terms of the information theory between the given covariance matrix and correlated random variables (in terms of relative entropy). The content obtained allows readers to better perceive concepts, comprehend techniques, and properly execute software programs for future study on the topic’s science and implementations. It also helps readers grasp the themes’ fundamental concepts to study the application of multivariate sets of data in Gaussian distribution. The simulation results also convey the behavior of different elliptical interpretations based on the multivariate Gaussian distribution with entropy for real-world applications in our daily lives, including information coding, nonlinear signal detection, etc. Involving the relative entropy and mutual information as well as the potential correlated covariance analysis, a wide range of information is addressed, including basic application concerns as well as clinical diagnostics to detect the multi-disease effects. Understanding the ways knowledge concerning an external variable or the reciprocal information of its parts can assist in characterizing and inferring the underlying mechanics and function of the system. This goal has driven the development of several techniques for dissecting the elements of a set of variables’ combined entropy or for dissecting the contributions of a set of variables to the mutual information about the variable of interest. In actuality, this association and its modifications exist for any input signal and the widest range of Gaussian pathways, comprising discrete-time and continuous-time pathways in scalar or vector forms.In a more general way, mutual information and mean-square error (MSE) are the fundamental concepts of information theory and estimation theory, respectively. In contrast to the minimum MSE (MMSE), which determines how precisely each input sample can be restored using the channel’s outcomes, the input-output mutual information is an estimation of whether the information can be consistently delivered over a channel given a specific input signal. An inactive functioning characterization for mutual information is provided by the substantial relevance of mutual information to estimation and filtering. Therefore, the significance of identity is not only obvious, but the link is also fascinating and merits an in-depth explanation ,2,3. RelConsidering the specific instance of parametric computation (or Gaussian inputs), correlations relating to causal and non-causal estimation errors have been investigated in ,10, invoIn the multivariate scenario, the challenges of breaking down mutual information into redundancy and complementary sections have nevertheless been significantly increased. The maximum entropy framework allows for a more straightforward generalization of the efficiency measurements to the multivariate case ,27. The Although there are some valuable references detailing entropy-related topics, both discrete and continuous, they may not be easily accessible to some readers from the existing publications. Therefore, in this present study, we propose an extension of the bivariate Gaussian distribution technique to calculate multivariate redundant metrics inside the maximum entropy context. The importance of the maximum entropy approach in the multivariate scenario, where it offers constraints for the actual redundancy, unique information, and efficiency terms under logical presumptions shared by additional criteria, acts as the motivation for this particular focus ,34. The The remainder of this paper is organized as follows. A brief review of the geometry of the Gaussian distribution is reviewed in In this section, the background relations of the Gaussian distribution from different parametric points of view will be discussed. The exploratory objective of the fundamental analysis is to identify “the framework” in multivariate datasets. Ordinary least-squares regression and principal component analysis (PCA), respectively, analyze the measurements for dependency (the predicted connection between particular components) and rigidity (the degree of prominence of the probability density function (pdf) around a low-dimensional axis) for bivariate Gaussian distributions. Mutual information, an established measure of dependency, is not an accurate indicator of rigidity since it is not invariant with an opposite rotation of the parameters. For bivariate Gaussian distributions, a suitable rotating invariant compactness measure is constructed and demonstrated to reduce the corresponding PCA measure.For the uncorrelated data, which has zero covariance, the ellipse is not rotated and the axis is aligned. The radii of the ellipse in both directions are the variances. Geometrically, a not-rotated ellipse at point  and radii The general probability density function for the multivariate Gaussian is given by the following:For bivariate Gaussian distributions, the mean and covariance matrix are given by the following:Variance measures the variation of a single random variable, whereas covariance is a measure of the two random variables varying together. With the covariance, we can calculate the entries of the covariance matrix, which is a square matrix. In addition, the covariance matrix is symmetric. The diagonal entries of the covariance matrix are the variances; however, the other entries are the covariances. Due to this reason, the covariance matrix is often called the variance-covariance matrix.s, known as the Mahalanobis radius of the ellipsoid:s such that confidence p is met. Since the data are multivariate Gaussian-distributed, the left-hand side of the equation is the sum of squares of Gaussian-distributed samples, which follows a χ2 distribution. A χ2 distribution is defined by the degrees of freedom, and since we have two dimensions, the number of degrees of freedom is two. Now, we have calculated the probability with the sum, and therefore s has a certain value under a χ2 distribution.A typical way to visualize two-dimensional Gaussian-distributed data is by plotting a confidence ellipse. The distance χ2 table or simply using the relationship s.This ellipse with a probability contour defines the region of a minimum area (or volume in the multivariate case) containing a given probability under the Gaussian assumption. The equation can be solved using a The Mahalanobis distance accounts for the variance of each variable and the covariance between variables.In the general case, covariances ▪It accounts for the fact that the variances in each direction are different;▪It accounts for the covariance between variables;▪It reduces to the familiar Euclidean distance for uncorrelated variables with unit variance.Based on Equations (2) and (7), the bivariate Gaussian distributions can be represented as follows:The length of the ellipse axes is a function of the given probability of the chi-squared distribution with 2 degrees of freedom The simplest similarity transformation method for eigenvalue computation is the Jacobi method, which deals with the standard eigenproblems. In the multivariate Gaussian distribution, the covariance matrix When ScalingThe covariance matrix can be presented by its eigenvectors and eigenvalues: The covariance matrix can be written as 2.RotationThe similarity transform is applied to obtain the relationship between 3.Translationp, which can be plotted by calculating the radii, its center, and the rotation. Here, With the given data To generate the sampling points that meet the specified correlation, the following procedure can be followed. Given two random variables When In the following, two case studies involve more illustrations:(1) Equal variances for two random variables with nonzero Case 1: fixed correlation coefficient. As an example, when Case 2: increasing the correlation coefficient (2) Unequal variances for two random variables, Case 1: Case 2: (3) Variation of the ellipses for the various positive and negative correlations. For a given variance, when Differential entropy  is a concept in information theory that began as an attempt by Claude Shannon to extend the idea of (Shannon) entropy, a measure of the average surprise of a random variable, to continuous probability distributions. Unfortunately, Shannon did not derive this formula and rather just assumed it was the correct continuous analog of discrete entropy, but it is not . The actIn the following discussion, differential entropy and relative entropy are measured in bits, which are used in the definition. Instead, if ln is used, it is then measured in nats, and the only difference in the expression is the If we have a continuous random variable multivariate Gaussian distribution Let tance as :(35)E[:For the case of a multivariate Gaussian distribution, we have:In this section, various important issues regarding relative entropy (Kullback–Leibler divergence) are discussed. Despite the aforementioned flaws, there is a possibility of information theory in the continuous case. A key result is that the definitions for relative entropy and mutual information follow naturally from the discrete case and retain their usefulness.The relative entropy is a type of statistical distance that provides a measure of probability distribution (1) If (2) If –If –If (3) If When When A sensitivity analysis of the relative entropy due to changes in variance and mean is carried out. The gradient of (1) (2) (3) (4) The optimal condition for each of the above cases can be:X and Y has the following relationships:Mutual information is one of many quantities that measures one random variable and tells us about another. It is a dimensionless quantity with  units of bits and can be thought of as the reduction in uncertainty about one random variable given knowledge of another. The mutual information X and Y given by:X and Y are perfectly correlated, the mutual information is infinite. It can be seen that Let’s consider the mutual information between the correlated Gaussian variables On the other hand, considering the additive white Gaussian noise (AWGN) channel, shown in This paper intends to serve the readers as a supplement note for the multivariate Gaussian distribution with its entropy, relative entropy, and mutual information. The illustrative examples are discussed to provide further insights into the geometric interpretation and visualization, enabling the readers to correctly interpret the theory for future design. The fundamental objective is to study the application of multivariate sets of data to a Gaussian distribution. This paper examines broad measurements of structure for Gaussian distributions, which show that they can be described in terms of the information theory between the given covariance matrix and correlated random variables (in terms of relative entropy). To develop the multivariate Gaussian distribution with entropy and mutual information, several significant methodologies are presented through the discussion supported by illustrations, both technically and statistically. The content obtained allows readers to better perceive concepts, comprehend techniques, and properly execute software programs for future study on the topic’s science and implementations. It also helps readers grasp the themes’ fundamental concepts. Involving the relative entropy and mutual information as well as the potential correlated covariance analysis based on differential equations, a wide range of information is addressed, from basic to application concerns. Moreover, the proposed techniques of multivariate Gaussian distribution and mutual information are intended to inspire new applications of information theory to a number of areas, including information coding, nonlinear signal detection, and clinical diagnostic testing, particularly when data from improved testing equipment becomes accessible.


Commercialized since 2019, emicizumab (Hemlibra) was available only in French hospital pharmacies for prophylaxis of hemophilia A with or without inhibitors. Since June 15, 2021, patients can choose between a hospital and community pharmacy. These changes in the care pathway have important organizational consequences for patients, their relatives, and health professionals. Two training programs are available for community pharmacists: the “HEMOPHAR” training program proposed by the national reference center for hemophilia and the Roche training program proposed by the laboratory that markets the product.The PASODOBLEDEMI study aims to evaluate the direct impact of the training programs provided to community pharmacists in the context of the dispensing of emicizumab, and to evaluate patients’ satisfaction with their treatment whether they choose dispensation from a community pharmacy or retained dispensation from the hospital pharmacy.Reaction), the knowledge acquired during the training (Learning), the professional practice of community pharmacists during dispensing of the product (Behavior), and patients’ satisfaction related to the treatment whether it is dispensed from a hospital or from a community pharmacy (Results).We designed a cross-sectional study based on the 4-level Kirkpatrick evaluation model: the immediate reaction of community pharmacists following training (Considering that single outcome measures cannot adequately reflect the complexity of this new organization, the Kirkpatrick evaluation model provides 4 distinct outcomes: the immediate reaction after the HEMOPHAR training program, the level of knowledge acquired after the HEMOPHAR training program, the impact of training on professional practice, and patient satisfaction with access to emicizumab. We developed specialized questionnaires for each of the 4 levels of the Kirkpatrick evaluation model. All community pharmacists involved in dispensing emicizumab, whether they have followed the HEMOPHAR or the Roche training program or neither, were eligible for inclusion. All patients with severe hemophilia A were eligible, irrespective of inhibitor use, age, treatment with emicizumab, and whether they chose dispensation from a community pharmacy or retained dispensation from a hospital pharmacy.The new organization for dispensing emicizumab to patients with hemophilia A in French community pharmacies must be accompanied by optimal safety and quality conditions due to the risk of serious and urgent bleeding situations in the management of rare bleeding diseases. The elaboration of the PASODOBLEDEMI protocol has already a positive impact with the commitment of all health professionals, physicians, hospital and community pharmacists, and the patient community. The results will be disseminated among the French authorities and will enable, if necessary, proposing this access model to other rare diseases.ClinicalTrials.gov NCT05449197, https://clinicaltrials.gov/ct2/show/NCT05449197?term=NCT05449197; ClinicalTrials.gov NCT05450640, https://clinicaltrials.gov/ct2/show/NCT05450640?term=NCT05450640DERR1-10.2196/43091 Severe hemophilia A is an inherited bleeding disorder due to the deficiency of clotting factor VIII (FVIII), which causes bleeds occurring internally into joints and muscles, or external bleeding from minor cuts, surgical procedures, or injuries. The frequency and intensity of bleeding depends on the level of FVIII deficiency. In high-income countries, the life expectancy of patients with severe hemophilia A is decreased by 37%, the prevalence is estimated to be approximately 6 per 100,000 males, and prevalence at birth is to be approximately 9.5 cases per 100,000 males . ConventEmicizumab (Hemlibra) is a laboratory-engineered protein that works by performing a key function in the clotting cascade that is normally carried out by the FVIII protein -12. It cIn 2019, emicizumab received marketing authorization for severe hemophilia A with or without an inhibitor in Europe . This drThese changes in the dispensing circuit have important organizational consequences for community pharmacists, becoming both new stakeholders and contacts in the patient care pathway . The effThe Kirkpatrick model (KM) represents a reference for the evaluation of training programs. Studies of various designs and purposes were addressed using the KM; for example, to evaluate a nutritional education program provided by health care professionals , to evalThe popularity of the KM can be traced to several factors . First, The first level of evaluation consists of collecting immediate feedback from participants after completing the training. This information can be used to determine which elements of the training are working well or appreciated, and which ones need to be improved. Indicators such as participation rate, completion rate, or time spent on training are typically collected to supplement participant feedback.Learning objectives or targeting expected effects of training. When pretraining data are missing, the knowledge acquired post training is evaluated in accordance with the expected knowledge.The second level is to accurately measure what participants did or did not learn during the training. Usually, the KM suggests a pre- and posttraining evaluation to quantify progress, for example, through knowledge tests or competency interviews. In contrast to immediate reactions to training, this level allows for the measurement of specific outcomes by identifying Behavior, data collection and feedback experience are needed to give participants the opportunity to apply the skills they learned during training; for example, by exposing them to a simulated situation. It is important to mention that a lack of behavioral change does not necessarily mean that the training was ineffective.The third level is to determine if the training had a direct impact on the participants' behaviors. This level of evaluation is the most time-consuming because it takes several weeks or months for participants to build confidence and apply their knowledge in their professional practice. To measure The fourth level consists of assessing the impact of behavioral changes of the participants on the systemic organization, and in determining if the training reached the expected impact or improved the organization.We designed a cross-sectional study based on the KM. The first 3 levels are based on the data directly collected from the pharmacists. Level 1 refers to the evaluation of the immediate reaction of community pharmacists who followed the HEMOPHAR e-learning program and level 2 to their knowledge acquisition. Level 3 consists of evaluating the professional practice of both hospital and community pharmacists in the dispensation of emicizumab. The fourth level of the KM refers to the patients’ satisfaction related to treatment, whether dispensed from a hospital or a community pharmacy .Reaction and Learning. All community pharmacists involved in the dispensing of emicizumab since June 15, 2021, whether they have followed the HEMOPHAR training program or the Roche training program or neither, were eligible for the evaluation of Behavior. Retired community pharmacists are excluded, as are those who have changed practice locations and are no longer practicing in a community pharmacy dispensing emicizumab.Community pharmacists who received personalized login codes for the HEMOPHAR e-learning program from the national reference center for hemophilia were eligible for inclusion in this study for the evaluation of All patients with severe hemophilia A, with or without an inhibitor, regardless of age, treatment with emicizumab, and whether they chose dispensation from a community pharmacy or retained dispensation from a hospital pharmacy, were eligible for the evaluation of the results. For those younger than 18 years, a legal representative fills out the questionnaire, and for those aged 18 years or older who need assistance in completing the questionnaire, this may be provided by caregivers or relatives.Reaction. The CRA is also able to incite community pharmacists—who have received their connexion codes but who have not yet started the HEMOPHAR learning program—to finalize the HEMOPHAR training program. During the HEMOPHAR training program, community pharmacists also complete 4 quizzes related to the following sections: presentation of the disease, therapeutic management, organization of care, and practice in the community pharmacy. The responses to the quizzes will be used to evaluate Learning. All community pharmacists are invited to complete the e-questionnaire related to Behavior at least 3 months after the implementation of the organization. Patients treated with emicizumab are invited to complete the appropriate questionnaire related to Results, an e-questionnaire specific to dispensation from hospital pharmacies, and a second e-questionnaire specific to dispensation from community pharmacies.A clinical research associate (CRA) is specifically dedicated to contact community pharmacists, informing them of the study modalities and outcomes, and inviting them to complete the e-questionnaires at the appropriate time . ImmediaReaction was intentionally short and composed of 8 questions, including 5 questions based on the 4-item Likert-scale  and 3 closed-ended questions . Following the recommendations of the scientific committee, the content of the e-questionnaires has evolved by integrating operational and organizational aspects and optimizing literacy. The e-questionnaires were finally tested in real-life conditions on a sample of eligible populations. The content of the questionnaires was finally validated by the scientific committee in July 2022.Reaction, Learning, and Behavior, and NCT05450640 related to the evaluation of Results).The study complies with the reference methodology for studies and evaluations in the health field ; therefoReaction and Behavior; this also allowed the linking of data between evaluation levels. The e-questionnaire related to Results is accessible to eligible patients via a QR code or a specific URL presented on a paper information note, hand-delivered by the community pharmacist or hospital pharmacist when the patient comes for treatment or consultation.All e-questionnaires may be filled out using a PC or mobile device. The hospital and community pharmacists are invited by email to complete the e-questionnaires accessible using a login and password sent by the CRA for the evaluation of Data collection for the first 3 levels started on July 1, 2022, and for the fourth level, the questionnaires for patients were available since September 12, 2022. The study ended on December 31, 2022.The availability of emicizumab in community pharmacies represents a significant advancement of the care pathway for patients with hemophilia A. The direct expected benefit concerns the improvement of the patients’ satisfaction by reducing the mental burden due to the geographical and organizational constraints to hospital pharmacies . As obseThe new organization for dispensing emicizumab to patients with hemophilia A in French community pharmacies must be accompanied by optimal safety and quality conditions due to the risk of serious and urgent bleeding situations in the management of rare bleeding diseases. Based on the KM, the PASODOBLEDEMI study focuses on the evaluation of the training program and patient satisfaction 1 year after the implementation of the community-based dispensing of emicizumab. Widely used in the literature , the KM The KM presents limitations  because Other methodologies have been developed and used for evaluation of training programs, but which were not adapted to the PASODOBLEDEMI study. For instance, the Context-Inputs-Process-Product model (or the Stufflebeam model) ,32 is baThe elaboration of the PASODOBLEDEMI protocol has already had a positive impact with the commitment of all health professionals, physicians, hospital and community pharmacists, as well as the patient community. The results will be disseminated to the French authorities and will enable, if necessary, proposing this access model to other rare diseases.