In vehicular networks, vehicles download vehicular information for various applications, including safety, convenience, entertainment, and social interaction, from the corresponding content servers via stationary roadside units. Since sufficient RSUs might be difficult to deploy due to rough geographical conditions or high deployment costs, vehicular networks can feature uncovered outage zones between two neighboring RSUs. In these outage zones, vehicles cannot download content, and thus the vehicle networks are defined as intermittently connected vehicular networks. In intermittently connected vehicular networks, the download delay and traffic overhead on the backhaul links are increased due to the large size of the content requested by vehicle users and the long distances between RSUs. Using the mobility information of vehicles, several schemes have been proposed to solve this issue by precaching and relaying content via multiple relaying vehicles in the outage zone. However, because they involved the individual ranking of vehicles for precaching and allocated all of the available precaching amounts to the top-ranking vehicles, they decreased the success rate of content requests and the fairness of vehicle precaching. To overcome the problem of these previous schemes, this paper proposes a multiple precaching vehicle selection (MPVS) scheme that efficiently selects a content-precaching vehicle group with multiple precaching vehicles to precache relayed content in outage zones. To achieve this, we first designed numerical models to decide the necessity and the amount of precaching and to calculate the available precaching amounts of vehicles. Next, MPVS calculates all available vehicle sets and ranks each set based on the available precaching amount. Then, the content-precaching vehicle group is identified from the sets by considering both set rankings and vehicle communication overheads. MPVS also provides a content downloading process through the content-precaching vehicle group in the outage zone. Simulation results conducted in various environments with a content request model and a highway mobility model verified that MPVS was superior to a representative previous scheme. With the fast development in wireless communications and vehicular technologies, vehicular networks containing smart vehicles such as autonomous cars, equipped with sophisticated sensors and intelligent analysis tools, have evolved to provide intelligent transport services ,2. TheseWith the ever-increasing scale of vehicular content, such as multimedia content comprising images, music, and video clips, the communication capacities of vehicular networks might not be able to deliver content to vehicles from a single RSU ,13. VehiMany precaching schemes based on the mobility information of vehicles have been proposed for selecting effective precaching vehicles in ICVNs ,18,19,20Therefore, this paper proposes a multiple precaching vehicle selection scheme named MPVS for efficiently selecting a content-precaching vehicle group with multiple precaching vehicles for precaching and relaying content in outage zones of ICVNs, through which high precaching fairness and request success rates can be achieved. To achieve this, we first designed a numerical model to decide the necessity and amount of precaching by comparing the total amount of requested content and the download capacity of the requester vehicle. Next, in the case of content precaching, we determined the available precaching amount of each vehicle in the communication coverage of an RSU, which was used to select the content-precaching vehicle group. Then, the available precaching amount was calculated based on the duration and amount of downloading and relaying according to the mobility information of the vehicle. To select the content-precaching vehicle group with multiple precaching vehicles, in contrast to the existing scheme based on ranking individual vehicles, we next calculated all available sets from the vehicles in the communication coverage of the RSU and ranked each of them based on the total available precaching amount. Then, the content-precaching vehicle group was identified from the sets by considering both the rankings of the sets and the connection overheads with multiple precaching vehicles. With the selected content-precaching vehicle group, we next developed a content downloading process for the requester vehicle in the outage zone. Lastly, we conducted simulations in various environments to evaluate the performance of MPVS. For our simulations, we designed a content request model based on Poisson distribution, Zipf’s law, and Gaussian distribution. Each vehicle decided on a request for its intended content based on Zipf’s law, which reflected its popularity, at any time according to Poisson distribution; the size of the content was dependent on Gaussian distribution. We additionally designed a highway mobility model wherein vehicles traveled on a straight road with acceleration and speed determined based on Gaussian distribution to reflect a realistic highway scenario. By comparing MPVS and adaptive multiple-relay selection (AMRS)  based onThe remainder of the paper is organized as follows: In vehicular networks, a delay is a very critical issue, because it is directly connected to user safety and the quality of service (QoS) for users. In the case of base-station-centric networks, due to the packet loss and scheduling resulting from an increased demand for larger-sized content, which is hard for a base station (BS) with wireless resource limitations and a wide communication coverage area to meet, vehicles can suffer long delays and buffering, such as in crowded airports and at concerts. When wireless resources are abundant, the huge demand for content can be distributively solved by covering the entire network area through the deployment of many RSUs with a relatively narrow communication coverage area. However, in traditional IP-based networks, vehicles suffer repeated delays in accessing the content server when frequently transitioning between the coverage areas of each RSU due to their high speed of travel.To address this issue, many researchers have studied CCVNs, which apply the concept of content-centric networks CCNs ,22) to v to v22])In order to reduce this access delay in CCVNs, precaching schemes in RSUs to provide the requested content via V2I communication have been studied by many researchers ,27,28,29First, precaching schemes based on request prediction were studied, aiming to precache content that had a high probability of being requested before the vehicles made the requests ,26,27. OMobility prediction-based precaching schemes have been investigated to precache the content that will be requested by predicting the movement of vehicles ,28,29. ZTo cover these outage zones, many researchers have studied precaching schemes involving other vehicles to provide the requested content via V2V communication within outage zones in CCVNs ,19,20,30To improve the performance in covering outage zones, many researchers have studied V2V precaching schemes, which select multiple vehicles as relaying vehicles ,19,20. GWe considered all groups that could become a content-precaching vehicle group based on their ability to provide the requested content within the outage zone. We prioritized selecting groups containing fewer relaying vehicles to ensure a high success rate for content requests and improve the overall performance.We set the proportion of dwell time used to precache the requested content by each relaying vehicle in the selected group within the current RSU’s coverage. This was in contrast to existing V2V precaching schemes, wherein all the abundant dwell time of relaying vehicles was spent precaching, resulting in an inability to request or receive their own content. By controlling the proportion of dwell time used by each relaying vehicle, we improved the fairness of content request allocation.We designed a content request model to evaluate the proposed scheme. Each vehicle decided whether to request content at a given time according to Poisson distribution. When the vehicle decided to request content, the requested content was decided based on Zipf’s law. Then, the size of the content was decided based on Gaussian distribution.We designed a highway mobility model wherein vehicles traveled with acceleration and speed determined based on Gaussian distribution, reflecting a realistic highway scenario. We also considered a highway scenario that had no drastic directional changes, with all vehicles traveling on a straight road.In this paper, we introduce the MPVS scheme to guarantee high fairness for every vehicle. To achieve this purpose, our contributions are as follows:In this section, we present the network model and overview of the proposed scheme, MPVS.L discrete levels within a range from 0 km/h to the maximum regulation speed of the road. We defined the set of vehicle speed levels as In this paper, we considered the network shown in een them . Every RGenerally, RSUs cannot be deployed across the whole area covered by roads in CCVNs owing to several geographical constraints and high deployment costs. As a result, two neighboring RSUs might have an outage zone between them, as shown in If a vehicle wants to download its intended content while moving to its destination, it makes an interest packet for the intended content. When it enters the communication coverage area of an RSU, it sends the interest packet to the RSU to request the intended content. In this paper, we refer to a vehicle sending an interest packet to an RSU as a requester vehicle. On receiving the interest packet, the RSU checks whether it has the content in its caching storage. If the RSU does not have the content, it also requests, downloads, and saves the content from a corresponding content server or another RSU that has the content. Once it possesses the content, the RSU checks whether it has enough time to provide all of the requested content to the requester vehicle and decides the necessity of precaching the content at the next RSU. To achieve this, it judges whether it can download all of the content to the requester vehicle in its communication coverage area by comparing the total amount of requested content and the amount downloadable by the requester vehicle in its communication coverage area. The downloadable amount for the requester vehicle is calculated using both the remaining travel time in the communication coverage area of the RSU and the V2I transmission rate of the RSU. If the downloadable amount is larger than the total amount, then the RSU can fully download all of the content to the requester vehicle in its communication coverage area and does not need to select a content-precaching vehicle group. Thus, the requester vehicle can finish the content downloading process in the communication coverage area of the RSU.On the other hand, if the total amount is larger than the downloadable amount, then the RSU cannot fully download all of the content to the requester vehicle in its communication coverage area and needs to select a content-precaching vehicle group to relay the precaching content to the requester vehicle in the outage zone. When the RSU selects the content-precaching vehicle group for the content requested by the requester vehicle, it ranks all possible sets formed by all the vehicles in its communication coverage area. The ranking of a set is determined by the total available precaching amounts of the vehicles in the set. An appropriate content-precaching vehicle group is selected from all sets by considering both the set rankings determined by the content-precaching amounts of the vehicles and the communication overheads caused by connections with multiple vehicles in order to achieve the performance goals of MPVS. Then, the RSU fairly allocates the precaching amounts for each vehicle in the set selected as the content-precaching vehicle group in proportion to the vehicle’s available precaching amount. As shown in In this section, we describe the MPVS scheme. MPVS consists of four phases: (1) the calculation of the downloadable content amount, (2) the calculation of the content-precaching amount, (3) the selection of a content-precaching vehicle group, and (4) the downloading of content through the content-precaching vehicle group. The first phase is to calculate the amount of content that a vehicle can download while within the RSU’s coverage area, in order to determine the necessity of selecting a content-precaching vehicle group. The second phase is to calculate the content-precaching amount of every vehicle in the communication coverage area of the RSU, which is needed to select a content-precaching vehicle group. The third phase is to select the content-precaching vehicle group based on both the set rankings determined by the content-precaching amounts of the vehicles and the communication overheads caused by connections with multiple vehicles. Lastly, the fourth phase is to provide the downloaded content to the requester vehicle through the content-precaching vehicle group in the outage zone. We sequentially present the four phases in detail in the following four subsections. Generally, a requester vehicle Next, ng works , we assuAfter obtaining the downloadable amount To deliver the remaining amount eme AMRS  ranked eTo determine the available precaching amount of a vehicle Since every vehicle might have a different storage capacity, Thus, U is the distance of the outage zone between U. After both Next, one calculates the relaying time and amount of a vehicle  follows:tmax=Uvre follows:tmax=UvreUsing Equations  and 8),,8), RSUjPractically, In MPVS, In MPVS, when N is the maximum value of p and can be denoted as p and q are the number of vehicles in the subset and the order of groups with the same number of vehicles, respectively; Then, We define these element sets in follows: ssEach vehicle On the other hand, if multiple candidate sets p value in Next, one chooses the sets with the lowest number of vehicles among all sets in Then, Next, To fairy allocate a smaller content precaching load to vehicles in the content-precaching vehicle group, the scheme selects the set from all sets in If For example, if a requester vehicle requests 150  schemes , V3 withUsually, a requester vehicle However, if After In this section, we evaluate the performance of the proposed scheme, MPVS, by performing a simulation on NS3. In order to evaluate the scheme’s performance in terms of the reliability and fairness in requesting a vehicle’s content, we first describe the simulation environment and matrix for comparison in To evaluate the performance of the proposed scheme, MPVS, we simulated requests for content in a highway scenario using NS3 . On a stWhen selecting a comparison scheme for evaluating the proposed scheme, there were two compelling reasons to consider a scheme that incorporated similar characteristics to the proposed scheme. First, the comparison scheme needed to employ a similar mathematical model for calculating the downloadable or precaching amount of content. This ensured a fair and meaningful comparison. By selecting a scheme with a similar mathematical framework, we could directly compare the outcomes and assess the relative strengths and weaknesses of the different approaches in a consistent manner. Secondly, it was important to choose a scheme that involved multiple vehicles as precaching nodes, mirroring the scenario in which the proposed scheme operated. By selecting a comparison scheme that shared this characteristic, we could evaluate the performance of the proposed scheme under conditions that closely resembled real-world settings. Therefore, in order to evaluate the performance of the proposed scheme, we compared it with the existing V2V precaching scheme called AMRS . The exiRequest success rate (%): A vehicle that is selected as a relaying vehicle cannot request or receive its own intended content because it spends its entire dwell time within the coverage area of the current RSU precaching the requested content for other requester vehicles. Therefore, the vehicle suffers a very long delay until it reaches the next RSU. To measure this request failure, we evaluated the request success rate, which is the ratio of the number of successful content requests to the total number of requests. It is directly related to user QoS and reliability because it affects delays. Thus, it is a critical factor for content delivery to vehicles in CCVNs.F): In the AMRS scheme, the relaying vehicle that has abundant dwell time spends all of its dwell time precaching, which is unfair to this vehicle. To measure the fairness for the selected relaying vehicles, we evaluated the precaching fairness based on Shannon’s diversity index as follows:Precaching fairness : The request decision period is a parameter that determines how often vehicles decide to request content, and it reflects the impact on performance as the number of requests from vehicles increases. Therefore, it reflects the performance according to the number of requester vehicles when the number of candidate vehicles is fixed. A shorter decision period means that vehicles make content request decisions more frequently, leading to an increase in the number of requester vehicles that an RSU has to select as relaying vehicles. As a result, the relaying vehicles may spend more of their dwell time on the requests of other vehicles, which can affect their ability to request their own content.Requested content size (GB): The requested content size is the average size of the requested content and indicates the number of candidate vehicles required. Therefore, it reflects the performance according to the number of candidate vehicles required when the number of requester vehicles is fixed. If the size of the requested content is too small, the precaching fairness is less affected by selecting a single relaying vehicle because it requires fewer candidate vehicles. As the size of the requested content increases, the selection of requester vehicles differs in each scheme. If the size of the requested content is too large, each requester vehicle employs a large number of candidate vehicles as relaying vehicles, resulting in a decrease in the request success rate.Vehicle density (/km): The vehicle density is the number of vehicles on a 1 km stretch of the straight road. Therefore, it reflects the performance when the number of candidate vehicles and the number of requester vehicles grow at the same rate. When the number of vehicles is small, fewer requester vehicles require fewer relaying vehicles, which means that other vehicles have a higher success rate in their requests; however, this comes at the expense of fewer candidate available vehicles, so it is not possible to select a better group. If the number of vehicles is large enough that a better group can be selected, the precaching fairness of the proposed scheme is improved. However, if the number of vehicles is too large, the number of requester vehicles increases, requiring a larger number of candidate vehicles, and the request success rate decreases. For example, if the number of requesting vehicles quadruples, more candidate vehicles are required because the best groups are exhausted and the next best group must be selected from the remaining candidate vehicles.Then, for performance comparison, we implemented four environmental parameters, as follows:In conclusion, the high-speed nature of ICVNs presents challenges in meeting increased content demands and addressing outage zones where RSU coverage may be limited. Existing V2V precaching schemes have focused on delivering the maximum amount of content to the requester vehicle within the outage zone, but this approach often results in relaying vehicles consuming all their dwell time, leaving no opportunity for them to request or receive their own content. To address this issue, we proposed the MPVS scheme, which ranks a group of candidate vehicles that can serve as relaying vehicles and allocates them to precache a fair amount of content. First, we modeled the amount of content that could be downloaded and precached by the candidate vehicles with mathematical formulas and used these formulas to select the content-precaching vehicle group that could provide the maximum amount of content to the requester vehicle. Then, we ensured fairness by allocating an equal proportion of the requested content to each relaying vehicle in the selected group. To evaluate the performance of our proposed scheme, we designed a highway mobility model with a straight road, wherein vehicle speed and acceleration followed a Gaussian distribution. We also designed a content request model based on Poisson distribution for content request decision periods, Zipf’s law for content popularity, and Gaussian distribution for content size. The simulation results in various environments showed that our proposed MPVS scheme achieved greater fairness compared to the existing AMRS V2V precaching scheme, indicating an improved request success rate.However, there are several areas that could be explored further to enhance the feasibility and applicability of our research. First, we could consider a realistic mobility model in an urban scenario. Therefore, as a next step, we intend to extend our research to urban scenarios, where vehicular networks face distinct challenges due to high-density traffic; complex road networks ; and heterogeneous communication environments. By considering the unique characteristics of urban environments, such as traffic congestion and signal interference, we could develop tailored solutions to optimize content delivery, mitigate latency, and improve overall network performance for real scenarios. Additionally, we could consider a realistic content consumption model. To further enhance the realism of our research, it is essential to develop a more accurate content consumption model. In practice, content popularity, user preferences, and content caching behavior can be dynamic and complex. Furthermore, users often decide after a short time to stop watching the requested content  and proceed to request other content. By incorporating real-world data and considering factors such as user behavior, content dynamics, and temporal variations, we could create more realistic content consumption models, leading to improved performance evaluations and more accurate predictions. In addition, we could use machine learning to solve real-world problems and improve various performance aspects.


Necroptosis is a recently discovered form of regulated cell death characterized by the disruption of plasma membrane integrity and the release of intracellular content. Mixed lineage kinase domain-like (MLKL) protein is the main player of this cell death pathway as it mediates the final step of plasma membrane permeabilization. Despite the significant progress in our knowledge of the necroptotic pathway and MLKL biology, the precise mechanism of how MLKL functions remain unclear. To understand in what way MLKL executes necroptosis, it is crucial to decipher how the molecular machinery of regulated cell death is activated in response to different stimuli or stressors. It is also indispensable to unveiling the structural elements of MLKL and the cellular players that are required for its regulation. In this review, we discuss the key steps that lead to MLKL activation, possible models that explain how it becomes the death executor in necroptosis, and its emerging alternative functions. We also summarize the current knowledge about the role of MLKL in human disease and provide an overview of existing strategies aimed at developing new inhibitors that target MLKL for necroptosis intervention.  In contrast to accidental necrosis, apoptosis was long considered the only form of regulated cell death. However, the concept of regulated necrosis (RN) emerged to describe a type of cell death that phenotypically resembles necrosis, but, rather than accidental, it is triggered upon stimulation . There aNecroptosis is a caspase-independent form of RN that relies on the activity of the pseudokinase Mixed Lineage Kinase domain-Like (MLKL) protein . Upon acIn this review, we provide a comprehensive overview of the molecular mechanism and the biological relevance of MLKL. We cover different aspects of MLKL biology, ranging from the activation of the necroptotic pathway and its relation to other types of cell death to the structural determinants and regulatory steps that determine its function as a death effector. Finally, we summarize the direct involvement of MLKL in the pathology of different human diseases and provide an overview of the current efforts to target MLKL with small molecules for research and clinical purposes.Necroptosis was first described as a type of necrotic cell death alternative to apoptosis occurring in mouse fibroblasts in response to the Tumor Necrosis Factor (TNF) . Ten yeaAmong all the ways in which necroptosis can be triggered, the TNF-induced pathway is the best characterized . Here, tUnder the conditions in which RIPK1 is deubiquitinated, the alternative complex IIb  is then formed . ComplexThe ripoptosome–necrosome axis is also effective in TNF-Related Apoptosis-Inducing Ligand (TRAIL) and Fas ligand pathway stimulation, both converging in RIPK1 activation ,30,31 F. In bothRIPK3 and MLKL can also be activated by RHIM domain-containing proteins other than RIPK1, constituting what is known as the non-canonical necrosome . One of MLKL structure is composed of a four-helix bundle (4HB) and a pseudokinase (psK) domain, linked by an interdomain brace region  Figure A. The 4HThe nature of the interaction between MLKL and RIPK3 and their dynamics before and during necroptosis are still controversial. Structural studies of the human and mouse MLKL indicate that there may be significant differences between these orthologs because both proteins are not interchangeable . It has RIPK3-mediated phosphorylation of specific residues is a critical step in the activation of MLKL. Essential residues include T357/S358 in human MLKL  and S345Besides phosphorylation, the role of MLKL ubiquitylation (or ubiquitinylation) has recently emerged as another type of post-translational modification (PTM) required for its regulation. Ubiquitylated variants of MLKL have been specifically detected after necroptosis stimulation in different studies ,51,52. AUpon necroptosis, phosphorylated MLKL forms oligomers that translocate to cellular membranes. However, the mechanism and structural requirements of this process are still under debate. Although the exact stoichiometry of MLKL oligomers is not well-established, different studies suggest that they can range from trimers, tetramers, hexamers, and octamers, to higher-order oligomers . FurtherThe molecular principles that determine MLKL translocation to cellular membranes also remain unclear. Early studies employing cellular fractionation identified the plasma membrane as the main target of MLKL activity . This piIn the last decade, our knowledge about how MLKL is regulated has dramatically increased. The clear definition of the hallmarks and structural determinants required for its activation have opened new avenues on our journey to unveil the job of MLKL in the cell. Still, how MLKL promotes the final and key step of plasma membrane permeabilization during necroptosis and how its activity is related to its possible non-deadly roles remain highly controversial. Next, we will discuss current models that explain the biological function of MLKL.There is a consensus that the plasma membrane translocation of MLKL oligomers is mediated by the interaction between the phosphatidylinositol phospholipids and a cluster of positively charged residues in the 4HB domain . This no2+ . I. I1, wasuse MLKL . Mechaniar range . However(VEGFR2) , and bot(VEGFR2) .1, with an indole moiety, was selected as a starting molecule that underwent further optimization. Improved derivatives (compounds 5 and 7) were characterized by an enhanced binding affinity that was still in the micromolar concentration range (>50 µM). It was discovered that both compounds bind to a hydrophobic pocket that is located at the end of the 4HB domain, opposite to C86, the target residue of irreversible inhibitors of MLKL. Interestingly, the detergent nonyl-maltoside, which, together with phytic acid, acts as an activator of the 4HB domain and can compete with compound 5 for binding to MLKL. This evidence opened the possibility that these compounds could inhibit MLKL in cell-based assays. This notion is based on the similarity of these detergents with inositol phosphates, which are required for MLKL oligomerization and translocation to membranes [5 could not be tested in cells due to its poor membrane permeability, and it was not active in an in vitro liposome leakage assay. Therefore, additional optimization is still required to prove their efficacy as MLKL inhibitors. The reversible and allosteric modes of interaction with the 4HB domain of MLKL characterize the third and last class of inhibitors under development . This tyembranes . UnfortuMLKL is the most important player in the execution of necroptosis, a type of RN that is triggered under conditions in which the activity of caspase-8 is compromised. In recent years, the cell death field has progressed in understanding how MLKL is regulated to execute necroptosis. Answers to many open questions remain elusive, thus limiting our ability to modulate necroptosis in a targeted fashion to promote human health. How does interconnectivity with other forms of regulated cell death contribute to the outcome of MLKL activity in different physiological settings? What are the common nodes that determine cell fate or the decision of which type of cell death dominates? At the molecular level, we still do not know all the key cellular players that modulate MLKL function in different contexts or the exact mechanism of how this intriguing protein mediates membrane permeabilization and, ultimately, cell death. Can MLKL-mediated membrane perturbation lead to other cellular processes that are independent of its role as a killer? Furthermore, we are just starting to grasp the involvement of MLKL in different human pathologies. Finding out whether the deregulation of MLKL is relevant to the development of human diseases is essential to identifying which interventions could benefit from targeting MLKL and necroptosis. Ongoing efforts to elucidate the structural mechanisms of MLKL activation will enable future strategies to inhibit necroptosis for the treatment of life-threatening diseases.


The healthcare industry has made significant progress in the diagnosis of heart conditions due to the use of intelligent detection systems such as electrocardiograms, cardiac ultrasounds, and abnormal sound diagnostics that use artificial intelligence (AI) technology, such as convolutional neural networks (CNNs). Over the past few decades, methods for automated segmentation and classification of heart sounds have been widely studied. In many cases, both experimental and clinical data require electrocardiography (ECG)-labeled phonocardiograms (PCGs) or several feature extraction techniques from the mel-scale frequency cepstral coefficient (MFCC) spectrum of heart sounds to achieve better identification results with AI methods. Without good feature extraction techniques, the CNN may face challenges in classifying the MFCC spectrum of heart sounds. To overcome these limitations, we propose a capsule neural network (CapsNet), which can utilize iterative dynamic routing methods to obtain good combinations for layers in the translational equivariance of MFCC spectrum features, thereby improving the prediction accuracy of heart murmur classification. The 2016 PhysioNet heart sound database was used for training and validating the prediction performance of CapsNet and other CNNs. Then, we collected our own dataset of clinical auscultation scenarios for fine-tuning hyperparameters and testing results. CapsNet demonstrated its feasibility by achieving validation accuracies of 90.29% and 91.67% on the test dataset. Cardiovascular diseases (CVDs) remain a major global health concern that causes significant numbers of deaths and morbidities. In clinical practice, auscultation is one of the non-invasive methods for assessing the cardiovascular system and detecting pathological cardiac conditions, such as arrhythmias, valve disorders, and heart failure. Heart sounds serve as a valuable initial indicator for evaluating diseases, guiding further diagnostic tests, and playing a pivotal role in the early detection of CVDs. The PCG recordings  of theseThe capsule neural network (CapsNet) has been widely used in various medical fields in recent years. CapsNet ,23 is a This paper uses deep learning to establish an intelligent auscultation assistance system to aid in the diagnosis of heart murmurs. Auscultation is used to record the subjects’ heart sounds to represent the clinical situation more accurately. Among the many studies and results on this topic, we hope that our study will provide novel insights regarding the application of a capsule neural network (CapsNet) to diagnose heart murmurs. CapsNet uses vectors to analyze and detect features, identifying differences in the positions of components and assessing them with good results. To better address the translation equivariance of input features, we use the softmax function to emphasize spatial attention, highlighting energy disparities between time and frequencies in spectral images. The primary capsules are intensified to encode the presence of a particular feature as well as its location in the input MFCC spectrum. We compare the results of CapsNet with those of traditional convolutional neural networks in terms of recognizing abnormal heart sound features. The 2016 PhysioNet heart sound database is used to train and validate the prediction performance of CapsNet. Various convolutional neural networks are compared to CapsNet in this study. In addition, we collect our own dataset to fine-tune the hyperparameters and test results in clinical auscultation scenarios. CapsNet exhibits the best prediction ability, which fits our purposes of improving the precision and efficiency of heart disease diagnosis, providing doctors with more powerful aids, and providing patients with better diagnosis and treatment experiences.CapsNet is an extension of traditional convolutional neural networks designed to address some of their limitations. Compared to CNNs, CapsNet stores features as vectors and maintains the distances and corresponding relationships between them. This leads to more accurate classification, improved translation invariance, and the ability to learn with less data.(a)Signal segmentation: Each segment typically corresponds to a fixed time duration in seconds. The default time duration of each segment is 5 s, which corresponds to 220.5 k samples at a sampling rate of 44.1 kHz.(b)Downsampling: Downsampling can be performed to decrease the computational load and storage requirements while preserving the essential information in the heart signal. Our downsampling rate was reduced from 44.1 kHz to 2 kHz, as in the 2016 PhysioNet heart sound database. With this downsampling rate, the integrity of heart sounds below 1 kHz is maintained.(c)Normalization: This step is the process of scaling the heart sound signal to a standard range between −1 and 1 to prevent clipping or distortion.(d)MFCC spectrum analysis: To extract features from the audio data, the mel-frequency cepstral coefficients (MFCCs) can be computed using a signal processing library such as librosa . MFCCs c(a)Routing initialization: The output of the primary capsule layer is a set of capsule vectors The primary capsule layer in CapsNet is responsible for extracting local features from the input data of the convolution layers and encoding them into capsule vectors. Dynamic routing is used in the primary capsule layer to determine the weights for combining the input data to form the capsule vectors. The dynamic routing algorithm for the primary capsule layer consists of the following steps:W is the width, c is the number of channels, and the convolutional layer has S. Then, the primary capsules N is the number of capsules per spatial location w is the weight of the k-th filter at position k-th filter. These coefficients of capsule vectors are initialized randomly.(b)Routing iteration: The routing algorithm iteratively updates the coupling coefficients based on the agreement between the capsule vectors and the output vectors of the higher layer capsules. The goal is to increase the coupling coefficients between capsules that are in agreement and decrease the coupling coefficients between capsules that are not in agreement.The convolutional layer applies a set of learnable filters to the input data to extract local features. The output of the convolutional layer is a set of feature maps, where each map corresponds to a different filter. The input data are denoted by g., ReLU ), w is ti-th capsule vector and j-th higher layer capsule:i-th capsule to the j-th capsule in the next layer.The output vectors of the capsules in the layer above are normalized with a nonlinear activation function named Squash to ensure that they have a magnitude between 0 and 1. The squash function ensures that the length of the output vectors represents the probability that a specific feature or entity exists, and it is used in the routing process to determine how much information is passed between capsule vectors r-th iteration of the routing algorithm, the routing coefficients between the i-th primary capsule and the j-th higher layer capsule are calculated as follows:i-th primary capsule and the j-th higher layer capsule, which is defined as:To address the translation equivariance of input features, we use the softmax function to emphasize spatial attention, highlighting energy disparities between time and frequencies in spectral images. During the M is the number of capsules in the digit capsule layer, r, and j is obtained by squashing again with the weighted sum of the prediction vectors:Note that The primary capsules output a vector of activations that indicate the presence of a feature at a particular location. These activations are fed into a nonlinear activation function, which digitizes them to produce a binary output.T is a digitization threshold.As described in the above steps, the output of the primary capsule layer is input to the digital capsule layer, which is responsible for classification. The input of the digital capsule layer consists of the high-level feature vectors, and vectors for each class are the output. The length of these output vectors represents the probability of the input belonging to each class. The length of the output vectors is calculated using the Euclidean norm. The binary output represents the presence or absence of a feature at a particular location. The margin loss is then used to calculate the difference between the predicted output and the true label. This loss encourages a margin of at least a certain distance between the predicted output and the true label, which helps to prevent overfitting. The margin loss function is defined as follows:A summary of the CapsNet neural network architecture is listed in The 2016 PhysioNet Heart Sound database is a public database derived from heart sound recordings collected in various clinical or nonclinical  settings and contains 3251 recordings of both normal and abnormal heart sounds. Normal recordings come from healthy subjects, while abnormal recordings come from patients with confirmed heart disease. The heart sound recordings range from 5 s to over 120 s. It is crucial to understand the characteristics of heartbeats, especially the first and second heart sounds, represented as S1 and S2, respectively. These sounds can be heard as vibrations throughout the entire cardiac structure, which can be recorded as time series representations. The 2016 PhysioNet heart sound dataset provides valuable information on the typical frequency range for each type of heart sound, with murmurs having a diverse frequency range and respiration having a frequency range of 200–700 Hz. In this study, mel-frequency cepstral coefficient (MFCC) spectrum analysis was used to analyze the heart sound recordings. The MFCCs capture important audio signal features and translate them to a 2D spectrum image that can help detect cardiac abnormalities. As shown in To train and verify the proposed method, we divided the 3251 recording samples into two datasets: 70% for the training dataset, containing 2276 recordings, and 30% for the validation dataset, containing 975 recordings. The specifications of the computer we used are as follows: 11th Gen Intel(R) Core(TM) i7-11370H @ 3.30 GHz CPU, 16.0 GB RAM, and an NVIDIA GeForce RTX 3070 laptop as the GPU for training the model. Programming was conducted with Python 3.6.8 and TensorFlow 1.15 for the deep learning framework.The confusion matrix for the validation result is listed in We also compared the results of the training and validation datasets with those of other deep learning network architectures in All the individuals participating in the study were cardiology patients who were aged 0 to 50 and consented to the study. The recorded data were approved by the Institutional Review Board of Taichung Veterans General Hospital . In this case study, physicians labeled cardiac audio signals with a diagnosis by cardiac ultrasound. The collection dataset consists of recordings from 56 patients in clinical auscultation scenarios. The dataset was then split as follows: 75% for the training dataset, containing 42 recordings for fine-tuning purposes, and 25% for the test dataset, containing 14 recordings for final testing.The heart sounds of each participant were recorded at four different points, as shown in By contemplating the incorporation of a new recording device, the improvement of AI’s diagnostic proficiency in clinical auscultation tests can be realized by refining a pretrained model through the inclusion of As shown in Different methods to adjust the learning rate during training were tested, including the ReduceLROnPlateau function, learning rate decay, and fixed learning rate. While a fixed learning rate can work well in certain cases, the other two methods offer adaptability and responsiveness to improve model convergence and achieve higher accuracy. The ReduceLROnPlateau function with learning rate decay leads to the best performance, maintains higher performance by decaying the learning rate, and achieves the highest accuracy on the test set. Additionally, the learning rate decay strategy outperforms the fixed learning rate approach. After fine-tuned testing, we plotted the best settings for the margin loss and accuracy in Compared to conventional CNNs, CapsNet has a significantly different structure and method of processing information. CapsNet has a unique capsule layer structure that enables it to capture spatial hierarchical relationships more effectively and encode possible changes. Thus, CapsNet can preserve the spatial relationships between various parts of an object, while traditional CNNs may lose this information. Moreover, CapsNet’s dynamic routing algorithm allows the model to decide which information to pass to the next layer, making it highly robust against small image changes.Considering these results when selecting a model for a specific task is important when focusing on balancing high training accuracy and generalization to new data. CapsNet achieves the highest overall performance and high training and test accuracies. Compared to the other deep convolutional neural network models, CapsNet is the only model to achieve convergence.This study proposes a CapsNet model for classifying cardiac auscultation and compares various convolutional neural networks to predict normal or abnormal heartbeat sounds. We find that CapsNet can achieve good convergence using only MFCCs as data input, leading to fine-tuned hyperparameters and achieving good performance with a small number of training epochs. The feasibility of CapsNet is demonstrated by its ability to achieve an average test accuracy of 90.29% on the validation dataset from the 2016 PhysioNet heart sound database and 91.67% on the test dataset collected in clinical auscultation scenarios. As a result, the uniqueness and significance of CapsNet lie in its ability to handle the translation equivariance of spectrum features. In contrast, translation invariance in conventional convolution neural networks with pooling falls short of object transformation equivariance. When dealing with the heart sound MFCC spectrum, there is a distinct sound positioning of energy differences between time and frequencies in the spectral images.Given the limited databases used in this study, the results should be considered preliminary. Therefore, in future works, it is essential to test and calibrate the proposed model on larger databases that include a more extensive range of patients and various rhythm abnormalities to ensure that the proposal is reliable and effective for diagnosing and treating different types of heartbeat abnormalities.


We describe the experimental set-up in detail, outline the pitfalls of repeated retinal vessel analyses in an experimental set-up of several hours, and address issues that arise from the simultaneous use of two different assessment tools. Finally, we demonstrate the robustness and variability of the reactivity of retinal vessels to hypercapnia at baseline as well as their reproducibility over time using two anesthetic protocols common for neurovascular research. In summary, the procedures described in this protocol allow us to directly compare retinal and cerebral vascular beds and help to substantiate the role of the retina as a “window to the brain.”Many recent research projects have described typical chronic changes in the retinal vasculature for diverse neurovascular and neurodegenerative disorders such as stroke or Alzheimer's disease. Unlike cerebral vasculature, retinal blood vessels can be assessed non-invasively by retinal vessel analysis. To date, there is only a little information about potential simultaneous reactions of retinal and cerebral vessels in acute neurovascular diseases. The field of applications of retinal assessment could significantly be widened if more information about potential correlations between those two vascular beds and the feasibility of non-invasive retinal vessel analysis in acute neurovascular disease were available. Here, we present our protocol for the simultaneous assessment of retinal and cerebral vessels in an acute setting in anesthetized rats using a non-invasive retinal vessel analyzer and a superficial tissue imaging system for laser speckle contrast analysis  In an experiment lasting several hours, we outline pitfalls concerning repeated retinal vessel analyses and address issues arising from the simultaneous use of two different assessment systems. We give application examples of vascular reactivity to a hypercapnia challenge in both vascular beds, cerebral and retinal, characterizing three types of retinal vessel reactivity. Finally, we present our experience with two common anesthetic protocols for neurovascular research.All materials used in the experiments are listed in via a closed brain window. With this method, the effects of acute neurovascular events such as hemorrhage, stroke, or trauma can be monitored live. Our procedure allows us to directly compare both vascular beds and helps to substantiate the role of the retina as a “window to the brain.” We describe the surgical preparation in detail and specify the complex experimental set-up for the assessment of cerebral blood flow (CBF) by the laser speckle analysis and of retinal vascular diameters by means of the Imedos-RVA for small animals. In addition, two anesthetic protocols and the narcotics' effects on the cerebral and retinal vessels are described. The demonstrative examples used in this article are taken from the analysis performed in the context of our previous, already published study .ad libitum. All rats were kept on a 12-h light–dark cycle (07:00–19:00), a temperature of 22 ± 2 degrees, and a humidity of 55 ± 5%. They were submitted to an adaptation period of at least 7 days before being used in experiments. Health monitoring was performed according to the Federation of European Laboratory Animal Science Associations (FELASA) recommendations  with a weight of ~300 g were housed in groups of two or three at the Institute for Laboratory Animal Science of RWTH Aachen University  in type 2000P cages, with food  and water As corneal desiccation can significantly affect imaging quality, it is essential to repeatedly moisturize the rats' eye with a transparent eye ointment and cover it with a coated swab  right after anesthesia induction. To prevent undesired eye bulb rotation see  and to eRetinal measurements require a fully dilated pupil. The use of muscarinic antagonists is recommended as alpha antagonists can influence the diameter of the retinal vessels and thus falsify the results .via continuous intravenous infusion: for this purpose, the fentanyl continuous infusion system was replaced by a syringe pump containing ketamine, xylazine, and vecuronium. As soon as a drop in blood pressure occurred (approximately after 5–10 min), the isoflurane flow was reduced to 0.5–1%. After another 10 min, the supply of isoflurane was stopped.The induction of anesthesia was performed with isoflurane and fentanyl as described earlier. After the implantation of the closed bone window, anesthesia was slowly switched from Iso to K/X  In the following, we present our protocol for the surgical procedures and the step-by-step set-ups of cerebral blood flow measurement and retinal vessel analyses .Note: Routinely monitor respiration rate, body temperature, heart rate, systemic oxygen saturation, and systemic arterial pressure as well as arterial blood gases throughout surgery to maintain physiological cardiac and respiratory functions. The respiratory rate is set based on regular blood gas analyses every 60 min and adjusted if necessary. Before the application of muscle relaxant, routinely test reflexes to determine a sufficient depth of the anesthesia. After the application of the muscle relaxant, check the sufficient depth of anesthesia via control of heart rate and blood pressure.- - For cranial window implantation, place the animal in a prone position in a stereotactic frame after injecting ropivacaine to the base of both ears for ear bar fixation.Note: At this step, it is very important to prevent bleeding from the surrounding tissue as continuous bleeding will interfere with the speckle contrast imaging later.- Prepare the closed cranial window see : After s- Determine the position of the cranial window over the somatosensory cortex with the center of the window ~8 mm caudal and 2.5 mm lateral to bregma and ~12 × 5 mm in size over the right hemisphere. Then, thin the skull bone with the drill under constant cooling with saline until the cerebral vessels are visible and the skull starts to become flexible. A very thin bone lamella should be preserved, still covering the brain. Regularly test the softness of the skull with forceps by gently pressing on the drilled area. The skull bone is thin enough to be easily depressed, while the bone lamella remains intact. The window is completed when the cerebral vessels are visible, and the bone is thinned out evenly in all areas.Note: In our experiments, we performed this step under an operating microscope. It is very important to grind down the skull bone without too much pressure as any bleeding/trauma of the brain  will interfere with laser speckle contrast and may impair vascular reactivity later. Give special attention to the area of the coronal suture as bleeding will occur more frequently here. An effective way to stop bleeding from the skull is to drill without saline for a short period of time. We avoided the use of hemostatic products as vasoconstriction may potentially falsify the results of the cerebral blood flow measurement.- Note: The wax wall must be watertight; we recommend testing this before covering it with a cover slip.- If there is no active bleeding anymore, place an ~2-mm-high wax wall around the window. Make sure that the skull bone and the area around the window are completely dry. Place a prepared wax wall around the window and smooth the inner and outer parts of the wax wall out to the edge of the window to ensure water tightness. - Fill the window with saline and then cover it with a cover slip to ensure stable conditions for the speckle analysis throughout the measuring period.- Proceed with the set-up of the required measuring tools.- Set-up of the laser speckle system : the used CCD camera , with 4.65 μm × 4.65 μm pixel size and 1,024 pixel × 768 pixel resolution, has a dynamic range of 12 bit and a final frame rate of 0.5 Hz (average of 30 frames). The moving average was set to 10, and an exposure time of 10,000 μs was used.- Place the animal under the STIS while remaining in the stereotactic frame to constantly measure and record CBF free of moving artifacts  within the microcirculation of the somatosensory cortex. - Assemble the retinal camera (DVA) on a small vibration-damped lifting jack to allow 360 degrees of movement. Shield the set-up from light. Set the illumination light of the DVA system (530 nm) to the max. 5%  for positioning.Note: In our experience, this angle allowed the depiction of the papilla, which was necessary for the preinstalled imaging software. The correct positioning and alignment of the camera were essential for the quality of the image and correct measurements.- Switch the room light off before removing the rat's eye coverage and place the DVA in front of the left eye. Position the camera at an angle <90 degrees and slightly align it from earlier see . Note: I- Continuously moisten the rat's left eye and ensure that the pupil is fully dilated before starting the measurement.Note: Give attention to any Vibrissae or hairs between the eye and the lens and remove them if necessary.- Align a custom-made contact lens  mounted on a micromanipulator centrally in front of the rat's left eye. Then, place the DVA lens so close to the contact lens that a circular cone of light is visible on the contact lens. The DVA lens and the contact lens must be aligned parallel to ensure an identical incidence angle of the light. via imaging software to achieve an alignment in which the optic disk is centered. Further optimize the image quality by opening or closing the aperture or adjusting the brightness.- Fine-tune the camera settings via the preinstalled software. If the check is successfully completed, a static image automatically appears to select the corresponding vessel areas. Note: Deactivation of the built-in image quality check is not recommended to ensure measurement quality.- Perform the image quality check Note: Due to the illumination at 530 nm sensitive to hemoglobin oxygenation, the identification of veins, which appeared darker and wider, and arteries is simple. We recommend a 2.5 times papillary diameter distance for laying the ROIs. It is also important to select vessel sections that have the highest contrast and sharpest image quality (see).- Mark the desired number of vessel sections. Note: By starting the video recording tool, detailed offline analysis is possible. The length of the video recordings and associated analyses can be individually set and adjusted according to the needs of the experimental schedule.- Wait for the system to check and confirm the selected areas. In case of rejection, re-marking or selection of a new vessel area must be performed. In this study protocol, hypercapnia challenges were induced to test and compare the regulatory function of the retinal and cerebral vessel reactions.2).- First, perform a blood gas analysis for the baseline value of the arterial partial pressure of carbon dioxide  was particularly important to improve imaging quality.The laser speckle system could reliably measure the blood flow increase during hypercapnia in both anesthetic protocols. For illustration, two typical examples from both groups of anesthesia are given in The measurements of the vessel diameter of the retinal vessels did not give as homogeneous results as those of the cerebral vessels. The detailed analysis provided in our recent publication , continuous moistening of the eye, directly at the onset of anesthesia, was essential. For this purpose, transparent ophthalmic gel proved to be the best choice; moistening with the lens in place can also be performed by dropping physiological sodium chloride solution on the eye. If the measurements are preceded by a longer surgical phase as in our study, a coated swab should cover the eye or surgical closure of the lid should be considered. During the measurements, it became apparent that the fitted contact lens significantly improved image quality and also protected the cornea from drying out. To perform retinal measurements, it is necessary to fully dilate the pupil using a mydriatic agent. Alpha antagonists must be avoided, as they can influence the diameters of the retinal vessels and thus falsify the results  , Recklinghausen, Germany.CC-D, GS, and UL: conceived and designed the experiments and the study protocol. LW, AB-H, WA, SP, UL, and CC-D: constructed experimental set up. LW: performed the experiments. LW, CC-D, and UL: interpretation of the data and illustrations. CC-D and LW: first drafting of the manuscript. AB-H, TS, GS, WA, UL, HC, SP, and CC-D: critical review of the manuscript. All authorship requirements have been met and the final manuscript was critically revised and approved by all authors.


This article presents the nonlinear investigation of the thermal and mechanical buckling of orthotropic annular/circular single-layer/bilayer nanoplate with the Pasternak and Winkler elastic foundations based on the nonlocal strain gradient theory. The stability equations of the graphene plate are derived using higher-order shear deformation theory (HSDT) and first-order shear deformation theory (FSDT) considering nonlinear von Karman strains. Furthermore, this paper analyses the nonlinear thermal and mechanical buckling of the orthotropic bilayer annular/circular nanoplate. HSDT provides an appropriate distribution for shear stress in the thickness direction, removes the limitation of the FSDT, and provides proper precision without using a shear correction coefficient. To solve the stability equations, the differential quadratic method (DQM) is employed. Additionally, for validation, the results are checked with available papers. The effects of strain gradient coefficient, nonlocal parameter, boundary conditions, elastic foundations, and geometric dimensions are studied on the results of the nondimensional buckling loads. Finally, an equation is proposed in which the thermal buckling results can be obtained from mechanical results (or vice versa). Nanoplates including graphene sheets can be named as one category of eminent materials for the next generation of nanodevices. Graphene sheets can be utilized in the manufacture of many nanodevices like sensors and memory devices  and therExperimental investigations have proved that there are size-dependent effects on the mechanical properties at the nanostructures . TherefoNarendar  perused It is noticed that in the former analyses, the small-scale effect in sort of the stress nonlocality led to a softening–stiffness effect, while the strain gradient size dependency resulted in a hardening–stiffness effect. Consequently, various nonclassical continuum theories of elasticity have been presented to prognosticate various size dependencies in the mechanical features of nanostructures. The theory of nonlocal strain gradients is one of the prominent models for analyzing size-dependent mechanical features. Contrary to classical elasticity theory, the nonlocal strain gradient theory can consider the influences of stiffness–hardening and stiffness–softening by assuming the strain and stress gradient. Therefore, Lim and his colleagues  studied Some analyses have been carried out with respect to the nonlocal strain gradient theory . For exaOne of the important issues in evaluating the stability of various structures is the buckling analysis, which has drawn the attention of many researchers to perform research on it. The term buckling refers to the loss of stability, or in other words, when the structure changes from stable equilibrium to unstable equilibrium, the structure undergoes buckling. In fact, the behavior of the structure under load in which with a small increase in load a disproportionate increase in displacement occurs in the structure is called buckling, and the amount of force for which the structure buckles is called critical buckling load . There aDQM is one of the numerical methods that has been employed by many authors ,37. The FSDT accounts for the shear deformation influences by the way of linear variation of in-plane displacements through the thickness. Because the FSDT violates the conditions of zero transverse shear stresses on the top and bottom surfaces, a shear correction factor (which can depend on many parameters) is needed to compensate for the error caused by a constant shear strain assumption through the thickness. The HSDTs account for the shear deformation influences and satisfy the zero transverse shear stresses on the top and bottom surfaces; therefore, a shear correction factor is not needed. HSDTs are modelled based on the assumption of higher-order variations of in-plane displacements or both in-plane and transverse displacements through the thickness. Some of HSDTs are computational costs because with each additional power of the thickness coordinate, an additional unknown can be added to the model . Also, tUntil now, the nonlocal strain gradient theory with HSDT and FSDT has not been carried out for studying the nonlinear thermal as well as mechanical buckling of the orthotropic annular/circular nanoplate via DQM. Furthermore, the buckling analysis of a bilayer annular/circular nanoplate with elastic foundations is also studied. The effects of the nonlocal parameter, strain gradient coefficient, boundary conditions, geometric dimensions, and elastic foundations on the results of the nondimensional buckling loads are investigated. From the results, it can be concluded that the effect of the nonlocal parameter on the buckling of the circular/annular nanoplate is more significant than the types of boundary conditions or elastic foundations. Also, it is noticed that a bilayer nanoplate cannot be assumed as an equivalent single-layer nanoplate (with the same thickness as the bilayer nanoplate) to gain the results of the buckling of the nanoplate. The results of the current article can be a benefit for the design as well as improvement of nanostructured devices, including circular gate transistors, microswitches, and so on.r, θ, and z axes clarified by U, V, and W, respectively.r and z axes, respectively. Furthermore, θ axis. Also, the function g(z) can be mentioned as:Taking into account the HSDT, the displacement field can be written in the f (z) and y* can be assumed as various functions utilized in different papers which are listed in The nonlinear strains, considering von Karman’s presumptions, can be written as Equations (3)–(7):It is noted since the symmetric assumption is considered, Equations (5) and (7) are equal to zero.NL) of the force and momentum resultants can be clarified as:The nonlocal form  are obtained asBy zeroing Also, Equation (16) can be rewritten asThe nonlocal strain gradient theory  was suggested by Lim et al. :(18)(1−μfined as (19)(1−μIt should be mentioned in Equation (19), The nonlocal form can be mentioned asThe force and moment resultants in the local form can be written asMoreover, the resultants in terms of displacements are gained as follows:The equilibrium equations of a monolayer axisymmetric circular/annular nanoplate considering Pasternak and Winkler elastic foundations can be locally written asTo derive the stability equations and determine the critical buckling force, the adjacent equilibrium method is used. Therefore, displacements are replaced by the following equations:Therefore, for the resultants of force and momentBy substituting Equation (37) into equilibrium Equations (33)–(35), Equations (38)–(40) are obtained:In Equations (38)–(40), by omitting the terms that have only zero subscript and setting terms related to the preload state equal to zero and considering the uniform compressive load, we haveTherefore, the stability equations in terms of local stresses are written in the form of Equations (42)–(44):Numerous graphene layers can be employed to fix their weak buckling strengths. Therefore, graphene plates are set on top of each other by means of van der Waals bonds, generating graphene layers . Van deri = 1 shows the top layer and i = 2 illustrates the bottom layer)Equilibrium equations considering the bilayer annular/circular nanoplate with the Pasternak–Winkler elastic foundation can be procured similar to the procedure used for the single-layer nanoplate. Furthermore, the annular/circular displacement fields of the axisymmetric bilayer nanoplate can be written as  of the top and bottom layers, the following equations are considered:In addition, the stability equations can be presented for the thermal buckling of circular and annular plates. Moreover, the only difference between the equations of thermal buckling compared to mechanical buckling is in the strains. Consequently, the stress and moment resultants change. The nonlinear strains, taking into account von Karman’s assumptions, can be written as Equations (56)–(58):The local stress resultants  according to displacements are as follows:In order to derive the stability equations from the equilibrium equations and determine the critical buckling temperature using the adjacent equilibrium technique, the equilibrium equations are obtained in the form of Equations (38)–(40). In those equations, by ignoring the terms that only have a zero subscript, zeroing the terms related to the preload state, and knowing that in thermal bucklingStability equations in terms of local stresses are written in the form of Equations (62)–(64):i = 1) and the second layer (i = 2)) can be written as follows:The stability equations in terms of local stresses (considering the first layer (The boundary conditions for the annular/circular plate can be assumed asClamped (C):Simply supported (S):Free (F):Because of the very small values that exist on the nanoscale, and for the ease of calculations, Equation (72) is introduced to convert the equations of the nanoplate nondimensional:N are the weight constant and the total number of nodes in the direction of r, respectively. For the first-order derivative, the weighting constants can be gained asDQM is one of the most efficient and elegant techniques for the numerical solution of partial differential equations used by many authors (which are briefly explained in the Introduction). This method is obtained from the quadratic integration technique, which expresses the integral at one point in the direction of the domain and relies on all points along that direction. Moreover, the value of dependency can be obtained using weight constants:n et al.   there are three equations and four unknowns, whose unknowns are displacement components of the plate N nodes, the matrix form of equations includes 3*N algebraic equations and 3*N + 1 unknowns. Since solving these algebraic equations and unknowns are long and time-consuming, Maple software 2023 was used to solve it. So, in the computer program, the determinant of the matrix of coefficients should be equal to zero Also, for a better understanding of applying DQM, an example of the discrete form of the equations can be seen in In this part, various factors are studied to identify their effect on the nondimensional buckling load of the annular/circular nanoplate. For this purpose, HSDT, FSDT, and the nonlocal strain gradient theory are utilized with the aid of DQM. Moreover, to validate the procedure, the current results are compared with the results of references. Also, the following assumptions are considered (if not mentioned in the text):To verify accuracy and validity, the present results (gained using both FSDT and HSDT) in the clamped boundary condition are compared with the reference, which shows good accuracy . In addiFrom From h/r = 0.05 and h/r = 0.06. As can be deduced by increasing the nonlocal parameter, the non-dimensional buckling load obtained from HSDT and FSDT differ significantly. Also, by comparing these two figures, it can be seen that in the higher thickness-to-radius ratios the difference between FSDT and HSDT increases more significantly.In this section, to validate the research, the current results of thermal buckling of circular/annular plates are compared with the results of valid reference, and then the results of the relevant diagrams are presented. In order to validate the numerical results of the present article and the solution technique and compare them with the results of Ref. , the dimIn this comparison, the dimensionless parameter of the thermal buckling of the isotropic graphene plate for the annular nanoplate assuming various boundary conditions, radius ratios, and thickness-to-radius ratios is given in To better observe the differences between the present study with the reference , the perFinally, by comparing the equations and checking the results for both thermal and mechanical analyses, it is found that with the following equation, thermal and mechanical buckling analyses can be related to each other:It is noted that in Equation (93), h (0.34 nm) and the single-layer nanoplate considering a thickness of 2*h (0.68 nm) for different boundary conditions. In fact, this part studies the probability of replacing a single-layer nanoplate (considering double thickness) with a bilayer nanoplate. It can be concluded that a bilayer nanoplate cannot be considered a single-layer nanoplate with the same thickness (as the bilayer nanoplate) for obtaining the exact results of the buckling analysis. Furthermore, the results obtained from the equivalent single-layer nanoplate with double thickness overestimate the real results gained using a bilayer nanoplate. This can be justified because of the van der Waals interaction that exists between the layers of bilayer nanoplate, which is an approximately weak force. If the buckling loads are strong enough, then molecules break free of the van der Waals forces that hold them together. Thus, the results of a single-layer plate are not similar to those of a bilayer plate.In the higher thickness-to-radius ratios, the difference between FSDT and HSDT increases more significantly.The influence of the nonlocal coefficient on the buckling analysis of circular/annular nanoplate is more significant than the types of boundary conditions or elastic foundations.A bilayer nanoplate cannot be considered an equivalent single-layer nanoplate (with the same thickness as the bilayer nanoplate) to obtain the results of the buckling analysis of nanoplate. Furthermore, the results obtained from the equivalent single-layer nanoplate with double thickness overestimate the real results gained using a bilayer nanoplate.In this paper, the nonlinear mechanical and thermal buckling of the circular and annular (single layer/bilayer) nanoplate using the nonlocal strain gradient theory considering both HSDT and FSDT is carried out. DQM is employed to solve the governing equations of the annular/circular nanoplate. Also, the results were compared with other references that showed good agreement. Some of the results of this article can be summarized as follows:


In this study, we comprehensively investigate the structure and operational principles of the Rotary Direct Drive Electro-Hydraulic Pressure Servo Valve (RDDPV). Our objective is to establish the dynamics equations governing the motor, slide valve, and bias mechanism of the valve. Additionally, we construct a mathematical model for the servo valve controller, while ensuring the linearization of the controller model. Furthermore, we conduct an in-depth analysis of the static characteristics of the valve, including linearity, dead zone, hysteresis loop, and zero drift. Regarding the dynamic characteristics, we establish a dynamic mathematical model for the RDDPV valve. Subsequently, we subject the servo valve to analysis with a focus on frequency response and dynamic response, using the control current as the input and the pressure as the output. To perform these analyses, we employ the software package SIMULINK of MATLAB, facilitating dynamic simulations. Remarkably, the simulation results exhibit the valve's conformity to design requirements, underscoring its suitability for subsequent research and development endeavors. Through our rigorous investigation, we offer essential technical support for the forthcoming stages of the valve's research and development, thereby laying a robust foundation for its further advancement. Klarecki analyzed the influence of electronic controller parameters on the dynamic characteristics of electro-hydraulic servo system3. With respect to related researches in China, Songjing et al.4 studied the vibration noise of torque motor, and in their work, the self-excited vibration of the torque motor is suppressed by adding magnetic fluid to the working clearance. At present, there are relatively few researches on the dynamic characteristics of rotary direct drive electro-hydraulic pressure servo valve.The rotary direct drive electro-hydraulic pressure control servo valve (hereinafter referred to as RDDPV)5. Notably, in 1966, IBM pioneered the voice coil motor6, which subsequently found application in the direct drive of hydraulic slide valves by companies like Parker. Additionally, piezoelectric ceramics, renowned for their high energy density and force output, have progressively been integrated into direct-drive valves. To address the limited output displacements of piezoelectric ceramics, Beihang proposed a compact hydraulic displacement amplification structure, significantly enhancing slide valve stroke in limited space, thereby augmenting control flow rate and response frequency of the direct-drive valve7.In response to the imperative of further reducing size to facilitate integration within narrow servo control systems, such as aircraft engine control, ongoing efforts both domestically and internationally have sought to improve motor configurations, slide valve movement, and mechanical drive interfaces8, proposing a rotary valve-type direct-drive valve that effectively reduces the hydrodynamic force during spool motion by controlling the throttle port size through rotary motion of the slide valve. In a separate development, Zhejiang University of Technology introduced a fast response 2D valve, driven by a stepper motor to rotate the slide valve. The high and low-pressure holes, along with spiral grooves on the shoulder of the spool, form a hydraulic resistance half-bridge, enabling precise servo control of the slide valve's horizontal position9. Currently employed in missile servo control, it is noteworthy that the 2D valve’s spool drive follows the same configuration as traditional two-stage valves with the same hydraulic pressure. Consequently, its response frequency and zero characteristics are susceptible to drift due to changes in external factors such as oil supply pressure and temperature.Another innovation was introduced by a study10. Notably, these rotary drive mechanisms facilitate the conversion of motor rotarymotion into linear motion of the slide valve, with the motor rotation and slide valve translation direction arranged perpendicular to the direction of the servo valve. This structural arrangement renders the linear direct-drive valve more compact and less sensitive to external vibrations affecting the slide valve’s movement. Woward company has successfully commercialized rotary direct-drive valves based on this principle. Internationally, rotary direct-drive valves have found progressive applications in aircraft electronic anti-skid brakes, aircraft rudder and engine control, and other fields.In the 1990s, a novel structure called the Rotary Direct Drive Electro-Hydraulic Pressure Control Servo Valve (RDDPV) emerged, featuring diverse rotary drive mechanisms that convert motor torque into valve torque and further to servo valve torqueDespite these advancements, the development of rotary direct-drive electro-hydraulic servo valves remains in a nascent stage. The selection of structural parameters, particularly those at the drive interface, still lacks clarity, and a theoretical basis for design and manufacture is yet to be fully established.12. The valve adopts the form of electric feedback for servo control; the angle displacement sensor feeds back the rotation angle of torque motor to the sensor to form a closed-loop of motor position; the pressure sensor feeds back the pressure of the working chamber to provide external closed-loop control of pressure13.The working principle of rotary direct drive electro-hydraulic pressure servo valve (RDDPV) is illustrated in Fig. h.Figure In the initial state, the central axis of the cylindrical hole coincides with the Y axis; when the motor rotates, the ball center rotates around the motor axis, and its movement can be decomposed into movement in the X and Z directions; the ball's movement in the X direction drives the spool to translate, thereby changing the throttling area of the oil inlet and return ports; the movement in the Z direction drives the spool to rotate around the X axis.14:The motor rotor is under the electromagnetic driving torque of15:The kinetic equation of the motor rotor isDuring the opening process, the slide valve has movement in two directions: translation along the axial direction of slide valve and rotation around the central axis of slide valve. By decomposing the movement in two directions, we have:In the slide valve, the spool has clearance fit with the valve sleeve. Due to the pressure difference between the two ends of spool, the liquid in the clearance will form asymmetric pressure distribution from the high pressure end to the low pressure end, which can be called the pressure on the slide valve side. According to the slit flow theory of fluid mechanics, the pressure on the slide valve side changes with the clearance size. If the clearance changes symmetrically along the longitudinal axis of the spool, the resultant pressure on the slide valve side is zero. However, when the clearance changes asymmetrically along the longitudinal axis of the spool, the resultant pressure on the side slide valve side is not zero, and the side pressure friction is formed with the movement of the spool.6:Therefore, asymmetrical pressure on the slide valve side can be caused by non-concentric spool and sleeve or asymmetrical clearance due to various reasons such as machining accuracy or assembly, which will further lead to side pressure friction. If the pressure on slide valve side further acts on the spool surface and makes it eccentric, the clearance will become even more asymmetrical, and the pressure on the spool side will increase. In severe cases, the oil film between the spool and valve sleeve will be destroyed, resulting in dry friction, which significantly increases the friction between the spool and sleeve, resulting in “hydraulic clamping” and equipment failure. The friction force can be represented asThe steady-state hydraulic force is the hydraulic force on the spool due to changes of flow rate and direction when fluid flows into the valve cavity and passes through the control window of the valve, and it is always in the direction trying to close the control window of the slide valve. According to the momentum theorem, the steady-state hydraulic force is:16:The transient hydraulic force is generated by the acceleration of fluid. Assuming that the oil cannot be compressed, and the oil quality in the valve cavity remains unchanged, the change rate of oil speed in the valve cavity is Set the axial distance between the inlet and outlet of the slide valve as hen, Eq.  can be mAccording to the continuity equation, the flow in the valve cavity is the flow at the valve port, and the throttling formula can be obtained:According to the above Equation, we can obtain:In general, the impact of xv17:h is the distance from the center of the ball to the plane, e is the eccentricity distance between the eccentric shaft and the motor rotation center,The motor rotates and drives the eccentric mechanism, the eccentric mechanism pushes the spool to move linearly, and the eccentric ball has eccentric rotation, which also drives the spool to rotate around its axis. Therefore, the spool movement can be decomposed into linear movement along the X axis and rotation around the X axis. As shown in Fig. According to Fig. 18:The main functions realized by controller include signal conditioning, closed-loop pressure control, feedback control of motor angle and PWM amplification. Among them, signal conditioning is to convert the input control current signal −3 m. According to Eq. −3 m. AccTo sum up, the kinetic equation of the motor rotor at the operating point can be obtained as:19:E = 1000 MPa is the bulk modulus of oil, and Considering the oil compressibility, the output brake pressure of slide valve and the spool displacement has the relationship ofThe static characteristic curve of RDDPV is as shown in Fig. The ratio of the maximum deviation of the nominal pressure curve from the nominal pressure gain profile to the rated current is called linearity.According to the linearity analysis curve in Fig. 20. Therefore, when the differential current only changes slightly, the spool will not have displacement . This small variation range of differential current not sufficient to change the output signal is called the static characteristic dead zone of the servo valve. According to the simulation results of static characteristics, the dead zone of the RDDPV valve can be obtained, which about 0.4 × 10−3A.When the input signal  of the electro-hydraulic servo valve changes, the spool must overcome certain resistance to have displacement21. The hysteresis analysis curve is shown in Fig. Between positive and negative rated currents, the percentage of the maximum difference between the two currents that produce the output pressure of the system and the rated current is called hysteresis when cycling at a speed that does not dynamically workThe hysteresis of the servo valve is caused by the magnetic hysteresis of the force (torque) motor and the oil clearance of the valve. The oil clearance of the valve is caused by friction and the clearance of the mechanical fastening part. The hysteresis loop value changes with the current, when the current is small, the hysteresis decreases with constant amplitudes, so hysteresis generally won't not affect the system stability. The loop value caused by the oil clearance is a fixed value, and the oil clearance will significantly increase when the oil dirty, which might cause system instability.The servo valve is adjusted under the specified test conditions according to the test standards. When the working conditions  change, the zero position of the valve will shift. The ratio of the change of zero-bias current caused by changes in working conditions such as pressure and temperature to the rated current is called zero drift. When the oil supply pressure is changed to 11 MPa, the static characteristic curve is as shown in Fig. Combining the equation, the transfer function block diagram of the RDDPV pressure servo valve can be obtained, as shown in Fig. PID control of the pressure external closed loop. Pressure sensor  will be converted into the corresponding voltage by the hydraulic pressure The main structural parameters of RDDPV are listed in Table te is motor mechanical constant,Dv is the diameter of the spool end face, mv is the spool mass, xv0 is the pre-compression of the reset spring, h is the distance from the center of the ball to the plane, Rc is the motor internal resistance, kt is the current moment coefficient, U is the slide valve pre-opening, Jβv is the spool rotational inertia, kv is the reset spring stiffness, e is the eccentricity distance between the eccentric shaft and the motor rotation center, V is the load chamber volum.In Table 22. A dynamic mathematical model is constructed based on the analysis of the RDDPV valve. The frequency response and dynamic response of the servo valve are analyzed with the control current as the input and the pressure as the output. The software package SIMULINK of MATLAB is used for dynamic simulation.The dynamic characteristics of a valve are generally represented using the frequency response. The frequency response of the RDDPV valve is the complex ratio of the output displacement of the slide valve to the current when the input current has constant-amplitude variable-frequency sinusoidal variation within a certain frequency rangeThe step response is used to illustrate the transient response of the valve. The step response is the tracking process of the step input current by the output pressure when the load pressure is zero under the rated pressure. Considering the step response of the RDDPV valve, when the oil supply pressure is 3000psi, the control current of 10 mA to 60 mA is input, and the step response curve is obtained, as shown in Fig. When the input current amplitude is in the range of 0.01A to 0.06A, the step response is mainly analyzed. As shown in Fig. This study delved into the structure and operational principles of the Robot Rotary Direct Drive Electro-Hydraulic Pressure Servo Valve (RDDPV). By establishing dynamic models for the motor, slide valve, and eccentric mechanism within the valve, as well as a mathematical model for the controller, we comprehensively examined various static characteristics of the valve, including linearity, dead zone, hysteresis, and zero drift.Furthermore, leveraging the dynamic mathematical model of the RDDPV valve, we conducted in-depth analyses of the frequency response and dynamic response of the servo valve, employing the control current as the input and pressure as the output. To achieve this, we utilized Simulink in the Matlab software package for dynamic simulation. The simulation results demonstrated that all performance indicators satisfactorily met the specified requirements, thus laying a robust foundation for subsequent analyses pertaining to reliability, durability, and anti-contamination.Through our rigorous investigation, we have provided a comprehensive understanding of the RDDPV system's behavior and validated its efficacy in meeting operational criteria. The insights gained from this study contribute to the optimization and further advancement of rotary direct drive electro-hydraulic pressure servo valves for various industrial applications.