Seismocardiography (SCG) is the noninvasive measurement of local vibrations of the chest wall produced by the mechanical activity of the heart and has shown promise in providing clinical information for certain cardiovascular diseases including heart failure and ischemia. Conventionally, SCG signals are recorded by placing an accelerometer on the chest. In this paper, we propose a novel contactless SCG measurement method to extract them from chest videos recorded by a smartphone. Our pipeline consists of computer vision methods including the Lucas–Kanade template tracking to track an artificial target attached to the chest, and then estimate the SCG signals from the tracked displacements. We evaluated our pipeline on 14 healthy subjects by comparing the vision-based SCG According to the American Heart Association, CVDs impose an enormous health and economic burden in the United States and worldwide2. This mortality rate and economic burden can be reduced by improving diagnostic methods and making them more accessible to achieve earlier detection of cardiac abnormalities. In that regard, routine monitoring of cardiac activity can increase the possibility of early diagnosis of CVDs. Current cardiac activity monitoring methods include both invasive (such as pulmonary artery catheterization3) and non-invasive techniques. The invasive techniques are usually performed in clinical facilities limiting their utility for routine remote monitoring of the patients. On the other hand, non-invasive methods such as electrocardiography (ECG) have been widely used to develop remote monitoring systems that can be used outside of healthcare facilities. Recent studies on seismocardiography (SCG), another non-invasive technique that records cardiovascular vibrations on the chest surface, suggested their potential in accurately estimating clinically significant parameters4. These vibrations can be measured in dorsoventral, right-to-left, and head-to-foot directions, and are caused by heart mechanical activities, such as mitral and aortic valves opening and closing, isovolumetric contraction, ejection, and rapid filling of left ventricle6. Since SCG measures the mechanical activity of the heart, it can provide complementary diagnostic information to other modalities such as ECG and pulse oximetry that evaluate the electrical activity of the heart and the blood oxygen level8. As a result, several studies demonstrated that SCG signals contain information that can be utilized to precisely investigate cardiac activity such as the timing of the opening and closing of the aortic and mitral valves10. Also, SCG signals have shown promise in detecting and monitoring a variety of cardiovascular diseases, such as coronary heart disease, myocardial infarction, ischemia, and hemorrhage17.In the United States, cardiovascular diseases (CVDs) are the number one leading cause of death, and they remained the top cause of death during the COVID-19 pandemic, accounting for 20.1% of all fatalities between March 2020 and October 202118, radars19, or even WiFi devices21 for non-contact vital sign monitoring. While these methods have demonstrated success in laboratory settings, their practical implementation for cardiac monitoring outside of laboratories or clinical facilities is impeded by their bulky or costly hardware. In recent years, with the proliferation of digital communication devices such as smartphones and laptops, the research community has become increasingly interested in computer vision-based remote cardiac activity monitoring23. Vision-based health assessment offers distinct benefits such as being non-contact, non-invasive, and easy to use. These methods have been used in different applications, including heart and respiration rate monitoring, heart rate variability assessment, and blood oxygen saturation evaluation28. However, to the best of our knowledge, the majority of computer vision-based cardiac monitoring studies mainly focused on measuring heart rate and did not extract low-amplitude high-frequency events from individual heartbeats relevant to SCG31.SCG signals are conventionally measured using accelerometers attached to the chest surface. With the advancement of sensors and technology, the concept of non-contact monitoring of cardiac activity has received increasing attention due to its numerous advantages over traditional techniques. Previous studies utilized various technologies including infrared sensorsThe aim of this study is to determine the feasibility of using a smartphone camera and computer vision to acquire a seismocardiogram. Thus, our primary objective is to estimate SCG signals in the right-to-left and head-to-foot directions from video using computer vision techniques, which could provide a novel method to investigate the cardiac-induced vibrations on the chest, and eventually build the foundation for developing an accessible low-cost cardiac monitor. Similar to capturing data from multiple accelerometers on the chest surface, we used a smartphone camera to track multiple target regions on the chest surface to measure the acceleration signals induced by the heart activity. The main advantage of the proposed method in this study is that it uses a smartphone camera to acquire data, which is relatively easy to set up and may be deployed immediately in emergency situations. Vision-based approaches also offer the ability to monitor multi-point measurements with a single camera sensor.The study protocol was approved by the institutional review board (IRB) of Mississippi State University and all research was performed in accordance with the guidelines and regulations described in the IRB protocol. A total of 14 subjects with no history of CVDs and from diverse backgrounds were recruited . Table All subjects were instructed to lay supine on a bed without additional body movements Fig. a. To min32.A smartphone  was used to videotape the upper chest of the subjects with an acquisition speed of 60 frames per second (fps) and resolution of In order to validate the vision-based SCG signals, a triaxial accelerometer  was placed underneath each QR code. The accelerometers were then attached to three locations on the sternum including the manubrium, the fourth costal notch, and the xiphoid process. A signal conditioner  was used to amplify the accelerometer outputs with a gain factor of 100. The amplified signals  with different sampling frequencies. Therefore, to synchronize the SCGmentclass2pt{minimOur vision-based SCG signal measurement is based on tracking artificial targets  on the chest surface. As shown in Fig. x and y directions as depicted in Fig. x- and y-axes. This step was done for each QR code separately to ensure that the x and y-axes of the video and accelerometers are as aligned as possible.To calculate the SCG signals in the 33 to measure the displacement of the QR codes attached on the chest. In this regard, we adapted the unified approach proposed in34 for the Lucas–Kanade method for QR code tracking, with the goal of minimizing the sum of the squared error between two images, i.e., the QR code itself and a video frame in which the QR code is being searched for. The minimization is done based on warping the video frame onto the coordinate frame of the QR code. Since this optimization is nonlinear, it is performed iteratively solving for increments to update previously known warping parameters.Computer vision methods are widely used for object tracking and displacement measurement in videos. Vision-based displacement estimation methods, such as tracking techniques and optical flow compute relative displacement by correlating successive image frames in a video. Template matching is the most prevalent tracking technique, which works by searching for the image regions that are most similar to a reference template. In the present study, we employed an optical flow-based template tracking method to extract the displacement information of the target regions on the chest. More specifically, we used the Lucas–Kanade template tracking algorithmI(x), let QR(x) is the target region defined from the first frame QR(x) to the successive frames W, which was parameterized by vector W transforms the pixel x in the coordinate frame of the QR(x) to the sub-pixel position W in the coordinate frame of the video frame W can be then computed using the following 2D image transformation, where the parameters u such that the warped image QR(x) are perfectly aligned. The region that matches the QR code in a new frame is determined by optimizing the parameters u to minimize the sum of squared difference error between QR(x) asx of the QR code and its corresponding pixel in the video frame W. The minimization of the expression in , and Jacobian of the warp function W. The first-order approximation of E with respect to H represents the u  of subjects was estimated using SCGmentclasspt{minimax and y directions using our computer vision pipeline for all three sensor locations. Figure x direction. Similar results were obtained for other subjects.Our goal was to understand if the SCG signals can be extracted from the chest videos recorded by a smartphone. We estimated the SCG signals in both We analyzed the vision-based estimations of x coordinate of each data point represents the correlation coefficient between the y-axis. Therefore, when both x and y directions demonstrate a low correlation with The temporal similarity of the ensemble averages of the SCGx and y directions for the middle accelerometer and QR code of subject 9 . The Euclidean distance between the gold-standard and vision-based signals was calculated from the distance matrices and used to calculate the similarity indices x and y coordinates of the data points in this graph represent the x and y directions was above 0.85. The average, maximum, and minimum similarity between the The similarity of the signals in the time domain was also investigated using DTW. The right panel of Fig. 4).Figure Bland–Altman plot was used to determine the level of agreement between the gold-standard als Fig. . Due to This work shows that cardiac-induced vibrations can be extracted from the videos recorded of the chest. We validated our vision-based pipeline by evaluating the similarity between the SCGThe SCGx (right-to-left), y (head-to-foot), and z  axes, each displaying a specific pattern. However, our vision-based pipeline could only estimate the SCG signals along the x and y directions. In the literature, most SCG studies including those that used a contactless measurement method, focused on the dorsoventral component of the SCG10. Although the dorsoventral component cannot be currently estimated by our method, it is plausible that additional and complementary diagnostic information can be extracted from the analysis of the right-to-left and head-to-foot SCG components7. For example, Shandhi et al. reported that the changes in the pulmonary artery mean pressure and the pulmonary capillary wedge pressure can be better estimated from the changes in the SCG signals along the x-axis14. In addition, in this study, the videos were captured with an acquisition speed of 60 fps, allowing us to estimate the SCG features up to 30 Hz, i.e., the infrasonic SCG features41. Since SCG signals may contain clinically relevant information for specific CVDs in the higher frequency ranges42, we will develop an experimental setup and pipeline to estimate the higher frequency features as well as the SCG dorsoventral components in our future efforts.When a triaxial accelerometer is placed on the chest, SCG components are measured in all three 4. The conventional methods to investigate SCG variability includes employing an array of accelerometers attached to the chest. For example, Azad et al. used 32 accelerometers in their array between the right and left anterior axillary and between the 2nd and 5th intercostal spaces43. Although increasing the number of sensors in such arrays can provide a better picture of the spatial distribution of SCG, it also makes the instrumentation and data acquisition process more expensive and labor-intensive. On the other hand, our vision-based pipeline can simultaneously estimate SCG signals from multiple points on the chest without affecting the computational cost of the data acquisition or analysis. For example, we tested our pipeline to obtain SCG signals from three locations on the sternum . This can consequently result in estimating SCGFurthermore, during the data acquisition and preprocessing, we tried to align the m frames. However, a serious problem in constructing such an adaptive tracking system is that, with every template update, a small error is added to the location of the template. The tracked region eventually drifts away from the actual template location as a result of the accumulation of these errors. Matthews et al.44 proposed a solution for this problem by correcting and updating the template using a combination of the reference templates retrieved from the initial and the most recent frames. In this feasibility study, we also used this strategy to correct and update the template by keeping the first template around, i.e., the QR code image extracted from the first frame QR(x) and utilizing it to correct the drift in In this work, we estimated the SCG signals from videos by tracking the motion of QR codes attached to the accelerometers on the chest. However, it is important to note that the accuracy of this method depends on the attachment quality of the QR code to the accelerometer. For example, a poorly attached QR code may compromise the SCGEventually, the high DTW similarity and the good agreement between the In this work, we have developed a vision-based pipeline to estimate the SCG signals in the right-to-left and head-to-foot directions from the chest videos recorded using a smartphone. We validated our pipeline by comparing the vision-based SCG signals with the gold-standard signals measured by tri-axial accelerometers. We have demonstrated that a relatively high correlation existed between the gold-standard and vision-based estimations of the SCG signals. Overall, this work demonstrates the possibility of extracting cardiac vibrations from normal phone videos. More studies can lead to a paradigm shift in developing accessible and affordable cardiac remote monitoring tools.


Compared to a stateless data plane, a stateful data plane offloads part of state information and control logic from a controller to a data plane to reduce communication overhead and improve packet processing efficiency. However, existing methods for implementing stateful data planes face challenges, particularly maintaining state consistency during packet processing and improving throughput performance. This paper presents a high-performance, FPGA (Field Programmable Gate Array)-based stateful packet processing approach, which addresses these challenges utilizing the PHV (Packet Header Vector) dynamic scheduling technique to ensure flow state consistency. Our experiments demonstrate that the proposed method could operate at 200 MHz while adding 3–12 microseconds latency. The method we proposed also provides a considerable degree of programmability. To face the emerging demands of network applications such as load balancing, TCP link tracing and stateful firewall ,2, the cThe emergence of the stateful data plane has addressed these issues. It adopted the “match-state-action” paradigm, which offloaded a portion of the controller’s logic and state information to the data plane. This reduced the communications overhead between the controller and the data plane and improved the packet processing speed. The data plane chose appropriate packet forwarding strategies based on the state information. However, the stateful data plane increased the hardware complexity of network devices and led to many new challenges in the designing and management of the stateful data plane.Significant progress has been made in the implementation methods of stateful data planes, such as P4 ,6, OpenSA match-action table that supports both stateful and stateless packet processing and can process 200 M PHV per second.A series of RISC-like instruction sets and corresponding hardware structure designed based on basic packet processing requirements.A hardware implementation method for PHV dynamic scheduling that is capable of achieving high-performance packet processing, flow state consistency, and maintaining the sequence of PHV input and output.In response to the mentioned challenges, we proposed an improved hardware design that can be implemented on FPGA to support programmability in the data plane. Our proposed approach could dynamically schedule the processing sequence of PHV based on the data dependency of flow states, enabling the data plane to achieve flow state consistency while minimizing hardware pipeline stalls. We also propose an optional reorder buffer that could ensure the output order of PHV is the same as the input order. Consequently, subsequent modules will not be affected by out-of-order executions. Additionally, a series of RISC-like instruction sets and corresponding hardware structures are designed to enhance programmability and provide support for out-of-order executions. The main contributions of this paper include:OpenFlow  was the OpenState  added a OPP (Open Packet Processor)  proposedFlowBlaze  was an iSDPA  proposedP4  are statIn summary, many related works have been proposed and implemented in a wide range of stateful network applications using hardware structures or high-level abstraction languages as platforms. Representative examples of stateful data plane applications include port knocking, stateful firewalls and TCP link tracing. These applications leverage the characteristics of the stateful data plane to reduce communication with the controller and improve data plane processing speed . They alWe propose an improved stateful data plane based on FPGA. The global state is shared by all packets entering the switch.The table state is shared by packets entering the same match-action table.The flow state is shared by packets matching the same table entry.The per-packet state is used by an individual data packet to pass information between different match-action tables.The overall architecture consists of hardware modules for storing and managing state information. The aforementioned storage module needs to solve the RAW hazard caused by frequent read/write operations and data dependency. Additionally, the consistency of flow states is the most important, as it determines the forwarding behavior of the data plane. The indiscriminate strong consistency guarantees for all state information will lead to a significant performance decrease in the packet process and lead to complex logic. Inspired by the article , we clasIn our implementation, the state information is associated with the address as a unique identifier. This facilitates management and improves lookup speed. Considering the trade-off between performance and complexity of the design, the consistency of flow states is implemented by hardware, and the management of global and table states is handled by the controller.In In The stateful match-action tables served as the fundamental building blocks of the stateful data plane. It has the following procedural sequence: by taking into consideration the input PHV, global state, table state and packet state, a unique key is generated. This key will be used in the match table and obtain the address of the PHV’s corresponding flow state. The flow state information is then attached by the address and fed into the issue queue. The issue queue schedules the PHV based on the dependency of the flow states, allowing out-of-order execution in the process block pipeline. The process block determines the behavior of state updates and PHV actions based on the configuration of the EFSM model abstract. The executed PHV will be stored in the reorder buffer and committed in order. The key differences between our work and previous research will be explained in the following subsection:The workflow of the stateful data plane can be summarized as read, update and write-back operations of the flow state. Therefore, the consistency of read after write operations is essential in ensuring behavior correctness. However, read and write operations occur nearly every clock cycle due to high-speed packet processing. Flow state read operation may not obtain the latest data from the flow state memory, resulting in the RAW hazards (true dependencies). This can occur because even though a PHV action is executed after a prior PHV action, the prior PHV action has been processed only partly through the pipeline. However, the out-of-order executions may affect subsequent modules. To address this problem, an optional hardware-based solution has been proposed to ensure flow state consistency in high-speed packet processing, which includes the PHV issue queue and PHV reorder buffer modules. As shown in Allocation Module: This module finds the free entry with the lowest address in the PHV Address Buffer and the free entry of PHV&State Mem. If no free entry is left, it will block the input data stream.Scoreboard: This module is a memory of flip flops that stores the status of the per-flow state and keeps track of per-flow state read and write operations. So, the number of flip flops is equal to the number of the flows. The scoreboard will be updated by the broadcast buses at every positive edge of the clock. So, this module is capable of detecting RAW hazards between the PHV’s corresponding flow states. The fields of used bits in the scoreboard indicate the validity of the input PHV’s flow state. Every time a new PHV enters, the system will check if the used bit is busy or not and read in the corresponding flow state. This module also checks the broadcast buses if there is a conflict in broadcast line and reads the line of the same flow address.PHV&State Mem: This module stores input PHV and its corresponding state information in the address of the memory given by the Allocation Module.PHV Addr Buffer: This module stores the address of the input PHV and its corresponding state in the lowest address free entry of the buffer given by the Allocation Module. Every entry includes the following fields: PHV&flow addr together with its ready bit (used to indicate whether the PHV has a dependency relationship), ROB (Reorder Buffer) ID. To maintain the old-first order in this buffer, bubble entry resulting from out-of-order dispatch needs to be considered. By shifting down the entries above the bubble entry, the issue queue could maintain the old-first rule. Additionally, this module associates an increasing ROB ID to each input PHV within the out-of-order window , which is used for PHV reordering.Select Module: In each clock cycle, the Select module will choose the lowest-address valid entry in the PHV Addr buffer, which is marked as ready to be dispatched. Then, this module dispatches the selected entry to the subsequent process block pipeline.Wake-up Module: This module continuously monitors the broadcast buses. Whenever the executed flow state address broadcasted matches the PHV Addr buffer’s entry, the corresponding flow state will be updated and marked as ready. If multiple entries match the broadcasted address, only the oldest one will be chosen as ready.In our proposed PHV issue queue, PHV and the corresponding state information can be considered as a combination of instructions and data. They will be dispatched to the process block pipeline for subsequent “match-action” execution. The issue queue will detect real-time RAW hazards between the input PHV and change the execution sequence of PHV to avoid hazards and reduce pipeline stalls. Similarly, the function of the aforementioned module is similar to the instruction issue queue in modern processor architecture ,22. As mThe core workflow of the PHV issue queue can be summarized as following two parts: First, based on the Scoreboard, potential RAW hazards between PHVs are detected. PHV that are not ready will be blocked, while allowing the irrelevant PHV to execute ahead. The wake-up module monitors the broadcast and activates the oldest PHV entries that have data dependencies. So, this nodule ensures that PHV of the same flow are dispatched in order and avoid RAW hazards, while allowing out-of-order launch for different flow PHVs. Second, the issue queue stores the input PHV and their corresponding states. Each cycle, ready PHV will be selected for dispatch into the pipeline, and the empty bubbles are eliminated by shifting operations. Below, there will be detailed explanations and figures about the mentioned workflow provided.In In The function of the Reorder Buffer is to store out-of-order executed PHVs and commit them in order. In our implementation, shown in Our approach chose to collapse the bubble entry in the issue queue and restrict the PHV in old-first order. This brought advantages that simplify the Select Module, as the PHV are arranged from top to bottom in descending order of their existing time, making it easy to use a priority encoder to select the oldest PHV that is ready to be executed. The Allocation module is also simplified by keeping the free entries in the upper region of the buffer. Additionally, the depth of the issue queue together with the size of the out-of-order window will determine the capabilities of dynamic scheduling. However, the issue queue’s depth bottleneck lies in the Wake-up module and the Select module’s hardware structure. The latency of the mentioned module exhibits a linear correlation with the depth of the issue queue, which means the larger the number of entries the issue queue contains, the higher the latency is. Therefore, it is necessary to decide on the issue queue parameters based on actual deployment requirements and the execution cycle of the process block needed. In EFSM Model: Based on the configured VLIW, the EFSM model calculates the vector-form condition evaluation results. The condition results and state information are used as input for the EFSM table, which could determine the address of the corresponding instructions for the processing strategy. The instructions will be fetched from the instruction RAM.State Update Block: Based on the input VLIW, the state update block performs the necessary operations to update the state.PHV Action Block: Based on the input VLIW, the PHV action block performs the necessary operations to modify the PHV.This section will introduce the design of the process block, which is the core of PHV modification and state update. The ready PHV and corresponding state information are dispatched into the process block via the issue queue, and the pipeline uses the EFSM (Extend Finite State Machine) abstraction to decide the forwarding strategies, as shown in Algorithm 1: Calculate the Number of TCP Retransmission Packetsif then   end ifThe PHV action and state update instruction are determined based on the match results of the EFSM model. Algorithm 1 shows a simple application running on a stateful data plane. It will count the number of TCP retransmission packets per flow, based on the size relationship between per flow sequence and packet sequence. To enhance programmability and flexibility, the data plane supports extracting arbitrary fields from the PHV and state registers according to the instructions, as shown in In Based on the proposed high-throughput data plane architecture above, we implemented a multi-stage stateful match-action table pipeline deployed on the Xilinx Zynq UltraScale+ FPGA chip on a Dell R740 server. Furthermore, we downloaded the generated bit file to the FPGA device. To generate test data streams, we utilized the IXIA high-speed network traffic generation tool and configured the stateful data plane as a simple Multi-Path network application. Limited by data bus width and the parser module, the PHV processing speed of the pipeline has redundancy, especially when dealing with a packet of large size. In our deployed multi-path applications, the data plane pipeline will not drop the packet. The packet loss only occurs in the FIFO used as the interface between different modules. The pipeline processing speed could not reach 200 Mpps due to bottlenecks in other modules such as the parser, deparser and data bus width. We verified this 200 Mpps capability in simulation software.Our specific parameters for hardware implementation are shown in With theoretical analysis and experiment, we evaluated the specific resource and module parameters of the implementation. Moreover, we use the same algorithms to compare our work and software implementation method. Forwarding latency is used as a performance comparison metric between hardware implementation and software implementation. The application was a simple stateful forwarding, and the packet’s outport was determined based on the flow state information. The stateful data plane dynamically determines whether to send packets to outport 0 or outport 1 by polling its current state. As shown in In this section, the issue queue’s depth (number of entries) parameters will be discussed. This parameter relates to PHV processing speed and the corresponding resource utilization in typical scenarios. Based on the experiment and analysis, we provide appropriate issue queue deployment parameters. Firstly, we define that the input packets processed by the current data plane belong to a certain number of equiprobable flows. Our pipeline design only supports stalling the pipeline and does not drop packets. The average execution cycle of PHV is used as the performance metric. The pipeline’s input was a continuous stream of 100 M packets of equiprobable 4, 6, 8, 10, 12, 16, 24 and 32 flows. We analyzed the relationship between the average PHV processing clock cycles and the depths of issue queue in different situations, as shown in The relationship between the number of issue queue entries and the FPGA hardware resources overhead is shown in In Due to the existence of up to 16 possible branches for updating the flow state, speculation techniques are difficult to implement in the stateful data plane. Therefore, considering only the delay metrics within the data plane pipeline, emitting in old-first order is the optimal choice. In our test, we configured the IXIA device to send packets at a rate of more than 80 Gbps to measure the throughput performance of our work. In this article, we propose a novel method for implementing stateful data planes, achieving a great improvement in data plane processing performance. Our proposed work could achieve a PHV processing speed of up to 200 M per second while adding 3–12 microseconds of latency. In addition, the PHV process capabilities per clock cycle have significantly improved compared with FlowBlaze . The PHV


However, there is a need for improved parameter fitting and data integration features in microbial community modeling. This study proposes a novel alternative strategy utilizing state-of-the-art dynamic flux balance analysis (dFBA) to provide a simple protocol enabling accurate replication of abundance data composition through dynamic parameter estimation and integration of metagenomic data. We used a recurrent optimization algorithm to replicate community distributions from three different sources: mock, in vitro, and clinical microbiome. Our results show an accuracy of 98% and 96% when using in vitro and clinical bacterial abundance distributions, respectively. The proposed modeling scheme allowed us to observe the evolution of metabolites. It could provide a deeper understanding of metabolic interactions while taking advantage of the high contextualization features of GEM schemes to fit the study case. The proposed modeling scheme could improve the approach in cases where external factors determine specific bacterial distributions, such as drug intake.The human gut is home to a complex array of microorganisms interacting with the host and each other, forming a community known as the microbiome. This community has been linked to human health and disease, but understanding the underlying interactions is still challenging for researchers. Standard studies typically use high-throughput sequencing to analyze microbiome distribution in patient samples. Recent advancements in meta-omic data analysis have enabled computational modeling strategies to integrate this information into an  For this study, all these values were fixed to Xmax,i = 50 g/L, thus limiting the growth of faster species and reaching a persistent excitation condition for the system. The value of Ks was fixed to a given value of 0.10, as indicated by [To keep the biological sense of the simulation, all the biomass concentrations were limited to the range [0, cated by . Nonethexi is the biomass concentration for each strain in the microbiome. In addition, k − th cycle in the reinforcement learning, and Jk qualifies the modeling strategy of the estimated aggregated biomass fraction. An early stop criterion for the algorithm was implemented where the value of Jk had to reach 0.001. Otherwise, the code was manually stopped if the function reached a local minimum.Considering the equation:AGORA database [Vmax, ks, and reference composition values) and (5) executing the code. This section details the outcome of the three examples we tested for the proposed modeling strategy using the recurrent gradient descent methodology. The data in the following sections present the results proportionally merged as a single system in the cases where the hierarchical strategy is applied  selecting the microbiome species, (2) retrieval of metabolic reconstructions for such species from the database , (3) selA. muciniphila, which had a w.e value five times higher . As shown in s higher . Additio ≤ 0.001 . The funin vitro and clinical bacterial distributions (Section 2.3). The results for the former show that after eighteen cycles of adaptation using the optimization algorithm, the distribution converges towards the in vitro experimental distribution values  represents a high affinity of the microorganisms for these compounds, resulting in rapid consumption of substrates. SCFA-producing bacteria such as B. fragilis and B. ovatus were included in the simulation, and their abundance percentage in the mock community  observe key metabolite evolution inside the nutritional space of the system. For instance, in our studies, the community compositions were replicated with a maximum weighted average error of 4% in clinical data. This certainty value comes from implementing the hierarchical gradient descent algorithm, and the value was in an acceptable range for error. Moreover, the numerical simulator implemented in this strategy allowed us to observe changes in the concentration of selected metabolites, which are important for inter-species and host interactions. While this depends directly on the chosen numerical simulator, the fact that we can observe these changes implies a complete integration of the optimization algorithm and the toolboxes. However, the results found in this work should be verified through experimental investigations.The modeling strategy considered in this study allowed us to: (1) include individual dynamic relationships and metabolite interchange between microbial species within the system’s framework; (2) reproduce The bacterial metabolic reconstructions can be further contextualized to better fit the studied system. A mechanistic understanding of microbiome communities is limited to the information available about the system . This liThe presented approach overcomes some limitations regarding the need for a significant amount of data to observe microbial behavior and interaction. The improvement lies in the combination of the mathematical model from the μbialSim numerical simulator and the modeling strategy based on the gradient descent algorithm, which is known for ts ability to work with relatively small amounts of data, as confirmed by our results. Lower error percentages are attributed to taking only the fractional composition of the distribution as a measure of error between the simulation and the reference values. This implies that the applicability of our strategy will improve as more kinetic experimental data becomes available.Dynamic modeling strategies employ different numerical methods to infer the kinetic parameters for the model –44. The in silico determination of the change of metabolites within the microbiome environment may help us to understand better the relation with the host and the alteration of the immune system, which is highly influenced by microbiome changes [The current work paves the road for a new modeling approach that complements GEM modeling strategies’ current state-of-the-art. We expect this modeling strategy for microbiome communities to be useful in facilitating the interpretation of metagenomic sequencing data in the context of metabolic interactions, mainly to study systems for which samples are hard to acquire. Moreover,  changes , 47–52.  changes , 54.in vitro experiments with complex microbiome compositions become challenging in laboratory settings.In conclusion, the combination of genome-scale metabolic modeling and the gradient descent optimization algorithm to infer bacterial kinetic and metabolic behavior provides promising opportunities for studying the gut microbiome and its interaction with the host without the need for extensive data. However, the accuracy of the simulation results is contingent upon the comprehensiveness of the model system description. Our tool is publicly available and expected to undergo further continuous development. The strategy is scalable and applicable to different GEM-based technologies. Potentially, it is feasible that the modeling technique can be scalable to different applications, such as the evaluation of external components to the nutritional space  in the microbial dynamics, especially when S1 Table(XLSX)Click here for additional data file.S1 Dataset(ZIP)Click here for additional data file.


Binary memristor crossbars have great potential for use in brain-inspired neuromorphic computing. The complementary crossbar array has been proposed to perform the Exclusive-NOR function for neuromorphic pattern recognition. The single crossbar obtained by shortening the Exclusive-NOR function has more advantages in terms of power consumption, area occupancy, and fault tolerance. In this paper, we present the impact of data density on the single memristor crossbar architecture for neuromorphic image recognition. The impact of data density on the single memristor architecture is mathematically derived from the reduced formula of the Exclusive-NOR function, and then verified via circuit simulation. The complementary and single crossbar architectures are tested by using ten 32 × 32 images with different data densities of 0.25, 0.5, and 0.75. The simulation results showed that the data density of images has a negative effect on the single memristor crossbar architecture while not affecting the complementary memristor crossbar architecture. The maximum output column current produced by the single memristor crossbar array decreases as data density decreases while the complementary memristor crossbar array architecture provides stable maximum output column currents. When recognizing images with data density as low as 0.25, the maximum output column currents of the single memristor crossbar architecture is reduced four-fold compared with the maximum currents from the complementary memristor crossbar architecture. This reduction causes the Winner-take-all circuit to work incorrectly and will reduce the recognition rate of the single memristor crossbar architecture. These simulation results show that the single memristor crossbar architecture has more advantages compared with the complementary crossbar architecture when the images do have not many different densities, and none of the images have very low densities. This work also indicates that the single crossbar architecture must be improved by adding a constant term to deal with images that have low data densities. These are valuable case studies for archiving the advantages of single memristor crossbar architecture in neuromorphic computing applications. Memristor was mathematically proposed in 1971 by Prof. L. O. Chua as basic as the three circuit elements, namely the resistor, inductor, and capacitor . The conHardware implementations of neural computing using memristor crossbars have achieved much success in the last decade ,15,16,17The first interesting architecture of binary memristor crossbar for brain-inspired neuromorphic computing is the complementary crossbar that performs the logical function of Exclusive-NOR for speech and image recognition . The twiIn previous work, to obtain the single crossbar architecture, a constant term in the expanded function of the Exclusive-NOR is omitted. Because all constant terms of all columns are omitted, so it does not affect the identification of the winner. The single memristor crossbar circuit was tested with 10 binary images. The tested images have a high number of 1 bits. Single crossbar architecture has not been tested with images with the low number of 1 bits. Bit 1 of binary image data is represented by a low resistance state memristor, which mainly produces the output column current in single memristor crossbar architecture. If the number of 1 bits is low, the output currents are all very small, which can impact the accuracy of output decision circuit. In this work, we find out the impact of data density on the operation of the single memristor crossbar architecture, in which a constant term of the expanded function of the Exclusive-NOR is omitted. This research shows an interesting result that the single memristor crossbar architecture has the advantage for images with high density, but does not work well with low-density images.A complementary memristor crossbar architecture has been proposed for the cognitive task of pattern recognition based on the Exclusive NOR operation to measure the similarity between the input pattern and the stored patterns. Complementary memristor crossbar architecture is composed of two complementary crossbar arrays, as conceptually shown in In Equation (1), n, the n × m in which The input vector The output current is then fed into a Winner-take-all circuit, which determines the maximum output current. If the Winner-take-all circuit shows that In the Winner-take-all circuit, ten comparators receive ten discharging voltages, from The single memristor crossbar architecture was proposed by utilizing the Exclusive-NOR function with only one memristor array . The ExcIn Equation (4), In Equation (5), So far, we can see that the single memristor crossbar array with bipolar input has the same functionality as the complementary memristor crossbar architecture for pattern recognition based on Exclusive-NOR operation. In Equation (4),  circuit . For a p3/Nb-doped SrTiO3 stacked layer and a memristor model that can be used to describe various memristive behaviors [The circuit simulations were performed to test the impact of data density on the performance of single memristor crossbar and the complementary memristor crossbar architectures. The simulations were performed using the SPECTRE circuit simulation provided by Cadence Design Systems Inc, San Jose, CA, USA . Memristehaviors ,30.As discussed in the previous section, it is essential to analyze the impact of data density of patterns on the complementary and the single memristor crossbar architectures. The data density of a binary image is defined as the percentage of bit 1 s in the image data. In particular, images with high data density will have a higher number of 1 bits, whereas images with low data density will have fewer 1 bits. In this paper, ten images are used to analyze the impact of data density on the performance of memristor crossbar architectures. The original images are presented in The original images are grayscale images with the size of 32 × 32. Binary images are produced by thresholding grayscale images. By varying the threshold, we obtain images with different data densities. The first three images  have a low data density of 0.25, the next three images  have a moderate data density of 0.5, and the last four images  have a high density of 0.75. These different data density images are then vectorized to the size of 1024 × 1 and stored in the memristor arrays of the complementary crossbar architecture and the single crossbar architecture. Each image is stored in a column of the array. Binary images with different data density produced by thresholding grayscale images are shown in In Binary images are represented by vectors of binary values. Each image is stored in one column of the memristor array for single crossbar architecture. For complementary crossbar architecture, each image is stored in two columns, one column in the memristor array and the other in the inverted memristor array, as mentioned before. Binary value 0 is represented by the high resistance state (HRS) memristor and binary 1 is represented by the low resistance state (LRS) memristor in the crossbar array. The HRS and LRS are 1 MΩ and 10 KΩ, respectively. The binary values 0 and 1 in the input vector are mapped to input voltages of 0 V and 1 V, respectively. The input image represented by the vector of input voltage is applied to the crossbar circuit. The output currents are produced at the bottom of columns according to the Ohm’s law and the Kirchoff’s current law. These output column currents are then compared to each other using a Winner-take-all circuit to determine the maximum column current, corresponding to the column containing the pre-stored image that best matches the input image. The Winner-take-all circuit is based on the discharge speeds of pre-charged capacitors, which are controlled by the output column currents, to find the fastest discharging capacitor. Therefore, the values of output column currents play an important role in the recognition accuracy of the memristor crossbar array architectures. The output column currents when recognizing ten input images with different data densities are shown in In contrast, with the single memristor crossbar architecture, the output column currents reduce when the data densities of input images are decreased, as shown in Because the Winner-take-all circuit is based on the output column currents, this reduction in the maximum output column current of the single memristor crossbar architecture should be considered. As represented in previous section, the output column currents from memristor crossbars cause the pre-charged capacitors, the We next analyze the discharging voltages, from As shown in In The single memristor crossbar is an optimized crossbar architecture for brain-inspired neuromorphic computing. The single memristor crossbar architecture consumes less power and occupies smaller area than the complementary memristor crossbar architecture. In addition, using only one memristor crossbar array can improve the fault tolerance of the memristor crossbar circuit. Here, the cross-point fault is one of the main causes that significantly reduces the accuracy of the memristor crossbar-base neuromorphic circuits . In thisIn this work, we present the impact of data density on the performance of the single memristor crossbar architecture and the complementary memristor crossbar architecture. The impact of data density on the performance of single crossbar architecture is mathematically figured out by analyzing the effect of the omitted constant term in the Exclusive-NOR operation. The observation is then verified by the circuit simulation for the recognition of images with different levels of density. The complementary crossbar architecture consumes more power and occupies a larger area compared with the single crossbar architecture; however, the complementary crossbar architecture does not depend on data density. Otherwise, single crossbar consumes less power and occupies smaller area than complementary crossbar but single crossbar degrades the performance with low data density images. This work recommends that to ensure the single crossbar architecture works correctly for binary image recognition application, binary images must have high number of 1 bits. Finally, this work also indicates that the single crossbar architecture must be improved by adding a constant term to deal with images that have low data densities. These are valuable case studies for archiving the advantages of single memristor crossbar architecture in neuromorphic computing applications.


Precipitation nowcasting is mainly achieved by the radar echo extrapolation method. Due to the timing characteristics of radar echo extrapolation, convolutional recurrent neural networks (ConvRNNs) have been used to solve the task. Most ConvRNNs have been proven to perform far better than traditional optical flow methods, but they still have fatal problems. These models lack differentiation in the prediction of echoes of different intensities, which leads to the omission of responses from regions with high intensities. Moreover, because it is difficult for these models to capture long-term feature dependencies among multiple echo maps, the extrapolation effect declines sharply over time. This paper proposes an embedded multi-layer attention module (MLAM) to address the shortcomings of ConvRNNs. Specifically, an MLAM mainly enhances attention to critical regions in echo images and the processing of long-term spatiotemporal features through the interaction between input and memory features in the current moment. Comprehensive experiments were conducted on the radar dataset HKO-7 provided by the Hong Kong Observatory and the radar dataset HMB provided by the Hunan Meteorological Bureau. Experiments show that ConvRNNs embedded with MLAMs achieve more advanced results than standard ConvRNNs. Precipitation nowcasting refers to the prediction of precipitation in a certain area in the next 2 h using available meteorological data. Severe convective weather, such as heavy precipitation, is characterized by rapid development and strong destructiveness, which are shown in precipitation nowcasting. The accuracy, reliability and timeliness of precipitation nowcasting are essential to mitigate the impact of severe convective weather events on the daily lives of many. At present, precipitation nowcasting is mainly based on radar echo extrapolation, that is, using the radar echo images generated by weather radars to predict the echo distribution in the future . SpecifiRadar echo extrapolation methods are mainly divided into traditional methods and extrapolation methods based on deep learning. The traditional radar echo extrapolation algorithms mainly include the cross-correlation method, cell centroid method and optical flow method ,4,5,6,7.With the improvement in big data processing capabilities, deep learning has developed rapidly and been applied to a variety of tasks to improve performance, such as in image processing, machine translation, intelligent healthcare and other fields. The deep learning model is good at learning the basic characteristics and change trends of data collectives from massive data, and its development provides a new method for studying radar echo extrapolation . The radThe radar extrapolation method based on CNNs can capture the spatial features of the echo pattern well, but it is difficult to deal with the time features contained in the echo sequence. Agrawal et al.  believesThe radar echo extrapolation method based on RNNs has greater advantages for processing echo sequences. Most existing spatiotemporal sequence networks are improved based on ConvLSTM . PredRNNHowever, as shown in We propose an improved cascaded dual attention module (CDAM) based on a self-attention module (SAM). CDAM can automatically adjust the feature weights of different positions in radar echo images and enhance the causal relationship between different features. Compared with other attention mechanisms, CDAM has a stronger ability to extract and abstract features. Therefore, it can enhance important details and slow down the blurring of extrapolated images.We combine the 3D convolutional block attention mechanism (3D-CBAM) and CDAM to propose a versatile MLAM. It strengthens the processing of key echo regions from a global perspective and grasps the trend of echoes.We design a new architecture so that the MLAM can be applied to ConvRNNs. Contrast experiments were conducted between ConvRNNs and ConvRNNs embedded with MLAMs. ConvRNNs with MLAMs achieve better results than standard ConvRNNs on radar echo datasets provided by the Hunan Meteorological Bureau and Hong Kong Observatory.In this paper, we propose a multi-layer attention module (MLAM). MLAMs not only alleviate the loss of important features faced by spatiotemporal sequence networks but can also be deployed as a general module in multiple spatiotemporal sequence networks. The main contributions of this paper are as follows:Specifically, the input and output of ConvRNNs are sequence data. In the vertical direction, information is propagated from the bottom up. The bottom layer processes the original input information, and the output of the top layer is the prediction of the next moment. By stacking layer by layer, ConvRNNs can fully extract important spatial feature information at multiple scales in each frame. In the horizontal direction, in order to satisfy the characteristics of long-term memory of spatiotemporal sequence tasks, the memory unit is used to record the important features of historical information.ConvLSTM is used as an example to illustrate the information transmission and update the formula of the basic model. The key equations of ConvLSTM are shown as follows:Here, the input Each feature processed by the self-attention module (SAM) records a correlation with the features of all locations as shown in The similarity score of each position is normalized by using the The feature of each location In order to ensure the stability and flexibility of the module, the final output The convolutional block attention module (CBAM) is a simple and efficient fusion attention module that can be directly applied to various networks. It is composed of the channel attention module and the spatial attention module and strengthens important features from the two dimensions of channel and space. Different from CBAM, as shown in As shown in The spatial attention module focuses on pixel positions that are decisive for the prediction in Two radar echo datasets are used in this paper, which are the HKO-7 provided by the Hong Kong Observatory and the HMB provided by the Hunan Meteorological Bureau. The following reasons show why we chose the HKO-7. Firstly, Shi et al. defined the precipitation prediction as a spatiotemporal sequence prediction task for the first time and validated ConvLSTM by using part of the data from HKO-7 . Later, HKO-7: HKO-7 was collected by the Hong Kong Observatory using the S-band single-polarization weather radar, which includes radar echo images from 2009 to 2015. The radar CAPPI images have an altitude of 2 km and cover an area of 512 km × 512 km in Hong Kong. A frame of radar echoes is obtained every six minutes, with a total of 240 frames throughout the day, each with a resolution of 480 × 480 pixels .HMB: The HMB was collected by several S-band weather radars provided by the Hunan Meteorological Bureau located in Changsha, Hunan Province . The dataset spans three years (2018–2020), which ensures the diversity of radar echo images. Moreover, there is a high temporal resolution of 6 min and a high spatial resolution of 2.5 km in the dataset. Therefore, the radar echo images can well reflect the important properties of rainfall particles.HKO-7: We followed the processing procedure for the HKO-7 similar to that described in . FirstlyHMB: Firstly, echo images with an effective echo area of less than 20% of the whole image were removed. Then, pixels with values ranging from 0 dBZ to 80 dBZ were retained in the echo image, and the pixels were processed as outliers. We used a sliding window of length 20 to slice the echo sequence. The processed dataset was divided into a training set of 15,600 sequences and a test set of 2000, each sequence consisting of 20 frames, with the first 10 frames for input and the last 10 frames for prediction. In order to minimize the image while maintaining the resolution of the image, the original radar echo image was trimmed to remove the boundary region and retain the 768 × 768 image area in the center, and the image was further compressed to 256 × 256 by the bilinear interpolation method.In the evolution of radar echoes, the echo motion that occurs at a certain moment is affected by the echo information of multiple historical moments. Therefore, it is vital to find the spatiotemporal information for high-quality radar echo extrapolation. The information comes from the information flow composed of multiple historical moments and is most relevant to the input of the current moment. We propose a cascaded dual attention module that performs an interaction between the input feature and the memory feature. The structure of the CDAM is shown in The SAM for The SAM for The modeling of long-term historical information is the basis of short-term prediction. The memory state feature Considering the temporal characteristics of radar echo extrapolation, we find that relevant features in the past have a great influence on the prediction results at the current moment. In traditional networks used for radar echo extrapolation, the memory cell tends to focus on local spatial features and ignores long-term global dependent information.The operation process of this module is divided into two steps, including the enhancement of historical key information and the extraction of relevant features, as shown in For radar echo extrapolation, the evolution of echoes at the current moment is affected by the echoes of multiple historical moments. In traditional ConvRNNs used for radar echo extrapolation, the memory cell tends to focus on local spatial features and ignores long-term global dependent information. Our proposed MLAM acts on multiple memory cells of the spatiotemporal sequence network, fully pays attention to and captures the key information in the memory information flow and effectively updates the memory information flow at every moment.For uniformly modeling radar echo movement trends and transient changes, a ConvRNN structure embedded with an MLAM is proposed in The application of the MLAM realizes the interaction of echo information across time slices, so that the network focuses on important features closely related to the prediction results, which better alleviates long-term memory loss in radar echo extrapolation.To verify that the MLAM is a universal module for improving the performance of spatiotemporal sequence networks, we selected five classical ConvRNNs commonly used for the radar extrapolation task, including ConvLSTM, ConvGRU, PredRNN, PredRNN++ and MotionRNN. The five original networks were compared with the ConvRNNs embedded with an MLAM. The implementation of the original model and MLAM+ConvRNNs is described in In order to accelerate the training process, Each echo image with the shape  was subsampled to the shape  before passing through the ConvRNNs. The ConvRNNs . All modIn order to make a more reasonable analysis of the experimental results, we used image quality evaluation indicators and meteorological evaluation indicators to jointly evaluate multiple models. The structural similarity index measure (SSIM), as an image quality index, was applied to our models. The Critical Success Index (CSI) and Probability of Detection (POD) were used as meteorological indicators to evaluate the results. The threshold method was used to focus on the pixel value in the echo map. Firstly, the pixel values in the prediction echo map and the ground truth echo map were converted by thresholding. If the pixel value was greater than the given threshold, the corresponding value of the pixel point was recorded as 1, otherwise it was recorded as 0. Then, we calculated the numbers of true positive points In general, precipitation may occur when the echo intensity is generally above 20 dBZ, and if echo intensity exceeds 30 dBZ, it is considered to have strong precipitation. Values of 20 dBZ, 30 dBZ and 40 dBZ were selected as thresholds to evaluate the prediction accuracy of models. Compared with the HKO-7, the strong echo area of the HMB dataset is large and concentrated. It means that the proportion of heavy rain in the HMB dataset is much higher than that in the HKO-7 dataset, as shown in To better compare all the results, we picked an instance from each of the two datasets and visualized them. As shown in the black box in The original ConvRNNs have insufficient ability to predict echo shape, especially ConvLSTM and ConvGRU, which show that echo boundaries between different intensities become blurred, and the quality of predicted images deteriorates over time. MLAM+ConvLSTM and MLAM+ConGRU both obtain more accurate prediction results, which improve the prediction of echo details and capture the motion trend of radar echoes to achieve a better long-term prediction effect. PredRNN, PredRNN++ and MotionRNN use spatiotemporal memory cells to store and process echo information. Therefore, their predictive performance is better than ConvLSTM.Our proposed MLAM consists of 3D-CBAM and CDAM. To verify the effectiveness of each module, different types of attention schemes are applied to the ConvLSTM model, including 3D-CBAM+ConvLSTM, CDAM+ConvLSTM and MLAM+ConvLSTM. To verify the effectiveness of the MLAM for high-echo processing, the CSI and POD curves at 40 dBZ at different forecast moments are described in The visualization of the radar echo extrapolation is shown in In this paper, we propose a general network module called MLAM to improve the accuracy of radar echo extrapolation. The MLAM is composed of widely used 3D-CBAM and newly proposed CDAM. First, we use 3D-CBAM to enhance key memory features of multiple historical moments, which dominate the evolution trend of radar echoes and enhance the long-term tracking and attention of the network for strong echoes. Then, the CDAM captures correlations between current-moment input features and historical features, which allows the network to adapt to instantaneous changes in radar echoes. Combining the above two improvements, the MLAM establishes the long-term global dependence among multi-frame echo images in time and space. It ensures that the historical echo features can guide the echo extrapolation on the current time step. This can alleviate the problems faced by the existing ConvRNN extrapolation method, such as insufficient prediction of high-intensity echo regions and the large area decline in echo intensity in the late prediction period.We conduct comparative experiments on two radar echo datasets, the HKO-7 provided by the Hong Kong Observatory and the HMB provided by the Hunan Meteorological Bureau. The quantitative results show that ConvRNNs with MLAMs are superior to traditional ConvRNNS in the quality of echo prediction, especially for the prediction of strong echoes. In addition, the ablation experiment is set up to fully evaluate the effectiveness of the 3D-CBAM and CDAM modules. Finally, the qualitative analysis of visualization examples shows that MLAM+ConvRNNs can better model the evolution of radar echoes than ConvRNNs, so as to achieve more accurate precipitation nowcasting.In the future, while maintaining the stability of the model and prediction performance, we will focus on long-term radar extrapolation tasks as much as possible to achieve a longer precipitation forecast. Furthermore, we will make full use of radar echo maps at different heights to further explore precipitation prediction tasks.


To implement state policies of zero-markup drug policy and medical service fee adjustment for public hospitals, this study constructed game models of the pharmaceutical supply chain, consisting of a drug supplier and a public hospital. The study obtained the optimal medical service level and pricing under the new state drug policies. In addition, it analyzed the impacts of the degree of public benefit of hospitals on the medical service level, the medical service price, and the drug price. Finally, from the perspective of cooperation between drug suppliers and public hospitals, the specialized coordination contract was designed to maximize overall social welfare. This study found an anomalous but meaningful conclusion: in the background of the zero-markup drug policy, a higher public benefit of hospitals could increase the drug prices, but it could reduce the medical service prices further to cut down on the overall treatment fees for the patients. The novel coordination contract can optimize the pharmaceutical supply chain and achieve a win-win situation for the drug suppliers, public hospitals, and patients. When the public benefit of hospitals is higher, the profit of a decentralized decision-making supply chain is greater than a centralized one, while the pharmaceutical supply chain will not coordinate itself. UndeWith the background of China’s zero-markup drug policy and considering the public benefit characteristics of hospitals, a theoretical model of the pharmaceutical supply chain is established in this study. The medical service level and service price as well as drug prices from suppliers are analyzed under the new policy. Then, from the perspective of cooperation between the hospital and drug supplier, a coordination contract is proposed to reach a win-win situation for all the pharmaceutical supply chain members and for social welfare. Moreover, the implementation of the coordination contract is comprehensively discussed in the background of the new policy.The rest of this study is arranged as follows: Section 2 is the literature review. Section 3 states the problem definition and hypothesis. Then, Section 4 compares equilibrium results between centralized and decentralized scenarios to explore the reason for supply chain inefficiency under a decentralized scenario. Section 5 proposes coordination contracts to maximize the overall social welfare. Section 6 gives the conclusion and significance of this study.2.Our study relates to two distinct areas of the existing literature: medical service pricing and pharmaceutical supply chain coordination contracts.2.1.Due to the drug markup policy, the price of the medical service is rigorously controlled by the regulatory authorities, and its value has been underestimated in the last several decades . Wang et2.2.In addition to the pricing of the medical services, the pharmaceutical supply chain coordination contract is another major topic in this study. Some previous studies  explored3.In the model of this study, the pharmaceutical supply chain consists of a drug supplier (m), a public hospital (h), and a group of patients. The drug supplier sells drugs to patients through a public hospital. Under the government’s zero-markup drug policy, the public hospital sells drugs to patients at the original prices ice ah . It is gThe patients’ individual utility as fully healthy is assumed to be As a rational consumer, patients could choose whether or not to receive treatment from the public hospital according to the principle of utility maximization, i.e., hospital . Assuminβ denotes the public benefit coefficient of the hospital, which satisfies β ∈ . The larger the coefficient β is, the higher the public benefit of the hospital will be. β = 0 indicates that the public hospital is a completely profit-driven institution. β = 1 indicates that the public hospital is a completely non-profit institution. Following the literature references , 38, the as ch .4.In this section, the equilibrium solutions of the pharmaceutical supply chain under decentralized decision-making (indicated by superscript D) and centralized decision-making (indicated by superscript C) scenarios are delivered first. An analysis of the decision-making of public hospitals and drug suppliers is provided. The causes of pharmaceutical supply chain inefficiency are discussed by comparing two equilibrium solutions in two decision-making scenarios.4.1.ha, and then the drug supplier makes decisions on the sales price of drugs Public hospitals are usually in a dominant position in the Chinese domestic pharmaceutical supply chain. The public hospitals usually define the medical service level Several theorems and propositions could be obtained by solving these equations via the backward induction method.Theorem 1:The equilibrium solutions of the pharmaceutical supply chain defined by the public hospital are:The equilibrium profit and utility of the public hospital are:The equilibrium profit and patient surplus number of the drug supplier are:The profit and social welfare of the pharmaceutical supply chain are:where Proposition 1:Proposition 1 shows that the public benefit of hospitals is the main factor affecting the level and price of medical services. At a higher value of public benefit, the price of medical services is low while the price of drugs is high. Further study indicates that for each unit of public benefit from hospital improvement, the price of medical services decreases faster than the increase in drug prices. It means that the overall fee  when This proposition implies that the level of medical services under decentralized decision-making is smaller than that under centralized decision-making, while the fee paid by the patient under decentralized decision-making is larger than the fee under centralized decision-making. As a result, social welfare is lower under decentralized decision-making than that under centralized decision-making.Under decentralized decision-making, the drug supplier and the public hospital make decisions based on their priorities, i.e., the drug supplier pursues maximum profit, and the public hospital pursues maximum total utility. Due to the inconsistency of decision objectives and the double marginalization caused by the two decisions, the pharmaceutical supply chain deviates from the overall optimization. As a result, the quality of medical service patients receive reduces, and the overall fee of medical treatment increases, leading to a reduction in the overall welfare level.From the perspective of the pharmaceutical supply chain, when the public benefit coefficient satisfies From the perspective of social welfare, the overall social welfare under decentralized decision-making is always lower than the centralized one, regardless of the change in the public benefit of hospitals. To explain the impacts of the public benefit of hospitals on supply chain profit and social welfare under both decision-making scenarios, From the figures, the individual rationality level of pharmaceutical supply chain members could affect the overall performance and social welfare under the decentralized decision-making scenario. To gain more benefits , both drug suppliers and the public hospital have incentives to design a rational contract to achieve higher profits and social welfare, which the centralized decision-making scenario can obtain. In this case, designing an effective contract could be the solution.5.When When Theorem 3:Under the contract of “cost sharing + fixed medical service fees + transfer payments,” the equilibrium solution of the pharmaceutical supply chain is:The profits of public hospitals and drug suppliers are:Theorem 3 shows that when the “cost-sharing + fixed medical service fee + transfer payment” contract between drug suppliers and public hospitals is enforced, the contract can trigger internal coordination within the pharmaceutical supply chain. The level of medical service that the patients received and the overall medical treatment fees  are the same as in the centralized decision-making scenarios. It means that patients get better service at lower prices, and the pharmaceutical supply chain gains greater profits under the “cost-sharing + fixed fee for medical services + transfer payments” contract. Due to The pharmaceutical supply chain gains greater profit under the coordination contract mechanism, but this profit needs to be rationally distributed among the supply chain members to meet their respective participation constraints. To implement the contract more effectively, the participant constraints of the supply chain members are suggested to be Proposition 4:1 and F2 can be calculated by the following equations:When When the public benefit is lower and the transfer payment satisfies To prove the validity of the coordination parameter Before the coordination of the pharmaceutical supply chain, the relative profit  difference of public hospitals was a monotonically increasing function of a fixed payment 6.In the background of the drug zero-markups policy, this study innovatively builds a game theoretical model between drug suppliers and public hospitals. The influences of public benefit character on the medical service level, medical service fee, and drug prices are comprehensively analyzed. By comparing the profits and overall social welfare under decentralized decision-making and centralized decision-making in the pharmaceutical supply chain, the reasons for the lower performance of the pharmaceutical supply chain system under decentralized decision-making scenario are revealed. A coordination contract is designed to boost cooperation and facilitate the transfer of profits between different members of the pharmaceutical supply chain. Some conclusions are drawn as follows:(1) In the background of the zero-markup drug policy, increasing the public benefit of hospitals can only reduce the price of medical services but not the price of drugs. The higher the public benefit of the hospital, the higher the level of medical services and the lower the overall fee for patients. Moreover, the increase in the public benefit of hospitals could improve both profits in the pharmaceutical supply chain and overall social welfare. From the perspective of profits, it is worth noting that simply increasing the public benefit of hospitals is advantageous to drug suppliers but will be resisted by hospitals.(2) When the public benefit of a hospital is high, the profits of the pharmaceutical supply chain under the decentralized decision-making scenario are lower than those of the centralized one. When the public benefit of hospitals is low, the profits of the pharmaceutical supply chain under decentralized decision-making are higher than those of the centralized one. However, the social welfare of the pharmaceutical supply chain under the decentralized decision-making scenario is always lower than that of the centralized one, regardless of the public benefit of the hospital. It means that when the public benefit of the hospital is low, both drug suppliers and the public hospital have incentives to design a rational contract to achieve higher profits and social welfare. When the public benefit of the public hospital is high, the pharmaceutical supply chain cannot achieve a favorable state of internal profit distribution and coordination.(3) When the public benefit of a hospital is low, the novel coordination contract of “cost sharing + fixed medical service fee + transfer payment” can coordinate the pharmaceutical supply chain to achieve a win-win profitable situation for all supply chain members and increase the patient surplus number. When the public benefit of hospitals is high, the pharmaceutical supply chain needs to receive external subsidies to achieve higher social welfare, such as government subsidies and donations from charitable organizations.The original contributions presented in the study are included in the article/NZ and SL contributed to the study design and wrote the manuscript drafts. GZ and CL supervised the study and provided suggestions for the revision of the manuscript drafts. SL, GZ, CL, and NY provided some reviews on the manuscript. All authors contributed to the article and approved the submitted version.


In the last few years, new noninvasive strategies have emerged as rehabilitative treatments for patients with stroke. Action observation treatment (AOT) is a rehabilitation approach based on the properties of the mirror neuron system with a positive impact on modifying cortical activation patterns and improving the upper limb kinematics. AOT involves the dynamic process of observing purposeful actions with the intention of imitating and then practicing those actions. In recent years, several clinical studies suggested the effectiveness of AOT in patients with stroke to improve motor recovery and autonomy in activities of daily living. However, a deeper knowledge of the behavior of the sensorimotor cortex during AOT seems to be essential.The aim of this clinical trial, conducted in 2 neurorehabilitation centers and in patients’ homes, is to investigate the effectiveness of AOT in patients with stroke, confirming the translational power of a tailored treatment. Particular emphasis will be placed on the predictive value of neurophysiological biomarkers. In addition, the feasibility and impact of a home-based AOT program will be investigated.A 3-arm, assessor-blinded, randomized controlled trial will be performed by enrolling patients with stroke in the chronic stage. A total of 60 participants will be randomly allocated to receive 15 sessions of AOT with different protocols , 3 sessions per week. The primary outcome will be assessed using the Fugl-Meyer Assessment-Upper Extremity scores. Secondary outcomes will be clinical, biomechanical, and neurophysiological assessment.The study protocol is part of a project (project code GR-2016–02361678) approved and funded by the Italian Ministry of Health. The study began with the recruitment phase in January 2022, and enrollment was expected to end in October 2022. Recruitment is now closed (December 2022). The results of this study are expected to be published in spring 2023. Upon completion of the analyses, we will examine the preliminary effectiveness of the intervention and neurophysiological outcomes.This study will be used to evaluate the effectiveness of 2 different AOT scenarios  in patients with chronic stroke and to assess the predictive value of neurophysiological biomarkers. Specifically, we will attempt to induce the functional modification of the cortical components by exploiting the features of the mirror neuron system, demonstrating relevant clinical, kinematic, and neurophysiological changes after AOT. With our study, we also want to provide, for the first time in Italy, the AOT home-based program while assessing its feasibility and impact.ClinicalTrials.gov NCT04047134; https://clinicaltrials.gov/ct2/show/NCT04047134DERR1-10.2196/42094 Stroke is a leading cause of death and one of the most common causes of long-term disability that interferes with good quality of life . CurrentOne such noninvasive strategy is the action observation treatment (AOT), supported by results collected through randomized controlled trials -10. ThisExtensive research over the last 20 years on human MNS -16 showeOn the basis of the MNS properties able to activate the sensory-motor system through the observation of actions as well as the execution of the same actions, the AOT is proving to be an innovative rehabilitative approach for recovery of patients with stroke in chronic stage with upper limb impairment; several findings are present in scientific literature ,23,27-31On the basis of these results, several clinical studies have been published in recent years, suggesting the effectiveness of AOT in improving motor recovery and autonomy in ADL ,20,24,32In our previous work, we administered AOT treatment to a group of patients with stroke and observed the predictive value of ERD of electroencephalography (EEG) alpha rhythm ie, 8-13 Hz) during rehabilitation tasks and at the end of the treatment, as a sign of neural plasticity. In addition, increased functional dexterity was found in patients with stroke in the subacute stage that had AOT compared with their peers who underwent a control treatment ) and a nonstructured interview.The variables related to the secondary instrumental outcomes  will be evaluated during the standardized pointing task described earlier.EEGLAB for artifact removal.All the data will be analyzed using MATLAB software (MathWorks Inc). Specifically, the EEG recordings will be preprocessed offline using the MATLAB’s toolbox called To perform a thorough assessment, different motor components of the affected upper extremity will be evaluated using the FMA-UE combined with 6 other scales.The FMA-UE ,35  and quality  of the use of the upper limb during ADL performance.The Motor Activity Log  assessesThe Nine Hole Peg Test  measuresThe following biomarkers will be used in the study:The EEG signal will be recorded  using 64 to 128 electrodes  during the pointing task (described earlier). Alpha (8-13 Hz), beta (14-30 Hz), and mu (8-13 Hz) bandwidths will be registered. EEG biomarkers will be ERD and ERS of alpha and beta rhythms, beta brain coherence, and mu rhythm suppression -50.Surface EMG signals from the activation of 2 pairs of agonist and antagonist muscles from 4 upper arm and shoulder muscles  will be recorded. Dual Ag-AgCl snap electrodes with an interelectrode spacing of 2 cm will be used during the acquisitions. A standard procedure, in accordance with Surface ElectroMyoGraphy for the Noninvasive Assessment of Muscles recommendations , will beKinematic parameters of the pointing motor task will be acquired at 100 Hz by using a 7-camera motion capture system . Spherical reflective markers for motion tracking will be placed on specific body landmarks. In addition, an inertial measurement unit will be placed over the metacarpophalangeal joint of the middle finger.The data acquired during the assessment trial with respect to the hand trajectory  will be evaluated using the following metrics, related to the entire turn :Number of peaks of the speed profile: If a point-to-point reaching movement has a low number of peaks, it means that few acceleration and deceleration periods are present .The smoothness described by Teulings’s index is the rate of change of the acceleration in a movement ; a lowerMovement accuracy will be evaluated using the normalized path length parameter, as described by Colombo et al ; essentiThe absolute hand path error, as computed by Franklin et al , is the The feasibility of the home-based treatment and the usability of the platform, as well as the participants’ satisfaction with the services, will be assessed by patients at the end of the intervention (T2) with the following scales:TAM  includesNonstructured interviews (adapted from the TAM) to investigate patients’ feelings.As the changes in the effects of upper limb AOT in patients with stroke on EEG biomarkers have not been previously investigated, we have estimated the sample size based on previously published studies ,59, compFor this outcome, an effect size of 0.495 ,61 is ext test or nonparametric statistical method will be used for quantitative data. Categorical data will be analyzed using chi-square or Fisher exact tests and the Wilcoxon test.The baseline characteristics of the participants will be summarized and compared. These include the descriptions of demographic data, symptoms, and general conditions. The 2-tailed Analysis of the primary outcome  will be performed using the per-protocol principle. Treatment effects will be compared using a 2-way repeated ANOVA for clinical measurements, considering “time”  as a within-subject factor and “group”  as a between-subject factor.In addition, the percentage of participants who passed the minimal clinically important differences of the FMA-UE will be compared using chi-square tests between the 3 groups.The mean power across the assessment “time”  related to the action observation condition will be implemented in a mixed-design ANOVA to evaluate significant changes. A separate ANOVA will be performed to assess power changes in the stimuli selection data, using “treatment”  as the between-subjects factor and action as the within-subjects factor. To assess the predictive value of biomarkers for AOT effectiveness, an analysis of covariance (ANCOVA) will be performed considering the clinical data as the dependent variable, the “group” as a fixed factor, and the biomarkers as covariates.Subsequently, to evaluate kinematic parameters recovery, a mixed design ANOVA will be implemented with “time” and “treatment” as within- and between-subjects factors, respectively.P<.05. For post hoc comparisons, the level of significance will be set at P<.017 after Bonferroni adjustment  for the comparison of interaction effects. Cohen d will be calculated to determine the effect size of the change in scores for the behavioral motor outcomes between the groups. Immediate training effects (data from T0-T2) and the durability of training effects (data from T2-T3) will be separately investigated using mixed effect models.The level of significance will be set at Clinical-neurophysiological correlations will also be analyzed: the correlation between the ERD and factors such as the clinical scale score will be studied. To evaluate the differences in trends related to the clinical evolution of the patients, we will define a new variable to group the participants according to the presence or absence of relevant clinical improvements. The relevant clinical improvement will be defined by a clinical specialist for this purpose.The study data will be collected and managed using REDCap electronic data capture tools hosted at the IRCCS San Raffaele Roma Hospital and Casa di Cura del Policlinico Hospital ,63. REDCThe ethics committees of both involved centers  reviewed and approved the study protocol .The institutional review boards of both centers approved the study and will receive study reports at the middle and end of the study and monitor the study implementation and data collection.Any deviations from the protocol will be promptly notified to the ethics committees and will be applied only after approval.This study will be conducted in accordance with the principles of the Declaration of Helsinki. Written informed consent forms will be obtained from each participant before the start of the study. Only those participants who provided informed written consent before starting will be included. During the study, written data will be stored in a closed cabinet; all data, after anonymization, will be entered into a REDCap electronic data capture repository. The input data will be double-checked by another research assistant. Personal data will be discarded after 5 years.The results of this study will be disseminated through peer-reviewed journals and national and international academic conferences only by the professionals directly involved in the clinical trial.Patients will be informed of the possibility of interrupting the study at any time they deem appropriate. Any interruption will be fully documented in the case report form by the investigators. The investigators shall make all reasonable efforts to maintain the patients who express a willingness to interrupt the participation in the study protocol.Patients may prematurely discontinue the study if any of the following conditions occur:Request from the patient, even if not motivatedWithdrawal of consent by the patient to participate in the studyModification of the psychophysical state of the patient, significantly altering at least one of the variables considered in the inclusion or exclusion criteriaThe occurrence of serious adverse reactions, which in the opinion of the investigator, make the continuation of the study impossibleAbsence from >3 consecutive experimental sessionInability of the patient to continue the study for organizational and personal reasonsParticipants will be identified from hospital records or among those who show interest in participating by seeing the initiative through the communication channels of the hospitals, posters, and networks; all of them will be contacted by phone. After obtaining permission, the physicians will visit and explain the study. If they agree, the research assistants will manage their recruitment. This will be performed every week to identify participants.The results of the evaluations will be released to the participants upon request. The results of this study will be presented at national and international patient organizations and to the general public.The study protocol is part of a project (project code GR-2016–02361678) approved and funded by the Italian Ministry of Health.The rationale of this study protocol is based on the AOT in patients with chronic stroke for upper limb rehabilitation. AOT relies on the MNS network to boost motor functions in patients affected by motor impairments, engaging the brain networks active during action execution. The imitation of observed gestures may increase the reorganization of the primary motor cortex, contributing to the formation of motor memories of the observed action, thus improving the physiological processes underlying motor learning ,30.It is well known that the MNS plays an essential role in considering the actions of others and in our ability to learn by imitation . FurtherOn the basis of these findings, the proposed study protocol aims to identify the effects of AOT and motor rehabilitative treatment on the clinical and functional status of patients with stroke through an advanced multidomain assessment and to infer the effects on brain plasticity.This study will be a starting point for the evaluation of the effectiveness of the 2 AOT scenarios proposed  in patients with chronic stroke , as well as for the assessment of the predictive value of neurophysiological biomarkers.Specifically, we will attempt to induce functional modification of the cortical components by exploiting the features of the MNS, demonstrating relevant clinical, kinematic, and neurophysiological changes after AOT.The added value of a multidomain assessment that includes test and clinical scales and kinematic and neurophysiological  outcomes aims to identify neurophysiological biomarkers capable of evaluating the effectiveness of AOT and confirming the translational power of a tailored rehabilitation treatment for chronic stroke.Moreover, as AOT is involved in the motor learning process and could be a useful addition to conventional therapy, an innovative home-based AOT program will be implemented in the framework of this protocol study. Indeed, the continuity of care and personalized rehabilitation for people who are affected by chronic diseases is often interrupted after transitioning from the hospital to the home environment .As a result of the COVID-19 pandemic, telerehabilitation and home care are growing rapidly, offering opportunities for integrating digital health interventions into community-based aging services. The COVID-19 pandemic has accelerated the adoption of technology and virtual care in patients’ homes, and this trend likely to stay after the pandemic. Although notable age differences in technology use remain, the adoption of key technologies by older adults is the new challenge. With this purpose, this study protocol will permit the investigation of whether a home-based program could be effective, especially in terms of exercise capacity and perceived ease of use, offering comparable benefits to hospital-based programs.The translational research results will ensure advances in the optimization and personalization of the rehabilitative process, both in hospitals and at home, thus improving upper limb motor functions and the quality of life of patients with chronic stroke.