The limited computation resource of the centralized controller and communication bandwidth between the control and data planes become the bottleneck in forwarding the packets in Software-Defined Networking (SDN). Denial of Service (DoS) attacks based on Transmission Control Protocol (TCP) can exhaust the resources of the control plane and overload the infrastructure of SDN networks. To mitigate TCP DoS attacks, DoSDefender is proposed as an efficient kernel-mode TCP DoS prevention framework in the data plane for SDN. It can prevent TCP DoS attacks from entering SDN by verifying the validity of the attempts to establish a TCP connection from the source, migrating the connection, and relaying the packets between the source and the destination in kernel space. DoSDefender conforms to the de facto standard SDN protocol, the OpenFlow policy, which requires no additional devices and no modifications in the control plane. Experimental results show that DoSDefender can effectively prevent TCP DoS attacks in low computing consumption while maintaining low connection delay and high packet forwarding throughput. Software-Defined Networking (SDN) decouples the control plane from the data plane, which introduces a more flexible way to manage the network with fine-grained and centralized control . The conThe reactive packet handling mechanism and the limited processing capability of the centralized controller become a bottleneck in SDN. It leads to performance degradation and security problem in SDN. When a packet comes which is not matched with the existing flow rules in the flow table, the data plane sends a packet-in message to the control plane for the decisions to handle the packets. An attacker can leverage this costly communication to launch SDN-aimed Denial of Service (DoS) attacks based on Transmission Control Protocol (TCP) attacks ,3,4. SpeHow to effectively prevent TCP DoS attacks from entering SDN?How to efficiently handle TCP DoS attacks while maintaining low computing consumption, low connection delay, and high packet forwarding throughput?To protect SDN against TCP DoS attacks, the following two challenges should be solved:For the first challenge, TCP DoS attack traffic is mixed with normal traffic in SDN. It is difficult to distinguish TCP DoS attack traffic from normal traffic; therefore, TCP DoS attack traffic cannot be prevented from entering SDN. Packets that incur table-miss cannot be simply dropped because normal packets will be dropped as well. The genuine attempts to establish a connection should be distinguished from the bogus attempts, and the packets of the attack connection should be filtered out. DoS attacks incur massive table-miss, consume the resources of the control plane and the data plane, and degrade the performance of SDN. So the second challenge is how to handle TCP DoS attacks while maintaining a low-cost way and high packet forwarding throughput.Some previous research work has been devoted to mitigating SDN-aimed DoS attacks. Avant-Guard, implemented into the software-based OpenFlow reference switch that has a slow userspace datapath, introduces a connection migration module on the data plane to identify attacks by verifying the handshake of each new TCP connection . FloodDeIn this paper, DoSDefender is proposed as a kernel-mode TCP DoS prevention framework in the data plane to protect SDN against TCP DoS attacks. All designs of DoSDefender conform to the de facto standard SDN protocol and OpenFlow policy, requiring no additional devices and no modification on the control plane. DoSDefender monitors traffic and detects TCP DoS attacks in the data plane. When DoS attacks are detected, DoSDefender begins to verify the validity of the attempts to establish a connection and relay all normal TCP data packets in kernel space between the source and the destination, as occurs during normal TCP sessions.DoSDefender is proposed as a kernel-mode TCP DoS prevention framework to verify the validity of the attempts to establish a connection from the source address and prevent TCP DoS attacks from entering SDN.DoSDefender migrates the connection between the source and the destination in kernel space while avoiding the extra consumption in copying packets between kernel space and user space in handling packets and improving the performance in defending TCP DoS attacks.DoSDefender is designed and implemented in the data plane to prevent TCP DoS attacks. Experimental evaluation shows that DoSDefender can effectively prevent TCP DoS attacks and protect the computation resource in the control plane while maintaining low connection delay and high packet forwarding throughput.To prevent TCP flood, our main technical contributions are as follows:The rest of the paper is organized as follows. In SDN, the switch handles the packets based on the existing flow rules received from the controller. After receiving incoming packets, the packets will be matched with the flow rules in the switch. When no flow rules in the flow table match the incoming packet (known as a table-miss), the packet is encapsulated in a packet-in message and sent to the controller by the switch. After the controller receives the packet-in, it computes a forwarding path and installs it as a flow rule in the switch with the flow-mod message. This reactive flow installation approach in SDN provides a more flexible way to manage and process packet.The reactive flow installation approach in SDN and the single point failure, limited computation resource of the centralized controller, could be leveraged by the attackers. TCP DoS attacks against SDN are depicted in The packet-in message and packet-out message incurred by TCP DoS attacks jam the bandwidth between the controller and the switch, exhaust the computation resource in the controller, increase the latency of forwarding packets, degrade the available bandwidth for forwarding packets, and overload the flow table in the switch by installing useless flow rules in a short time. TCP DoS attacks significantly degrade the performance of SDN.Software-Defined Networking, as the new network architecture, provides a global view of the network and centralized and fine-grained management of network flows. Due to single-point failure, limited computation resources in the control plane, and communication bandwidth between the control plane and the data planes, TCP DoS attacks are serious security problems in SDN. Several approaches in DoS detection methods and defense mechanisms are provided in recent research to prevent SDN-aimed TCP DoS attacks. However, each of them has some challenges in real-world scenarios.A series of DoS attack detection and mitigation methods, classifying DoS traffic and normal traffic, have been proposed. SAFETY uses an entropy-based detection mechanism to mitigate TCP SYN flooding attacks in SDN . The ensAlthough a series of DoS attack detection and mitigation methods have been proposed Recently, DoS has become more sophisticated and not easy to be identified. The false-positive rate affects the desirable detection accuracy and protection effect.Various DoS defense mechanisms are proposed to protect SDN. Avant-Guard is implemented into the software-based OpenFlow reference switch that has a slow userspace datapath ,17. AvanSummarizing the above approaches, no satisfactory defense solution can effectively prevent TCP DoS attacks from entering SDN with low connection delay and high packet forwarding throughput. New schemes are needed to protect SDN against TCP DoS attacks at a low cost.To address the DoS Attacks problems discussed in the previous sections, we introduce DoSDefender, an efficient kernel-mode defense framework against SDN-aimed TCP DoS attacks implemented in the data plane. DoSDefender prevents TCP DoS attacks from entering SDN and effectively handle TCP DoS attacks in low computing consumption while maintaining low connection delay and high packet forwarding throughput. The detailed design of DoSDefender in Open vSwitch, commonly used as the data plane, is presented in this section.DoSDefender extends the data plane with two additional components: (1) DoS detection and (2) connection proxy. The kernel datapath in Open vSwitch receives the incoming packets from the network interface card (NIC). Then the kernel datapath matches the packet header fields and follows the cached per transport connection forwarding decisions from ovs-vswitchd in user space to handle the packets. When the first packet of a new connection comes, it is delivered to ovs-vswitchd , which is used to detect DoS attacks. When a DoS attack is detected, a connection proxy in kernel space is triggered to start filtering failed TCP connections and preventing TCP DoS attacks from entering SDN in the data plane prior to delivering the packet to ovs-vswitchd , e.g., packet number, packet size, flow number, and average duration per flow. DoS detection continues monitoring the network status and traffic feature for attack detection, as Q-MIND . Self-orAttackers generally flood the network by sending a massive of TCP SYN packets with forged source addresses. The forged packets do not establish a valid TCP connection but incur a massive of table-miss packets in the data plane. The table-miss will trigger a massive packet-in message from the data plane to the control plane and consume the communication bandwidth, CPU computation resource, and memory in the control plane and data plane.The object of a connection proxy is to verify the validity of the attempts to establish a TCP connection from the source address and prevent TCP DoS attacks from entering the network. Connection proxy can differentiate the sources that will completely establish the connections from those that will not. The packets in the established connection can be permitted to enter the network. Connection proxy in the data plane migrates the TCP connection and relays the packets between the source and the destination, which includes TCP handshake, data, and FIN/RST. A connection proxy in kernel space can avoid copying packets between kernel space and user space, degrading performance when migrating connections and relaying packets.Connection proxy constructs deterministic finite state automaton, which consists of four stages: (1) Initial State, (2) Verifying Source, (3) Migrating Connection, (4) Relaying Packets. The state conversions in the scheme are shown in When an SYN packet arrives and a new TCP connection begins, the state of the connection proxy transmits from Initial State to Verifying Source, and the connection proxy verifies the validity of the connection from the source based on the completion of the TCP three-way handshake. If the connection is valid, the state of connection proxy transmits from Verifying Source to Migrating Connection. The connection proxy attempts to establish a TCP connection with the destination in the state of Migrating Connection. If the connection is established, the state of the connection proxy is transmitted to Relaying Packets. Packets are relayed between the source and the destination until the connection is closed. If the condition is not met or an exception occurs during the state transition, the state of the connection proxy will return back to Initial State. To illustrate connection proxy, consider the interaction shown in (1) Initial StateWhen a TCP packet with SYN arrives, it means a new TCP connection. The connection proxy begins to filter each connection. The connection proxy caches the packet and searches in the cached proxy table. If it not exists, the connection proxy adds a new connection item for the packet in the proxy table. The address, sequence number, acknowledgment number, etc., of the source and the destination in the packets are filled in the new connection item of the proxy table. The state of the new item in the proxy table is set to Verifying Source, and the packet will be further processed in Verifying Source. If it exists, the packet will proceed in the current state of the corresponding connection item in the proxy table.(2) Verifying SourceConnection proxy verifies the validity of the attempts to establish a new connection from the source, A and distinguishes the genuine attempts to establish a connection from the bogus attempts. The connection proxy pretends to be the destination, B and replies TCP packet with SYN/ACK, the second packet of a three-way handshake to A. The window size of the packet is set to zero to prevent A from sending data packets before the packet processing in the states of Verifying Source and Migrating Connection are finished. If A sends back the third packet of a three-way handshake with the right sequence number and acknowledgment number, A is identified as a normal node that wants to establish a real TCP connection and not a DoS attacker. The state of the connection proxy will be transmitted to Migrating Connection. Otherwise, if A is identified as an abnormal node, the packets will be dropped.(3) Migrating ConnectionMigrating Connection pretends to be A and establishes a new TCP connection with B by sending a TCP SYN packet to B. When the packet with SYN/ACK from B is received, the connection proxy sends back a packet with ACK. Once the proxy connection with B is established, the connection proxy sends A a packet with the right acknowledgment number, sequence number, and normal window size. Then, A can send data packets. The state of the corresponding connection proxy is transmitted from Migrating Connection to Relaying Packets.(4) Relaying PacketsWhen a new incoming packet arrives, it will be searched in the proxy table. If matched, the packets with the modified sequence number and acknowledgment number will be forwarded to the peer. When the packet with RST/FIN arrives, it means that the TCP connection needs to be closed, and the responding connection item of the packet will be removed from the proxy table.DoSDefender is implemented in the data plane to evaluate the effect for preventing TCP DoS attacks in the de facto standard SDN, OpenFlow network. The experiment environment for preventing TCP DoS attacks is depicted in To evaluate DoSDefender, we launch the SDN-aimed TCP DoS attacks in three scenarios: (i) data plane with Open vSwitch, (ii) data plane with Avant-Guard, and (iii) data plane with DoSDefender. Iperf3 is used to generate normal traffic and measure the available bandwidth from the normal user to the server. NetSniff-ng is used by the attacker to generate TCP DoS attacks against the server.The attacker launches 1 Mpps TCP DoS attack on the server. The rate of DoS packets received by the server in three scenarios is depicted in The attacker launches 1 Mpps TCP DoS traffic in the experiment. The controller’s CPU utility is depicted in The average delay in establishing a connection that finishes a three-way handshake in three scenarios is depicted in Normal traffic is generated to measure the available bandwidth between the normal user and the server. The available bandwidth in three scenarios is depicted in TCP DoS attacks significantly degrade the performance of SDN and consume the resources of the control plane by leveraging a reactive centralized packet processing mechanism with the match-action paradigm. To mitigate this security threat, we introduce DoSDefender, an efficient kernel-mode TCP DoS prevention framework in the data plane to prevent TCP DoS attacks from entering SDN. DoSDefender monitors the ingress traffic in the data plane and detects DoS attacks. In the TCP DoS attacks case, every packet with TCP SYN arrives; DoSDefender verifies the validity of the attempts to establish a new TCP connection from the source. The TCP packets of the valid flow can be forwarded, and those of the invalid flow will be dropped. DoSDefender migrates the connection and relays the packets between the source and the destination in kernel space which can avoid the extra overhead of copying packets between kernel space and user space and degrade the performance. Compared with previous work, DoSDefender can effectively prevent TCP DoS attacks and protect the controller’s computation resource while maintaining low connection delay and high packet forwarding throughput. DoSDefender is easy to deploy without requiring no additional devices and no modification on the control plane. For future work, we will extend DoSDefender to better support more sophisticated attacks and non-TCP DoS attacks which are based on UDP or ICMP protocols.


The dynamic measurement and identification of structural deformation are essential for structural health monitoring. Traditional contact-type displacement monitoring inevitably requires the arrangement of measurement points on physical structures and the setting of stable reference systems, which limits the application of dynamic displacement measurement of structures in practice. Computer vision-based structural displacement monitoring has the characteristics of non-contact measurement, simple installation, and relatively low cost. However, the existing displacement identification methods are still influenced by lighting conditions, image resolution, and shooting-rate, which limits engineering applications. This paper presents a data fusion method for contact acceleration monitoring and non-contact displacement recognition, utilizing the high dynamic sampling rate of traditional contact acceleration sensors. It establishes and validates an accurate estimation method for dynamic deformation states. The structural displacement is obtained by combining an improved KLT algorithm and asynchronous multi-rate Kalman filtering. The results show that the presented method can help improve the displacement sampling rate and collect high-frequency vibration information compared with only the vision measurement technique. The normalized root mean square error is less than 2% for the proposed method. In structural health monitoring, it is necessary to deploy sensors to monitor the structure’s response. These sensors collect important data on various aspects of the structure, such as vibrations and displacements ,2. TheseThere are many means of directly measuring the displacement response of a structure in the field of structural engineering, which include pull-wire displacement gauges, linear variable differential transformers (LVDT) , laser DWith the development of high-quality, low-cost optical cameras and lenses in recent years, structural monitoring and inspection–based computer vision have gradually become a hot topic. Numerous displacement estimation methods, such as template matching ,30,31, fTo estimate displacement in a high sampling rate, vision-based measurements at a low sampling rate and acceleration measurements at a high sampling rate can be combined as well. The study by Roberts et al.  highlighUtilizing the high dynamic sampling rate of traditional contact acceleration sensors, this paper introduces a data fusion approach for contact acceleration monitoring and non-contact displacement recognition, constructing and validating an accurate estimation method for critical dynamic deformation states in structures. This paper is structured as follows: Optical flow refers to the pattern of apparent motion of objects in an image between two frames due to either the motion of the object or the camera. For instance, in Under the pixel window, the error function is constructed:Set the partial derivative of The following formula can be obtained from Taylor’s expansion:The substitution of Equation (4) into Equation (3) leads to, and The following equation can be obtained from Equation (5):Equation (7) is solved by an iterative method to obtain the value of EF (ORB) . The HarEF (ORB)  is an efThe overall pyramidal tracking algorithm proceeds as follows: as an initial layer 0, the original image is used, and the image is reduced by m et al.  providesm et al.  The papeThis section uses video preprocessing to correct the distortion caused by the wide-angle lens typically used in consumer-grade cameras. A chessboard pattern is used to calibrate the camera to correct lens distortion . The calThis study used two separate acquisition systems to collect data from the camera and the accelerometer.Due to varying sampling rates and data sources, time synchronization is critical before fusing them. As a result, it was necessary to synchronize the data in time. As shown in The scale factor λ, determined by the distance between the camera and the target object, translates the image pixel values into real-world metric values, as shown below.After time synchronization, the displacements obtained from both methods are truncated to the same length. The scale factor is then estimated using the least squares method. By implementing these steps, potential discrepancies in the displacements can be minimized, and the study results can be reliable.Consequently, this approach improves the accuracy and reliability of the displacement estimation, particularly in cases where the initial displacements may not meet the small motion assumption. Furthermore, by incorporating image translation, the proposed method demonstrates its adaptability to various scenarios, enhancing its practical applicability and performance. After translating the image, the KLT algorithm calculates the optical flow between the reference frame and the current frame to obtain the average velocity of the selected feature points, which is used to determine their average displacement.In the Equation (9), The Kalman filter is a widely used method for data processing that estimates data by continuously predicting and correcting in the time domain. In general, the sampling frequency of the accelerometer is higher than the frame rate of the video. Smyth and Wu  used a mIn the case of asynchronous situations, Ma et al.  categoriSuppose Assume that during type 1, only acceleration is considered. The Since no other measurement is available in this time interval,In type 2, the prior state The posterior state and its covariance were calculated as follows:Here, In type 3, the prior state and covariance are estimated according to the following state estimation:As described in Equation (8), the actual displacement is the product of the scale factor and the pixel displacement. Therefore, according to the law of error transfer, the variance of the displacement measurement can be calculated by the following equation:This paper compares two commonly used motion estimation methods: (a) a feature-matching-based method  and (b) The proposed method for drift-free large motion measurement is investigated in a laboratory experiment to determine its performance and its sensitivity to the video’s frame rate. NRMSE):To quantify the measurement accuracy of the results, the error analysis is conducted using the normalized root-mean-square error (Under case (1), the scale factor calculation results proposed in this paper are shown in In the Kalman filter process, the noise parameter q is selected as The vision sample frequency was modified to investigate the influence of the vision sample frequency further and reduce computation time. In case (1), by resampling the video and reducing the sampling frequency to 50 Hz, 25 Hz, and 10 Hz, it can be found that as the sampling frequency decreases, the NRMSE values increase to 0.91%, 1.52%, and 1.51%, respectively, as shown in In case (2), the input frequency at the base of the structure was set to 4 Hz, with an amplitude of 30 mm, allowing for the evaluation of the effectiveness of the proposed method under large displacement and high-frequency vibration conditions. As in previous tests, the laser displacement sensor at the top of the structure was used as a reference for calculating the error values. This experimental setup aimed to demonstrate the accuracy and reliability of the proposed method in large amplitude and high-frequency vibrations.The computational time for each frame is presented in Case (3) presents the displacement of the frame under the excitation of the El Centro earthquake wave. Due to the frame’s flexibility, unlike case (1) and case (2), the top-floor displacement is primarily governed by the frequency of the structure. In Case (3), the time history curves and NRMSE values were calculated for different video sampling rates, as shown in Under earthquake conditions, the NRMSE values decrease for the given conditions, indicating that the proposed method exhibits robustness. This improved performance demonstrates the method’s ability to maintain accuracy and reliability even in challenging situations. The method’s robustness is crucial in practical applications, where dynamic conditions and external disturbances can significantly impact the quality and reliability of displacement estimates.Power spectral density (PSD) is a function used to describe the energy distribution of a signal in the frequency domain. PSD is frequently used in signal processing and communication systems to describe the spectral characteristics of noise and signals.This paper uses an accelerometer and computer vision techniques to fuse contact monitoring and non-contact tracking data of structural dynamics to exploit both advantages fully. In response to the shortcomings that computer vision techniques cannot capture high-frequency vibration information of structures and require additional parameters to estimate the scaling factor, while accelerometers cannot monitor low-frequency displacements and have zero drift, this paper proposes to fuse data from computer vision and accelerometers using Kalman filtering to calculate the scaling factor using the least squares method.The method’s reliability is also verified by using a frame structure shaker table test. The results show that (1) the method can reliably estimate the scale factor. (2) In the time domain, the NRMSE value is effectively reduced, and the overall displacement measurement accuracy is improved. (3) In the frequency domain range, the proposed data fusion method compensates for the low sampling rate of pure computer vision and effectively improves the signal-to-noise ratio of displacement data in the higher-order mode range.The study also investigated the impact of lowering the sampling frequency on the video vision technique. The findings reveal that the accuracy of the displacements is only slightly affected when the sampling frequency is decreased from 100 to 10 Hz. The fused displacements’ power spectral densities remain unchanged, even though the sampling frequency is reduced to a tenth of its original value. This demonstrates that the proposed fused method is a feasible and efficient alternative for measuring displacement in civil engineering structures.


In the field of genomics and personalized medicine, it is a key issue to find biomarkers directly related to the diagnosis of specific diseases from high-throughput gene microarray data. Feature selection technology can discover biomarkers with disease classification information.We use support vector machines as classifiers and use the five-fold cross-validation average classification accuracy, recall, precision and F1 score as evaluation metrics to evaluate the identified biomarkers. Experimental results show classification accuracy above 0.93, recall above 0.92, precision above 0.91, and F1 score above 0.94 on eight microarray datasets.This paper proposes a two-stage hybrid biomarker selection method based on ensemble filter and binary differential evolution incorporating binary African vultures optimization (EF-BDBA), which can effectively reduce the dimension of microarray data and obtain optimal biomarkers. In the first stage, we propose an ensemble filter feature selection method. The method combines an improved fast correlation-based filter algorithm with Fisher score. obviously redundant and irrelevant features can be filtered out to initially reduce the dimensionality of the microarray data. In the second stage, the optimal feature subset is selected using an improved binary differential evolution incorporating an improved binary African vultures optimization algorithm. The African vultures optimization algorithm has excellent global optimization ability. It has not been systematically applied to feature selection problems, especially for gene microarray data. We combine it with a differential evolution algorithm to improve population diversity.Compared with traditional feature selection methods and advanced hybrid methods, the proposed method achieves higher classification accuracy and identifies excellent biomarkers while retaining fewer features. The experimental results demonstrate the effectiveness and advancement of our proposed algorithmic model. In bioinformatics, DNA microarray technology can obtain a large number of gene expressions at once time, but only a few of these genes are directly relevant to the diagnosis and prediction of specific diseases, which we refer to as biomarkers. It is important to investigate how biomarkers can be discovered and modeled for classification. However, gene microarray data has the characteristics of high dimensionality, few samples and high redundancy that traditional machine learning models cannot be directly used for microarray data mining, so researchers usually use feature selection technology to discover biomarkers in gene microarray data . The purAccording to the current study, a single feature selection method cannot effectively identify significant features. However, the application of hybrid feature selection methods to extract the most informative genes has achieved good results . The hybAlmutiri et al. proposed a feature selection method based on chi-square statistic and support vector machine (SVM) with recursive feature elimination (SVMRFE). In the first stage, chi-square was used to calculate the correlation between genes and category labels, and the top 10% genes in the correlation degree were used as candidate subsets, and SVMRFE was used to further select 10 genes with rich classification information. The experimental results proved that the classification results are improved compared to the methods in previous studies . Al-WajiResearchers usually use a single filter method to perform initial dimensionality reduction on microarray data. This method lacks stability and ignores the interaction between features, potentially filtering out excellent features.Although these studies can achieve high classification accuracy, they do not pay attention to controlling the number of retained features, which may contain redundant features.Microarray data has continuity, but the situation in which the spatial search process is in a discrete state is generally ignored.In the previous work, we proposed a two-stage hybrid feature selection method, named MMBDE [However, we discover that the following problems usually exist in the current research on hybrid feature selection algorithms:ed MMBDE . In the An ensemble filter method that combines an improved fast correlation-based filter method with fisher score is proposed. It can perform preliminary dimensionality reduction on microarray data and provide an excellent candidate feature pool for downstream wrapped method.A hybrid wrapped method, BDBA, is proposed, which is binary differential evolution incorporating binary African vultures optimization. And a segmental adaptive fitness calculation method is designed. High classification accuracy can be obtained while retaining a small number of features.The evolution operator of binary differential evolution algorithm is improved. The African vultures optimization algorithm (AVOA) is binarily quantized, and its best vulture selection strategy is improved. so that they can deal with feature selection problems in discrete spaces.The rest of this paper is organized as follows. The “In this paper, we further improve the MMBDE algorithm and propose a new two-stage feature selection method. In the first stage, an ensemble filter method is used to perform preliminary dimensionality reduction on the microarray data to obtain a stable and excellent candidate feature pool. In the second stage, the binary differential evolution algorithm was further improved, and the African vulture optimization was added to it to improve the performance of the algorithm. Experimental results demonstrate that the propose method in this paper outperforms MMBDE on most datasets. The main contributions of our paper are the following:To demonstrate the effectiveness of the proposed ensemble filter method, we make the single fisher score method and the mRMR method used in MMBDE as comparative experiments. Specifically, three feature selection methods are used on eight datasets, then each method yields eight feature pools. To ensure fairness, we make each method obtain the same dimensionality of the feature pool on the same dataset. Since the dimensionality of the feature pool obtained by the ensemble filter method is unpredictable, while the remaining two methods can intercept a subset of features with specified dimensionality based on feature ranking. Therefore, we use the feature pool dimension obtained by the ensemble filter method as a criterion. The specific dimensional information is shown in Fig. Among the eight datasets, our ensemble filter method outperformed fisher score on five datasets. On the Lymphoma, Gastric1 and Prostate datasets, the average classification accuracy corresponding to the feature pool obtained by ensemble filter method was significantly higher than fisher score, while on the Leukemia and Gastric2 datasets, the ensemble filter method outperforms fisher score by a small margin. Only on the Colon and ALL1 datasets, the feature pool filtered by fisher score is better than the ensemble filter method, while on the ALL_AML dataset, the fisher score advantage is not obvious. In general, the ensemble filter method outperforms fisher score alone on more than half of the datasets, and achieves an overall average classification accuracy In this subsection, we analyze the adaptive crossover factor parameter In BDBA, the adaptive cross factor mentclass2pt{minimIn Table G and population size NP) of our BDBA and traditional binary differential evolution method were kept consistent. In addition, the scaling factor F and crossover factor CR of the traditional binary differential evolution method take the common value of 0.5.Since the differential evolutionary algorithm is not suitable for dealing with discrete-space optimization-seeking problems, the traditional binary differential evolution method uses a sigmoid function to discretize the solution set. To ensure the fairness of the comparison experiments, the values of the common parameters , and the difference was statistically significant  database In this section, we mainly introduce the two-stage feature selection algorithm proposed in this paper. The overall framework of the algorithm is shown in Fig. The original data usually contains noise, which will inevitably affect the performance of the algorithm and cause errors in the experimental results. Therefore, we need to clean and standardize the data. In the data cleaning stage, the repeated features in the data are averaged first, then Tukey’s test is used to detect outliers in the data, and the KNN model is used to fill in outliers and missing values. Then, z-score normalization is performed on the cleaned data to remove dimensional effects between different feature data.The classic FCBF algorithm uses symmetric uncertainty (SU) to measure the correlation between features and class labels, and the redundancy between features. First, an appropriate threshold is set to eliminate features with weak correlation to obtain a subset of candidate features. Then, in each round of iteration, the feature with the largest correlation in the candidate feature subset is taken out of the candidate set as a salient feature and added to the optimal feature subset. Next, the approximate Markov blanket principle is applied to eliminate other features in the candidate set with high redundancy with the salient features, until the candidate set is empty, then the final optimal feature subset is obtained . Comparedis represents the manhattan distance between the sample The complementarity between features is also called information collaboration or information interaction, which indicates that the classification information that two features can provide by working together may be greater than the sum of the information contained in each of the two features . It can r represents the correlation coefficient, and x and y, respectively. When calculating the correlation between features, x and y correspond to two different feature vectors, respectively. We refer to the specific operation of T-test when filtering features that are not related to class labels [x and y correspond to the vector The pearson correlation coefficient is used to quantify and estimate the correlation between features and category tags and the redundancy between features. The calculation method of the pearson correlation coefficient is shown in Eq. s labels . When caument}Si , and thex, x on the dataset, the calculation method is shown in Eq. x on the dataset, and the calculation method is as Eq. n represents the number of samples, x, and x. In Eq. y on the feature dimension x.In order to avoid the unstable results of a single correlation-based filter method, fisher score is also used to select the top 100 features in the dataset, and finally the intersection of the two feature subsets obtained by the improved FCBF and fisher score is provided to the downstream wrapped method. fisher score is an effective filter feature selection method. Its core concept is that the features with strong discriminative performance are shown as small intra-class distances as possible, and inter-class distances as large as possible . The calDifferential evolution was first proposed by Storn and Price in 1997 . It is aAVOA simulates the foraging and navigation behavior of African vultures. The vultures determine different foraging strategies based on the hunger level they feel. The algorithm can be divided into four independent stages: in the first stage, determine the best vulture; in the second stage, the hunger rate of the vultures is calculated; the third stage is the exploration stage, which includes updating the individual position in two ways: moving randomly or approaching the best vulture at a random distance; the fourth stage is the exploitation stage, including the transitional stage of updating individual positions in a siege-fight or rotating flight, and the later exploitation stage of approaching outstanding individuals in a more drastic way. Details of the above movement strategies are available in the paper .It is worth noting that the individual position update in AVOA does not completely and independently enter the third and fourth stages in sequence, but adds a certain exploitation mechanism in the early exploration process through the starvation rate, which avoids AVOA from falling into local optimality, and accelerates the convergence of the algorithm while ensuring that the AVOA does not diverge too much. In addition, the setting of the transition stage can make the population evolution proceed smoothly and improve the optimization performance of the algorithm. However, AVOA is more suitable for dealing with engineering problems of searching for optimal solutions in continuous space. Feature selection for microarray data is a solution optimization problem in discrete space, in which individuals need to be represented by binary vector codes . Therefore, we propose a binary african vultures optimization algorithm (BAOVA) to binary quantify AVOA. In addition, the optimization process of AVOA can be briefly understood as the process of increasing the degree of approaching the best vulture. However, AVOA’s selection of the best vulture is limited to the two vultures with the first and second fitness, which will have a negative impact on the algorithm’s early exploration ability. For this reason, in BAOVA, we use the opposition-based Learning (OL) method to obtain new individuals to select the best vultures for AVOA.G represents the maximum number of iterations and g represents the current number of iterations. The algorithm flow of BDBA is shown in Fig. SR designed in AVOA. The BDBA’s flowchart is shown in Fig. How to effectively combine IBDE with BAVOA and establish a stable, robust and efficient overall algorithm model is an important issue. BAVOA is used to enhance the exploration ability of the algorithm. In BDBA, if the proportion of BAVOA is too small, it will not be able to play its role effectively, and if the proportion of BAVOA is too large, it will affect the local development ability of BDBA, which will easily lead to slow algorithm convergence, and it is difficult to find excellent feature subset. We refer to the strategy of combining bat algorithm and differential evolution in the paper . And we G is too large, it will waste computing resources. We set it to 500 under the condition that the algorithm converges. The larger the value of NP, the greater the population diversity, but too large NP will cause the algorithm to converge slowly, which is not conducive to the local optimization of the algorithm. According to the size of the input feature pool, we set it to 30. The experimental parameters of BDBA are shown in Table Since improved binary AVOA uses the basic framework of AVOA, the parameters F is the inertial adaptive scaling factor, which is calculated by Eq. F, respectively. Since the value in the individual vector is binary, diffF gradually decreases as the number of iterations increases. The larger F, the better for the global search, and the smaller F is for the local search. In this way, the ability of algorithm exploration and exploitaion can be balanced to a certain extent. The calculation method of the mutation vector pr is used to ensure that the final binary vector is close to 0 or 1. The calculation method of pr is shown in Eq. In the mutation stage of IBDE, we propose a new mutation operator, which can effectively control the number of retained features and improve the convergence speed of the algorithm. The calculation method of the difference vector diff mentclasspt{minimamentclasspt{minimaCR is shown in Eq. G is the maximum number of iterations. We can obtain the trial vector CR, and the calculation method is shown in Eq. acc is the five-fold cross-classification accuracy rate obtained from the microarray data corresponding to the individual vector x, num is the number of retained features, L is the individual dimension, and In the crossover stage, we propose an adaptive crossover factor, which aims to gradually improve the convergence ability of the algorithm during the evolution. The calculation method of OL can effectively make the offspring obtain better solutions . We propThe method of AVOA algorithm to update the random position of vultures in the exploration stage is not suitable for the calculation of binary vectors, so we have improved it, as shown in Eq. As mentioned earlier, the vulture positions updated by AVOA get continuous solutions, so we need to discretize these continuous solutions. The transformation is achieved by using the sigmoid function to compress the continuous decompression in each dimension. In order to better conform to the movement mechanism of the individual during the transformation process, we perform a translation operation on the sigmoid function. The calculation method is shown in Eq.


Coevolution is an important biological process that shapes interacting proteins – may it be physically interacting proteins or consecutive enzymes in a metabolic pathway, such as the biosynthetic pathways for secondary metabolites. Previously, we developed FunOrder, a semi-automated method for the detection of co-evolved genes, and demonstrated that FunOrder can be used to identify essential genes in biosynthetic gene clusters from different ascomycetes. A major drawback of this original method was the need for a manual assessment, which may create a user bias and prevents a high-throughput application. Here we present a fully automated version of this method termed FunOrder 2.0. In the improved version, we use several mathematical indices to determine the optimal number of clusters in the FunOrder output, and a subsequent k-means clustering based on the first three principal components of a principal component analysis of the FunOrder output to automatically detect co-evolved genes. Further, we replaced the BLAST tool with the DIAMOND tool as a prerequisite for using larger proteome databases. Potentially, FunOrder 2.0 may be used for the assessment of complete genomes, which has not been attempted yet. However, the introduced changes slightly decreased the sensitivity of this method, which is outweighed by enhanced overall speed and specificity. Every form of life known to humankind is subjected to evolution. This process shapes and forms all biological systems on the macroscopic and molecular levels. Thus, understanding and detecting evolutionary processes substantially contributes to understanding life forms and life itself. An important evolutionary process is the so-called coevolution. This is defined as a “process of reciprocal evolutionary change that occurs between pairs of species or among groups of species as they interact with one another” . This deIn a previous study, we described a semi-automated method for the identification of coevolutionary linked genes, named FunOrder . ThereinIn the previous publication, we demonstrated the functionality and applicability of this method by identifying essential genes in biosynthetic gene clusters (BGCs) of ascomycetes . Fungal The obvious major shortcoming of the original FunOrder method is the final manual assessment which prevents full automation and high-throughput analyses. Further, the detection of co-evolved genes may be useful to address a broad range of biological problems related to the molecular coevolution of genes or proteins in all forms of life. Notably, this requires the compilation and integration of suitable proteome databases; for the application in plants or mammals, larger databases will be needed. In this study, we describe an improved version of the method, termed FunOrder 2.0 which overcomes the two mentioned limitations. For an automated detection of co-evolving genes, we determine the optimal number of gene groups in the FunOrder output and then use k-means clustering based on the first three principal components of a PCA. Further, we replace BLAST with the faster DIAMOND tool  to enablWithin the previously developed workflow  Figure with DIAThe first and second R-scripts aim to determine the co-evolved genes (clusters in the PCA) automatically. To this end, the first three principal components of the PCAs are considered in a k-means clustering approach. In the first R-script, the optimal number of clusters is initially determined by NbClust  using 28The third R-script is a revised version of the R-script used in the original FunOrder method . It was https://github.com/gvignolle/FunOrder (doi: 10.5281/zenodo.6914845). Details on all included scripts can be found in the ReadMe file on the GitHub repository. FunOrder 2.0 requires some dependencies, for details and links to all dependencies please refer to the ReadMe file.The software bundle is written in the BASH (Bourne Again Shell) environment and is deposited in the GitHub repository https://github.com/gvignolle/FunOrder.For the evaluation of FunOrder 2.0 and comparison to the original method, we used the same control gene clusters (GC) as in the original study . As benc“The internal coevolutionary quotient (ICQ) expresses how many genes in a GC or proteins in a protein set are co-evolved according to the previously defined threshold for strict and combined distances within the distance matrices of an analyzed GC (or protein set).”  The ICQ Equation 1. ICQ = internal coevolutionary quotient; g = number of strict distances< 0.7 and combined distances<=  in all matrices; d = number of genes in the GC    took 1 mTo test, whether the integration of DIAMOND might have altered the ability of FunOrder to detect coevolution, we analyzed the same control gene clusters (GCs) we had previously used to evaluate the original FunOrder method  and calcAs mentioned, a major limitation of the original FunOrder method was the need for a manual assessment of the output, during which the proteins are grouped into clusters based on different data visualizations . In thisThe first R-script for automated clustering initially determines the optimal number of gene clusters within the first three principal components of the PCAs using the R Package NbClust . This paTo test how this automated cluster definition compares to the previously performed manual cluster definition, we analyzed the same 30 BGCs as in our previous study. To observe only the influence of the automated cluster definition, we kept the BLAST tool for the initial database search still in place Figure 1Next, we tested the simultaneous influence of DIAMOND and the automated clustering on the overall performance of FunOrder 2.0 during the analysis of fungal BGCs. To this end, we performed the same comparative analysis of the benchmark BGCs as described above. The results were very similar to the automated analysis using the BLAST analysis Table S3Aspergillus terreus (lov)   with 17 The integration of the DIAMOND tool and the automated detection of co-evolved genes improved the run time and total analysis time, allowing high throughput analysis of protein sets and GCs without the risk of user bias. In general, the automated cluster definition appears more stringent than the manual assessment, which resulted in improved specificity and precision and a slightly reduced sensitivity during the analysis of fungal BGCs by FunOrder 2.0 compared to the original method. In summary, we consider the integration of a fully automated cluster definition a major improvement, as the advantages  outweigh the slightly reduced sensitivity.Recently, Steenwyk et al. established another method for the calculation of co-evolution. The comprehensive PhyKIT tool calculates the covarying evolutionary rates of orthologous genes using correlation of relative evolutionary rates between orthologues (CovER function) . This apAs demonstrated, FunOrder 2.0 can be used to determine the essential genes in fungal BGCs, but this is not the only potential application of FunOrder 2.0. As protein coevolution can be used to predict protein-protein interactions and biosynthetically linked enzymes , FunOrdevia threshold optimizing (best-obtained distinction of positive and negative control gene clusters). Please also refer to the technical guidelines for construction and integration of the database at the GitHub repository https://github.com/gvignolle/FunOrder.FunOrder 2.0 is provided with a database of ascomycete proteomes and can therefore be used for the detection of coevolution of proteins in this fungal division. For other divisions, classes, or even kingdoms, a suitable new proteome database must be compiled and tested. As mentioned, the integration of the DIAMOND tool enables the integration of larger databases. However, at least 25 different proteomes must be used, because the phylogenetic trees are calculated with a maximum of 20 homologous sequences. Naturally, the proteomes should be of high quality (best RNASeq derived). The proteomes shall be equally distributed among the taxonomic rank to be analyzed but also take the size of the different subordinate ranks into consideration. Put differently, if a division contains 4 small classes, and two large classes, the database should contain proteomes of all six classes, but more from the larger classes than from the smaller classes. The database shall be a representative sample of the phylogenetic group to be analyzed. This also means that highly diverse phylogenetic groups need to be over-represented in comparison to evolutionary uninventive clades. Further, evolutionary outliers and special clades shall be considered in the database design. For instance, if a phylum contains a family that is the only member of its class, the user needs to decide whether that family shall be part of the proteome database at all, depending on the size and importance of the family. If the family shall be considered, several proteomes need to be included in the database, otherwise, the evolutionary distances of the tested proteins might be too large to be successfully evaluated by FunOrder. Any new database must be tested thoroughly according to the procedure we described previously . This mehttps://github.com/gvignolle/FunOrder). We have also used Zenodo to assign a DOI to the repository: 10.5281/zenodo.6914845.The FunOrder tool, the relevant database, the sequences, and the FunOrder output of the negative control GCs and the positive control BGCs are available in the GitHub repository  [P 34036 to CZ] and TU Wien (https://www.tuwien.at/) [Ph.D. program TU Wien bioactive]. The funders had no role in the study design, data collection, and analysis, decision to publish, or preparation of the manuscript.This study was supported by the Austrian Science Fund (FWF, Author GV was employed by the company AIT Austrian Institute of Technology GmbH. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


The use of nanomaterials as a means of recovering heavy and light oil from petroleum reservoirs has increased over the preceding twenty years. Most researchers have found that injecting a nanoparticle dispersion (nanofluids) has led to good results and increased the amount of oil that can be recovered. In this research, we aim to imitate the three-dimensional hexagonal prism in the existence of SiO2 and Al2O3 nanoparticles for better oil recovery. Porosity ( As a result, oil is the dominant source of energy for the time being. As a result, it is critical to extract as much oil as possible from existing wells before moving on to more newly discovered reserves. Companies and governments desired to obtain more oil out of these reservoirs after the first and second rounds of oil recovery, so they employed enhanced oil recovery (EOR) to recover the trapped oil deposited in the reservoirs. When primary and secondary recovery procedures are not possible, EOR technologies are used to extract more crude oil from the ground's surface. Some methods involve exploiting oil field energy or injecting materials into reservoirs. Typically, primary and secondary recovery technologies can only extract 20–40% of the oil from a reservoir. Nevertheless, EOR can extract 30–60% of the oil from a reservoir . It is aThe use of nanotechnology in EOR increases oil recovery because the incorporation of nanoparticles (NPs) in the flooding process significantly improves EOR by modifying wettability, fluid behavior, trapped oil mobility, rock fusion, and decreasing interfacial tension (IFT) . MultiplIn the past few years, scientists have tried out different ways to use nanoflooding to improve oil recovery. In these tests, the amount of oil recovered from porous medium was shown to be more altered by nanofluids with varied nanoparticles and different operation settings than by water flooding. Most of the time, tests such as rheology (which examines changes in viscosity), surface tension, wettability, and core flooding are used to assess how well the EOR process works. The use of nanofluids in EOR has been studied to see how different nanoparticles and their properties affect the amount of oil that can be retrieved from porous media . These eThe majority of study on nano-flooding has been experimental, but scientists can advance the area and take a helpful step towards industrializing the procedure by using modelling. In this case, the model results can be a helpful addition to the experimental data. Although nanoflooding has been used in several experimental studies in the field of EOR, very few research projects have focused on the numerical and modelling aspects of this procedure. Nano-flooding modelling for EOR can be carried out by anticipating the flow transfer of nanoparticles in porous media. When modelling flow transfer using nanoparticles, it is common to consider both the surface forces of the nanoparticles and the surface of the rock in the porous medium that is present during flow transfer. The wettability change phenomenon of rock surfaces is connected to nanoparticle absorption in porous media. This phenomenon defines both the relative permeability and capillary pressure curves. As a result, the variation in capillary pressure and relative permeability of the phases that occurs as a direct result of the wettability of the surrounding environment is used to characterize and mimic the process .Ju et al.  did a nuBased on the previously discussed research, injecting various nanofluids improves a variety of properties such as wettability, IFT reduction, rheology, mobility control, and more. It should be noted that, although certain mechanisms influence reservoir rock features, others influence and modify trapped oil characteristics. It should be emphasized that EOR is based on several mechanisms that will function to produce EOR. Injecting nanofluids into a porous medium containing petroleum product provides the foundation for several of these mechanisms, including the previously described ones. As a result, nanofluids and nanoparticles can be regarded as potential EOR process approaches.In this study, we simulate a nanofluid-injected, increased oil recovery hexagonal prism cavity. In this research, a method known as finite volume is used to numerically solve the governing equations. Moreover, the oil recovery rate in a 3D hexagonal prism cavity hasn't been investigated in any of the earlier investigations. The cavity's shape is being researched because it closely resembles the actual characteristics of the heterogeneous porous reservoir. By examining the effects of various volume fractions and porosities, flow rates, and permeability at various times, the goal of this work is to compute the oil recovery rate using nanofluid injection. In the flooding process, silicon and aluminium nanoparticles are employed.2i.The flow considered to be as one dimensional.ii.Reservoir rock assumed to be clean sandstone.iii.Fluids are considered as incompressible.iv.The fluid flow obeys Darcy’s Lawv.Fluid is Newtonian fluid.vi.The chemical reaction between the nanoparticles is neglected.vii.Fluid flow assumed to be isothermal.viii.Initially viscosity and density of the water and oil are constant.The assumptions behind the mathematical model that simulates two-phase flow with dispersed nanoparticles in three dimesional hexagoanl prism to find oil recovery rate are as follows:To get better results from a reservoir simulation, it is very important to make the correct flow geometry and include the physical properties. In this flooding process, we investigated the silica and aluminium nanoparticles to find out the oil recovery rate, and the physical properties of these nanoparticles along with reservoir parameters are shown in 2.1The following set of nonlinear partial differential (NPDEs) equations constitutes the two-phase math model for 3D hexagonal prism geometry: It is possible to calculate the capillary pressure using a logarithmic approach. We suppose the saturation equation is 0.15 since oil reserves typically have some water in them. We will determine the velocities, pressures, and saturations of oil and water employing Eqs. The values of The values of Eqs. The values of The I. Cs and B. Cs for hexagonal prisms are given below from Eqs. 2.2Grid independence analysis is essential for checking the accuracy and reliability of simulation results and validating the numerical models that are used in simulations. Throughout the simulation analysis procedure, the most cell-dense mesh was chosen in this study. We solved our model on eight different grids to validate the oil recovery parameters over time. 2.3The veracity of the model can be assessed by contrasting its predictions with the findings of an experiment . In this3This research paper investigates the impact of a 3D porous hexagonal prism-shaped cavity to determine enhanced oil recovery by nanofluid injection. The ANSYS Fluent software simulates the partial differential equation system using the finite volume method (FVM). Porosity (In In the presence of silica and aluminium nanoparticles, it is also discovered that including the time parameter in the simulation process has a positive impact on the oil recovery rate. As time goes on, so does the rate of oil recovery, and the maximum oil recovery rate is reached after the 8-h simulations. It is also observed that when porosity decreases the oil recovery increase in both SiO2 and Al2O3 cases. The maximum oil recovery for SiO2 at final pore volume is 98% which is at 0.1 porosity. It is also important to explain that when the values of porosities decrease the oil recovery decreases due to the nature of the reservoir geometry. Moreover, it has been found that at 0.1, the greatest oil recovery rate is reached. Dinesh et al.  also fouIn This graph shows that when nanofluids (The effect of the oil recovery at different pore volumes for both nanoparticles is shown in 4•The maximum oil recovery is attained at low values of mass flow rate in the 3D hexagonal prism in the presence of silicon and aluminium nanoparticles.•The effect of porosity has a positive impact on the flooding process, and at low porosity values, the recovery rate is very high.•The VF of nanoparticles increases the oil recovery rate, and the maximum oil recovery in SiO2 nanoparticles is 99%. In our problem, the most oil can be extracted from a rock with low porosity and a high concentration of nanoparticles.•It is also observed that the use of SiO2 gives a better oil recovery rate than Al2O3.In this paper, the numerical investigation of a three-dimensional hexagonal porous cavity is pursued to predict out the oil recovery by investigating different nanoparticles. To find out the oil recovery, the parameters of volume fraction, porosity, flow rate, and relative permeability are studied. Based on the results, the following are the conclusions and remarks:Mudasar Zafar: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.Hamzah Sakidin: Conceived and designed the experiments; Performed the experiments; Contributed reagents, materials, analysis tools or data.Mikhail Sheremet: Performed the experiments; Contributed reagents, materials, analysis tools or data.Iskandar Dzulkarnain: Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.Roslinda Nazar: Performed the experiments; Analyzed and interpreted the data.Abdullah Al-Yaari: Conceived and designed the experiments; Analyzed and interpreted the data.Nur Asyatumaila Mohamad Asri: Performed the experiments; Analyzed and interpreted the data; Wrote the paper.Mohd Zuki Salleh: Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data.Shazia Bashir: Performed the experiments; Contributed reagents, materials, analysis tools or data; Wrote the paper.No data was used for the research described in the article.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


A novel wideband parametric baseband macromodeling technique for passive photonic devices and circuits is presented. It allows to efficiently estimate the baseband scattering representations of a linear, passive photonic system as a function of a set of design variables, such as geometrical layout or substrate features. The proposed technique relies on the interpolation of macromodels computed via a complex vector fitting (CVF) algorithm, by adopting a methodology based on amplitude and frequency scaling that preserves, by construction, the physical properties of the system, such as causality, stability and passivity. For a specified combination of the design parameters, a rational CVF model is derived that can be simulated by a wide range of ordinary differential equation (ODE) solvers or circuit simulators. Additionally, time-domain simulations using the computed model can be performed at arbitrary optical carrier frequencies, thus allowing for the simulation of multi-wavelength systems. Two application examples are presented to demonstrate the flexibility and advantages of the proposed method. However, today there exists a wide gap between what the technology can deliver and the functionality engineers need to design and simulate PICs2. Since traditional electromagnetic (EM) modelling techniques6 are not suitable for directly simulating larger circuits, the more common approach is to use circuit-level modelling, which needs compact and efficient behavioral models that can substitute for the expensive EM simulations while ensuring a comparable accuracy.Driven by datacom and telecom applications, and enabled by the growing number of mature manufacturing and prototyping facilities (fabs), there is a growing trend to scale the complexity of 9, modulators12, and photodetectors15. However, the vast majority of photonic components are linear and passive devices whose behaviour is best defined in the frequency-domain in terms of a scattering matrix. However, since simulation of active and passive devices is always performed in the time-domain17, there is also a need for accurate and efficient time-domain models of passive devices. As many passive devices in photonics circuits are constructed using parametric layout designs (i.e. the user can adjust dimensions using parameters), there is also a need to construct the corresponding parametric circuit models, whose behaviour is characterized by the design and control parameters that describe the physical properties of the structure. The quality of these models, in terms of computation speed, accuracy and coverage of the design space, is key for the design, analysis and optimization of large-scale photonic circuits.In general, photonic components for PICs can be divided in two broad classes: active and passive devices. A great number of models for active components, which are usually formulated in the time-domain, has been presented in the literature: examples include lasers19 demonstrate how to derive time-domain models for passive devices like waveguides and directional couplers; however, these models rely on simple analytic expressions that make it very difficult to capture complex photonic phenomena such as higher-order dispersion and wavelength-dependent effects. To address this issue, the techniques22 perform the time-domain modeling starting from the frequency-domain scattering parameters, therefore being capable of accurately modeling the aforementioned nonidealities. The convolution-based method17 directly applies inverse Fourier transform to the scattering parameters to obtain a non-parametric impulse response, which can be used for time-domain simulation. In practice though, the scattering parameters are band-limited or truncated, and this method often leads to violations of physical properties, such as causality and passivity23. The recently proposed work by Ye et al.22 on the other hand, performs the modeling by computing a stable and passive baseband state-space model via the robust complex vector fitting (CVF) algorithm. Such a model, which consists of a set of coupled ordinary differential equations (ODE) is supported by many commercial and open-source time-domain solvers. However, despite the attractive features of the latter technique, the models are non-parametric and their use is hence limited to performing circuit level design and optimization. For every design variation of the component, and even for each simulation at a different carrier wavelength, a new CVF model must be constructed, which often triggers one or more expensive EM simulation.There are only a few publications in the literature that describe how to build accurate and efficient circuit models for passive components. The contributions22 and Ferranti et al.24, can be summarized as follows: (1) We derive a closed-form mathematical expression for the parameter dependency on the optical carrier frequency of the baseband macromodels22. This leads to the development of a wideband macromodel that can be simulated at any optical carrier frequency, making it suitable for the representation of multi-wavelength systems, (2) by leveraging the parameterization in terms of optical carrier frequency, the local interpolation scheme25, previously applied in microwave engineering, is extended with an additional frequency shifting coefficient for the computation of parametric baseband macromodels, capable of accurately predicting the complex behaviour of parametric passive photonic devices over the entire design space both in the frequency- and time-domain, (3) a wideband parametric baseband macromodel is proposed by combining the parameterization in terms of optical carrier frequency with design parameters. It is demonstrated that physical properties such as causality, stability, and passivity are preserved throughout the entire design space. Unlike traditional approaches that require numerous electromagnetic simulations with high computational costs for varying design parameters, our novel wideband parametric baseband model can be used to simulate device behavior as part of a circuit within a large continuous design space, eliminating the need for additional expensive EM simulations and significantly accelerating the design process. Notably, the presented parametric macromodel in this study can be seamlessly integrated into surrogate-based optimization frameworks26. To the author’s best knowledge, this is the first and only parametric macromodeling algorithm for photonic components reported in the literature to date.Thus, the literature exhibits a striking and practically relevant gap that this work seeks to fill. The novelty and the technical contribution of this work, which builds upon our previous research reported in Ye et al.22, which is one of the two major ingredients of the parametric macromodeling framework proposed in the paper. Although the concepts introduced here are not new, they are essential for understanding our work.This section briefly summarizes the CVF algorithm22 allows one to adopt relatively large time steps when carrying out time-domain simulations, thereby significantly relaxing memory requirements and speeding up the computation time. In this section, the reader is introduced to the concept of baseband equivalent signals and systems since the theory is key for the derivation of the parametric model.Given the high frequencies of optical electromagnetic waves (200–300 THz), direct modelling of the EM waveform in the time domain is not a very efficient approach for circuit simulation, as it would require fs-scale time steps. Therefore, the common approach is to model the modulated envelope (in amplitude and phase) around a carrier frequency, which is sometimes referred to as a ‘baseband model’. The baseband modeling approach followed by the CVF algorithmA(t) and a(t) is centered around 27. The baseband equivalent signal representation of (a(t) and it is widely used for the analysis of photonic systems. The signals a(t) and a(t) and The excitation signals of optical communication systems are usually defined as amplitude and/or phase modulated optical carriers in the formS(f) and Now, the baseband equivalent of a bandpass system can be defined by applying the same concepts, as is illustrated in Fig. 22, which starts from the scattering parameters of the photonic device under study in order to accurately capture non-ideal behaviours, such as higher-order dispersion, wavelength-dependent losses and backscattering. The scattering parameters are either acquired through measurements or can be simulated using electromagnetic modeling techniques such as finite difference time domain (FDTD)3, eigenmode expansion (EME)4, finite element (FE)5 or beam-propagation method (BPM)6. Once the scattering parameters have been obtained, their corresponding baseband representation is derived, and the CVF algorithm can be used to compute a model suitable for time-domain simulations, as described in the following.The novel parametric modeling technique presented in this work relies on the CVF algorithm22n is the number of ports of the system under study. Starting from the rational model  in state-space form as22n-port baseband system, corresponding to the RF modulated envelope of the photonic signal, 22. For future reference, it is worth noting that it is possible to express Eq.  the conditions for stability and passivity of baseband rational models is given in Ye et al.21. In this section, we give an overview of the essential notions that will be used in the rest of the manuscript to evaluate stability and passivity of the proposed parametric modeling approach.When considering physical passive devices, like wavelength filters or other interferometric structures, it is essential for reliable time-domain simulation that the equivalent models are both stable and passive. If this is not the case, the mathematical representation can be the root cause of non-physical numerical instabilities during circuit simulations, especially when these circuits would contain feedback loops22.A state-space model is stable if the real part of all the eigenvalues of the 20, the passivity definition and conditions for complex-valued linear baseband systems are presented. In particular, there are two passivity constraints that the baseband scattering parameters s such that An efficient and accurate method to assess the passivity of state-space models in the form  at the optical carrier frequency A - B, C and D. Note that the macromodel ..\documenhe model  as13\doccromodel  is passi22: since a new rational model must be computed for every value of interest of the carrier frequency, it is beneficial to consider a more limited frequency range, corresponding only to the spectrum of the modulated optical input signals around the carrier frequency . Indeed, considering a smaller frequency range may reduce the number of poles (and thus the size of the the corresponding system of ODEs) needed by the model to reach the desired accuracy in the entire bandwidth. Hence, for a similar accuracy, a wideband baseband macromodel can offer higher flexibility compared to the reference CVF approach, but it can have a larger computational complexity. Both modeling methodologies are illustrated in Fig. In order to take advantage of the modeling flexibility offered by the novel wideband approach, it may be useful to consider a large range of frequencies when computing the model, for example the entire operating range of the PIC under study, typically defined between 187.5 and 200 THz. From a mathematical standpoint, there are no restrictions on the values of ce model . In this33. Unfortunately, the calculation of such models is not a trivial task. In particular, guaranteeing model passivity uniformly over the entire design space introduces substantial technical challenges and makes it difficult to build parametric macromodels that are concurrently accurate, compact and passive.Parametric macromodels accurately predict the complex behaviour of high-speed multiport systems that are characterized by frequency and other design variablesroot macromodels interpolation34 and multivariate rational fitting37. The first strategy constructs a guaranteed passive parametric macromodel by interpolating a set of passive frequency-dependent macromodels , computed for different parameter configurations in the design space. Despite this approach being robust and straightforward, it is not very compact and the number of poles of the resulting model is generally higher than the number of poles of each of the macromodels. The second approach aims to compute an implicit and global parameterization of the complex dynamic behaviour by means of multivariate rational fitting. Main advantages of this technique are the compact formulation of the parametric numerator and denominator in a closed form analytic expression and the model order that does not scale with the dimension of the design space. The main drawback with many of the proposed multivariate fitting schemes is the passivity enforcement, which either may miss small passivity violations or is known to be over-conservative, leading to a model with reduced accuracy37.The literature describes two principal strategies: vector fitting (VF)38, a technique extensively used for the modeling of distributed microwave devices. Since the VF technique operates at bandpass, it is not applicable for the modeling and simulations of PICs. To overcome this limitation, we propose to build parametric baseband macromodels via the CVF modeling procedure22, based on root macromodels interpolation.In the literature, the aforementioned parametric macromodeling techniques have all been presented in the context of 24 and relies on the computation of several frequency-dependent rational pole residue models for different parameter sets in the design space. Whereas in Ferranti et al.24 the rational models are computed by means of VF, given that we are targeting circuits operating at optical frequencies, the models here are built following the CVF algorithm22. The result of this initial step is a set of univariate macromodels, stable and passive, which we call root macromodels, and which serve as starting point to build the desired parametric macromodel.The proposed modeling technique is a baseband adaptation of Ferranti et al.sequential sampling approach40. The main idea is to partition the design space in suitable sub-regions, for example hyperrectangles. Only the vertexes of the hyperrectangles are chosen to compute root macromodels in pole/residue form. Then, in each point within the chosen hyperrectangle a model in pole/residue form can be calculated by interpolating the root macromodels that define its vertexes. These macromodels can then be used for frequency- or time-domain simulations. This choice makes the technique in Ferranti et al.24 a local interpolation scheme: only few macromodels determine the model’s predictions in a small portion of the overall design space. Note that, in contrast, in global interpolation approaches all the macromodels computed in the entire design space contribute to the model’s predictions. If the accuracy of the macromodel, defined in this work as the maximum absolute error (MAE) between the original frequency response g) and the estimated response by the parametric baseband macromodel g), is not sufficient in a specific sub-region, that portion of the design space is divided in smaller hyperrectangles, and the modeling procedure is iterated again until the desired accuracy is reached in the entire design space. The main advantage of this modeling strategy is that a designer has only to choose the desired accuracy and the parametric macromodel is built in an automated way. The sequential sampling scheme used in this work is described in details in Chemmangat et al.39. An application example of this modeling strategy in a design space of two variables is given in Fig. Note that the choice of the points in the design space where to compute the root macromodels can be automated by following a M-dimensional cell-region of the design space as 24 at a point g is then obtained as a combination of root macromodels and corresponding amplitude and frequency scaling coefficients by adopting the same multilinear interpolation scheme used to parameterize the scaling coefficients24 perform well at bandpass for the modeling of microwave devices, but as we will explain, their modeling capabilities are significantly reduced when applied at the baseband for the representation of PICs. Photonic scattering parameters s with the frequency scaling coefficient M. This means that, for devices with a dynamic and wideband frequency response that require root macromodels with a high number of poles, the state-space model . Following the sequential sampling strategycromodel .22 demonstrated that the complex-valued model  and electromagnetic simulations in Lumerical FDTD Solutions (Ansys).In this numerical example we discuss the time-domain simulation of a 4-channel arrayed waveguide grating (AWG), used to separate four RF signals modulated on different optical carriers. The Layout of the AWG, comprising the input star coupler, the output star coupler and a bundle of waveguides, is designed and simulated using the AWG Designer module from Luceda IPKISS. The star couplers of the AWG are simulated by computing the field output of the input apertures with CAMFR, Luceda’s eigenmode expansion tool, propagating it in the free propagation region, and performing mode overlaps to collect the fields at the output apertures. The delay lines are modeled as linear dispersive waveguides whereas dispersion in the star couplers is ignored and they are only simulated for a single wavelength. The final layout and transmission spectrum of the AWG is illustrated in Figs. The in-phase component of the input port (P5) is excited with four on-off keying (OOK) signals The scattering parameters of the device are evaluated in Luceda IPKISS over the frequency range  THz. In this example, 1001 frequency samples are used, and they are uniformly distributed over the frequency range of interest. Next, the scattering parameters are shifted to baseband using cromodel , which cNext to the wideband baseband macromodel, which is valid over a broad frequency range, four reference CVF models with 14 poles and a BW of lsim routine. To demonstrate the compatibility of the proposed technique with commercial photonic circuit simulators, the wideband baseband model  and developing a parametric macromodel for each of these individual components. This would enable users to construct more extensive and intricate circuits using these pre-evaluated primitives, potentially offering a more scalable solution, especially within the context of the foundry model. However, this strategy demands further investigation and will be explored as a topic for future research.Supplementary Information.