Current wireless-inertial fusion positioning systems widely adopt empirical propagation models of wireless signals and filtering algorithms such as the Kalman filter or the particle filter. However, empirical models of system and noise usually have lower accuracy in a practical positioning scenario. The biases of predetermined parameters would enlarge the positioning error through layers of systems. Instead of dealing with empirical models, this paper proposes a fusion positioning system based on an end-to-end neural network, along with a transfer learning strategy for improving the performance of neural network models for samples with different distributions. Verified by Bluetooth-inertial positioning in a whole floor scenario, the mean positioning error of the fusion network was 0.506 m. The proposed transfer learning method improved the accuracy of the step length and rotation angle of different pedestrians by 53.3%, the Bluetooth positioning accuracy of various devices by 33.4%, and the average positioning error of the fusion system by 31.6%. The results showed that our proposed methods outperformed filter-based methods in challenging indoor environments. Location navigation service is one of the indispensable technologies for the modern society and scientific development. However, the current Global Navigation Satellite System (GNSS) is usually unable to locate effectively indoors due to irregular attenuation of GNSS signals caused by the occlusion of clouds, building walls, and ceilings. During the last decades, many efforts have been made to study how to leverage any indoor wireless signals to provide indoor navigation services, and indoor positioning technology was born. At present, mainstream indoor positioning technologies include Wi-Fi  or the particle filter (PF). However, in many practical positioning scenarios, the complexity of the fusion system or a single system is usually very high. For example, for pedestrian navigation, it is quite challenging to model a step-heading estimation system (SHS) or the distribution characteristics of wireless signals in the environment. Besides, the increase in the system complexity will enlarge the influence on the parameter error to the final state estimation. Although many studies apply machine learning techniques to deal with the complexity of a single positioning system, fusion is still based on filtering algorithms. However, it is rather challenging to determine the noise parameters in the filtering methods, especially the noise of the wireless positioning, which is irregularly distributed in the whole area. If wireless positioning adopts the fingerprinting method, the noise should be analyzed area by area. Furthermore, by assigning specific values to the covariance matrixes of process and observation, the accuracy of the noise parameter is compromised. Considering those factors, deep learning is a more straightforward way to accurately model the noise and build the whole model at the same time. In this study, we propose a fusion localization system based on an end-to-end neural network and a transfer learning strategy for improving the performance of the neural network model for samples with different distributions. Furthermore, we verified our methods in a Bluetooth-inertial fusion positioning scenario considering the low cost, quick deployment of the commercial Bluetooth beacons, and the convenience of leveraging built-in smartphone sensors. Our contributions are summarized as follows:1) An end-to-end trainable neural network-based inertial-wireless fusion positioning system, namely SmartFPS, is first proposed. Besides, a training procedure based on multi-task learning is also proposed. Large field experiments were performed, and results showed that our method could outperform filter-based fusion systems by 36.5% when optimal parameters were set for the particle filter.2) A transfer learning strategy for SmartFPS is proposed based on the generative adversarial network (GAN) to deal with device heterogeneity and other factors in practical positioning scenarios. Simultaneously training the GAN-based network with labeled data in the source domain and the unlabeled data in the target domain improved the positioning accuracy by over 50%, compared with training SmartFPS with the source domain dataset.In wireless-inertial fusion localization systems, the processing and modeling of inertial sensors, wireless signals, and their fusion method must be carefully considered. In recent decades, inertial navigation and indoor wireless positioning have been studied individually, from empirical modeling to machine learning. Fusion methods, especially filtering methods, have also improved to cope with complex processes and non-Gaussian noise. This section will discuss the development of these three components in fusion positioning separately to show the advantages of replacing all empirical models with deep learning.Pedestrian inertial navigation mainly includes the strap-down inertial navigation system (SINS) Bortz,  and the As for SINS, even if there is only a small error in the angle estimation, the final position result will be affected exponentially through multi-layer transfer. The effect of this error is especially severe for low-cost MEMS sensors in smartphones. Usually, the extended Kalman filter (EKF) can be used to lower this error.One measure to deal with the drift problem is to close the integrating loop periodically by imposing external constraints on the system. The most widely used constraint method is the zero velocity update (ZUPT) Foxlin, . ZUPT isTo simplify the modeling of inertial navigation, a deep learning-based method, IONet , angle of arrival (AOA), and time of flight (TOF). However, due to the advantage of simple implementation, most wireless-based positioning solutions adopt the RSS feature. RSS-based wireless positioning algorithms generally have three types: proximity  wireless signals. In practical positioning scenarios, due to the consideration of deployment costs, the distance between wireless beacons is large, and inevitably, there will be environmental interference or occlusion. Therefore, it is challenging to collect three LOS signals continuously. Even though three LOS signals exist, the signal-to-noise ratio (SNR) is low in specific locations due to high noise and weak signal. As a result, trilateration positioning often has low robustness.Fingerprint positioning technology is widely used to solve the problem of wireless positioning under a low SNR. Fingerprint positioning technology mainly collects RSS values from different wireless beacons at various locations in the scene in the offline stage, and the combination of these measurement values becomes the fingerprint information of the location. After deploying the system, the RSS combination of online measurements  is compared with offline measurements to estimate user location. Many machine learning methods, such as K-nearest neighbors (KNN) and support vector machine (SVM), and deep learning methods, such as multi-layer perceptron (MLP), can be used to solve fingerprint matching problems. Fingerprint localization algorithms usually need to survey the environment to obtain fingerprints or characteristics of the environment, so it is also called scene analysis localization technology.The filtering algorithm is one of the most widely used fusion algorithms in mainstream indoor fusion positioning systems. At present, the filtering algorithms applied in the positioning fusion algorithm mainly include (1) the discrete Bayesian filter   The fusion positioning system with a complete network structure can realize end-to-end computing output, which is easier to train and deploy than the positioning system with networks fused by filtering algorithms. Each positioning network of the network and filtering algorithm need to output noise matrixes during training, and the noise matrix is difficult to represent by individual parameters for complex systems. Therefore, such training and fusion methods are complicated, and the implementation is cumbersome.2) Compared with the Kalman filter, SmartFPS does not require all noises to be white noise, and there is no need to pre-determine the noise coefficient. It can approximate any white noise or colored noise through data training.3) The fusion positioning system with a complete network structure is faster than the particle filter, and the time cost of SmartFPS estimation is generally in milliseconds. In contrast, the time cost of the particle filter will be much higher if the number of particles is large. The particle filter will also cause problems such as loss of diversity over time, so parameters such as particle resampling need to be adjusted.x, accy, accz, gyrox, gyroy, gyroz). The LSTM network generally processes a time series of data, which in this research scenario are the accelerometer and gyroscope data in a time window. The length of the window can be selected according to different application scenarios. For example, in this study, a time window of 1 s is used by considering the frequency of pedestrian steps.The inertial encoder network in the fusion positioning network is an inertial navigation feature extraction network based on the Bi-LSTM network. Its input is the 6-axis accelerometer and gyroscope data in the inertial unit of the smart device, and the signal data set at 1 step can be expressed as  as the output and achieved excellent performance in accuracy. However, this may cause a problem when the pedestrian keeps walking straightly at a constant speed. In this case, the velocity vector should be possible in all directions so that the trained network is not decoupled from the map. We also found that the trained inertial network with this objective is difficult to fuse with the wireless encoder. The author of RoNIN, although not discussing this point in their work, may have tried to fix this issue by randomly rotating the inertial data for data augmentation before training. However, this method could significantly increase the amount of training data and lower the training speed, which is cumbersome for model transfer learning in a new scenario. Unlike RoNIN, we adopt the step length and the rotation angle, which are completely decoupled from the map.One primary concern for the inertial encoder is its objective, which represents its physical meaning and may influence the fusion performance. In fact, the inertial encoder derives from former studies of deep learning-based inertial navigation. We carefully select the objective of the inertial encoder among all the related works, such as IONet  of the pedestrian. The target is set as the root mean square error of the two-dimensional coordinate vector and the direction vector, with a scale factor of κ.The fusion decoder network is a two-layer LSTM network structure. The hidden state and the unit state of the network are initialized by the state of the previous moment. The input includes the inertial navigation features and the attention-selected wireless positioning signal features, which can be regarded as observations at the current moment. The role of the recurrent neural network here is similar to a filtering process. Unlike filtering algorithms, the noise and the observation are not separated, and the state and the noise feature of the last moment are also used as the hidden state to initialize the network unit. State quantities, observations, and system processes and noise are coupled through the network, thereby eliminating the tedious process of determining system noise values. Especially for the wireless location system based on fingerprint location, the noise at different locations is more difficult to quantify. The hidden state quantity output by the fusion decoder network will be further connected to two fully connected layers. The output of the last fully connected layer is the two-dimensional position coordinate vector  and direction vector , r represents the direction vector .where θ is the network parameter, Since SmartFPS is a large network consisting of several modules, the training procedure should be carefully treated. Since the encoders have different objectives, training them together may corrupt their physical meanings, causing the whole network to collapse. Training them individually and freezing their weights when training the fusion decoder is a good option but cumbersome. Therefore, we proposed a multi-task learning strategy to solve this problem. Multi-task learning Caruana,  is a braAlthough multi-task learning is generally used to improve learning efficiency, it can protect the integrity of the output features of the intermediate layer, and the fixed output positions can retain the physical meaning of the output of each sub-network.Since the environmental factors and device parameters are often different from the training data in practical scenarios, trained models often perform poorly. In this section, a transfer learning method is proposed to solve this problem based on the generative adversarial network mechanism. In this section, the attack factors that may cause the trained models to fail are discussed. Next, the proposed transfer learning method is explained in detail.To analyze the influence of different pedestrians on the characteristics of the inertial data, two testers collected inertial data by carrying the same device and walking back and forth along the same straight-line path. The pose of the smartphone in hand was similar to that of the training set. In addition to different pedestrian motions, different devices also cause the difference in data characteristics. Since the calibration methods can solve the problems such as bias and drift, we only consider the noise characteristics of the inertial device itself of different devices. To verify the difference in noise characteristics of inertial systems of different devices, two devices (Xiaomi Mi6 and ZTE A2017) are used to collect inertial data in a horizontal stationary state. Allan variance was used to analyze the noise components in the inertial data. The Allan variance curves of the accelerometer and gyroscope sequences of the two devices in the static state are shown in There are also differences in the wireless signal receivers of different mobile phone devices. To verify this problem, two mobile phones were placed horizontally on the table and kept the same distance from the Bluetooth beacon to collect RSS data. In general, there are irregular differences in the amplitude and noise characteristics of inertial and wireless signal data. Therefore, it is necessary to consider how to enhance the generalization performance of SmartFPS under those differences.The transfer learning algorithm of SmartFPS aims at training the first 3-layer CNN network layer in the wireless positioning network and the first 2-layer LSTM network in the inertial positioning network. Since the transfer learning methods of the two networks are similar, only the transfer learning method of the wireless positioning network is explained here.The wireless encoder aims to map the features of the wireless signal data sequence, so the transfer learning algorithm aims to train those layers and substitute the trained weights into the fusion positioning network. The transfer learning structure of the wireless positioning network is mainly based on the GAN network, a transfer learning strategy known for its success in image processing. GAN is composed of a generator and a discriminator. The generator's role is to produce a fake wireless sequence similar to the target domain according to the wireless positioning features of the source domain. The discriminator will judge whether the generator produces sequences similar to the target domain. Therefore, the generator will improve its performance with each training epoch, and eventually, the discriminator will not be able to make the right judgment.We also add a cycle-consistent loss to the network so that the generator network will include a source and a target domain generator. These two parts share one unique encoder. According to cycleGAN, the source domain generator network needs to restore the sequence of fake target domain signals generated by the target domain generator  to the source domain data. Similarly, the target domain generator network needs to restore the sequence of fake target domain signals generated by the source domain generator  to target domain data. Such a mechanism makes GAN less influenced by the generator network when the source and target data labels are poorly matched. In addition, a new loss function, identity loss, is often introduced when applying cycle-consistent loss. This mechanism means that data in the same domain should maintain the same data through the same domain generator network.We also introduce the reconstruction network in the network. The reconstruction network is a CNN structure, and its role is to restore the original signal using the encoder output features. Unlike the cycle-consistency loss mechanism, the reconstruction network is unique. Although the recovered signal will not be the same as the original signal, it can preserve the signal integrity as much as possible from the common characteristics of the source and target domains. This part is also to protect the encoder from being unduly influenced by the generative network. Since the GAN network needs to train the generator and the discriminator separately, we also divide the training of the inertial positioning network transfer learning network into two steps: (1) training the generator targets and (2) training the discriminator targets.The network forward propagation routes of the two targets are illustrated in The training procedure of wireless positioning encoder transfer learning is similar to training GAN. It is important to train only the generator or the discriminator alone while freezing the weights of the other network. However, the other goals can be trained together. The training procedure is listed in The experiments were conducted in the corridor area plus a whole laboratory area on one floor of the Chuangzhi Building, Nanjing, China, as shown in The training and test data were collected with the android phone facing the user by assuming that the user should keep an eye on the screen of the smartphone during positioning. The smartphone was swinging along with the user's arm. To collect training data of accelerometer, gyroscope and Bluetooth received signal strength data, Android phones, including Xiaomi Mi6 and Vivo x70 pro, were selected in this study. The sampling frequency of the inertial sensor is 200 Hz, and the sampling frequency of the Bluetooth signal is set to the highest in the system.In IONet, the Vicon system was used to track the position of the mobile phone. However, considering the difficulty of deploying the system in a large scene, we implemented a slam system to acquire positions. Different from RoNIN, where the Zenfone AR mobile phone used in it completely relies on the rear camera to calculate the slam, our research firstly uses the Lidar visual slam system of the iPhone, and the positioning accuracy is much higher than that of the Android tango system. Based on the ARkit library of iOS 15, this research implements an application that reads and saves the pose of the mobile phone in real time. At the same time, the application will also read the real-time inertial navigation data of the iPhone to facilitate time calibration with the Android data. The preprocessing procedure was similar to the work  in this area, the wireless encoder will fail or perform poorly. However, its influence on the whole fusion system is uncertain because of the assistance from the inertial sensor. To investigate how the number of beacons affects the performance of SmartFPS, we have considered two circumstances: (1) sparse deployment of beacons; (2) fewer or no beacons in one area.For the first circumstance, since 20 beacons are deployed in our test field, we increase the interval between beacons by turning off several beacons evenly, as shown in For the second circumstance, we turned off six beacons deployed at one corner, as shown in In general, decreasing the number of beacons has a much smaller influence on SmartFPS than the wireless encoder, indicating that the inertial encoder properly functioned in our fusion system.In this paper, an end-to-end deep learning-based wireless-inertial fusion positioning system, SmartFPS, and its transfer learning method are proposed. The features from sub-positioning networks are fused by a stateful LSTM network instead of filter-based methods. The multi-task learning method is adopted to simplify the training of SmarFPS and preserve the physical meaning of each sub-network. Furthermore, a GAN-based unsupervised transfer learning method is proposed to improve the performance of SmartFPS no matter the difference between pedestrians and devices. Field experiments are conducted, and the results show that our method significantly outperforms filter-based methods. SmartFPS showed high tolerance to larger noise factors compared with filter-based methods. Overall, our system can achieve an average positioning accuracy of 0.575 meters for different pedestrians and mobile phones.For future work, specific techniques such as ZUPT and map fusion could be adapted to SmartFPS's architecture. Another interesting idea is replacing the inertial encoder with a variant-step inertial encoder, which can be derived from footstep detection techniques. When the foot lands on the ground, the inertial data sequence will generally show a large jitter. At present, machine learning algorithms have been studied in pedestrian footstep detection research, and the method based on the neural network has high estimation accuracy. Therefore, based on SmartFPS, the time series data can be segmented by footstep detection technology, and the inertial encoder can be replaced by a network structure without a fixed step length. Since the motion attitude of the pedestrian is relatively stable during each step, it can be estimated that this technique can further improve the positioning accuracy of SmartFPS.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.LH were responsible for providing the study idea, experiment design, experiment execution, result analyses, and manuscript draft. YZ and JY were responsible for supervision, review, and funding acquisition. All authors contributed to the article and approved the submitted version.


Medium access control (MAC) protocols in ad hoc networks have evolved from single-channel independent transmission mechanisms to multi-channel concurrent mechanisms to efficiently manage the demands placed on modern networks. The primary aim of this study is to compare the performance of popular multi-channel MAC (MMAC) protocols under saturated network traffic conditions and propose improvements to the protocols under these conditions. A novel, dynamically adaptive MMAC protocol was devised to take advantage of the performance capabilities of the evaluated protocols in changing wireless ad hoc network conditions. A simulation of the familiar MAC protocols was developed based on a validated simulation of the IEEE 802.11 standard. Further, the behaviors and performances of these protocols are compared against the proposed MMAC protocols with a varying number of ad hoc stations and concurrent wireless channels in terms of throughput, Jain’s fairness index, and channel access delay. The results show that the proposed MMAC protocol, labeled E-SA-MMAC, outperforms the existing protocols in throughput by up to 11.9% under a constrained number of channels and in channel access delays by up to 18.3%. It can be asserted from these observations that the proposed approach provides performance benefits against its peers under saturated traffic conditions and other factors, such as the number of available wireless channels, and is suitable for dynamic ad hoc network deployments. In recent times, there has been an exponential growth of network-capable devices wirelessly connecting to the grid. Devices communicate over the internet through various means, such as 5G cellular ,2, Wi-FiWireless local area networks (WLANs) enable devices to communicate without requiring physical cable links connecting the network. The building blocks of WLANs involve the basic service set (BSS). The BSS can have two different architectures based on the presence or absence of the access point (AP) ,7.Ad hoc network: Does not contain any APs and devices communicate without it.Infrastructure network: The AP is the centralized node and all traffic flow through it.Dedicated control channel;Split phase;Common hopping;Parallel rendezvous.The focus of this study is on ad hoc network characteristic-decentralized topologies with nodes communicating as peers between themselves. In an ad hoc network, a single channel needs to be shared by several nodes, and the medium access control (MAC) protocol ,9,10 is The dedicated control channel approach splits the spectrum into one control channel and N-1 data channels where each node has two radio interfaces to operate in the control and data channel. Nodes are aware of the neighbor transmissions and no synchronization is needed. Due to the common control channel, no multi-channel hidden problem exists.The split phase, as the name suggests, divides the time into two phases—the contention and the data transfer phase. These two phases are fixed and always take place periodically. During the contention phase, all nodes listen to the common control channel, and those that succeed exchange data frames in the data exchange phase. Although the multi-channel hidden terminal is solved and tight global synchronization is needed.In common hopping, nodes follow a hopping sequence. The nodes that want to communicate stop at a frequency and communicate and then rendezvous with the hopping sequence. Hopping spreads the control signal and congestion is reduced on a particular channel, but tight global synchronization is also needed in this approach.A parallel rendezvous is similar to the common hopping approach but multiple handshakes occur simultaneously on all free channels.The multi-channel hidden terminal occurs when two nodes are busy in the data transmission in one channel and are unaware of control packets sent by other nodes that want to communicate on a particular channel. When these nodes return to the control channel, they might want to communicate on that busy channel, causing a collision [ollision ,19.The missing receiver occurs when the control packets sent to a receiver are not acknowledged due to it being busy in the data transmission with another node [her node .Deafness occurs when the intended receiver is busy in the data transmission and ignores the control packets sent to it [nt to it .Although the parallelism of MMAC protocols significantly improves throughput and reduce channel access delay compared to a single-channel approach , there aGenerally, the radio antennas of the wireless nodes can operate in one of two modes, omnidirectional or directional. Nodes using omnidirectional antennas can listen to communications and transmit data in all directions. Using omnidirectional antennas is beneficial since the nodes do not need to direct their antennas in a specific direction for communication. This makes omnidirectional antennas easy to install and less expensive. However, the disadvantage of these antennas is that there is less signal strength, which reduces their range. The chances of collision are also higher in this case because the nodes listen to communications from all directions. On the other hand, nodes using directional antennas can only communicate in a specific direction. Using this antenna provides higher connectivity and a longer range. Moreover, it reduces interference and allows multiple communications in close vicinity without interference. Nevertheless, with directional antennas, nodes have a deafness problem. The overall cost and complexities of these antennas are higher than omnidirectional antennas ,23,24.We propose an enhanced spectrally efficient asynchronous multi-channel MAC (E-SA-MMAC) protocol that utilizes the spectrum efficiently and increases the overall throughput in constrained environments.The proposed protocol solves the issues of the multi-channel hidden terminal and deafness by using omnidirectionally broadcast control packets.Further, a second protocol is proposed called Max-E-SA-MMAC, by modifying the backoff algorithm of the E-SA-MMAC, to improve fairness between the nodes.An adaptive MMAC protocol is proposed; we took advantage of the performance characteristics of the evaluated protocols by opting for the more ideal transmission mechanism in the changing network environments.An extensive performance evaluation of the proposed algorithms was carried out under three performance metrics—normalized throughput, Jain’s fairness index (JFI), and channel access delay.A full factorial design with analysis of variation (ANOVA) was also performed to analyze the impacts of the factors on the results.The objective of this research is to improve the performance and efficiency of the MMAC protocol and compare it with other protocols with varying factors, namely, the number of stations and channels. The primary contributions of this work are as follows:The rest of the paper is organized as follows. Numerous research was conducted on multi-channel MAC protocols that focus on the use of multiple channels to enhance network performance ,26,27. Fe space)  time to e space) ,40.MMAC improves the throughput significantly by having nodes transmitting on multiple channels . All chaThe first MMAC protocol considered in this work is a bidirectional multi-channel MAC (BiMMAC) ,43, whicThe authors of  proposedThe authors of  propose The spectrally efficient asynchronous multi-channel MAC (SA-MMAC)  enhancesThe proposed solution is divided into two sections: the first section describes the proposed protocol for high network load situations and the second presents a novel dynamic approach to utilize the strengths of the MMAC protocols simulated in this research for various wireless ad hoc network situations.The proposed solution, an enhanced SA-MMAC (E-SA-MMAC), extends the SA-MMAC protocol. E-SA-MMAC uses one common control channel and the rest as data channels out of all the orthogonal channels. The contention takes place in the control channel and successful nodes switch to negotiated data channels for data transmission.RTS: This frame is sent when a node has data to send and it also has additional information about the free channels.CTS: This frame is sent by the receiver to inform the sender of its reception of the RTS frame and it includes the channel that has been selected for data transmission.ATS: This frame is used to announce to the neighbors of both the sender and receiver nodes about the data transmission and the negotiated data channel that will be used by these nodes.The control frames exchanged in the control channel are as follows:Nodes contend in the control channel and successful nodes send RTS.Upon reception of RTS, the receiver replies with a CTS specifying the selected channel to use for data transmission. Moreover, it starts a timer, and upon expiration of this timer, it sends ATS.Upon reception of CTS, the sender checks the selected channel and sends ATS.Both nodes switch to the negotiated data channel after sending ATS and they commence data transmission. Two frames can be exchanged bi-directionally if the receiver also has data to send.If there are no available data channels, the nodes transmit in the control channel. In this protocol, we allow the transmission of two frames in the control channel.After data transmission, nodes return to the control channel and wait for two mandatory frame times to avoid collision with any ongoing transmission in the control channel.The proposed protocol adopts the idea of bidirectional data exchange between nodes in the data channel as well as the control channel to maximize the throughput of the network during peak traffic conditions. The above protocol operation is described in detail in This protocol utilizes spectrum more efficiently and throughput increases for high contention cases. The deafness and multi-channel hidden terminal problems are solved using the RTS-CTS-ATS exchange and mandatory waiting time. However, the delay incurred for nodes would be higher as more waiting time is needed for nodes to access channels. Additionally, compared to SA-MMAC the fairness would be lower due to two frames being sent in the control channel, increasing the waiting time for queued nodes. In addition to E-SA-MMAC, we propose Max-E-SA-MMAC, which has the same features as the originally proposed protocol but the backoff algorithm has been modified. Initially, the nodes start with [0, In this section, the authors present a novel approach to utilize the performance capabilities of the simulated MMAC protocols in different situations. In The simulation was developed following the conceptual model described by the flow diagrams in Each protocol python file involves running functions that mimic a network of a varying number of stations competing to access a wireless channel to transfer data to another station. This is modeled using array structures consisting of frames up to the maximum number of frames allowed as per the predefined simulation time. Another array is configured with random backoff periods from the 0 to After the contention mechanism, the model moves to the success event function with an assigned data transmission channel for two frame time units. This function, depending on the protocol, determines whether the station receiving the transmission is able to send a bidirectional data transmission in the same transmission window post-handshake. This function is the primary difference in the code between the protocols, with the exception of E-SA-MMAC and Max-E-SA-MMAC, as they differ in contention windows during a failure event scenario.The nodes are in a single collision domain and are in the transmission range of each other.The traffic pattern is in a high-load situation, where all nodes have data packets to send and contend for reservation of a channel.The data rate is considered to be at a fixed rate of 1 Mbps for both data and control packets.Simulations run for 10,000 data frames.The following assumptions are made for the simulation scope of the experimental environment and, subsequently, the performance evaluations of the results:Normalized throughput: This is calculated by dividing the total number of packets received (F). Where F indicates the frame size. Normalized throughput is calculated using Equation (Equation .(1)NormJain’s fairness index (JFI): Average fairness among nodes queued for channel access. This is obtained using Equation , Additionally, the interaction between the number of channels and the number of stations has the most significant effect with a 17.7% variation in the throughput compared to any other interaction combination. This implies that the number of channels and the number of stations match each other in terms of the effect they have on the throughput. The interaction between all three factors accounts for only 1.4% of the variation.Moreover, the table shows that the interaction between MMAC protocols and the number of channels has the largest effect with a 4.7% variation in the fairness from the interacting factors. Interactions between all factors account for 2.4% of the variation.Furthermore, the interaction between the number of stations and channels explains the greatest percentage of variation among the interactions of the factors with almost 13%. This implies that the number of stations and channels match each other in terms of the effect they have on the channel access delay. The interaction between all three factors accounts for only 0.4% of the variation and, therefore, is negligible.The assumption that the residuals are normally distributed is proven by the quantile–quantile plots for all three factors in In conclusion, the proposed E-SA-MMAC and Max-E-SA-MMAC protocols achieve greater throughput than the other MMAC protocols at the expense of fairness while the number of channels is low. Max-E-SA-MMAC adapts to the Further, we learned from the analysis of variation that protocols have a much smaller effect on the variation of throughput compared to the number of stations and the total number of channels. The number of channels has the greatest effect on the variation of throughput by a large margin. The ANOVA table for throughput also highlights the effect of the interaction between the number of channels and the number of stations on the variation of throughput. Lastly, MMAC protocols explain the majority of the variation in fairness, while the number of stations contributes to the majority of the channel access delay.For future work, the contention window should be adaptable, depending on the network sizes, and considering the mobility of nodes. Moreover, an optimization approach can be used to optimize the value of


In recent years, unmanned aerial vehicles (UAVs) have been applied in many fields owing to their mature flight control technology and easy-to-operate characteristics. No doubt, these UAV-related applications rely heavily on location information provided by the positioning system. Most UAVs nowadays use a global navigation satellite system (GNSS) to obtain location information. However, this outside-in 3rd party positioning system is particularly susceptible to environmental interference and cannot be used in indoor environments, which limits the application diversity of UAVs. To deal with this problem, in this paper, a stereo-based visual simultaneous localization and mapping technology (vSLAM) is applied. The presented vSLAM algorithm fuses onboard inertial measurement unit (IMU) information to further solve the navigation problem in an unknown environment without the use of a GNSS signal and provides reliable localization information. The overall visual positioning system is based on the stereo parallel tracking and mapping architecture (S-PTAM). However, experiments found that the feature-matching threshold has a significant impact on positioning accuracy. Selection of the threshold is based on the Hamming distance without any physical meaning, which makes the threshold quite difficult to set manually. Therefore, this work develops an online adaptive matching threshold according to the keyframe poses. Experiments show that the developed adaptive matching threshold improves positioning accuracy. Since the attitude calculation of the IMU is carried out based on the Mahony complementary filter, the difference between the measured acceleration and the gravity is used as the metric to online tune the gain value dynamically, which can improve the accuracy of attitude estimation under aggressive motions. Moreover, a static state detection algorithm based on the moving window method and measured acceleration is proposed as well to accurately calculate the conversion mechanism between the vSLAM system and the IMU information; this initialization mechanism can help IMU provide a better initial guess for the bundle adjustment algorithm (BA) in the tracking thread. Finally, a performance evaluation of the proposed algorithm is conducted by the popular EuRoC dataset. All the experimental results show that the developed online adaptive parameter tuning algorithm can effectively improve the vSLAM accuracy and robustness. Due to high flexibility and excellent maneuverability, UAVs have become one of the most popular aerial vehicle platforms over the past few years. Moreover, the outdoor applications of UAVs are well known to the public, while this paper focuses on visual positioning in GPS-denied environments. Therefore, several indoor applications of UAVs are particularly illustrated. For example, UAVs can provide appropriate assistance to humans for those high-risk missions such as rescue operations and indoor equipment maintenance in nuclear power plants . BesidesUAVs can obtain location and attitude information through many different types of sensors. Depending on the signal source, the sensors can be classified into outside-in types, such as GNSS, VICON (a motion capture system), laser scanner, ultra-wideband (UWB), Wi-Fi, and so on. However, the information from this type of sensor cannot be acquired without the pre-set external facilities. As a consequence, these outside-in localization methods cannot work properly in unexplored environments. On the contrary, inside-out types, such as onboard cameras, radars, light detection and ranging (LiDAR), etc., can receive information independently without any 3rd equipment. In terms of computational power requirements, even though using inside-out type sensors is more costly to sense the ego-motion of UAVs, they can deal with the autonomous navigation problem in unknown or even dynamic environments compared to outside-in type sensors and have significant advantages in hardware cost considerations as well. Moreover, the inside-out perception strategy offers UAVs the ability to sense the environment, also known as mapping. The mapping capability is essential for real-time obstacle avoidance, trajectory planning, and other related autonomous functions. All in all, it can be inferred that SLAM technology based on the inside-out type sensors will play a pivotal role in the development of autonomous UAVs under GPS-denied environments.The vSLAM is favored by UAV developers for its lightweight and low-power consumption camera sensors. Moreover, rich color information not only makes the map more valuable but also has excellent potential for removing dynamic obstacles ,4,5,6. IAlthough vSLAM is capable of achieving effective exploration in a GPS-denied environment, the associated algorithms involve a considerable number of parameters or thresholds. In general, these parameters are not only fixed after system startup but also mostly lack intuitive physical meaning, making it difficult to have a well-founded manual adjustment. For UAVs with aggressive motions or in complex operating environments, these parameters require instant online updates to keep the system in optimal condition. For the above reasons, the concept of dynamic threshold is introduced into the field of vSLAM, such as dynamically adjusting threshold value , which cOnline adaptive parameter tuning for feature matching threshold, which lacks physical meaning.Online adaptive Fusion and motion compensation loop design between vSLAM and IMU.In fact, not only the vSLAM system has the requirement of online parameter adjustment, but also the Mahony complementary filter  for UAVsThe matching threshold and the The proposed online adaptive parameter tuning algorithm can effectively improve the pose estimation accuracy and can enhance frame per second (FPS) by up to 70% and 29%, respectively, in the EuRoC dataset.The developed motion compensation loop subroutine can effectively utilize IMU information to improve the anti-shading robustness of the original vSLAM performance. Moreover, incorporating the presented online adaptive parameter tuning algorithm can further improve the robustness to a higher level.Following the above-mentioned issues, the further proposed online adaptive parameter tuning algorithm and motion compensation loop in this paper has the following three primary contributions.This paper develops a proposed online adaptive parameter tuning algorithm based on the S-PTAM , whose pz-axis, while the right and bottom of the shooting direction as the x-axis and y-axis, respectively. The optical center of the camera is taken as the origin. The body frame is the same as the z-axis parallel to the front shooting direction but different from the camera frames; the upper and right sides of the shooting direction are the x-axis and the y-axis. The world frame whose z-axis is parallel to gravity is defined by instruments that provide ground truth poses, such as the Vicon tracking system or Leica MS50. In order to show the definition of all frames more clearly, EuRoC  dataset It must be noted that the vSLAM system does not know any information about the world frame during the positioning process, which means that the world frame cannot be used as the reference frame to describe the pose, so it is necessary to introduce the navigation frame. In this paper, the first left camera frame, after activating the vSLAM system, is defined as the navigation frame, and all subsequent positioning information is described as the left camera frame with respect to the navigation frame, as shown in The current tracking frame is treated as a keyframe as long as it meets the keyframe selection criteria. It is worth mentioning that the core strategy of keyframe selection is to check whether the whole map can provide enough feature points for the current tracking frame to match. S-PTAM in  selects S-PTAM  will useBy searching for keyframes that have a covisibility relationship with the previous tracking frame, the map points that may be observed at that moment can be quickly predicted from the global map, namely the submap. Then, the initial guess of the left camera pose can be predicted by the constant velocity motion model, which can combine with frustum culling to further remove the map points that cannot be seen in the submap, and further obtain the local map. Thereafter, matching features between the stereo image at the moment and the local map are conducted. Finally, according to the matching result, BA is applied to obtain the optimal pose, which takes the output of the constant velocity motion model as the initial guess. The overall tracking thread is to repeat the above steps continuously. The associated detailed flowchart is summarized in The output of the constant velocity motion model may be a weak initial guess, especially when UAVs are in aggressive motions such as sharp turnings or lost image information.The optimization of the BA is highly dependent on the accuracy of feature matching.There are two noteworthy points for the aforementioned algorithm flow chart:In other words, the initial guess and the outliers of the matching pair must be handled carefully during the development process. For the former, this paper will obtain a more reliable value by using IMU information, which will be explained clearly in Before feature matching, feature extraction is performed on the stereo images to find the 2D static feature points, which consist of two parts, key points and descriptors. It is worth mentioning that the key points cannot be matched directly, while the further extracted descriptors allow the key points have the ability to describe the surrounding areas, which makes it possible to perform feature matching. In this paper, the Shi-Tomasi corner detection algorithm  proposedThe BRIEF descriptor is a 256-bit binary vector, therefore, the Hamming distance is adopted to evaluate the feature similarity. For example, if there are two binary vectors, such as 10001 and 01011, with three different bits in the same position between them, then the Hamming distance is defined as three. As a result, the larger the Hamming distance, the lower the similarity of the two vectors. Following the above description, in this paper, each 3D map point on the local map is checked against all the feature points on the current stereo images by the brute-force feature matching algorithm, further matching those with the minimum Hamming distance and below the matching threshold. The illustration of the overall matching algorithm is shown in Before constructing the BA cost function, the camera model must be established first. The pinhole model is often used to describe the conversion mechanism between the camera frame and the pixel frame. The projection can be expressed as:In essence, the BA algorithm is to solve for the optimal camera poses and map point positions by minimizing the re-projection error and its cost function can be expressed as Equation (3).After defining the cost function, the derivatives of the state, i.e., camera poses  algebra , this prFirstly, define a small pose perturbation as shown in Equation (7).Equation (7) can be written in the form of Lie algebra by logarithmic mapping, shown as follows.Alternatively, Equation (8) can be written as Equation (10) by exponential mapping.An additional similar marker Then, the derivative of the re-projection error for small pose perturbation  can be obtained by the chain rule.Therefore, according to Equations (1) and (14), the first term The derivative of the re-projection error with respect to the pose is obtained by substituting Equations (15) and (16) into Equation (13), which yieldsThe derivative of the re-projection error with respect to the map point can be obtained by using the chain rule again, which givesIt is worth noting that the first term Substituting Equations (15) and (19) into Equation (18) yieldsAccording to Equations (17) and (20), the Jacobian matrix of Based on the Jacobian matrix Equation (21), the increment of state can be solved by applying Levenberg–Marquardt algorithm (LM) to further obtain the optimal camera poses and map point positions. That isIn each optimization iteration, the state will be continuously updated according to Equation (24) until the increment However, it is worth noting that BA is sensitive to outliers, namely feature mismatching. To solve this issue, some strategies for filtering outliers must be designed. In this paper, the Huber loss will be used to deal with this problem.Different from the square error expressed in Equation (3), the cost function is now modified as follows by considering the Huber loss.A detailed derivation and explanation about how to realize the outliers suppression into the state increment calculation shown in Equation (22) are given in the following. With the use of the Huber function (26), let us redefine the problem as searching for a state increment By using the Taylor expansion, the first-order approximation can be obtainedUsing the chain rule, the derivative of the cost function with respect to the state increment can be expressed bymth element of the vector According to Equations (26) and (31), the detailed configuration of the diagonal matrix Substituting Equation (29) into Equation (30) yieldsIf Equation (35) is zero, one hasCompared with Equation (22), obviously, the cost function with Huber loss is almost equivalent to iteratively reweighted least squares (IRLS). Therefore, based on Equations (36) and (24), the BA algorithm with outlier rejection can be carried out to obtain the optimal camera poses and map point positions.Following the above description, not only the sensitivity of the BA with respect to the initial value but also the resistance against outliers will be tested. More specifically, the ground truth pose of the camera  and (43), the attitude error correction (44) should have a premise. The acceleration measurement is supposed to contain gravity information only to truly reflect the accumulated error of attitude. In other words, the compensation timing of Equation (44) should be restricted. Put simply, when the difference between acceleration measurement and gravity is greater than a threshold Based on the above description, a confidence level is considered to represent the difference between the acceleration measurement and gravity. For example, the smaller the difference between the two, the less the UAV’s acceleration there is in acceleration measurement, which can reflect the accumulated error more truly. Based on this motivation, this paper further proposes an adaptive The following presents several adjustment strategies  to analyze the accuracy improvement.Pure Integration (control group):The attitude is directly obtained by integrating the angular velocity according to Equation (38).Arctan Method (control group):Directly obtain the Euler angle directly through Equation (45).Pure Mahony (control group):No matter if the difference between acceleration measurement and gravity is smaller than the threshold Conditional Method :If the difference between acceleration measurement and gravity is greater than the threshold Adaptive Method Version. 1 :Based on the Conditional Method, Adaptive Method Version. 2 :Based on the Adaptive Method Version.1, a minor change is madeAdaptive Method Version. 3 :Based on the Adaptive Method Version.2, modify Equation (47) as the following adaption lawExamining rding to , MH_04_dWith the above introduction and analysis of the Mahony complementary filter, it is obvious that the attitude calculated through the IMU is relative to the gravity frame, while the information obtained by vSLAM is relative to the navigation frame. Therefore, information alignment from the IMU gravity frame to the vSLAM navigation frame is essential for pose compensation.Equation (49) shows the process of converting the IMU information into the same reference frame as vSLAM.However, even in the stationary status, the accelerometer inevitably contains high-frequency noise and thereby causes inaccurate pose estimation. An LPF, as shown in Equation (50), is applied to suppress the high-frequency noise appearing in the acceleration measurementsAfter filtering the acceleration measurements, they are placed into a moving window (500 pieces in size). When the moving window is full, the judgment procedure will be triggered. If the standard deviation in this moving window is less than y-axis first, and the x-axis of the rotated gravity frame will be parallel to the opposite direction of gravity. Based on the coordinate configuration, when the UAV is stationary, the relationship between acceleration measurements and gravity can be expressed byIn order to fit the body frame setup and facilitate the calculation of Substituting Equation (53) into Equation (52) givesAccording to Equation (54), Let Note that the settings of According to Equations (56) and (58), And the flowchart of the The estimated After obtaining the accurate However, due to the double integration used in Equation (60), the position Thus, the reset position After obtaining the reset position and reset speed, Equation (60) can be performed again based on them. The overall compensation subroutine working in real-time is illustrated in In this section, the advantages of the proposed algorithm are verified by using the EuRoC dataset. Not only the pose estimation accuracy, FPS and anti-shading robustness are examined, but also the online adaptive tuning process of both matching thresholds and Case. 1: not to use both proposed online adaptive tuning algorithms.Case. 2: only use the online adaptive matching threshold tuning algorithm.Case. 3: only use the online adaptive Case. 4: use both proposed online adaptive tuning algorithms.This section mainly analyzes the estimation accuracy of the following four different strategies so as to independently evaluate the effort of both online adaptive tuning algorithms:Moreover, to validate the contribution of the proposed algorithm for localization accuracy objectively, the loop closure for drift compensation in the following experiments is not considered. Based on the above four conditions, the corresponding accuracy analysis results are shown in Experimental examinations clearly show that the proposed online adaptive matching threshold tuning algorithm can effectively improve the accuracy. In particular, in the MH_03_medium series, 63% and 70% accuracy improvement is achieved in RPE and ATE, respectively. Even though the accuracy did not improve in the MH_04_difficult series, the overall accuracy did not change drastically too much, and meanwhile, according to Since the IMU information is integrated into the vSLAM algorithm, the UAVs’ flight trajectories can temporarily rely on the motion compensation loop, which further enhances the overall anti-shading robustness of the original vSLAM. Following the above statement, the robustness of the overall system against shading will be examined. The examination method is to turn off the left and right camera images simultaneously to simulate the shading situation. In order to analyze the anti-shading performance more comprehensively, the following three vSLAM scenarios will be examined and analyzed.Case. A: without using both the online adaptive parameter tuning algorithm and the motion compensation loop subroutine.Case. B: only using motion compensation loop subroutine.Case. C: using the proposed online adaptive parameter tuning algorithm and the motion compensation loop subroutine.According to The trajectories of the anti-shading experiment are shown in In the following, we present the results of anti-shading robustness tests in parallel, as shown in UAVs are one of the most promising vehicles in recent years, and the underlying positioning technology is receiving more and more attention. However, the over-reliance on GPS has limited the application diversity of UAVs. In order to solve the navigation problem in GPS-denied or interferenced environments, the stereo vSLAM solution is gradually gaining attention. Therefore, this paper presents an improved UAVs vSLAM system based on the S-PTAM architecture and Mahony complementary filter. The proposed online adaptive matching threshold tuning algorithm and online adaptive


A theoretical investigation on electron transport properties of rectangular graphene quantum dots (GQDs) with non-centro-symmetric out-of-plane Gaussian deformation of elliptic type is presented. Different levels of deformation are explored to estimate system geometry optimal for potential electronic applications. Electronic properties of deformed GQDs are studied in terms of local density of states (LDOS), band-gap opening and equilibrium ballistic conductance. In particular, it was observed that the symmetry of spatial LDOS structure is directly linked with the symmetry of properly defined local strain field (LSF) map, for a wide energy range. The relationship confirms qualitatively predictions obtained on the basis of the concept of a pseudomagnetic field, used in continuum models of graphene, including strain induced effects. The conductance spectra of deformed GQD as a device connected to semi-infinite graphene armchair nanoribbons as reservoirs are studied in a frame of tight-binding (TB) model in combination with non-equilibrium Green’s-functions technique (NEGF). In the former, the electronic states largely depend on the edge structure and on the width of the GNR, in the latter the electrical properties depend on the shape of the edges and on the diameter of the CNT. Dependence of the electron transport on the geometry has been studied theoretically and experimentally in many structures characterized by non-uniform geometry, in particular in the ballistic regime. The motion of charge carriers can be considered ballistic, when the constriction length of the device is on the scale of mean-free path length of the material. One of the most known devices of this type is the geometric diode4. The geometric diode is a ballistic transport device providing electric rectification due to geometrical asymmetry. In many materials, energy bands exhibit a discrete number of inequivalent local minima or maxima for specific values of momenta, usually known as valleys6. These valleys seem to be ideal candidates for components of a binary variable or pseudospin. In the case of graphene in particular, different schemes have been proposed to achieve valley-electronic filtering depending on geometrical deformation, also referred to as valley polarization, i.e. generating a charge current composed of electron states from only one valley. Strain-induced effects in graphene has been the topic of a large number of theoretical works aimed at understanding the impact of controlled geometrical deformations on electronic properties12. Most of theoretical study focus on strain produced by a centrosymmetric Gaussian out-of-plane deformation15. They have been already produced experimentally on suitable substrates16 and also with STM methods17. Confining states within deformed GNR, symmetry properties of LDOS, conductance spectra and pseudospin polarization have been studied in the frame of TB approximation18. The effects of an external electric field, the influence of edge roughness on conduction properties of deformed GNRs with centrosymmetric Gaussian bump have been studied using TB model and NEGF transport formalism19.Geometry-induced effects in 2D materials has emerged in recent years as an active area of research due to potential use for electronic purposes. The coupling of geometrical and electronic properties seems to be a promising tool for the design of electronic devices with a desired electric transport properties. A representative example of the interplaying between geometry and the electronic band structure in graphene systems are graphene nanoribbons (GNRs) and carbon nanotubes (CNTs)on state and low conductance in off state. The necessary condition to achieve such a conductance property is the existence of sufficiently large energy gap and relatively high conductance outside the gap. We note that recent studies on electron transport properties of GNRs, focused on the energy gap opening mechanism19 and valley filtering mechanism6, are limited to centrosymmetric Gaussian bumps or pure Gaussian folds. In particular, it has been shown that centrosymmetric Gaussian deformation strongly modifies the electronic properties of all types of ribbon structures and leads to a strong reduction of electron transmission in high-energy regions19. Investigations presented in this paper show that for the systems with comparable number of transmission modes as considered in the paper19, fundamental requirements related to transport properties (large transport gap and good conductance for higher energies) can be satisfied simultaneously for properly deformed GQD as an effect of geometric anisotropy, modeled by Gaussian deformation, of an elliptic type.In this work, I investigate the impact of anisotropic Gaussian deformation on static electronic properties of GQDs and on electron transport in armchair graphene system given in Fig. discrete representation of the Hamiltonian, such as that obtained within the finite difference method or in TB approximation. The discrete representation allows for easily determination of contact operators describing couplings between the device and leads. Also, using such a representation, the calculation of appropriate Green’s functions reduces to performing numerical operations directly on matrices. In the case of graphene systems, a commonly used and the most suitable for transport purposes is a single-orbital TB model for the s, semi-empirical TB Hamiltonian reads26. One of the choice in representing a finite simulation domain is the abrupt termination of the simulation domain with a hard-wall BC. Such abrupt termination in the atomistic basis set results in the creation of dangling bonds25. The dangling bonds will form surface states that typically cover a broad energy range and often litter the central energy region of the fundamental band gap. To model GNRs in a more realistic treatment we can the easiest assume that edge carbon atoms are passivated with hydrogen, so that there are no dangling bonds at the edge and parasitic boundary condition induced states are eliminated. On the other hand, this treatment requires some modification of TB parameters corresponding to edge atoms since the presence of C–H bonds introduces carbon atoms on edge with a different nature. One should be noted here that the edge effects can be taken into account simply by modifying the transfer energy 23. However, as it has been shown in the paper27 the modification of band structure introduced by edge corrections is small, though some of metallic armchair nanoribbons become semiconducting. This, however, works to the advantage of our search, as we are looking for effects leading, among other, to increasing of the energy gap. For this reason, further calculations are performed using the Hamiltonian (Eq. In order to investigate transport properties of any system, it is convenient to use some mentclass2pt{minimmentclass2pt{minimith and jth is modified to2828. ith and jth sites. The on-site energies are supposed to be unchanged and 30. The source of these corrections however is the presence of d-orbitals in the TB model that is not the case of graphene.In the presence of the Gaussian deformation the system is described by the Hamiltonian Eq. , in whicz of atoms within an elliptic Gaussian deformed region is defined asx- and y-directions. The Gaussian bump defined in Eq. (31. For the system given in Fig. W of the GQD is given by the integer M, where M stands for the number of dimer lines counted along the zigzag edge, L of the GQD is determined by the integer N, where N is the number of the zigzag lines along the armchair edge, M and N.The coordinate mentclass2pt{minimmentclass2pt{minim33. As we can see in Fig. E is given by3333. The LDOS at the jth lattice site is given by3334. We note that equilibrium conductance is obtained from transmission simply as p is an integer number. The first group contains semimetalic GNRs, the two remaining groups correspond to semiconducting GNRs. In the present study M is taken as an odd number.The quantum transport properties are studied using TB model coupled to the NEGF formalism22. This property remains valid for a finite unstrained system, like the rectangular GQD, considered in this study. We can see in Fig. petals of this flower are located on armchair directions of the GQD. On the other hand, we can see in part b of Fig. 6.In Fig. In Fig. 19. Figure x-direction. The bump size in the y-direction is fixed on the value corresponding to the centrosymmetric case. We can see that due to elliptical deformation the energy gap increases with decreasing y-direction, is given. In this case, a larger band-gap is created, however the conductance is strongly suppressed outside the gap. Conductance spectra given in Fig. In Fig. In Fig. on and off states in the field-effect nano-transistor, with GQDs built in.In Fig. gutter with decreasing depth, oriented along the transport direction. Contrary to the centrosymmetric bumps or strictly Gaussian-fold deformations considered in many papers, this kind of the deformation provides a large transport gap and high transmission outside the gap, that is comparable with the transmission of perfect GNRs. These two features are fundamental from the point of view of practical nanoscale electronics applications. In the case of field-effect transistors in particular, the achievement of a high on/off ratio is directly dependent on these characteristics. One should be also added that discussed in this paper cases are representative examples of whole family of armchair GNR systems having the form GNR-GQD-GNR and obtained results are universal in the sense that they do not depend on particular integer number M, defining one of the three family members.In this paper I studied static electronic properties and equilibrium transport properties of rectangular graphene quantum dots with non-centrosymmetric Gaussian deformation. Quantum transport has been studied within NEGF formalism for system with deformed GQD as a central scattering region connected to semi-infinite GNRs as leads, having perfect geometry. The connection between symmetry of spatial LDOS structure and the symmetry of local strain field has been observed, for a wide energy range. By investigating several types of deformation, I estimated optimal configuration of the armchair GNR system with elliptic Gaussian deformation, suitable for potential electronic applications. The optimal configuration corresponds to the extended elliptic deformation having a geometry of a Supplementary Information.


Over the past decade, Markov State Models (MSM) have emerged as powerful methodologies to build discrete models of dynamics over structures obtained from Molecular Dynamics trajectories. The identification of macrostates for the MSM is a central decision that impacts the quality of the MSM but depends on both the selected representation of a structure and the clustering algorithm utilized over the featurized structures. Motivated by a large molecular system in its free and bound state, this paper investigates two directions of research, further reducing the representation dimensionality in a non-parametric, data-driven manner and including more structures in the computation. Rigorous evaluation of the quality of obtained MSMs via various statistical tests in a comparative setting firmly shows that fewer dimensions and more structures result in a better MSM. Many interesting findings emerge from the best MSM, advancing our understanding of the relationship between antibody dynamics and antibody–antigen recognition. With AlphaFold2 advancing protein structure determination to computational models that now reach the accuracy of experimentally-resolved models ,2, severOver the past decade, Markov State Models (MSM) have emerged as powerful methodologies to build discrete models of dynamics over trajectories obtained in silico via Molecular Dynamics (MD) simulation ,6. Most Connections with the energy landscape that governs the structural dynamics of a molecule have largely been ignored, even though the concept of a basin in the energy landscape promises to connect more directly to that of a macrostate. The reasons vary and include the long-standing lack of trust in the accuracy of energy functions and, perhaps, more importantly, the open questions between connecting the definition of a basin to practical implementations over a set of structure–energy samples.Work in ,13 leverMotivated by this body of work and practical challenges, we posit here the following: (a) further reducing the representation dimensionality in a non-parametric, data-driven manner may improve the quality of an MSM by providing better state space discretization; (b) including more structures in the computation is then possible and promises a higher quality MSM even without the access to energetics.This paper investigates these two research directions. It does so by bringing back a shape-based representation of a molecular tertiary structure, the Ultrafast Shape Recognition (USR) coordinates . These cThe context that motivates the computational study in this paper is that of aiming to understand the impact of antigen binding on the dynamics of Immunoglobulin G (IgG), which binds to cognate antigens. Since Zwanzig’s first report on short memory approximations in 1983 , MSMs haAs in our previous work ,16, we mThe identification of macrostates for the MSM is a critical component. According to theory, structures capable of rapid inter-conversion should be aggregated into the same macrostate; structures with slow inter-conversion rate should be separated into different macrostates . In pracWork in ,16 operaThe particular systems that motivate the work presented in this paper are the IgGs, which are central in providing us with immunity to pathogens and tumors. As such, they represent common template for antibody drugs . We now Several studies suggest that allosteric effects during antibody–antigen recognition  with botThe MD simulations from which we extract structures for analysis in this paper are reported in detail in . ConclusMD Simulation Protocol: We briefly review the MD protocol in . The strWork in  carried The systems were solvated by TIP3P water molecules, and sodium and chlorides were added to neutralize the system and to achieve a total concentration of 150 mM. The overall sizes of simulated systems contain around 567,640 atoms (including water atoms as solvent). The systems were energy minimized for 5000 conjugate gradient steps, where the protein was fixed and water molecules and counterions could move, followed by additional 5000 conjugate gradient steps, where all atoms move. In the equilibrium stage, each system was gradually relaxed by a series of dynamic cycles, in which the harmonic restraints on proteins were gradually removed to optimize the protein–water interactions. In the production stage, all simulations were performed using the NPT ensemble at 310 K. All MD simulations were performed using the NAMD  softwareStructures are extracted with the mdconvert command-line script from the MDTraj Python library over a given MD trajectory file in the .dcd format. We extract frames every 4 ps, resulting in a total of 160,000 structures for the free antibody and the antibody–antigen complex, respectively.CA atoms) yields the best MSM model; however, all MSM models have various shortcomings in relation to diverse rigorous statistical tests.The large sizes of the free and bound antibody prompt work in  to consiWe first relate the USR-based representation that we propose as fast yet accurate in this paper. We then place it in the context of the process that harnesses MD trajectories into an MSM model of dynamics. Finally, we describe the various statistical tests that evaluate the quality of an MSM model and set the stage for the evaluation related in features, and the process via which such features are obtained is referred to as featurization. Whether in the free antibody or the antigen-bound antibody setting, we represent a structure as a 12-dimensional point, utilizing the following process to compute 12 coordinates from a given structure. First, given a structure in three dimensions, four points of reference are identified over it:1.The molecular centroid (ctd);2.The closest atom to ctd (cst);3.The furthest atom from ctd (fct);4.The furthest atom to fct (ftf).In MSM terminology, the coordinates employed to represent a tertiary or quaternary structure are more generally referred to as The Euclidean distances of all the atoms in a structure to each of the four reference points yield four separate distance distributions. Each distribution is summarized with its first three moments , yielding over the four distributions the 12 coordinates/features representing a structure and thereby capturing the geometry and shape of the structure.Note that this representation presents a significant reduction from several thousand Cartesian coordinates to 12 (USR) coordinates. Given the known curse of dimensionality for clustering algorithms , such saThe first MSM-construction decision is how to featurize the structures, which is addressed via the USR coordinates as described above. We recall that we compare here to an alternative featurization . Consider a vertex u that is not a local minimum. From each such vertex, there are many edges to follow. The one that maximizes the negative gradient calculated as shown above is selected to arrive at a next vertex. This process is repeated until we arrive at a local minimum. Vertices from which this process terminate at the same local minimum are then assigned to that minimum and the basin associated with it. Further details can be found in [The second decision is how to group conformations into clusters/macrostates. In , the confound in . We notefound in ,55,56,57k allows us to identify an optimal number of clusters in this setting.In this paper, we utilize this approach to identify basins over conformation–energy samples obtained from the MD simulations. We recall that our conformations are 12-dimensional points (of USR coordinates). Unlike work in , where ti has been assigned to a macrostate j has been assigned to a macrostate j follows i in some MD trajectory, the number of counts keeping track of transitions from Once the basins or clusters are obtained to be employed as macrostates, the next step is to utilize the temporal information in the MD trajectories to compute state-to-state probabilities of transition. Briefly, let us assume that some conformation As in other MSM-based studies of dynamics, we make use of two main tests, the Convergence Analysis and the Chapman–Kolmogorov (CK) test, which evaluate whether an MSM is memory-less. In a memory-less MSM, the conditional probability distribution of future macrostates should only depend on the current macrostate and not on the prior macrostates.The convergence analysis tests whether the selected lag time guarantees that the assignment of conformations in macrostates obeys the Markov property. This selection is an important decision, as it may yield to a loss of temporal and spatial resolution and in turn impact the quality of the constructed MSM. If the assignment of conformations into mascrostates obeys the Markov property, this means that conformations within a state inter-convert to other conformations in the same state on timescales faster than the selected lag time but transition to conformations in other states on slower timescales. This property is verified via visualization of the generated implied timescale plot of the model relaxation timescale versus model lag time. One looks for an exponential decay to the system equilibrium; the implied timescales plot needs to exhibit convergence within a few steps .The Chapman–Kolmogorov (CK) test computes the probability of transition between meta-stable states for increasing lag times. Given an MSM estimated at lag time  Work in  shows th Work in . SpecifiWe consider two separate systems: the free antibody and the antigen–antibody complex. For each system, we construct three separate MSMs based on the combination of featurization choice and clustering algorithm.Setting-A: This setting utilizes the CA-based representation and basin finding over 5000 structure–energy samples; as reported in , energieSetting-B: The second setting changes the CA-based representation to the USR-based representation of 12 coordinates per structure to represent those 5000 structure–energy samples.Setting-C: The third model expands to 160,000 structures  and employs the k-medoidsalgorithm.Each model (corresponding to each setting) is evaluated via the convergence analysis and CK tests. The best MSM in each setting is related in greater detail, providing insights on the dynamics of the free and bound antibody and changes to dynamics upon antigen binding.We now evaluate each of the three MSMs obtained on the free antibody data via the convergence analysis and CK tests to determine the best model capturing the free antibody dynamics.s states, with s varying from 1 to the total number of states identified.We now evaluate each of the three MSMs obtained on the antigen-bound antibody data via the convergence analysis and CK tests to determine the best model capturing the free antibody dynamics.We relate a run-time comparison in According to the Convergence Analysis and CK tests, as well the run-time analysis, the best MSM obtained for both the free and antigen-bound antibody is that obtained from Setting-C. In the next set of analyses, we focus on the MSM model obtained from this setting.First, we shed light on the state space discretization in a comparative setting. The procedure described in The juxtapositions in While the application setting that motivates the computational study in this paper is elucidating the impact of antigen binding on the dynamics of Immunoglobulin G (IgG), our study focuses on practical design choices that hamper the quality of MSMs integrating MD trajectories. Whether focusing on a free antigen or an antigen-bound one, the number of atoms in a molecular system can approach several hundred thousand. Even reducing to the central carbon atoms does not significantly reduce the number of atoms or dimensions. For the particular systems in this study, this number exceeds 20,000 atoms (for free antibody) and 21,000 atoms (for the antigen-bound antibody), respectively.Such a high dimensionality of the structure space poses real challenges for the clustering algorithms on which MSM construction packages rely for state space discretization. In turn, the quality of MSMs suffers, as diagnosed by various statistical tests. Even employing dimensionality reduction techniques, such as PCA and TICA, does not promise a remedy . In thisThe related MSM models stand up to various statistical tests, and the state-to-state dynamics they reveal for the free and antigen-bound antibody allow for drawing interesting insights. The MSMs show that, with antigen binding, there are considerable state-to-state transitions. These suggest that the antigen-bounded form may provide many dynamic processes to further enhance co-factor binding of the antibody in the next step. We also observe that the antigen binding reduces the number of macro-states. Actually, these insights suggest that the directions we investigated in this paper advance our understanding of the relationship between antibody dynamics and antibody–antigen recognition.


Electrochemical impedance spectroscopy (EIS) is the golden tool for many emerging biomedical applications that describes the behavior, stability, and long-term durability of physical interfaces in a specific range of frequency. Impedance measurements of any biointerface during in vivo and clinical applications could be used for assessing long-term biopotential measurements and diagnostic purposes. In this paper, a novel approach to predicting impedance behavior is presented and consists of a dimensional reduction procedure by converting EIS data over many days of an experiment into a one-dimensional sequence of values using a novel formula called day factor (DF) and then using a long short-term memory (LSTM) network to predict the future behavior of the DF. Three neural interfaces of different material compositions with long-term in vitro aging tests were used to validate the proposed approach. The results showed good accuracy in predicting the quantitative change in the impedance behavior , in addition to good prediction of the similarity between the actual and the predicted DF signals, which expresses the impedance fluctuations among soaking days. The DF approach showed a lower computational time and algorithmic complexity compared with principal component analysis (PCA) and provided the ability to involve or emphasize several important frequencies or impedance range in a more flexible way. The biointerface is a physical contact area between a biological medium, including biological tissue, and a medium of another biomaterial component including organic/inorganic compounds . The priSome biointerfaces consist of conductive parts and interaction with an electrical medium for recording, measuring, and/or stimulating purposes . To measTherapies based on regenerative techniques are promising and emerging technologies that aim to produce stem cells and their progeny on a large scale. Concerning these techniques, impedance-based cellular assays (IBCAs) are considered a sufficient approach to study stem cell properties; furthermore, they can deliver quantitative and highly sensitive results that can be easily automated and scalable, and the literature has demonstrated its ability to monitor stem cell regeneration, differentiation, and maturation ,11. TranBased on the above, EIS performance and impedance analysis are the golden tools for many emerging biomedical applications. In contrast, those types of measurements have multidimensional outcomes related to the environment, frequencies, and applied voltage. Thus, they require huge efforts to track or design online diagnostic systems, which will rely on machine learning tools in the near future. Dimensionality reduction of impedance data has been reported previously in several in vivo applications. Impedance indices are proposed to extract pertinent features from the impedance spectrum, such as the magnitude index (MIX), the phase index (PIX), the real part index (RIX), and the imaginary part index (IMIX), where those indices compare values at 20 and 500 kHz to diagnose oral mucosa . Known aThe related works  show thaThe impedance dataset of this study was established based on the characterization of the recording sites of three neural microarrays using EIS. The properties of each microarray are illustrated as follows.The flexible micro-ECoG device A was fabA 32-channel microelectrode array B was forA polyimide-based flexible ECoG microarray C with 16The three mentioned ECoG microarrays in this paper were characterized using the EIS tool for 11 soaking days with different parameters and instruments as shown in Bode and Nyquist diagrams are the most common data representation tools of impedance measurements that give abstract information about the electrical performance of the tested interface , but theTo avoid this complexity in EIS evaluation and to prepare preprocessed data for the prediction of neural interface impedance and to provide some flexibility in features contribution, we propose and implemented a new formula that converts multidimensional EIS outcomes (impedance amplitude/frequency/soaking day) to a one-dimensional signal or series of values according to EIS days as shown in Equations (1) and (2):d) day, or normalized DF of (d) day to the first day d).d}) was normalized to the The name of the formula is day factor (DF) which expresses the EIS measurements during the same day in the normalized form to the day factor of the first soaking day. The unique value of Since DF values represent only soaking days, the outcomes will be discrete values, and soaking days can have a time gap of at least two or three days between each sequenced soaking day. Therefore, to convert the DF values into a continuous signal, we used the Curve Fitting Toolbox™ functions in MATLAB, which allowed us to fit to and smooth the DF data points.After preparing a one-dimensional DF signal of values that expressed the impedance behavior of the neural interface. We used the principle of time series forecasting or signal behavior prediction using an LSTM network.An LSTM network is a type of recurrent neural that uses a series of observations to become familiar with sequence prediction problems. LSTM is specifically designed to avoid the long-term dependency problem and save/retrieve information for long periods. By training a sequence-to-sequence regression after shifting the training data for one-time step, we would be able to predict the values of the next time steps for the same data sequence .The LSTM network in this research was used as a forecasting method  for a va States) . All comThe fitted DF signal after implementing splines approximation became the high-sampled signal. By predicting each DF part using LSTM, we would had actual and predicted signals. The traditional metrics for measuring performance, such as accuracy and sensitivity, were not useful for evaluating the outcome of our prediction approach. To obtain more informative measures, we propose two ways to evaluate prediction accuracy as follows.To measure the accuracy of predicted DF as an absolute or quantitative value, we calculated the difference between the last value of the actual DF signal and the last value of the predicted one. Then, we normalized it to the maximum range of the actual DF, which gave us the relative error of the predicted signal; thus, (1-error) expresses the accuracy of the equality between the actual and the predicted DF as shown in Equation (3).cov : The covariance between two random variables A and B;A.After measuring the final value quantitatively, we should evaluate the behavior of predicted signals such as the slope and the similarity with the actual one. Where the correlation coefficient of two random variables is a measure of their linear dependence, we can thus consider the correlation coefficient of the two actual and predicted DF as an accurate measure of similarity. If each DF signal has N scalar observations, then the Pearson correlation coefficient, in percentage, is defined as in Equation (4):The Results Section handles each microarray separately by collecting the impedance data of the examined microarray, implementing the day factor (DF) formula on the impedance data and, finally, using the DF signal with the LSTM network to examine the impedance prediction of each post-soaking day based on the previous days as training input. The used ECoG microarrays contained many recording sites that could be characterized; thus, the upcoming results are concerned with the average impedance amplitude of all recording sites, which are expressed as one impedance value for each frequency and soaking day.The impedance analysis of the 11 soaking days showed stable values of impedance as shown in By implementing the DF formula using Equations (1) and (2), we obtained the DF signal B that exStarting from the third soaking day, we considered the DF values of the previous days as training data for the LSTM network; then, we used the LSTM to predict the next day, which was the fourth day (for example). We repeated the procedure by predicting the fifth day using the last four days, etc. The predicted and actual DF data of day 11 are visualized in The prediction accuracy for each soaking day using the previous days is illustrated in The impedance measurements of the 11 soaking days are depicted in The predicted values of day 11 were relatively close to the actual one, in addition to the slope and steps, which made the accuracy of the AFS and ACC higher than 90% C,D.The prediction accuracy for each soaking day using the previous days is illustrated in The impedance analysis of the 11 soaking days showed stable values of impedance as shown in The normalized DF depicts the changes in the impedance, where on day 5 and 9 during soaking A, we canThe predicted and actual DF data of day 11 are visualized in The prediction accuracy of each soaking day using the previous days is illustrated in PCA is a very popular dimensionality reduction technique. PCA has been applied in many fields of bioinformatics  and, espBiointerface technology has become an important addition to many medical and clinical applications. Its main use as a biomedium tester or monitor requires long-term reliability and periodic evaluation of its performance in terms of its ability to obtain accurate measurements from targeted areas. EIS has been used widely in measuring the impedance and electrochemical properties of any biointerface device, where EIS can provide information regarding the interface and surrounding environment.Concerning neural interface, EIS measurements can provide a detailed examination regarding the electrical properties and the biostability of neural implants and microarrays either in in vitro or in vivo applications. Recently, measuring circuits of EIS were embedded within the structure of neural microchips to conduct periodic EIS tests and to evaluate the efficiency of long-term implantation in living tissue . In the By comparing the performance of DF and PCA using the same datasets, we found that both give the same distribution and resolution of impedance changes, but DF had two better features than PCA. The first feature is the lower computational time and algorithmic complexity . This feThe DF signal or the proposed approach for the impedance data reduction can offer or suggest a solution for clinical and biomedical applications. For example, localized bioimpedance analysis (BIA) can assess soft tissue hydration and cell membrane integrity using noninvasive electrical measurements, but the main challenge in this technique is to standardize a protocol that allows for the assessment of any person , where DToday, LSTM applications are mainly concerned with predicting upcoming events or signals ,30,31. IIn this research, we proposed an approach that can summarize the multidimensional data of EIS and convert them into a one-dimensional signal (DF) that expresses the overall changes in the impedance in a relative way by normalizing EIS trails to the early first trail. The DF approach showed a lower computational time and algorithmic complexity compared with PCA and provided the ability to easily involve or emphasize several important frequencies or impedance range. An LSTM network was used with the DF signal to study the ability to predict the potential changes that could be used soon within microchip structures to predict and avoid undesirable consequences. The DF formula could be generalized to express the phase changes in the impedance and use the DF of the amplitude and phase to obtain a more powerful estimation of the biointerface performance.