It seems that core muscle function affects lower extremity stiffness, and can function as a performance index in athletes. Although performed in healthy volunteers, this study may have implications for injury prevention, highlighting the necessity to perform interspersed endurance training using the different body parts of the kinetic chain. Core stability is the ability to control the position and motion of the trunk over the pelvis and legs to allow the optimum production and transfer of force to the terminal segment in sporting activities. The effect of fatigue, especially core muscle fatigue, on stiffness as a performance index requires more study. This research aimed to investigate the effect of the core stabilization muscles’ fatigue on lower limb stiffness during hopping. Thirty active basketball players participated in this study . The hopping test (15 jumps) was performed before and after the fatigue protocol in three states including at a preferred (no frequency control), maximum, and 2.2 Hz frequency on the force plate. The stiffness of the lower extremities was measured before and after the fatigue protocol. The results of the dependent t-test showed core muscle fatigue led to reduced lower extremity stiffness under all three hopping-test conditions by 15.3–15.9% ( A loss of core stability can expose one to the risk of injury and proper training can reduce the probability of injury . In addiIn the healthcare sector, performing daily activities without pain is desirable, but in the field of competition, achieving the best performance with the lowest risk of injury is a concern . Due to Despite the complex dynamics of the neuromuscular system, simple mass-spring models can acceptably describe these movements . StiffneSeveral methods under natural conditions have been devised for determining stiffness, which measure this variable at the lowest level (stiffness of muscles and tendons), middle level (stiffness of a joint and its surrounding structures), and highest level (stiffness of the limb or the entire body). Various methods have been presented to determine stiffness in biomechanics research. One of these methods is the mass-spring model, which is capable of describing some of human motion. The stiffness obtained from this method is a combination of stiffness values from all body structures and can be influenced by muscle activity levels, nerve reflexes, and individual strategy in the movement . The mosA wide range of research in this field has given attention to studying mechanical stiffness (stiffness of the leg and lower extremity) during exercises such as running, walking, and hopping. Hopping is a biomechanical movement that mimics the spring-like motion of kangaroos and is commonly employed as a clinical test to evaluate the mechanical stiffness and elastic properties of muscles and tendons in the lower extremities ,18. It s2) participated in this quasi-experimental study design. Participants were invited to the laboratory and the implementation process of the tests was explained. Participants were recruited via announcements to university basketball players.Thirty young male basketball players . The participants were informed about the details of the study and provided their written informed consent before study enrolment. Informed consent was obtained from all the participants and procedures were conducted according to the Declaration of Helsinki. Participants were assessed for laterality and were right-side dominant for all criteria, which was identified by using the ball kicking test. The inclusion criteria consisted of age range of 18 to 25 years, no history of injury in the past six months, and experience in playing basketball for at least 3 years. The exclusion criteria consisted of neuromuscular disorders or cardio-vascular problems .At first, anthropometric characteristics including the weight, height, and length of the subjects were measured and recorded. The participants were taught how to hop. The hopping test was performed in three states including at a preferred , maximum, and 2.2 Hz frequency. Subjects performed a warm-up protocol (including 5 min running at their desired speed and 5 min static stretching), before the hopping test. In the preferred hopping test, the subject performed arbitrary hopping. The jump height and frequency were not controlled. In the 2.2 Hz hopping test, a metronome was used and the subjects were asked to coordinate their jumps with the metronome rhythm. Finally, subjects performed a hopping test with a maximum jump height and minimum contact time. All three tests included these considerations: The hopping test was performed vertically and each test was constructed of 15 consecutive jumps. To reduce the effect of the upper limb and shoes on the hopping test, subjects’ hands were put on their waists and they were barefoot. All three hopping tests were performed on both legs, with each leg acting as a pair, to evaluate the mechanical stiffness and elastic properties of muscles and tendons in the lower extremities. The subjects were allowed to practice to ensure the proper implementation of the hopping.The fatigue protocol developed by Abt et al. 2007) was used to measure core stability muscle fatigue in multiple planes of movement . Benjami07 was uslegK) was calculated using the equation of McMahon et al. (1990) [legK was calculated by dividing the maximum vertical ground reaction force (maxF) by the downward displacement of the center of mass (Δy) during the ground-contact phase (Equation (1)). The maxF contact data were extracted directly from force plate data. Various methods have been proposed to calculate Δy. In this study, using the subject’s mass and GRF, the acceleration was calculated. Finally, Δy was determined through double integration of the acceleration data.Force plate  ground reaction force (GRF) data during hopping in the pre- and post-test was recorded at 1000 Hz. The data were filtered with a zero-lag fourth-order low-pass Butterworth filter at 50 Hz . The GRF. (1990) . The Klet test with a significance level of α ≤ 0.05 was used.The mechanical stiffness for each of the five jumps (jumps six to ten) was calculated and the average of these values was normalized to the subject weight. t-test was used to find the significant differences between the pre-test and post-test. Due to the sequential use of the paired-samples t-test, the Bonferroni correction was used to counterbalance the multiple testing applied [Statistical analysis was performed using SPSS software (version 22). Descriptive statistics were used to analyze baseline data for demographic data. The Shapiro–Wilk test results indicated that all data were normally distributed. A paired-samples  applied ; therefot-test showed that core muscle fatigue significantly reduced lower-limb stiffness during preferred hopping by 15.33%, 15.9%, and 15.44% compared to the preferred , 2.2 Hz  and maximum hopping , respectively. Mean and standard deviation of stiffness during preferred, 2.2 Hz, and maximum hopping in pre- and post-test core muscle fatigue reported in The results of the dependent We assumed that core muscle fatigue leads to changes in the stiffness of the lower extremity during the performance of hopping. The results of the study show a reduction in the stiffness of the lower extremity during all three types of hopping following core muscle fatigue. Because many lower-extremity injuries, especially those of the ankle and knee, occur during landing, the hopping maneuver was selected. In performing functional skills that are accompanied by weight loading, stiffness can be affected by muscles, tendons, ligaments, and the skeletal alignment, which works as a unit to modify the rotational stiffness of a joint while making contact with the ground . The rotGiven that fatigue influences these factors, it seems that stiffness also changes as a result of muscle fatigue. The changing of control strategies caused by fatigue can affect the probability of the risk of lower-extremity injury. It is still unknown and requires further investigation how core muscle fatigue is conducive to changes in lower-extremity stiffness. Given that the core muscles are essential to create a stable surface for the proper movement of the upper and lower extremities, core muscle fatigue can affect sports activities . BiomechIt has been reported that the stiffness of the lower extremity has a significant role in improving the performance of running, jumping and hopping exercises, which are seen in many sports. Athletes who use stiffness characteristics more efficiently save more elastic energy during landing, which consequently results in a more concentric force in the push off. This state delays fatigue and ultimately increases running speed . The relCore stabilization depends on the ability to control the body in response to internal forces and external disturbances. These forces consist of forces produced from the distal parts of the body as well as expected and unexpected external disturbances . It is bAlternatively, fatigue can be considered as a generalized and not only a localized phenomenon. A recent systematic review lends some experimental support to the generalized non-local muscle fatigue effect, particularly when examining specific types of performance outcomes, like the hopping tasks examined in this study .Because fatigue reduces the speed of neural transfer, the ability to produce compensatory contractions around joints might be reduced and is conducive to weaknesses of neuromuscular control and further changes in the joint’s condition. Also, more variability in the range of joint movement might reduce the balance in the absence of corrective muscle actions . Given tThe results of the present study have shown the effect of the fatigue of core stabilizing muscles on the stiffness of the lower extremity during hopping, which can be used to enhance training foundations for athletic performance, injury prevention, and rehabilitation. This significant topic has highlighted injury prevention methods and aided towards enhancing the quality of performances of athletic protocols, and has highlighted the necessity to pay more attention to the better quality of training components. According to the advent of more effective spring-like hopping over running, perhaps it is possible to use stiffness in hopping as a more proper index for the level of elastic properties of the muscular system. During hopping, the foot stiffness is equal to the vertical stiffness, and it is extracted by dividing the vertical force of the ground by the displacement of the center of mass. Active muscular stiffness is the main factor in the modification of disturbances and the establishment of dynamic stability. The deterioration of this factor causes the growth of disturbances and places the joint at the end of the ROM, which causes an increase in the tension of ligaments and a risk of injury. The required stiffness for achieving the highest level of performance in sports activity might put the athlete at risk of injury. So, we have to consider an optimum level of stiffness that caters for injury-free sports participation, while maintaining a high level of performance at the same time.This study provided some valuable insights into the effects of core stabilization muscle fatigue on the lower-limb stiffness of basketball players, but it had several limitations. First, it only included male basketball players. Since female athletes have a higher injury risk in similar activities than men, future studies should investigate the gender effect. Second, in addition to fatigue, other factors that can affect the stiffness of the lower limbs of athletes, such as diet and training, should be considered. Finally, in order to better identify the traumatic factors caused by lower-limb stiffness in athletes, future studies should record the activity of working muscles through electromyography as well as kinematic variables of the lower limb.According to the results of this study, there was a significant decrease in the amount of lower-extremity stiffness measured at various frequencies during a fatigue protocol targeting the trunk stabilizing muscles, applied in a group of healthy basketball players. Training programs with an aim to increase the endurance enhancement of the stabilizing muscles of the trunk may lead to less severe deteriorations of lower-limb stiffness, which may improve performance as well as act as an injury prevention mechanism for the safe participation in various athletic activities involving the lower limb.


The main focus of this article is to mathematically formulate the microfluidics-based mechanical system for nanofluids. A 50:50 mixture of propylene glycol (PG) and water is used as a heat transfer fluid because of its tremendous anti-freezing properties, and nontoxicity and it is safe to be utilized at the domestic level. Titanium dioxide (titania) nanoparticles are suspended in the working fluid to enhance its heat transfer ability. The fluid flow is induced by electroosmosis in a microtube, which is further assisted by cilia beating. The impacts of Joule heating and non-linear thermal radiation are also considered. The simplification of the dimensionless system is done under lubrication theory and the Debye-Hückel linearization principle. The nonlinear system of equations is executed for a numerical solution by adopting the symbolic mathematical software Maple 17 using the command “dsolve” along with the additional command “numeric” to get the numerical solution. This command utilizes a low-ordered method along with accuracy-enhancing schemes such as the deferred correction technique and Richardson extrapolation to get a numerical answer of desired accuracy, where we can choose the accuracy level and mesh points according to our requirements. The detailed analysis of results obtained from the numerical treatment of the considered problem indicates that the efficiency of the PG + water enhances due to the suspension of the nanoparticles and heat is rapidly removed from the system. Further, the velocity of the fluid is augmented by decreasing the thickness of the electric double layer and raising the strength of the electric field in the forwarding direction. Recently, Khan and Sasmal2 investigated the electroosmotic flow phenomenon for both Newtonian and viscoelastic fluids through a porous environment containing long micropores. An investigation on the coupled impact of pressure-driven flow and electrokinetics is carried out by Yuan et al.3 where they did not ignore the adverse pressure impact on electroosmotic flow. A mathematical model for electroosmotic transport of two immiscible fluids is developed and analyzed by Alyousef et al.4 in which they utilized the Ellis fluid model for the viscoelastic behavior of the considered fluid. Cilia beating is a natural mechanism of physiology that generates effective stroke and recovery stroke. Due to an effective stroke, water/fluid moves backward and cilia move forward. Due to recovery strokes, cilia further come back to their original position. These effective recovery strokes are rhythmic processes and generate metachronal waves. Cilia beating is a key mechanism of the respiratory system that cleans dust particles. In some physiological systems, cilia work as sensors and actuators. Some of the basic studies9 on cilia transport and its roles have been reported. From a natural perspective, it is an essential mechanism of the physiological system. Based on the extensive role of this mechanism, nowadays, there are challenging demands for artificial cilia and artificial magnetic cilia for the sensors and actuators10, for rotating machines to compute the frequency11, for fluid pumping12, and many more. Inspired by the natural and artificial roles of the cilia beating in fluid dynamics and biomedical sciences, most recently researchers have developed some mathematical models on the cilia-assisted rheological fluid flow19 and MHD fluid flow23 where they have discussed the effects of key parameters such as cilia length, the eccentricity of the metachronal waves, curvature of the flow geometry, magnetic field and rheological parameters on fluid pumping. In order to enhance the efficiency of microfluidic devices, different flow-causing mechanisms can be combined to achieve improved flow and heat transfer rates. The electroosmotic flows, triggered by ciliary motion can be helpful in the development of electromechanical devices at the microscale such as in micro and nanofluidic pumps, hemodialysis, cooling chips, microfabricated liquid devices, etc. Owing to the stunning efficiency of combined ciliary-actuated electroosmotic flows, recently few researchers have put forward their efforts in investigating the properties of flow driven by the combined phenomenon. Abdelsalam and Zaher24 studied the impact of electroosmotic forces on the movement of sperm in a ciliated cervical canal in which they employed the hyperbolic-tangent fluid to model the cervical fluid. Imran et al.25 investigated the heat transfer properties of Williamson fluid flow where the fluid flow is generated by electroosmosis and cilia beating in the micro-ciliated channel. Some more significant studies are reported by26, Ijaz et al.27, and Javed et al.28.Most substances acquire a net surface charge when they come across an aqueous polar medium. Due to the interaction between a charged surface and ionic species, the diffuse layer is generated. The ions in the diffuse layer experience an axial body force in the presence of an external force. Such a kind of motion is termed as electroosmosis which is considered as a very suitable mechanism for transportation purposes in microfluidic devices. In recent years, microfluidic devices have been triggered by the growing needs of biomedical engineering as well as energy systems. For the fabrication of microfluidics devices, there is a need to develop theoretical as well as experimental models of electroosmotic flow with heat transfer assisted by the various pumping mechanisms. Xuan et al.29 in a comparative study, it is the most suitable anti-freezing fluid, especially for use in domestic-level devices. Shojaeizadeh et al.30 performed an experiment to investigate the performance of a flat plate solar cell using different concentrations of PG in water. They observed that upon increasing the concentration of PG in water from 25 to 75%, an improvement in the efficiency of the solar cell occurs. Jugar and Crook31 compared the performance of PG and EG with their different concentrations in water and concluded that it is necessary to maintain a 50/50 concentration of water and antifreeze in order to keep a balance between heat transfer properties and antifreeze protection.Solar thermal technology consists of setups that collect the energy from the sun and convert it into heat energy. This heat energy is then stored by using water as a working fluid and utilized in various applications. The components of a solar heating system contain a source for collecting the solar energy, i.e. collector, a means of exchanging the heat using the flow of the fluid, namely the heat transfer circuit, the heat transferring fluid, and an energy storage system. In a climate, where there occur extreme temperature conditions in different parts of the year, the usage of anti-boiling and anti-freezing fluids is recommended in order to avoid damage to the solar system due to corrosion, overheating, and freezing. For this purpose, multiple types of anti-freezing agents are present, such as ethylene glycol (EG), tri-ethylene glycol, propylene glycol (PG), etc., which have the capability of protecting the solar system from freezing and rust. But these antifreeze agents in their pure form do not possess good thermal properties, which is the main requirement of a solar system. Therefore, a mixture of these anti-freezing liquids with water is utilized for this purpose. Out of different antifreeze/water solutions, the most commonly used solution is propylene glycol/water solution. Due to its low cost, high performance, low corrosivity, least toxicity, and environmentally friendly nature, as found by Heinonen et al.2), which is one of the oxides of titanium, was first discovered from ilmenite in 1791. Due to its high refractive index, and low chances of decolorization, it is mainly used in pigments32. However, other than its large-scale usage in pigments, TiO2 is also used in enamels, water purification, cosmetics, food items33, and in energy storage devices. Titanium dioxide is most beneficial when utilized in the form of small particles  due to its enhanced light absorption tendency, photocatalytic reduction, and high surface photoactivity. Titanium dioxide nanomaterials are employed as photocatalysts in water purification as they can effectively degrade the organic and inorganic pollutants present in wastewater35. Due to the semiconducting nature of titanium dioxide nanoparticles, they are widely utilized in electronic components, catalytical electrodes, and solar cells. Titanium dioxide nanoparticles are very preferable to be used in domestic-level devices due to their non-toxic nature36 and easy and cost-effective availability.Titanium dioxide  in the conventional heat transfer fluids. The extraordinarily high heat transfer ability of these new-generation fluids triggers their usage in pharmaceuticals, nano-scaled lubrication in rocket engines, cooling/heating of electronic devices, vehicle thermal management, solar cells, and many more. Such promising applications of nanofluids attracted the fluid dynamists to investigate such kinds of fluid and even more innovative fluids having more than one type of solid nanoparticles which are usually named as “hybrid nanofluids”. In an experimental study performed by Javidan and Moghadam38 an effective cooling for photovoltaic cells is tested by using SiC/water nanofluid as a cooling agent. Saleem et al.39 investigated the importance of thermophoresis and Brownian motion on the motion of water consisting of three different types of nanoparticles. Elnaqeeb et al.40 presented the importance of dual stretching and suction in the flow of water-based ternary-hybrid nanofluids by assuming multiple shapes and densities of nanoparticles. Animasaun et al.41 studied the motion of water, containing carbon nanotubes, copper, and graphene nanoparticles of different shapes, over stagnant moveable walls. They concluded that a minimum value of local skin friction coefficient can be achieved when a larger fraction of nanoparticles are used. Many other investigations focusing on the applications of multiple types of nanofluids are contributed by Rasool et al.42, Adnan and Ashraf43, Xiu et al.44, and Shah et al.45.The heat transfer mechanism offered by ordinary fluids such as ethylene glycol, water, engine oils, etc. is highly inefficient due to their innate poor conductivity. As already mentioned the heat transfer process is one of the major factors affecting the efficiency of solar cells but the addition of antifreeze in water lowers its heat transfer ability. In order to overcome the demands of energy-efficient devices in this modern era, a new class of fluid offering potentially improved heat transfer rates is required. It was Choi2 nanofluid can provide a sufficient rate of heat transfer along with the most important constraint of non-toxicity. So the aim here is to investigate the heat and mass transfer capability of propylene-glycol/water-based TiO2 nanofluid which is driven by the combined influence of cilia beating and the electroosmotic forces. Nevertheless, none of the studies have focused on the mathematical model of the cilia-assisted electroosmotic flow of nanofluids which could be applicable in various biomedical and energy fields. Based on research gaps, herein, a mathematical model is presented to study the propylene glycol + water-based TiO2 nanofluids flow driven by the electroosmosis and cilia beating in a microtube. The present results suggest that this model can be applied to the household solar system. This model is structured in the form of an introduction followed by mathematical formulation and numerical solutions. Thereafter, a thorough discussion of simulated results has been presented. In last, the concluding remarks of the present analysis have been listed.Due to the above-mentioned advantages of the propylene-glycol/water mixture and titanium dioxide nanoparticles, a combination of these two as a nanofluid can be adapted to work as heat transfer fluid in domestic-level devices. Propylene-glycol/water-based TiOc towards the right  solution-based titanium dioxide nanoparticles through a ciliated tube. A metachronal wave produced by the cumulative beating of cilia travels with the speed see Fig. . FurtherImposing no-slip conditions across the tube walls, the velocity of the fluid adjacent to the cilia is the same as the velocity of the cilia, therefore, the axial Using the relations given in Eqs. –2) in E in E2) i2) nanoparticles driven by the combined metachronal wave and the electroosmotic body forces. The considered nanofluid exhibits the Newtonian characteristics which are governed through the Navier–Stokes equation. The conservation equations for the nanofluid are formulated by employing the Buongiorno flow model along with the relation of thermal conductivity and viscosity proposed by Corcione’s model. The electric potential distribution within the fluid medium is governed by the linearized Poisson-Boltzmann equation and simplified under the Debye-Hückel approximation of low zeta potential. The heat transfer analysis is performed in the presence of nonlinear thermal radiation and Joule heating. The slip conditions for temperature and zero mass flux for the nanoparticle volume fraction are applied across tube walls.This analysis focuses on the flow phenomenon of PG/water solution-based titanium dioxide 21) in thThe Boltzmann distribution for the local ionic density of each ionic species is defined as:Substituting the Boltzmann relations in Eq. , we get,In order to linearize Eq. , we can E in Eq.  which reSubject to the appropriate boundary conditions defined belowEquation (30) can be solved directly to get an analytical expression for the potential field as:st kind.Here The suitable boundary conditions in the dimensionless form are prescribed as:The instantaneous volume flow rate in the laboratory frame is given asThe dimensionless time-averaged mean flow rate in the laboratory and moving frame is defined asSo we getThe linearized Poisson-Boltzmann solution is solved analytically and the resulting expression for electric potential is utilized in the momentum equation. The simplified set of governing equations is defined in Eqs. –26) is  is 26) iThe main purpose of this section is to outline the impact of the various physical factors on the flow phenomenon of propylene-based titanium dioxide nanofluid through graphical results. The nanoparticles of an average diameter of about 10 nm are dispersed at an initial temperature of 303 K. The fluid flow pattern is visualized by plotting the contour graphs for stream function. Graphical results are prepared by choosing the direction of the applied electric field in such a way that assists the flow of the fluid generated by the beating of the cilia. However, the effect of removing the electric field and reversing the direction of the electric field is also observed. From the mathematical point of view, negative values of the electroosmotic velocity parameter represent the forwarding direction electric field and positive values characterize the opposing electric field. A volume fraction of up to 0.06 vol% of titanium dioxide nanoparticles is scattered in the PG + water solution. The thermophysical attributes of the base solution and nanoparticles are calculated at 303 K and are listed in Table This subsection is devoted to facilitating an insight into the influence of various involved on the velocity distribution of PG + water solution base titanium dioxide nanofluid. The effect of the cilia length parameter on the fluid velocity is characterized in Fig. The trapping phenomenon is one of the key features associated with the flows following the pattern of peristaltic pumping. In this process, few streamlines under special circumstances enclose a quantity of the fluid known as trapped bolus which is carried along with the metachronal wave. The area enclosed by the trapping bolus and its shape is mainly affected by involved physical parameters. Therefore, in Figs. The alteration in the temperature subject to variation in different embedded parameters is displayed in Figs. The non-dimensional Nusselt number is expressed as:Figures Physically a rise in the length of the cilia corresponds to an increase in the amplitude of the metachronal wave as well as in its wavelength, therefore, the fluid velocity is boosted for larger entclass1pt{minimaentclass1pt{minimaFor growth in the radiation parameter, the process of conductive heat transfer from the fluid medium is boosted which in turn reduces the temperature profile See Fig. . The JouNusselt number quantifies the relative measure of heat transfer by convection as compared to conductive heat transfer. It can be concluded from Figs. See Fig. . The resPropylene glycol and water-based Titania nanofluid is the most suitable heat transfer fluid in the household solar device which enhances heat transfer capability with the reduction of fluid temperature.The application of the electric field along the positive axial direction boosts the fluid velocity which results in the rapid removal of the heat from the system.The length of cilia involved in generating the fluid motion strongly influence the velocity, temperature, and trapping phenomenon and it also boosts the heat transfer tendency of the fluidIncreasing the thermal radiation parameter results in the reduction of fluid temperature.Herein, a theoretical investigation has been conducted to study the heat transfer characteristics of 50:50 PG + water -based ionic solution whose motion is driven by the combined effects of electroosmotic body forces and the beating of the cilia. In presence of nonlinear thermal radiation and Joule heating, a nonlinear coupled system of governing equations is simulated by mathematical software Maple 17. The significant findings of the current analysis are listed as:


Virtual network embedding (VNE), as the key challenge of network resource management technology, lies in the contradiction between online embedding decision and pursuing long-term average revenue goals. Most of the previous work ignored the dynamics in Virtual Network (VN) modeling, or could not automatically detect the complex and time-varying network state to provide a reasonable network embedding scheme. In view of this, we model a network embedding framework where the topology and resource allocation change dynamically with the number of network users and workload, and then introduce a deep reinforcement learning method to solve the VNE problem. Further, a dynamic virtual network embedding algorithm based on Deep Reinforcement Learning (DRL), named DVNE-DRL, is proposed. In DVNE-DRL, VNE is modeled as a Markov Decision Process (MDP), and then deep learning is introduced to perceive the current network state through historical data and embedded knowledge, while utilizing reinforcement learning decision-making capabilities to implement the network embedding process. In addition, we improve the method of feature extraction and matrix optimization, and consider the characteristics of virtual network and physical network together to alleviate the problem of redundancy and slow convergence. The simulation results show that compared with the existing advanced algorithms, the acceptance rate and average revenue of DVNE-DRL are increased by about 25% and 35%, respectively. Network virtualization can decouple network services from their physical network hardware, and allow network users to program their own network services. Through network virtualization technology, traditional network providers can be divided into two roles: service providers and physical network providers. The former's task is to create customized virtual networks (VNS) to provide end-to-end network services to users, while the latter mainly maintains infrastructure provider (InP) devices so that service providers can adopt them to host their services at an acceptable business cost6. It turns out that good coordination between these two roles can improve the practicality and commercial value of physical network devices. The application of network virtualization technology depends on the algorithms that can instantiate the virtual network on the infrastructure to optimize the layout of service-related indicators. This algorithm is often referred to as "virtual network embedding (VNE)"/"virtual network mapping (VNM)" algorithm. VNE solves how to provide virtual network request (VNR) and allocate physical network nodes and link resources for them reasonably and efficiently. Virtual network requests (VNRs) usually contain multiple constraints such as node attributes and link attributes , request admission, and dynamic requirements. Therefore, if all the above network constraints are taken into account, the VNE problem is going to be a very difficult problem. It has been proved that the solution process of VNE is also NP-hard even if only node and link constraints are considered, which means that accurate solutions of VNE problems cannot be obtained in the actual complex network environment8.In modern society, with the increasing number of users and various types of network services, the current Internet architecture and management methods are facing great pressure, so many promising network management technologies emerge. Network virtualization, as one of the key technologies of the next generation Internet, aims to overcome the resistance caused by the current Internet's response to changes in network structureNeglecting the dynamic changes of users in the process of network service business, including changes in the number of user resource requirements and network topology corresponding to business types.Manually develop a set of rules and assumptions. Although the model and constraint rules are simplified, it is often not possible to automatically detect complex and time-varying network states to provide the most reasonable network embedding scheme for the current network state.At present, in order to reduce computational complexity and running time, virtual network embedding problems usually add assumptions or simplify constraints in a heuristic way to reduce solution space and obtain suboptimal solutions within acceptable complexity. However, traditional virtual network solutions often have the following drawbacks:11. In particular, deep reinforcement learning, as a widely used algorithm in machine learning, integrates the powerful understanding ability of deep learning in perceptual problems and the decision-making ability of reinforcement learning, demonstrating great potential in handling complex tasks (such as Go12) or complex control tasks (such as autonomous driving13). For the virtual network embedding problem in this article, as shown in Fig. In recent years, machine learning algorithms have made exciting new achievements in the fields of big data, machine learning, and artificial intelligence, especially in natural language understanding and object detection. Machine learning algorithms can collect a large amount of data within a period of time for processing, and automatically learn statistical information from the data, so as to make classification or predictionWe propose a new dynamic network embedding framework, in which the virtual network topology and resource requirements change dynamically with the workload and connection form in different time periods, which can better meet the more actual network state of network users.We analyze the feature relationship between virtual network and physical network, extract effective network feature information as deep reinforcement learning training sample data, reduce RLA training redundancy and improve convergence speed.We establish a DRL model based on solving VNE problems, and focus on designing corresponding reward and punishment functions and information feedback mechanisms to improve mapping efficiency and reduce the average cost of network embedding.We design and implement a dynamic virtualization algorithm based on deep reinforcement learning strategy network (DVNE-DRL), and test the performance of the algorithm by comparing with the three algorithms through simulation experiments.In view of the above analysis, this article introduces deep reinforcement learning into the virtual network embedding problem in order to dynamically optimize the virtual network mapping process. We focus on deep reinforcement learning methods in machine learning and discuss how reinforcement learning agents (RLA) can be used to detect real-time network state and enable dynamic virtual network mapping. We first divide the network request data into a training set and a test set for training a deep reinforcement learning agent and evaluating its performance, respectively. Then, an artificial neural network called policy network is designed to observe the state of the physical network and output the node mapping results, while using policy gradients to train the historical network request data through backpropagation. The exploration strategy is used in the training phase to find a better solution, while the greedy strategy is used in the evaluation phase to fully evaluate the effectiveness of the agent. Finally, this article proposes a dynamic virtual network embedding/mapping algorithm DVNE-DRL based on reinforcement learning, which can use historical network request data to obtain mapping knowledge and apply it to deep reinforcement learning based on policy network, so as to efficiently solve the virtual network embedding problem in this article. In summary, the main work of this article is as follows:Simulation results show that RLA can extract knowledge from historical data and extend it to incoming requests. In addition, by strengthening the interaction between the learning agent and the environment, and using the reward and punishment mechanism to make itself iterative learning, the virtual network embedding process is automatically optimized. The proposed DVNE-DRL algorithm is significantly superior to superior to some existing new virtual network mapping algorithms in terms of long-term average network revenue and acceptance rate.The remainder of this article is structured as follows: Section "8. In view of this, many researchers have designed different styles of embedding scenes, and thus proposed corresponding VNE algorithms in recent years. There are many different division rules for the classification of virtual network embedding algorithms. For example, according to the accuracy of the embedding result, it can be divided into exact solution algorithms and heuristic/meta-heuristic algorithms. Among them, the exact solution algorithm can find the optimal solution within a certain time range. When the scale of the problem is large, the application of the exact solution algorithm usually has two purposes: provide a feasible solution to the problems and to provide an initial solution for the heuristic method. For example, Liu14 et al. reduced the process of node embedding and link embedding to a discrete nonlinear combinatorial optimization problem, proposed a new exact deembedding method, and established a mathematical description of the relationship between node embedding and link embedding. Most of the heuristic/meta-heuristic algorithm literature focuses on the study of related natural body algorithms. For example, Song et al.16 designed a single-stage dual heuristic particleswarm optimization algorithm to solve VNE, aiming at coordinating node embedding and link embedding. Heuristics play an active role in certain social applications and technological contexts. However, the analysis shows that traditional VNE solutions have several similar shortcomings. More importantly, the dynamic characteristic of VNE is often ignored during embedding, such as resource allocation of virtual nodes and links, virtual topology, number of physical network resources, and network embedding process.The VNE problem mentioned above is a typical NP-hard problem, which means that only an approximate optimal solution can be obtained through the correlation design algorithm17 et al. proposed a fuzzy based multi-criteria decision making technique, using membership function of node parameters to prepare node embeddings, and verifies the proposed strategy under dynamic physical infrastructure conditions. Minardi18 et al. proposed a hybrid binary linear programming (MBLP) formula for the dynamic topology-aware VNE (DTA-VNE) algorithm, in which dynamic embedding is planned for each virtual network request (VNR) given prior information about the evolution of the network over time. Xiao et al.19 proposed a dynamic resource requirement prediction algorithm based on RBF incremental design, which uses the improved RBF to predict user resource demand and real distributes resources according to the predicted results to reduce resource allocation redundancy. Thakur et al.20 established a multi-domain SDN network VNE model based on irregular cell learning automata (ICLA), extended VDN-CLA by considering dynamic traffic migration, and realized resource optimal routing to improve throughput and reduce end-to-end latency. He et al.21 used spectral clustering to extract physical network features to distinguish the dynamic regions of interest and find embedding regions with energy-saving potential of virtual networks.According to whether the user resource requirements change dynamically in the embedding process, it can be divided into static virtual network embedding algorithm and dynamic virtual network embedding algorithm. Dynamic VNEs have higher complexity and uncertainty than static VNEs. Generally, the dynamism of a virtual network includes the following points: the dynamism of the underlying physical network, the dynamism of virtual network requests, and the dynamism of the arrival and departure of virtual network events during the network service process. Thiruvenkadam24. Practice has proven that RL has superior decision-making ability due to the effective interaction between learning agents and the environment. Generally, the machine learning algorithm follows the overall design of a time line, in which at each time step t, the agent interacts with the environment to obtain a new environment state st, then takes corresponding candidate actions according to the environment state, and finally transfers the environment state to the lower st + 1. At present, in solving VNE problems with machine learning, Lim et al.25 proposed a layered cooperative multi-agent reinforcement learning algorithm to optimize the VNE problem by maximizing the average benefit, minimizing the average cost, and increasing the request acceptance rate. Yuan et al.26 proposed a VNE algorithm based on RL model and found the corresponding VNE embedding method through RL proxy. Yao et al.27 proposed a VNE algorithm based on single-layer policy network. The RL agent collects the historical embedding data of the virtual network and optimizes the VNE embedding strategy using the policy gradient descent method. The VNE algorithm proposed by Yao et al.28 and Dolati et al.29 combines deep learning (DL) and RL, which also provides some inspirations for solving VNE problems. At present, VNE solutions based on machine learning mainly adopt DL, RL or graph theory32. Among, RL can connect and map environments and behaviors to maximize the functional value of intelligent systems. In RL agent learning, the environment evaluates the quality of the current action through feedback rather than directly determining which action the reinforcement learning system (RLS) should take. In practical applications, the external environment is usually complex and difficult to form significant information characteristics, that is, the RL agent provides little information, which also leads to the need for RLS to learn from their own experience to complete the target optimization. In view of the above mentioned, the VNE problem in this article also has the similar problems mentioned above, such as the complex and changeable network environment and insufficient information. Therefore, deep reinforcement learning is gradually beginning to play an important role33 and has become a popular mainstream method to solve the VNE problem.In most previous research work, physical network information and virtual network embedding knowledge hidden in historical network request data are often ignored. However, in practice, the historical virtual network requests can reflect the time distribution and resource demand characteristics of the future network. In recent years, some ideas of machine learning algorithms have been introduced into the design of virtual network embedding algorithms, and good results have been achievedVirtual network embedding is the process of allocating corresponding physical resources to logical networks with resource requirements on shared physical networks. The shared physical network can be abstracted as a weighted undirected graph, marked as entclass1pt{minimaAs in the previous study, the VNR embedding process is divided into node embedding and link embedding stages. Since VNE is a NP-hard problem, according to different computing models and embedding strategies, various available embedding schemes can be generated to meet the virtual request network generated by Internet users. Figure As shown in Fig. We assume that VNRs arrive successively on the time axis. Whenever a new VNR arrives, the network provider will decide to accept or reject it according to the relevant attribute constraints. In reality, network providers usually maximize their revenue and benefits by effectively utilizing limited physical resources. In view of this, we define network revenue as:Generally, changes in the number of network users will lead to changes in the topology of the virtual network, and fluctuations in business workload will affect the configuration of virtual network resources. The virtual network whose structure configuration or resource configuration changes with time is called dynamic virtual network, and the embedding process is called dynamic VNE. As shown in Fig. Figure DRL combines the advantages of deep learning and reinforcement learning, in which the agent can be well trained in the policy network to obtain better dynamic VNE results. We will introduce the embedding principle and process of DVNE-DRL algorithm, including the network feature extraction, DRL policy network, reward function for VNE, and pseudo-code description of DVNE-DRL algorithm.The virtual network embedding problem is actually to find a physical network that meets the node and link constraints for each incoming virtual network request. We can model the network embedding process as a Markov decision process, and then use reinforcement learning to solve it. The specific description process is shown in Fig. In general, a Markov decision process can be defined as a quintuple entclass1pt{minimav. Then the state and state space can be expressed as formula  to form a feature matrix for environmental agent training. A deep understanding of the feature relationship between the two is essential to fundamentally understand the reinforcement learning agent to effectively map its state. In a real network embedding environment, physical nodes and virtual nodes have many characteristics, such as CPU resources, location, connection bandwidth and degree. There are also many feature points used to describe the relationship between them. We have extracted the following five features:(1) CPU computing power gap (GP_CPU)The CPU of a physical node is the most important feature of a embedding node. If the computing resources of the physical node are sufficient, the node resource request in VNR will be mapped to the physical node with high probability. When the physical node has less computing resources, the virtual node will give priority to other physical nodes with sufficient computing resources, so as to avoid bottleneck nodes and improve the load balancing performance of the entire network. Therefore, the CPU computing power gap between virtual nodes and physical nodes is the most important and decisive feature.(2) Distance between nodesIn the process of virtual node embedding, selecting nodes with reasonable geographical locations for embedding can greatly reduce the number of forwarding nodes in link embedding, thereby reducing link bandwidth occupancy and utilizing network resources more reasonably. Therefore, the distance feature extraction between nodes is an important factor to measure the success rate of embedding.(3) Degree gap (DG_NN)The degree of a physical node represents the degree to which the physical node is connected to other physical nodes. Nodes with better connectivity will be preferentially selected as embedding nodes, which is beneficial to improve the success rate of subsequent link embedding and the network acceptance rate on the one hand. On the other hand, it can effectively prevent the occurrence of blocking in the physical network.(4) Sum of bandwidth gap (GP_BW)The bandwidth connected to the physical nodes and the connectivity between the nodes are described from the perspective of bandwidth. The richer the bandwidth resources, the greater the connection probability between the virtual node and the physical node, that is, the more ideal the link embedding option.(5) Sum of the distance between the mapped node and the node (DS_MNN)The sum of the distances between the mapped node and the node is the sum of the distances from other nodes in the virtual network request to the node before the node request is mapped. This attribute is zero when the first node in the request is mapped. When the second node is mapped, the attribute is the distance from the mapped node to this node. Similarly, when the next request node is mapped, the attribute is the distance from all other nodes that have been mapped to this node. This attribute describes the total distance between the mapped nodes, so the smaller the attribute is, the better the node should be selected for the embedding request. That is, a combination of nodes with a smaller number of hops between nodes can effectively save link resources of the physical network. In other words, extracting the feature of the sum of the distance between the virtual node that has been mapped on the physical node and the current virtual node is very important for reducing the embedding cost.In fact, physical nodes have many more characteristics than those listed above. The physical network information increases as the features increase, so the learning agent is more capable. But extracting too many features increases the computational complexity. Use the extracted five node features to describe the node state, and then normalize the feature values to 0–1 to remove the peculiar sample data to get X'.k denote the feature vector of the kth physical node. All the features are spliced together, and the attribute matrix A of the node can be obtained. We train the learning agent using the feature vectors as input to the policy network.Let Sk are constructed into a feature matrix for strengthening learning input.All the above physical nodes AThe state space of the VNE problem is a continuous value, so this article constructs a node embedding policy network, introduces a policy-based method in reinforcement learning, and uses an agent to optimize the entire training model. The policy network includes input layer, convolutional layer, softmax layer, filter layer and output layer as shown in Fig. h represents the kth output of the softmax, a is the weight vector, and b is the bias term. In the softmax layer, k is converted into the probability of each physical node being selected, and a high probability node is selected for embedding to obtain a better embedding result. The formula , and the network revenue and cost function are respectively defined as the following formulas  and 11)11), so wNetwork load balancing can reduce the occurrence of bottleneck nodes, thereby increasing the network acceptance rate. To balance the workload among the physical network nodes, learning agents are encouraged to choose physical nodes with more node resources. The selection of the node embedding scheme directly affects the later link embedding. Link load balancing is closely related to the user’s information transfer efficiency. In order to avoid link congestion, a link with rich resources should also be selected for embedding. Therefore, we use the above two links. Influencing factors are added to the reward function:ck is the decay factor, which shrinks a little at each time step, which ensures that frequently selected actions can be kept for a period of time, while unselected actions will gradually decay to 0. The above approach filters out actions that are not frequently chosen, thereby eliminating the danger of training falling into a suboptimal state.During the training process, the policy may fall into a sub-optimal state, so we should avoid repeatedly generating the same action embedding policy, and encourage the policy to transfer to other actions that are not selected. Therefore, we want to set an eligibility check at a certain period to ensure that the current training does not get stuck in repeated steps. To this end, this factor should also be considered in the reward function design:In summary, the DVNE-DRL algorithm uses the trained policy network to complete the entire embedding process dynamically and outputs the global optimal virtual network embedding scheme. Compared to a custom set of rules and assumptions for manual rules, simple mathematical calculations lead to embedding schemes. DVNE-DRL interacts with the environment and uses the reward learning optimal embedding mechanism for dynamic feedback, which can effectively discover the representation of the physical network and the virtual network. The relationship between requests is detected, and the dynamic changes of the virtual network over time are detected to efficiently complete the virtual network embedding. Algorithm I and algorithm dichotomy show the training and testing process of the network. Algorithm III shows the overall processing process of deep reinforcement learning in online network embedding. The specific pseudocode is as follows:In this section, we analyze the time complexity of the DVNE-DRL algorithm. We know that the computational complexity of a deep neural network algorithm is defined as the number of operations of the model. The number of operations of a deep neural network with fully connected layers is determined by the number of computing units of the network model, including the input dimension, the number of neurons in each hidden layer, the output layer dimension, and the number of layers of the neural network. In the VNE scenario of this paper, assuming that the dimension of the input adjacency matrix is (1) Acceptance rateThe acceptance rate represents the comparison between the number of VNRs successfully embedded and the total number of VNRs arriving at time t = 0 to time T, which is defined as formula :24\docum(2) Network average costThe average network cost represents the resource consumption of successfully embedded VNR events, which mainly includes node resources and link embedding resources. It can be defined as the ratio of the total resources allocated to VNRs to the total number of VNRs arriving within t = 0 to T as shown in formula :25\docum(3) Link pressureThe link pressure is a reflection of bandwidth consumption, which is expressed as the ratio of the physical bandwidth resources occupied by the successfully embedded VNR virtual link to the initial resources of the physical link, as shown in formula :26\docum(4) Network revenueThe network revenue reflects the operating income of the network provider, that is, the ratio between the profit obtained by the VNR successfully embedded and the total service time from t = 0 to T, which can be defined as formula :27\docum35 tool is used to generate the physical network and VNRs topology. Then, the feature information of the network topology is extracted and input into the reinforcement learning framework TensorFlow2.037 built in Anaconda3 environment for simulation training and result analysis. We first build a physical network topology with 100 nodes and 800 links as an abstract form of the underlying physical network. The number of physical node resources and link resources follows the standard Poisson distribution of 50–100. Secondly, in the VNR event, the topology is the resource attribute of randomly created virtual nodes and virtual links. The number of virtual nodes is evenly distributed between 2 and 20, and the probability of connection between nodes is 0.8. The number of virtual node resource requirements and link bandwidth resource requirements is evenly distributed between 1 and 50. All node position constraints D of VNR are constant. In addition, it is assumed that the number of VNRs arriving according to the time axis follows a Poisson distribution with an average of 5, and the life of each VNR follows an exponential distribution with an average life of 500 time units. Finally, we tested the resource utilization of 1000 VNR events with different arrival time and service time within 8000 time units, and carried out the index evaluation record and analysis of the results as shown in Section "In this article, GT-ITMFrom the above Figs. As shown in Fig. 38, D-ViNE38, GRC-VNE39 and MCST-VNE40 can almost cover most perspectives of existing algorithms for comparison. The description of each algorithm is shown in Table To show the performance of DVNE-DRL proposed in this article, we selected R-ViNEAs shown in Fig. As shown in Fig. As shown in Fig. As shown in Fig. In view of the fact that most of the previous work ignored the dynamic nature of virtual network modeling, or could not automatically detect complex time-varying network states to provide a reasonable network embedding scheme, this article first proposed a new dynamic virtual network embedding framework, in which the user's resource requirements and the business network topology change dynamically over time to meet the actual situation of more real network resources. Then, a dynamic virtual network embedding algorithm DVNE-DRL based on deep reinforcement learning is proposed, which improves the feature extraction and matrix optimization methods of DRL and considers the characteristics of both virtual network and physical network. Finally, the performance of DVNE-DRL algorithm is verified by simulation. DVNE-DRL algorithm combines the strong understanding ability of deep learning and the decision-making ability of reinforcement learning, perceives and understands the current network information through historical data and embedded knowledge, and uses the decision-making ability of reinforcement learning to select the appropriate embedding method for the new VNR. We adopt four algorithms, MCST-VNE, GRC-VNE, D-ViNE and R-ViNE, which tend to solve the embedding/mapping problem with different strategies, and illustrate the performance of DVNE-DRL from four performance evaluation indicators: admission rate, average cost, link pressure and long-term average revenue. The simulation results show that the proposed DVNE-DRL algorithm has good performance in the evaluation index.The future research of virtual network embedding algorithm mainly focuses on the following two aspects: (1) analyze the dynamic resource requirements of users, and refine the design of dynamic virtual network embedding framework. (2) Based on historical operational data and dynamic requirements of different dedicated services, design virtual network embedding algorithms with higher efficiency based on deep reinforcement learning to better meet the dynamic nature of virtual network embedding.


Accurate and robust camera pose estimation is essential for high-level applications such as augmented reality and autonomous driving. Despite the development of global feature-based camera pose regression methods and local feature-based matching guided pose estimation methods, challenging conditions, such as illumination changes and viewpoint changes, as well as inaccurate keypoint localization, continue to affect the performance of camera pose estimation. In this paper, we propose a novel relative camera pose regression framework that uses global features with rotation consistency and local features with rotation invariance. First, we apply a multi-level deformable network to detect and describe local features, which can learn appearances and gradient information sensitive to rotation variants. Second, we process the detection and description processes using the results from pixel correspondences of the input image pairs. Finally, we propose a novel loss that combines relative regression loss and absolute regression loss, incorporating global features with geometric constraints to optimize the pose estimation model. Our extensive experiments report satisfactory accuracy on the 7Scenes dataset with an average mean translation error of 0.18 m and a rotation error of 7.44° using image pairs as input. Ablation studies were also conducted to verify the effectiveness of the proposed method in the tasks of pose estimation and image matching using the 7Scenes and HPatches datasets. In recent years, the development of deep learning and computer vision technologies ,2,3 has Current image-based camera pose estimation methods are greatly affected by challenging scenes, especially illumination changes, viewpoint changes, etc. These problems lead to inaccurate image-based pose estimation. End-to-end methods based on features and descriptors, such as LIFT , L2-Net To address the aforementioned issues and leverage the geometric constraints between global feature image pairs, the model design is based on a combination of the deformable network method ,15  and inaccurate keypoint positioning, leading to more robust and accurate camera pose estimation;We propose a novel loss that integrates the detection and description loss based on local features with the relative pose loss function based on global features. This novel loss function enhances the accuracy of camera pose estimation by jointly optimizing local and global feature representations, leading to improved performance compared to existing methods;The proposed method is evaluated on benchmark datasets, including HPatches and 7Scenes. The HPatches dataset provides diverse image patches for illumination, viewpoint, and scale evaluation, while the 7Scenes dataset offers realistic indoor sequences for accuracy and stability testing. The experimental results verify the effectiveness of the proposed method for image-matching tasks and camera pose estimation tasks, and demonstrate its superiority compared to state-of-the-art methods.The main contributions of the paper are as follows:The remainder of this paper is organized as follows. According to the processing order of the descriptor and detector in the feature matching method, sparse local feature matching consists of the following branches: (1) detect-then-describe approaches that include keypoint detection stages with robust and efficient handcrafted detectors  , SUSAN . KinectFusion provides the camera’s extrinsic parameters in the 7Scenes dataset.The pinhole camera model projects objects from the world coordinate system to the 2D pixel plane through the camera plane. In this model, Since the same point in the real world has the same coordinates in the world coordinate system, it is possible to obtain the world coordinates from the pixel coordinates in the first image through coordinate transformation. Then, the pixel coordinates of the same point in the second image can be obtained from its world coordinates. This allows us to obtain pixel correspondences between the image pairs.This section presents the framework of the proposed method, which is an end-to-end camera pose estimation network based on relative pixel correspondences and the multi-level deformable network. We also introduce our designed loss function, which includes the global features and local description-detection features loss. To enhance the modeling ability of convolutional neural networks with fixed geometric structures, a deformable convolution is introduced. It learns offset locations of spatial samples in target tasks ,15 throuThe deformable network has the ability to densely estimate local changes in the images and model the transformation of CNNs by learning the offsets added in the spatial sampling locations. The framework of the deformable network is shown in R to sample the input feature map x in a dense and local manner [R. The output of a single location, y can be computed as follows:The goal of the deformable convolutional network (DCN)  is to iml manner . The locDCN enhances the regular convolution by additionally learning the sampling offset  {Δpk|k=1ectively .Obtaining features from low-resolution feature maps may limit positioning accuracy. Restoring spatial resolution has proven effective in improving positioning accuracy, such as using other feature decoders  or emplSpecifically, the method utilizes a feature hierarchical structure composed of several levels of The advantages of multi-level detection are embodied in three aspects. First, it uses a multi-level detection method, which conforms to the classic space theory  because After performing feature extraction through the aforementioned multi-level deformable network, the subsequent multi-layer perceptron outputs the estimated posture location and rotation of the 3D feature through the fully connected layer. Since the network operates on input image pairs, a group of identical networks is copied to form a set of parallel networks that accept input image pairs. Finally, the network output contains a set of image pairs. The pose, feature map, and score feature map of the image are used in the subsequent split calculation process. Among them, the output of the last convolutional layer in the multi-level network is a feature map, and the weighted sum of the score map is transformed into a score feature map.The specific calculation process is as follows: first, obtain the feature maps of the network conv1, conv3, and conv8 layers as input. Then, normalize the feature map by dividing each value by the largest value in the feature map. Next, fill the feature map with mirroring and perform two-dimensional average pooling with a step size of 1 and a pooling area size of 5 to obtain a feature map with the same size as the input. Subtract the normalized feature map and the pooled feature map from the average value of the pooled feature map to obtain the maximum scores on the channel and local levels, respectively. The maximum score multiplied by the maximum value is bilinearly interpolated to the original input image size to obtain the score feature map corresponding to the feature map; the weight coefficient is multiplied and the final score feature map is obtained.The last three layers of L2-Net, conv6, conv7, and conv8, are replaced by DCN. To calculate multi-level features, conv1, conv3, and conv8 are selected. The weighted proportion in Equation , or theon  make the detection map sparse by suppressing the non-maximum value of the space part. Selecting the detected point Among them, In order to consider both the on-channel and local scores, all feature maps are multiplied and maximized to obtain a score map:The score is obtained by performing image-level normalization on the pixel point The schematic of the detection loss is shown in In order to use a single neural network to train the detection and description process at the same time, it is necessary to use a loss function that optimizes the detection and description while targeting local features, so that the key points in the detection process are repeatable in viewpoint changes and illumination changes. During the description process, each descriptor is intentionally made different from each other to avoid mismatches. The ternary boundary ranking loss is used to optimize the descriptors while maintaining their distinctiveness. To increase the optimization of the repeatability of the detector, the loss of the detection item For global features, in addition to the loss function of learnable weights that can constrain geometric information, MapNet  proposesi and j represent the index values of a pair of image pairs, Among them, The 7Scenes dataset  is releaThe HPatches dataset  includesBatch size of 4. This choice balances computational efficiency and memory usage;Number of matching correspondences of 128. This value is commonly used in related literature for keypoint matching tasks ;Training iterations of 1000. This value was determined based on empirical experimentation to achieve optimal convergence and performance;Balancing factors between detection loss and description loss, absolute loss and relative loss, and local loss and global loss, all set to 1. These values were chosen to give equal importance to different components of the loss function, which could also achieve better performance according to the experiments;Initial learning rate of The experiment was implemented with PyTorch  on NVIDIWe use a batch size of 4, with 128 matching correspondences. The balancing factors between the detection loss and description loss, the absolute loss and the relative loss, and the local loss and global loss are all set to 1. The training iterations are set to 1000, with an initial learning rate of the Adam  solver fGiven the index gap of 10 and a total of 2 images, we can obtain a set of image pairs from the 7Scenes dataset, which includes depth images, color images, and camera intrinsic and extrinsic parameters. Through image processing and epipolar geometry, the pixel correspondences of the image pairs could be computed.Taking the image pair with an index gap of 400 as an example, the process is illustrated in We evaluate the performance of local descriptors on the HPatches dataset using the following metrics: (1) keypoint repeatability It is essential to obtain robust and accurate image-matching results efficiently in challenging environmental conditions. The most popular image-matching methods could be divided into sparse matching (including detection and description processes) and dense matching (including description processes). In order to verify the performance of our proposed network on the pose estimation task, we conducted experiments and compared the results with several competing methods that use multiple images or videos as input on the 7Scenes dataset. VidLoc , MapNet Furthermore, To evaluate the effectiveness of each module used in the network, and to quickly conduct the experiment, we select the heads scene of the 7Scenes dataset, which has the smallest number of images, and the results from the heads scene could represent the performance of the 7Scenes dataset. The ablation study experiment was conducted for 100 iterations with a learning rate of In this paper, we propose a regression-based camera pose estimation framework that consists of a multi-level deformable network for feature extraction and a loss function that fuses multi-view features with both local rotation invariance and global rotation consistency. To address challenges such as changing environments and motion blur in datasets, we design the feature extraction network and multi-level network to be robust and accurate. Our experiments on the 7Scenes and HPatches datasets show that our proposed network outperforms competing methods in accuracy and robustness. We demonstrate that correspondences produced by camera sensors, including RGB and depth cameras, can outperform local detection and description optimization integrated with global feature supervision, which leverages the rotation consistency of global features and the rotation invariance of local features. Moreover, the features captured within global and local supervision are also suitable for image matching. In future work, we will apply the learnable balancing factor to the loss to improve the model scalability and portability, and will try to add other common sensors, e.g., IMUs, to improve indoor localization performance and apply these methods to robot navigation and planning to enable smarter living.


The inter-teardrops line (IT line) and the upper rim of the obturator foramen (UOF) had smaller angles with the IFH line. The bi-ischial line (BI line) was relatively inaccurate in measurements. We recommend using the IT line as the TAP when the lower boundary of the teardrops is clear and the shapes of the teardrops on both sides of the pelvis are symmetrical. When there is no deformation of the obturator foramen on pelvic AP radiographs, the UOF is also a good choice for the TAP. We do not recommend the BI line as the TAP.Currently, orthopedic surgeons mainly use the inter-teardrop line (IT-line) as the transverse mechanical axis of the pelvis (TAP) for postoperative evaluation of total hip arthroplasty (THA). However, the teardrop is often unclear in the pelvis anteroposterior (AP) radiographs, which makes postoperative evaluation of THA difficult. In this study, we attempted to identify other clear and accurate axes for postoperative evaluation of THA. We calculated the mean and standard deviation of these angles and tested the significance of these angles using  Total hip arthroplasty (THA) is regarded as one of the most successful and cost-effective interventions in modern orthopedics ,2,3. TheThe transverse mechanical axis of the pelvis (TAP) can help physicians evaluate the pelvic inclination angle ,9, locatOrthopedic surgeons mainly use the inter-teardrops line (IT line) to represent the TAP ,25,26. TAlthough the IT line shows good accuracy as measuring the TAP, the teardrop or its lower edge is often not visible in pelvis AP radiographs. Clinically, which anatomical landmark should be used as an alternative of the teardrop remains inconclusive. The lack of a clear TAP creates difficulties for orthopedic surgeons to assess the postoperative condition of THA patients. Orthopedic surgeons sometimes use other TAPs for measurements, but there is no comprehensive research explaining the accuracy of these TAPs. We conducted this study to identify other clear and accurate axes to represent the TAP for postoperative evaluation and further development of rehabilitation plans for THA.We reviewed 120 pelvis AP radiographs from 1 November 2022 to 31 December 2022 at Taipei Medical University Shuang-Ho Hospital. In order to determine which TAP could best measure the position of the femoral head under normal circumstances, we excluded patients with obvious abnormalities or with acetabular implants, and this is because severe arthritis or artificial placement of acetabular implants may both cause changes to the hip rotation center. Our exclusion criteria included patients under the age of 20 (n = 9), images without clear teardrops (n = 94), images without completely presented iliac crests (n = 22), patients with acetabular implants (n = 36), patients with significant deformation of the anatomy of the pelvis or femoral head  (n = 15), and images where the obturator foramen was without clear boundaries. (n = 2). Due to the need to compare the relative positions between each TAP and the femoral head, and since the femoral head center is the hip rotation center under normal conditions, we set the reference axis as the inter-femoral-head-centers line (IFH line). The following five axes, the supracristal line (SC line), bi-ischial line (BI line), inter-teardrops line (IT line), and the upper and lower rim of the obturator foramen (UOF and LOF), were selected as candidates representing the TAP. The reference axis and the other five axes were drawn by connecting the corresponding anatomic landmarks on both sides of the pelvis. The IFH line was defined as the line connecting the femoral head centers. The center of the femoral head was located by drawing a circle that fits the femoral head. The SC line was defined as the line connecting the highest points of both the iliac crests. The BI line was defined as the line connecting the ischial tuberosities. The IT line was defined as the line connecting the lower edges of the teardrops. The UOF was defined as the line connecting the highest points of the obturator foramens. The LOF was defined as the line connecting the lowest points of the obturator foramens. It is worth mentioning that the exact upper border of the obturator foramen may be obscured by the bone in front. The measurer should carefully identify the true upper border of the obturator foramen based on the brightness variation of its border on the image in order to trace the UOF accurately. .Our self-developed program “PelvicAxis” was used to measure the included angles between the reference axis (the IFH line), and the pelvic axes . Since wt-test was used to compare whether the included angle between an axis and the reference axis was statistically significantly. If the TAP can accurately measure the position of the femoral head under normal conditions, then the included angle should not be significantly different from 0. To compare the measurement performance of the commonly used IT line with the other four TAPs, we conducted two sample t-tests to compare the mean of ∠RIT with ∠RSC, ∠RBI, ∠RUO, and ∠RLO, respectively. We also divided the sample into subgroups of different genders and age ranges for analysis. For outlier analysis, we visualize the overall dispersion of the data using a boxplot and define outliers based on the distribution shown in the plot. As each subject’s data point contains five angles and the degree of dispersion among the five angles varies, we select the two data points with the highest deviation for each TAP’s included angle as our final outliers, which means we have a total of 10 outliers. We removed the outliers, conducted another analysis on the overall data, and discussed the possible reasons for the occurrence of outliers in the discussion section. Reliability analysis was used to analyze interobserver and intraobserver reliability and the outcome was presented as the intraclass correlation coefficient (ICC). As we wanted to reflect the most accurate measurement situation, we used the raw measurement data without taking the absolute value to calculate the ICC. Data were analyzed using IBM Corp. Released 2010. IBM SPSS Statistics for Windows, Version 19.0. Armonk, NY: IBM Corp.Because our research primarily aimed to measure the deviations of the angles between TAPs and the reference axis, we took the absolute value of all measured values before calculating the mean and standard deviation of the angles. One-sample Overall, 94 (34.2%) radiographs had the problem of unclear teardrops, which was our main reason for exclusion. For the 36 excluded radiographs with acetabular implant, there were 13 (36%) radiographs without clear teardrops. For the 239 (=275 − 36) radiographs without acetabular implants, there were 81 (=94 − 13) (33.9%) radiographs without clear teardrops. Among all 275 radiographs, only 2 (1%) radiographs had the problem of unclear obturator foramen boundaries and such a situation did not appear on radiographs with acetabular implants.Our final analysis comprised 58 males and 62 females; their ages ranged from 20 to 96 years old. The average age of our subjects was 56.1 years old, and the standard deviation of our subjects’ age was 21.2 years old .We found that ∠RIT and ∠RUO had smaller means and standard deviations in the overall sample, different gender groups, and different age groups, indicating that the IT line and UOF were the two TAPs with higher precision. Moreover, the mean values of ∠RIT and ∠RUO did not show significant differences in results except for the elderly subgroup. ∠RBI had the largest means in the overall sample, different gender groups, and different age groups, indicating that BI line is the least precise among the 5 TAPs. The mean values of ∠RSC and ∠RLO fell between ∠RUO and ∠RBI. None of the mean values of the angles differed significantly from 0, indicating that the five TAPs are not perfectly parallel to the IFH line. In the outlier analysis, we found that the data distribution of RIT and RUO was the most concentrated. However, after removing some outliers, the mean values of each angle were still significantly different from 0. The ICC values of ∠RIT and ∠RUO were lower than that of other angles. Despite the lower reliability of these two angles, both still have a moderate level of reliability.The teardrop is recognized as the best landmark for measuring acetabular cup position ,25,26. TDespite its accuracy, the teardrop is often not clear, making it incompetent as a landmark. According to our data, 34.2% of pelvic AP radiographs cannot use the teardrop as a pelvic landmark. In addition, our clinical experience shows that the teardrop may be worn away during the THA operation, making it less effective as a landmark after surgery. In this regard, our data showed that radiographs with acetabular components had a slightly higher proportion of teardrops that are not clear compared with radiographs without acetabular components (36% versus 33.9%). It is important to find other alternative landmarks since more than 1/3 of patients who underwent THA cannot use teardrops as a landmark for postoperative evaluation.In our research, we found that the UOF is also a good pelvic landmark, probably because of its closeness to the teardrop. By definition, the lower rim of the teardrop is adjacent to the UOF . Massin The ICC of the measurements of ∠RIT and ∠RUO were lower compared with the other three angles in the assessment of intra- and interobserver reliability. We speculate that this was because these two angles were smaller, making the ICC of these two angles more sensitive to the measurement differences. Another possible reason for their lower reliability is that the lower edge of the teardrops and the upper edge of the obturator foramen are less distinct compared with the other three pelvic landmarks. Despite being less reliable than the other three angles, measurements of ∠RIT and ∠RUO still exhibit a moderate level of reliability.Identifying the causes of these outliers can help us clarify the conditions for applying each TAP. In As for the difference in the five included angles between the five TAPs and the reference axis, we suspect it is caused by image distortion, pelvic asymmetry, and the uneven protrusions on the pelvis landmark. Pelvic AP radiographs are susceptible to 3D variations of pelvic orientation such as pelvic tilt, obliquity, and rotation, resulting in image distortion ,35. PelvThere are significant differences in pelvic anatomy between males and females. These differences also exist in several anatomic landmarks related to TAP. Harris et al. found significant differences in the distance between the lateral border of the teardrop and the anteromedial insertion of the transverse acetabular ligament between the sexes . BombaciIn our study, there are slight differences in different age groups. Not many studies focused on the relationship between age and pelvic anatomy. In the study done by Boudriot et al., when using teardrops as the reference point to find the hip rotation center, the results of the group over 60 years old were significantly different from the other age groups . AlthougIn addition to the postoperative evaluation, we believe that the outcome of our study also has the potential to assist in the development of more appropriate physiotherapy. Physiotherapy after THA is crucial for the restoration of the patient’s functional outcome. It can help build hip abductor strength and improve mobility, gait speed, and cadence after THA ,41. The The clinical significance of this study lies in establishing the appropriate TAPs and their applicable conditions. Orthopedic surgeons were previously unsure which pelvic landmark to use as a reference point for drawing TAPs when the teardrops were unclear. Orthopedic surgeons may occasionally use TAPs other than the IT line for measurements, but there is currently no comprehensive research that elucidates the accuracy of these alternative TAPs. Our study clarified the deviation between each TAP and the IFH line and also identified the possible reasons for outliers in each axis measurement. Orthopedic surgeons can perform postoperative evaluations of LLD, hip rotation center, and pelvic inclination angle measurements in THA based on our recommendations regarding which TAP to use in which situation see .There were some limitations in our study. The patients we selected were not completely healthy patients, but patients without severe hip abnormalities on pelvic AP radiographs. Although the orthopedic diseases in these patients had not yet caused significant damage to the anatomy of the hip joint, they may still have some impact on the measurements. Additionally, our research on which axis is more representative of the TAP was based on the pelvis AP radiograph of patients without the acetabular component. However, we believe that the same axis will still be useful in patients after THA. Acetabular implants are installed in the hip joints, while the landmarks that make up the TAPs are located on the pelvis. Therefore, the presence of acetabular implants should not have a significant impact on the effectiveness of the TAPs.In conclusion, we recommend using the IT line as the TAP when the lower boundary of the teardrops is clear and the shapes of the teardrops on both sides of the pelvis are symmetrical. When there is no deformation of the obturator foramen on pelvic AP radiographs, the UOF is also a good choice for the TAP. If the aforementioned two axes are difficult to delineate, then the SC line and UOF will be the next consideration for the TAP. We do not recommend the BI line as the TAP.


One’s working memory process is a fundamental cognitive activity which often serves as an indicator of brain disease and cognitive impairment. In this research, the approach to evaluate working memory ability by means of electroencephalography (EEG) analysis was proposed. The result shows that the EEG signals of subjects share some characteristics when performing working memory tasks. Through correlation analysis, a working memory model describes the changes in EEG signals within alpha, beta and gamma waves, which shows an inverse tendency compared to Zen meditation. The working memory ability of subjects can be predicted using multi-linear support vector regression (SVR) with fuzzy C-mean (FCM) clustering and knowledge-based fuzzy support vector regression (FSVR), which reaches the mean square error of 0.6 in our collected data. The latter, designed based on the working memory model, achieves the best performance. The research provides the insight of the working memory process from the EEG aspect to become an example of cognitive function analysis and prediction. Cognition is an important part of human brain activity which affects our thinking and behavior, and cognitive impairment is often related to many brain diseases such as Alzheimer’s disease. Electroencephalography (EEG) researchers can acquire the signals of brain activity, so-called “brain waves”, for further analysis. Many brain states, such as emotion and cognitive load, have been discovered in previous research. A study in 2016 estimated the cognitive load using EEG connectivity measures . The claThe study of cognitive load has been covered in previous studies ,8. The bWorking memory processing is an important part of cognition which involves short-term memory and thinking. The evaluation of working memory ability has seldom been addressed in previous research. A study in 2020 predicted working memory ability based on EEG by functional data analysis . Least aTwo propositions for the working memory model are described in terms of EEG analysis.The FSVR approach is proposed to evaluate working memory ability based on EEG signals.In this research, we will focus on the entire evaluation of one’s working memory ability based on EEG analysis. The mechanism of working memory processing was discovered in terms of neurological aspects, looking further into the characteristics of EEG signals in different brain regions and states. On the other hand, the fuzzy support vector regression (FSVR) models are designed using the discovery from the mechanism of working memory processing and compared to other machine learning algorithms. The discussion of working memory processing from the EEG aspect will be covered in the whole article. The main contributions are as follows:The preparations of materials are demonstrated in this section. Dataset 1 was acquired with the 10-10 system Neuroscan device by the National Taiwan University Robotics Lab. We used this dataset as the main material to propose the working memory model and the algorithms. Dataset 2 is an open source dataset available since 2022 created by the University of Salford (UK), Aston University (UK) and University College Dublin (Ireland) . This daIn dataset 1, an experiment comprised 20 subjects, 17 males and 3 females, between the ages of 22 and 24 with Bachelor’s degrees as their minimum level of education. To ensure that their mental states were relaxed and without fatigue, the subjects were instructed to sleep sufficiently the previous night and they rested for about 10 min before the experiment. The electrodes were selected according to their corresponding brain areas, which are located in the prefrontal lobe (Fpz), frontal lobe , temporal lobe , parietal lobe , and the occipital lobe . These 10 electrodes fully cover the entire cerebrum, and the analysis of EEG features is separated among these regions.The main objective of the experiment was to measure the EEG signals of the subjects and the time spent in each task. The whole procedure was divided into three sessions. In session 1, the subjects were asked to stare at the whiteboard for 1 min and think of nothing. The data recorded in this session constituted the brain waves in resting state. In session 2, the subjects conducted the memory task with 8 numbers. In session 3, the subjects conducted the memory task with 12 tokens. The subjects could interact with a gamer interface and each session was conducted 3 times. In the memory task, the subjects were asked to find the pair of cards with the same numbers or tokens. If the cards with the same items were chosen, these two cards disappeared. If cards with different items were chosen, these remained on the screen. The more accurate the subjects remembered, the faster the task was completed. Eventually, the time consumption was defined as the cognitive performance. A picture of the task is shown in Z-score, which is the standard representation of cognitive ability and is the same as the Wechsler Adult Intelligence Scale. Since one’s working memory process is regarded as a part of human intelligence, one’s working memory performance was denoted by a Z-score as shown in Equation  is utilized to measure different types of memory . The CogThis section demonstrates the algorithms used in data processing and analysis. Using feature extraction, the EEG signals are integrated into the vector of features which includes the characteristics of working memory processing. The knowledge-based fuzzy SVR (FSVR) will be introduced, and the multi-linear SVR with fuzzy C-mean (FCM) clustering is also utilized to construct prediction models. The flowchart representing the FSVR design and process is shown in The EEG signals are preprocessed for cleaner data. EEG signals are easily affected by muscle movement and eye blinks , and theAfter preprocessing, the fast Fourier transform is taken to calculate the band power. The features extracted from signals under specific spectra are called the band power ratio (BPratio), which is defined in Equations –4), as , as 4), f(x) with bias b, as shown in Equation (Support vector regression (SVR) has been applied to many regressive problems to predict a continuous output . Solved Equation . The kerZ-score and serve as the input. As shown in Z-score Z-score Knowledge-based fuzzy SVR (FSVR) is a combination of the SVR regression part and the fuzzy logic part. It is designed based on the working memory model proposed in this research, which will be discussed in the next section. The procedure of designing the fuzzy logic part is the same as that of the traditional fuzzy logic controller. The BPratios of the alpha, beta and gamma waves from the same channel are transformed by the The fuzzy logic part of knowledge-based FSVR serves as a feature transformer which changes the original feature vector with a length of 30 into the new feature vector with a length of 10. These 10 new features stand for the degree satisfying the rule of a working memory model in each channel. The proposed model balances the requirements of explanation and performance, which modifies the features by fuzzy rules with scientific knowledge and achieves a high prediction performance.x corresponding to the centroid Multi-linear SVR with FCM clustering is a modified fuzzy SVR regressing data by multiple SVR models proposed in . Given fEquation .(6)ck=ΣUsing FCM clustering, each of the clusters has one regression model. The input feature vector is projected onto the fuzzy membership degree space of multi-clusters, and the output is the fusion of multi-linear SVR model. In this research, multi-linear SVR with fuzzy C-mean clustering is implemented to predict the working memory performance. The data are first regressed by SVR with a Gaussian kernel to set up the baseline. If the predicted error of the single data is less than the threshold (<0.5), this point will be included to the clustering set which decides the final model. The model is trained under certain amounts of clusters, which comprise hyperparameters needing to be tuned (integer 2 to 10). Input data are transformed into the fuzzy membership degree and finally construct the whole model. The results compared to other algorithms will be discussed in the next section.To fully investigate the working memory process, statistical analysis was applied to dataset 1, as required in our experiments and measurements. EEG signals demonstrate several characteristics of the working memory process based on which the working memory ability can be more accurately predicted with an explainable model.The positions of EEG channels are related to the functional division of the cerebral cortex. The superior frontal gyrus was located in the prefrontal lobe , corresponding to the high cognitive function including decision making and planning. cuneus is located in the occipital lobe, corresponding to the processing and integration of visual information. These two brain regions are related to the working memory task in our experiments. The following analysis will be focused on the channels in the superior frontal gyrus, cuneus and full brain region.Proposition 1. The alpha waveform decreases, while the beta and gamma waveforms increase during the working memory process.This requires the functions of thinking and focusing, rather than relaxing. As shown in To discover the relation between working memory ability and waveform energy, a correlation analysis was conducted. The working memory performance was defined as the inverse ratio of time consumption. Since Proposition 1 was not satisfied in the superior frontal gyrus, the following analysis will be focused on the cuneus and full brain region. The relation between performance and wave form energy shows the tendency in the full region. There is a negative relation in Proposition 2. The energy of the alpha waveform shows negative effects on working memory performance while beta and gamma waveforms have positive effects on the working memory performance.As shown in Summarizing the two propositions and the discovered EEG signal characteristics, we propose a working memory model for waveform aspects with two equations. Equation  shows thEquation  describeZen meditation is a traditional Buddhist art which is often related to the effects of releasing mental stress and relaxing. A previous study  divided The working memory abilities of subjects in dataset 1 are predicted using the method proposed in this research. The models built by different approaches are shown in p-value from statistics correlation analysis. Based on this model, the working memory ability was predicted and the brain state during the working memory process was discovered. It is proven that one’s working memory ability can be evaluated from EEG signals using knowledge-based FSVR and multi-linear SVR with FCM clustering. The proposed method not only balances the explanation and performance of model, but also goes through train–test validation on the working memory EEG dataset compared to other regression models. The results demonstrate that knowledge-based FSVR achieves the best performance in the regression problem of dataset 1, and multi-linear SVR with FCM clustering achieves the best performance in the regression problem in dataset 2. Our study demonstrates an example of cognitive function evaluation by EEG measurement. In the future, other higher cognitive abilities can be evaluated based on the proposed methods.In this research, the main objective was to discover the working memory ability in terms of the EEG aspect, and we designed the experiment for the measurement. The working memory model of the EEG aspect was proposed with a correlation analysis, which discovered that the usage of the working memory process involves the energy change in waveform energy, and the working memory performance was related to the change in waveform energy. The model was supported by the significant