With the deepening of China’s aging process, changes in the age structure of the population affect the industrial structure and consumption structure in different ways and have a knock-on effect on the whole economic system. Therefore, aging is one of the objective factors affecting future carbon emissions in China. This study analyzes the impact mechanism of aging-related consumption trend on carbon emission efficiency (CEE) based on panel data of 30 Chinese provinces from 2000 to 2019. The results show that the aging-related consumption trend is conducive to the improvement of regional CEE, and the mediation transmission mechanism of industrial structure adjustment is obvious, with a coefficient of 0.1496. The core industry closely linked to the demand for aging-related consumption is consumer services. The promotion of the consumption demand of the aging in the eastern region on the CEE and the transmission stimulation of the industrial structure adjustment are the most obvious. The mediation effect in the central and western regions is relatively weak, and the aging-related consumption demand has not formed a positive interaction with the aging industry. Therefore, improving the market construction of products and services for the aging is beneficial to achieve a virtuous cycle of aging-related consumption upgrading and carbon emission efficiency. This research can provide insights for China to promote industrial structure transformation within the aging trend and also help China meet its carbon neutrality target on schedule. The intensity of carbon emission is closely related to the characteristics of industrial structure, among which the tertiary industry has the lowest carbon emission intensity  quantify aging-related consumption trend and analyze the mechanism of its impact on regional carbon emission efficiency; (2) verify the mediation effect of industrial structure adjustment and further consider two specific types of aging-related industries to explain the endogenous driving force of aging-related consumption trend on industrial structure adjustment; and (3) investigate the regional heterogeneity of aging-related consumption trend and mediation effects to identify the carbon emission reduction potential in specific regions. The results of this study can provide scientific guidance for China to formulate low-carbon industrial development policies in the context of population aging.Besides the primary energy structure  the SBM model based on undesirable output to measure the carbon emission efficiency of 30 provinces in China  from 2000 to 2019. The SBM model introduces slack and residual variables into the linear programming equation model, compensating for the neglect of the input–output slack problem in traditional data envelopment analysis (DEA) models , each with m input indicators xi , q1 desirable outputs yr , and q2 undesirable outputs bt = . The model is as follows:Assuming that there are  ρ is the carbon efficiency of the DMU.λ is the weight. A DMU’s efficiency value for the year is efficient if the efficiency value ρ ≥ 1.In Eq. , ρ is th2 emission. The description of input and output variables is shown in Table In an undesirable output-based SBM model, each decision unit includes several input variables and output variables. In this study, the input variables are labor force, fixed capital, and energy consumption. The desirable output is the gross regional product, and the undesirable output is the CO2 emission from energy consumption (except heat and electricity) is estimated using the methodology recommended by the IPCC:COj2 is the CO2 emission of the j energy; Ej is the consumption of the j energy ; Gj is the net calorific value of the j energy; Aj is the CO2 emission coefficient; and Bj is the carbon oxidation factor.1In Eq. , CO2j isElectricity and heat are different from their traditional fossil counterparts. The annual carbon emission factors for electricity and heat depend on the type and proportion of energy consumed in the energy conversion process. In this paper, the carbon emission factors for electricity and heat are calculated using the following equation:t respectively; i energy consumed of heat and electricity production in year t respectively; t in China.Among them, CEE is carbon emission efficiency; age represents the dependency ratio of the elderly population: and cons is the consumption structure. Since population aging promotes the upgrading of consumption structure related to the demand of the elderly, there is a synergistic effect between aging and consumption structure when considering its effect on carbon emission efficiency, so this study constructs an interaction term of age*cons and uses it to reflect the aging-related consumption trend. X represents a series of control variables, including regional economic development level (pgdp), foreign direct investment (fdi), technological innovation (tech), energy structure (es), urbanization level (urz), and human capital (hc).This paper uses a mediation effects model to quantify the impact of the rising demand for aging-related consumption on carbon emission efficiency. First, the Tobit model is adopted as a benchmark model to analyze the impact of population aging and consumption structure on carbon emissions efficiency. The Tobit model is a limited dependent variable regression model that describes the association between a non-negative dependent variable and the independent variables when data are censored or truncated. Since the relative efficiency scores obtained from the Super-SBM-DEA model are a series of discrete variables that are censored from the left-hand side of 0 , the proportion of high-tech industries (ahti), and the per capita output value of the health and resident services industry of the elderly population (hrs). When the estimated results of λ3 and η are significant, the mediation effect is valid. If at least one of λ3 and η is not significant, the existence of the mediation effect needs to be determined by Sobel’s test.Logically, the aging-related consumption trend should affect the carbon emission efficiency through the transmission mechanism of adjusting the industrial structure. In order to identify whether this transmission mechanism exists, this study constructs the following mediation effect model:The calculation results of the Super-SBM-DEA model based on undesirable output are shown in Fig. The elderly dependency ratio is chosen to measure the degree of aging in a region, expressed as the share of the population aged 65 and over in the working age (15–64) population  and consumption structure (cons). As shown in Fig. age*cons represents an upgrading of aging-related consumption demand, indicating a deepening of aging-related consumption trend.This study characterizes the aging-related consumption trend by constructing an interaction term between population aging  in Table cons on carbon efficiency is negative. It is related to that the consumption structure measured in this paper includes consumption of household equipment and daily necessities and housing energy consumption. When considering the impact of consumption structure on carbon efficiency, the scale of residents’ consumption of industrial manufacturing products and household energy is larger than that of products in the tertiary sector.As shown in Table Aging leads to a rise in the average age of the labor force, which is an important factor affecting the physical state and skill level of workers Feyrer . The oldBut on the demand side, aging-related consumption trend is directly related to the increase of the income level and consumption ability of the elderly Addessi . With thpgdp, fdi, tech, and hc are significantly positive, implying that each of these control variables has a positive effect on the regional carbon emission efficiency improvement.According to model (2) in Table Regional economic development is conducive to the improvement of carbon emission efficiency. This is due to China’s transition from a “crude” economic growth model to an “intensive” sustainable development model  in Table age*cons is significantly positive, indicating that the upgrading of the consumption demand due to population aging is an important way for it to promote the advanced adjustment of industrial structure. After controlling for the demand-side effects, the supply-side factors such as the rise in the average age of the workforce and the decline in labor productivity will hinder the upgrading of the industrial structure  is significantly positive, indicating that there is a significant mediation effect. The expansion of the scale of the tertiary sector contributes to the improvement of carbon emission efficiency in production by gradually replacing the excess capacity of the secondary sector. Therefore, the research hypothesis 2 is proved to be correct.As shown in model 4) in Table  in Tableage*cons decreases from 7.4123 to 4.8387, proving that the aging-related consumption trend is contributing to the improvement of the regional carbon emission efficiency level by promoting the advanced industrial structure. In the context of an aging population, the growing demand for aging-related consumption will lead to a rapid increase in products and services in the silver-haired sectors due to the transmission mechanism between the supply and demand structure , the effect of ind on CEE is still significantly positive, which are consistent with the previous results, indicating that aging-related consumption trend does contribute to the improvement of carbon emission efficiency by promoting the upgrading of industrial structure. Therefore, the robustness test confirms that the results of the baseline regression and mediation effects model are reliable.To test the robustness of the estimation results of the baseline regression, this section chooses to replace the measure of population aging by using the ratio of the population aged 65 years or older to the total population at the end of the year in each province. The results are shown in Table Considering the demand characteristics of the elderly, the scope of the silver-haired industry does not include all tertiary sectors, but rather focuses on the consumer services sector  was used as a mediation variable to analyze the transmission mechanism between the aging-related consumption trend and carbon emission efficiency within the secondary sector. As shown in models (1) and (2) in Table ahti is positively correlated with CEE, the effect of age*cons on ahti is insignificant, indicating that the deepening of aging does not significantly promote the development of high-technology industries. For Sobel test, the Z value is 1.3480 and P = 0.1777, meaning the mediation effect is not significant.First, the proportion of age-related high-tech industries  is used as the mediation variable. The results of the empirical analysis are shown in models (3) and (4) in Table hrs is used as the explanatory variable, the coefficient of age*cons is significantly positive, and hrs is significantly positively correlated with CEE, confirming that the mediation effect stands. The growth of the silver-haired service sectors helps to accelerate the low-carbon development of the industry.Secondly, in order to verify the specific transmission mechanism of the aging-related consumption trend at the tertiary industry level, the per capita silver-haired services output for the elderly , indicating that the growth of the healthcare sector and residential services, which are most closely linked to the elderly in the context of population aging, is the core transmission mechanism through which aging-related consumption trend contributes to the improvement of regional carbon efficiency. It can be concluded that the positive impact of aging-related consumption trend on industrial structure upgrading is mainly reflected in the growth and expansion of the health care and residential services (Liu and Peng In model (4) in Table Due to the imbalance in China’s regional economic development, there are significant disparities among the development levels of the three industries in different regions. There may be heterogeneity in the socio-economic impacts of population aging in regions with different levels of development. Therefore, this paper classifies the research sample into three sub-samples: eastern, central, and western regionage*cons and ind are significant positive. There is a strong mediation effect of industrial structure adjustment. Models (3) and (4) in Table age*cons on ind, as well as CEE in the central region, are not significant. Whether the mediation mechanism of ind holds needs to be determined using the Sobel test. The Z value of the Sobel test is 0.3883 and P = 0.6978, which cannot reject the original hypothesis, so the mediation effect is not significant. The aging-related consumption trend in the western region has a positive impact on industrial structure upgrading (see in model (5) in Table As shown in models (1) and (2) in Table For the eastern region, aging-related consumption trend can help promote the transformation of the local secondary industry to the tertiary industry, achieve the upgrading of the industrial structure, and, thus, significantly improve local carbon emission efficiency. It is closely related to the high standard of living in the eastern region with a well-developed social welfare guarantee system Zhang . Above tThere is no mediation effect of aging-related consumption trend and industrial structure adjustment in the central region. The main reason is related to the fact that the current dominant industries in the central region are still dominated by industrial raw material processing and equipment manufacturing  the impact of aging-related consumption trend is conducive to promoting the carbon emission efficiency. (2) There is a mediation effect mechanism of industrial structure adjustment. The transformation of China’s aging-related consumption demand has significantly contributed to the adjustment of the advanced industrial structure, thus improving carbon emission efficiency. (3) The core industry closely linked to the demand for aging-related consumption is consumer services, which are mainly health and medical care and residential services. (4) The mediation effect of the industrial structure adjustment on the improvement of carbon emission efficiency in the eastern region is obvious, but that in the central and western regions is relatively weak. The aging demand in the central and western regions fails to form a positive interaction with the low-carbon development of the local economy.The upgrading of consumption structure due to aging-related consumption trend can contribute to low-carbon economic growth by promoting the advanced industrial structure and improving the efficiency of regional carbon emissions. As China’s aging process continues to deepen, the government needs to ensure investment in the aging careers and build a sound system of social welfare guarantee to maintain the financial resources of the retired elderly. Chinese government should learn from the multi-level pension system models of developed countries, improving the legally mandatory public pension scheme to provide fundamental guarantee for the elderly in their twilight years. At the same time, enterprises should be urged to pay occupational pensions for their employees, and preferential policies should be introduced to encourage individuals to participate in personal pension savings plans. By broadening individual sources of income in their twilight years, elderly populations can be assured of a consumption capacity that matches their multiple demands.On the supply side, it is necessary to continuously promote the construction of markets for the silver-haired industries and increase capital investment in corresponding industries such as healthcare and residential services, elderly service facilities, elderly living goods, elderly real estate, elderly tourism, and elderly education, and these industries are clean tertiary industries. The development of these industries will not only stimulate the consumption desire of the elderly but also enhance the level of industrial structure and contribute to sustainable economic development. However, the supply of aging services solely relying on the state’s financial resources is not sufficient, the development of aging-related industries requires diversified sources of funding, and the involvement of social capital can effectively fill the gap. By enriching the investment corpus, the competitive behavior of the market can be utilized to make the allocation of resources in the aging-related service sectors more reasonable.More importantly, the aging health and service industries require knowledge in a variety of fields, such as medicine, pharmacy, nursing, and psychology. There is a need to accelerate the training of talents and promote the specialization of practitioners in aging-related industries. Government departments can cultivate a group of high-level integrated talents for aging health services by cooperating with universities in discipline construction. They can also fully mobilize the enthusiasm and creativity of professional and technical personnel through a sound talent evaluation and incentive mechanism. For irregularities in the aging market, the relevant departments still need to strengthen the legalization of aging-related industries and regulate the market order, such as improving the social insurance law and establishing a universal long-term care insurance system, using laws and regulations to provide support for the benign development of the silver-haired industries.In addition, the eastern region is developing ahead of the central and western regions, so it is urgent to learn from the eastern experience to promote the industrial upgrading driving effect of the aging-related consumption trend in the central and western regions. Population aging is an irreversible trend; the central and western regions should focus on fostering the vitality of the silver-haired market while developing locally advantageous industries. Local governments should target the development of aging services and focus on the training of professionals, tax breaks, and subsidies for home purchase and residence are needed to enhance the willingness of professional talents to reside locally, following the example of the eastern region to accumulate capital for the development of the technical services through the retention of talents.While this study provides valuable insights, it is important to acknowledge its limitations and propose future research directions. Firstly, this study fails to discuss the effect of different levels of aging because of data missing. Significant differences in cognition and habits between older and younger seniors can lead to specific consumption tendencies, which have uncertain effects on industrial structure adjustment. Further quantification of elderly population number in different age groups is needed to clarify their impact on industrial low-carbon development. Secondly, due to data limitations, some specific service industries closely related to aging demands, such as the long-term care industry, were not considered in this study. But from a long-term perspective, the health care industry is a crucial growth point for the future development of the silver-haired services. Therefore, expanding the dataset to identify synergies between the growth of the elderly population and the development of the long-term care industry and its contribution to low-carbon economy is an important direction for future research.


The two trapped quantum particles interacting problem is generalized to three dimensions, and the exact Coulomb potential is used. The system is solved by expanding the wavefunction in terms of the isotropic harmonic oscillator eigenfunctions and Hydrogen atom eigenfunctions independently, showing that each one results in a prime approximation for different domains of the normalized coupling constant of the relative interactions, suggesting that the combination of the basis is enough to build a well-suited base for the non-approximate problem. The results are compared to previous works that use a model of approximate finite-rage soft-core interaction model of the problem to give insights into the many-body states of strongly correlated ultracold bosons and fermions. We conclude that the proposed three-dimensional approach facilitates the distinction between bosons and fermions while the solutions given by the expansions better define the behavior of the particles for repulsive potentials. In addition, we discuss the substantial differences between our work and the previous approximate model. Problems previously considered only of academic and theoretical nature are now the basis of several emergent quantum technologies.Quantum control is a rapidly growing field of research developed in response to the limitations of classical control techniques, which are inadequate for controlling quantum phenomena essential for a wide range of applications, including quantum computing, quantum sensing, and quantum communication. It has played a crucial role in addressing one of the biggest challenges in quantum computing: decoherence. Decoherence limits the time a quantum system can remain in a quantum state and thus leads to errors in quantum computing. By developing controlling techniques, researchers have been able to extend the coherence time of qubits, enabling more complex computations to be performed. Ultra-cold atoms provide an excellent platform for studying and implementing these quantum-controlling techniques. Because of their low temperatures and well-defined quantum states, ultra-cold atoms can be manipulated and controlled with high precision using external fields. Thanks to the advances in technology in the last two decades, which allow not only to create a system of ultra-cold atoms but to manipulate each particle and control the interaction between them with great accuracy6, which has been studied in various ways16 in the past. However, most of these works approximate the interaction by replacing the Coulomb potential with simpler choices to try to construct exact analytical solutions. For example, a quasi-exact solution to the Schrödinger equation for two interacting particles was obtained by Busch et al.9 using a delta-like interaction, a model that was later extended to Gaussian-shaped potentials17. Analytical solutions for more complex interactions, like dipole-dipole, are increasingly needed because of the limitations observed18. For example, depending on the length scale or the size of the trap, one should study and use different considerations, like the van der Waals interaction for short scale, Coulomb corrections19, s-wave scattering length characterizing low-energy atomic collisions, or atomic collisions for traps whose size is comparable to the size associated with the atomic interaction20.The two-body system represents one of the most fundamental frameworks for interacting system of trapped atoms and the building foundation of few- and many-body physics24. This is true with all other simplified models previously cited and those before Kościk and Sowiński7, whose work is used as the primary reference in this paper. In the spirit of keep developing new simplified models from which we could build more complex physics, Kościk et al. proposed a finite-rage soft-core interaction model of two trapped interacting quantum particles as an approximation of the Coulomb potential and many properties of the system were derived. Similar to the comparison they made with Busch et al. 9, mainly focusing on the spectral properties of the system, we will aim to enlarge the already vast pool of studies made in this area but focusing not on the quasi-exact solution, but on devising a proper base to numerically construct solutions to the non-approximate interaction between two particles trapped in a harmonic oscillator.In addition, the study of quantum particles trapped in a harmonic oscillator represents a useful approximation of the microsystems trapped in an optical lattice, so a precise understanding of the interactions in this elementary model may help comprehend the physics occurring in more complex and realistic systems. For instance, stationary solutions are helpful to study the non-equilibrium dynamic of two atomsHence, we present the generalization of this problem by considering the numerical solution to the exact Coulomb interaction potential in the diagonalization of the relative motion Hamiltonian between the two trapped particles. To do so, we use the three-dimensional isotropic harmonic oscillator eigenfunctions to expand the Hamiltonian and solve the eigenproblem, studying the system behavior when considering the combined harmonic and hydrogen-atom systems. Two distinguishable domains are identified and a clear suggestion on how to build the Hilbert space for a more in detail study is deduced: a combination of the harmonic eigenfunctions, which work nicely for the limit of a repulsive interaction; and Hydrogen atom eigenfunctions, which provide a good approximation for an attractive interaction. A proper combination might be enough to build a well-suited base for the exact Coulomb potential problem between these limits.7 is to consider three dimensions, so we have a system described by the following Hamiltonian:V corresponds to the Coulomb potential. We use boldface to indicate vectors and normal font to refer to their norm. Using the standard transformation to the coordinates of the center of mass:spherical harmonic functions are eigenfunctions of 7, where a strength interaction parameter V and a range parameter a that describes the distance in which the particles interact with each other are needed. In our case, as we do not approximate the Coulomb interaction, we consider the range parameter The first step we take to generalize the work of Kościk and SowińskiAs m in Eq.  to buildStarting with the known solution to the three-dimensional IHO:Continuing with the eigenproblem, we end up with the following equation using  and 4)884)8\docuConversely, using the radial part of the HA eigenfunctionsr to Eq. , namely,Equations  and 12)12) summan-th energy value to converge. For example, when going from For simplicity, we will analyze the case of particles with equal mass, so n by Eq. . In factWe then contrast these results using second-order perturbation theory to check that the approximation converges to the proper result. A further check is made by rearranging the Hamiltonian to obtain the known Hydrogen atom energy levels as follows: we haveOn the other hand, calculating the matrix elements with HA eigenfunctions to solve the diagonalization problem with the expansion of the harmonic potential, produces, as expected, a poor result as HA eigenfunctions do not form a complete basis if we do not consider the scattering states: Hydrogen atom eigenfunctions on their own, despite converging, does not work and results in wrong values for the system energy levels.A further study of the behavior of the system is made by analyzing how the energy levels change by the coupling factor γ in Eq.  and compmentclass2pt{minimmentclass2pt{minimiltonian , which amentclass2pt{minim7 have suggested. Moreover, the exact solution using FEM shows that there is also degeneracy between neighboring bosonic and fermionic energy levels for the highly attractive potential. Another meaningful difference between symmetric and antisymmetric particles is that the fermion eigenfunction converges faster to the expected result due to the Pauli exclusion principle.Finally, as we mention in Eq. , the disWe focused on the non-approximate Coulomb interaction between two trapped particles using the isotropic harmonic oscillator and Hydrogen atom eigenfunctions independently to expand the relative motion Hamiltonian between two trapped quantum particles and numerically solve the eigenproblem by diagonalization, showing that each of these functions has complementary domains in which they result in a good approximation to the system. The IHO eigenfunctions are an ideal base for the repulsive potential but also work for weak attraction, resulting in adequate approximations for values up to mentclass2pt{minimmentclass2pt{minimmentclass2pt{minimAs we think that the expansion in the IHO basis may be useful for further studies, we include the coefficients of the IHO expansion for a number of Our model, which has just one variable coefficient to explore the attraction and repulsion between trapped particles, captures qualitatively the results from previous works and deepens the understanding of what features are specific to the election of a particular potential. Thus it expands on the problem that started with Busch et al. In addition, our analysis clearly distinguishes between the behavior of bosons and fermions, a characterization that comes naturally with a three-dimensional approach. With the exact potential, substantial differences are observed in degeneracy for bosonic and fermionic energy levels: degeneracy is observed between neighboring eigenenergies for highly attractive systems, as Fig. Supplementary Information 1.Supplementary Information 2.


This paper introduces a novel high-certainty visual servo algorithm for a space manipulator with flexible joints, which consists of a kinematic motion planner and a Lyapunov dynamics model reference adaptive controller. To enhance kinematic certainty, a three-stage motion planner is proposed in Cartesian space to control the intermediate states and minimize the relative position error between the manipulator and the target. Moreover, a planner in joint space based on the fast gradient descent algorithm is proposed to optimize the joint’s deviation from the centrality. To improve dynamic certainty, an adaptive control algorithm based on Lyapunov stability analysis is used to enhance the system’s anti-disturbance capability. As to the basic PBVS  algorithm, the proposed method aims to increase the certainty of the intermediate states to avoid collision. A physical experiment is designed to validate the effectiveness of the algorithm. The experiment shows that the visual servo motion state in Cartesian space is basically consistent with the planned three-stage motion state, the average joint deviation index from the centrality is less than 40%, and the motion trajectory consistency exceeds 90% under different inertial load disturbances. Overall, this method reduces the risk of collision by enhancing the certainty of the basic PBVS algorithm. The visual servo method is crucial for capturing target objects in space, serving as the foundation for future on-orbit facility maintenance . HoweverThe position-based visual servo (PBVS) method uses the feedback information of the target position obtained from image processing to guide the motion of the manipulator. It does not suffer from the problem of image Jacobian singularity, leading to higher global stability . ConsequCurrently, there is a lack of literature specifically addressing the dynamic control methods for the visual servo process of manipulators. However, there are many studies on suppressing the vibration of flexible space manipulators, which can be used for reference. T. Hao derived the dynamic equation of a general flexible joint manipulator and proposed a static feedback linearization controller to achieve accurate trajectory tracking of the end effector in Cartesian space . M.H. KoBased on the research of previous scholars, this paper proposes a systematic visual servo control strategy for flexible joint space manipulators from an engineering application perspective. The strategy includes position-based visual servo control, motion planning, and dynamic control and aims to address the safety risks of the classical PBVS method. This paper makes contributions to the visual servo control of space manipulators as below.The method of motion certainty as a key factor in ensuring the safety of visual servo control for space manipulators is introduced in this paper. The safety risks are analyzed from both kinematic and dynamic perspectives, and a high-certainty visual servo control framework is proposed to address these risks.A motion planner is proposed that combines three-stage motion planning in Cartesian space with motion planning in joint space, aiming to minimize deviation from the centrality. The issue of uncertain intermediate states in classical PBVS algorithms is addressed by this method.An adaptive control method for the flexible joint dynamics is proposed in this paper using a Lyapunov-based stability analysis approach. The visual servo control system for space manipulators during dynamic target tracking is, thus, enhanced in robustness.A full-dimensional ground experiment was conducted using a physical mirror method to verify the high-deterministic visual servo control strategy for safety. The experiment was performed in a ground gravity environment, and a simple yet effective method was used to demonstrate the efficacy of the proposed strategy.The remainder of this paper is organized as follows. In The manipulator’s visual servo system consists of four parts: chaser spacecraft, manipulator, hand-eye camera measurement system, and target spacecraft, as illustrated in The high-certainty visual servo controller consists of four components: the coordinate converter, the Cartesian-space motion planner, a joint-space motion planner, and the dynamic controller, as depicted in The coordinate converter maps the target position measured by the camera to the position relative to the manipulator’s base coordinate system based on the manipulator’s configuration. Once the chaser spacecraft approaches the target, the hand-eye camera captures images of the target and then calculates the target’s position and pose matrix, The Cartesian space motion planner controls the motion state of the visual servo process and keeps the space manipulator in a certain state to the target, thereby mitigating the risk of uncertainty. See The visual servo algorithm operates in the manipulator’s base coordinate system. A three-stage motion planning strategy in Cartesian space, building upon the classical PBVS method, is introduced to gradually reduce the distance between the manipulator and the target, as shown in At the beginning of the visual servo process, the direction with the largest error is selected as the feeding direction, while the other two directions are treated as non-feeding directions. The first stage is the aiming and alignment stage. In this stage, the manipulator tracks steadily in the non-feeding direction while maintaining the current position in the feeding direction. The allowable error thresholds in all three directions are set to The second stage is the feed tracking stage. In this stage, the manipulator maintains stable tracking in the X-Y-Z directions. The expected target position in the feeding direction is denoted as The third stage is the fast capture stage. In this stage, the manipulator performs stable tracking in the three directions of X-Y-Z. The expected position in the feed direction is denoted as To ensure reliable capture, the motion planning parameters must satisfy the following relationships:The manipulator with redundant degrees of freedom has infinite kinematic inverse solutions, theoretically. Numerical iterative methods can be employed to calculate the inverse kinematics, working as joint-space motion planners. A typical calculation approach using the pseudoinverse of the Jacobian matrix is used to determine the joint velocities corresponding to the desired TCP pose velocities. Integrating these joint velocities yields the next cycle’s joint positions . DefininH is optimal, as shown in Equation (5).The above iterative process can control the joint motion trajectory so that the joint position–related objective function H function to be as close as possible.To ensure faster convergence , the iteThe minimum value of the least two-norm equation above satisfies the following constraints:Among them, The joint space motion planning steps can be summarized as follows.(1)Calculate the Cartesian velocity from the starting position and the target position (2)q configuration x(q).Calculate the Jacobi matrix for the current joint angle (3)M =N =kM and kN.According to the equation (4)N matrix and calculate kB and Do LU decomposition of (5)kU from k, Bk,MCalculate (6)Calculation (7)Repeat steps 2 to 7 until the iterative steps are completed.The space manipulator has a large structural span, and the joint’s transmission is generally designed with light and flexible materials. As shown in The engineering feasibility is taken into account by simplifying the flexible joint of the space manipulator as a spring-damper system with stiffness K and viscous friction f, as shown in The undamped oscillation frequency According to the above equation, an increase in joint load inertia or a decrease in joint stiffness will lead to a decrease in system damping and a decrease in the undamped natural oscillation frequency. Since the fundamental frequency of the space manipulator structure is generally low, this can easily lead to overshoot or even instability of the system. In order to achieve effective joint control, it is necessary to control the stiffness and damping of the joint dynamics control system within the expected range. Therefore, the joint dynamics model reference adaptive controller shown in The 7-DOF space manipulator dynamics model is as follows:The joint position and velocity are taken as state vectors, and the dynamics model is transformed into a state space model.Assuming a constant system of joint flexibility link stiffness, the kinetic equation for the joint position is established as:The joint position and velocity are taken as state 2 × 2 dimensional vectors, and the differential equations of joint dynamics are transformed into a state space model.Establish the control input equation, which consists of two parts: state feedback and motor angle feedforward.Substitute the input equation into the dynamic state equation of the manipulatorAmong themThe above equation is the closed-loop control state model of the space manipulator’s arm joint. Define the system’s systematic error as shown in the following equation.Calculation of the purpose of adaptive control equation .(33)V=eAccording to Lyapunov stability theory, V is a negative definite matrix, thenIn turn, the adaptive control rate is:The space manipulator operates in a microgravity environment with small joint torques, making it unable to work in a gravity environment on the ground. To verify the effectiveness of the visual servo control strategy for the space manipulator in orbit, a physical mirror experiment system was designed. The purpose of this mirror system is to map the joint motion state of the space manipulator, which cannot move “upright” onto the mirror manipulator in real-time, allowing for the reproduction of the space manipulator’s three-dimensional motion in a gravity environment .Joint motion decoupling: The space manipulator is mounted on a marble air bearing platform. First, the manipulator is decoupled into two independent parts by fixing the “elbow” structure, which consists of a 3-degree-of-freedom mechanism and a 4-degree-of-freedom mechanism. Air bearing devices are then designed for the two manipulators with fewer degrees of freedom, allowing all joints to rotate. Joint motion mirroring: The motion state, including position and speed information, of the joints of the space manipulator is transmitted in real-time through the fieldbus network to the mirror manipulator. The mirror manipulator drives its joints to track the received motion state in real time, reproducing the three-dimensional motion of the space manipulator.Closed-loop information link: The mirror manipulator moves with the hand-eye camera (which is mounted on the mirror manipulator). The hand-eye camera captures the target position and feeds it back to the space manipulator visual servo controller via the fieldbus. The controller then uses the visual servo algorithm to calculate the error, complete the motion planning and dynamics calculation, and generate joint motion instructions to drive the joints of the space manipulator on the air bearing platform. The system information link is shown in The CAN2.0B standard  is appliThe objective optimization function used in the experiment for joint space is the joint deviation center index, and its calculation method is shown in the following equations:The visual servo algorithm verification experiment is conducted in two stages. The first stage verifies the effectiveness of the dynamic adaptive control algorithm (details can be found in The dynamic adaptive control experiment is conducted by comparing the consistency of joint motion response when the manipulator captures the same target under different disturbance conditions. The specific steps of the experiment are as follows:Step 1: Install the space manipulator on the air bearing device and keep joints 2, 4, and 6 in a microgravity state. This test method is called the planar motion method, as shown in Step 2: Carry out the capture experiment with the mirror experiment system as shown in Step 3: Compare the motion data of the three joints in Steps 1 and 2 as the quantitative analysis of the effectiveness of the dynamic adaptive algorithm. If the motion curves in Steps 1 and 2 are substantially similar, it indicates that the joint adaptive control algorithm possesses robust anti-disturbance capabilities. The effectiveness of the dynamic adaptive control algorithm was quantified by calculating the difference in the sum of the absolute values of joint dynamic tracking errors. The evaluation criteria are defined as below:The left parts of The whole process verification experiment of the visual servo algorithm was performed using the physical mirror experiment system to execute the high-deterministic visual servo algorithm. The target simulator controlled the captured target to move randomly in the directions X or Y or Z at a speed of less than 50 mm/s. The manipulator approached and captured space targets under the guidance of the hand-eye camera. During the experiment, the measured values of the target position of the hand-eye camera and the motion responses of the 7 joints of the manipulator were recorded. The experimental process is depicted in According to the visual servo strategy, the manipulator completes the sequential switching of the three stages with no significant fluctuation. This paper proposes a high-certainty visual servo control framework for a space manipulator. The framework is designed to address the uncertainty of the motion, which can lead to collision during the process. The framework includes a three-stage motion planning strategy in Cartesian space and motion optimization in joint space using the gradient descent method. Additionally, an adaptive control algorithm for space manipulator dynamics based on Lyapunov stability analysis is proposed to reduce the interference of model parameter changes on the motion control performance and improve the robustness of the manipulator. The experimental results show that the high-certainty algorithm has a motion response consistency of 93.2% in the presence of external inertia disturbance, demonstrating strong robustness to the perturbation of the model. The visual servo experiment successfully completed the three-stage switching of the Cartesian space, effectively improving the certainty of the intermediate state of the visual servo. The average value of the joint deviation center index was 0.3986, indicating that the joints have a strong safety margin.The results of comprehensive experiments indicate that the proposed high-certainty visual servo control strategy for flexible space manipulators with redundant joints is effective in enhancing the certainty of the visual servo process. Although this paper analyzes the impact of the visual servo algorithm on security from the perspective of kinematics and dynamics and proposes corresponding solutions, the coupling analysis of dynamics and kinematics control algorithms has not yet been carried out. Therefore, future studies will focus on investigating their coupling relationship and further improving the security of the visual servo method.


Feature extraction is an important process for the automatic recognition of synthetic aperture radar targets, but the rising complexity of the recognition network means that the features are abstractly implied in the network parameters and the performances are difficult to attribute. We propose the modern synergetic neural network (MSNN), which transforms the feature extraction process into the prototype self-learning process by the deep fusion of an autoencoder (AE) and a synergetic neural network. We prove that nonlinear AEs  with ReLU activation functions reach the global minimum when their weights can be divided into tuples of M-P inverses. Therefore, MSNN can use the AE training process as a novel and effective nonlinear prototypes self-learning module. In addition, MSNN improves learning efficiency and performance stability by making the codes spontaneously converge to one-hots with the dynamics of Synergetics instead of loss function manipulation. Experiments on the MSTAR dataset show that MSNN achieves state-of-the-art recognition accuracy. The feature visualization results show that the excellent performance of MSNN stems from the prototype learning to capture features that are not covered in the dataset. These representative prototypes ensure the accurate recognition of new samples. With the development of synthetic aperture radar (SAR) technology, the explosive growth of SAR images has presented new challenges for highly accurate target recognition. Compared with manual feature extraction methods ,2,3,4, dDuring the application of AE to SAR, a fusion model of AE and the synergetic neural network (SNN) is proposed . AE-extrIn this paper, we investigate the fusion method of AE and SNN and propose the modern SNN (MSNN) model. More than a decade before the formal introduction of AE, researchers showed that the weight matrices of the encoder and the decoder from single-layer linear AE are mutual M-P inverse if the loss function reaches a stationary point, including one global minimum and multiple saddle points , which aThe objective of this paper is to propose an SNN-AE fusion model MSNN to learn nonlinear prototypes as representative features of SAR images to improve recognition accuracy. The contributions of this paper are (1) proposing the fusion model of SNN and AE with complementary strengths, (2) proposing the prototype self-learning method to enhance feature representativeness and visualization, and (3) attributing the recognition performance of deep learning to the effective learning of unobserved features.This paper is structured as follows. V [Synergetics use dynamic systems to study the dynamic process of multiple subsystems from disordered states to ordered states . SNN, asa of SNN  with therse of V ,31, Syn (1)ξ=V+xξnew=Syn. Construct x, each i has two possible values, so x corresponding to the same i. The possible values of The weights of the global minimum-converged AE can be divided into tuples of M-P inverses. The working process of the nonlinear AE layer isThe above conclusion also applies to stacked AE. The stacked AE can be regarded as applying multiple equivalent matrices X of size K and stride 1, the following output can be obtained:K, and put them together as O of size X and 1 as the last dimension; the convolution is equivalent toThe convolutional and transposed convolutional layer can be transformed into equivalent fully connected layers, so the above conclusion can be generalized to convolutional AE. By inputting a feature map M subcodes M SNNs for N iterations.The structure of MSNN is shown in H. When a single SNN is used to receive H different positions for the value one, and thus the total number of possible codes is also H. The limited code number means that many samples correspond to one code; however, only one code can be reconstructed to one output. Such an output is usually composed of the common features among those samples, which makes it difficult to cover the representative information. Features lacking representation will damage both the visualization and the recognition performances. When multiple SNNs receive M SNNs increases to M, so the one-to-one correspondence between the input and M.We introduce multiple SNNs to ensure the reconstruction quality of the decoder by extending the possible values of V has linearly independent columns, P is to zero, the better the parameters are trained. Note that the loss function of the coder is still P is only for convergence verification; it is not involved in any parameter tuning process.The previous sections only prove that the stacked AE and convolutional AE weights are tuples of M-P inverses when the global minimum is reached, yet the actual convergence state requires additional verification. From For error backpropagation, Syn repeatedly imposes a polynomial function onto the input, which may lead to the gradient exploding or vanishing. The gradient problem is so severe that conventional means such as gradient clipping can barely circumvent the non-convergence. Therefore, we used the gradient bypass technique ,33 from i. i is exponential to the number of neurons with ReLU activation, and even infinite with other activations, so the calculation of equivalence matrices is time-consuming or even non-traversable. In addition, most of these matrices will not occur in the application due to the limited number of training samples and the intrinsic connection among codes; therefore, it is inefficient and difficult to discover the core prototypes by this approach. Alternatively, we derived the visualization results by inputting a specific code to the decoder. For example, one-hot codes were input to observe individual prototypes, and clustering centers of inner-class codes were input to observe their common features.The visualization of extracted features can be easily achieved using the recall of MSNN. Although the MSNN prototypes can be derived theoretically by calculating the decoder’s equivalent matrices, the number of equivalence matrices is enormous and difficult to filter. From We designed experiments using SAR images of 10 different military carriers from the MSTAR dataset . The carM parts, input to the SNN, and iterated I times. The hyperparameter The encoder of the MSNN contained 4 convolutional layers and 1 fully connected layer with the channel configuration 32–64–64–64. This channel configuration ensures that the code dimension is not larger than the input and avoids overparameterization of AE. The kernel size was 4, the stride was 1, and the padding was 1. Due to the limitation of the transpose convolutional layer, having an identical configuration to the convolutional layer is not enough to obtain an output with an equal size to the input. Therefore, we used the common structure to ensure identical data size. Each convolutional layer was followed by a dropout of r than 1 , so thisas AdamW  for fastas AdamW  approachP reduced from the order of The feature recognition results of MSNN were optimized with a hyperparameter grid search with ablation test, as shown in For the MSNN training speed, the network contains 4 convolutional layers, 4 transposed convolutional layers, 1 fully connected layer, and a set of SNN with 16 iterations. SNNs work in parallel and can be approximated as 16 network layers. Therefore, the training speed of the MSNN is roughly equivalent to that of a 25-layer deep network. We used an RTX 3070 graphics card and CUDA 11.6 + pytorch 1.12 environment to compare the time required for one epoch of MSNN with several other methods, and the results are shown in We first evaluated the effectiveness of the prototypes by counting the average percentage of one-hot codes and zero vectors of subcodes. One-hot represents one prototype that learns the feature. The higher the percentage, the better the effectiveness. The total percentage of the one-hot and zero vectors can characterize the convergence of each SNN. The higher the percentage, the more networks reach convergence. The statistics of the training and test sets are shown in K = 8 and visualized the binarized clustering centers. The results are shown in We then visualized the prototype patterns obtained by the MSNN self-learning. Since the prototypes of each SNN capture partial sample features and their combination is nonlinear, the visualization of single prototypes is vague and indistinguishable. Therefore, we clustered similar codes of inner-class training samples by K-means using In this paper, we proposed the use of an AE-SNN fusion model MSNN for the feature recognition task of SAR images. AE solves SNN’s lack of prototype nonlinear learning, and SNN improves the efficiency and stability of AE coding regularization and offers a simple and effective feature visualization approach. Experiments on the unpreprocessed MSTAR dataset showed that MSNN obtained the optimal feature recognition performance, and the feature visualization results show that these excellent results originate from the network’s effective prototype learning, which spontaneously captures representative features that are not covered in the training set. It is worth noting that the feature extraction and visualization of MSNN are based on the premise that the critical information is located at the center of the SAR image. For data with a more complex distribution, the features learned by MSNN will be more abstract, so more sophisticated visualization methods need to be developed to ensure performance. In addition, the recognition performance of MSNN on partially missing, mislabeled, and new category samples also needs more studies to achieve a broader application. Target recognition by the fusion of SAR images and high-resolution range profile (HRRP) is a research hotspot. We plan to apply MSNN to SAR-HRRP feature matching and feature fusion to further improve the recognition accuracy.


A coupling mechanism between flicker noise and hot carrier degradation (HCD) is revealed in this work. Predicting the flicker noise properties of fresh and aged devices is becoming essential for circuit designs, requiring an understanding of the fundamental noise behaviors. While certain models for fresh devices have been proposed, those for aged devices have not been reported yet because of the lack of a clear mechanism. The flicker noise of aged FinFETs is characterized based on the measure-stress-measure (MSM) method and analyzed from the device physics. It is found that both the mean and deviations of the noise power spectral density increase compared with the fresh counterparts. A coupling mechanism is proposed to explain the trap time constants, leading to the trap characterizations in their energy profiles. The amplitude and number of contributing traps are also changing and are dependent on the mode of HCD and determined by the position of the induced traps. A microscopic picture is developed from the perspective of trap coupling, reproducing well the measured noise of advanced nanoscale FinFETs. The finding is important for accurate flicker noise calculations and aging-aware circuit designs. Flicker noise plays an important role in analog/RF circuit designs, such as in causing phase noise and jitter . On the Considering that the HCD in advanced FinFETs is attributed to the interface states and traps in the dielectric ,13,14, tIn this paper, in order to solve the problem of the inaccurate prediction of flicker noise after HCD, the coupling effect between traps induced by HCD and traps which generate flicker noise is studied. The impacts of HCD traps on flicker noise in different Vgs/Vds regions are covered. HCD has an impact on the amplitude distribution and coupling strength of traps. The conventional model based on carrier number fluctuation theory and mobility fluctuation theory describes the worst-case using corner models. On the contrary, the statistical model considering the coupling effect between flicker noise and HCD agrees excellently with the measurement data of advanced technology nodes before and after HCD. With an improved accuracy compared with conventional models, the revealed coupling mechanism is meaningful in predicting flicker noise accurately in FinFET and Gate-All-Around (GAA) circuit designs .Foundry-level 16/14 nm pFinFETs are used to explore the impacts of HCD on flicker noise. In this work, the classical measure-stress-measure (MSM) method is adopted by incorporating low-frequency noise characterizations for the experiment data. Considering the two HCD modes, the single vibrational excitation (SVE) and multiple vibrational excitation (MVE) , and posid/Id2 at the given bias is plotted in grey lines, with the mean and deviations represented by the circles. It is seen that the aged devices suffer from severer flicker noise after HCD.The flicker noise properties of fresh and aged FinFETs with HCD of MVE are shown in Considering the nature of flicker noise as the superposition of individual trap-induced noises , the freThe trap capture/emission time (CET) maps  are plotAt the same time, the fine modeling of the flicker noise reveals that the trap properties have been changed after the HCD. A coupling theory based on the inelastic trapping/de-trapping mechanism  is shownt, and the relaxation energy S. In the inelastic tunneling theory, the trap time constant τ is determined by [th, σ0, ΔBE, fE, and At the microscopic level, three parameters are associated with each trap, including the trap amplitude ΔId, trap energy Emined by :(1)τ=1nvt changes after degradation, while the time constant distribution is almost unchanged. From Equation (2), the activation energy ΔBE is determined by the relative energy level t–EfE and relaxation energy S. The HCD not only changes the trap energy distribution but also induces a threshold voltage shift. As a result, the relative trap energy distribution remains almost unchanged, as shown in Based on this, we can extract energy distributions from the CET map in The amplitude (ΔId) distribution before and after degradation is shown in 2 characteristics. From the flicker noise modeling [Summing the total number of traps together with the individual contribution to the noise spectrum, we reproduce the flicker noise property, including both the mean and standard deviation. While each trap contributes to noise as a Lorentzian-type spectrum, the summation may present the 1/f characteristics when the number of traps is large or the mixed 1/f and 1/fmodeling , the numThe trap number in each device is extracted by combining the frequency and time domain characterizations. The same devices are characterized to check the possible changes in the trap number after HCD. The coupling effect between the traps induced by HCD and the traps that generate flicker noise will lead to a change in the coupling strength between the flicker noise traps. This will lead to changes in the amplitude distribution of flicker noise traps, which may change the number of RTN traps. Therefore, the coupling effect between the traps induced by HCD and the traps which generate flicker noise can be studied by the change in the number of RTN traps. It shows the opposite trend under different bias conditions. In most devices, the number of traps remains unchanged after both the SVE and MVE stress bias conditions. After the SVE stress bias condition, more devices with a decreased number of traps are observed as compared with those with an increased number of traps. On the contrary, after the MVE stress bias condition, there are more devices with an increased number of traps contributing to noise as compared with those with a decreased number of traps.The change in the number of traps and the amplitudes are indeed correlated to the coupling effect between traps. Traps induced by different bias stress conditions have different impacts on the coupling. This is because of the different locations of the new traps generated by different processes . The traWith the above evidence of trap coupling, the flicker noise properties of FinFETs after HCD should be understood by incorporating the coupling effects in the statistical model.In this work, the flicker noise properties of FinFETs after HCD are studied. The characterizations and analysis show that the time constants of the associated traps are not changing significantly, in contrast to their amplitudes, especially with the SVE-type stress. These results suggest the importance of trap coupling between the HCD-induced traps and those contributing to the flicker noise. Changes in the number of traps are also understood with the coupling theory. With these findings, the flicker noise of aged FinFETs could be well reproduced. Based on this conclusion, a complete reliability model covering the coupling mechanism could be further developed, and the flicker noise properties in the next-generation GAA technology could also be further studied.


Vital node discovery is a hotspot in network topology research. The key is using the Internet’s routing characteristics to remove noisy paths and accurately describe the network topology. In this manuscript, a vital regional routing nodes discovery algorithm based on routing characteristics is proposed. We analyze the stability of multiple rounds of measurement results to overcome the single vantage point’s path deviation. The unstable paths are eliminated from the regional network which is constructed through probing for target area, and the pruned topology is more in line with real routing rules. Finally, we weight the edge based on the actual network’s routing characteristics and discover vital nodes in combination with the weighting degree. Unlike existing algorithms, the proposed algorithm reconstructs the network topology based on communication and transforms unweighted network connections into weighted connections. We can evaluate the node importance in a more realistic network structure. Experiments on the Internet measurement data (275 million probing results collected in 107 days) demonstrate that: the proposed algorithm outperforms four existing typical algorithms. Among 15 groups of comparison in 3 cities, our algorithm found more (or the same number) backbone nodes in 10 groups and found more (or the same number) national backbone nodes in 13 groups. Although existing vital nodes discovery research has achieved rich results, the research seldom considers the actual routing situation of the Internet. The routing characteristics of the actual Internet greatly affect the characterization of the vital nodes of regional networks. How to obtain accurate regional network topology is of great practical significance for discovering vital nodes in target areas.The expansion of the Internet brings unprecedented pressure to network operation and maintenance (O &M). On account of limited resources, network O &M personnel would pay more attention to the vital nodes in the network to guarantee the network’s quality of service (QoS). Vital nodes discovery can mine out the important routing nodes in the network, help network O &M personnel optimize O &M strategies, improve efficiency, and prevent catastrophic failures. Besides, this work can also provide a reference for optimizing existing network protocols and help the network recover more quickly and efficiently after node failure2, Clustering Coefficient3, K-shell Decomposition4, Closeness Centrality (CC)5, Betweenness Centrality (BC)6.In addition, some new methods have also been proposed recently. Xu et al.7 proposed a new node-centring method called unsigned Laplacian feature vector centring, considering the mutual influence between nodes and their incident edges. Ullah et al.8 provided a Local-and-Global-Centrality (LGC) measuring algorithm to identify the vital nodes through handling local as well as global topological aspects of a network simultaneously. To address the issues of low accuracy and high complexity in traditional online social networks(OSNs), Luo et al.9 built a relationship matrix resolving model to identify vital nodes by complying with community, which is capable of effectively identifying influential nodes in the network. Li et al.10 presented a novel local centrality to identify vital nodes by combining the influence of the node itself and neighbor as well as clustering coefficient information. Rezaei et al.11 proposed a data-driven vital node identification method based on machine learning to address the weak adaptability of heuristic methods based on mathematical expressions.The research on vital nodes discovery originated from graph theory research based on complex networks. Although these methods do not consider the characteristics of the actual Internet, they still have guiding significance for existing research. Methods in this category include Degree Centrality (DC)12 presented two randomized algorithms. Michele et al.13 used an adaptive sampling technique to sample the data in the topology graph to reduce the calculation cost of BC and approximated the BC of vital nodes in the original topology on this basic. Dong et al.14 proposed a localized strategy that can find vital nodes without global knowledge of the network. Sunil15 provided a GNN-based  inductive framework to approximate BC using the message passing mechanism. These methods are almost all based on the macro-statistical characteristics of graphs16, and pay less attention to the routing characteristics of the actual Internet.In recent years, some researchers have optimized the computational process based on such methods to deal with large-scale data. Matteo et al.17 proposed Traffic Load Centrality (TLC). TLC simulates the transmission process of network data packets, and only uses the transmission on the shortest path to describe the load carried by the node, which is used to describe the node’s importance. Linton et al.18 proposed Flow Betweenness Centrality (FBC) by considering the shortest path and the non-shortest paths at the same time. FBC believes that the larger the proportion of paths passing through a node among all the non-repeated paths in the network, the more critical the node is. Shlomi et al.19 combined FBC and network routing and proposed the Routing Betweenness Centrality (RBC). They assumed that the routing table is known and mined vital nodes according to the number of paths connected by the target node. Leonardo et al.20 proposed the Load Centrality (LC), which mined vital nodes in the network by calculating the expected load on the routing nodes. Alain et al.21 considered the heterogeneity of edges between nodes in real-world networks and introduced the Weighted Degree Centrality to measure the importance of nodes. To address the issue of low-degree nodes tending to have higher clustering coefficients, Xuefei et al.22 proposed the Weighted Clustering Coefficient to assess top-k key nodes by taking into account both the node’s clustering coefficient and its degree. This kind of methods regulate the characteristics of the network such as path, traffic and protocol to a certain extent, and mine the vital nodes on this basis. These methods solve some phenomena on the Internet, but they are still difficult to adapt to the actual network.Unlike the above methods, another research takes certain characteristics of the actual Internet into account. Ulrik et al.We propose a network topology denoising method based on stable paths. This method can effectively reduce the data processing scale and reveal the role of stable paths in actual networks.We combine the edge-weighting method with stable paths, which can accurately describe the role of edges between nodes.Experiments on the Internet measurement data (275 million probing results collected in 107 days) of Chengdu, Zhengzhou, and Hangzhou in China demonstrate that: Compared with the classical algorithms , the proposed algorithm can better describe the importance of nodes in the target area and can find more accurate backbone nodes.The structure of this manuscript is organized as follows. In section In view of the above problems and the difficulty of obtaining the Internet routing tables, this manuscript proposes an algorithm for discovering vital nodes in regional networks based on stable path analysis. The main idea is to obtain stable paths from the vantage points to the target based on a large number of repeated and long-term probing, and the vital nodes is discovered based on statistical theory. First, we deploy vantage points inside and outside the target area, and the path information between nodes of the target area is obtained through Internet measurement. On this basis, a preliminary topology graph is constructed. Second, we extract the stable paths of the target network from measured path information and eliminate the unstable paths to denoise the constructed preliminary network topology. Finally, we weight the edges according to the number of stable paths passing through adjacent nodes, and rank the nodes according to the weighting results. The main contributions of this manuscript are the following:The communication among nodes on the Internet is determined by routing rules, which are difficult to obtain directly. However, these routing rules can be approximated by a large number of repeated probes and statistical analyses. In addition, there is a large amount of path information in the massive data measured. The path information contains stable paths determined by the routing rules. This is similar to travel planning on the highway in real life, the planned route is fixed when there is no congestion. Therefore, it is possible to obtain a stable path from the vantage point to the target through Internet measurement and construct a network topology composed of only stable paths. Based on this idea, this section proposes an algorithm for discovering vital nodes in regional networks based on stable path analysis. The proposed algorithm is based on stability analysis of multi-round measurement results to overcome path deviation caused by a single measurement, eliminate unstable paths in the network, and obtain a regional network topology that is more in line with real routing rules. Unlike existing algorithms, this algorithm reconstructs the network topology based on traffic, transforming the unweighted internet into a weighted connection, and studying node importance assessment in a structure closer to the actual internet. This can effectively overcome the inapplicability of traditional algorithms on non-cooperative networks whose size, node relationships and routing rules are almost unknown to us. Figure The main steps of the algorithm are as follows.Step 1: Deploy the vantage points. When only a single vantage point is used to probe the target IP, the measurement results are prone to spatial offset and accidental. Therefore, a set of vantage points A, and Step 2: Acquire the preliminary topology of the target area. Firstly, retrieve the IP address segments A from databases D such as IPIP, WHOIS, and IP2location  to weight the edges of the denoised topology, we can obtain a weighted topology of the target area. The weights represent the actual traffic carried by the edges.Step 5: Identify the vital nodes in the regional network. Calculate the routing weighted degree centrality (RWDC) of each node in the topological graph, and rank the nodes according to RWDC, then identify the vital nodes in the regional network. The calculation of the Routing Weighted Degree Centrality for node G, A and extracts the nodes and edges of target area A based on the measurement paths (a path from the probe source to the target node) to construct the initial topology structure of target area A (lines 1-5). Then, count the number of occurrences of all measurement paths and retain the path with the highest number of occurrences as a stable path to construct a denoised graph Among the paths between node N times probing in time t is denoted as p is denoted as The set of paths between As shown in Fig. Path 1: Path 2: Path 3: Path 4: The path with the most occurrence times is Path 2, which accounted for 98.38% of the total number of paths. Therefore, Path 2 is the stable path from the vantage point to p in p.The proposed method takes the number of stable paths passing through an edge as the weight of the edge. If all stable paths in the network are denoted as For ease of understanding, this section describes the method of edge-weighting based on routing characteristics with the example in Fig. As shown in Fig. Stable path 1: Stable path 2: Stable path 3: So the weight of edge  of all nodes in Fig. Consider the weight of the edge and calculate the weighted degree centrality (WDC) of all nodes in Fig. As can be seen from Tables In the existing research, the mining of vital nodes based on the weighting method are not based on the actual topology data, they are still the mining of the mathematical characteristics of the known topology. The proposed algorithm starts with the actual data, and the proposed weighting method is closer to actual network characteristics, which can better reflect the importance of different edges in the network.In order to verify the feasibility and effectiveness of the proposed algorithm, this section conducts the vital nodes discovery experiment. In the case of obtaining the actual communication paths between all nodes-in-pairs in the target area, we can get the most accurate results of vital nodes discovery. However, this requires deploying a probe at each node in the target network, which is difficult for a medium-sized city. Therefore, this section selects some vantage points to carry out continuous probing (last 107 days) on the IP addresses of the target area. The measurement results could approximate the communication of actual networks. The experimental results show that the performance of the proposed algorithm is better than existing algorithms, indicating that the approximation method is reasonable.Experimental setup in the data acquisition stage are shown in Table A represents the target areas, D represents the IP address databases, V represents vantage points, and T represents the cycle of probing.In Table Considering the realistic conditions, this section chooses three cities in China, including Chengdu, Sichuan Province, Hangzhou, Zhejiang Province, and Zhengzhou, Henan Province as the target areas. Then, select the IP address blocks located in the target areas from 6 IP address databases, retain the IP blocks that have appeared in at least 3 IP address databases to form the IP block set 25. Based on this situation, this section selects one IP from each /24 IP block to construct the target set V .The real subnet structure and division method are difficult to obtain directly, so this section extracts IP addresses from network segments for probing. IPes in the same network segment are often similar in routing strategy, geographical location and other settings, and often belong to the same organization26 developed by CAIDA for Internet measurement. The IP address blocks of the three target cities were selected from 6 IP address databases, including IPIP, Whois, IPPlus, IP2location, Maxmind and IPcn released in November 2019.This section uses ScamperThere are 12,748,117 IP addresses in the three target cities, and the three target IP sets contain 60,337 target IP addresses in total. The number of IP addresses and target IP addresses of the three cities are shown in Table Due to the unique situation of the layered architecture of China’s Internet, the communication between Internet Service Providers (ISP) without interconnection needs to be forwarded through Internet Exchange Points (IXP) deployed in specific cities. Therefore, in order to avoid the interference of cross-city data, this section only selects a single operator for experimentation. This manuscript uses the data of China Telecom in the above data set as an example to conduct the following vital nodes discovery experiments.After obtaining the topological data of target cities, the weighted network topology graph could be constructed and denoised based on the stable paths to obtain the routing weighted degree centrality (RWDC) of the nodes. This section conducted the following three experiments: Experiment on the effect of different Internet measurement durations on the algorithm’s performance, comparison experiment of nodes discovery before and after denoising, and comparison experiment of the proposed algorithm and baseline algorithms. The experimental results are validated according to the existing database.Notations used in this section are listed in Table This section compares the network size and ranking results on measurement results collected in 5 days (60 rounds), 40 days (360 rounds) and 107 days 1,284 rounds), respectively. Take Chengdu as an example to show the results, as shown in Tables 4 rounds,As can be seen from Table This shows that in the case of a large difference in measurement duration, the number of paths, edges, and nodes have significant changes in the obtained topology graph. However, the data scale after denoising does not change much, as well as the vital nodes discovery results of the proposed algorithm. At the same time, when the measurement duration is short, it is impossible to find enough vital nodes because the number of stable paths is insufficient. Therefore, it is necessary to mine the vital nodes after the data collection reaches a certain scale. When the number of stable paths is sufficient, the proposed algorithm can discover all the vital nodes that can be mined under this vantage point.This section compares the scale of networks and ranking accuracy before and after denoising, and the results are shown in Table B respectively represent the number of national backbone node / provincial backbone node / backbone nodes among the top-k nodes in the ranking results. As can be seen from Table Table The green/orange/blue sectors in Fig. Combining the results in Table To validate the effectiveness of the proposed algorithm, the result obtained by RWDC is compared with those of DC, BC and RBC. The corresponding relationship between RWDC and DC, BC, RBC are shown in Fig. The abscissa in Fig. To compare the accuracy of the 4 metrics, this section uses existing public databases to verify the results. The comparison results are shown in Table In Table Taking the results of Hangzhou as an example, it can be seen from Fig. Take the experimental results in Chengdu as an example, the top-10 nodes and validation results under the 4 metrics are shown in Table According to Table The experimental results demonstrate that the proposed algorithm can find more backbone nodes than DC, BC and RBC, and the results are more accurate.This manuscript proposes an algorithm for discovering vital nodes in regional networks based on stable path analysis. The network topology denoising method based on stable paths proposed by this algorithm can effectively reduce the scale of processed data, and the edge-weighting method based on routing characteristics can significantly distinguish the role of edges in actual communication. Experimental results show that, the proposed algorithm can find more vital nodes than existing algorithms. However, due to the impact of load balancing and the limitation of the deployment of vantage points, this algorithm cannot find all the vital nodes in the target area. This is determined by stable paths passed by the experimentally deployed vantage points. For this reason, we will study how to deploy vantage points to obtain a relatively complete regional network topology in future work, then improve the discovery ability of vital nodes in the target area.


Dental articulation holds crucial and fundamental importance in the design of dental restorations and analysis of prosthetic or orthodontic occlusions. However, common traditional and digital articulators are difficult and cumbersome in use to effectively translate the dental cast model to the articulator workspace when using traditional facebows. In this study, we have developed a personalized virtual dental articulator that directly utilizes computed tomography (CT) data to mathematically model the complex jaw movement, providing a more efficient and accurate way of analyzing and designing dental restorations. By utilizing CT data, Frankfurt’s horizontal plane was established for the mathematical modeling of virtual articulation, eliminating tedious facebow transfers. After capturing the patients’ CT images and tracking their jaw movements prior to dental treatment, the jaw-tracking information was incorporated into the articulation mathematical model. The validation and analysis of the personalized articulation approach were conducted by comparing the jaw movement between simulation data  and real measurement data. As a result, the proposed virtual articulator achieves two important functions. Firstly, it replaces the traditional facebow transfer process by transferring the digital dental model to the virtual articulator through the anatomical relationship derived from the cranial CT data. Secondly, the jaw movement trajectory provided by optical tracking was incorporated into the mathematical articulation model to create a personalized virtual articulation with a small Fréchet distance of 1.7 mm. This virtual articulator provides a valuable tool that enables dentists to obtain diagnostic information about the temporomandibular joint (TMJ) and configure personalized settings of occlusal analysis for patients. The dental industry has undergone significant changes in recent years with the rapid growth of digital dentistry ,2,3. AdvFirst known by the work of Dr. Daniel T. Evens in 1840 , the artFor decades, a number of different methods have been developed for jaw movement assessment. An ultrasound device was developed quite early for jaw movement measurement . ElectroA complete digital workflow now involves the use of digital or virtual articulators for restoration design and even orthodontic occlusion analysis ,23. In oThe aim of this study is to develop a virtual articulator capable of reproducing personalized jaw movements and establish a digital workflow for creating a virtual articulation by utilizing jaw movement and information obtained from CT scans. The patient’s jaw movement is tracked before dental treatment, and this information is integrated into the articulation mechanism to construct a personalized mathematical model of jaw movement. The development of the virtual articulator involves the utilization of C++ and OpenGL libraries, with the application of VTK and ITK libraries for jaw extraction software. This model serves as a valuable tool for dentists and dental technicians in prosthesis design or treatment planning, particularly in cases where the patient is not physically present at the clinic. Furthermore, the mathematical model enables precise control over mandibular movement without the need for a mechanical or digital articulator. This eliminates the cumbersome process of employing a facebow for transferring digital cast models to the articulator space. The workflow for constructing the personalized virtual articulation is depicted in Mandibular movement is determined by the activities of TMJs, with the condyles being crucial components in expressing these movements . The preFor the inverse kinematic analysis, we consider the coordinates of the condyle positions in the initial (centric relation) state as The displacement of the incisal tip from Combining Equations (4)–(6), we have the following:The lateral excursion will move its position following the condylar path to From Equations (12)–(14), we derive a set of 6 constraint equations to solve the 6-degree-of-freedom problem for l method . The samIn the traditional  articulator procedure, ensuring the correct positional relationship between the articulator hinge axis and the dental mold in space requires transferring the maxillary dental mold to the articulator using a facebow. Similarly, in the virtual articulation process, it is also necessary to transfer this relationship correctly to the virtual articulator in order to simulate articulating motion that is consistent with the human body’s motion. The mechanical facebow mechanism consists of a body defining a reference plane, a bite fork, and a bracket structure connecting the bite fork and the facebow body, as shown in In virtual articulation, the reference plane was defined similarly to the traditional facebow transfer, using two rear reference points and one front reference point based on CT data. In this study, either the Frankfurt plane or Camper’s plane can be used as the reference plane . If the In order to obtain the CT images that include the complete jaw and TMJ information, we use SIEMENS Emotion 6  a to captIn this research, a dual-marker optical tracking system including an eyeglass frame combined with the tracking marker and a 3D-printed splint was used to track the relative movement of the upper jaw and lower jaw, respectively . Before lication .(15)PloTo register the tracking markers to the virtual articulator coordinate system, we used 3D scanning to scan the human face with the upper tracking marker. The human face was matched with the CT skin surface mesh using the ICP algorithm , therebyThrough the above derivation, we can track the movement of any point on the lower jaw, in which the movement trajectory of the condyles and the incisal edge of the incisor can be used as the information required for personalized articulation. Since the tracking system uses the calculation of the relative movement of the upper and lower markers, it can reproduce the relative movement between the upper and lower jaws.The accuracy of simulation and modeling can be verified by comparing simulation data to measurement data. In this work, we aim to evaluate the accuracy of the jaw motion mathematical model by estimating differences between the simulated trajectory of jaw motion and the (measured) real trajectory. The real trajectory is obtained by optically measuring the pose of the lower jaw (including rotation and translation) to obtain the condyle positions using lower jaw geometry from CT/CBCT. Meanwhile, the simulated trajectory is obtained by using the mathematical articulation model to inversely calculate the condyle positions from the measured incisor edge points. Various error indices can be used to estimate the difference between the two trajectories using sampled discrete data points. One commonly used error index is the average trajectory error (equation :(17)ATEaTo verify the accuracy of the personalized mathematical model of jaw movement derived in this study, a set of experimental methods was designed for accuracy verification analysis. The principle of this verification method is to compare the trajectory of the left and right condyles with the trajectory of the simulation when the jaw moves. Initially, posture estimation of the tracking marker during the mandible movement was used to derive the related positions of the condyles, thereby obtaining a moving trajectory of the left and right condyles. Then, the recorded position of the incisal edge was used in conjunction with the mathematical model of mandibular movement derived in this study to inversely calculate the corresponding left and right condyle positions. Consequently, a simulated movement trajectory of the left and right condyles was obtained. Finally, the accuracy indicator was obtained by comparing the similarity of the two curves. The process is illustrated in In computer vision and computational geometry fields, the Fréchet distance  is commoThe digital teeth model was positioned within the virtual articulator coordinate system in accordance with human anatomy, achieved through the registration of the digital teeth model with the cranial CT model. The condyles of the virtual articulator were matched with the corresponding human condyles identified in the CT data. Given the nearly spherical shape of the condyle, a spherical fitting approach was employed, utilizing a ball to conform to the condyle’s morphology. The centroids of the fitted balls were then employed as posterior reference points.In this work, a user interface was implemented to enable users to select reference points on the cranial CT model, as illustrated in Following the affixation of two fiducial markers onto the upper and lower jaws, the patient was required to adjust the occlusal relationship to the centric occlusion (CO) position as the initial position of the tracking. Once confirming that the two markers are within the working range of the camera, the tracking can be started. The tracking results were subsequently combined with the cranial surface mesh model. In particular, the movement trajectory of the condyles during the protrusion and lateral excursions can be recorded. The tracking outcomes allow physicians to diagnose TMJ disorders during mandibular movement. Furthermore, these results can be used to personalize the condylar path of the virtual articulator.In this work, a computer simulation program was built based on the personalized mathematical model of jaw movement, which can perform dynamic occlusion simulation and display the patient’s upper and lower jaws, condylar paths, and interference points during occlusion. This simulation program provides useful information to assist dentists in designing dentures or other dental-related products. Its interface is shown in The system moves the incisal point according to the incisal guidance path and calculates the posture of the mandible at different positions on the path. However, the motion path is programmable based on our mathematical model and changes with the collision of the upper and lower jaw teeth. For interference checking, we employ sphere collision detection and adjust the motion path according to the interference between teeth during the motion. Therefore, this approach enables users to design new prostheses effectively. By exploiting the virtual articulator, they can simulate the patient’s occlusal path during forward, left, and right protrusions, as shown in Most mechanical articulators adopt a fixed straight-line or a curve pattern for representing the condylar path. However, the condylar path is in fact a personalized 3-dimensional trajectory. In this work, to combine the mandibular motion information with the mathematical model of the articulation, the condylar path obtained by the above tracking method was fitted and combined with the mathematical model of the articulation. The articulation has two adjustment parameters that represent the shape of the condyle projection in the horizontal and sagittal planes . TherefoThe points on the condylar path of the protrusion process were projected onto the sagittal plane and fitted with a quadratic curve, which contains the personalized condyle shape and condylar inclination;At the same time, the condylar path on the working side was projected onto the horizontal plane and fitted with a straight line. This linear trajectory represents the movement of the condyle during lateral motion on the working side, corresponding to the Bennett angle of the articulation, as shown in The curve equations of these two two-dimensional planes can be combined into a three-dimensional curve in space, as shown in Equation (18).This 3-dimensional curve  can be determined by a curve fitting regression process. The result can be represented as a parametric B-Spline or NURBS  curve in 3D space, as shown in This personalized condylar curve equation replaces the fixed articulator mechanism of traditional mechanical articulators, so that a personalized mathematical model of jaw movement can be obtained. When tracking the mandible, the incisal edge movement trajectory of the patient’s protrusion and lateral excursions are also recorded, as shown in Experiments were conducted on the occlusal paths of anterior protrusion and lateral excursions. Each movement was conducted from the CO position to the extreme position, back and forth twice. After adding the mandibular motion information to the mathematical model of the articulator, we imported the positions of the incisal edge to calculate the positions of the condyles. The data were analyzed to compare the condylar trajectories between the direct tracking measurement and the inverse calculation from the incisal edge. The trajectory comparison results are presented in The discrete Fréchet distances  for eachBased on the results of the experiment, we found that the Fréchet distance between the tracked mandible movement and the simulated condyle movement in this study was approximately 1.7 mm.Our study provides a comprehensive digital workflow for developing a personalized virtual articulator using CT scans and jaw movement data from patients. The results verify that the constructed mathematical model effectively controls mandibular movement without the need for a mechanical or digital articulator. From raw CT scan data, we successfully segmented the upper and lower jaws for subsequent registration. Through the registration of the digital teeth model with the cranial CT model, the digital teeth model was positioned within the virtual articulator coordinate system. As a result, the condyles of the virtual articulator were matched with the corresponding human condyles. The jaw motion tracking allowed for recording the movement trajectory of the condyles during protrusion and lateral excursions. This capability opens up applications for the developed virtual articulator in TMJ disorder diagnosis. The developed software program based on available libraries such as C++ and OpenGL enables simulating the positions of occlusal paths on patients. The personalized condylar curve obtained serves as a substitute for the rigid articulator mechanism inherent in conventional mechanical articulators. This innovation allows the derivation of a customized mathematical representation of jaw movements. Furthermore, the tracked mandible movement and the simulated condyle movement were verified through an acceptable Fréchet distance of 1.7 mm to demonstrate the feasibility of the proposed model.Nowadays, there are commercial digital articulators such as the Ceramill Map 300 CAD/CAM system by Amann Girrbach  , Dental Every individual possesses a unique articulation and occlusion. To personalize individual articulation, a mathematical articulation model and the following personalized parameters must be determined: Bennett angle , condyleThere are several commercial jaw-motion tracking systems that use high-resolution optical scanning devices, such as Zebris   and ModjIn contrast, our proposal integrates a mathematical jaw motion model that combines CT data analysis to identify and register anatomical/geometric attributes, such as condylar distance, reference planes, and patient-specific condylar paths. This integrated information provides an individualized jaw motion model that can be used for programmable jaw motion and occlusal analysis. Simulation results from the software built based on the mathematical model demonstrate its capability to work accurately with various mandible postures. The main difference between our proposal and systems like Zebris or Modjaw is that their occlusion analysis is based on either recorded jaw motion paths or the kinematic analysis of lab-based digital mechanical articulators. In other words, their occlusal analysis still relies on lab-based mechanical articulators but is digitally implemented. The choice of the type of mechanical articulator used will influence the occlusion analysis results significantly. Conversely, our proposal is based on a generalized mathematical jaw motion model that accounts for both static patient anatomy (from CBCT) and dynamic patient-specific condyle movements. Our model can program the jaw motion dynamically to satisfy various functional requirements such as occlusion analysis or splint design. Additionally, compared to the hinge axis arbitrarily established by the traditional facebow, this study’s definition aligns more closely with the human anatomy structure. With the CT data-defined reference plane, aligning the human skull and virtual articulator becomes easier without relying on the traditional mechanical facebow. Artificial intelligence (AI) applications in the medical field in general, and dentistry in particular, have become increasingly prevalent and providing substantial value over the past two decades ,43. WithThe Fréchet distance result indicates an average deviation of the condyle position during the simulation of occlusal movement at 1.7 mm, accounting for errors from intra-oral scans, CT scans, registration, marker tracking, and mathematical modeling. The limitations of the laboratory equipment with low accuracy contribute to the overall error in this study, which is reflected in the value of the Fréchet distance. While this research demonstrates the feasibility and effectiveness of the proposed solution in the university research environment and laboratory setting, there is room for improvement in accuracy. This could be achieved by employing higher-resolution cameras or commercial optical tracking devices. As modern camera technology continues to advance, we anticipate an enhancement in the accuracy of jaw tracking. In this study, we focused on building a digital workflow for the development of a personalized virtual articulator, without delving into extensive clinical applications. Nevertheless, the methodology involved experiments on human samples, utilizing CT scan images and capturing real jaw movement. Along with reported results, the developed virtual articulator demonstrates to be feasible for various clinical applications such as TMJ disorder diagnosis  and occlThis research work presents the development of a personalized virtual articulator constructed from CT data and jaw movement information. Such an approach enables the creation of a unique mathematical model of dental articulation, which can be utilized by dental professionals in prosthesis design and treatment planning. With this method, digital simulation of patient-specific occlusion can be performed remotely, even when the patient is not present in the clinic.