Distributed Nash Equilibrium Seeking Strategies Under Quantized Communication

This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization o players' objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized informa tion flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respec tively. Through Lyapunov stability analysis, it is shown that play ers' actions can be steered to a neighborhood of the Nash equilib rium with logarithmic and uniform quantizers, and the quanti fied convergence error depends on the parameter of the quan tizer for both undirected and directed cases. A numerical exam ple is given to verify the theoretical results.

Magnetopause properties at the dusk magnetospheric flank from global magnetohydrodynamic simulations,the kinetic Vlasov equilibrium,and in situ observations--Potential implications for SMILE

We derived the properties of the terrestrial magnetopause(MP)from two modeling approaches,one global–fluid,the other local–kinetic,and compared the results with data collected in situ by the Magnetospheric Multiscale 2(MMS2)spacecraft.We used global magnetohydrodynamic(MHD)simulations of the Earth’s magnetosphere(publicly available from the NASA-CCMC[National Aeronautics and Space Administration–Community Coordinated Modeling Center])and local Vlasov equilibrium models(based on kinetic models for tangential discontinuities)to extract spatial profiles of the plasma and field variables at the Earth’s MP.The global MHD simulations used initial solar wind conditions extracted from the OMNI database at the time epoch when the MMS2 observes the MP.The kinetic Vlasov model used asymptotic boundary conditions derived from the same in situ MMS measurements upstream or downstream of the MP.The global MHD simulations provide a three-dimensional image of the magnetosphere at the time when the MMS2 crosses the MP.The Vlasov model provides a one-dimensional local view of the MP derived from first principles of kinetic theory.The MMS2 experimental data also serve as a reference for comparing and validating the numerical simulations and modeling.We found that the MP transition layer formed in global MHD simulations was generally localized closer to the Earth(roughly by one Earth radius)from the position of the real MP observed by the MMS.We also found that the global MHD simulations overestimated the thickness of the MP transition by one order of magnitude for three analyzed variables:magnetic field,density,and tangential speed.The MP thickness derived from the local Vlasov equilibrium was consistent with observations for all three of these variables.The overestimation of density in the Vlasov equilibrium was reduced compared with the global MHD solutions.We discuss our results in the context of future SMILE(Solar wind Magnetosphere Ionosphere Link Explorer)campaigns for observing the Earth’s MP.

Numerical analysis for the free-boundary current reversal equilibrium in the AC plasma current operation in a tokamak

In recent decades, tokamak discharges with zero total toroidal current have been reported in tokamak experiments, and this is one of the key problems in alternating current(AC) operations.An efficient free-boundary equilibrium code is developed to investigate such advanced tokamak discharges with current reversal equilibrium configuration. The calculation results show that the reversal current equilibrium can maintain finite pressure and also has considerable effects on the position of the X-point and the magnetic separatrix shape, and hence also on the position of the strike point on the divertor plates, which is extremely useful for magnetic design, MHD stability analysis, and experimental data analysis etc. for the AC plasma current operation on tokamaks.

Kinetic equilibrium reconstruction with internal safety factor profile constraints on EAST tokamak

Reconstruction of plasma equilibrium plays an important role in the analysis and simulation of plasma experiments. The kinetic equilibrium reconstruction with pressure and edge current constraints has been employed on EAST tokamak. However, the internal safety factor(q) profile is not accurate. This paper proposes a new way of incorporating q profile constraints into kinetic equilibrium reconstruction. The q profile is yielded from the Polarimeter Interferometer(POINT)reconstruction. Virtual probes containing information on q profile constraints are added to inputs of the kinetic equilibrium reconstruction program to obtain the final equilibrium. The new equilibrium produces a more accurate internal q profile. This improved method would help analyze EAST experiments.

Equilibrium Strategy of the Pursuit-Evasion Game in Three-Dimensional Space

The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper,we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer's three-degree-of-freedom control and the evader's relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs(HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer's speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium.

Multi-Objective Equilibrium Optimizer for Feature Selection in High-Dimensional English Speech Emotion Recognition

Speech emotion recognition(SER)uses acoustic analysis to find features for emotion recognition and examines variations in voice that are caused by emotions.The number of features acquired with acoustic analysis is extremely high,so we introduce a hybrid filter-wrapper feature selection algorithm based on an improved equilibrium optimizer for constructing an emotion recognition system.The proposed algorithm implements multi-objective emotion recognition with the minimum number of selected features and maximum accuracy.First,we use the information gain and Fisher Score to sort the features extracted from signals.Then,we employ a multi-objective ranking method to evaluate these features and assign different importance to them.Features with high rankings have a large probability of being selected.Finally,we propose a repair strategy to address the problem of duplicate solutions in multi-objective feature selection,which can improve the diversity of solutions and avoid falling into local traps.Using random forest and K-nearest neighbor classifiers,four English speech emotion datasets are employed to test the proposed algorithm(MBEO)as well as other multi-objective emotion identification techniques.The results illustrate that it performs well in inverted generational distance,hypervolume,Pareto solutions,and execution time,and MBEO is appropriate for high-dimensional English SER.

Phase equilibrium data prediction and process optimizationin butadiene extraction process

In response to the lack of reliable physical parameters in the process simulation of the butadiene extraction,a large amount of phase equilibrium data were collected in the context of the actual process of butadiene production by acetonitrile.The accuracy of five prediction methods,UNIFAC(UNIQUAC Functional-group Activity Coefficients),UNIFAC-LL,UNIFAC-LBY,UNIFAC-DMD and COSMO-RS,applied to the butadiene extraction process was verified using partial phase equilibrium data.The results showed that the UNIFAC-DMD method had the highest accuracy in predicting phase equilibrium data for the missing system.COSMO-RS-predicted multiple systems showed good accuracy,and a large number of missing phase equilibrium data were estimated using the UNIFAC-DMD method and COSMO-RS method.The predicted phase equilibrium data were checked for consistency.The NRTL-RK(non-Random Two Liquid-Redlich-Kwong Equation of State)and UNIQUAC thermodynamic models were used to correlate the phase equilibrium data.Industrial device simulations were used to verify the accuracy of the thermodynamic model applied to the butadiene extraction process.The simulation results showed that the average deviations of the simulated results using the correlated thermodynamic model from the actual values were less than 2%compared to that using the commercial simulation software,Aspen Plus and its database.The average deviation was much smaller than that of the simulations using the Aspen Plus database(>10%),indicating that the obtained phase equilibrium data are highly accurate and reliable.The best phase equilibrium data and thermodynamic model parameters for butadiene extraction are provided.This improves the accuracy and reliability of the design,optimization and control of the process,and provides a basis and guarantee for developing a more environmentally friendly and economical butadiene extraction process.

Magnetic diagnostics layout design for CFETR plasma equilibrium reconstruction

Plasma equilibrium reconstruction provides essential information for tokamak operation and physical analysis.An extensive and reliable set of magnetic diagnostics is required to obtain accurate plasma equilibrium.This study designs and optimizes the magnetic diagnostics layout for the reconstruction of the equilibrium of the plasma according to the scientific objectives,engineering design parameters,and limitations of the Chinese Fusion Engineering Test Reactor(CFETR).Based on the CFETR discharge simulation,magnetic measurement data are employed to reconstruct consistent plasma equilibrium parameters,and magnetic diagnostics'number and position are optimized by truncated Singular value decomposition,verifying the redundancy reliability of the magnetic diagnostics layout design.This provides a design solution for the layout of the magnetic diagnostics system required to control the plasma equilibrium of CFETR,and the developed design and optimization method can provide effective support to design magnetic diagnostics systems for future magnetic confinement fusion devices.

Probabilistic Analysis of Slope Using Finite Element Approach and Limit Equilibrium Approach around Amalpata Landslide of West Central, Nepal

The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have different slope inclinations. The lower bench, located above the basement, consistently fails and sets others up for failure. The fluctuating water level of the slope, which travels down the slope masses, exacerbates the slide problem. The majority of these rocks are Amalpata landslide area experiences several structural disruptions. The area’s stability must be evaluated in order to prevent and control more harm from occurring to the nearby agricultural land and people living along the slope. The slopes’ failures increase the damages of house existing in nearby area and the erosion of the slope. Two modeling techniques the finite element approach and the limit equilibrium method were used to simulate the slope. The findings show that, in every case, the terrace above the basement is where the majority of the stress is concentrated, with a safety factor of near unity. Using probabilistic slope stability analysis, the failure probability was predicted to be between 98.90% and 100%.

Enhanced Hybrid Equilibrium Strategy in Fog-Cloud Computing Networks with Optimal Task Scheduling

More devices in the Intelligent Internet of Things(AIoT)result in an increased number of tasks that require low latency and real-time responsiveness,leading to an increased demand for computational resources.Cloud computing’s low-latency performance issues in AIoT scenarios have led researchers to explore fog computing as a complementary extension.However,the effective allocation of resources for task execution within fog environments,characterized by limitations and heterogeneity in computational resources,remains a formidable challenge.To tackle this challenge,in this study,we integrate fog computing and cloud computing.We begin by establishing a fog-cloud environment framework,followed by the formulation of a mathematical model for task scheduling.Lastly,we introduce an enhanced hybrid Equilibrium Optimizer(EHEO)tailored for AIoT task scheduling.The overarching objective is to decrease both the makespan and energy consumption of the fog-cloud system while accounting for task deadlines.The proposed EHEO method undergoes a thorough evaluation against multiple benchmark algorithms,encompassing metrics likemakespan,total energy consumption,success rate,and average waiting time.Comprehensive experimental results unequivocally demonstrate the superior performance of EHEO across all assessed metrics.Notably,in the most favorable conditions,EHEO significantly diminishes both the makespan and energy consumption by approximately 50%and 35.5%,respectively,compared to the secondbest performing approach,which affirms its efficacy in advancing the efficiency of AIoT task scheduling within fog-cloud networks.

Analysis of Drug Medical Insurance Access Pricing Based on the Perspective of Binary Equilibrium

Objective To study the influencing factors in the process of national medical insurance negotiation and drug pricing from the dualistic equilibrium perspective,and to provide reference for the harmonious management of drug pricing in China.Methods Through the literature analysis and policy review,the pricing subject,pricing basis and price control system in the pricing process of medical-accessed medicines were analyzed from the perspective of binary equilibrium and harmonious management.Results and Conclusion It is found that four balances in the drug pricing process,two balances in pricing basis and three balances in price control system need to be considered,respectively.Drug pricing is the key content of national medical insurance access,which is also the hotspot of the policy in the pharmaceutical fields in recent years.Drug pricing not only reflects the value of drugs,but also reflects a lot of top-level designs of binary equilibriums in medical insurance policy.While the rational design of drug pricing requires the joint efforts of the government,pharmaceutical companies and relevant experts to comprehensively consider many equilibriums,so as to improve the relevant systems.

Critical anomaly and finite size scaling of the self-diffusion coefficient for Lennard Jones fluids by non-equilibrium molecular dynamic simulation

We use non-equilibrium molecular dynamics simulations to calculate the self-diffusion coefficient, D, of a Lennard Jones fluid over a wide density and temperature range. The change in self-diffusion coefficient with temperature decreases by increasing density. For density ρ＊ = ρσ3 = 0.84 we observe a peak at the value of the self-diffusion coefficient and the critical temperature T＊ = kT/ε = 1.25. The value of the self-diffusion coefficient strongly depends on system size. The data of the self-diffusion coefficient are fitted to a simple analytic relation based on hydrodynamic arguments. This correction scales as N-α, where α is an adjustable parameter and N is the number of particles. It is observed that the values of a 〈 1 provide quite a good correction to the simulation data. The system size dependence is very strong for lower densities, but it is not as strong for higher densities. The self-diffusion coefficient calculated with non-equilibrium molecular dynamic simulations at different temperatures and densities is in good agreement with other calculations fronl the literature.

Distributed Nash Equilibrium Seeking for General Networked Games With Bounded Disturbances

This paper is concerned with anti-disturbance Nash equilibrium seeking for games with partial information.First,reduced-order disturbance observer-based algorithms are proposed to achieve Nash equilibrium seeking for games with firstorder and second-order players,respectively.In the developed algorithms,the observed disturbance values are included in control signals to eliminate the influence of disturbances,based on which a gradient-like optimization method is implemented for each player.Second,a signum function based distributed algorithm is proposed to attenuate disturbances for games with secondorder integrator-type players.To be more specific,a signum function is involved in the proposed seeking strategy to dominate disturbances,based on which the feedback of the velocity-like states and the gradients of the functions associated with players achieves stabilization of system dynamics and optimization of players'objective functions.Through Lyapunov stability analysis,it is proven that the players'actions can approach a small region around the Nash equilibrium by utilizing disturbance observerbased strategies with appropriate control gains.Moreover,exponential(asymptotic)convergence can be achieved when the signum function based control strategy(with an adaptive control gain)is employed.The performance of the proposed algorithms is tested by utilizing an integrated simulation platform of virtual robot experimentation platform(V-REP)and MATLAB.

Fully Distributed Nash Equilibrium Seeking for High-Order Players With Actuator Limitations

This paper explores the problem of distributed Nash equilibrium seeking in games, where players have limited knowledge on other players' actions. In particular, the involved players are considered to be high-order integrators with their control inputs constrained within a pre-specified region. A linear transformation for players' dynamics is firstly utilized to facilitate the design of bounded control inputs incorporating multiple saturation functions. By introducing consensus protocols with adaptive and time-varying gains, the unknown actions for players are distributively estimated. Then, a fully distributed Nash equilibrium seeking strategy is exploited, showcasing its remarkable properties: (1) ensuring the boundedness of control inputs;(2) avoiding any global information/parameters;and (3) allowing the graph to be directed. Based on Lyapunov stability analysis, it is theoretically proved that the proposed distributed control strategy can lead all the players' actions to the Nash equilibrium. Finally, an illustrative example is given to validate effectiveness of the proposed method.

The equilibrium composition in Ge_xSi_1-_x/Si self-assembled alloy quantum dot

The equilibrium composition in strained quantum dot is the result of both elastic relaxation and chemical mixing effects, which have a direct relationship to the optical and electronic properties of the quantum-dot-based device. Using the method of moving asymptotes and finite element tools, an efficient technique has been developed to compute the composition profile by minimising the Gibbs free energy in self-assembled alloy quantum dot. In this paper, the composition of dome-shaped CexSi1-x/Si quantum dot is optimized, and the contribution of the different energy to equilibrium composition is discussed. The effect of composition on the critical size for shape transition of pyramid-shaped GeSi quantum dot is also studied.

Rapid evolution of T2/S-RNase genes in Fragaria linked to multiple transitions from self-incompatibility to self-compatibility

The T2/RNase gene family is widespread in eukaryotes,and particular members of this family play critical roles in the gametophytic self-incompatibility(GSI) system in plants.Wild diploid strawberry(Fragaria)species have diversified their sexual systems via self-incompatible and self-compatible traits,yet how these traits evolved in Fragaria remains elusive.By integrating the published and de novo assembled genomes and the newly generated RNA-seq data,members of the RNase T2 gene family were systematically identified in six Fragaria species,including three self-incompatible species(Fragaria nipponica,Fragaria nubicola,and Fragaria viridis) and three self-compatible species(Fragaria nilgerrensis,Fragaria vesca,and Fragaria iinumae).In total,115 RNase T2 genes were identified in the six Fragaria genomes and can be classified into three classes(Ⅰ-Ⅲ) according to phylogenetic analysis.The identified RNase T2 genes could be divided into 22 homologous gene sets according to amino acid sequence similarity and phylogenetic and syntenic relationships.We found that extensive gene loss and pseudogenization coupled with small-scale duplications mainly accounted for variations in the RNase T2 gene numbers in Fragaria.Multiple copies of homologous genes were mainly generated from tandem and segmental duplication events.Furthermore,we newly identified five S-RNase genes in three self-incompatible Fragaria genomes,including two in F.nipponica,two in F.viridis,and one in F.nubicola,which fit for typical features of a pistil determinant,including highly pistil-specific expression,highly polymorphic proteins and alkaline isoelectric point(pI),while no S-RNase genes were found in all three selfcompatible Fragaria species.Surprisingly,these T2/S-RNase genes contain at least one large intron(>10 kb).This study revealed that the rapid evolution of T2/S-RNase genes within the Fragaria genus could be associated with its sexual mode,and repeated evolution of the self-compatible traits in Fragaria was convergent via losses of S-RNase.

Quantum-Inspired Equilibrium Optimizer for Linear Antenna Array

With the rapid development of communication technology,the problem of antenna array optimization plays a crucial role.Among many types of antennas,line antenna arrays(LAA)are the most commonly applied,but the side lobe level(SLL)reduction is still a challenging problem.In the radiation process of the linear antenna array,the high side lobe level will interfere with the intensity of the antenna target radiation direction.Many conventional methods are ineffective in obtaining the maximumside lobe level in synthesis,and this paper proposed a quantum equilibrium optimizer(QEO)algorithm for line antenna arrays.Firstly,the linear antenna array model consists of an array element arrangement.Array factor(AF)can be expressed as the combination of array excitation amplitude and position in array space.Then,inspired by the powerful computing power of quantum computing,an improved quantum equilibrium optimizer combining quantum coding and quantum rotation gate strategy is proposed.Finally,the proposed quantum equilibrium optimizer is used to optimize the excitation amplitude of the array elements in the linear antenna array model by numerical simulation to minimize the interference of the side lobe level to the main lobe radiation.Six differentmetaheuristic algorithms are used to optimize the excitation amplitude in three different arrays of line antenna arrays,the experimental results indicated that the quantum equilibrium optimizer is more advantageous in obtaining the maximum side lobe level reduction.Compared with other metaheuristic optimization algorithms,the quantum equilibrium optimizer has advantages in terms of convergence speed and accuracy.

The extraction of aromatics using N-methylpyrrolidone: Liquid-liquidequilibrium determination and mechanism exploration

LLE data of cyclooctane/3-methylpentane + benzene/toluene + N-methylpyrrolidone (NMP) at 298.15 Kand 313.15 K under a pressure of 101.3 kPa were measured in this work. The Othmer-Tobias and Handequations were adopted to validate the reliability of LLE data, where the correlation coefficients (R2) wereclose to unity, indicating the high reliability of the experimental data. The experimental data were analyzed using the distribution coefficient (D) and separation factor (S), and the effect of NMP extracting benzene and toluene from aromatics was explored. Meanwhile, the reason for the different extractionefficiencies of benzene and toluene using NMP was analyzed by quantum chemical calculations. TheNRTL and UNIQUAC thermodynamic models were used to correlate the liquid–liquid equilibrium data,and the relevant binary interaction parameters were obtained. The calculated root mean square deviation(RMSD) were all less than 0.0063, indicating that the obtained binary interaction parameters can be usedto simulate and calculate the extraction of aromatics using NMP.

Region coverage control for multiple stratospheric airships with combined self-/event-triggered mechanism

The region coverage control problem of multiple stratospheric airships system is firstly addressed in this paper.Towards it,we propose a two-layer control framework with the artificial potential field(APF)-based region coverage control law and the adaptive tracking control law.The APF-based region coverage control law ensures the coverage task is achieved until every single stratospheric airship ends up performing station keeping where near the respective global minimum point,in which an innovative solution to the local minimum problem is put forward.The adaptive tracking control law is designed to realize motion control using tracking the desired velocity and angular velocity given by coverage control law,with the consideration of several practical control problems as unknown individual differences and external disturbances.To save resources,the combined self-/event-triggered mechanism designed therein significantly reduces the times of state information transmission and control law calculation.The effectiveness of the proposed control framework is verified through simulations.

Measurement and prediction of isothermal vapor–liquid equilibrium of a-pinene+camphene/longifolene+abietic acid+palustric acid+neoabietic acid systems

The vapor–liquid equilibrium(VLE)data of a-pinene+camphene+[abietic acid+palustric acid+neoabietic acid]and a-pinene+longifolene+[abietic acid+palustric acid+neoabietic acid]systems at 313.15 K,333.15 K and 358.15 K were measured by headspace gas chromatography(HSGC).These data was compared with the predictions value by conductor-like screening model for realistic solvation(COSMO-RS).Moreover,the calculated data of COSMO-RS and Non-Random Two-Liquids(NRTL)models showed good agreement with the experimental data.It was found that the three resin acids inhibited the volatility of a-pinene,camphene and longifolene and resulted in the decrease of total pressure.Moreover,HE(HB)contributes the most to the excess enthalpy and the hydrogen bonding interaction is the dominant intermolecular force of a-pinene,camphene and longifolene with the three resin acids.In addition,the geometric structures optimization and binding energy were obtained by the DFT to further illustrate the hydrogen bonding interaction and the effects of the addition of the three resin acids on the isothermal VLE.