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.

Semi-analytical steady-state response prediction for multi-dimensional quasi-Hamiltonian systems

The majority of nonlinear stochastic systems can be expressed as the quasi-Hamiltonian systems in science and engineering. Moreover, the corresponding Hamiltonian system offers two concepts of integrability and resonance that can fully describe the global relationship among the degrees-of-freedom(DOFs) of the system. In this work, an effective and promising approximate semi-analytical method is proposed for the steady-state response of multi-dimensional quasi-Hamiltonian systems. To be specific, the trial solution of the reduced Fokker–Plank–Kolmogorov(FPK) equation is obtained by using radial basis function(RBF) neural networks. Then, the residual generated by substituting the trial solution into the reduced FPK equation is considered, and a loss function is constructed by combining random sampling technique. The unknown weight coefficients are optimized by minimizing the loss function through the Lagrange multiplier method. Moreover, an efficient sampling strategy is employed to promote the implementation of algorithms. Finally, two numerical examples are studied in detail, and all the semi-analytical solutions are compared with Monte Carlo simulations(MCS) results. The results indicate that the complex nonlinear dynamic features of the system response can be captured through the proposed scheme accurately.

A Posteriori Stabilized Sixth-Order Finite Volume Scheme with Adaptive Stencil Construction:Basics for the 1D Steady-State Hyperbolic Equations

We propose an adaptive stencil construction for high-order accurate finite volume schemes a posteriori stabilized devoted to solve one-dimensional steady-state hyperbolic equations.High accuracy(up to the sixth-order presently)is achieved,thanks to polynomial recon-structions while stability is provided with an a posteriori MOOD method which controls the cell polynomial degree for eliminating non-physical oscillations in the vicinity of dis-continuities.We supplemented this scheme with a stencil construction allowing to reduce even further the numerical dissipation.The stencil is shifted away from troubles(shocks,discontinuities,etc.)leading to less oscillating polynomial reconstructions.Experimented on linear,Burgers',and Euler equations,we demonstrate that the adaptive stencil technique manages to retrieve smooth solutions with optimal order of accuracy but also irregular ones without spurious oscillations.Moreover,we numerically show that the approach allows to reduce the dissipation still maintaining the essentially non-oscillatory behavior.

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.

Secondary steady-state and time-periodic flows from a basic flow with square array of odd number of vortices

In a magnetohydrodynamic(MHD)driven fluid cell,a plane non-parallel flow in a square domain satisfying a free-slip boundary condition is examined.The energy dissipation of the flow is controlled by the viscosity and linear friction.The latter arises from the influence of the Hartmann bottom boundary layer in a three-dimensional(3D)MHD experiment in a square bottomed cell.The basic flow in this fluid system is a square eddy flow exhibiting a network of N~2 vortices rotating alternately in clockwise and anticlockwise directions.When N is odd,the instability of the flow gives rise to secondary steady-state flows and secondary time-periodic flows,exhibiting similar characteristics to those observed when N=3.For this reason,this study focuses on the instability of the square eddy flow of nine vortices.It is shown that there exist eight bi-critical values corresponding to the existence of eight neutral eigenfunction spaces.Especially,there exist non-real neutral eigenfunctions,which produce secondary time-periodic flows exhibiting vortices merging in an oscillatory manner.This Hopf bifurcation phenomenon has not been observed in earlier investigations.

High-Intensity Interval Training v/s Steady-State Cardio in Rehabilitation of Neurological Patients

Neuropathy is nerve damage that can cause chronic neuropathic pain, which is challenging to cure and has a significant financial burden. Exercise therapies, including High-Intensity Interval Training (HIIT) and steady-state cardio, are being explored as potential treatments for neuropathic pain. This systematic review compares the effectiveness of HIIT and steady-state cardio for improving function in neurological patients. This article provides an overview of the systematic review conducted on the effects of exercise on neuropathic patients, with a focus on high-intensity interval training (HIIT) and steady-state cardio. The authors conducted a comprehensive search of various databases, identified relevant studies based on predetermined inclusion criteria, and used the EPPI automation application to process the data. The final selection of studies was based on validity and relevance, with redundant articles removed. The article reviews four studies that compare high-intensity interval training (HIIT) to moderate-intensity continuous training (MICT) on various health outcomes. The studies found that HIIT can improve aerobic fitness, cerebral blood flow, and brain function in stroke patients;lower diastolic blood pressure more than MICT and improve insulin sensitivity and skeletal muscle mitochondrial content in obese individuals, potentially helping with the prevention and management of type 2 diabetes. In people with multiple sclerosis, acute exercise can decrease the plasma neurofilament light chain while increasing the flow of the kynurenine pathway. The available clinical and preclinical data suggest that further study on high-intensity interval training (HIIT) and its potential to alleviate neuropathic pain is justified. Randomized controlled trials are needed to investigate the type, intensity, frequency, and duration of exercise, which could lead to consensus and specific HIIT-based advice for patients with neuropathies.

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.

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.

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.

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.

Intrinsic correlation between the generalized phase equilibrium condition and mechanical behaviors in hydrate-bearing sediments

The phase equilibrium and mechanical behaviors of natural gas hydrate-bearing sediment are essential for gas recovery from hydrate reservoirs.In heating closed systems,the temperature-pressure path of hydrate-bearing sediment deviates from that of pure bulk hydrate,reflecting the porous media effect in phase equilibrium.A generalized phase equilibrium equation was established for hydrate-bearing sediments,which indicates that both capillary and osmotic pressures cause the phase equilibrium curve to shift leftward on the temperature-pressure plane.In contrast to bulk hydrate,hydrate-bearing sediment always contains a certain amount of unhydrated water,which keeps phase equilibrium with the hydrate within the hydrate stability field.With changes in temperature and pressure,a portion of pore hydrate and unhydrated water may transform into each other,affecting the shear strength of hydrate-bearing sediment.A shear strength model is proposed to consider not only hydrate saturation but also the change in temperature and pressure of hydrate-bearing sediment.The model is validated by experimental data with various hydrate saturation,temperature and pressure conditions.The deformation induced by partial dissociation was studied through depressurization tests under constant effective stress.The reduction in gas pressure within the hydrate stability field indeed caused sediment deformation.The dissociation-induced deformation can be reasonably estimated as the difference in volume between hydrate-bearing and hydrate-free sediments from the compression curves.

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.

Lithium-Ion Battery Pack Based on Fuzzy Logic Control Research on Multi-Layer Equilibrium Circuits

In order to solve the problem of inconsistent energy in the charging and discharging cycles of lithium-ion battery packs,a new multilayer equilibrium topology is designed in this paper.The structure adopts a hierarchical structure design,which includes intra-group equilibrium,primary inter-group equilibrium and secondary inter-group equilibrium.This structure greatly increases the number of equilibrium paths for lithium-ion batteries,thus shortening the time required for equilibrium,and improving the overall efficiency.In terms of control strategy,fuzzy logic control(FLC)is chosen to control the size of the equilibrium current during the equilibrium process.We performed rigorous modeling and simulation of the proposed system by MATLAB and Simulink software.Experiments show that the multilayer equilibrium circuit structure greatly exceeds the traditional single-layer equilibrium circuit in terms of efficacy,specifically,the Li-ion battery equilibrium speed is improved by 12.71%in static equilibrium,14.48%in charge equilibrium,and 11.19%in discharge equilibrium.In addition,compared with the maximum value algorithm,the use of the FLC algorithm reduces the equalization time by about 3.27%and improves the energy transfer efficiency by about 66.49%under the stationary condition,which verifies the feasibility of the equalization scheme.

Nash Equilibrium of a Fixed-Sum Two-Player Game

It is well established that Nash equilibrium exists within the framework of mixed strategies in strategic-form non-cooperative games. However, finding the Nash equilibrium generally belongs to the class of problems known as PPAD (Polynomial Parity Argument on Directed graphs), for which no polynomial-time solution methods are known, even for two-player games. This paper demonstrates that in fixed-sum two-player games (including zero-sum games), the Nash equilibrium forms a convex set, and has a unique expected payoff. Furthermore, these equilibria are Pareto optimal. Additionally, it is shown that the Nash equilibrium of fixed-sum two-player games can theoretically be found in polynomial time using the principal-dual interior point method, a solution method of linear programming.

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.

Steady-state entanglement and heat current of two coupled qubits in two baths without rotating wave approximation

We study the steady-state entanglement and heat current of two coupled qubits, in which two qubits are connected with two independent heat baths(IHBs) or two common heat baths(CHBs). We construct the master equation in the eigenstate representation of two coupled qubits to describe the dynamics of the total system and derive the solutions in the steadystate with stronger coupling regime between two qubits than qubit–baths. We do not make the rotating wave approximation(RWA) for the qubit–qubit interaction, and so we are able to investigate the behaviors of the system in both the strong coupling regime and the weak coupling regime, respectively. In an equilibrium bath, we find that the entanglement decreases with the bath temperature and energy detuning increasing under the strong coupling regime. In the weak coupling regime,the entanglement increases with coupling strength increasing and decreases with the bath temperature and energy detuning increasing. In a nonequilibrium bath, the entanglement without RWA is useful for entanglement at lower temperatures.We also study the heat currents of the two coupled qubits and their variations with the energy detuning, coupling strength and low temperature. In the strong(weak) coupling regime, the heat current increases(decreases) with coupling strength increasing when the temperature of one bath is lower(higher) than the other, and the energy detuning leads to a positive(negative) effect when the temperature is low(high). In the weak coupling regime, the variation trend of heat current is opposite to that of coupling strength for the IHB case and the CHB case.

Observing the steady-state visual evoked potentials with a compact quad-channel spin exchange relaxation-free magnetometer

We observed the steady-state visually evoked potential(SSVEP) from a healthy subject using a compact quad-channel potassium spin exchange relaxation-free(SERF) optically pumped magnetometer(OPM). To this end, 30 s of data were collected, and SSVEP-related magnetic responses with signal intensity ranging from 150 fT to 300 f T were observed for all four channels. The corresponding signal to noise ratio(SNR) was in the range of 3.5–5.5. We then used different channels to operate the sensor as a gradiometer. In the specific case of detecting SSVEP, we noticed that the short channel separation distance led to a strongly diminished gradiometer signal. Although not optimal for the case of SSVEP detection, this set-up can prove to be highly useful for other magnetoencephalography(MEG) paradigms that require good noise cancellation.Considering its compactness, low cost, and good performance, the K-SERF sensor has great potential for biomagnetic field measurements and brain-computer interfaces(BCI).