This study investigates the influence of runaway current in runaway plasmas on the dynamics of sawtooth oscillations and resultant loss of runaway electrons(RE)using the 3D magnetohydrodynamic(MHD)code M3D-C^(1)(Jardi...This study investigates the influence of runaway current in runaway plasmas on the dynamics of sawtooth oscillations and resultant loss of runaway electrons(RE)using the 3D magnetohydrodynamic(MHD)code M3D-C^(1)(Jardin et al 2012 J.Comput.Sci.Discovery 6014002).Using an HL-2A-like equilibrium,we confirm that in the linear phase,the impact of REs on resistive internal kink instabilities is consistent with previous research.In the nonlinear phase,as the runaway current fully replaces the plasmas current,we observe a significant suppression of sawtooth oscillations,with the first sawtooth cycle occurring earlier compared to the case without runaway current.Following the first sawtooth collapse,plasma current density,runaway current density,and safety factor(q)flatten within the q=1 surface,albeit displaying fine structures.Subsequently,the growing high torodial(n)and poloidal(m)mode number modes disrupt the magnetic surfaces,leading to the loss of REs outside the q=1 surface,while minimally affecting the majority of REs well-confined within it.Thus,in the current model,the physical processes associated with the presence of sawtooth oscillations do not effectively dissipate runaway current,as REs are assumed to be collisionless.In addition,the final profile of runaway current density exhibits increased steepening near the q=1 surface in contrast to the initial profile,displaying a distinctive corrugated inhomogeneity influenced by the growing fluctuation of the n=0 component.Finally,detailed convergence tests are conducted to validate the numerical simulations.展开更多
This paper studies the reachability problem of the switched linear discrete singular （SLDS） systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based o...This paper studies the reachability problem of the switched linear discrete singular （SLDS） systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems.展开更多
Why heavily parameterized neural networks(NNs) do not overfit the data is an important long standing open question. We propose a phenomenological model of the NN training to explain this non-overfitting puzzle. Our li...Why heavily parameterized neural networks(NNs) do not overfit the data is an important long standing open question. We propose a phenomenological model of the NN training to explain this non-overfitting puzzle. Our linear frequency principle(LFP) model accounts for a key dynamical feature of NNs: they learn low frequencies first, irrespective of microscopic details. Theory based on our LFP model shows that low frequency dominance of target functions is the key condition for the non-overfitting of NNs and is verified by experiments. Furthermore,through an ideal two-layer NN, we unravel how detailed microscopic NN training dynamics statistically gives rise to an LFP model with quantitative prediction power.展开更多
This paper addresses the state estimation for a class of nonlinear time-varying stochastic systems with both uncertain dynam-ics and unknown measurement bias.A novel extended state based Kalman filter(ESKF)algorithm i...This paper addresses the state estimation for a class of nonlinear time-varying stochastic systems with both uncertain dynam-ics and unknown measurement bias.A novel extended state based Kalman filter(ESKF)algorithm is developed to estimate the original state,the uncertain dynamics and the measurement bias.It is shown that the estimation error of the proposed algorithm is bounded in the mean square sense.Also,the estimation of the measurement bias asymptotically converges to its true value,such that the infuence of measurement bias is eliminated.Furthermore,the asymptotic optimality of the estima-tion result is proved while the uncertain dynamics approaches to a constant vector.Finally,a simulation study for harmonic oscillator system model is provided to ilustrate the effectiveness of proposed method.展开更多
In this paper,we study how to design filters for nonlinear uncertain systems over sensor networks.We intoduce two Kalmantype nonlinear fitrs in centralied and dstrbute frameworks.Moreover,the tuning method for the par...In this paper,we study how to design filters for nonlinear uncertain systems over sensor networks.We intoduce two Kalmantype nonlinear fitrs in centralied and dstrbute frameworks.Moreover,the tuning method for the parameters of the filteres is established to ensure the consistency,i.e..the mean square error is upper bounded by a known parameter matrix at each time.We apply the consistent fiters to the track to-track association analysis of multi targets with uncertain dynamics.A novel track to-track asocaion algoritm is proposed to idenify whether two tracks are from the same target.It is proven that the resulting probability of mis.asociation is lower than the desired threshold.Numerical simulations on track.to track association are given to show the ffetives of the methods.展开更多
In this paper we deal with a nonlinear interaction problem between an incompressible viscous fluid and a nonlinear thermoelastic plate.The nonlinearity in the plate equation corresponds to nonlinear elastic force in v...In this paper we deal with a nonlinear interaction problem between an incompressible viscous fluid and a nonlinear thermoelastic plate.The nonlinearity in the plate equation corresponds to nonlinear elastic force in various physically relevant semilinear and quasilinear plate models.We prove the existence of a weak solution for this problem by constructing a hybrid approximation scheme that,via operator splitting,decouples the system into two sub-problems,one piece-wise stationary for the fluid and one time-continuous and in a finite basis for the structure.To prove the convergence of the approximate quasilinear elastic force,we develop a compensated compactness method that relies on the maximal monotonicity property of this nonlinear function.展开更多
A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and ...A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and regularity of the constructed solution.The key ingredients are the Holder continuity estimates of the heat kernel in both spatial and time variables.With these finer estimates,we obtain higher order regularity of the constructed solution to Navier-Stokes equation,so that all of the derivatives in the equation of conservative form are in the strong sense.Moreover,this regularity also allows us to identify a function space such that the stability of the solutions can be established there,which eventually implies the uniqueness.展开更多
Supercapacitors(SCs)have become increasingly important in electrical energy storage and delivery owing to their high power densities and long lifetimes.Aqueous SCs are promising for large-scale engineering application...Supercapacitors(SCs)have become increasingly important in electrical energy storage and delivery owing to their high power densities and long lifetimes.Aqueous SCs are promising for large-scale engineering applications because of their low cost and safety.However,the low operating voltage and low energy density of aqueous SCs severely limit their practical applications.In this study,a nanoscale dielectric layer is grafted onto a graphene electrode to achieve both a high operating voltage and enhanced capacitance.Compared with an SC without dielectric grafting,a dielectric-enhanced SC(DESC)shows a higher capacitance by 2200%.The mechanism of the capacitance enhancement can be attributed to three factors:the dielectric polarization,the ions desolvation by the dielectric,and the enhanced quantum capacitance from charge transfer and ion adsorption in the polymer molecules.In addition,a 2.5 V pouch DESC with a 1 M KCl electrolyte is confirmed to cycle up to 50,000 times with a capacitance retention of 87.5%.The DESC presents the optimal electrochemical properties after it is grafted with a 5 nm dielectric layer.This study provides new insights into the design of high-voltage and high-energy-density aqueous SCs.展开更多
Retinoic acid inducible gene-I(RIG-I)is a caspase recruitment domain(CARD)containing protein that acts as an intracellular RNA receptor and senses virus infection.After binding to double stranded RNA(dsRNA)or 5′-trip...Retinoic acid inducible gene-I(RIG-I)is a caspase recruitment domain(CARD)containing protein that acts as an intracellular RNA receptor and senses virus infection.After binding to double stranded RNA(dsRNA)or 5′-triphosphate single stranded RNA(ssRNA),RIG-I transforms into an open conformation,translocates onto mitochondria,and interacts with the downstream adaptor mitochondrial antiviral signaling(MAVS)to induce the production of type Ⅰ interferon and inflammatory factors via IRF3/7 and NF-κB pathways,respectively.Recently,accumulating evidence suggests that RIG-I could function in non-viral systems and participate in a series of biological events,such as inflammation and inflammation related diseases,cell proliferation,apoptosis and even senescence.Here we review recent advances in antiviral study of RIG-I as well as the functions of RIG-I in other fields.展开更多
Node dynamics and network topologies play vital roles in determining the network features and network dynamical behaviors.Thus it is of great theoretical significance and practical value to recover the topology struct...Node dynamics and network topologies play vital roles in determining the network features and network dynamical behaviors.Thus it is of great theoretical significance and practical value to recover the topology structures and system parameters of uncertain complex networks with available information. This paper presents an adaptive anticipatory synchronization-based approach to identify the unknown system parameters and network topological structures of uncertain time-varying delayed complex networks in the presence of noise. Moreover, during the identification process, our proposed scheme guarantees anticipatory synchronization between the uncertain drive and constructed auxiliary response network simultaneously. Particularly, our method can be extended to several special cases. Furthermore, numerical simulations are provided to verify the effectiveness and applicability of our method for reconstructing network topologies and node parameters. We hope our method can provide basic insight into future research on addressing reconstruction issues of uncertain realistic and large-scale complex networks.展开更多
In this paper, PID（proportional-integral-derivative） controllers will be designed to solve the tracking problem for a class of coupled multi-agent systems, where each agent is described by a second-order high-dimens...In this paper, PID（proportional-integral-derivative） controllers will be designed to solve the tracking problem for a class of coupled multi-agent systems, where each agent is described by a second-order high-dimensional nonlinear uncertain dynamical system, which only has access to its own tracking error information and does not need to communicate with others. This paper will show that a 3-dimensional manifold can be constructed based on the information about the Lipschitz constants of the system nonlinear dynamics, such that whenever the three parameters of each PID controller are chosen from the manifold, the whole multi-agent system can be stabilized globally and the tracking error of each agent approaches to zero asymptotically. For a class of coupled first-order multi-agent nonlinear uncertain systems, a PI controller will be designed to stabilize the whole system.展开更多
The distance-based regression model has many applications in analysis of multivariate response regression in various ?elds, such as ecology, genomics, genetics, human microbiomics, and neuroimaging. It yields a pseudo...The distance-based regression model has many applications in analysis of multivariate response regression in various ?elds, such as ecology, genomics, genetics, human microbiomics, and neuroimaging. It yields a pseudo F test statistic that assesses the relation between the distance(dissimilarity) of the subjects and the predictors of interest. Despite its popularity in recent decades, the statistical properties of the pseudo F test statistic have not been revealed to our knowledge. This study derives the asymptotic properties of the pseudo F test statistic using spectral decomposition under the matrix normal assumption, when the utilized dissimilarity measure is the Euclidean or Mahalanobis distance. The pseudo F test statistic with the Euclidean distance has the same distribution as the quotient of two Chi-squared-type mixtures. The denominator and numerator of the quotient are approximated using a random variable of the form ξχ_d^2+ η, and the approximate error bound is given. The pseudo F test statistic with the Mahalanobis distance follows an F distribution.In simulation studies, the approximated distribution well matched the "exact" distribution obtained by the permutation procedure. The obtained distribution was further validated on H1N1 in?uenza data, aging human brain data, and embryonic imprint data.展开更多
基金supported in part by the National Key R&D Program of China (No.2022YFE03040002)the Natural Science Foundation of Sichuan (No.2022NSFSC1814)+3 种基金National Natural Science Foundation of China (Nos.12305246,12175053 and 12261131622)the Italian Ministry of Foreign Affairs (No.CN23GR02)the Fundamental Research Funds for the Central Universitiessupported by US Department of Energy (No.DE-AC0209CH11466)。
文摘This study investigates the influence of runaway current in runaway plasmas on the dynamics of sawtooth oscillations and resultant loss of runaway electrons(RE)using the 3D magnetohydrodynamic(MHD)code M3D-C^(1)(Jardin et al 2012 J.Comput.Sci.Discovery 6014002).Using an HL-2A-like equilibrium,we confirm that in the linear phase,the impact of REs on resistive internal kink instabilities is consistent with previous research.In the nonlinear phase,as the runaway current fully replaces the plasmas current,we observe a significant suppression of sawtooth oscillations,with the first sawtooth cycle occurring earlier compared to the case without runaway current.Following the first sawtooth collapse,plasma current density,runaway current density,and safety factor(q)flatten within the q=1 surface,albeit displaying fine structures.Subsequently,the growing high torodial(n)and poloidal(m)mode number modes disrupt the magnetic surfaces,leading to the loss of REs outside the q=1 surface,while minimally affecting the majority of REs well-confined within it.Thus,in the current model,the physical processes associated with the presence of sawtooth oscillations do not effectively dissipate runaway current,as REs are assumed to be collisionless.In addition,the final profile of runaway current density exhibits increased steepening near the q=1 surface in contrast to the initial profile,displaying a distinctive corrugated inhomogeneity influenced by the growing fluctuation of the n=0 component.Finally,detailed convergence tests are conducted to validate the numerical simulations.
基金This work was supported by the National Natural Science Foundation of China (No. 6022130, 60334040, 60428304).
文摘This paper studies the reachability problem of the switched linear discrete singular （SLDS） systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems.
基金Supported by the National Key R&D Program of China(Grant No.2019YFA0709503)the Shanghai Sailing Program+3 种基金the Natural Science Foundation of Shanghai(Grant No.20ZR1429000)the National Natural Science Foundation of China(Grant No.62002221)Shanghai Municipal of Science and Technology Project(Grant No.20JC1419500)the HPC of School of Mathematical Sciences at Shanghai Jiao Tong University。
文摘Why heavily parameterized neural networks(NNs) do not overfit the data is an important long standing open question. We propose a phenomenological model of the NN training to explain this non-overfitting puzzle. Our linear frequency principle(LFP) model accounts for a key dynamical feature of NNs: they learn low frequencies first, irrespective of microscopic details. Theory based on our LFP model shows that low frequency dominance of target functions is the key condition for the non-overfitting of NNs and is verified by experiments. Furthermore,through an ideal two-layer NN, we unravel how detailed microscopic NN training dynamics statistically gives rise to an LFP model with quantitative prediction power.
基金This work was partly supported by National Key R&D Program of China(No.2018YFA0703800)the National Nature Science Foundation of China(Nos.I 1931018,61633003-3)the Beijing Advanced Innovation Center for Intelligent Robots and Systems(No.2019IRS09).
文摘This paper addresses the state estimation for a class of nonlinear time-varying stochastic systems with both uncertain dynam-ics and unknown measurement bias.A novel extended state based Kalman filter(ESKF)algorithm is developed to estimate the original state,the uncertain dynamics and the measurement bias.It is shown that the estimation error of the proposed algorithm is bounded in the mean square sense.Also,the estimation of the measurement bias asymptotically converges to its true value,such that the infuence of measurement bias is eliminated.Furthermore,the asymptotic optimality of the estima-tion result is proved while the uncertain dynamics approaches to a constant vector.Finally,a simulation study for harmonic oscillator system model is provided to ilustrate the effectiveness of proposed method.
基金the National Natural Science Foundation of China(Nos.11931018,61973299)the Beijing Advanced Innovation Center for Intelligent Robots and Systems(No.2019IRS09).
文摘In this paper,we study how to design filters for nonlinear uncertain systems over sensor networks.We intoduce two Kalmantype nonlinear fitrs in centralied and dstrbute frameworks.Moreover,the tuning method for the parameters of the filteres is established to ensure the consistency,i.e..the mean square error is upper bounded by a known parameter matrix at each time.We apply the consistent fiters to the track to-track association analysis of multi targets with uncertain dynamics.A novel track to-track asocaion algoritm is proposed to idenify whether two tracks are from the same target.It is proven that the resulting probability of mis.asociation is lower than the desired threshold.Numerical simulations on track.to track association are given to show the ffetives of the methods.
基金partially supported by National Natural Science Foundation of China(11631008)。
文摘In this paper we deal with a nonlinear interaction problem between an incompressible viscous fluid and a nonlinear thermoelastic plate.The nonlinearity in the plate equation corresponds to nonlinear elastic force in various physically relevant semilinear and quasilinear plate models.We prove the existence of a weak solution for this problem by constructing a hybrid approximation scheme that,via operator splitting,decouples the system into two sub-problems,one piece-wise stationary for the fluid and one time-continuous and in a finite basis for the structure.To prove the convergence of the approximate quasilinear elastic force,we develop a compensated compactness method that relies on the maximal monotonicity property of this nonlinear function.
基金partially the National Key R&D Program of China(2022YFA1007300)the NSFC(11901386,12031013)+2 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences(XDA25010403)the NSFC(11801194,11971188)the Hubei Key Laboratory of Engineering Modeling and Scientific Computing。
文摘A global weak solution to the isentropic Navier-Stokes equation with initial data around a constant state in the L^(1)∩BV class was constructed in[1].In the current paper,we will continue to study the uniqueness and regularity of the constructed solution.The key ingredients are the Holder continuity estimates of the heat kernel in both spatial and time variables.With these finer estimates,we obtain higher order regularity of the constructed solution to Navier-Stokes equation,so that all of the derivatives in the equation of conservative form are in the strong sense.Moreover,this regularity also allows us to identify a function space such that the stability of the solutions can be established there,which eventually implies the uniqueness.
基金supported by the National Natural Science Foundation of China(Nos.U19A20105,52003153,22005186,52103303 and 52207027)Program of Shanghai Academic Research Leader(No.21XD1401600).
文摘Supercapacitors(SCs)have become increasingly important in electrical energy storage and delivery owing to their high power densities and long lifetimes.Aqueous SCs are promising for large-scale engineering applications because of their low cost and safety.However,the low operating voltage and low energy density of aqueous SCs severely limit their practical applications.In this study,a nanoscale dielectric layer is grafted onto a graphene electrode to achieve both a high operating voltage and enhanced capacitance.Compared with an SC without dielectric grafting,a dielectric-enhanced SC(DESC)shows a higher capacitance by 2200%.The mechanism of the capacitance enhancement can be attributed to three factors:the dielectric polarization,the ions desolvation by the dielectric,and the enhanced quantum capacitance from charge transfer and ion adsorption in the polymer molecules.In addition,a 2.5 V pouch DESC with a 1 M KCl electrolyte is confirmed to cycle up to 50,000 times with a capacitance retention of 87.5%.The DESC presents the optimal electrochemical properties after it is grafted with a 5 nm dielectric layer.This study provides new insights into the design of high-voltage and high-energy-density aqueous SCs.
文摘Retinoic acid inducible gene-I(RIG-I)is a caspase recruitment domain(CARD)containing protein that acts as an intracellular RNA receptor and senses virus infection.After binding to double stranded RNA(dsRNA)or 5′-triphosphate single stranded RNA(ssRNA),RIG-I transforms into an open conformation,translocates onto mitochondria,and interacts with the downstream adaptor mitochondrial antiviral signaling(MAVS)to induce the production of type Ⅰ interferon and inflammatory factors via IRF3/7 and NF-κB pathways,respectively.Recently,accumulating evidence suggests that RIG-I could function in non-viral systems and participate in a series of biological events,such as inflammation and inflammation related diseases,cell proliferation,apoptosis and even senescence.Here we review recent advances in antiviral study of RIG-I as well as the functions of RIG-I in other fields.
基金supported by the National Key Research and Development Program of China(Grant No.2016YFB0800401)the National Natural Science Foundation of China(Grant Nos.61621003,61532020 and11472290)
文摘Node dynamics and network topologies play vital roles in determining the network features and network dynamical behaviors.Thus it is of great theoretical significance and practical value to recover the topology structures and system parameters of uncertain complex networks with available information. This paper presents an adaptive anticipatory synchronization-based approach to identify the unknown system parameters and network topological structures of uncertain time-varying delayed complex networks in the presence of noise. Moreover, during the identification process, our proposed scheme guarantees anticipatory synchronization between the uncertain drive and constructed auxiliary response network simultaneously. Particularly, our method can be extended to several special cases. Furthermore, numerical simulations are provided to verify the effectiveness and applicability of our method for reconstructing network topologies and node parameters. We hope our method can provide basic insight into future research on addressing reconstruction issues of uncertain realistic and large-scale complex networks.
基金supported by the National Natural Science Foundation of China under Grant No.11688101
文摘In this paper, PID（proportional-integral-derivative） controllers will be designed to solve the tracking problem for a class of coupled multi-agent systems, where each agent is described by a second-order high-dimensional nonlinear uncertain dynamical system, which only has access to its own tracking error information and does not need to communicate with others. This paper will show that a 3-dimensional manifold can be constructed based on the information about the Lipschitz constants of the system nonlinear dynamics, such that whenever the three parameters of each PID controller are chosen from the manifold, the whole multi-agent system can be stabilized globally and the tracking error of each agent approaches to zero asymptotically. For a class of coupled first-order multi-agent nonlinear uncertain systems, a PI controller will be designed to stabilize the whole system.
基金supported by National Natural Science Foundation of China (Grant No. 11722113)
文摘The distance-based regression model has many applications in analysis of multivariate response regression in various ?elds, such as ecology, genomics, genetics, human microbiomics, and neuroimaging. It yields a pseudo F test statistic that assesses the relation between the distance(dissimilarity) of the subjects and the predictors of interest. Despite its popularity in recent decades, the statistical properties of the pseudo F test statistic have not been revealed to our knowledge. This study derives the asymptotic properties of the pseudo F test statistic using spectral decomposition under the matrix normal assumption, when the utilized dissimilarity measure is the Euclidean or Mahalanobis distance. The pseudo F test statistic with the Euclidean distance has the same distribution as the quotient of two Chi-squared-type mixtures. The denominator and numerator of the quotient are approximated using a random variable of the form ξχ_d^2+ η, and the approximate error bound is given. The pseudo F test statistic with the Mahalanobis distance follows an F distribution.In simulation studies, the approximated distribution well matched the "exact" distribution obtained by the permutation procedure. The obtained distribution was further validated on H1N1 in?uenza data, aging human brain data, and embryonic imprint data.
