The present paper deals with the problem of assessing the local influence in a growth curve model with Rao's simple covariance structure. Based on the likelihood displacement,the curvature measure is employed to e...The present paper deals with the problem of assessing the local influence in a growth curve model with Rao's simple covariance structure. Based on the likelihood displacement,the curvature measure is employed to evaluate the effects of some minor perturbations on the statistical inference, thus leading to the large curvature direction, which is the most critical diagnostic statistic in the context of the local influence analysis. As an application, the common covariance-weighted perturbation scheme is thoroughly considered.展开更多
The problem considered here is to assess the Bayesian influence on the unknown param-eter matrices in a grwoth curve model with the general covariance structure.Under the non-information prior distribution assumption,...The problem considered here is to assess the Bayesian influence on the unknown param-eter matrices in a grwoth curve model with the general covariance structure.Under the non-information prior distribution assumption,the Kullback-Leibler divergence is employed to eval-uate the effect of a designated response matrix on the posterior distribution of the parameter matrix.展开更多
In practice,the model structure,parameters and time-delay of the actual process may vary simultaneously.However,the general identification methods of the 3 items are performed with separate procedures which is very in...In practice,the model structure,parameters and time-delay of the actual process may vary simultaneously.However,the general identification methods of the 3 items are performed with separate procedures which is very inconvenient in practical application.In view of the fact that variable selection procedure can ensure a compact model with robust input-output,relation and in order to explore the feasibility of variable selection algorithm for the simultaneous identification of process structure,parameters and time-delay,non-negative garrote(NNG)algorithm is introduced and applied to system identification and the corresponding procedures are presented.The application of NNG variable selection algorithm to the identification of single input single output(SISO)system,multiple input multiple output(MIN1O)system and Wood-Berry tower industry are investigated.The identification accuracy and the time-series variable selection results are analyzed and compared between NNG and ordinary least square(OLS)algorithms.The derived excellent results show that the proposed NNG-based modeling algorithm can be utilized for simultaneous identification of the model structure,parameters and time-delay with high precision.展开更多
Based upon the covariant prolongation structures theory, we construct the sl（2, R）×R（p） prolongation structure for Konno-Asai-Kakuhata equation. By taking two and one-dimensional prolongation spaces, we obtai...Based upon the covariant prolongation structures theory, we construct the sl（2, R）×R（p） prolongation structure for Konno-Asai-Kakuhata equation. By taking two and one-dimensional prolongation spaces, we obtain the inverse scattering equations given by Konno et al. and the corresponding Riccati equation. The Baecklund transformations are also presented.展开更多
In this paper, we investigate the Gross-Pitaevskii (GP) equation which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and c...In this paper, we investigate the Gross-Pitaevskii (GP) equation which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping by the Covariant Prolongation Structure Theory. As a result, we obtain general forms of Lax-Pair representations. In addition, some hidden structural symmetries that govern the dynamics of the GP equation such as SL(2,R), SL(2,C), Virasoro algebra, SU(1,1) and SU(2) are unearthed. Using the Riccati form of the linear eigenvalue problem, infinite number of conservation laws of the GP equation is explicitly constructed and the exact analytical soliton solutions are obtained by employing the simple and straightforward Hirota’s bilinear method.展开更多
We investigate the coupled inhomogeneous nonlinear Schrodinger equation by the covariant prolongationstructure theory, and obtain its Lax's representation. Moreover, we present the corresponding Riccati equations,...We investigate the coupled inhomogeneous nonlinear Schrodinger equation by the covariant prolongationstructure theory, and obtain its Lax's representation. Moreover, we present the corresponding Riccati equations, Backlundtransformation, and one-soliton solution.展开更多
The integrability of a （2＋1）-dimensional super nonlinear evolution equation is analyzed in the framework of the fermionie covariant prolongation structure theory. We construct the prolongation structure of the mult...The integrability of a （2＋1）-dimensional super nonlinear evolution equation is analyzed in the framework of the fermionie covariant prolongation structure theory. We construct the prolongation structure of the multidimen- sional super integrable equation and investigate its Lax representation. Furthermore, the Backlund transformation is presented and we derive a solution to the super integrable equation.展开更多
Computer vision(CV)methods for measurement of structural vibration are less expensive,and their application is more straightforward than methods based on sensors that measure physical quantities at particular points o...Computer vision(CV)methods for measurement of structural vibration are less expensive,and their application is more straightforward than methods based on sensors that measure physical quantities at particular points of a structure.However,CV methods produce significantly more measurement errors.Thus,computer vision-based structural health monitoring(CVSHM)requires appropriate methods of damage assessment that are robust with respect to highly contaminated measurement data.In this paper a complete CVSHM framework is proposed,and three damage assessment methods are tested.The first is the augmented inverse estimate(AIE),proposed by Peng et al.in 2021.This method is designed to work with highly contaminated measurement data,but it fails with a large noise provided by CV measurement.The second method,as proposed in this paper,is based on the AIE,but it introduces a weighting matrix that enhances the conditioning of the problem.The third method,also proposed in this paper,introduces additional constraints in the optimization process;these constraints ensure that the stiffness of structural elements can only decrease.Both proposed methods perform better than the original AIE.The latter of the two proposed methods gives the best results,and it is robust with respect to the selected coefficients,as required by the algorithm.展开更多
High-dimensional covariance matrices have attracted much attention of statisticians and econometricians during the past decades.Vast literature is devoted to the research in high-dimensional covariance matrices.Howeve...High-dimensional covariance matrices have attracted much attention of statisticians and econometricians during the past decades.Vast literature is devoted to the research in high-dimensional covariance matrices.However,most of them are for constant covariance matrices.In many applications,constant covariance matrices are not appropriate,e.g.,in portfolio allocation,dynamic covariance matrices would make much more sense.Simply assuming each entry of a covariance matrix is a function of time to introduce a dynamic structure would not work.In this paper,we are going to introduce a class of high-dimensional dynamic covariance matrices in which a kind of additive structure is embedded.We will show the proposed high-dimensional dynamic covariance matrices have many advantages in applications.An estimation procedure is also proposed to estimate the proposed high-dimensional dynamic covariance matrices.Asymptotic properties are built to justify the proposed estimation procedure.Intensive simulation studies show the proposed estimation procedure works very well when sample size is finite.Finally,we apply the proposed high-dimensional dynamic covariance matrices,together with the proposedestimation procedure,to portfolio allocation.The results look very interesting.展开更多
In this paper I have shown that squeezed modified quantum vacua have an effect on the background geometry by solving the semi-classical Einstein Field Equations in modified vacuum. The resultant geometry is similar to...In this paper I have shown that squeezed modified quantum vacua have an effect on the background geometry by solving the semi-classical Einstein Field Equations in modified vacuum. The resultant geometry is similar to (anti) de Sitter spacetime. This geometry could explain the change of causal structure—speed of light—in such vacua without violating diffeomorphism covariance or causality. The superluminal propagation of photons in Casimir vacuum is deduced from the effective electromagnetic action in the resultant curved geometry. Singling between different vacua is shown not to violate causality as well when the geometric effect on the null rays is considered, causing a refraction of those rays when traveling between unbounded and modified vacua.展开更多
Neurodegenerative disorders,including Alzheimer’s disease(AD),Parkinson’s disease(PD),and amyotrophic lateral sclerosis,impose a considerable social and economic burden on society and have dramatic consequences for ...Neurodegenerative disorders,including Alzheimer’s disease(AD),Parkinson’s disease(PD),and amyotrophic lateral sclerosis,impose a considerable social and economic burden on society and have dramatic consequences for individuals and their families.The majority of existing interventions have been found to be capable of only a slight modification of disease progression or to moderately delay significant functional decline in motor,cognitive,or mental domains.展开更多
THROUGHOUT this note, the following notations are used: For a matrix A, A】0 means thatA is positive definite symmetric; R （A）, A′and A<sup>-</sup> stand for the column space, transposeand any g-inverse...THROUGHOUT this note, the following notations are used: For a matrix A, A】0 means thatA is positive definite symmetric; R （A）, A′and A<sup>-</sup> stand for the column space, transposeand any g-inverse of A respectively; P<sub>A</sub> = A （A′A）<sup>-</sup> A′and P<sub>A</sub> = I<sub>k</sub> - P<sub>A</sub>, where I<sub>k</sub> is theidentity matrix of order k that is the number of rows in A. R<sup>m×n</sup> is the totality of m×n realmatrices.展开更多
One type of covariance structure is known as blocked compound symmetry.Recently,Roy et al.(J Multivar Anal 144:81–90,2016)showed that,assuming this covariance structure,unbiased estimators are optimal under normality...One type of covariance structure is known as blocked compound symmetry.Recently,Roy et al.(J Multivar Anal 144:81–90,2016)showed that,assuming this covariance structure,unbiased estimators are optimal under normality and described hypothesis testing for independence as an open problem.In this paper,we derive the distributions of unbiased estimators and consider hypothesis testing for independence.Representative test statistics such as the likelihood ratio criterion,Waldstatistic,Rao’s score statistic,and gradient statistic are derived,and we evaluate the accuracy of the test using these statistics through numerical simulations.The power of the Wald test is the largest when the dimension is high,and the power of the likelihood ratio test is the largest when the dimension is low.展开更多
The paper starts examining some ideas of Einstein and Rovelli about space and spacetime in the context of the general theory of relativity and identifying a connection among them.I continue drawing a parallel between ...The paper starts examining some ideas of Einstein and Rovelli about space and spacetime in the context of the general theory of relativity and identifying a connection among them.I continue drawing a parallel between those ideas in the field of physics and the conception of space in mathematics according to Riemann’s revolutionary view,basis of the elaboration of the mathematical structures used in general relativity.In analogy with Einstein’s and Rovelli’s ideas about physical space,I come to formulate the idea that it is not appropriate to think that,in forming a riemannian manifold(the mathematical object representing spacetime),the metric field places itself in a space pre-existing to it and it may do this differently.According to this idea,I formulate a critical remark about Earman and Norton’s famous hole argument focused on the rejection of the active interpretation of general covariance.I compare then my critical remark about the hole argument with the position of Weatherall on it.I conclude with some critical remarks on moderate structural realism about spacetime and proposing an interpretation of Einstein’s assertion that spacetime“does not claim existence on its own,but only as a structural quality of the field”.展开更多
An improved method for estimation of causal effects from observational data is demonstrated. Applications in medicine have been few, and the purpose of the present study is to contribute new clinical insight by means ...An improved method for estimation of causal effects from observational data is demonstrated. Applications in medicine have been few, and the purpose of the present study is to contribute new clinical insight by means of this new and more sophisticated analysis. Long term effect of medication for adult ADHD patients is not resolved. A model with causal parameters to represent effect of medication was formulated, which accounts for time-varying confounding and selection-bias from loss to follow-up. The popular marginal structural model (MSM) for causal inference, of Robins et al., adjusts for time-varying confounding, but suffers from lack of robustness for misspecification in the weights. Recent work by Imai and Ratkovic?[1][2] achieves robustness in the MSM, through improved covariate balance (CBMSM). The CBMSM (freely available software) was compared with a standard fit of a MSM and a naive regression model, to give a robust estimate of the true treatment effect in 250 previously non-medicated adults, treated for one year, in a specialized ADHD outpatient clinic in Norway. Covariate balance was greatly improved, resulting in a stronger treatment effect than without this improvement. In terms of treatment effect per week, early stages seemed to have the strongest influence. An estimated average reduction of 4 units on the symptom scale assessed at 12 weeks, for hypothetical medication in the 9 - 12 weeks period compared to no medication in this period, was found. The treatment effect persisted throughout the whole year, with an estimated average reduction of 0.7 units per week on symptoms assessed at one year, for hypothetical medication in the last 13 weeks of the year, compared to no medication in this period. The present findings support a strong and causal direct and indirect effect of pharmacological treatment of adults with ADHD on improvement in symptoms, and with a stronger treatment effect than has been reported.展开更多
The stability of the linear chain structure of three α clusters for 12C against the bending and fission is investigated in the cranking covariant density functional theory, in which the equation of motion is solved o...The stability of the linear chain structure of three α clusters for 12C against the bending and fission is investigated in the cranking covariant density functional theory, in which the equation of motion is solved on a 3D lattice with the inverse Hamiltonian and the Fourier spectral methods. Starting from a twisted three α initial configuration, it is found that the linear chain structure is stable when the rotational frequency is within the range of ~2.0-~2.5 MeV. Beyond this range, the final states are not stable against fission. By examining the density distributions and the occupation of single-particle levels, however, these fissions are found to arise from the occupation of unphysical continuum with large angular momenta. To properly remove these unphysical continuum, a damping function for the cranking term is introduced. Eventually, the stable linear chain structure could survive up to the rotational frequency ~3.5 MeV, but the fission still occurs when the rotational frequency approaches ~4.0 MeV.展开更多
文摘The present paper deals with the problem of assessing the local influence in a growth curve model with Rao's simple covariance structure. Based on the likelihood displacement,the curvature measure is employed to evaluate the effects of some minor perturbations on the statistical inference, thus leading to the large curvature direction, which is the most critical diagnostic statistic in the context of the local influence analysis. As an application, the common covariance-weighted perturbation scheme is thoroughly considered.
文摘The problem considered here is to assess the Bayesian influence on the unknown param-eter matrices in a grwoth curve model with the general covariance structure.Under the non-information prior distribution assumption,the Kullback-Leibler divergence is employed to eval-uate the effect of a designated response matrix on the posterior distribution of the parameter matrix.
基金This work was supported by National Natural Science Foundation of China(No.61171145).
文摘In practice,the model structure,parameters and time-delay of the actual process may vary simultaneously.However,the general identification methods of the 3 items are performed with separate procedures which is very inconvenient in practical application.In view of the fact that variable selection procedure can ensure a compact model with robust input-output,relation and in order to explore the feasibility of variable selection algorithm for the simultaneous identification of process structure,parameters and time-delay,non-negative garrote(NNG)algorithm is introduced and applied to system identification and the corresponding procedures are presented.The application of NNG variable selection algorithm to the identification of single input single output(SISO)system,multiple input multiple output(MIN1O)system and Wood-Berry tower industry are investigated.The identification accuracy and the time-series variable selection results are analyzed and compared between NNG and ordinary least square(OLS)algorithms.The derived excellent results show that the proposed NNG-based modeling algorithm can be utilized for simultaneous identification of the model structure,parameters and time-delay with high precision.
文摘Based upon the covariant prolongation structures theory, we construct the sl（2, R）×R（p） prolongation structure for Konno-Asai-Kakuhata equation. By taking two and one-dimensional prolongation spaces, we obtain the inverse scattering equations given by Konno et al. and the corresponding Riccati equation. The Baecklund transformations are also presented.
文摘In this paper, we investigate the Gross-Pitaevskii (GP) equation which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping by the Covariant Prolongation Structure Theory. As a result, we obtain general forms of Lax-Pair representations. In addition, some hidden structural symmetries that govern the dynamics of the GP equation such as SL(2,R), SL(2,C), Virasoro algebra, SU(1,1) and SU(2) are unearthed. Using the Riccati form of the linear eigenvalue problem, infinite number of conservation laws of the GP equation is explicitly constructed and the exact analytical soliton solutions are obtained by employing the simple and straightforward Hirota’s bilinear method.
基金Supported by Beijing Jiao-Wei Key Project KZ200810028013the Natural Science Foundation of China under Grant No. 10871135
文摘We investigate the coupled inhomogeneous nonlinear Schrodinger equation by the covariant prolongationstructure theory, and obtain its Lax's representation. Moreover, we present the corresponding Riccati equations, Backlundtransformation, and one-soliton solution.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11605096,11547101 and 11601247
文摘The integrability of a （2＋1）-dimensional super nonlinear evolution equation is analyzed in the framework of the fermionie covariant prolongation structure theory. We construct the prolongation structure of the multidimen- sional super integrable equation and investigate its Lax representation. Furthermore, the Backlund transformation is presented and we derive a solution to the super integrable equation.
基金National Science Centre,Poland Granted Through the Project 2020/39/B/ST8/02615。
文摘Computer vision(CV)methods for measurement of structural vibration are less expensive,and their application is more straightforward than methods based on sensors that measure physical quantities at particular points of a structure.However,CV methods produce significantly more measurement errors.Thus,computer vision-based structural health monitoring(CVSHM)requires appropriate methods of damage assessment that are robust with respect to highly contaminated measurement data.In this paper a complete CVSHM framework is proposed,and three damage assessment methods are tested.The first is the augmented inverse estimate(AIE),proposed by Peng et al.in 2021.This method is designed to work with highly contaminated measurement data,but it fails with a large noise provided by CV measurement.The second method,as proposed in this paper,is based on the AIE,but it introduces a weighting matrix that enhances the conditioning of the problem.The third method,also proposed in this paper,introduces additional constraints in the optimization process;these constraints ensure that the stiffness of structural elements can only decrease.Both proposed methods perform better than the original AIE.The latter of the two proposed methods gives the best results,and it is robust with respect to the selected coefficients,as required by the algorithm.
文摘High-dimensional covariance matrices have attracted much attention of statisticians and econometricians during the past decades.Vast literature is devoted to the research in high-dimensional covariance matrices.However,most of them are for constant covariance matrices.In many applications,constant covariance matrices are not appropriate,e.g.,in portfolio allocation,dynamic covariance matrices would make much more sense.Simply assuming each entry of a covariance matrix is a function of time to introduce a dynamic structure would not work.In this paper,we are going to introduce a class of high-dimensional dynamic covariance matrices in which a kind of additive structure is embedded.We will show the proposed high-dimensional dynamic covariance matrices have many advantages in applications.An estimation procedure is also proposed to estimate the proposed high-dimensional dynamic covariance matrices.Asymptotic properties are built to justify the proposed estimation procedure.Intensive simulation studies show the proposed estimation procedure works very well when sample size is finite.Finally,we apply the proposed high-dimensional dynamic covariance matrices,together with the proposedestimation procedure,to portfolio allocation.The results look very interesting.
文摘In this paper I have shown that squeezed modified quantum vacua have an effect on the background geometry by solving the semi-classical Einstein Field Equations in modified vacuum. The resultant geometry is similar to (anti) de Sitter spacetime. This geometry could explain the change of causal structure—speed of light—in such vacua without violating diffeomorphism covariance or causality. The superluminal propagation of photons in Casimir vacuum is deduced from the effective electromagnetic action in the resultant curved geometry. Singling between different vacua is shown not to violate causality as well when the geometric effect on the null rays is considered, causing a refraction of those rays when traveling between unbounded and modified vacua.
文摘Neurodegenerative disorders,including Alzheimer’s disease(AD),Parkinson’s disease(PD),and amyotrophic lateral sclerosis,impose a considerable social and economic burden on society and have dramatic consequences for individuals and their families.The majority of existing interventions have been found to be capable of only a slight modification of disease progression or to moderately delay significant functional decline in motor,cognitive,or mental domains.
文摘THROUGHOUT this note, the following notations are used: For a matrix A, A】0 means thatA is positive definite symmetric; R （A）, A′and A<sup>-</sup> stand for the column space, transposeand any g-inverse of A respectively; P<sub>A</sub> = A （A′A）<sup>-</sup> A′and P<sub>A</sub> = I<sub>k</sub> - P<sub>A</sub>, where I<sub>k</sub> is theidentity matrix of order k that is the number of rows in A. R<sup>m×n</sup> is the totality of m×n realmatrices.
文摘One type of covariance structure is known as blocked compound symmetry.Recently,Roy et al.(J Multivar Anal 144:81–90,2016)showed that,assuming this covariance structure,unbiased estimators are optimal under normality and described hypothesis testing for independence as an open problem.In this paper,we derive the distributions of unbiased estimators and consider hypothesis testing for independence.Representative test statistics such as the likelihood ratio criterion,Waldstatistic,Rao’s score statistic,and gradient statistic are derived,and we evaluate the accuracy of the test using these statistics through numerical simulations.The power of the Wald test is the largest when the dimension is high,and the power of the likelihood ratio test is the largest when the dimension is low.
文摘The paper starts examining some ideas of Einstein and Rovelli about space and spacetime in the context of the general theory of relativity and identifying a connection among them.I continue drawing a parallel between those ideas in the field of physics and the conception of space in mathematics according to Riemann’s revolutionary view,basis of the elaboration of the mathematical structures used in general relativity.In analogy with Einstein’s and Rovelli’s ideas about physical space,I come to formulate the idea that it is not appropriate to think that,in forming a riemannian manifold(the mathematical object representing spacetime),the metric field places itself in a space pre-existing to it and it may do this differently.According to this idea,I formulate a critical remark about Earman and Norton’s famous hole argument focused on the rejection of the active interpretation of general covariance.I compare then my critical remark about the hole argument with the position of Weatherall on it.I conclude with some critical remarks on moderate structural realism about spacetime and proposing an interpretation of Einstein’s assertion that spacetime“does not claim existence on its own,but only as a structural quality of the field”.
文摘An improved method for estimation of causal effects from observational data is demonstrated. Applications in medicine have been few, and the purpose of the present study is to contribute new clinical insight by means of this new and more sophisticated analysis. Long term effect of medication for adult ADHD patients is not resolved. A model with causal parameters to represent effect of medication was formulated, which accounts for time-varying confounding and selection-bias from loss to follow-up. The popular marginal structural model (MSM) for causal inference, of Robins et al., adjusts for time-varying confounding, but suffers from lack of robustness for misspecification in the weights. Recent work by Imai and Ratkovic?[1][2] achieves robustness in the MSM, through improved covariate balance (CBMSM). The CBMSM (freely available software) was compared with a standard fit of a MSM and a naive regression model, to give a robust estimate of the true treatment effect in 250 previously non-medicated adults, treated for one year, in a specialized ADHD outpatient clinic in Norway. Covariate balance was greatly improved, resulting in a stronger treatment effect than without this improvement. In terms of treatment effect per week, early stages seemed to have the strongest influence. An estimated average reduction of 4 units on the symptom scale assessed at 12 weeks, for hypothetical medication in the 9 - 12 weeks period compared to no medication in this period, was found. The treatment effect persisted throughout the whole year, with an estimated average reduction of 0.7 units per week on symptoms assessed at one year, for hypothetical medication in the last 13 weeks of the year, compared to no medication in this period. The present findings support a strong and causal direct and indirect effect of pharmacological treatment of adults with ADHD on improvement in symptoms, and with a stronger treatment effect than has been reported.
基金supported by the National Key R&D Program of China(Grant Nos.2018YFA0404400,and 2017YFE0116700)the National Natural Science Foundation of China(Grant Nos.11621131001,and 11875075)the Laboratory Computing Resource Center at Argonne National Laboratory
文摘The stability of the linear chain structure of three α clusters for 12C against the bending and fission is investigated in the cranking covariant density functional theory, in which the equation of motion is solved on a 3D lattice with the inverse Hamiltonian and the Fourier spectral methods. Starting from a twisted three α initial configuration, it is found that the linear chain structure is stable when the rotational frequency is within the range of ~2.0-~2.5 MeV. Beyond this range, the final states are not stable against fission. By examining the density distributions and the occupation of single-particle levels, however, these fissions are found to arise from the occupation of unphysical continuum with large angular momenta. To properly remove these unphysical continuum, a damping function for the cranking term is introduced. Eventually, the stable linear chain structure could survive up to the rotational frequency ~3.5 MeV, but the fission still occurs when the rotational frequency approaches ~4.0 MeV.
