Aiming at the shortcoming that certain existing blockingmatching algorithrns, such as full search, three-step search, and dia- mond search algorithms, usually can not keep a good balance between high acoaracy and low ...Aiming at the shortcoming that certain existing blockingmatching algorithrns, such as full search, three-step search, and dia- mond search algorithms, usually can not keep a good balance between high acoaracy and low computational complexity, a block-maching motion estimation algorithm based on two-step search is proposed in this paper. According to the fact that the gray values of adjacent pixels will not vary fast, the algorithm employs an interlaced search pattem in the search window to estimate the motion vector of the objectblock. Simulation and actual experiments demanstrate that the proposed algmithm greatly outperforms the well-known three-step search and dianond search algoritlam, no matter the motion vector is large or small. Comparedc with the full search algorithm, the proposed one achieves similar peffomance but requires much less computation, therefore, the algorithm is well qualified for real-time video image processing.展开更多
Based on an orthogonal frequency division multiplexing(OFDM) training symbol with L identical parts, a novel carrier frequency offset (CFO) estimator is proposed for OFDM systems. The CFO is estimated in two steps, fi...Based on an orthogonal frequency division multiplexing(OFDM) training symbol with L identical parts, a novel carrier frequency offset (CFO) estimator is proposed for OFDM systems. The CFO is estimated in two steps, fine estimate and coarse estimate. In the first step, the fine estimation is performed based on the principle of minimum variance. However, the fine estimation has ambiguity since its estimate range is limited. In the second step, the coarse estimation is obtained, which results in a larger estimate range but less precision. Using the coarse estimation, the ambiguity of fine estimation is resolved. To fully use the correlation among L identical parts, the fine estimation resolved the ambiguity and the coarse estimation are optimally combined to obtain the final estimation. Furthermore, the estimation variance of the proposed method is derived. Simulation results demonstrate that the novel two-step estimator outperforms the conventional two-step estimator in terms of estimate performance and computational complexity.展开更多
Under the assumption that the nonlinear operator has Lipschitz continuous divided differences for the first order,we obtain an estimate of the radius of the convergence ball for the two-step secant method.Moreover,we ...Under the assumption that the nonlinear operator has Lipschitz continuous divided differences for the first order,we obtain an estimate of the radius of the convergence ball for the two-step secant method.Moreover,we also provide an error estimate that matches the convergence order of the two-step secant method.At last,we give an application of the proposed theorem.展开更多
The generalized estimating equations(GEE) approach is perhaps one of the most widely used methods for longitudinal data analysis. While the GEE method guarantees the consistency of its estimators under working correla...The generalized estimating equations(GEE) approach is perhaps one of the most widely used methods for longitudinal data analysis. While the GEE method guarantees the consistency of its estimators under working correlation structure misspecification, the corresponding efficiency can be severely affected. In this paper, we propose a new two-step estimation method in which the correlation matrix is assumed to be a linear combination of some known working matrices. Asymptotic properties of the new estimators are developed.Simulation studies are conducted to examine the performance of the proposed estimators. We illustrate the methodology with an epileptic data set.展开更多
The recently developed DOC kernels technique has been successful in the stability and convergence analysis for variable time-step BDF2 schemes.However,it may not be readily applicable to problems exhibiting an initial...The recently developed DOC kernels technique has been successful in the stability and convergence analysis for variable time-step BDF2 schemes.However,it may not be readily applicable to problems exhibiting an initial singularity.In the numerical simulations of solutions with initial singularity,variable time-step schemes like the graded mesh are always adopted to achieve the optimal convergence,whose first adjacent time-step ratio may become pretty large so that the acquired restriction is not satisfied.In this paper,we revisit the variable time-step implicit-explicit two-step backward differentiation formula(IMEX BDF2)scheme to solve the parabolic integro-differential equations(PIDEs)with initial singularity.We obtain the sharp error estimate under a mild restriction condition of adjacent time-step ratios r_(k):=T_(k)/T_(k-1)<r_(max)=4.8645(k≥3)and a much mild requirement on the first ratio,i.e.r_(2)>0.This leads to the validation of our analysis of the variable time-step IMEX BDF2 scheme when the initial singularity is dealt by a simple strategy,i.e.the graded mesh t_(k)=T(k/N)^(γ).In this situation,the convergence order of O(N^(-min(2,γα))is achieved,where N denotes the total number of mesh points andαindicates the regularity of the exact solution.This is,the optimal convergence will be achieved by taking%γ_(opt)=2/α.Numerical examples are provided to demonstrate our theoretical analysis.展开更多
The digital economy has become an important driver for stimulating economic growth.The digital economy has now widely penetrated the fields of economy and society,providing new opportunities for the develop‐ment of u...The digital economy has become an important driver for stimulating economic growth.The digital economy has now widely penetrated the fields of economy and society,providing new opportunities for the develop‐ment of urban-rural integration.Based on panel data for 30 provinces in China from 2011 to 2020,this study constructed an index system for the integration of the digital economy and the development of urban-rural areas and conducted a systematic measurement analysis.Additionally,we used a two-step system of GMM estimation to analyze the impact of the digital economy on the development of urban-rural integra‐tion.The findings demonstrate the significant imbalance paradox of China’s digital economy development,which is shown in a gradient where the eastern region is higher than the center and the central region is higher than the west.Urban-rural integration levels in China fluctuate and display geographical variance,typically displaying high levels in the east and low levels in the west.Urban-rural integration is significantly encouraged by the digital economy,yet it varies in variability between different areas and dimensions.Addi‐tionally,rural human capital moderates the favorable effects of the digital economy on urban-rural integra‐tion.As a result,in order to achieve the integrated development of urban and rural areas,it is imperative to fully exploit the active role of the digital economy,better support the development of rural revitalization,bridge the“digital divide”between urban and rural development,and build a strong foundation for the for‐mation of a digital urban-rural integrated development pattern with urban and rural areas and common con‐struction and sharing.展开更多
To solve the frame delay problem and match the previous frame,Plapous et al.[IEEE Transactions on Audio,Speech,and Language Processing,2006,14(6):2098–2108]introduced a novel approach called two-step noise reduction(...To solve the frame delay problem and match the previous frame,Plapous et al.[IEEE Transactions on Audio,Speech,and Language Processing,2006,14(6):2098–2108]introduced a novel approach called two-step noise reduction(TSNR)technique to improve the performance of the speech enhancement system.However,TSNR approach results in spectral peaks of short duration and the broken spectral outlier,which degrade the spectral characteristics of the speech.To solve this problem,a cepstral smoothing step is added in order to remove these spectral peaks brought by TSNR approach.Theory analysis shows that the proposed approach can effectively smooth the spectral peaks and keep the spectral outlier so as to protect the speech characteristics.Experiment results also show that the proposed approach can bring significant improvement compared to decision-directed(DD)and TSNR approaches,especially in non-stationary noisy environments.展开更多
Semivarying coefficient models are frequently used in statistical models.In this paper,under the condition that the coefficient functions possess different degrees of smoothness,a two-stepmethod is proposed.In the cas...Semivarying coefficient models are frequently used in statistical models.In this paper,under the condition that the coefficient functions possess different degrees of smoothness,a two-stepmethod is proposed.In the case,one-step method for the smoother coefficient functions cannot beoptimal.This drawback can be repaired by using the two-step estimation procedure.The asymptoticmean-squared error for the two-step procedure is obtained and is shown to achieve the optimal rate ofconvergence.A few simulation studies are conducted to evaluate the proposed estimation methods.展开更多
The problem of estimating high-dimensional Gaussian graphical models has gained much attention in recent years. Most existing methods can be considered as one-step approaches, being either regression-based or likeliho...The problem of estimating high-dimensional Gaussian graphical models has gained much attention in recent years. Most existing methods can be considered as one-step approaches, being either regression-based or likelihood-based. In this paper, we propose a two-step method for estimating the high-dimensional Gaussian graphical model. Specifically, the first step serves as a screening step, in which many entries of the concentration matrix are identified as zeros and thus removed from further consideration. Then in the second step, we focus on the remaining entries of the concentration matrix and perform selection and estimation for nonzero entries of the concentration matrix. Since the dimension of the parameter space is effectively reduced by the screening step,the estimation accuracy of the estimated concentration matrix can be potentially improved. We show that the proposed method enjoys desirable asymptotic properties. Numerical comparisons of the proposed method with several existing methods indicate that the proposed method works well. We also apply the proposed method to a breast cancer microarray data set and obtain some biologically meaningful results.展开更多
This study analyzes the role of financial development(FD)on the impact of technologi-cal innovation(TI)on six environmental quality indicators for the 25 economies that are part of the Organization for Economic Cooper...This study analyzes the role of financial development(FD)on the impact of technologi-cal innovation(TI)on six environmental quality indicators for the 25 economies that are part of the Organization for Economic Cooperation and Development for the period from 2000 to 2019.We use a two-step dynamic generalized method of moments approach to understand this relationship.The results show that FD augments the posi-tive effects of TI on four of the six environmental indicators,namely ecological foot-print,adjusted net savings,pressure on nature,and environmental performance.However,no significant effects on environmental sustainability and environmental vulnerability indices were found.When considering all of the environmental quality indicators,TI appears to enhance environmental quality.We find evidence to support the existence of the environmental Kuznets curve in the context of each environmen-tal indicator and economic growth.Moreover,FD and energy consumption appear to accelerate environmental degradation.Based on these results,FD should be viewed as an important parameter in designing policies for innovation to achieve the goal of net-zero carbon emissions.Highlights.Technological innovation and environmental quality nexus is studied.The moderating role of financial development is analyzed.Six different environmental quality indicators are used for OECD countries.Financial development intensifies the environmental benefits of innovation.•The EKC hypothesis is confirmed for all six environmental indicators.展开更多
A numerical method based on the explicit two-step method in time direction and the mixed finite element method in spatial direction is presented for the symmetric regularized long wave(SRLW)equation.The optimal a prio...A numerical method based on the explicit two-step method in time direction and the mixed finite element method in spatial direction is presented for the symmetric regularized long wave(SRLW)equation.The optimal a priori error estimates(O((∆t)^(2)+h^(m+1)+h^(k+1)))for fully discrete explicit two-step mixed scheme are derived.Moreover,a numerical example is provided to confirm our theoretical results.展开更多
基金supported by the Lab Open Fund of Beijing Microchemical Research Institute(P2008026EB)
文摘Aiming at the shortcoming that certain existing blockingmatching algorithrns, such as full search, three-step search, and dia- mond search algorithms, usually can not keep a good balance between high acoaracy and low computational complexity, a block-maching motion estimation algorithm based on two-step search is proposed in this paper. According to the fact that the gray values of adjacent pixels will not vary fast, the algorithm employs an interlaced search pattem in the search window to estimate the motion vector of the objectblock. Simulation and actual experiments demanstrate that the proposed algmithm greatly outperforms the well-known three-step search and dianond search algoritlam, no matter the motion vector is large or small. Comparedc with the full search algorithm, the proposed one achieves similar peffomance but requires much less computation, therefore, the algorithm is well qualified for real-time video image processing.
基金Foundation of Donghua University,China (No.104100044027)
文摘Based on an orthogonal frequency division multiplexing(OFDM) training symbol with L identical parts, a novel carrier frequency offset (CFO) estimator is proposed for OFDM systems. The CFO is estimated in two steps, fine estimate and coarse estimate. In the first step, the fine estimation is performed based on the principle of minimum variance. However, the fine estimation has ambiguity since its estimate range is limited. In the second step, the coarse estimation is obtained, which results in a larger estimate range but less precision. Using the coarse estimation, the ambiguity of fine estimation is resolved. To fully use the correlation among L identical parts, the fine estimation resolved the ambiguity and the coarse estimation are optimally combined to obtain the final estimation. Furthermore, the estimation variance of the proposed method is derived. Simulation results demonstrate that the novel two-step estimator outperforms the conventional two-step estimator in terms of estimate performance and computational complexity.
基金supported by National Natural Science Foundation of China(11771393,11371320,11632015)Zhejiang Natural Science Foundation(LZ14A010002,LQ18A010008)Scientific Research Fund of Zhejiang Provincial Education Department(FX2016073)
文摘Under the assumption that the nonlinear operator has Lipschitz continuous divided differences for the first order,we obtain an estimate of the radius of the convergence ball for the two-step secant method.Moreover,we also provide an error estimate that matches the convergence order of the two-step secant method.At last,we give an application of the proposed theorem.
基金Supported by the National Natural Science Foundation of China(No.11471068)
文摘The generalized estimating equations(GEE) approach is perhaps one of the most widely used methods for longitudinal data analysis. While the GEE method guarantees the consistency of its estimators under working correlation structure misspecification, the corresponding efficiency can be severely affected. In this paper, we propose a new two-step estimation method in which the correlation matrix is assumed to be a linear combination of some known working matrices. Asymptotic properties of the new estimators are developed.Simulation studies are conducted to examine the performance of the proposed estimators. We illustrate the methodology with an epileptic data set.
基金supported by the NSFC(Grant No.12171376)the Fundamental Research Funds for the Central Universities(Grant No.2042021kf0050)and WHU-2022-SYJS-0002+1 种基金Yana Di is partially supported by the NSFC(Grant Nos.12271048,12171042)the Guangdong Key Laboratory(Grant No.2022B1212010006).
文摘The recently developed DOC kernels technique has been successful in the stability and convergence analysis for variable time-step BDF2 schemes.However,it may not be readily applicable to problems exhibiting an initial singularity.In the numerical simulations of solutions with initial singularity,variable time-step schemes like the graded mesh are always adopted to achieve the optimal convergence,whose first adjacent time-step ratio may become pretty large so that the acquired restriction is not satisfied.In this paper,we revisit the variable time-step implicit-explicit two-step backward differentiation formula(IMEX BDF2)scheme to solve the parabolic integro-differential equations(PIDEs)with initial singularity.We obtain the sharp error estimate under a mild restriction condition of adjacent time-step ratios r_(k):=T_(k)/T_(k-1)<r_(max)=4.8645(k≥3)and a much mild requirement on the first ratio,i.e.r_(2)>0.This leads to the validation of our analysis of the variable time-step IMEX BDF2 scheme when the initial singularity is dealt by a simple strategy,i.e.the graded mesh t_(k)=T(k/N)^(γ).In this situation,the convergence order of O(N^(-min(2,γα))is achieved,where N denotes the total number of mesh points andαindicates the regularity of the exact solution.This is,the optimal convergence will be achieved by taking%γ_(opt)=2/α.Numerical examples are provided to demonstrate our theoretical analysis.
基金Ministry of Education Humanities and Social Science Foundation Youth Project“Micro-quantification,Action Mechanism and Impact Research on Financialization of Entity Enterprises”[Grant number.19YJC790106]National Social Science Fund“Mechanism Analysis and Optimization Path Research of Digital Finance Supporting the Im‐provement of Development Efficiency of SMEs”[Grant number.21BJY047]+2 种基金Science and Technology Research Program of Chongqing Education Commission of China:“Optimization Path Research of Or‐ganizational Effectiveness of SOEs in Chongqing Based on Multi-Level Organizational Citizenship Behavior”[Grant number.17SKG036]Chongqing Social Science Planning Major Project“Research on the Technological Progress Path and Countermeasure System of Innovation-driven Manufacturing Upgrade in Chongqing”[Grant num‐ber.2020ZDJJ01]Chongqing Municipal Education Commission Hu‐manities and Social Sciences Research Project“Western Region Finan‐cial Development and Manufacturing Traditional Comparative Advan‐tage Transformation:Efficiency Measurement,Action Mechanism and Research on Spatial Effects”[Grant number.20SKGH040].
文摘The digital economy has become an important driver for stimulating economic growth.The digital economy has now widely penetrated the fields of economy and society,providing new opportunities for the develop‐ment of urban-rural integration.Based on panel data for 30 provinces in China from 2011 to 2020,this study constructed an index system for the integration of the digital economy and the development of urban-rural areas and conducted a systematic measurement analysis.Additionally,we used a two-step system of GMM estimation to analyze the impact of the digital economy on the development of urban-rural integra‐tion.The findings demonstrate the significant imbalance paradox of China’s digital economy development,which is shown in a gradient where the eastern region is higher than the center and the central region is higher than the west.Urban-rural integration levels in China fluctuate and display geographical variance,typically displaying high levels in the east and low levels in the west.Urban-rural integration is significantly encouraged by the digital economy,yet it varies in variability between different areas and dimensions.Addi‐tionally,rural human capital moderates the favorable effects of the digital economy on urban-rural integra‐tion.As a result,in order to achieve the integrated development of urban and rural areas,it is imperative to fully exploit the active role of the digital economy,better support the development of rural revitalization,bridge the“digital divide”between urban and rural development,and build a strong foundation for the for‐mation of a digital urban-rural integrated development pattern with urban and rural areas and common con‐struction and sharing.
基金partially supported by the National Natural Science Foundation of China(Grant Nos.61005004,61175011,and 61171193)the Next-Generation Broadband Wireless Mobile Communications Network Technology Key Project(No.2011ZX03002-005-01)+1 种基金the 111 project(No.B08004)Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry.
文摘To solve the frame delay problem and match the previous frame,Plapous et al.[IEEE Transactions on Audio,Speech,and Language Processing,2006,14(6):2098–2108]introduced a novel approach called two-step noise reduction(TSNR)technique to improve the performance of the speech enhancement system.However,TSNR approach results in spectral peaks of short duration and the broken spectral outlier,which degrade the spectral characteristics of the speech.To solve this problem,a cepstral smoothing step is added in order to remove these spectral peaks brought by TSNR approach.Theory analysis shows that the proposed approach can effectively smooth the spectral peaks and keep the spectral outlier so as to protect the speech characteristics.Experiment results also show that the proposed approach can bring significant improvement compared to decision-directed(DD)and TSNR approaches,especially in non-stationary noisy environments.
基金supported in part by the National Natural Science Foundation of China under Grant No. 10871072Shanxi's Natural Science Foundation of China under Grant No. 2007011014
文摘Semivarying coefficient models are frequently used in statistical models.In this paper,under the condition that the coefficient functions possess different degrees of smoothness,a two-stepmethod is proposed.In the case,one-step method for the smoother coefficient functions cannot beoptimal.This drawback can be repaired by using the two-step estimation procedure.The asymptoticmean-squared error for the two-step procedure is obtained and is shown to achieve the optimal rate ofconvergence.A few simulation studies are conducted to evaluate the proposed estimation methods.
基金National Natural Science Foundation of China (Grant No. 11671059)。
文摘The problem of estimating high-dimensional Gaussian graphical models has gained much attention in recent years. Most existing methods can be considered as one-step approaches, being either regression-based or likelihood-based. In this paper, we propose a two-step method for estimating the high-dimensional Gaussian graphical model. Specifically, the first step serves as a screening step, in which many entries of the concentration matrix are identified as zeros and thus removed from further consideration. Then in the second step, we focus on the remaining entries of the concentration matrix and perform selection and estimation for nonzero entries of the concentration matrix. Since the dimension of the parameter space is effectively reduced by the screening step,the estimation accuracy of the estimated concentration matrix can be potentially improved. We show that the proposed method enjoys desirable asymptotic properties. Numerical comparisons of the proposed method with several existing methods indicate that the proposed method works well. We also apply the proposed method to a breast cancer microarray data set and obtain some biologically meaningful results.
基金This research paper did not receive any financial aid from any source.
文摘This study analyzes the role of financial development(FD)on the impact of technologi-cal innovation(TI)on six environmental quality indicators for the 25 economies that are part of the Organization for Economic Cooperation and Development for the period from 2000 to 2019.We use a two-step dynamic generalized method of moments approach to understand this relationship.The results show that FD augments the posi-tive effects of TI on four of the six environmental indicators,namely ecological foot-print,adjusted net savings,pressure on nature,and environmental performance.However,no significant effects on environmental sustainability and environmental vulnerability indices were found.When considering all of the environmental quality indicators,TI appears to enhance environmental quality.We find evidence to support the existence of the environmental Kuznets curve in the context of each environmen-tal indicator and economic growth.Moreover,FD and energy consumption appear to accelerate environmental degradation.Based on these results,FD should be viewed as an important parameter in designing policies for innovation to achieve the goal of net-zero carbon emissions.Highlights.Technological innovation and environmental quality nexus is studied.The moderating role of financial development is analyzed.Six different environmental quality indicators are used for OECD countries.Financial development intensifies the environmental benefits of innovation.•The EKC hypothesis is confirmed for all six environmental indicators.
基金supported by the National Natural Science Fund of China(11061021,11301258 and 11361035)the Scientific Research Projection of Higher Schools of Inner Mongolia(NJZZ12011 and NJZY13199)+1 种基金the Natural Science Fund of Inner Mongolia Province(2012MS0106 and 2012MS0108)the Program of Higher-level talents of Inner Mongolia University(125119).
文摘A numerical method based on the explicit two-step method in time direction and the mixed finite element method in spatial direction is presented for the symmetric regularized long wave(SRLW)equation.The optimal a priori error estimates(O((∆t)^(2)+h^(m+1)+h^(k+1)))for fully discrete explicit two-step mixed scheme are derived.Moreover,a numerical example is provided to confirm our theoretical results.
