In this note,the authors revisit the envelope dimension reduction,which was first introduced for estimating a sufficient dimension reduction subspace without inverting the sample covariance.Motivated by the recent dev...In this note,the authors revisit the envelope dimension reduction,which was first introduced for estimating a sufficient dimension reduction subspace without inverting the sample covariance.Motivated by the recent developments in envelope methods and algorithms,the authors refresh the envelope inverse regression as a flexible alternative to the existing inverse regression methods in dimension reduction.The authors discuss the versatility of the envelope approach and demonstrate the advantages of the envelope dimension reduction through simulation studies.展开更多
Multi-dimensional arrays are referred to as tensors.Tensor-valued predictors are commonly encountered in modern biomedical applications,such as electroencephalogram(EEG),magnetic resonance imaging(MRI),functional MRI(...Multi-dimensional arrays are referred to as tensors.Tensor-valued predictors are commonly encountered in modern biomedical applications,such as electroencephalogram(EEG),magnetic resonance imaging(MRI),functional MRI(fMRI),diffusion-weighted MRI,and longitudinal health data.In survival analysis,it is both important and challenging to integrate clinically relevant information,such as gender,age,and disease state along with medical imaging tensor data or longitudinal health data to predict disease outcomes.Most existing higher-order sufficient dimension reduction regressions for matrix-or array-valued data focus solely on tensor data,often neglecting established clinical covariates that are readily available and known to have predictive value.Based on the idea of Folded-Minimum Average Variance Estimation(Folded-MAVE:Xue and Yin,2014),the authors propose a new method,Partial Dimension Folded-MAVE(PF-MAVE),to address regression mean functions with tensor-valued covariates while simultaneously incorporating clinical covariates,which are typically categorical variables.Theorems and simulation studies demonstrate the importance of incorporating these categorical clinical predictors.A survival analysis of a longitudinal study of primary biliary cirrhosis(PBC)data is included for illustration of the proposed method.展开更多
The goal of this study was to determine the spatiotemporal characteristics of mangrove distribution and fragmentation patterns from 1988 through 2019 in Dongzhaigang.Land cover datasets were generated for Dongzhaigang...The goal of this study was to determine the spatiotemporal characteristics of mangrove distribution and fragmentation patterns from 1988 through 2019 in Dongzhaigang.Land cover datasets were generated for Dongzhaigang for multiple years via a decision tree method based on a classification and regression tree(CART)algorithm using Landsat time series images.Spatiotemporal transform and fragmentation patterns of mangrove distribution were separately assessed with a transfer matrix of land cover types and a landscape pattern index.The classification method combined with multi-band images showed good accuracy,with overall accuracy higher than 90%.Mangrove areas in 1988,1999,2009,and 2019 were 2050,1875,1818,and 1750 ha,respectively,with decreases mainly due to conversion to aquaculture ponds and farmland.A mangrove growth index(MGI)was proposed,reflecting the water-mangrove relationship,showing positive mangrove growth from 1988–2009 and negative growth from 2009–2019.Study results indicated anthropogenic factors play a leading role in the extent and scale of mangrove effects over the past 30 years.According to the analysis results,corresponding management and protection measures are proposed to provide reference for the sustainable development of Dongzhaigang Mangrove Wetland ecosystem.展开更多
Transit managers can use Intelligent Transportation System technologies to access large amounts of data to monitor network status.However,the presentation of the data lacks structural information.Existing single-netwo...Transit managers can use Intelligent Transportation System technologies to access large amounts of data to monitor network status.However,the presentation of the data lacks structural information.Existing single-network description technologies are ineffective in representing the temporal and spatial characteristics simultaneously.Therefore,there is a need for complementary methods to address these deficiencies.To address these limitations,this paper proposes an approach that combines Network Snapshots and Temporal Paths for the scheduled system.A dual information network is constructed to assess the degree of operational deviation considering the planning tasks.To validate the effectiveness,discussions are conducted through a modified cosine similarity calculation on theoretical analysis,delay level description,and the ability to identify abnormal dates.Compared to some state-of-the-art methods,the proposed method achieves an average Spearman delay correlation of 0.847 and a relative distance of 3.477.Furthermore,case analyses are invested in regions of China's Mainland,Europe,and the United States,investigating both the overall and sub-regional network fluctuations.To represent the impact of network fluctuations in sub-regions,a response loss value was developed.The times that are prone to fluctuations are also discussed through the classification of time series data.The research can offer a novel approach to system monitoring,providing a research direction that utilizes individual data combined to represent macroscopic states.Our code will be released at https://github.com/daozhong/STPN.git.展开更多
In this paper,we study two types of the Ding injective dimensions of complexes.First,we provide some equivalent characterizations of the dimension related to the special Ding injec-tive preenvelopes.Furthermore,we con...In this paper,we study two types of the Ding injective dimensions of complexes.First,we provide some equivalent characterizations of the dimension related to the special Ding injec-tive preenvelopes.Furthermore,we consider the relationship between the dimensions Dipd(Y)and Did(Y)of the complex Y,where Dipd(Y)denotes the dimension associated with special Ding injective preenvelopes,and Did(Y)denotes the dimension associated with DG-injective resolutions.It is demonstrated that Dipd(Y)=Did(Y)for any bounded complex Y.展开更多
In this manuscript,we consider a non-autonomous dynamical system.Using the Carathéodory structure,we define a BS dimension on an arbitrary subset and obtain a Bowen’s equation that illustrates the relation of th...In this manuscript,we consider a non-autonomous dynamical system.Using the Carathéodory structure,we define a BS dimension on an arbitrary subset and obtain a Bowen’s equation that illustrates the relation of the BS dimension to the Pesin-Pitskel topological pressure given by Nazarian[24].Moreover,we establish a variational principle and an inverse variational principle for the BS dimension of non-autonomous dynamical systems.Finally,we also get an analogue of Billingsley’s theorem for the BS dimension of non-autonomous dynamical systems.展开更多
The proliferation of high-dimensional data and the widespread use of complex models present central challenges in contemporary statistics and data science.Dimension reduction and model checking,as two foundational pil...The proliferation of high-dimensional data and the widespread use of complex models present central challenges in contemporary statistics and data science.Dimension reduction and model checking,as two foundational pillars supporting scientific inference and data-driven decisionmaking,have evolved through the collective wisdom of generations of statisticians.This special issue,titled"Recent Developments in Dimension Reduction and Model Checking for regressions",not only aims to showcase cutting-edge advances in the field but also carries a distinct sense of academic homage to honor the groundbreaking and enduring contributions of Professor Lixing Zhu,a leading scholar whose work has profoundly shaped both areas.展开更多
Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when ta...Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.展开更多
In this paper,the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannia...In this paper,the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannian manifolds.The authors rigorously establish statistical properties of the estimators,providing formal proofs of their consistency and asymptotic behaviors.The effectiveness of our method is demonstrated through extensive simulations and applications to real-world datasets which highlight its practical utility for complex data with non-Euclidean structures.展开更多
Classical linear discriminant analysis(LDA)(Fisher,1936)implicitly assumes the classification boundary depends on only one linear combination of the predictors.This restriction can lead to poor classification in appli...Classical linear discriminant analysis(LDA)(Fisher,1936)implicitly assumes the classification boundary depends on only one linear combination of the predictors.This restriction can lead to poor classification in applications where the decision boundary depends on multiple linear combinations of the predictors.To overcome this challenge,the authors first project the predictors onto an envelope central space and then perform LDA based on the sufficient predictor.The performance of the proposed method in improving classification accuracy is demonstrated in both synthetic data and real applications.展开更多
As a significant city in the Yangtze River Delta regions,Hefei has experienced rapid changes in the sources of air pollution due to its high-speed economic development and urban expansion.However,there has been limite...As a significant city in the Yangtze River Delta regions,Hefei has experienced rapid changes in the sources of air pollution due to its high-speed economic development and urban expansion.However,there has been limited research in recent years on the spatial-temporal distribution and emission of its atmospheric pollutants.To address this,this study conducted mobile observations of urban roads using the Mobile-DOAS instrument from June 2021 to May 2022.The monitoring results exhibit a favourable consistent with TROPOMI satellite data and ground monitoring station data.Temporally,there were pronounced seasonal variations in air pollutants.Spatially,high concentration of HCHO and NO_(2)were closely associated with traffic congestion on roadways,while heightened SO_(2)levels were attributed to winter heating and industrial emissions.The study also revealed that with the implementation of road policies,the average vehicle speed increased by 95.4%,while the NO concentration decreased by 54.4%.In the estimation of urban NO_(x)emission flux,it was observed that in temporal terms,compared with inventory data,the emissions calculated viamobile measurements exhibitedmore distinct seasonal patterns,with the highest emission rate of 349 g/sec in winter and the lowest of 142 g/sec in summer.In spatial terms,the significant difference in emissions between the inner and outer ring roads also suggests the presence of the city’s primary NO_(x)emission sources in the area between these two rings.This study offers data support for formulating the next phase of air pollution control measures in urban areas.展开更多
“Multidimensional international world”refers to understanding the world through multiple dimensions beyond traditional economic or political measures,fostering cross-cultural collaboration,and creating systems that ...“Multidimensional international world”refers to understanding the world through multiple dimensions beyond traditional economic or political measures,fostering cross-cultural collaboration,and creating systems that balance global integration with local needs.This also includes management of global business operations across diverse cultures in a multipolar international landscape.The paper briefs the developed and already tested in numerous applications high-level Spatial Grasp Model and Technology(SGT),which can help investigate and manage complex systems with a holistic spatial approach effectively covering various physical and virtual dimensions,their interrelations,and integration as a whole.Different areas will be investigated with examples of practical solutions in them and their combinations in a high-level Spatial Grasp Language(SGL),the key element of SGT.This allows for the creation and distributed management of very large spatial networks with different orientation which can be self-spreading,self-analyzing,self-modifying,and self-recovering in complex terrestrial and celestial environments,and also organize dynamic multi-networking solutions supporting global evolution and integrity.展开更多
In the current situation of decelerating economic expansion,examining the digital economy(DE)as a novel economic model is beneficial for the local economy’s sustainable and high-quality development(HQD).We analyzed p...In the current situation of decelerating economic expansion,examining the digital economy(DE)as a novel economic model is beneficial for the local economy’s sustainable and high-quality development(HQD).We analyzed panel data from the Yellow River(YR)region from 2013 to 2021 and discovered notable spatial variances in the composite index and coupling coordination of the two systems.Specifically,the downstream region exhibited the highest coupling coordination,while the upstream region had the lowest.We identified that favorable factors such as economic development,innovation,industrial upgrading,and government intervention can bolster the coupling.Our findings provide a valuable framework for promoting DE and HQD in the YR region.展开更多
Accurate traffic flow prediction has a profound impact on modern traffic management. Traffic flow has complex spatial-temporal correlations and periodicity, which poses difficulties for precise prediction. To address ...Accurate traffic flow prediction has a profound impact on modern traffic management. Traffic flow has complex spatial-temporal correlations and periodicity, which poses difficulties for precise prediction. To address this problem, a Multi-head Self-attention and Spatial-Temporal Graph Convolutional Network (MSSTGCN) for multiscale traffic flow prediction is proposed. Firstly, to capture the hidden traffic periodicity of traffic flow, traffic flow is divided into three kinds of periods, including hourly, daily, and weekly data. Secondly, a graph attention residual layer is constructed to learn the global spatial features across regions. Local spatial-temporal dependence is captured by using a T-GCN module. Thirdly, a transformer layer is introduced to learn the long-term dependence in time. A position embedding mechanism is introduced to label position information for all traffic sequences. Thus, this multi-head self-attention mechanism can recognize the sequence order and allocate weights for different time nodes. Experimental results on four real-world datasets show that the MSSTGCN performs better than the baseline methods and can be successfully adapted to traffic prediction tasks.展开更多
The phenomenon of photothermally induced transparency(PTIT)arises from the nonlinear behavior of an optical cavity,resulting from the heating of mirrors.By introducing a coupling field in the form of a standing wave,P...The phenomenon of photothermally induced transparency(PTIT)arises from the nonlinear behavior of an optical cavity,resulting from the heating of mirrors.By introducing a coupling field in the form of a standing wave,PTIT can be transitioned into photothermally induced grating(PTIG).A two-dimensional(2D)diffraction pattern is achieved through the adjustment of key parameters such as coupling strength and effective detuning.Notably,we observe first,second,and third-order intensity distributions,with the ability to transfer probe energy predominantly to the third order by fine-tuning the coupling strength.The intensity distribution is characterized by(±m,±n),where m,n=1,2,3.This proposed 2D grating system offers a novel platform for manipulating PTIG,presenting unique possibilities for enhanced functionality and control.展开更多
The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets.The Black–Scholes model for pricing stock options has been app...The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets.The Black–Scholes model for pricing stock options has been applied to various payoff structures,and options trading is based on Black and Scholes’principle of dynamic hedging to estimate and assess option prices over time.However,the Black–Scholes model requires severe constraints,assumptions,and conditions to be applied to real-life financial and economic problems.Several methods and approaches have been developed to approach these conditions,such as fractional Black–Scholes models based on fractional derivatives.These fractional models are expected since the Black–Scholes equation is derived using Ito’s lemma from stochastic calculus,where fractional derivatives play a leading role.Hence,a fractional stochastic model that includes the basic Black–Scholes model as a special case is expected.However,these fractional financial models require computational tools and advanced analytical methods to solve the associated fractional Black–Scholes equations.Nevertheless,it is believed that the fractal nature of economic processes permits to model economical and financial markets problems more accurately compared to the conventional model.The relationship between fractional calculus and fractals is well-known in the literature.This study introduces a generalized Black–Scholes equation in fractal dimensions and discusses its role in financial marketing.In our analysis,we consider power-laws properties for volatility,interest rated,and dividend payout,which emerge in several empirical regularities in quantitative finance and economics.We apply our model to study the problem of pricing barrier option and we estimate the values of fractal dimensions in both time and in space.Our model can be used to obtain the prices of many pay-off models.We observe that fractal dimensions considerably affect the solutions of the Black–Scholes equation and that,for fractal dimensions much smaller than unity,the call option increases significantly.We prove that fractal dimensions are a powerful tool to obtain new results.Further details are analyzed and discussed.展开更多
Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)...Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)x∈B(x,ψ(n))for infinitely many n}forα≥log|λ_(d)/λ_(1)|,whereψis a positive decreasing function defined onℕand its lower order at infinity isα=lim inf_(n→∞)-logψ(n)/n.In the case that A is diagonalizable overℚwith integral eigenvalues,we obtain the dimension formula.展开更多
In the past decade,financial institutions have invested significant efforts in the development of accurate analytical credit scoring models.The evidence suggests that even small improvements in the accuracy of existin...In the past decade,financial institutions have invested significant efforts in the development of accurate analytical credit scoring models.The evidence suggests that even small improvements in the accuracy of existing credit-scoring models may optimize profits while effectively managing risk exposure.Despite continuing efforts,the majority of existing credit scoring models still include some judgment-based assumptions that are sometimes supported by the significant findings of previous studies but are not validated using the institution’s internal data.We argue that current studies related to the development of credit scoring models have largely ignored recent developments in statistical methods for sufficient dimension reduction.To contribute to the field of financial innovation,this study proposes a Dimension Reduction Assisted Credit Scoring(DRA-CS)method via distance covariance-based sufficient dimension reduction(DCOV-SDR)in Majorization-Minimization(MM)algorithm.First,in the presence of a large number of variables,the DRA-CS method results in greater dimension reduction and better prediction accuracy than the other methods used for dimension reduction.Second,when the DRA-CS method is employed with logistic regression,it outperforms existing methods based on different variable selection techniques.This study argues that the DRA-CS method should be used by financial institutions as a financial innovation tool to analyze high-dimensional customer datasets and improve the accuracy of existing credit scoring methods.展开更多
Spatial-temporal traffic prediction technology is crucial for network planning,resource allocation optimizing,and user experience improving.With the development of virtual network operators,multi-operator collaboratio...Spatial-temporal traffic prediction technology is crucial for network planning,resource allocation optimizing,and user experience improving.With the development of virtual network operators,multi-operator collaborations,and edge computing,spatial-temporal traffic data has taken on a distributed nature.Consequently,noncentralized spatial-temporal traffic prediction solutions have emerged as a recent research focus.Currently,the majority of research typically adopts federated learning methods to train traffic prediction models distributed on each base station.This method reduces additional burden on communication systems.However,this method has a drawback:it cannot handle irregular traffic data.Due to unstable wireless network environments,device failures,insufficient storage resources,etc.,data missing inevitably occurs during the process of collecting traffic data.This results in the irregular nature of distributed traffic data.Yet,commonly used traffic prediction models such as Recurrent Neural Networks(RNN)and Long Short-Term Memory(LSTM)typically assume that the data is complete and regular.To address the challenge of handling irregular traffic data,this paper transforms irregular traffic prediction into problems of estimating latent variables and generating future traffic.To solve the aforementioned problems,this paper introduces split learning to design a structured distributed learning framework.The framework comprises a Global-level Spatial structure mining Model(GSM)and several Nodelevel Generative Models(NGMs).NGM and GSM represent Seq2Seq models deployed on the base station and graph neural network models deployed on the cloud or central controller.Firstly,the time embedding layer in NGM establishes the mapping relationship between irregular traffic data and regular latent temporal feature variables.Secondly,GSM collects statistical feature parameters of latent temporal feature variables from various nodes and executes graph embedding for spatial-temporal traffic data.Finally,NGM generates future traffic based on latent temporal and spatial feature variables.The introduction of the time attention mechanism enhances the framework’s capability to handle irregular traffic data.Graph attention network introduces spatially correlated base station traffic feature information into local traffic prediction,which compensates for missing information in local irregular traffic data.The proposed framework effectively addresses the distributed prediction issues of irregular traffic data.By testing on real world datasets,the proposed framework improves traffic prediction accuracy by 35%compared to other commonly used distributed traffic prediction methods.展开更多
The inversion of large sparse matrices poses a major challenge in geophysics,particularly in Bayesian seismic inversion,significantly limiting computational efficiency and practical applicability to largescale dataset...The inversion of large sparse matrices poses a major challenge in geophysics,particularly in Bayesian seismic inversion,significantly limiting computational efficiency and practical applicability to largescale datasets.Existing dimensionality reduction methods have achieved partial success in addressing this issue.However,they remain limited in terms of the achievable degree of dimensionality reduction.An incremental deep dimensionality reduction approach is proposed herein to significantly reduce matrix size and is applied to Bayesian linearized inversion(BLI),a stochastic seismic inversion approach that heavily depends on large sparse matrices inversion.The proposed method first employs a linear transformation based on the discrete cosine transform(DCT)to extract the matrix's essential information and eliminate redundant components,forming the foundation of the dimensionality reduction framework.Subsequently,an innovative iterative DCT-based dimensionality reduction process is applied,where the reduction magnitude is carefully calibrated at each iteration to incrementally reduce dimensionality,thereby effectively eliminating matrix redundancy in depth.This process is referred to as the incremental discrete cosine transform(IDCT).Ultimately,a linear IDCT-based reduction operator is constructed and applied to the kernel matrix inversion in BLI,resulting in a more efficient BLI framework.The proposed method was evaluated through synthetic and field data tests and compared with conventional dimensionality reduction methods.The IDCT approach significantly improves the dimensionality reduction efficiency of the core inversion matrix while preserving inversion accuracy,demonstrating prominent advantages in solving Bayesian inverse problems more efficiently.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.12301365supported by the National Natural Science Foundation of China under Grant No.2241200071Guangdong Basic and Applied Basic Research Foundation under Grant No.2023A1515110001。
文摘In this note,the authors revisit the envelope dimension reduction,which was first introduced for estimating a sufficient dimension reduction subspace without inverting the sample covariance.Motivated by the recent developments in envelope methods and algorithms,the authors refresh the envelope inverse regression as a flexible alternative to the existing inverse regression methods in dimension reduction.The authors discuss the versatility of the envelope approach and demonstrate the advantages of the envelope dimension reduction through simulation studies.
文摘Multi-dimensional arrays are referred to as tensors.Tensor-valued predictors are commonly encountered in modern biomedical applications,such as electroencephalogram(EEG),magnetic resonance imaging(MRI),functional MRI(fMRI),diffusion-weighted MRI,and longitudinal health data.In survival analysis,it is both important and challenging to integrate clinically relevant information,such as gender,age,and disease state along with medical imaging tensor data or longitudinal health data to predict disease outcomes.Most existing higher-order sufficient dimension reduction regressions for matrix-or array-valued data focus solely on tensor data,often neglecting established clinical covariates that are readily available and known to have predictive value.Based on the idea of Folded-Minimum Average Variance Estimation(Folded-MAVE:Xue and Yin,2014),the authors propose a new method,Partial Dimension Folded-MAVE(PF-MAVE),to address regression mean functions with tensor-valued covariates while simultaneously incorporating clinical covariates,which are typically categorical variables.Theorems and simulation studies demonstrate the importance of incorporating these categorical clinical predictors.A survival analysis of a longitudinal study of primary biliary cirrhosis(PBC)data is included for illustration of the proposed method.
基金financially supported by the National Natural Science Foundation of China(Nos.U2244225 and 42020104005)the Ministry of Education of China(111 Project)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)and China Geological Survey(No.DD20211391)。
文摘The goal of this study was to determine the spatiotemporal characteristics of mangrove distribution and fragmentation patterns from 1988 through 2019 in Dongzhaigang.Land cover datasets were generated for Dongzhaigang for multiple years via a decision tree method based on a classification and regression tree(CART)algorithm using Landsat time series images.Spatiotemporal transform and fragmentation patterns of mangrove distribution were separately assessed with a transfer matrix of land cover types and a landscape pattern index.The classification method combined with multi-band images showed good accuracy,with overall accuracy higher than 90%.Mangrove areas in 1988,1999,2009,and 2019 were 2050,1875,1818,and 1750 ha,respectively,with decreases mainly due to conversion to aquaculture ponds and farmland.A mangrove growth index(MGI)was proposed,reflecting the water-mangrove relationship,showing positive mangrove growth from 1988–2009 and negative growth from 2009–2019.Study results indicated anthropogenic factors play a leading role in the extent and scale of mangrove effects over the past 30 years.According to the analysis results,corresponding management and protection measures are proposed to provide reference for the sustainable development of Dongzhaigang Mangrove Wetland ecosystem.
文摘Transit managers can use Intelligent Transportation System technologies to access large amounts of data to monitor network status.However,the presentation of the data lacks structural information.Existing single-network description technologies are ineffective in representing the temporal and spatial characteristics simultaneously.Therefore,there is a need for complementary methods to address these deficiencies.To address these limitations,this paper proposes an approach that combines Network Snapshots and Temporal Paths for the scheduled system.A dual information network is constructed to assess the degree of operational deviation considering the planning tasks.To validate the effectiveness,discussions are conducted through a modified cosine similarity calculation on theoretical analysis,delay level description,and the ability to identify abnormal dates.Compared to some state-of-the-art methods,the proposed method achieves an average Spearman delay correlation of 0.847 and a relative distance of 3.477.Furthermore,case analyses are invested in regions of China's Mainland,Europe,and the United States,investigating both the overall and sub-regional network fluctuations.To represent the impact of network fluctuations in sub-regions,a response loss value was developed.The times that are prone to fluctuations are also discussed through the classification of time series data.The research can offer a novel approach to system monitoring,providing a research direction that utilizes individual data combined to represent macroscopic states.Our code will be released at https://github.com/daozhong/STPN.git.
基金Supported by the National Natural Science Foundation of China(Grant No.12061061)the Young Talents Team Project of Gansu Province(Grant No.2025QNTD49)+1 种基金Lanshan Talent Project of Northwest Minzu University(Grant No.Xbmulsrc202412)Longyuan Young Talents of Gansu Province.
文摘In this paper,we study two types of the Ding injective dimensions of complexes.First,we provide some equivalent characterizations of the dimension related to the special Ding injec-tive preenvelopes.Furthermore,we consider the relationship between the dimensions Dipd(Y)and Did(Y)of the complex Y,where Dipd(Y)denotes the dimension associated with special Ding injective preenvelopes,and Did(Y)denotes the dimension associated with DG-injective resolutions.It is demonstrated that Dipd(Y)=Did(Y)for any bounded complex Y.
基金supported by the NSFC(12461012)and the NSF of Chongqing(CSTB2024NSCQ-MSX1246).
文摘In this manuscript,we consider a non-autonomous dynamical system.Using the Carathéodory structure,we define a BS dimension on an arbitrary subset and obtain a Bowen’s equation that illustrates the relation of the BS dimension to the Pesin-Pitskel topological pressure given by Nazarian[24].Moreover,we establish a variational principle and an inverse variational principle for the BS dimension of non-autonomous dynamical systems.Finally,we also get an analogue of Billingsley’s theorem for the BS dimension of non-autonomous dynamical systems.
文摘The proliferation of high-dimensional data and the widespread use of complex models present central challenges in contemporary statistics and data science.Dimension reduction and model checking,as two foundational pillars supporting scientific inference and data-driven decisionmaking,have evolved through the collective wisdom of generations of statisticians.This special issue,titled"Recent Developments in Dimension Reduction and Model Checking for regressions",not only aims to showcase cutting-edge advances in the field but also carries a distinct sense of academic homage to honor the groundbreaking and enduring contributions of Professor Lixing Zhu,a leading scholar whose work has profoundly shaped both areas.
基金funded by National Natural Science Foundation of China(Nos.12402142,11832013 and 11572134)Natural Science Foundation of Hubei Province(No.2024AFB235)+1 种基金Hubei Provincial Department of Education Science and Technology Research Project(No.Q20221714)the Opening Foundation of Hubei Key Laboratory of Digital Textile Equipment(Nos.DTL2023019 and DTL2022012).
文摘Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.
文摘In this paper,the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannian manifolds.The authors rigorously establish statistical properties of the estimators,providing formal proofs of their consistency and asymptotic behaviors.The effectiveness of our method is demonstrated through extensive simulations and applications to real-world datasets which highlight its practical utility for complex data with non-Euclidean structures.
文摘Classical linear discriminant analysis(LDA)(Fisher,1936)implicitly assumes the classification boundary depends on only one linear combination of the predictors.This restriction can lead to poor classification in applications where the decision boundary depends on multiple linear combinations of the predictors.To overcome this challenge,the authors first project the predictors onto an envelope central space and then perform LDA based on the sufficient predictor.The performance of the proposed method in improving classification accuracy is demonstrated in both synthetic data and real applications.
基金supported by the National Natural Science Foundation of China(Nos.U19A2044,42105132,42030609,41975037,and 42105133)the National Key Research and Development Program of China(No.2022YFC3703502)+1 种基金the Plan for Anhui Major Provincial Science&Technology Project(No.202203a07020003)Hefei Ecological Environment Bureau Project(No.2020BFFFD01804).
文摘As a significant city in the Yangtze River Delta regions,Hefei has experienced rapid changes in the sources of air pollution due to its high-speed economic development and urban expansion.However,there has been limited research in recent years on the spatial-temporal distribution and emission of its atmospheric pollutants.To address this,this study conducted mobile observations of urban roads using the Mobile-DOAS instrument from June 2021 to May 2022.The monitoring results exhibit a favourable consistent with TROPOMI satellite data and ground monitoring station data.Temporally,there were pronounced seasonal variations in air pollutants.Spatially,high concentration of HCHO and NO_(2)were closely associated with traffic congestion on roadways,while heightened SO_(2)levels were attributed to winter heating and industrial emissions.The study also revealed that with the implementation of road policies,the average vehicle speed increased by 95.4%,while the NO concentration decreased by 54.4%.In the estimation of urban NO_(x)emission flux,it was observed that in temporal terms,compared with inventory data,the emissions calculated viamobile measurements exhibitedmore distinct seasonal patterns,with the highest emission rate of 349 g/sec in winter and the lowest of 142 g/sec in summer.In spatial terms,the significant difference in emissions between the inner and outer ring roads also suggests the presence of the city’s primary NO_(x)emission sources in the area between these two rings.This study offers data support for formulating the next phase of air pollution control measures in urban areas.
文摘“Multidimensional international world”refers to understanding the world through multiple dimensions beyond traditional economic or political measures,fostering cross-cultural collaboration,and creating systems that balance global integration with local needs.This also includes management of global business operations across diverse cultures in a multipolar international landscape.The paper briefs the developed and already tested in numerous applications high-level Spatial Grasp Model and Technology(SGT),which can help investigate and manage complex systems with a holistic spatial approach effectively covering various physical and virtual dimensions,their interrelations,and integration as a whole.Different areas will be investigated with examples of practical solutions in them and their combinations in a high-level Spatial Grasp Language(SGL),the key element of SGT.This allows for the creation and distributed management of very large spatial networks with different orientation which can be self-spreading,self-analyzing,self-modifying,and self-recovering in complex terrestrial and celestial environments,and also organize dynamic multi-networking solutions supporting global evolution and integrity.
基金supported by the National Office for Philosophy and Social Sciences(grant reference 22&ZD067).
文摘In the current situation of decelerating economic expansion,examining the digital economy(DE)as a novel economic model is beneficial for the local economy’s sustainable and high-quality development(HQD).We analyzed panel data from the Yellow River(YR)region from 2013 to 2021 and discovered notable spatial variances in the composite index and coupling coordination of the two systems.Specifically,the downstream region exhibited the highest coupling coordination,while the upstream region had the lowest.We identified that favorable factors such as economic development,innovation,industrial upgrading,and government intervention can bolster the coupling.Our findings provide a valuable framework for promoting DE and HQD in the YR region.
基金supported by the National Natural Science Foundation of China(Grant Nos.62472149,62376089,62202147)Hubei Provincial Science and Technology Plan Project(2023BCB04100).
文摘Accurate traffic flow prediction has a profound impact on modern traffic management. Traffic flow has complex spatial-temporal correlations and periodicity, which poses difficulties for precise prediction. To address this problem, a Multi-head Self-attention and Spatial-Temporal Graph Convolutional Network (MSSTGCN) for multiscale traffic flow prediction is proposed. Firstly, to capture the hidden traffic periodicity of traffic flow, traffic flow is divided into three kinds of periods, including hourly, daily, and weekly data. Secondly, a graph attention residual layer is constructed to learn the global spatial features across regions. Local spatial-temporal dependence is captured by using a T-GCN module. Thirdly, a transformer layer is introduced to learn the long-term dependence in time. A position embedding mechanism is introduced to label position information for all traffic sequences. Thus, this multi-head self-attention mechanism can recognize the sequence order and allocate weights for different time nodes. Experimental results on four real-world datasets show that the MSSTGCN performs better than the baseline methods and can be successfully adapted to traffic prediction tasks.
文摘The phenomenon of photothermally induced transparency(PTIT)arises from the nonlinear behavior of an optical cavity,resulting from the heating of mirrors.By introducing a coupling field in the form of a standing wave,PTIT can be transitioned into photothermally induced grating(PTIG).A two-dimensional(2D)diffraction pattern is achieved through the adjustment of key parameters such as coupling strength and effective detuning.Notably,we observe first,second,and third-order intensity distributions,with the ability to transfer probe energy predominantly to the third order by fine-tuning the coupling strength.The intensity distribution is characterized by(±m,±n),where m,n=1,2,3.This proposed 2D grating system offers a novel platform for manipulating PTIG,presenting unique possibilities for enhanced functionality and control.
基金Rami Ahmad El-Nabulsi has received funding from the Czech National Agency of Agricultural 533 Research,project QK22020134“Innovative fisheries management of a large reservoir”.
文摘The Black–Scholes equation is one of the most important partial differential equations governing the value of financial derivatives in financial markets.The Black–Scholes model for pricing stock options has been applied to various payoff structures,and options trading is based on Black and Scholes’principle of dynamic hedging to estimate and assess option prices over time.However,the Black–Scholes model requires severe constraints,assumptions,and conditions to be applied to real-life financial and economic problems.Several methods and approaches have been developed to approach these conditions,such as fractional Black–Scholes models based on fractional derivatives.These fractional models are expected since the Black–Scholes equation is derived using Ito’s lemma from stochastic calculus,where fractional derivatives play a leading role.Hence,a fractional stochastic model that includes the basic Black–Scholes model as a special case is expected.However,these fractional financial models require computational tools and advanced analytical methods to solve the associated fractional Black–Scholes equations.Nevertheless,it is believed that the fractal nature of economic processes permits to model economical and financial markets problems more accurately compared to the conventional model.The relationship between fractional calculus and fractals is well-known in the literature.This study introduces a generalized Black–Scholes equation in fractal dimensions and discusses its role in financial marketing.In our analysis,we consider power-laws properties for volatility,interest rated,and dividend payout,which emerge in several empirical regularities in quantitative finance and economics.We apply our model to study the problem of pricing barrier option and we estimate the values of fractal dimensions in both time and in space.Our model can be used to obtain the prices of many pay-off models.We observe that fractal dimensions considerably affect the solutions of the Black–Scholes equation and that,for fractal dimensions much smaller than unity,the call option increases significantly.We prove that fractal dimensions are a powerful tool to obtain new results.Further details are analyzed and discussed.
基金supported by the Science Foundation of China University of Petroleum,Beijing(2462023SZBH013)the China Postdoctoral Science Foundation(2023M743878)+2 种基金the Postdoctoral Fellowship Program of CPSF(GZB20240848)supported partially by the NSFC(12271176)the Guangdong Natural Science Foundation(2024A1515010946).
文摘Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)x∈B(x,ψ(n))for infinitely many n}forα≥log|λ_(d)/λ_(1)|,whereψis a positive decreasing function defined onℕand its lower order at infinity isα=lim inf_(n→∞)-logψ(n)/n.In the case that A is diagonalizable overℚwith integral eigenvalues,we obtain the dimension formula.
文摘In the past decade,financial institutions have invested significant efforts in the development of accurate analytical credit scoring models.The evidence suggests that even small improvements in the accuracy of existing credit-scoring models may optimize profits while effectively managing risk exposure.Despite continuing efforts,the majority of existing credit scoring models still include some judgment-based assumptions that are sometimes supported by the significant findings of previous studies but are not validated using the institution’s internal data.We argue that current studies related to the development of credit scoring models have largely ignored recent developments in statistical methods for sufficient dimension reduction.To contribute to the field of financial innovation,this study proposes a Dimension Reduction Assisted Credit Scoring(DRA-CS)method via distance covariance-based sufficient dimension reduction(DCOV-SDR)in Majorization-Minimization(MM)algorithm.First,in the presence of a large number of variables,the DRA-CS method results in greater dimension reduction and better prediction accuracy than the other methods used for dimension reduction.Second,when the DRA-CS method is employed with logistic regression,it outperforms existing methods based on different variable selection techniques.This study argues that the DRA-CS method should be used by financial institutions as a financial innovation tool to analyze high-dimensional customer datasets and improve the accuracy of existing credit scoring methods.
基金supported by the Beijing Natural Science Foundation(Certificate Number:L234025).
文摘Spatial-temporal traffic prediction technology is crucial for network planning,resource allocation optimizing,and user experience improving.With the development of virtual network operators,multi-operator collaborations,and edge computing,spatial-temporal traffic data has taken on a distributed nature.Consequently,noncentralized spatial-temporal traffic prediction solutions have emerged as a recent research focus.Currently,the majority of research typically adopts federated learning methods to train traffic prediction models distributed on each base station.This method reduces additional burden on communication systems.However,this method has a drawback:it cannot handle irregular traffic data.Due to unstable wireless network environments,device failures,insufficient storage resources,etc.,data missing inevitably occurs during the process of collecting traffic data.This results in the irregular nature of distributed traffic data.Yet,commonly used traffic prediction models such as Recurrent Neural Networks(RNN)and Long Short-Term Memory(LSTM)typically assume that the data is complete and regular.To address the challenge of handling irregular traffic data,this paper transforms irregular traffic prediction into problems of estimating latent variables and generating future traffic.To solve the aforementioned problems,this paper introduces split learning to design a structured distributed learning framework.The framework comprises a Global-level Spatial structure mining Model(GSM)and several Nodelevel Generative Models(NGMs).NGM and GSM represent Seq2Seq models deployed on the base station and graph neural network models deployed on the cloud or central controller.Firstly,the time embedding layer in NGM establishes the mapping relationship between irregular traffic data and regular latent temporal feature variables.Secondly,GSM collects statistical feature parameters of latent temporal feature variables from various nodes and executes graph embedding for spatial-temporal traffic data.Finally,NGM generates future traffic based on latent temporal and spatial feature variables.The introduction of the time attention mechanism enhances the framework’s capability to handle irregular traffic data.Graph attention network introduces spatially correlated base station traffic feature information into local traffic prediction,which compensates for missing information in local irregular traffic data.The proposed framework effectively addresses the distributed prediction issues of irregular traffic data.By testing on real world datasets,the proposed framework improves traffic prediction accuracy by 35%compared to other commonly used distributed traffic prediction methods.
基金partly supported by Hainan Provincial Joint Project of Sanya Yazhou Bay Science and Technology City(2021JJLH0052)National Natural Science Foundation of China(42274154,42304116)+2 种基金Natural Science Foundation of Heilongjiang Province,China(LH2024D013)Heilongjiang Postdoctoral Fund(LBHZ23103)Hainan Yazhou Bay Science and Technology City Jingying Talent Project(SKJC-JYRC-2024-05)。
文摘The inversion of large sparse matrices poses a major challenge in geophysics,particularly in Bayesian seismic inversion,significantly limiting computational efficiency and practical applicability to largescale datasets.Existing dimensionality reduction methods have achieved partial success in addressing this issue.However,they remain limited in terms of the achievable degree of dimensionality reduction.An incremental deep dimensionality reduction approach is proposed herein to significantly reduce matrix size and is applied to Bayesian linearized inversion(BLI),a stochastic seismic inversion approach that heavily depends on large sparse matrices inversion.The proposed method first employs a linear transformation based on the discrete cosine transform(DCT)to extract the matrix's essential information and eliminate redundant components,forming the foundation of the dimensionality reduction framework.Subsequently,an innovative iterative DCT-based dimensionality reduction process is applied,where the reduction magnitude is carefully calibrated at each iteration to incrementally reduce dimensionality,thereby effectively eliminating matrix redundancy in depth.This process is referred to as the incremental discrete cosine transform(IDCT).Ultimately,a linear IDCT-based reduction operator is constructed and applied to the kernel matrix inversion in BLI,resulting in a more efficient BLI framework.The proposed method was evaluated through synthetic and field data tests and compared with conventional dimensionality reduction methods.The IDCT approach significantly improves the dimensionality reduction efficiency of the core inversion matrix while preserving inversion accuracy,demonstrating prominent advantages in solving Bayesian inverse problems more efficiently.
