Markowitz Portfolio theory under-estimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiase...Markowitz Portfolio theory under-estimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiased estimation of this risk under specific model assumptions. Norm constrained portfolios have recently been studied to keep the effective dimension low. In this paper we consider three sets of high dimensional data, the stock market prices for three countries, namely US, UK and India. We compare the Markowitz efficient frontier to those obtained by unbiasedness corrections and imposing norm-constraints in these real data scenarios. We also study the out-of-sample performance of the different procedures. We find that the 2-norm constrained portfolio has best overall performance.展开更多
Nonlinear transforms have significantly advanced learned image compression(LIC),particularly using residual blocks.This transform enhances the nonlinear expression ability and obtain compact feature representation by ...Nonlinear transforms have significantly advanced learned image compression(LIC),particularly using residual blocks.This transform enhances the nonlinear expression ability and obtain compact feature representation by enlarging the receptive field,which indicates how the convolution process extracts features in a high dimensional feature space.However,its functionality is restricted to the spatial dimension and network depth,limiting further improvements in network performance due to insufficient information interaction and representation.Crucially,the potential of high dimensional feature space in the channel dimension and the exploration of network width/resolution remain largely untapped.In this paper,we consider nonlinear transforms from the perspective of feature space,defining high-dimensional feature spaces in different dimensions and investigating the specific effects.Firstly,we introduce the dimension increasing and decreasing transforms in both channel and spatial dimensions to obtain high dimensional feature space and achieve better feature extraction.Secondly,we design a channel-spatial fusion residual transform(CSR),which incorporates multi-dimensional transforms for a more effective representation.Furthermore,we simplify the proposed fusion transform to obtain a slim architecture(CSR-sm),balancing network complexity and compression performance.Finally,we build the overall network with stacked CSR transforms to achieve better compression and reconstruction.Experimental results demonstrate that the proposed method can achieve superior ratedistortion performance compared to the existing LIC methods and traditional codecs.Specifically,our proposed method achieves 9.38%BD-rate reduction over VVC on Kodak dataset.展开更多
To solve the high-dimensionality issue and improve its accuracy in credit risk assessment,a high-dimensionality-trait-driven learning paradigm is proposed for feature extraction and classifier selection.The proposed p...To solve the high-dimensionality issue and improve its accuracy in credit risk assessment,a high-dimensionality-trait-driven learning paradigm is proposed for feature extraction and classifier selection.The proposed paradigm consists of three main stages:categorization of high dimensional data,high-dimensionality-trait-driven feature extraction,and high-dimensionality-trait-driven classifier selection.In the first stage,according to the definition of high-dimensionality and the relationship between sample size and feature dimensions,the high-dimensionality traits of credit dataset are further categorized into two types:100<feature dimensions<sample size,and feature dimensions≥sample size.In the second stage,some typical feature extraction methods are tested regarding the two categories of high dimensionality.In the final stage,four types of classifiers are performed to evaluate credit risk considering different high-dimensionality traits.For the purpose of illustration and verification,credit classification experiments are performed on two publicly available credit risk datasets,and the results show that the proposed high-dimensionality-trait-driven learning paradigm for feature extraction and classifier selection is effective in handling high-dimensional credit classification issues and improving credit classification accuracy relative to the benchmark models listed in this study.展开更多
An algorithm, Clustering Algorithm Based On Sparse Feature Vector (CABOSFV),was proposed for the high dimensional clustering of binary sparse data. This algorithm compressesthe data effectively by using a tool 'Sp...An algorithm, Clustering Algorithm Based On Sparse Feature Vector (CABOSFV),was proposed for the high dimensional clustering of binary sparse data. This algorithm compressesthe data effectively by using a tool 'Sparse Feature Vector', thus reduces the data scaleenormously, and can get the clustering result with only one data scan. Both theoretical analysis andempirical tests showed that CABOSFV is of low computational complexity. The algorithm findsclusters in high dimensional large datasets efficiently and handles noise effectively.展开更多
Clustering high dimensional data is challenging as data dimensionality increases the distance between data points,resulting in sparse regions that degrade clustering performance.Subspace clustering is a common approac...Clustering high dimensional data is challenging as data dimensionality increases the distance between data points,resulting in sparse regions that degrade clustering performance.Subspace clustering is a common approach for processing high-dimensional data by finding relevant features for each cluster in the data space.Subspace clustering methods extend traditional clustering to account for the constraints imposed by data streams.Data streams are not only high-dimensional,but also unbounded and evolving.This necessitates the development of subspace clustering algorithms that can handle high dimensionality and adapt to the unique characteristics of data streams.Although many articles have contributed to the literature review on data stream clustering,there is currently no specific review on subspace clustering algorithms in high-dimensional data streams.Therefore,this article aims to systematically review the existing literature on subspace clustering of data streams in high-dimensional streaming environments.The review follows a systematic methodological approach and includes 18 articles for the final analysis.The analysis focused on two research questions related to the general clustering process and dealing with the unbounded and evolving characteristics of data streams.The main findings relate to six elements:clustering process,cluster search,subspace search,synopsis structure,cluster maintenance,and evaluation measures.Most algorithms use a two-phase clustering approach consisting of an initialization stage,a refinement stage,a cluster maintenance stage,and a final clustering stage.The density-based top-down subspace clustering approach is more widely used than the others because it is able to distinguish true clusters and outliers using projected microclusters.Most algorithms implicitly adapt to the evolving nature of the data stream by using a time fading function that is sensitive to outliers.Future work can focus on the clustering framework,parameter optimization,subspace search techniques,memory-efficient synopsis structures,explicit cluster change detection,and intrinsic performance metrics.This article can serve as a guide for researchers interested in high-dimensional subspace clustering methods for data streams.展开更多
Dear Editor,This letter presents a novel latent factorization model for high dimensional and incomplete (HDI) tensor, namely the neural Tucker factorization (Neu Tuc F), which is a generic neural network-based latent-...Dear Editor,This letter presents a novel latent factorization model for high dimensional and incomplete (HDI) tensor, namely the neural Tucker factorization (Neu Tuc F), which is a generic neural network-based latent-factorization-of-tensors model under the Tucker decomposition framework.展开更多
In this paper a high-dimension multiparty quantum secret sharing scheme is proposed by using Einstein-Podolsky-Rosen pairs and local unitary operators. This scheme has the advantage of not only having higher capacity,...In this paper a high-dimension multiparty quantum secret sharing scheme is proposed by using Einstein-Podolsky-Rosen pairs and local unitary operators. This scheme has the advantage of not only having higher capacity, but also saving storage space. The security analysis is also given.展开更多
Information analysis of high dimensional data was carried out through similarity measure application. High dimensional data were considered as the a typical structure. Additionally, overlapped and non-overlapped data ...Information analysis of high dimensional data was carried out through similarity measure application. High dimensional data were considered as the a typical structure. Additionally, overlapped and non-overlapped data were introduced, and similarity measure analysis was also illustrated and compared with conventional similarity measure. As a result, overlapped data comparison was possible to present similarity with conventional similarity measure. Non-overlapped data similarity analysis provided the clue to solve the similarity of high dimensional data. Considering high dimensional data analysis was designed with consideration of neighborhoods information. Conservative and strict solutions were proposed. Proposed similarity measure was applied to express financial fraud among multi dimensional datasets. In illustrative example, financial fraud similarity with respect to age, gender, qualification and job was presented. And with the proposed similarity measure, high dimensional personal data were calculated to evaluate how similar to the financial fraud. Calculation results show that the actual fraud has rather high similarity measure compared to the average, from minimal 0.0609 to maximal 0.1667.展开更多
Three high dimensional spatial standardization algorithms are used for diffusion tensor image(DTI)registration,and seven kinds of methods are used to evaluate their performances.Firstly,the template used in this paper...Three high dimensional spatial standardization algorithms are used for diffusion tensor image(DTI)registration,and seven kinds of methods are used to evaluate their performances.Firstly,the template used in this paper was obtained by spatial transformation of 16 subjects by means of tensor-based standardization.Then,high dimensional standardization algorithms for diffusion tensor images,including fractional anisotropy(FA)based diffeomorphic registration algorithm,FA based elastic registration algorithm and tensor-based registration algorithm,were performed.Finally,7 kinds of evaluation methods,including normalized standard deviation,dyadic coherence,diffusion cross-correlation,overlap of eigenvalue-eigenvector pairs,Euclidean distance of diffusion tensor,and Euclidean distance of the deviatoric tensor and deviatoric of tensors,were used to qualitatively compare and summarize the above standardization algorithms.Experimental results revealed that the high-dimensional tensor-based standardization algorithms perform well and can maintain the consistency of anatomical structures.展开更多
We deal with the boundedness of solutions to a class of fully parabolic quasilinear repulsion chemotaxis systems{ut=∇・(ϕ(u)∇u)+∇・(ψ(u)∇v),(x,t)∈Ω×(0,T),vt=Δv−v+u,(x,t)∈Ω×(0,T),under homogeneous Neumann...We deal with the boundedness of solutions to a class of fully parabolic quasilinear repulsion chemotaxis systems{ut=∇・(ϕ(u)∇u)+∇・(ψ(u)∇v),(x,t)∈Ω×(0,T),vt=Δv−v+u,(x,t)∈Ω×(0,T),under homogeneous Neumann boundary conditions in a smooth bounded domainΩ⊂R^N(N≥3),where 0<ψ(u)≤K(u+1)^a,K1(s+1)^m≤ϕ(s)≤K2(s+1)^m withα,K,K1,K2>0 and m∈R.It is shown that ifα−m<4/N+2,then for any sufficiently smooth initial data,the classical solutions to the system are uniformly-in-time bounded.This extends the known result for the corresponding model with linear diffusion.展开更多
In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. B...In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.展开更多
Nonconvex penalties including the smoothly clipped absolute deviation penalty and the minimax concave penalty enjoy the properties of unbiasedness, continuity and sparsity,and the ridge regression can deal with the co...Nonconvex penalties including the smoothly clipped absolute deviation penalty and the minimax concave penalty enjoy the properties of unbiasedness, continuity and sparsity,and the ridge regression can deal with the collinearity problem. Combining the strengths of nonconvex penalties and ridge regression（abbreviated as NPR）, we study the oracle property of the NPR estimator in high dimensional settings with highly correlated predictors, where the dimensionality of covariates pn is allowed to increase exponentially with the sample size n. Simulation studies and a real data example are presented to verify the performance of the NPR method.展开更多
Machine learning-assisted prediction of polymer properties prior to synthesis has the potential to significantly accelerate the discovery and development of new polymer materials.To date,several approaches have been i...Machine learning-assisted prediction of polymer properties prior to synthesis has the potential to significantly accelerate the discovery and development of new polymer materials.To date,several approaches have been implemented to represent the chemical structure in machine learning models,among which Mol2Vec embeddings have attracted considerable attention in the cheminformatics community since their introduction in 2018.However,for small datasets,the use of chemical structure representations typically increases the dimensionality of the input dataset,resulting in a decrease in model performance.Furthermore,the limited diversity of polymer chemical structures hinders the training of reliable embeddings,necessitating complex task-specific architecture implementations.To address these challenges,we examined the efficacy of Mol2Vec pre-trained embeddings in deriving vectorized representations of polymers.This study assesses the impact of incorporating Mol2Vec compound vectors into the input features on the efficacy of a model reliant on the physical properties of 214 polymers.The results will hopefully highlight the potential for improving prediction accuracy in polymer studies by incorporating pre-trained embeddings or promote their utilization when dealing with modestly sized polymer databases.展开更多
This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software implementation.The C++software package called AdaM-D...This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software implementation.The C++software package called AdaM-DG,implementing the aSG-DG method,is available on GitHub at https://github.com/JuntaoHuang/adaptive-multiresolution-DG.The package is capable of treating a large class of high dimensional linear and nonlinear PDEs.We review the essential components of the algorithm and the functionality of the software,including the multiwavelets used,assembling of bilinear operators,fast matrix-vector product for data with hierarchical structures.We further demonstrate the performance of the package by reporting the numerical error and the CPU cost for several benchmark tests,including linear transport equations,wave equations,and Hamilton-Jacobi(HJ)equations.展开更多
Super-resolution(SR)imaging has been widely used in several fields like remote sensing and microscopy.However,it is challenging for existing SR approaches to capture SR images in a single shot,especially in dynamic im...Super-resolution(SR)imaging has been widely used in several fields like remote sensing and microscopy.However,it is challenging for existing SR approaches to capture SR images in a single shot,especially in dynamic imaging scenarios.展开更多
Tailoring multiple degrees-of-freedom(DoFs)to achieve high-dimensional laser field is crucial for advancing optical technologies.While recent advancements have demonstrated the ability to manipulate a limited number o...Tailoring multiple degrees-of-freedom(DoFs)to achieve high-dimensional laser field is crucial for advancing optical technologies.While recent advancements have demonstrated the ability to manipulate a limited number of DoFs,most existing methods rely on bulky optical components or intricate systems that employ time-consuming iterative methods and,most critically,the on-demand tailoring of multiple DoFs simultaneously through a compact,single element—remains underexplored.In this study,we propose an intelligent hybrid strategy that enables the simultaneous and customizable manipulation of six DoFs:wave vector,initial phase,spatial mode,amplitude,orbital angular momentum(OAM)and spin angular momentum(SAM).Our approach advances in phase-only property,which facilitates tailoring strategy experimentally demonstrated on a compact metasurface.A fabricated sample is tailored to realize arbitrary manipulation across six DoFs,constructing a 288-dimensional space.Notably,since the OAM eigenstates constitute an infinite dimensional Hilbert space,this proposal can be further extended to even higher dimensions.Proof-of-principle experiments confirm the effectiveness in manipulation capability and dimensionality.We envision that this powerful tailoring ability offers immense potential for multifunctional photonic devices across both classical and quantum scenarios and such compactness extending the dimensional capabilities for integration on-chip requirements.展开更多
Two-dimensional(2D)nanomaterials,including graphene,titanium carbide(MXenes),montmorillonite,and boron nitride,etc.,have excellent mechanical,electrical,and thermal properties and good biocompatibility,which show prom...Two-dimensional(2D)nanomaterials,including graphene,titanium carbide(MXenes),montmorillonite,and boron nitride,etc.,have excellent mechanical,electrical,and thermal properties and good biocompatibility,which show promising applications in aerospace,flexible electronics,and biomedicine[1,2].It remains a great challenge to scalable assemble the 2D nanomaterials into highperformance macroforms for realizing these commercial applications.Natural nacre is a typical 2D nanocomposite composed of 95 vol%aragonite flakes and 5 vol%biopolymer and possesses unique mechanical properties owing to its ordered layered structure and sophisticated interface interactions[3].Inspired by the relationship between microstructure and macro-property of nacre,various assembly strategies have been developed to fabricate high-performance 2D nanocomposites by improving interlayer connectivity,alignment。展开更多
Testing the association of two high-dimensional random vectors is of fundamental importance in the statistical theory and applications.In this paper,we propose a new test statistic based on the Frobenius norm and subt...Testing the association of two high-dimensional random vectors is of fundamental importance in the statistical theory and applications.In this paper,we propose a new test statistic based on the Frobenius norm and subtracting bias technique,which is generally applicable to high-dimensional data without restricting the distributional Assumptions.The limiting null distribution of the proposed test is shown to be a random variable combining a finite chi-squared-type mixture with a normal approximation.Our proposed test method can also be a normal approximation or a finite chi-squared-type mixtures under additional regularity conditions.To make the test statistic applicable,we introduce a wild bootstrap method and demonstrate its validity.The finite-sample performance of the proposed test via Monte Carlo simulations reveals that it performs better at controlling the empirical size than some existing tests,even when the normal approximation is invalid.Real data analysis is devoted to illustrating the proposed test.展开更多
This paper investigates the moment selection and parameter estimation problem of highdimensional unconditional moment conditions. First, the authors propose a Fantope projection and selection(FPS) approach to distingu...This paper investigates the moment selection and parameter estimation problem of highdimensional unconditional moment conditions. First, the authors propose a Fantope projection and selection(FPS) approach to distinguish the informative and uninformative moments in high-dimensional unconditional moment conditions. Second, for the selected unconditional moment conditions, the authors present a generalized empirical likelihood(GEL) approach to estimate unknown parameters. The proposed method is computationally feasible, and can efficiently avoid the well-known ill-posed problem of GEL approach in the analysis of high-dimensional unconditional moment conditions. Under some regularity conditions, the authors show the consistency of the selected moment conditions, the consistency and asymptotic normality of the proposed GEL estimator. Two simulation studies are conducted to investigate the finite sample performance of the proposed methodologies. The proposed method is illustrated by a real example.展开更多
A large-scale dynamically weighted directed network(DWDN)involving numerous entities and massive dynamic interaction is an essential data source in many big-data-related applications,like in a terminal interaction pat...A large-scale dynamically weighted directed network(DWDN)involving numerous entities and massive dynamic interaction is an essential data source in many big-data-related applications,like in a terminal interaction pattern analysis system(TIPAS).It can be represented by a high-dimensional and incomplete(HDI)tensor whose entries are mostly unknown.Yet such an HDI tensor contains a wealth knowledge regarding various desired patterns like potential links in a DWDN.A latent factorization-of-tensors(LFT)model proves to be highly efficient in extracting such knowledge from an HDI tensor,which is commonly achieved via a stochastic gradient descent(SGD)solver.However,an SGD-based LFT model suffers from slow convergence that impairs its efficiency on large-scale DWDNs.To address this issue,this work proposes a proportional-integralderivative(PID)-incorporated LFT model.It constructs an adjusted instance error based on the PID control principle,and then substitutes it into an SGD solver to improve the convergence rate.Empirical studies on two DWDNs generated by a real TIPAS show that compared with state-of-the-art models,the proposed model achieves significant efficiency gain as well as highly competitive prediction accuracy when handling the task of missing link prediction for a given DWDN.展开更多
文摘Markowitz Portfolio theory under-estimates the risk associated with the return of a portfolio in case of high dimensional data. El Karoui mathematically proved this in [1] and suggested improved estimators for unbiased estimation of this risk under specific model assumptions. Norm constrained portfolios have recently been studied to keep the effective dimension low. In this paper we consider three sets of high dimensional data, the stock market prices for three countries, namely US, UK and India. We compare the Markowitz efficient frontier to those obtained by unbiasedness corrections and imposing norm-constraints in these real data scenarios. We also study the out-of-sample performance of the different procedures. We find that the 2-norm constrained portfolio has best overall performance.
基金supported by the Key Program of the National Natural Science Foundation of China(Grant No.62031013)Guangdong Province Key Construction Discipline Scientific Research Capacity Improvement Project(Grant No.2022ZDJS117).
文摘Nonlinear transforms have significantly advanced learned image compression(LIC),particularly using residual blocks.This transform enhances the nonlinear expression ability and obtain compact feature representation by enlarging the receptive field,which indicates how the convolution process extracts features in a high dimensional feature space.However,its functionality is restricted to the spatial dimension and network depth,limiting further improvements in network performance due to insufficient information interaction and representation.Crucially,the potential of high dimensional feature space in the channel dimension and the exploration of network width/resolution remain largely untapped.In this paper,we consider nonlinear transforms from the perspective of feature space,defining high-dimensional feature spaces in different dimensions and investigating the specific effects.Firstly,we introduce the dimension increasing and decreasing transforms in both channel and spatial dimensions to obtain high dimensional feature space and achieve better feature extraction.Secondly,we design a channel-spatial fusion residual transform(CSR),which incorporates multi-dimensional transforms for a more effective representation.Furthermore,we simplify the proposed fusion transform to obtain a slim architecture(CSR-sm),balancing network complexity and compression performance.Finally,we build the overall network with stacked CSR transforms to achieve better compression and reconstruction.Experimental results demonstrate that the proposed method can achieve superior ratedistortion performance compared to the existing LIC methods and traditional codecs.Specifically,our proposed method achieves 9.38%BD-rate reduction over VVC on Kodak dataset.
基金This work is partially supported by grants from the Key Program of National Natural Science Foundation of China(NSFC Nos.71631005 and 71731009)the Major Program of the National Social Science Foundation of China(No.19ZDA103).
文摘To solve the high-dimensionality issue and improve its accuracy in credit risk assessment,a high-dimensionality-trait-driven learning paradigm is proposed for feature extraction and classifier selection.The proposed paradigm consists of three main stages:categorization of high dimensional data,high-dimensionality-trait-driven feature extraction,and high-dimensionality-trait-driven classifier selection.In the first stage,according to the definition of high-dimensionality and the relationship between sample size and feature dimensions,the high-dimensionality traits of credit dataset are further categorized into two types:100<feature dimensions<sample size,and feature dimensions≥sample size.In the second stage,some typical feature extraction methods are tested regarding the two categories of high dimensionality.In the final stage,four types of classifiers are performed to evaluate credit risk considering different high-dimensionality traits.For the purpose of illustration and verification,credit classification experiments are performed on two publicly available credit risk datasets,and the results show that the proposed high-dimensionality-trait-driven learning paradigm for feature extraction and classifier selection is effective in handling high-dimensional credit classification issues and improving credit classification accuracy relative to the benchmark models listed in this study.
文摘An algorithm, Clustering Algorithm Based On Sparse Feature Vector (CABOSFV),was proposed for the high dimensional clustering of binary sparse data. This algorithm compressesthe data effectively by using a tool 'Sparse Feature Vector', thus reduces the data scaleenormously, and can get the clustering result with only one data scan. Both theoretical analysis andempirical tests showed that CABOSFV is of low computational complexity. The algorithm findsclusters in high dimensional large datasets efficiently and handles noise effectively.
文摘Clustering high dimensional data is challenging as data dimensionality increases the distance between data points,resulting in sparse regions that degrade clustering performance.Subspace clustering is a common approach for processing high-dimensional data by finding relevant features for each cluster in the data space.Subspace clustering methods extend traditional clustering to account for the constraints imposed by data streams.Data streams are not only high-dimensional,but also unbounded and evolving.This necessitates the development of subspace clustering algorithms that can handle high dimensionality and adapt to the unique characteristics of data streams.Although many articles have contributed to the literature review on data stream clustering,there is currently no specific review on subspace clustering algorithms in high-dimensional data streams.Therefore,this article aims to systematically review the existing literature on subspace clustering of data streams in high-dimensional streaming environments.The review follows a systematic methodological approach and includes 18 articles for the final analysis.The analysis focused on two research questions related to the general clustering process and dealing with the unbounded and evolving characteristics of data streams.The main findings relate to six elements:clustering process,cluster search,subspace search,synopsis structure,cluster maintenance,and evaluation measures.Most algorithms use a two-phase clustering approach consisting of an initialization stage,a refinement stage,a cluster maintenance stage,and a final clustering stage.The density-based top-down subspace clustering approach is more widely used than the others because it is able to distinguish true clusters and outliers using projected microclusters.Most algorithms implicitly adapt to the evolving nature of the data stream by using a time fading function that is sensitive to outliers.Future work can focus on the clustering framework,parameter optimization,subspace search techniques,memory-efficient synopsis structures,explicit cluster change detection,and intrinsic performance metrics.This article can serve as a guide for researchers interested in high-dimensional subspace clustering methods for data streams.
基金supported by the National Natural Science Foundation of China(62272078)Chongqing Natural Science Foundation(CSTB2023NSCQ-LZX0069)the Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN202300210)
文摘Dear Editor,This letter presents a novel latent factorization model for high dimensional and incomplete (HDI) tensor, namely the neural Tucker factorization (Neu Tuc F), which is a generic neural network-based latent-factorization-of-tensors model under the Tucker decomposition framework.
基金Project supported by the National Fundamental Research Program （Grant No 001CB309308）, China National Natural Science Foundation （Grant Nos 60433050, 10325521, 10447106）, the Hang-Tian Science Fund, the SRFDP program of Education Ministry of China and Beijing Education Committee （Grant No XK100270454）.
文摘In this paper a high-dimension multiparty quantum secret sharing scheme is proposed by using Einstein-Podolsky-Rosen pairs and local unitary operators. This scheme has the advantage of not only having higher capacity, but also saving storage space. The security analysis is also given.
基金Project(RDF 11-02-03)supported by the Research Development Fund of XJTLU,China
文摘Information analysis of high dimensional data was carried out through similarity measure application. High dimensional data were considered as the a typical structure. Additionally, overlapped and non-overlapped data were introduced, and similarity measure analysis was also illustrated and compared with conventional similarity measure. As a result, overlapped data comparison was possible to present similarity with conventional similarity measure. Non-overlapped data similarity analysis provided the clue to solve the similarity of high dimensional data. Considering high dimensional data analysis was designed with consideration of neighborhoods information. Conservative and strict solutions were proposed. Proposed similarity measure was applied to express financial fraud among multi dimensional datasets. In illustrative example, financial fraud similarity with respect to age, gender, qualification and job was presented. And with the proposed similarity measure, high dimensional personal data were calculated to evaluate how similar to the financial fraud. Calculation results show that the actual fraud has rather high similarity measure compared to the average, from minimal 0.0609 to maximal 0.1667.
基金Supported by the National Key Research and Development Program of China(2016YFC0100300)the National Natural Science Foundation of China(61402371,61771369)+1 种基金the Natural Science Basic Research Plan in Shaanxi Province of China(2017JM6008)the Fundamental Research Funds for the Central Universities of China(3102017zy032,3102018zy020)
文摘Three high dimensional spatial standardization algorithms are used for diffusion tensor image(DTI)registration,and seven kinds of methods are used to evaluate their performances.Firstly,the template used in this paper was obtained by spatial transformation of 16 subjects by means of tensor-based standardization.Then,high dimensional standardization algorithms for diffusion tensor images,including fractional anisotropy(FA)based diffeomorphic registration algorithm,FA based elastic registration algorithm and tensor-based registration algorithm,were performed.Finally,7 kinds of evaluation methods,including normalized standard deviation,dyadic coherence,diffusion cross-correlation,overlap of eigenvalue-eigenvector pairs,Euclidean distance of diffusion tensor,and Euclidean distance of the deviatoric tensor and deviatoric of tensors,were used to qualitatively compare and summarize the above standardization algorithms.Experimental results revealed that the high-dimensional tensor-based standardization algorithms perform well and can maintain the consistency of anatomical structures.
基金Supported by the National Natural Science Foundation of China(Grant No.11601140,11401082,11701260)Program funded by Education Department of Liaoning Province(Grant No.LN2019Q15).
文摘We deal with the boundedness of solutions to a class of fully parabolic quasilinear repulsion chemotaxis systems{ut=∇・(ϕ(u)∇u)+∇・(ψ(u)∇v),(x,t)∈Ω×(0,T),vt=Δv−v+u,(x,t)∈Ω×(0,T),under homogeneous Neumann boundary conditions in a smooth bounded domainΩ⊂R^N(N≥3),where 0<ψ(u)≤K(u+1)^a,K1(s+1)^m≤ϕ(s)≤K2(s+1)^m withα,K,K1,K2>0 and m∈R.It is shown that ifα−m<4/N+2,then for any sufficiently smooth initial data,the classical solutions to the system are uniformly-in-time bounded.This extends the known result for the corresponding model with linear diffusion.
基金supported by the Natural Science Foundation of China under Grant Nos.60804008,61174048and 11071263the Fundamental Research Funds for the Central Universities and Guangdong Province Key Laboratory of Computational Science at Sun Yat-Sen University
文摘In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.
基金Supported by the National Natural Science Foundation of China(Grant No.11401340)China Postdoctoral Science Foundation(Grant No.2014M561892)+1 种基金the Foundation of Qufu Normal University(Grant Nos.bsqd2012041xkj201304)
文摘Nonconvex penalties including the smoothly clipped absolute deviation penalty and the minimax concave penalty enjoy the properties of unbiasedness, continuity and sparsity,and the ridge regression can deal with the collinearity problem. Combining the strengths of nonconvex penalties and ridge regression（abbreviated as NPR）, we study the oracle property of the NPR estimator in high dimensional settings with highly correlated predictors, where the dimensionality of covariates pn is allowed to increase exponentially with the sample size n. Simulation studies and a real data example are presented to verify the performance of the NPR method.
基金the framework of the program of state support for the centers of the National Technology Initiative(NTI)on the basis of educational institutions of higher education and scientific organizations(Center NTI"Digital Materials Science:New Materials and Substances"on the basis of the Bauman Moscow State Technical University).
文摘Machine learning-assisted prediction of polymer properties prior to synthesis has the potential to significantly accelerate the discovery and development of new polymer materials.To date,several approaches have been implemented to represent the chemical structure in machine learning models,among which Mol2Vec embeddings have attracted considerable attention in the cheminformatics community since their introduction in 2018.However,for small datasets,the use of chemical structure representations typically increases the dimensionality of the input dataset,resulting in a decrease in model performance.Furthermore,the limited diversity of polymer chemical structures hinders the training of reliable embeddings,necessitating complex task-specific architecture implementations.To address these challenges,we examined the efficacy of Mol2Vec pre-trained embeddings in deriving vectorized representations of polymers.This study assesses the impact of incorporating Mol2Vec compound vectors into the input features on the efficacy of a model reliant on the physical properties of 214 polymers.The results will hopefully highlight the potential for improving prediction accuracy in polymer studies by incorporating pre-trained embeddings or promote their utilization when dealing with modestly sized polymer databases.
基金supported by the NSF grant DMS-2111383Air Force Office of Scientific Research FA9550-18-1-0257the NSF grant DMS-2011838.
文摘This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software implementation.The C++software package called AdaM-DG,implementing the aSG-DG method,is available on GitHub at https://github.com/JuntaoHuang/adaptive-multiresolution-DG.The package is capable of treating a large class of high dimensional linear and nonlinear PDEs.We review the essential components of the algorithm and the functionality of the software,including the multiwavelets used,assembling of bilinear operators,fast matrix-vector product for data with hierarchical structures.We further demonstrate the performance of the package by reporting the numerical error and the CPU cost for several benchmark tests,including linear transport equations,wave equations,and Hamilton-Jacobi(HJ)equations.
基金National Natural Science Foundation of China(62201165,62475270,62471147)National Key Research and Development Program of China(2024YFF0505601,2024YFF0505602,2024YFF0505600).
文摘Super-resolution(SR)imaging has been widely used in several fields like remote sensing and microscopy.However,it is challenging for existing SR approaches to capture SR images in a single shot,especially in dynamic imaging scenarios.
基金supported by the National Key Research and Development Program of China(2022YFB3607700)National Natural Science Foundation of China(62350011,62375014)+1 种基金Beijing Natural Science Foundation(1232031)Special Fund for Basic Scientific Research of Central Universities of China(2024CX11002).
文摘Tailoring multiple degrees-of-freedom(DoFs)to achieve high-dimensional laser field is crucial for advancing optical technologies.While recent advancements have demonstrated the ability to manipulate a limited number of DoFs,most existing methods rely on bulky optical components or intricate systems that employ time-consuming iterative methods and,most critically,the on-demand tailoring of multiple DoFs simultaneously through a compact,single element—remains underexplored.In this study,we propose an intelligent hybrid strategy that enables the simultaneous and customizable manipulation of six DoFs:wave vector,initial phase,spatial mode,amplitude,orbital angular momentum(OAM)and spin angular momentum(SAM).Our approach advances in phase-only property,which facilitates tailoring strategy experimentally demonstrated on a compact metasurface.A fabricated sample is tailored to realize arbitrary manipulation across six DoFs,constructing a 288-dimensional space.Notably,since the OAM eigenstates constitute an infinite dimensional Hilbert space,this proposal can be further extended to even higher dimensions.Proof-of-principle experiments confirm the effectiveness in manipulation capability and dimensionality.We envision that this powerful tailoring ability offers immense potential for multifunctional photonic devices across both classical and quantum scenarios and such compactness extending the dimensional capabilities for integration on-chip requirements.
文摘Two-dimensional(2D)nanomaterials,including graphene,titanium carbide(MXenes),montmorillonite,and boron nitride,etc.,have excellent mechanical,electrical,and thermal properties and good biocompatibility,which show promising applications in aerospace,flexible electronics,and biomedicine[1,2].It remains a great challenge to scalable assemble the 2D nanomaterials into highperformance macroforms for realizing these commercial applications.Natural nacre is a typical 2D nanocomposite composed of 95 vol%aragonite flakes and 5 vol%biopolymer and possesses unique mechanical properties owing to its ordered layered structure and sophisticated interface interactions[3].Inspired by the relationship between microstructure and macro-property of nacre,various assembly strategies have been developed to fabricate high-performance 2D nanocomposites by improving interlayer connectivity,alignment。
基金Supported by National Natural Science Foundation of China(Grant Nos.12271370 and 12371294)the Youth Academic Innovation Team Construction project of the Capital University of Economics and Business(Grant No.QNTD202303)New Young Teachers’Research Initiation Fund Project,Capital University of Economics and Business(Grant No.XRZ2021046)。
文摘Testing the association of two high-dimensional random vectors is of fundamental importance in the statistical theory and applications.In this paper,we propose a new test statistic based on the Frobenius norm and subtracting bias technique,which is generally applicable to high-dimensional data without restricting the distributional Assumptions.The limiting null distribution of the proposed test is shown to be a random variable combining a finite chi-squared-type mixture with a normal approximation.Our proposed test method can also be a normal approximation or a finite chi-squared-type mixtures under additional regularity conditions.To make the test statistic applicable,we introduce a wild bootstrap method and demonstrate its validity.The finite-sample performance of the proposed test via Monte Carlo simulations reveals that it performs better at controlling the empirical size than some existing tests,even when the normal approximation is invalid.Real data analysis is devoted to illustrating the proposed test.
基金supported by the Postdoctoral Oriented Fund of Yunnan Province under Grant No.W8163007the National Natural Science Foundation of China under Grant No. 11961079。
文摘This paper investigates the moment selection and parameter estimation problem of highdimensional unconditional moment conditions. First, the authors propose a Fantope projection and selection(FPS) approach to distinguish the informative and uninformative moments in high-dimensional unconditional moment conditions. Second, for the selected unconditional moment conditions, the authors present a generalized empirical likelihood(GEL) approach to estimate unknown parameters. The proposed method is computationally feasible, and can efficiently avoid the well-known ill-posed problem of GEL approach in the analysis of high-dimensional unconditional moment conditions. Under some regularity conditions, the authors show the consistency of the selected moment conditions, the consistency and asymptotic normality of the proposed GEL estimator. Two simulation studies are conducted to investigate the finite sample performance of the proposed methodologies. The proposed method is illustrated by a real example.
基金supported in part by the National Natural Science Foundation of China(61772493)the CAAI-Huawei MindSpore Open Fund(CAAIXSJLJJ-2020-004B)+4 种基金in part by the Natural Science Foundation of Chongqing of China(cstc2019jcyjjq X0013)in part by the Pioneer Hundred Talents Program of Chinese Academy of Sciencesin part by the Deanship of Scientific Research(DSR)at King Abdulaziz UniversityJeddahSaudi Arabia(FP-165-43)。
文摘A large-scale dynamically weighted directed network(DWDN)involving numerous entities and massive dynamic interaction is an essential data source in many big-data-related applications,like in a terminal interaction pattern analysis system(TIPAS).It can be represented by a high-dimensional and incomplete(HDI)tensor whose entries are mostly unknown.Yet such an HDI tensor contains a wealth knowledge regarding various desired patterns like potential links in a DWDN.A latent factorization-of-tensors(LFT)model proves to be highly efficient in extracting such knowledge from an HDI tensor,which is commonly achieved via a stochastic gradient descent(SGD)solver.However,an SGD-based LFT model suffers from slow convergence that impairs its efficiency on large-scale DWDNs.To address this issue,this work proposes a proportional-integralderivative(PID)-incorporated LFT model.It constructs an adjusted instance error based on the PID control principle,and then substitutes it into an SGD solver to improve the convergence rate.Empirical studies on two DWDNs generated by a real TIPAS show that compared with state-of-the-art models,the proposed model achieves significant efficiency gain as well as highly competitive prediction accuracy when handling the task of missing link prediction for a given DWDN.
