Five-valued Boolean functions play an important role in the design of symmetric cryptography.While the design and properties of single-output almost optimal five-valued spectra Boolean functions have been extensively ...Five-valued Boolean functions play an important role in the design of symmetric cryptography.While the design and properties of single-output almost optimal five-valued spectra Boolean functions have been extensively studied over the past few decades,there has been limited research on the construction of almost optimal five-valued spectra vectorial Boolean functions.In this paper,we present a construction method for even-variable 2-output almost optimal five-valued spectra balanced Boolean functions,whose Walsh spectra values belong to the set{0,±2^(n/2),±2^(n/2+1)},at the same time,we discuss the existence of sufficient conditions in the construction.Additionally,this paper presents a novel construction method for balanced single-output Boolean functions with even variables featuring a special five-valued spectral structure,whose Walsh spectra values are constrained to the set{0,±2^(n/2),±3·2^(n/2)}.These functions provide new canonical examples for the study of Boolean function spectral theory.展开更多
We prove the M?bius disjointness conjecture in short intervals for a class of skew products on the 2-torus,which includes Furstenberg’s example of irregular flows.
Disjoint sampling is critical for rigorous and unbiased evaluation of state-of-the-art(SOTA)models e.g.,Attention Graph and Vision Transformer.When training,validation,and test sets overlap or share data,it introduces...Disjoint sampling is critical for rigorous and unbiased evaluation of state-of-the-art(SOTA)models e.g.,Attention Graph and Vision Transformer.When training,validation,and test sets overlap or share data,it introduces a bias that inflates performance metrics and prevents accurate assessment of a model’s true ability to generalize to new examples.This paper presents an innovative disjoint sampling approach for training SOTA models for the Hyperspectral Image Classification(HSIC).By separating training,validation,and test data without overlap,the proposed method facilitates a fairer evaluation of how well a model can classify pixels it was not exposed to during training or validation.Experiments demonstrate the approach significantly improves a model’s generalization compared to alternatives that include training and validation data in test data(A trivial approach involves testing the model on the entire Hyperspectral dataset to generate the ground truth maps.This approach produces higher accuracy but ultimately results in low generalization performance).Disjoint sampling eliminates data leakage between sets and provides reliable metrics for benchmarking progress in HSIC.Disjoint sampling is critical for advancing SOTA models and their real-world application to large-scale land mapping with Hyperspectral sensors.Overall,with the disjoint test set,the performance of the deep models achieves 96.36%accuracy on Indian Pines data,99.73%on Pavia University data,98.29%on University of Houston data,99.43%on Botswana data,and 99.88%on Salinas data.展开更多
The integration of the Lab model with the extended histogram of oriented gradients （EHOG） is proposed to improve the accuracy of human appearance matching across disjoint camera views under perturbations such as ill...The integration of the Lab model with the extended histogram of oriented gradients （EHOG） is proposed to improve the accuracy of human appearance matching across disjoint camera views under perturbations such as illumination changes and different viewing angles. For the Lab model that describes the global information of observations, a sorted nearest neighbor clustering method is proposed for color clustering and then a partitioned color matching method is used to calculate the color similarity between observations. The Bhattacharya distance is employed for the textural similarity calculation of the EHOG which describes the local information. The global information, which is robust to different viewing angles and scale changes, describes the observations well. Meanwhile, the use of local information, which is robust to illumination changes, can strengthen the discriminative ability of the method. The integration of global and local information improves the accuracy and robustness of the proposed matching approach. Experiments are carried out indoors, and the results show a high matching accuracy of the proposed method.展开更多
In order to decrease the calculation complexity of connectivity reliability of road networks, an improved recursive decomposition arithmetic is proposed. First, the basic theory of recursive decomposition arithmetic i...In order to decrease the calculation complexity of connectivity reliability of road networks, an improved recursive decomposition arithmetic is proposed. First, the basic theory of recursive decomposition arithmetic is reviewed. Then the characteristics of road networks, which are different from general networks, are analyzed. Under this condition, an improved recursive decomposition arithmetic is put forward which fits road networks better. Furthermore, detailed calculation steps are presented which are convenient for the computer, and the advantage of the approximate arithmetic is analyzed based on this improved arithmetic. This improved recursive decomposition arithmetic directly produces disjoint minipaths and avoids the non-polynomial increasing problems. And because the characteristics of road networks are considered, this arithmetic is greatly simplified. Finally, an example is given to prove its validity.展开更多
In this paper, extracting parallelizatio n from the sum of disjoint products approach is discussed. A general framework of parallelizing disjoint products approach is presented. And a parallel version of the newest...In this paper, extracting parallelizatio n from the sum of disjoint products approach is discussed. A general framework of parallelizing disjoint products approach is presented. And a parallel version of the newest disjoint products algorithm is implemented. The results of testing s how the effect is so good to get linear speedups.展开更多
It is well known that the Two-step Weighted Least-Squares(TWLS) is a widely used method for source localization and sensor position refinement. For this reason, we propose a unified framework of the TWLS method for jo...It is well known that the Two-step Weighted Least-Squares(TWLS) is a widely used method for source localization and sensor position refinement. For this reason, we propose a unified framework of the TWLS method for joint estimation of multiple disjoint sources and sensor locations in this paper. Unlike some existing works, the presented method is based on more general measurement model, and therefore it can be applied to many different localization scenarios.Besides, it does not have the initialization and local convergence problem. The closed-form expression for the covariance matrix of the proposed TWLS estimator is also derived by exploiting the first-order perturbation analysis. Moreover, the estimation accuracy of the TWLS method is shown analytically to achieve the Cramér-Rao Bound(CRB) before the threshold effect takes place. The theoretical analysis is also performed in a common mathematical framework, rather than aiming at some specific signal metrics. Finally, two numerical experiments are performed to support the theoretical development in this paper.展开更多
Let E be an Archimedean Riesz algebra possessing a weak unit element e and a maximal disjoint system {e,: i∈I} in which e, is a projection element for each i. The principal band generated by eiis denoted by B(ei). T...Let E be an Archimedean Riesz algebra possessing a weak unit element e and a maximal disjoint system {e,: i∈I} in which e, is a projection element for each i. The principal band generated by eiis denoted by B(ei). The main result in this paper says that if there exists a completely regular Hausdorff space X such that E is Riesz algebra isomorphic to C(X) then for every i ∈ I there exists a completely regular Hausdorff space X, such that B(ei) is Riesz algebra isomorphic to C(Xi). Under an additional condition the inverse holds.展开更多
This research developed a hybrid position-channel network (named PCNet) through incorporating newly designed channel and position attention modules into U-Net to alleviate the crack discontinuity problem in channel an...This research developed a hybrid position-channel network (named PCNet) through incorporating newly designed channel and position attention modules into U-Net to alleviate the crack discontinuity problem in channel and spatial dimensions. In PCNet, the U-Net is used as a baseline to extract informative spatial and channel-wise features from shield tunnel lining crack images. A channel and a position attention module are designed and embedded after each convolution layer of U-Net to model the feature interdependencies in channel and spatial dimensions. These attention modules can make the U-Net adaptively integrate local crack features with their global dependencies. Experiments were conducted utilizing the dataset based on the images from Shanghai metro shield tunnels. The results validate the effectiveness of the designed channel and position attention modules, since they can individually increase balanced accuracy (BA) by 11.25% and 12.95%, intersection over union (IoU) by 10.79% and 11.83%, and F1 score by 9.96% and 10.63%, respectively. In comparison with the state-of-the-art models (i.e. LinkNet, PSPNet, U-Net, PANet, and Mask R–CNN) on the testing dataset, the proposed PCNet outperforms others with an improvement of BA, IoU, and F1 score owing to the implementation of the channel and position attention modules. These evaluation metrics indicate that the proposed PCNet presents refined crack segmentation with improved performance and is a practicable approach to segment shield tunnel lining cracks in field practice.展开更多
The algorithm is based on constructing a disjoin kg t set of the minimal paths in a network system.In this paper, cubic notation was used to describe the logic function of a network in a well-balanced state,and then t...The algorithm is based on constructing a disjoin kg t set of the minimal paths in a network system.In this paper, cubic notation was used to describe the logic function of a network in a well-balanced state,and then the sharp-product operation was used to construct the disjoint minimal path set of the network.A computer program has been developed,and when combined with decomposition technology,the reliability of a general lifeline network can be effectively and automatically calculated.展开更多
Direct soil temperature(ST)measurement is time-consuming and costly;thus,the use of simple and cost-effective machine learning(ML)tools is helpful.In this study,ML approaches,including KStar,instance-based K-nearest l...Direct soil temperature(ST)measurement is time-consuming and costly;thus,the use of simple and cost-effective machine learning(ML)tools is helpful.In this study,ML approaches,including KStar,instance-based K-nearest learning(IBK),and locally weighted learning(LWL),coupled with resampling algorithms of bagging(BA)and dagging(DA)(BA-IBK,BA-KStar,BA-LWL,DA-IBK,DA-KStar,and DA-LWL)were developed and tested for multi-step ahead(3,6,and 9 d ahead)ST forecasting.In addition,a linear regression(LR)model was used as a benchmark to evaluate the results.A dataset was established,with daily ST time-series at 5 and 50 cm soil depths in a farmland as models’output and meteorological data as models’input,including mean(T_(mean)),minimum(Tmin),and maximum(T_(max))air temperatures,evaporation(Eva),sunshine hours(SSH),and solar radiation(SR),which were collected at Isfahan Synoptic Station(Iran)for 13 years(1992–2005).Six different input combination scenarios were selected based on Pearson’s correlation coefficients between inputs and outputs and fed into the models.We used 70%of the data to train the models,with the remaining 30%used for model evaluation via multiple visual and quantitative metrics.Our?ndings showed that T_(mean)was the most effective input variable for ST forecasting in most of the developed models,while in some cases the combinations of variables,including T_(mean)and T_(max)and T_(mean),T_(max),Tmin,Eva,and SSH proved to be the best input combinations.Among the evaluated models,BA-KStar showed greater compatibility,while in most cases,BA-IBK and-LWL provided more accurate results,depending on soil depth.For the 5 cm soil depth,BA-KStar had superior performance(i.e.,Nash-Sutcliffe efficiency(NSE)=0.90,0.87,and 0.85 for 3,6,and 9 d ahead forecasting,respectively);for the 50 cm soil depth,DA-KStar outperformed the other models(i.e.,NSE=0.88,0.89,and 0.89 for 3,6,and 9 d ahead forecasting,respectively).The results con?rmed that all hybrid models had higher prediction capabilities than the LR model.展开更多
The present paper deals with the gracefulness of unconnected graph （jC_（4n））∪P_m,and proves the following result：for positive integers n,j and m with n≥1,j≥2,the unconnected graph（jC_（4n））∪P_m is a gracef...The present paper deals with the gracefulness of unconnected graph （jC_（4n））∪P_m,and proves the following result：for positive integers n,j and m with n≥1,j≥2,the unconnected graph（jC_（4n））∪P_m is a graceful graph for m=j-1 or m≥n＋j,where C_（4n） is a cycle with 4n vertexes,P_m is a path with m＋1 vertexes,and（jC_（4n））∪P_m denotes the disjoint union of j-C_（4n） and P_m.展开更多
In this article, we present several equivalent conditions ensuring the disjoint supercyclicity of finite weighted pseudo-shifts acting on an arbitrary Banach sequence space.The disjoint supercyclic properties of weigh...In this article, we present several equivalent conditions ensuring the disjoint supercyclicity of finite weighted pseudo-shifts acting on an arbitrary Banach sequence space.The disjoint supercyclic properties of weighted translations on locally compact discrete groups,the direct sums of finite classical weighted backward shifts, and the bilateral backward operator weighted shifts can be viewed as special cases of our main results. Furthermore, we exhibit an interesting fact that any finite bilateral weighted backward shifts on the space ?~2(Z) never satisfy the d-Supercyclicity Criterion by a simple proof.展开更多
基金National Natural Science Foundation of China(62272360)。
文摘Five-valued Boolean functions play an important role in the design of symmetric cryptography.While the design and properties of single-output almost optimal five-valued spectra Boolean functions have been extensively studied over the past few decades,there has been limited research on the construction of almost optimal five-valued spectra vectorial Boolean functions.In this paper,we present a construction method for even-variable 2-output almost optimal five-valued spectra balanced Boolean functions,whose Walsh spectra values belong to the set{0,±2^(n/2),±2^(n/2+1)},at the same time,we discuss the existence of sufficient conditions in the construction.Additionally,this paper presents a novel construction method for balanced single-output Boolean functions with even variables featuring a special five-valued spectral structure,whose Walsh spectra values are constrained to the set{0,±2^(n/2),±3·2^(n/2)}.These functions provide new canonical examples for the study of Boolean function spectral theory.
基金Supported by the National Key Reserarch and Development Program of China (Grant No.2021YFA1000700)。
文摘We prove the M?bius disjointness conjecture in short intervals for a class of skew products on the 2-torus,which includes Furstenberg’s example of irregular flows.
基金the Researchers Supporting Project number(RSPD2024R848),King Saud University,Riyadh,Saudi Arabia.
文摘Disjoint sampling is critical for rigorous and unbiased evaluation of state-of-the-art(SOTA)models e.g.,Attention Graph and Vision Transformer.When training,validation,and test sets overlap or share data,it introduces a bias that inflates performance metrics and prevents accurate assessment of a model’s true ability to generalize to new examples.This paper presents an innovative disjoint sampling approach for training SOTA models for the Hyperspectral Image Classification(HSIC).By separating training,validation,and test data without overlap,the proposed method facilitates a fairer evaluation of how well a model can classify pixels it was not exposed to during training or validation.Experiments demonstrate the approach significantly improves a model’s generalization compared to alternatives that include training and validation data in test data(A trivial approach involves testing the model on the entire Hyperspectral dataset to generate the ground truth maps.This approach produces higher accuracy but ultimately results in low generalization performance).Disjoint sampling eliminates data leakage between sets and provides reliable metrics for benchmarking progress in HSIC.Disjoint sampling is critical for advancing SOTA models and their real-world application to large-scale land mapping with Hyperspectral sensors.Overall,with the disjoint test set,the performance of the deep models achieves 96.36%accuracy on Indian Pines data,99.73%on Pavia University data,98.29%on University of Houston data,99.43%on Botswana data,and 99.88%on Salinas data.
基金The National Natural Science Foundation of China(No.60972001)the Science and Technology Plan of Suzhou City(No.SG201076)
文摘The integration of the Lab model with the extended histogram of oriented gradients （EHOG） is proposed to improve the accuracy of human appearance matching across disjoint camera views under perturbations such as illumination changes and different viewing angles. For the Lab model that describes the global information of observations, a sorted nearest neighbor clustering method is proposed for color clustering and then a partitioned color matching method is used to calculate the color similarity between observations. The Bhattacharya distance is employed for the textural similarity calculation of the EHOG which describes the local information. The global information, which is robust to different viewing angles and scale changes, describes the observations well. Meanwhile, the use of local information, which is robust to illumination changes, can strengthen the discriminative ability of the method. The integration of global and local information improves the accuracy and robustness of the proposed matching approach. Experiments are carried out indoors, and the results show a high matching accuracy of the proposed method.
基金The National Key Technology R& D Program of Chinaduring the 11th Five-Year Plan Period (No.2006BAJ18B03).
文摘In order to decrease the calculation complexity of connectivity reliability of road networks, an improved recursive decomposition arithmetic is proposed. First, the basic theory of recursive decomposition arithmetic is reviewed. Then the characteristics of road networks, which are different from general networks, are analyzed. Under this condition, an improved recursive decomposition arithmetic is put forward which fits road networks better. Furthermore, detailed calculation steps are presented which are convenient for the computer, and the advantage of the approximate arithmetic is analyzed based on this improved arithmetic. This improved recursive decomposition arithmetic directly produces disjoint minipaths and avoids the non-polynomial increasing problems. And because the characteristics of road networks are considered, this arithmetic is greatly simplified. Finally, an example is given to prove its validity.
文摘In this paper, extracting parallelizatio n from the sum of disjoint products approach is discussed. A general framework of parallelizing disjoint products approach is presented. And a parallel version of the newest disjoint products algorithm is implemented. The results of testing s how the effect is so good to get linear speedups.
基金co-supported by the National Natural Science Foundation of China (Nos. 61201381, 61401513 and 61772548)the China Postdoctoral Science Foundation (No. 2016M592989)+1 种基金the Self-Topic Foundation of Information Engineering University, China (No. 2016600701)the Outstanding Youth Foundation of Information Engineering University, China (No. 2016603201)
文摘It is well known that the Two-step Weighted Least-Squares(TWLS) is a widely used method for source localization and sensor position refinement. For this reason, we propose a unified framework of the TWLS method for joint estimation of multiple disjoint sources and sensor locations in this paper. Unlike some existing works, the presented method is based on more general measurement model, and therefore it can be applied to many different localization scenarios.Besides, it does not have the initialization and local convergence problem. The closed-form expression for the covariance matrix of the proposed TWLS estimator is also derived by exploiting the first-order perturbation analysis. Moreover, the estimation accuracy of the TWLS method is shown analytically to achieve the Cramér-Rao Bound(CRB) before the threshold effect takes place. The theoretical analysis is also performed in a common mathematical framework, rather than aiming at some specific signal metrics. Finally, two numerical experiments are performed to support the theoretical development in this paper.
文摘Let E be an Archimedean Riesz algebra possessing a weak unit element e and a maximal disjoint system {e,: i∈I} in which e, is a projection element for each i. The principal band generated by eiis denoted by B(ei). The main result in this paper says that if there exists a completely regular Hausdorff space X such that E is Riesz algebra isomorphic to C(X) then for every i ∈ I there exists a completely regular Hausdorff space X, such that B(ei) is Riesz algebra isomorphic to C(Xi). Under an additional condition the inverse holds.
基金support from the Ministry of Science and Tech-nology of the:People's Republic of China(Grant No.2021 YFB2600804)the Open Research Project Programme of the State Key Labor atory of Interet of Things for Smart City(University of Macao)(Grant No.SKL-IoTSC(UM)-2021-2023/ORPF/A19/2022)the General Research Fund(GRF)project(Grant No.15214722)from Research Grants Council(RGC)of Hong Kong Special Administrative Re gion Government of China are gratefully acknowledged.
文摘This research developed a hybrid position-channel network (named PCNet) through incorporating newly designed channel and position attention modules into U-Net to alleviate the crack discontinuity problem in channel and spatial dimensions. In PCNet, the U-Net is used as a baseline to extract informative spatial and channel-wise features from shield tunnel lining crack images. A channel and a position attention module are designed and embedded after each convolution layer of U-Net to model the feature interdependencies in channel and spatial dimensions. These attention modules can make the U-Net adaptively integrate local crack features with their global dependencies. Experiments were conducted utilizing the dataset based on the images from Shanghai metro shield tunnels. The results validate the effectiveness of the designed channel and position attention modules, since they can individually increase balanced accuracy (BA) by 11.25% and 12.95%, intersection over union (IoU) by 10.79% and 11.83%, and F1 score by 9.96% and 10.63%, respectively. In comparison with the state-of-the-art models (i.e. LinkNet, PSPNet, U-Net, PANet, and Mask R–CNN) on the testing dataset, the proposed PCNet outperforms others with an improvement of BA, IoU, and F1 score owing to the implementation of the channel and position attention modules. These evaluation metrics indicate that the proposed PCNet presents refined crack segmentation with improved performance and is a practicable approach to segment shield tunnel lining cracks in field practice.
基金Key Project of Science and Technology from the State Plan Committee.No.101-9914003
文摘The algorithm is based on constructing a disjoin kg t set of the minimal paths in a network system.In this paper, cubic notation was used to describe the logic function of a network in a well-balanced state,and then the sharp-product operation was used to construct the disjoint minimal path set of the network.A computer program has been developed,and when combined with decomposition technology,the reliability of a general lifeline network can be effectively and automatically calculated.
文摘Direct soil temperature(ST)measurement is time-consuming and costly;thus,the use of simple and cost-effective machine learning(ML)tools is helpful.In this study,ML approaches,including KStar,instance-based K-nearest learning(IBK),and locally weighted learning(LWL),coupled with resampling algorithms of bagging(BA)and dagging(DA)(BA-IBK,BA-KStar,BA-LWL,DA-IBK,DA-KStar,and DA-LWL)were developed and tested for multi-step ahead(3,6,and 9 d ahead)ST forecasting.In addition,a linear regression(LR)model was used as a benchmark to evaluate the results.A dataset was established,with daily ST time-series at 5 and 50 cm soil depths in a farmland as models’output and meteorological data as models’input,including mean(T_(mean)),minimum(Tmin),and maximum(T_(max))air temperatures,evaporation(Eva),sunshine hours(SSH),and solar radiation(SR),which were collected at Isfahan Synoptic Station(Iran)for 13 years(1992–2005).Six different input combination scenarios were selected based on Pearson’s correlation coefficients between inputs and outputs and fed into the models.We used 70%of the data to train the models,with the remaining 30%used for model evaluation via multiple visual and quantitative metrics.Our?ndings showed that T_(mean)was the most effective input variable for ST forecasting in most of the developed models,while in some cases the combinations of variables,including T_(mean)and T_(max)and T_(mean),T_(max),Tmin,Eva,and SSH proved to be the best input combinations.Among the evaluated models,BA-KStar showed greater compatibility,while in most cases,BA-IBK and-LWL provided more accurate results,depending on soil depth.For the 5 cm soil depth,BA-KStar had superior performance(i.e.,Nash-Sutcliffe efficiency(NSE)=0.90,0.87,and 0.85 for 3,6,and 9 d ahead forecasting,respectively);for the 50 cm soil depth,DA-KStar outperformed the other models(i.e.,NSE=0.88,0.89,and 0.89 for 3,6,and 9 d ahead forecasting,respectively).The results con?rmed that all hybrid models had higher prediction capabilities than the LR model.
文摘The present paper deals with the gracefulness of unconnected graph （jC_（4n））∪P_m,and proves the following result：for positive integers n,j and m with n≥1,j≥2,the unconnected graph（jC_（4n））∪P_m is a graceful graph for m=j-1 or m≥n＋j,where C_（4n） is a cycle with 4n vertexes,P_m is a path with m＋1 vertexes,and（jC_（4n））∪P_m denotes the disjoint union of j-C_（4n） and P_m.
基金supported by the Research Project of Tianjin Municipal Education Commission(2017KJ124)
文摘In this article, we present several equivalent conditions ensuring the disjoint supercyclicity of finite weighted pseudo-shifts acting on an arbitrary Banach sequence space.The disjoint supercyclic properties of weighted translations on locally compact discrete groups,the direct sums of finite classical weighted backward shifts, and the bilateral backward operator weighted shifts can be viewed as special cases of our main results. Furthermore, we exhibit an interesting fact that any finite bilateral weighted backward shifts on the space ?~2(Z) never satisfy the d-Supercyclicity Criterion by a simple proof.
