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 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
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
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
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
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
We estimate the number of disjoint open subsets in Rn, which can support area-decreasing minimal graphs. This result generalizes the related results of Li-Wang and Tkachev for minimal hypersurfaces to higher codimensi...We estimate the number of disjoint open subsets in Rn, which can support area-decreasing minimal graphs. This result generalizes the related results of Li-Wang and Tkachev for minimal hypersurfaces to higher codimensional case.展开更多
Let denote the maximum number of disjoint bases in a matroid . For a connected graph , let , where is the cycle matroid of . The well-known spanning tree packing theorem of Nash-Williams and Tutte characterizes graphs...Let denote the maximum number of disjoint bases in a matroid . For a connected graph , let , where is the cycle matroid of . The well-known spanning tree packing theorem of Nash-Williams and Tutte characterizes graphs with . Edmonds generalizes this theorem to matroids. In [1] and [2], for a matroid with , elements with the property that have been characterized in terms of matroid invariants such as strength and -partitions. In this paper, we consider matroids with , and determine the minimum of , where is a matroid that contains as a restriction with both and . This minimum is expressed as a function of certain invariants of , as well as a min-max formula. These are applied to imply former results of Haas [3] and of Liu et al. [4].展开更多
Mobile Ad-hoc Network (MANET) consists of mobile nodes that are connected via very dynamic multi-hop channels. Routing in MANET is a challenging task that has received great attention from researchers. In this paper w...Mobile Ad-hoc Network (MANET) consists of mobile nodes that are connected via very dynamic multi-hop channels. Routing in MANET is a challenging task that has received great attention from researchers. In this paper we present Maximally Spatial Disjoint Multipath routing protocol (MSDM) which is a modification of AOMDV protocol. MSDM finds paths which are spatially separated and maximally disjointed. We think that sending various packets over spatially disjointed paths reduces the probability of collision occurrence and allows concurrent transmission over the set of different selected paths. Performance comparison of MSDM and AOMDV using GloMoSim simulator shows that MSDM is able to achieve a considerable improvement regarding some performance metrics such as delay, routing packets overhead, and network throughput.展开更多
In a wireless sensor network, routing messages between two nodes s and t with multiple disjoint paths will increase the throughput, robustness and load balance of the network. The existing researches focus on finding ...In a wireless sensor network, routing messages between two nodes s and t with multiple disjoint paths will increase the throughput, robustness and load balance of the network. The existing researches focus on finding multiple disjoint paths connecting s and t efficiently, but they do not consider length constraint of the paths. A too long path will be useless because of high latency and high packet loss rate. This paper deals with such a problem: given two nodes s and t in a sensor network, finding as many as possible disjoint paths connecting s and t whose lengths are no more than L, where L is the length bound set by the users. By now, we know that this problem is not only NP hard but also APX complete [1,2], which means that there is no PTAS for this problem. To the best of our knowledge, there is only one heuristic algorithm proposed for this problem [3], and it is not suitable for sensor network because it processes in a centralized way. This paper proposes an efficient distributed algorithm for this problem. By processing in a distributed way, the algorithm is very communication efficient. Simulation results show that our algorithm outperforms the existing algorithm in both aspects of found path number and communication efficiency.展开更多
The authors p oint out a problem in the article of Ref.(Xiong Hongyun,Rong Ximin.Maximal disjoint systems in Riesz space and representation.Acta Math Sinica ,1998,41(4):763-766.)and revise it.Let E be an Archimed ean ...The authors p oint out a problem in the article of Ref.(Xiong Hongyun,Rong Ximin.Maximal disjoint systems in Riesz space and representation.Acta Math Sinica ,1998,41(4):763-766.)and revise it.Let E be an Archimed ean Riesz space possessing a weak unit e and a maximal disjoint division{e i:i∈I} in which each e i is a proj ection element. Concerning the following statements:(1) There exists a completel y regular Hausdorff space X such that E is Riesz isomorphic to C(X);(2) For every i∈I there exi sts a completely regular Hausdorff space X i such that the band generated by e i is Riesz isomorphic to C(X i).It is shown that (1) implies (2),and find some conditions for the inverse bein g true are found.Furthermore,if each X i in (2) is a compact Ha usdorff space, a necessary and sufficient condition is established under which E can be represented as a C(X) for some compact Hausdorff space X.As corollaries, corresponding results for late rally complete Riesz spaces are obtained.展开更多
The existence of several non-symmetric balanced incomplete block designs (BIBDs) is still unknown. This is because the non-existence property for non-symmetric BIBDs is still not known and also the existing constructi...The existence of several non-symmetric balanced incomplete block designs (BIBDs) is still unknown. This is because the non-existence property for non-symmetric BIBDs is still not known and also the existing construction methods have not been able to construct these designs despite their design parameters satisfying the necessary conditions for the existence of BIBD. The study aimed to bridge this gap by introducing a new class of non-symmetric BIBDs. The proposed class of BIBDs is constructed through the combination of disjoint symmetric BIBDs. The study was able to determine that the total number of disjoint symmetric BIBDs (n) with parameters (v = b, r = k, λ) that can be obtained from an un-reduced BIBD with parameters (v, k) is given by n = r - λ. When the n symmetric disjoint BIBDs are combined, then a new class of symmetric BIBDs is formed with parameters v<sup>*</sup><sup> </sup>= v, b<sup>*</sup><sup> </sup>= nb, r<sup>*</sup><sup> </sup>= nr, k<sup>*</sup><sup> </sup>= k, λ<sup>*</sup><sup> </sup>= λ, where 2≤ n ≤ r - λ. The study established that the non-existence property of this class of BIBD was that when is not a perfect square then v should be even and when v<sup>*</sup><sup> </sup>is odd then the equation should not have a solution in integers x, y, z which are not all simultaneously zero. In conclusion, the study showed that this construction technique can be used to construct some non-symmetric BIBDs. However, one must first construct the disjoint symmetric BIBDs before one can construct the non-symmetric BIBD. Thus, the disjoint symmetric BIBDs must exist first before the non-symmetric BIBDs exist.展开更多
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.
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.
基金supported by zhongdian grantof NSFC (A010501)NSFC-NSF (1081112053)supported by NSFC (10701025)
文摘We estimate the number of disjoint open subsets in Rn, which can support area-decreasing minimal graphs. This result generalizes the related results of Li-Wang and Tkachev for minimal hypersurfaces to higher codimensional case.
文摘Let denote the maximum number of disjoint bases in a matroid . For a connected graph , let , where is the cycle matroid of . The well-known spanning tree packing theorem of Nash-Williams and Tutte characterizes graphs with . Edmonds generalizes this theorem to matroids. In [1] and [2], for a matroid with , elements with the property that have been characterized in terms of matroid invariants such as strength and -partitions. In this paper, we consider matroids with , and determine the minimum of , where is a matroid that contains as a restriction with both and . This minimum is expressed as a function of certain invariants of , as well as a min-max formula. These are applied to imply former results of Haas [3] and of Liu et al. [4].
文摘Mobile Ad-hoc Network (MANET) consists of mobile nodes that are connected via very dynamic multi-hop channels. Routing in MANET is a challenging task that has received great attention from researchers. In this paper we present Maximally Spatial Disjoint Multipath routing protocol (MSDM) which is a modification of AOMDV protocol. MSDM finds paths which are spatially separated and maximally disjointed. We think that sending various packets over spatially disjointed paths reduces the probability of collision occurrence and allows concurrent transmission over the set of different selected paths. Performance comparison of MSDM and AOMDV using GloMoSim simulator shows that MSDM is able to achieve a considerable improvement regarding some performance metrics such as delay, routing packets overhead, and network throughput.
文摘In a wireless sensor network, routing messages between two nodes s and t with multiple disjoint paths will increase the throughput, robustness and load balance of the network. The existing researches focus on finding multiple disjoint paths connecting s and t efficiently, but they do not consider length constraint of the paths. A too long path will be useless because of high latency and high packet loss rate. This paper deals with such a problem: given two nodes s and t in a sensor network, finding as many as possible disjoint paths connecting s and t whose lengths are no more than L, where L is the length bound set by the users. By now, we know that this problem is not only NP hard but also APX complete [1,2], which means that there is no PTAS for this problem. To the best of our knowledge, there is only one heuristic algorithm proposed for this problem [3], and it is not suitable for sensor network because it processes in a centralized way. This paper proposes an efficient distributed algorithm for this problem. By processing in a distributed way, the algorithm is very communication efficient. Simulation results show that our algorithm outperforms the existing algorithm in both aspects of found path number and communication efficiency.
文摘The authors p oint out a problem in the article of Ref.(Xiong Hongyun,Rong Ximin.Maximal disjoint systems in Riesz space and representation.Acta Math Sinica ,1998,41(4):763-766.)and revise it.Let E be an Archimed ean Riesz space possessing a weak unit e and a maximal disjoint division{e i:i∈I} in which each e i is a proj ection element. Concerning the following statements:(1) There exists a completel y regular Hausdorff space X such that E is Riesz isomorphic to C(X);(2) For every i∈I there exi sts a completely regular Hausdorff space X i such that the band generated by e i is Riesz isomorphic to C(X i).It is shown that (1) implies (2),and find some conditions for the inverse bein g true are found.Furthermore,if each X i in (2) is a compact Ha usdorff space, a necessary and sufficient condition is established under which E can be represented as a C(X) for some compact Hausdorff space X.As corollaries, corresponding results for late rally complete Riesz spaces are obtained.
文摘The existence of several non-symmetric balanced incomplete block designs (BIBDs) is still unknown. This is because the non-existence property for non-symmetric BIBDs is still not known and also the existing construction methods have not been able to construct these designs despite their design parameters satisfying the necessary conditions for the existence of BIBD. The study aimed to bridge this gap by introducing a new class of non-symmetric BIBDs. The proposed class of BIBDs is constructed through the combination of disjoint symmetric BIBDs. The study was able to determine that the total number of disjoint symmetric BIBDs (n) with parameters (v = b, r = k, λ) that can be obtained from an un-reduced BIBD with parameters (v, k) is given by n = r - λ. When the n symmetric disjoint BIBDs are combined, then a new class of symmetric BIBDs is formed with parameters v<sup>*</sup><sup> </sup>= v, b<sup>*</sup><sup> </sup>= nb, r<sup>*</sup><sup> </sup>= nr, k<sup>*</sup><sup> </sup>= k, λ<sup>*</sup><sup> </sup>= λ, where 2≤ n ≤ r - λ. The study established that the non-existence property of this class of BIBD was that when is not a perfect square then v should be even and when v<sup>*</sup><sup> </sup>is odd then the equation should not have a solution in integers x, y, z which are not all simultaneously zero. In conclusion, the study showed that this construction technique can be used to construct some non-symmetric BIBDs. However, one must first construct the disjoint symmetric BIBDs before one can construct the non-symmetric BIBD. Thus, the disjoint symmetric BIBDs must exist first before the non-symmetric BIBDs exist.
