Bush type fractal functions were defined by means of the expression of Cantor series of real numbers. The upper and lower bound estimates for the K-dimension of such functions were given. In a typical case, the fracta...Bush type fractal functions were defined by means of the expression of Cantor series of real numbers. The upper and lower bound estimates for the K-dimension of such functions were given. In a typical case, the fractal dimensional relations in which the K-dimension equals the box dimension and packing dimension were presented; moreover, the exact Holder exponent were obtained for such Bush type functions.展开更多
In this paper. based on large deviation formulas established in stronger topology generated by Hlder norm, we obtain the functional limit theorems for C-R increments of k-dimensional Brownian motion in Hlder norm
Thek-dimensional Piatetski-Shapiro prime number problem fork?3 is studied. Let π(x 1 c 1,?,c k ) denote the number of primesp withp?x, $p = [n_1^{c_1 } ] = \cdots [n_k^{c_k } ]$ , where 1<c 1<?<c k are fixed...Thek-dimensional Piatetski-Shapiro prime number problem fork?3 is studied. Let π(x 1 c 1,?,c k ) denote the number of primesp withp?x, $p = [n_1^{c_1 } ] = \cdots [n_k^{c_k } ]$ , where 1<c 1<?<c k are fixed constants. It is proved that π(x;c 1,?,c k ) has an asymptotic formula ifc 1 ?1 +?+c k ?1 >k?k/(4k 2+2).展开更多
Verifying the integrity of a hard disk is an important concern in computer forensics,as the law enforcement party needs to confirm that the data inside the hard disk have not been modified during the investigation.A t...Verifying the integrity of a hard disk is an important concern in computer forensics,as the law enforcement party needs to confirm that the data inside the hard disk have not been modified during the investigation.A typical approach is to compute a single chained hash value of all sectors in a specific order.However,this technique loses the integrity of all other sectors even if only one of the sectors becomes a bad sector occasionally or is modified intentionally.In this paper we propose a k-dimensional hashing scheme,kD for short,to distribute sectors into a kD space,and to calculate multiple hash values for sectors in k dimensions as integrity evidence.Since the integrity of the sectors can be verified depending on any hash value calculated using the sectors,the probability to verify the integrity of unchanged sectors can be high even with bad/modified sectors in the hard disk.We show how to efficiently implement this kD hashing scheme such that the storage of hash values can be reduced while increasing the chance of an unaffected sector to be verified successfully.Experimental results of a 3D scheme show that both the time for computing the hash values and the storage for the hash values are reasonable.展开更多
为解决近年来用户行业变化特性加剧导致的难以准确辨识用户档案信息变动的问题,文中提出一种基于数据驱动的负荷特征异常辨识方法。首先,提出一种两阶段行业典型负荷形态构建方法,利用基于层次密度的含噪声应用空间聚类(hierarchical de...为解决近年来用户行业变化特性加剧导致的难以准确辨识用户档案信息变动的问题,文中提出一种基于数据驱动的负荷特征异常辨识方法。首先,提出一种两阶段行业典型负荷形态构建方法,利用基于层次密度的含噪声应用空间聚类(hierarchical density-based spatial clustering of applications with noise,HDBSCAN)提取用户在不同场景下的典型日负荷曲线,并利用改进的K-means算法对提取出的典型日负荷曲线进行聚类分析,构建行业的典型负荷形态;其次,提出一种多维场景负荷特征异常智能研判方法,通过构造用户的负荷特征,使用熵权法评估行业典型场景的相对重要性,并采用单分类支持向量机(one-class support vector machine,OCSVM)算法量化每个场景下的用户负荷特征的异常程度,通过加权计算得到用户的综合嫌疑得分并排序,从而实现对负荷特征异常用户的准确辨识。最后,采用某地区实际用户数据进行算例验证。仿真结果表明,所提方法在行业典型负荷场景构建及负荷特征异常辨识方面表现出良好的可行性与实用价值。展开更多
Unlike the detection of marked on-street parking spaces,detecting unmarked spaces poses significant challenges due to the absence of clear physical demarcation and uneven gaps caused by irregular parking.In urban citi...Unlike the detection of marked on-street parking spaces,detecting unmarked spaces poses significant challenges due to the absence of clear physical demarcation and uneven gaps caused by irregular parking.In urban cities with heavy traffic flow,these challenges can result in traffic disruptions,rear-end collisions,sideswipes,and congestion as drivers struggle to make decisions.We propose a real-time detection system for on-street parking spaces using YOLO models and recommend the most suitable space based on KD-tree search.Lightweight versions of YOLOv5,YOLOv7-tiny,and YOLOv8 with different architectures are trained.Among the models,YOLOv5s with SPPF at the backbone achieved an F1-score of 0.89,which was selected for validation using k-fold cross-validation on our dataset.The Low variance and standard deviation recorded across folds indicate the model’s generalizability,reliability,and stability.Inference with KD-tree using predictions from the YOLO models recorded FPS of 37.9 for YOLOv5,67.2 for YOLOv7-tiny,and 67.0 for YOLOv8.The models successfully detect both marked and unmarked empty parking spaces on test data with varying inference speeds and FPS.These models can be efficiently deployed for real-time applications due to their high FPS,inference speed,and lightweight nature.In comparison with other state-of-the-art models,our models outperform them,further demonstrating their effectiveness.展开更多
基金The National Natural Science Foundation of China (No.10171080)
文摘Bush type fractal functions were defined by means of the expression of Cantor series of real numbers. The upper and lower bound estimates for the K-dimension of such functions were given. In a typical case, the fractal dimensional relations in which the K-dimension equals the box dimension and packing dimension were presented; moreover, the exact Holder exponent were obtained for such Bush type functions.
文摘In this paper. based on large deviation formulas established in stronger topology generated by Hlder norm, we obtain the functional limit theorems for C-R increments of k-dimensional Brownian motion in Hlder norm
基金Project supported by the National Natural Science Foundation of China (Grant No. 19801021)the Natural Science Foundation of Shandong Province (Grant No. Q98A02110).
文摘Thek-dimensional Piatetski-Shapiro prime number problem fork?3 is studied. Let π(x 1 c 1,?,c k ) denote the number of primesp withp?x, $p = [n_1^{c_1 } ] = \cdots [n_k^{c_k } ]$ , where 1<c 1<?<c k are fixed constants. It is proved that π(x;c 1,?,c k ) has an asymptotic formula ifc 1 ?1 +?+c k ?1 >k?k/(4k 2+2).
基金Project supported by the Research Grants Council of Hong Kong SAR,China (No. RGC GRF HKU 713009E)the NSFC/RGC Joint Research Scheme (No. N_HKU 722/09)HKU Seed Fundings for Basic Research (Nos. 200811159155 and 200911159149)
文摘Verifying the integrity of a hard disk is an important concern in computer forensics,as the law enforcement party needs to confirm that the data inside the hard disk have not been modified during the investigation.A typical approach is to compute a single chained hash value of all sectors in a specific order.However,this technique loses the integrity of all other sectors even if only one of the sectors becomes a bad sector occasionally or is modified intentionally.In this paper we propose a k-dimensional hashing scheme,kD for short,to distribute sectors into a kD space,and to calculate multiple hash values for sectors in k dimensions as integrity evidence.Since the integrity of the sectors can be verified depending on any hash value calculated using the sectors,the probability to verify the integrity of unchanged sectors can be high even with bad/modified sectors in the hard disk.We show how to efficiently implement this kD hashing scheme such that the storage of hash values can be reduced while increasing the chance of an unaffected sector to be verified successfully.Experimental results of a 3D scheme show that both the time for computing the hash values and the storage for the hash values are reasonable.
文摘为解决近年来用户行业变化特性加剧导致的难以准确辨识用户档案信息变动的问题,文中提出一种基于数据驱动的负荷特征异常辨识方法。首先,提出一种两阶段行业典型负荷形态构建方法,利用基于层次密度的含噪声应用空间聚类(hierarchical density-based spatial clustering of applications with noise,HDBSCAN)提取用户在不同场景下的典型日负荷曲线,并利用改进的K-means算法对提取出的典型日负荷曲线进行聚类分析,构建行业的典型负荷形态;其次,提出一种多维场景负荷特征异常智能研判方法,通过构造用户的负荷特征,使用熵权法评估行业典型场景的相对重要性,并采用单分类支持向量机(one-class support vector machine,OCSVM)算法量化每个场景下的用户负荷特征的异常程度,通过加权计算得到用户的综合嫌疑得分并排序,从而实现对负荷特征异常用户的准确辨识。最后,采用某地区实际用户数据进行算例验证。仿真结果表明,所提方法在行业典型负荷场景构建及负荷特征异常辨识方面表现出良好的可行性与实用价值。
基金supports this paper.Project Nos.NSTC-112-2221-E-324-003 MY3,NSTC-111-2622-E-324-002 and NSTC-112-2221-E-324-011-MY2.
文摘Unlike the detection of marked on-street parking spaces,detecting unmarked spaces poses significant challenges due to the absence of clear physical demarcation and uneven gaps caused by irregular parking.In urban cities with heavy traffic flow,these challenges can result in traffic disruptions,rear-end collisions,sideswipes,and congestion as drivers struggle to make decisions.We propose a real-time detection system for on-street parking spaces using YOLO models and recommend the most suitable space based on KD-tree search.Lightweight versions of YOLOv5,YOLOv7-tiny,and YOLOv8 with different architectures are trained.Among the models,YOLOv5s with SPPF at the backbone achieved an F1-score of 0.89,which was selected for validation using k-fold cross-validation on our dataset.The Low variance and standard deviation recorded across folds indicate the model’s generalizability,reliability,and stability.Inference with KD-tree using predictions from the YOLO models recorded FPS of 37.9 for YOLOv5,67.2 for YOLOv7-tiny,and 67.0 for YOLOv8.The models successfully detect both marked and unmarked empty parking spaces on test data with varying inference speeds and FPS.These models can be efficiently deployed for real-time applications due to their high FPS,inference speed,and lightweight nature.In comparison with other state-of-the-art models,our models outperform them,further demonstrating their effectiveness.
