In mathematics, space encompasses various structured sets such as Euclidean, metric, or vector space. This article introduces temporal space—a novel concept independent of traditional spatial dimensions and frames of...In mathematics, space encompasses various structured sets such as Euclidean, metric, or vector space. This article introduces temporal space—a novel concept independent of traditional spatial dimensions and frames of reference, accommodating multiple object-oriented durations in a dynamical system. The novelty of building temporal space using finite geometry is rooted in recent advancements in the theory of relationalism which utilizes Euclidean geometry, set theory, dimensional analysis, and a causal signal system. Multiple independent and co-existing cyclic durations are measurable as a network of finite one-dimensional timelines. The work aligns with Leibniz’s comments on relational measures of duration with the addition of using discrete cyclic relational events that define these finite temporal spaces, applicable to quantum and classical physics. Ancient formulas have symmetry along with divisional and subdivisional orders of operations that create discrete and ordered temporal geometric elements. Elements have cyclically conserved symmetry but unique cyclic dimensional quantities applicable for anchoring temporal equivalence relations in linear time. We present both fixed equivalences and expanded periods of temporal space offering a non-Greek calendar methodology consistent with ancient global timekeeping descriptions. Novel applications of Euclid’s division algorithm and Cantor’s pairing function introduce a novel paired function equation. The mathematical description of finite temporal space within relationalism theory offers an alternative discrete geometric methodology for examining ancient timekeeping with new hypotheses for Egyptian calendars.展开更多
Recently,dealing with the non-Euclidean data and its characterization is considered as one of the major issues by researchers.The first problem arises while defining the distinction among Euclidean and non-Euclidean g...Recently,dealing with the non-Euclidean data and its characterization is considered as one of the major issues by researchers.The first problem arises while defining the distinction among Euclidean and non-Euclidean geometry with its examples.The second problem arises while dealing with the non-Euclidean geometry in true,false,and uncertain regions.The third problem arises while investigating some patterns in non-Euclidean data sets.This paper focused on tackling these issues with some real-life examples in data processing,data visualization,knowledge representation,and quantum computing.展开更多
The relation between the circum-radius and the in-radius of an n-dimensional simplex in E^n is studied.Two new generalizations of Euler inequality for the n-dimensional simplex are established.Besides,we obtain some s...The relation between the circum-radius and the in-radius of an n-dimensional simplex in E^n is studied.Two new generalizations of Euler inequality for the n-dimensional simplex are established.Besides,we obtain some stronger generalizations of Euler inequality for the n-dimensional simplex than previously known results.展开更多
In this letter a new skeletonization algorithm is proposed. It combines techniques of fast construction of Euclidean Distance Maps(EDMs), ridge extraction, Hit-or-Miss Transformation(HMT) of structuring elements and t...In this letter a new skeletonization algorithm is proposed. It combines techniques of fast construction of Euclidean Distance Maps(EDMs), ridge extraction, Hit-or-Miss Transformation(HMT) of structuring elements and the set operators. It first produces the EDM image with no more than 4 passes through an image of any kinds, and then the ridge image is extracted by applying a turn-on scheme and performing a rain-fall elimination to accelerate the processing. The one-pixel wide skeleton is finally acquired by carrying out the HMTs of two structure elements and the SUBTRACT and OR operations. Experimental results obtained by practical applications are also presented.展开更多
A new method for constructing Quasi-Cyclic (QC) Low-Density Parity-Check (LDPC) codes based on Euclidean Geometry (EG) is presented. The proposed method results in a class of QC-LDPC codes with girth of at least 6 and...A new method for constructing Quasi-Cyclic (QC) Low-Density Parity-Check (LDPC) codes based on Euclidean Geometry (EG) is presented. The proposed method results in a class of QC-LDPC codes with girth of at least 6 and the designed codes perform very close to the Shannon limit with iterative decoding. Simulations show that the designed QC-LDPC codes have almost the same performance with the existing EG-LDPC codes.展开更多
Recommendation system can greatly alleviate the "information overload" in the big data era. Existing recommendation methods, however, typically focus on predicting missing rating values via analyzing user-it...Recommendation system can greatly alleviate the "information overload" in the big data era. Existing recommendation methods, however, typically focus on predicting missing rating values via analyzing user-item dualistic relationship, which neglect an important fact that the latent interests of users can influence their rating behaviors. Moreover, traditional recommendation methods easily suffer from the high dimensional problem and cold-start problem. To address these challenges, in this paper, we propose a PBUED(PLSA-Based Uniform Euclidean Distance) scheme, which utilizes topic model and uniform Euclidean distance to recommend the suitable items for users. The solution first employs probabilistic latent semantic analysis(PLSA) to extract users' interests, users with different interests are divided into different subgroups. Then, the uniform Euclidean distance is adopted to compute the users' similarity in the same interest subset; finally, the missing rating values of data are predicted via aggregating similar neighbors' ratings. We evaluate PBUED on two datasets and experimental results show PBUED can lead to better predicting performance and ranking performance than other approaches.展开更多
文摘In mathematics, space encompasses various structured sets such as Euclidean, metric, or vector space. This article introduces temporal space—a novel concept independent of traditional spatial dimensions and frames of reference, accommodating multiple object-oriented durations in a dynamical system. The novelty of building temporal space using finite geometry is rooted in recent advancements in the theory of relationalism which utilizes Euclidean geometry, set theory, dimensional analysis, and a causal signal system. Multiple independent and co-existing cyclic durations are measurable as a network of finite one-dimensional timelines. The work aligns with Leibniz’s comments on relational measures of duration with the addition of using discrete cyclic relational events that define these finite temporal spaces, applicable to quantum and classical physics. Ancient formulas have symmetry along with divisional and subdivisional orders of operations that create discrete and ordered temporal geometric elements. Elements have cyclically conserved symmetry but unique cyclic dimensional quantities applicable for anchoring temporal equivalence relations in linear time. We present both fixed equivalences and expanded periods of temporal space offering a non-Greek calendar methodology consistent with ancient global timekeeping descriptions. Novel applications of Euclid’s division algorithm and Cantor’s pairing function introduce a novel paired function equation. The mathematical description of finite temporal space within relationalism theory offers an alternative discrete geometric methodology for examining ancient timekeeping with new hypotheses for Egyptian calendars.
基金国家自然科学基金(61305038,61273249,61502282)海洋公益性行业科研专项经费资助项目(201505002)+2 种基金自主系统与网络控制教育部重点实验室广东省生物医学工程重点实验室资助the National Engineering Research Center for Tissue Restoration and Reconstruction~~
文摘Recently,dealing with the non-Euclidean data and its characterization is considered as one of the major issues by researchers.The first problem arises while defining the distinction among Euclidean and non-Euclidean geometry with its examples.The second problem arises while dealing with the non-Euclidean geometry in true,false,and uncertain regions.The third problem arises while investigating some patterns in non-Euclidean data sets.This paper focused on tackling these issues with some real-life examples in data processing,data visualization,knowledge representation,and quantum computing.
基金Foundation item： Supported by the National Science Foundation of China（60671051） Supported by the Foundation of Anhui Higher School（KJ2009A45）
文摘The relation between the circum-radius and the in-radius of an n-dimensional simplex in E^n is studied.Two new generalizations of Euler inequality for the n-dimensional simplex are established.Besides,we obtain some stronger generalizations of Euler inequality for the n-dimensional simplex than previously known results.
文摘In this letter a new skeletonization algorithm is proposed. It combines techniques of fast construction of Euclidean Distance Maps(EDMs), ridge extraction, Hit-or-Miss Transformation(HMT) of structuring elements and the set operators. It first produces the EDM image with no more than 4 passes through an image of any kinds, and then the ridge image is extracted by applying a turn-on scheme and performing a rain-fall elimination to accelerate the processing. The one-pixel wide skeleton is finally acquired by carrying out the HMTs of two structure elements and the SUBTRACT and OR operations. Experimental results obtained by practical applications are also presented.
基金Supported by the National Key Basic Research Program (973) Project (No. 2010CB328300)the 111 Project (No. B08038)
文摘A new method for constructing Quasi-Cyclic (QC) Low-Density Parity-Check (LDPC) codes based on Euclidean Geometry (EG) is presented. The proposed method results in a class of QC-LDPC codes with girth of at least 6 and the designed codes perform very close to the Shannon limit with iterative decoding. Simulations show that the designed QC-LDPC codes have almost the same performance with the existing EG-LDPC codes.
基金supported in part by the National High‐tech R&D Program of China (863 Program) under Grant No. 2013AA102301technological project of Henan province (162102210214)
文摘Recommendation system can greatly alleviate the "information overload" in the big data era. Existing recommendation methods, however, typically focus on predicting missing rating values via analyzing user-item dualistic relationship, which neglect an important fact that the latent interests of users can influence their rating behaviors. Moreover, traditional recommendation methods easily suffer from the high dimensional problem and cold-start problem. To address these challenges, in this paper, we propose a PBUED(PLSA-Based Uniform Euclidean Distance) scheme, which utilizes topic model and uniform Euclidean distance to recommend the suitable items for users. The solution first employs probabilistic latent semantic analysis(PLSA) to extract users' interests, users with different interests are divided into different subgroups. Then, the uniform Euclidean distance is adopted to compute the users' similarity in the same interest subset; finally, the missing rating values of data are predicted via aggregating similar neighbors' ratings. We evaluate PBUED on two datasets and experimental results show PBUED can lead to better predicting performance and ranking performance than other approaches.
