Let G be a simple connected graph with vertex set V（G） and edge set E（G）.The augmented Zagreb index of a graph G is defined asAZI（G） =∑uv∈E（G）(d;d;/（d;+ d;-2）);,and the atom-bond connectivity index（ABC in...Let G be a simple connected graph with vertex set V（G） and edge set E（G）.The augmented Zagreb index of a graph G is defined asAZI（G） =∑uv∈E（G）(d;d;/（d;+ d;-2）);,and the atom-bond connectivity index（ABC index for short） of a graph G is defined asABC（G） =∑uv∈E（G）(（d;+ d;-2）/d;d;),where d;and d;denote the degree of vertices u and v in G,respectively.In this paper,trees with given diameter minimizing the augmented Zagreb index and maximizing the ABC index are determined,respectively.展开更多
Variations in vegetation are closely related to climate change, but understanding of their characteristics and causes remains limited. As a typical semi-humid and semi-arid cold plateau region, it is important to unde...Variations in vegetation are closely related to climate change, but understanding of their characteristics and causes remains limited. As a typical semi-humid and semi-arid cold plateau region, it is important to understand the knowledge of long term Normalized Difference Vegetation Index(NDVI) variations and find the potential causes in the source region of the Yangtze River. Based on four tree-ring width chronologies, the regional mean NDVI for July and August spanning the period 1665–2013 was reconstructed using a regression model, and it explained 43.9% of the total variance during the period 1981–2013. In decadal, the reconstructed NDVI showed eight growth stages(1754–1764, 1766–1783, 1794–1811, 1828–1838, 1843–1855, 1862–1873, 1897–1909, and 1932–1945)and four degradation stages(1679–1698, 1726–1753, 1910–1923, and 1988–2000). And based on wavelet analysis, significant cycles of2–3 yr and 3–8 yr were identified. In additional, there was a significant positive correlation between the NDVI and the Palmer Drought Severity Index(PDSI) during the past 349 yr, and they were mainly in phase. However, according to the results of correlation analysis between different grades of drought/wet and NDVI, there was significant asymmetry in extreme drought years and extreme wet years. In extreme drought years, NDVI was positively correlated with PDSI, and in extreme wet years they were negatively correlated.展开更多
Determinations of fracture network connections would help the investigators remove those ＂meaningless＂ no-flow-passing fractures, providing an updated and more effective fracture network that could considerably impr...Determinations of fracture network connections would help the investigators remove those ＂meaningless＂ no-flow-passing fractures, providing an updated and more effective fracture network that could considerably improve the computation efficiency in the pertinent numerical simulations of fluid flow and solute transport. The effective algorithms with higher computational efficiency are needed to accomplish this task in large-scale fractured rock masses. A new approach using R tree indexing was proposed for determining fracture connection in 3D stochastically distributed fracture network. By com- paring with the traditional exhaustion algorithm, it was observed that from the simulation results, this approach was much more effective; and the more the fractures were investigated, the more obvious the advantages of the approach were. Furthermore, it was indicated that the runtime used for creating the R tree indexing has a major part in the total of the runtime used for calculating Minimum Bounding Rectangles （MBRs）, creating the R tree indexing, precisely finding out fracture intersections, and identifying flow paths, which are four important steps to determine fracture connections. This proposed approach for the determination of fracture connections in three-dimensional fractured rocks are expected to provide efficient preprocessing and critical database for practically accomplishing numerical computation of fluid flow and solute transport in large-scale fractured rock masses.展开更多
Existing speech retrieval systems are frequently confronted with expanding volumes of speech data.The dynamic updating strategy applied to construct the index can timely process to add or remove unnecessary speech dat...Existing speech retrieval systems are frequently confronted with expanding volumes of speech data.The dynamic updating strategy applied to construct the index can timely process to add or remove unnecessary speech data to meet users’real-time retrieval requirements.This study proposes an efficient method for retrieving encryption speech,using unsupervised deep hashing and B+ tree dynamic index,which avoid privacy leak-age of speech data and enhance the accuracy and efficiency of retrieval.The cloud’s encryption speech library is constructed by using the multi-threaded Dijk-Gentry-Halevi-Vaikuntanathan(DGHV)Fully Homomorphic Encryption(FHE)technique,which encrypts the original speech.In addition,this research employs Residual Neural Network18-Gated Recurrent Unit(ResNet18-GRU),which is used to learn the compact binary hash codes,store binary hash codes in the designed B+tree index table,and create a mapping relation of one to one between the binary hash codes and the corresponding encrypted speech.External B+tree index technology is applied to achieve dynamic index updating of the B+tree index table,thereby satisfying users’needs for real-time retrieval.The experimental results on THCHS-30 and TIMIT showed that the retrieval accuracy of the proposed method is more than 95.84%compared to the existing unsupervised hashing methods.The retrieval efficiency is greatly improved.Compared to the method of using hash index tables,and the speech data’s security is effectively guaranteed.展开更多
In recent years, a growing number of math contents are available on the Web. When conventional search engines deal with mathematical expressions, the two-dimen- sion-al structure of mathematical expressions is lost, w...In recent years, a growing number of math contents are available on the Web. When conventional search engines deal with mathematical expressions, the two-dimen- sion-al structure of mathematical expressions is lost, which results in a low performance of math retrieval. While the retrieval technology specifically designed for mathematical expressions is not mature currently. Aiming at these problems, an improved mathematical expression indexing and matching method was proposed through employing full text index method to deal with the two-dimensional structure of mathematical expressions. Firstly, through the fully consideration of LaTeX formulae’ characteristics, a feature representation method of mathematical expressions and a clustering method of feature keywords were put forward. Then, an improved inter-relevant successive trees index model was applied to the construction of the mathematical expression index, in which the cluster algorithm of mathematical expression features was employed to solve the problem of the quantity growth of the trees in processing large amount of formulae. Finally, the matching algorithms of mathematical expressions were given which provide four query modes called exact matching, compatible matching, sub-expression matching and fuzzy matching. In browser/server mode, 110027 formulae were used as experimental samples. The index file size was 29.02 Mb. The average time of retrieval was 1.092 seconds. The experimental result shows the effectiveness of the method.展开更多
The number and composition of species in a community can be quantified withα-diversity indices,including species richness(R),Simpson’s index(D),and the Shannon-Wiener index(H΄).In forest communities,there are large ...The number and composition of species in a community can be quantified withα-diversity indices,including species richness(R),Simpson’s index(D),and the Shannon-Wiener index(H΄).In forest communities,there are large variations in tree size among species and individu-als of the same species,which result in differences in eco-logical processes and ecosystem functions.However,tree size inequality(TSI)has been largely neglected in studies using the available diversity indices.The TSI in the diameter at breast height(DBH)data for each of 99920 m×20 m forest census quadrats was quantified using the Gini index(GI),a measure of the inequality of size distribution.The generalized performance equation was used to describe the rotated and right-shifted Lorenz curve of the cumulative proportion of DBH and the cumulative proportion of number of trees per quadrat.We also examined the relationships ofα-diversity indices with the GI using correlation tests.The generalized performance equation effectively described the rotated and right-shifted Lorenz curve of DBH distributions,with most root-mean-square errors(990 out of 999 quadrats)being<0.0030.There were significant positive correlations between each of threeα-diversity indices(i.e.,R,D,and H’)and the GI.Nevertheless,the total abundance of trees in each quadrat did not significantly influence the GI.This means that the TSI increased with increasing spe-cies diversity.Thus,two new indices are proposed that can balanceα-diversity against the extent of TSI in the com-munity:(1−GI)×D,and(1−GI)×H’.These new indices were significantly correlated with the original D and H΄,and did not increase the extent of variation within each group of indices.This study presents a useful tool for quantifying both species diversity and the variation in tree sizes in forest communities,especially in the face of cumulative species loss under global climate change.展开更多
The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, whe...The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.展开更多
文摘Let G be a simple connected graph with vertex set V（G） and edge set E（G）.The augmented Zagreb index of a graph G is defined asAZI（G） =∑uv∈E（G）(d;d;/（d;+ d;-2）);,and the atom-bond connectivity index（ABC index for short） of a graph G is defined asABC（G） =∑uv∈E（G）(（d;+ d;-2）/d;d;),where d;and d;denote the degree of vertices u and v in G,respectively.In this paper,trees with given diameter minimizing the augmented Zagreb index and maximizing the ABC index are determined,respectively.
基金Under the auspices of the Second Tibetan Plateau Scientific Expedition and Research(STEP)Program(No.2019QZKK0103)National Natural Science Foundation of China(No.41772173,41405077)+1 种基金the Thousand Talents Program for High-end Innovation of Qinghai Provincethe Applied Basic Research Project of Qinghai Province(No.2019-zj-7045)。
文摘Variations in vegetation are closely related to climate change, but understanding of their characteristics and causes remains limited. As a typical semi-humid and semi-arid cold plateau region, it is important to understand the knowledge of long term Normalized Difference Vegetation Index(NDVI) variations and find the potential causes in the source region of the Yangtze River. Based on four tree-ring width chronologies, the regional mean NDVI for July and August spanning the period 1665–2013 was reconstructed using a regression model, and it explained 43.9% of the total variance during the period 1981–2013. In decadal, the reconstructed NDVI showed eight growth stages(1754–1764, 1766–1783, 1794–1811, 1828–1838, 1843–1855, 1862–1873, 1897–1909, and 1932–1945)and four degradation stages(1679–1698, 1726–1753, 1910–1923, and 1988–2000). And based on wavelet analysis, significant cycles of2–3 yr and 3–8 yr were identified. In additional, there was a significant positive correlation between the NDVI and the Palmer Drought Severity Index(PDSI) during the past 349 yr, and they were mainly in phase. However, according to the results of correlation analysis between different grades of drought/wet and NDVI, there was significant asymmetry in extreme drought years and extreme wet years. In extreme drought years, NDVI was positively correlated with PDSI, and in extreme wet years they were negatively correlated.
基金Supported by the Major State Basic Research Development Program of China （973 Program） （2010CB428804） the National Science Foundation ot China （40672172） and the Major Science and Technology Program for Water Pollution Control and Treatment（2009ZX07212-003）
文摘Determinations of fracture network connections would help the investigators remove those ＂meaningless＂ no-flow-passing fractures, providing an updated and more effective fracture network that could considerably improve the computation efficiency in the pertinent numerical simulations of fluid flow and solute transport. The effective algorithms with higher computational efficiency are needed to accomplish this task in large-scale fractured rock masses. A new approach using R tree indexing was proposed for determining fracture connection in 3D stochastically distributed fracture network. By com- paring with the traditional exhaustion algorithm, it was observed that from the simulation results, this approach was much more effective; and the more the fractures were investigated, the more obvious the advantages of the approach were. Furthermore, it was indicated that the runtime used for creating the R tree indexing has a major part in the total of the runtime used for calculating Minimum Bounding Rectangles （MBRs）, creating the R tree indexing, precisely finding out fracture intersections, and identifying flow paths, which are four important steps to determine fracture connections. This proposed approach for the determination of fracture connections in three-dimensional fractured rocks are expected to provide efficient preprocessing and critical database for practically accomplishing numerical computation of fluid flow and solute transport in large-scale fractured rock masses.
基金supported by the NationalNatural Science Foundation of China(No.61862041).
文摘Existing speech retrieval systems are frequently confronted with expanding volumes of speech data.The dynamic updating strategy applied to construct the index can timely process to add or remove unnecessary speech data to meet users’real-time retrieval requirements.This study proposes an efficient method for retrieving encryption speech,using unsupervised deep hashing and B+ tree dynamic index,which avoid privacy leak-age of speech data and enhance the accuracy and efficiency of retrieval.The cloud’s encryption speech library is constructed by using the multi-threaded Dijk-Gentry-Halevi-Vaikuntanathan(DGHV)Fully Homomorphic Encryption(FHE)technique,which encrypts the original speech.In addition,this research employs Residual Neural Network18-Gated Recurrent Unit(ResNet18-GRU),which is used to learn the compact binary hash codes,store binary hash codes in the designed B+tree index table,and create a mapping relation of one to one between the binary hash codes and the corresponding encrypted speech.External B+tree index technology is applied to achieve dynamic index updating of the B+tree index table,thereby satisfying users’needs for real-time retrieval.The experimental results on THCHS-30 and TIMIT showed that the retrieval accuracy of the proposed method is more than 95.84%compared to the existing unsupervised hashing methods.The retrieval efficiency is greatly improved.Compared to the method of using hash index tables,and the speech data’s security is effectively guaranteed.
文摘In recent years, a growing number of math contents are available on the Web. When conventional search engines deal with mathematical expressions, the two-dimen- sion-al structure of mathematical expressions is lost, which results in a low performance of math retrieval. While the retrieval technology specifically designed for mathematical expressions is not mature currently. Aiming at these problems, an improved mathematical expression indexing and matching method was proposed through employing full text index method to deal with the two-dimensional structure of mathematical expressions. Firstly, through the fully consideration of LaTeX formulae’ characteristics, a feature representation method of mathematical expressions and a clustering method of feature keywords were put forward. Then, an improved inter-relevant successive trees index model was applied to the construction of the mathematical expression index, in which the cluster algorithm of mathematical expression features was employed to solve the problem of the quantity growth of the trees in processing large amount of formulae. Finally, the matching algorithms of mathematical expressions were given which provide four query modes called exact matching, compatible matching, sub-expression matching and fuzzy matching. In browser/server mode, 110027 formulae were used as experimental samples. The index file size was 29.02 Mb. The average time of retrieval was 1.092 seconds. The experimental result shows the effectiveness of the method.
基金supported by the National Natural Science Foundation of China(32101260).
文摘The number and composition of species in a community can be quantified withα-diversity indices,including species richness(R),Simpson’s index(D),and the Shannon-Wiener index(H΄).In forest communities,there are large variations in tree size among species and individu-als of the same species,which result in differences in eco-logical processes and ecosystem functions.However,tree size inequality(TSI)has been largely neglected in studies using the available diversity indices.The TSI in the diameter at breast height(DBH)data for each of 99920 m×20 m forest census quadrats was quantified using the Gini index(GI),a measure of the inequality of size distribution.The generalized performance equation was used to describe the rotated and right-shifted Lorenz curve of the cumulative proportion of DBH and the cumulative proportion of number of trees per quadrat.We also examined the relationships ofα-diversity indices with the GI using correlation tests.The generalized performance equation effectively described the rotated and right-shifted Lorenz curve of DBH distributions,with most root-mean-square errors(990 out of 999 quadrats)being<0.0030.There were significant positive correlations between each of threeα-diversity indices(i.e.,R,D,and H’)and the GI.Nevertheless,the total abundance of trees in each quadrat did not significantly influence the GI.This means that the TSI increased with increasing spe-cies diversity.Thus,two new indices are proposed that can balanceα-diversity against the extent of TSI in the com-munity:(1−GI)×D,and(1−GI)×H’.These new indices were significantly correlated with the original D and H΄,and did not increase the extent of variation within each group of indices.This study presents a useful tool for quantifying both species diversity and the variation in tree sizes in forest communities,especially in the face of cumulative species loss under global climate change.
文摘The exponential Randić index has important applications in the fields of biology and chemistry. The exponential Randić index of a graph G is defined as the sum of the weights e 1 d( u )d( v ) of all edges uv of G, where d( u ) denotes the degree of a vertex u in G. The paper mainly provides the upper and lower bounds of the exponential Randić index in quasi-tree graphs, and characterizes the extremal graphs when the bounds are achieved.
