A proper edge coloring of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G, denoted by a (G), is the least number of colors in an acyclic edge coloring of G. Alon...A proper edge coloring of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G, denoted by a (G), is the least number of colors in an acyclic edge coloring of G. Alon et al. conjectured that a (G) Δ(G) + 2 for any graphs. For planar graphs G with girth g(G), we prove that a (G) max{2Δ(G) + 2, Δ(G) + 22} if g(G) 3, a (G) Δ(G) + 2 if g(G) 5, a (G) Δ(G) + 1 if g(G) 7, and a (G) = Δ(G) if g(G) 16 and Δ(G) 3. For series-parallel graphs G, we have a (G) Δ(G) + 1.展开更多
Satellite observation scheduling plays a significant role in improving the efficiency of satellite observation systems.Although many scheduling algorithms have been proposed,emergency tasks,characterized as importance...Satellite observation scheduling plays a significant role in improving the efficiency of satellite observation systems.Although many scheduling algorithms have been proposed,emergency tasks,characterized as importance and urgency（e.g.,observation tasks orienting to the earthquake area and military conflict area）,have not been taken into account yet.Therefore,it is crucial to investigate the satellite integrated scheduling methods,which focus on meeting the requirements of emergency tasks while maximizing the profit of common tasks.Firstly,a pretreatment approach is proposed,which eliminates conflicts among emergency tasks and allocates all tasks with a potential time-window to related orbits of satellites.Secondly,a mathematical model and an acyclic directed graph model are constructed.Thirdly,a hybrid ant colony optimization method mixed with iteration local search（ACO-ILS） is established to solve the problem.Moreover,to guarantee all solutions satisfying the emergency task requirement constraints,a constraint repair method is presented.Extensive experimental simulations show that the proposed integrated scheduling method is superior to two-phased scheduling methods,the performance of ACO-ILS is greatly improved in both evolution speed and solution quality by iteration local search,and ACO-ILS outperforms both genetic algorithm and simulated annealing algorithm.展开更多
In the blockchain,the consensus mechanism plays a key role in maintaining the security and legitimation of contents recorded in the blocks.Various blockchain consensus mechanisms have been proposed.However,there is no...In the blockchain,the consensus mechanism plays a key role in maintaining the security and legitimation of contents recorded in the blocks.Various blockchain consensus mechanisms have been proposed.However,there is no technical analysis and comparison as a guideline to determine which type of consensus mechanism should be adopted in a specific scenario/application.To this end,this work investigates three mainstream consensus mechanisms in the blockchain,namely,Proof of Work(PoW),Proof of Stake(PoS),and Direct Acyclic Graph(DAG),and identifies their performances in terms of the average time to generate a new block,the confirmation delay,the Transaction Per Second(TPS)and the confirmation failure probability.The results show that the consensus process is affected by both network resource(computation power/coin age,buffer size)and network load conditions.In addition,it shows that PoW and PoS are more sensitive to the change of network resource while DAG is more sensitive to network load conditions.展开更多
A proper k-edge coloring of a graph G is called adjacent vertex distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the color set of edges incident to u is not equal to the color set of edges ...A proper k-edge coloring of a graph G is called adjacent vertex distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the color set of edges incident to u is not equal to the color set of edges incident to v, where uv ∈E（G）. The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by χ＇αα（G）, is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. In this paper we prove that if G（V, E） is a graph with no isolated edges, then χ＇αα（G）≤32△.展开更多
A series of new 2,5-disubstituted-l,3,4-oxadiazole and 1,2,4-triazole derivatives were synthesized by hetero- cyclization of acid hydrazide I and thiosemicarbazide derivative 2. Furthermore, the acyclic C-nucleoside a...A series of new 2,5-disubstituted-l,3,4-oxadiazole and 1,2,4-triazole derivatives were synthesized by hetero- cyclization of acid hydrazide I and thiosemicarbazide derivative 2. Furthermore, the acyclic C-nucleoside analogs were prepared by cyclization of their corresponding sugar hydrazones by reaction with acetic anhydride. The antimicrobial activity of the prepared compounds was evaluated and some of the synthesized compounds revealed good activities against fungi.展开更多
An acyclic edge coloring of a graph G is a proper edge coloring such that there are no bichromatic cycles in G.The acyclic chromatic index χ'α(G) of G is the smallest k such that G has an acyclic edge coloring u...An acyclic edge coloring of a graph G is a proper edge coloring such that there are no bichromatic cycles in G.The acyclic chromatic index χ'α(G) of G is the smallest k such that G has an acyclic edge coloring using k colors.It was conjectured that every simple graph G with maximum degree Δ has χ'_α(G) ≤Δ+2.A1-planar graph is a graph that can be drawn in the plane so that each edge is crossed by at most one other edge.In this paper,we show that every 1-planar graph G without 4-cycles has χ'_α(G)≤Δ+22.展开更多
A proper edge coloring of a graph G is called adjacent vertex-distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the coloring set of edges incident with u is not equal to the coloring set of ...A proper edge coloring of a graph G is called adjacent vertex-distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the coloring set of edges incident with u is not equal to the coloring set of edges incident with v, where uv∈ E（G）. The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by X＇Aa（G）, is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. If a graph G has an adjacent vertex distinguishing acyclic edge coloring, then G is called adjacent vertex distinguishing acyclic. In this paper, we obtain adjacent vertex-distinguishing acyclic edge coloring of some graphs and put forward some conjectures.展开更多
This paper presents a factoring algorithm for computing source-to- K terminal (SKT) reliability, the probability that a source s can send message to a specified set of terminals K, in acyclic directed networks (AD-net...This paper presents a factoring algorithm for computing source-to- K terminal (SKT) reliability, the probability that a source s can send message to a specified set of terminals K, in acyclic directed networks (AD-networks) in which both nodes and edges can fail. Based on Pivotal decomposition theorem, a new formula is derived for computing the SKT reliability of AD-networks. By establishing a topological property of AD-networks, it is shown that the SKT reliability of AD- networks can be computed by recursively applying this formula. Two new Reliability- Preserving Reductions are also introduced. The recursion tree generated by the presented algorithm has at most 2 leaf nodes, where V and K are the numbers of nodes and terminals, respectively, while C is the number of the nodes satisfying some specified conditions. The computation complexity of the new algorithm is O (E. V. 2) in the worst case, where E is the number of edges. For source-to-all-terminal (SAT) reliability, its computation complexity is O(E). Comparison of the new algorithm with the existing ones indicates that the new algorithm is more efficient for computing the SKT reliability of AD-networks.展开更多
By employing a fixed point theorem due to Ding, Park and Jung, some existence theorems of solutions for equilibrium problems with lower and upper bounds are proved in noncompact topological spaces. These results furth...By employing a fixed point theorem due to Ding, Park and Jung, some existence theorems of solutions for equilibrium problems with lower and upper bounds are proved in noncompact topological spaces. These results further answer the open problem raised by Isac, Sehgal and Singh under much weaker assumptions.展开更多
With the integration of distributed generation and the construction of cross-regional long-distance power grids, power systems become larger and more complex.They require faster computing speed and better scalability ...With the integration of distributed generation and the construction of cross-regional long-distance power grids, power systems become larger and more complex.They require faster computing speed and better scalability for power flow calculations to support unit dispatch.Based on the analysis of a variety of parallelization methods, this paper deploys the large-scale power flow calculation task on a cloud computing platform using resilient distributed datasets(RDDs).It optimizes a directed acyclic graph that is stored in the RDDs to solve the low performance problem of the MapReduce model.This paper constructs and simulates a power flow calculation on a large-scale power system based on standard IEEE test data.Experiments are conducted on Spark cluster which is deployed as a cloud computing platform.They show that the advantages of this method are not obvious at small scale, but the performance is superior to the stand-alone model and the MapReduce model for large-scale calculations.In addition, running time will be reduced when adding cluster nodes.Although not tested under practical conditions, this paper provides a new way of thinking about parallel power flow calculations in large-scale power systems.展开更多
A proper edge k-coloring is a mappingΦ:E(G)-→{1,2,...,k}such that any two adjacent edges receive different colors.A proper edge k-coloringΦof G is called acyclic if there are no bichromatic cycles in G.The acyclic ...A proper edge k-coloring is a mappingΦ:E(G)-→{1,2,...,k}such that any two adjacent edges receive different colors.A proper edge k-coloringΦof G is called acyclic if there are no bichromatic cycles in G.The acyclic chromatic index of G,denoted by Xa(G),is the smallest integer k such that G is acyclically edge k-colorable.In this paper,we show that if G is a plane graph without 4-,6-cycles and intersecting 3-cycles,△(G)≥9,then Xa(G)≤△(G)+1.展开更多
Difunctionalization of alkynes represents a powerful and straightforward approach to the synthesis of complex molecules.However,the radical difunctionalization of alkynes mediated by bifunctional reagents remains chal...Difunctionalization of alkynes represents a powerful and straightforward approach to the synthesis of complex molecules.However,the radical difunctionalization of alkynes mediated by bifunctional reagents remains challenging and underexplored,despite significant progress having been made in alkene difunctionalization.Here,we report a novel arylsulfonylacetate skeleton in which aryl rings are attached to acetates through SO_(2),serving as a powerful bifunctional reagent for the alkylarylation of alkynes via vinyl-radical intermediate under photoredox conditions.This modular bifunctional reagent enables the simultaneous incorporation of a wide range of functional groups,including(hetero)aryl ring and alkyl carboxylate into alkynes,resulting in synthetically valuable all-carbon tetrasubstituted alkene derivatives.This transformation is distinguished by its redox-neutral nature,readily accessible starting materials,compatibility with diverse functional groups and its capacity to facilitate convergent synthesis.The utility of this approach was further demonstrated by the late-stage functionalization of complex molecules and the preparation of fluorescent molecules and anti-cancer drugs.展开更多
A proper vertex coloring of a graph G is acyclic if G contains no bicolored cycles.Given a list assignment L={L(v)|v∈V}of G,we say that G is acyclically L-colorable if there exists a proper acyclic coloringπof G suc...A proper vertex coloring of a graph G is acyclic if G contains no bicolored cycles.Given a list assignment L={L(v)|v∈V}of G,we say that G is acyclically L-colorable if there exists a proper acyclic coloringπof G such thatπ(v)∈L(v)for all v∈V.If G is acyclically L-colorable for any list assignment L with|L(v)|k for all v∈V(G),then G is acyclically k-choosable.In this paper,we prove that every planar graph G is acyclically 6-choosable if G does not contain 4-cycles adjacent to i-cycles for each i∈{3,4,5,6}.This improves the result by Wang and Chen(2009).展开更多
A proper edge coloring of a graph G is acyclic if there is no 2-colored cycle in G. The acyclic chromatic index of G, denoted by X＇a（G）, is the least number of colors such that G has an acyclic edge coloring. A gra...A proper edge coloring of a graph G is acyclic if there is no 2-colored cycle in G. The acyclic chromatic index of G, denoted by X＇a（G）, is the least number of colors such that G has an acyclic edge coloring. A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that X＇a（G） ≤△ A（G）＋ 22, if G is a triangle-free 1-planar graph.展开更多
Machine learning has a powerful potential for performing the template attack(TA) of cryptographic device. To improve the accuracy and time consuming of electromagnetic template attack(ETA), a multi-class directed acyc...Machine learning has a powerful potential for performing the template attack(TA) of cryptographic device. To improve the accuracy and time consuming of electromagnetic template attack(ETA), a multi-class directed acyclic graph support vector machine(DAGSVM) method is proposed to predict the Hamming weight of the key. The method needs to generate K(K ? 1)/2 binary support vector machine(SVM) classifiers and realizes the K-class prediction using a rooted binary directed acyclic graph(DAG) testing model. Further, particle swarm optimization(PSO) is used for optimal selection of DAGSVM model parameters to improve the performance of DAGSVM. By exploiting the electromagnetic emanations captured while a chip was implementing the RC4 algorithm in software, the computation complexity and performance of several multi-class machine learning methods, such as DAGSVM, one-versus-one(OVO)SVM, one-versus-all(OVA)SVM, Probabilistic neural networks(PNN), K-means clustering and fuzzy neural network(FNN) are investigated. In the same scenario, the highest classification accuracy of Hamming weight for the key reached 100%, 95.33%, 85%, 74%, 49.67% and 38% for DAGSVM, OVOSVM, OVASVM, PNN, K-means and FNN, respectively. The experiment results demonstrate the proposed model performs higher predictive accuracy and faster convergence speed.展开更多
Let R and S be Artin algebras and F be their triangular matrix extension via a bimodule sMR. We study totally acyclic complexes of projective F-modules and obtain a complete description of Gorenstein projective F-modu...Let R and S be Artin algebras and F be their triangular matrix extension via a bimodule sMR. We study totally acyclic complexes of projective F-modules and obtain a complete description of Gorenstein projective F-modules. We then construct some examples of Cohen-Macaulay finite and virtually Gorenstein triangular matrix algebras.展开更多
A proper edge colouring f of a graph G is called acyclic if there are no bichromatic cycles in the graph. The acyclic edge chromatic number or acyclic chromatic index, denoted by , is the minimum number of colours in ...A proper edge colouring f of a graph G is called acyclic if there are no bichromatic cycles in the graph. The acyclic edge chromatic number or acyclic chromatic index, denoted by , is the minimum number of colours in an acyclic edge colouring of G. In this paper, we discuss the acyclic edge colouring of middle, central, total and line graphs of prime related star graph families. Also exact values of acyclic chromatic indices of such graphs are derived and some of their structural properties are discussed.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 10871119)NaturalScience Foundation of Shandong Province (Grant No. Y2008A20).
文摘A proper edge coloring of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G, denoted by a (G), is the least number of colors in an acyclic edge coloring of G. Alon et al. conjectured that a (G) Δ(G) + 2 for any graphs. For planar graphs G with girth g(G), we prove that a (G) max{2Δ(G) + 2, Δ(G) + 22} if g(G) 3, a (G) Δ(G) + 2 if g(G) 5, a (G) Δ(G) + 1 if g(G) 7, and a (G) = Δ(G) if g(G) 16 and Δ(G) 3. For series-parallel graphs G, we have a (G) Δ(G) + 1.
基金supported by the National Natural Science Foundation of China (61104180)the National Basic Research Program of China(973 Program) (97361361)
文摘Satellite observation scheduling plays a significant role in improving the efficiency of satellite observation systems.Although many scheduling algorithms have been proposed,emergency tasks,characterized as importance and urgency（e.g.,observation tasks orienting to the earthquake area and military conflict area）,have not been taken into account yet.Therefore,it is crucial to investigate the satellite integrated scheduling methods,which focus on meeting the requirements of emergency tasks while maximizing the profit of common tasks.Firstly,a pretreatment approach is proposed,which eliminates conflicts among emergency tasks and allocates all tasks with a potential time-window to related orbits of satellites.Secondly,a mathematical model and an acyclic directed graph model are constructed.Thirdly,a hybrid ant colony optimization method mixed with iteration local search（ACO-ILS） is established to solve the problem.Moreover,to guarantee all solutions satisfying the emergency task requirement constraints,a constraint repair method is presented.Extensive experimental simulations show that the proposed integrated scheduling method is superior to two-phased scheduling methods,the performance of ACO-ILS is greatly improved in both evolution speed and solution quality by iteration local search,and ACO-ILS outperforms both genetic algorithm and simulated annealing algorithm.
基金the National Natural Science Foundation of China under Grant 61701059,Grant 61941114,and Grant 61831002,in part by the Fundamental Research Funds for the Central Universities of New TeachersProject,in part by the Chongqing Technological Innovation and Application Development Projects under Grant cstc2019jscx-msxm1322,and in part by the Eighteentg Open Foundation of State Key Lab of Integrated Services Networks of Xidian University under Grant ISN20-05.
文摘In the blockchain,the consensus mechanism plays a key role in maintaining the security and legitimation of contents recorded in the blocks.Various blockchain consensus mechanisms have been proposed.However,there is no technical analysis and comparison as a guideline to determine which type of consensus mechanism should be adopted in a specific scenario/application.To this end,this work investigates three mainstream consensus mechanisms in the blockchain,namely,Proof of Work(PoW),Proof of Stake(PoS),and Direct Acyclic Graph(DAG),and identifies their performances in terms of the average time to generate a new block,the confirmation delay,the Transaction Per Second(TPS)and the confirmation failure probability.The results show that the consensus process is affected by both network resource(computation power/coin age,buffer size)and network load conditions.In addition,it shows that PoW and PoS are more sensitive to the change of network resource while DAG is more sensitive to network load conditions.
基金Supported by the Natural Science Foundation of Gansu Province(3ZS051-A25-025)
文摘A proper k-edge coloring of a graph G is called adjacent vertex distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the color set of edges incident to u is not equal to the color set of edges incident to v, where uv ∈E（G）. The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by χ＇αα（G）, is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. In this paper we prove that if G（V, E） is a graph with no isolated edges, then χ＇αα（G）≤32△.
文摘A series of new 2,5-disubstituted-l,3,4-oxadiazole and 1,2,4-triazole derivatives were synthesized by hetero- cyclization of acid hydrazide I and thiosemicarbazide derivative 2. Furthermore, the acyclic C-nucleoside analogs were prepared by cyclization of their corresponding sugar hydrazones by reaction with acetic anhydride. The antimicrobial activity of the prepared compounds was evaluated and some of the synthesized compounds revealed good activities against fungi.
基金Research supported by the National Natural Science Foundation of China (No.12031018)Research supported by the National Natural Science Foundation of China (No.12071048)+3 种基金Research supported by the National Natural Science Foundation of China(No.12071351)Science and Technology Commission of Shanghai Municipality (No.18dz2271000)Doctoral Scientific Research Foundation of Weifang University (No.2021BS01)Natural Science Foundation of Shandong Province (No.ZR2022MA060)。
文摘An acyclic edge coloring of a graph G is a proper edge coloring such that there are no bichromatic cycles in G.The acyclic chromatic index χ'α(G) of G is the smallest k such that G has an acyclic edge coloring using k colors.It was conjectured that every simple graph G with maximum degree Δ has χ'_α(G) ≤Δ+2.A1-planar graph is a graph that can be drawn in the plane so that each edge is crossed by at most one other edge.In this paper,we show that every 1-planar graph G without 4-cycles has χ'_α(G)≤Δ+22.
基金supported by NSFC of China (No. 19871036 and No. 40301037)Faculty Research Grant,Hong Kong Baptist University
文摘A proper edge coloring of a graph G is called adjacent vertex-distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the coloring set of edges incident with u is not equal to the coloring set of edges incident with v, where uv∈ E（G）. The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by X＇Aa（G）, is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. If a graph G has an adjacent vertex distinguishing acyclic edge coloring, then G is called adjacent vertex distinguishing acyclic. In this paper, we obtain adjacent vertex-distinguishing acyclic edge coloring of some graphs and put forward some conjectures.
文摘This paper presents a factoring algorithm for computing source-to- K terminal (SKT) reliability, the probability that a source s can send message to a specified set of terminals K, in acyclic directed networks (AD-networks) in which both nodes and edges can fail. Based on Pivotal decomposition theorem, a new formula is derived for computing the SKT reliability of AD-networks. By establishing a topological property of AD-networks, it is shown that the SKT reliability of AD- networks can be computed by recursively applying this formula. Two new Reliability- Preserving Reductions are also introduced. The recursion tree generated by the presented algorithm has at most 2 leaf nodes, where V and K are the numbers of nodes and terminals, respectively, while C is the number of the nodes satisfying some specified conditions. The computation complexity of the new algorithm is O (E. V. 2) in the worst case, where E is the number of edges. For source-to-all-terminal (SAT) reliability, its computation complexity is O(E). Comparison of the new algorithm with the existing ones indicates that the new algorithm is more efficient for computing the SKT reliability of AD-networks.
文摘By employing a fixed point theorem due to Ding, Park and Jung, some existence theorems of solutions for equilibrium problems with lower and upper bounds are proved in noncompact topological spaces. These results further answer the open problem raised by Isac, Sehgal and Singh under much weaker assumptions.
基金supported by National Natural Science Foundation of China (No.51677072)
文摘With the integration of distributed generation and the construction of cross-regional long-distance power grids, power systems become larger and more complex.They require faster computing speed and better scalability for power flow calculations to support unit dispatch.Based on the analysis of a variety of parallelization methods, this paper deploys the large-scale power flow calculation task on a cloud computing platform using resilient distributed datasets(RDDs).It optimizes a directed acyclic graph that is stored in the RDDs to solve the low performance problem of the MapReduce model.This paper constructs and simulates a power flow calculation on a large-scale power system based on standard IEEE test data.Experiments are conducted on Spark cluster which is deployed as a cloud computing platform.They show that the advantages of this method are not obvious at small scale, but the performance is superior to the stand-alone model and the MapReduce model for large-scale calculations.In addition, running time will be reduced when adding cluster nodes.Although not tested under practical conditions, this paper provides a new way of thinking about parallel power flow calculations in large-scale power systems.
文摘A proper edge k-coloring is a mappingΦ:E(G)-→{1,2,...,k}such that any two adjacent edges receive different colors.A proper edge k-coloringΦof G is called acyclic if there are no bichromatic cycles in G.The acyclic chromatic index of G,denoted by Xa(G),is the smallest integer k such that G is acyclically edge k-colorable.In this paper,we show that if G is a plane graph without 4-,6-cycles and intersecting 3-cycles,△(G)≥9,then Xa(G)≤△(G)+1.
基金supported by the National Natural Science Foundation of China(21901199)Xi’an Jiaotong University(7121192002)。
文摘Difunctionalization of alkynes represents a powerful and straightforward approach to the synthesis of complex molecules.However,the radical difunctionalization of alkynes mediated by bifunctional reagents remains challenging and underexplored,despite significant progress having been made in alkene difunctionalization.Here,we report a novel arylsulfonylacetate skeleton in which aryl rings are attached to acetates through SO_(2),serving as a powerful bifunctional reagent for the alkylarylation of alkynes via vinyl-radical intermediate under photoredox conditions.This modular bifunctional reagent enables the simultaneous incorporation of a wide range of functional groups,including(hetero)aryl ring and alkyl carboxylate into alkynes,resulting in synthetically valuable all-carbon tetrasubstituted alkene derivatives.This transformation is distinguished by its redox-neutral nature,readily accessible starting materials,compatibility with diverse functional groups and its capacity to facilitate convergent synthesis.The utility of this approach was further demonstrated by the late-stage functionalization of complex molecules and the preparation of fluorescent molecules and anti-cancer drugs.
基金supported by National Natural Science Foundation of China (Grant Nos. 11071223 and 11101377)Natural Science Foundation of Zhejiang Province,China (Gran No. Z6090150)+1 种基金Zhejiang Innovation Project (Grant No. T200905)Zhejiang Normal University Innovation Team Program
文摘A proper vertex coloring of a graph G is acyclic if G contains no bicolored cycles.Given a list assignment L={L(v)|v∈V}of G,we say that G is acyclically L-colorable if there exists a proper acyclic coloringπof G such thatπ(v)∈L(v)for all v∈V.If G is acyclically L-colorable for any list assignment L with|L(v)|k for all v∈V(G),then G is acyclically k-choosable.In this paper,we prove that every planar graph G is acyclically 6-choosable if G does not contain 4-cycles adjacent to i-cycles for each i∈{3,4,5,6}.This improves the result by Wang and Chen(2009).
基金Supported by National Natural Science Foundation of China(Grant No.11271365)
文摘A proper edge coloring of a graph G is acyclic if there is no 2-colored cycle in G. The acyclic chromatic index of G, denoted by X＇a（G）, is the least number of colors such that G has an acyclic edge coloring. A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that X＇a（G） ≤△ A（G）＋ 22, if G is a triangle-free 1-planar graph.
基金supported by the National Natural Science Foundation of China(61571063,61202399,61171051)
文摘Machine learning has a powerful potential for performing the template attack(TA) of cryptographic device. To improve the accuracy and time consuming of electromagnetic template attack(ETA), a multi-class directed acyclic graph support vector machine(DAGSVM) method is proposed to predict the Hamming weight of the key. The method needs to generate K(K ? 1)/2 binary support vector machine(SVM) classifiers and realizes the K-class prediction using a rooted binary directed acyclic graph(DAG) testing model. Further, particle swarm optimization(PSO) is used for optimal selection of DAGSVM model parameters to improve the performance of DAGSVM. By exploiting the electromagnetic emanations captured while a chip was implementing the RC4 algorithm in software, the computation complexity and performance of several multi-class machine learning methods, such as DAGSVM, one-versus-one(OVO)SVM, one-versus-all(OVA)SVM, Probabilistic neural networks(PNN), K-means clustering and fuzzy neural network(FNN) are investigated. In the same scenario, the highest classification accuracy of Hamming weight for the key reached 100%, 95.33%, 85%, 74%, 49.67% and 38% for DAGSVM, OVOSVM, OVASVM, PNN, K-means and FNN, respectively. The experiment results demonstrate the proposed model performs higher predictive accuracy and faster convergence speed.
文摘Let R and S be Artin algebras and F be their triangular matrix extension via a bimodule sMR. We study totally acyclic complexes of projective F-modules and obtain a complete description of Gorenstein projective F-modules. We then construct some examples of Cohen-Macaulay finite and virtually Gorenstein triangular matrix algebras.
文摘A proper edge colouring f of a graph G is called acyclic if there are no bichromatic cycles in the graph. The acyclic edge chromatic number or acyclic chromatic index, denoted by , is the minimum number of colours in an acyclic edge colouring of G. In this paper, we discuss the acyclic edge colouring of middle, central, total and line graphs of prime related star graph families. Also exact values of acyclic chromatic indices of such graphs are derived and some of their structural properties are discussed.
