This article investigates the time-varying output group formation tracking control(GFTC)problem for heterogeneous multi-agent systems(HMASs)under switching topologies.The objective is to design a distributed control s...This article investigates the time-varying output group formation tracking control(GFTC)problem for heterogeneous multi-agent systems(HMASs)under switching topologies.The objective is to design a distributed control strategy that enables the outputs of the followers to form the desired sub-formations and track the outputs of the leader in each subgroup.Firstly,novel distributed observers are developed to estimate the states of the leaders under switching topologies.Then,GFTC protocols are designed based on the proposed observers.It is shown that with the distributed protocol,the GFTC problem for HMASs under switching topologies is solved if the average dwell time associated with the switching topologies is larger than a fixed threshold.Finally,an example is provided to illustrate the effectiveness of the proposed control strategy.展开更多
In this paper, we prove that if a torsion nilpotent group G is a weak semi-radicable group, then every Sylow p-group Gp is a central-by-finite p-group, and moreover Gp's center ζ(GP) satisfies |ζ(GP) : (ζ(GP))P...In this paper, we prove that if a torsion nilpotent group G is a weak semi-radicable group, then every Sylow p-group Gp is a central-by-finite p-group, and moreover Gp's center ζ(GP) satisfies |ζ(GP) : (ζ(GP))P| <∞, that is, ζ(GP) = D×F, where D is a divisible Abelian group, and F is a finite Abelian group.展开更多
Neuroscience (also known as neurobiology) is a science that studies the structure, function, development, pharmacology and pathology of the nervous system. In recent years, C. Cotardo has introduced coding theory into...Neuroscience (also known as neurobiology) is a science that studies the structure, function, development, pharmacology and pathology of the nervous system. In recent years, C. Cotardo has introduced coding theory into neuroscience, proposing the concept of combinatorial neural codes. And it was further studied in depth using algebraic methods by C. Curto. In this paper, we construct a class of combinatorial neural codes with special properties based on classical combinatorial structures such as orthogonal Latin rectangle, disjoint Steiner systems, groupable designs and transversal designs. These neural codes have significant weight distribution properties and large minimum distances, and are thus valuable for potential applications in information representation and neuroscience. This study provides new ideas for the construction method and property analysis of combinatorial neural codes, and enriches the study of algebraic coding theory.展开更多
Let ARDkCS（v） denote an almost resolvable directed k-cycle system of order v. It is clear that a necessary condition for the existence of an ARDkCS（v） is v=1（mod k）. For k：3,4,5 and 6, the existence of an ARDk...Let ARDkCS（v） denote an almost resolvable directed k-cycle system of order v. It is clear that a necessary condition for the existence of an ARDkCS（v） is v=1（mod k）. For k：3,4,5 and 6, the existence of an ARDkCS （v） had been completely solved. This paper shows that there exists an ARD7CS（v） if and only if v≡1 （rood 7） and v≥8.展开更多
Low-density parity-check （LDPC） codes were first presented by Gallager in 1962. They are linear block codes and their bit error rate （BER） performance approaches remarkably close to the Shannon limit. The LDPC cod...Low-density parity-check （LDPC） codes were first presented by Gallager in 1962. They are linear block codes and their bit error rate （BER） performance approaches remarkably close to the Shannon limit. The LDPC codes created much interest after the rediscovery by Mackay and Neal in 1995. This paper introduces some new LDPC codes by considering some combinatorial structures. We present regular LDPC codes based on group divisible designs which have Tanner graphs free of four-cycles.展开更多
The intersection problem for kite-GDDs is the determination of all pairs(T,s)such that there exists a pair of kite-GDDs(X,H,B_(1))and(X,H,B_(2))of the same type T satisfying|B_(1)∩B_(2)|=s.In this paper the intersect...The intersection problem for kite-GDDs is the determination of all pairs(T,s)such that there exists a pair of kite-GDDs(X,H,B_(1))and(X,H,B_(2))of the same type T satisfying|B_(1)∩B_(2)|=s.In this paper the intersection problem for a pair of kite-GDDs of type 2^(u)is investigated.Let J(u)={s:■a pair of kite-GDDs of type 2^(u)intersecting in s blocks};I(u)={0,1,...,b_(u)-2,b_(u)},where b_(u)=u(u-1)/2 is the number of blocks of a kite-GDD of type 2^(u).We show that for any positive integer u≥4,J(u)=I(u)and J(3)={0,3}.展开更多
High complexity and high latency are key problems for multiuser detection （MUD） to be applied to a mobile station in cellular networks. To tackle these problems, an interleave division multiple access （IDMA） based...High complexity and high latency are key problems for multiuser detection （MUD） to be applied to a mobile station in cellular networks. To tackle these problems, an interleave division multiple access （IDMA） based multiple access scheme, grouped spread IDMA （GSIDMA）, is proposed. In a GSIDMA system, lower complexity and latency for mobile stations can be achieved by appropriately dividing active users into different groups. The system model of GSIDMA is constructed and followed by analysing on its system capacity, complexity and latency, and bit error rate （BER） performance. The extrinsic information transfer （EXIT） chart is used to analyze the convergence behavior of the iteration process. The grouping method and interleavers-reuse issue for GSIDMA are also discussed preliminarily. The analyses and simulation results indicate that the complexity and latency of the proposed scheme are much lower than those of IDMA, whereas its BER performance is close to the latter. The properties of low complexity and low latency make it more feasible for the practical implementation.展开更多
In this paper, we investigate the existence of incomplete group divisible designs （IGDDs） with block size four, group-type （g, h） u and general index λ. The necessary conditions for the existence of such a design...In this paper, we investigate the existence of incomplete group divisible designs （IGDDs） with block size four, group-type （g, h） u and general index λ. The necessary conditions for the existence of such a design are that u ≥ 4, g ≥ 3h, λg（u 1） ≡ 0 （mod 3）, λ（g h）（u 1） ≡ 0 （mod 3）, and λu（u 1）（g 2 h 2 ） ≡ 0 （mod 12）. These necessary conditions are shown to be sufficient for all λ≥ 2. The known existence result for λ = 1 is also improved.展开更多
In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super- simple group divisible designs are useful in constructing other types ...In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super- simple group divisible designs are useful in constructing other types of super- simple designs which can be applied to codes and designs. In this article, the existence of a super-simple （5, 4）-GDD of group type gU is investigated and it is shown that such a design exists if and only if u ≥ 5, g（u - 2） ≥ 12, and u（u - 1）g^2≡ 0 （mod 5） with some possible exceptions.展开更多
In an anonymous secret sharing scheme the secret can be reconstructed without knowledge of which participants hold which shares. In this paper some constructions of anonymous secret sharing schemes with 2 thresholds b...In an anonymous secret sharing scheme the secret can be reconstructed without knowledge of which participants hold which shares. In this paper some constructions of anonymous secret sharing schemes with 2 thresholds by using combinatorial designs are given. Let v（t, w, q） denote the minimum size of the set of shares of a perfect anonymous （t, w） threshold secret sharing scheme with q secrets. In this paper we prove that v（t, w, q） - Θ（q） if t and w are fixed and that the lower bound of the size of the set of shares in [4] is not optimal under certain condition.展开更多
A Mendelsohn triple system of order v,MTS(v)for short,is a pair(X,B)where X is a v-set(of points)and B is a collection of cyclic triples on X such that every ordered pair of distinct points from X appears in exactly o...A Mendelsohn triple system of order v,MTS(v)for short,is a pair(X,B)where X is a v-set(of points)and B is a collection of cyclic triples on X such that every ordered pair of distinct points from X appears in exactly one cyclic triple of B.The cyclic triple(a,b,c)contains the ordered pairs(a,b),(b,c)and(c,a).An MTS(v)corresponds to an idempotent semisymmetric Latin square (quasigroup)of order v.An MTS(v)is called frame self-orthogonal,FSOMTS for short,if its associated semisymmetric Latin square is frame self-orthogonal.It is known that an FSOMTS(1~n)exists for all n≡1(mod 3)except n=10 and for all n≥15,n≡0(mod 3)with possible exception that n=18.In this paper,it is shown that(i)an FSOMTS(2~n)exists if and only if n≡0,1(mod 3)and n>5 with possible exceptions n ∈{9,27,33,39};(ii)an FSOMTS(3~n)exists if and only if n≥4,with possible exceptions that n ∈{6,14,18,19}.展开更多
Let v be a positive integer and let K be a set of positive integers. A （v, K, 1）-Mendelsohn design, which we denote briefly by （v, K, 1）-MD, is a pair （X, B） where X is a v-set （of points） and B is a collectio...Let v be a positive integer and let K be a set of positive integers. A （v, K, 1）-Mendelsohn design, which we denote briefly by （v, K, 1）-MD, is a pair （X, B） where X is a v-set （of points） and B is a collection of cyclically ordered subsets of X （called blocks） with sizes in the set K such that every ordered pair of points of X are consecutive in exactly one block of B. If for all t =1, 2,..., r, every ordered pair of points of X are t-apart in exactly one block of B, then the （v, K, 1）-MD is called an r-fold perfect design and denoted briefly by an r-fold perfect （v, K, 1）-MD. If K = {k） and r = k - 1, then an r-fold perfect （v, （k）, 1）-MD is essentially the more familiar （v, k, 1）-perfect Mendelsohn design, which is briefly denoted by （v, k, 1）-PMD. In this paper, we investigate the existence of 4-fold perfect （v, （5, 8}, 1）-Mendelsohn designs.展开更多
A Latin squares of order v with ni missing sub-Latin squares （holes） of order hi （1 〈= i 〈 k）, which are disjoint and spanning （i.e. ∑k i=l1 nihi = v）, is called a partitioned incomplete Latin squares and de...A Latin squares of order v with ni missing sub-Latin squares （holes） of order hi （1 〈= i 〈 k）, which are disjoint and spanning （i.e. ∑k i=l1 nihi = v）, is called a partitioned incomplete Latin squares and denoted by PILS. The type of PILS is defined by （h1n1 h2n2…hknk ）. If any two PILS inaset of t PILS of type T are orthogonal, then we denote the set by t-HMOLS（T）. It has been proved that 3-HMOLS（2n31） exist for n ≥6 with 11 possible exceptions. In this paper, we investigate the existence of 3-HMOLS（2nu1） with u ≥ 4, and prove that 3-HMOLS（2~u1） exist if n ≥ 54 and n ≥7/4u ＋ 7.展开更多
In this paper, we give some constructions of self-conjugate self-orthogonal diagonal Latinsquares (SCSODLS). As an application of such constructions we disproof the conjecture aboutSCSODLS and show that there exist SC...In this paper, we give some constructions of self-conjugate self-orthogonal diagonal Latinsquares (SCSODLS). As an application of such constructions we disproof the conjecture aboutSCSODLS and show that there exist SCSODLS of order V, whenever w=1 (mod 12), with thepossible exception of v∈ {13, 85, 133}.展开更多
文摘This article investigates the time-varying output group formation tracking control(GFTC)problem for heterogeneous multi-agent systems(HMASs)under switching topologies.The objective is to design a distributed control strategy that enables the outputs of the followers to form the desired sub-formations and track the outputs of the leader in each subgroup.Firstly,novel distributed observers are developed to estimate the states of the leaders under switching topologies.Then,GFTC protocols are designed based on the proposed observers.It is shown that with the distributed protocol,the GFTC problem for HMASs under switching topologies is solved if the average dwell time associated with the switching topologies is larger than a fixed threshold.Finally,an example is provided to illustrate the effectiveness of the proposed control strategy.
文摘In this paper, we prove that if a torsion nilpotent group G is a weak semi-radicable group, then every Sylow p-group Gp is a central-by-finite p-group, and moreover Gp's center ζ(GP) satisfies |ζ(GP) : (ζ(GP))P| <∞, that is, ζ(GP) = D×F, where D is a divisible Abelian group, and F is a finite Abelian group.
文摘Neuroscience (also known as neurobiology) is a science that studies the structure, function, development, pharmacology and pathology of the nervous system. In recent years, C. Cotardo has introduced coding theory into neuroscience, proposing the concept of combinatorial neural codes. And it was further studied in depth using algebraic methods by C. Curto. In this paper, we construct a class of combinatorial neural codes with special properties based on classical combinatorial structures such as orthogonal Latin rectangle, disjoint Steiner systems, groupable designs and transversal designs. These neural codes have significant weight distribution properties and large minimum distances, and are thus valuable for potential applications in information representation and neuroscience. This study provides new ideas for the construction method and property analysis of combinatorial neural codes, and enriches the study of algebraic coding theory.
基金Natural Science Research Leading Item ofJiangsu (No.04 DJ110144) Natural Out-standing Younger Science Foundation(No.60225007)and Postdoctoral ScienceFoundation of China(No.20020248024)
文摘Let ARDkCS（v） denote an almost resolvable directed k-cycle system of order v. It is clear that a necessary condition for the existence of an ARDkCS（v） is v=1（mod k）. For k：3,4,5 and 6, the existence of an ARDkCS （v） had been completely solved. This paper shows that there exists an ARD7CS（v） if and only if v≡1 （rood 7） and v≥8.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1107105611201114)
文摘Low-density parity-check （LDPC） codes were first presented by Gallager in 1962. They are linear block codes and their bit error rate （BER） performance approaches remarkably close to the Shannon limit. The LDPC codes created much interest after the rediscovery by Mackay and Neal in 1995. This paper introduces some new LDPC codes by considering some combinatorial structures. We present regular LDPC codes based on group divisible designs which have Tanner graphs free of four-cycles.
基金Supported by the National Natural Science Foundation of China(Grant No.11601137)the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Grant Nos.NJZY19231,NJZZ21052).
文摘The intersection problem for kite-GDDs is the determination of all pairs(T,s)such that there exists a pair of kite-GDDs(X,H,B_(1))and(X,H,B_(2))of the same type T satisfying|B_(1)∩B_(2)|=s.In this paper the intersection problem for a pair of kite-GDDs of type 2^(u)is investigated.Let J(u)={s:■a pair of kite-GDDs of type 2^(u)intersecting in s blocks};I(u)={0,1,...,b_(u)-2,b_(u)},where b_(u)=u(u-1)/2 is the number of blocks of a kite-GDD of type 2^(u).We show that for any positive integer u≥4,J(u)=I(u)and J(3)={0,3}.
基金supported by the National Natural Science Foundation of China (61171180)the National Basic Resaearch Program (923 Program) (2007CB31(0606))the Natural Sientific Research Innovation Foundation in Harbin Institute of Technology (HIT. NSRIF20011117)
文摘High complexity and high latency are key problems for multiuser detection （MUD） to be applied to a mobile station in cellular networks. To tackle these problems, an interleave division multiple access （IDMA） based multiple access scheme, grouped spread IDMA （GSIDMA）, is proposed. In a GSIDMA system, lower complexity and latency for mobile stations can be achieved by appropriately dividing active users into different groups. The system model of GSIDMA is constructed and followed by analysing on its system capacity, complexity and latency, and bit error rate （BER） performance. The extrinsic information transfer （EXIT） chart is used to analyze the convergence behavior of the iteration process. The grouping method and interleavers-reuse issue for GSIDMA are also discussed preliminarily. The analyses and simulation results indicate that the complexity and latency of the proposed scheme are much lower than those of IDMA, whereas its BER performance is close to the latter. The properties of low complexity and low latency make it more feasible for the practical implementation.
基金Supported by the National Natural Science Foundation of China (No. 10571043, 10771051, 11001182, 10901051)
文摘In this paper, we investigate the existence of incomplete group divisible designs （IGDDs） with block size four, group-type （g, h） u and general index λ. The necessary conditions for the existence of such a design are that u ≥ 4, g ≥ 3h, λg（u 1） ≡ 0 （mod 3）, λ（g h）（u 1） ≡ 0 （mod 3）, and λu（u 1）（g 2 h 2 ） ≡ 0 （mod 12）. These necessary conditions are shown to be sufficient for all λ≥ 2. The known existence result for λ = 1 is also improved.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11371121, 11371308, 11201114, 11301457）.
文摘In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super- simple group divisible designs are useful in constructing other types of super- simple designs which can be applied to codes and designs. In this article, the existence of a super-simple （5, 4）-GDD of group type gU is investigated and it is shown that such a design exists if and only if u ≥ 5, g（u - 2） ≥ 12, and u（u - 1）g^2≡ 0 （mod 5） with some possible exceptions.
基金Supported by the National Natural Science Foundation of China(No.10501049,90304012) 973 Project(No.2004CB318000)
文摘In an anonymous secret sharing scheme the secret can be reconstructed without knowledge of which participants hold which shares. In this paper some constructions of anonymous secret sharing schemes with 2 thresholds by using combinatorial designs are given. Let v（t, w, q） denote the minimum size of the set of shares of a perfect anonymous （t, w） threshold secret sharing scheme with q secrets. In this paper we prove that v（t, w, q） - Θ（q） if t and w are fixed and that the lower bound of the size of the set of shares in [4] is not optimal under certain condition.
基金Research supported by NSFC 10371002Partially supported by National Science Foundation under Grant CCR-0098093
文摘A Mendelsohn triple system of order v,MTS(v)for short,is a pair(X,B)where X is a v-set(of points)and B is a collection of cyclic triples on X such that every ordered pair of distinct points from X appears in exactly one cyclic triple of B.The cyclic triple(a,b,c)contains the ordered pairs(a,b),(b,c)and(c,a).An MTS(v)corresponds to an idempotent semisymmetric Latin square (quasigroup)of order v.An MTS(v)is called frame self-orthogonal,FSOMTS for short,if its associated semisymmetric Latin square is frame self-orthogonal.It is known that an FSOMTS(1~n)exists for all n≡1(mod 3)except n=10 and for all n≥15,n≡0(mod 3)with possible exception that n=18.In this paper,it is shown that(i)an FSOMTS(2~n)exists if and only if n≡0,1(mod 3)and n>5 with possible exceptions n ∈{9,27,33,39};(ii)an FSOMTS(3~n)exists if and only if n≥4,with possible exceptions that n ∈{6,14,18,19}.
基金supported by National Natural Science Foundation of China (Grant No.60873267)Zhejiang Provincial Natural Science Foundation of China (Grant No. Y607026)+1 种基金 sponsored by K. C. Wong Magna Fund in Ningbo Universitythe third author is supported by NSERC Grant OGP 0005320
文摘Let v be a positive integer and let K be a set of positive integers. A （v, K, 1）-Mendelsohn design, which we denote briefly by （v, K, 1）-MD, is a pair （X, B） where X is a v-set （of points） and B is a collection of cyclically ordered subsets of X （called blocks） with sizes in the set K such that every ordered pair of points of X are consecutive in exactly one block of B. If for all t =1, 2,..., r, every ordered pair of points of X are t-apart in exactly one block of B, then the （v, K, 1）-MD is called an r-fold perfect design and denoted briefly by an r-fold perfect （v, K, 1）-MD. If K = {k） and r = k - 1, then an r-fold perfect （v, （k）, 1）-MD is essentially the more familiar （v, k, 1）-perfect Mendelsohn design, which is briefly denoted by （v, k, 1）-PMD. In this paper, we investigate the existence of 4-fold perfect （v, （5, 8}, 1）-Mendelsohn designs.
基金Research supported by National Natural Science Foundation of China under Grant No. 60873267Zhejiang Provincial Natural Science Foundation of China under Grant No. Y607026sponsored by K. C. Wong Magna Fund at Ningbo University
文摘A Latin squares of order v with ni missing sub-Latin squares （holes） of order hi （1 〈= i 〈 k）, which are disjoint and spanning （i.e. ∑k i=l1 nihi = v）, is called a partitioned incomplete Latin squares and denoted by PILS. The type of PILS is defined by （h1n1 h2n2…hknk ）. If any two PILS inaset of t PILS of type T are orthogonal, then we denote the set by t-HMOLS（T）. It has been proved that 3-HMOLS（2n31） exist for n ≥6 with 11 possible exceptions. In this paper, we investigate the existence of 3-HMOLS（2nu1） with u ≥ 4, and prove that 3-HMOLS（2~u1） exist if n ≥ 54 and n ≥7/4u ＋ 7.
文摘In this paper, we give some constructions of self-conjugate self-orthogonal diagonal Latinsquares (SCSODLS). As an application of such constructions we disproof the conjecture aboutSCSODLS and show that there exist SCSODLS of order V, whenever w=1 (mod 12), with thepossible exception of v∈ {13, 85, 133}.
