Upper bounds on the queuenumber of k-ary n-cubes

A queue layout of a graph consists of a linear order of its vertices, and a partition of its edges into queues, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph G, denoted by qn(G), is called the queuenumber of G. Heath and Rosenberg [SIAM J. Comput. 21 (1992) 927-958] showed that boolean n-cube (i.e., the n-dimensional hypercube) can be laid out using at most n−1 queues. Heath et al. [SIAM J. Discrete Math. 5 (1992) 398-412] showed that the ternary n-cube can be laid out using at most 2n−2 queues. Recently, Hasunuma and Hirota [Inform. Process. Lett. 104 (2007) 41-44] improved the upper bound on queuenumber to n−2 for hypercubes. In this paper, we deal with the upper bound on queuenumber of a wider class of graphs called k-ary n-cubes, which contains hypercubes and ternary n-cubes as subclasses. Our result improves the previous bound in the case of ternary n-cubes. Let denote the n-dimensional k-ary cube. This paper contributes three main results as follows:

(1)

if n?3.

(2)

if n?2 and 4?k?8.

(3)

if n?1 and k?9.

     

On probabilistic n-ary hypergroups

The T-fuzzy n-ary subhypergroups of an n-ary hypergroup are defined by using triangular norms and some related properties are hence obtained. In particular, we consider the probabilistic version of n-ary hypergroups by using random sets and show that the fuzzy n-ary hypergroups defined by triangular norms are consequences of some probabilistic n-ary hypergroups under certain conditions. Some results on n-ary hypergroups recently given by Davvaz and Corsini are extended.     

Augmented k-ary n-cubes

We define an interconnection network AQ_n,k which we call the augmented k-ary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube AQ_n,k has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n-cube AQ_n,k: is a Cayley graph, and so is vertex-symmetric, but not edge-symmetric unless n = 2; has connectivity 4n − 2 and wide-diameter at most max{(n − 1)k − (n − 2), k + 7}; has diameter , when n = 2; and has diameter at most , for n ? 3 and k even, and at most , for n ? 3 and k odd.     

Q-ary search with one lie and bi-interval queries

The following search game is considered: there are two players, say Paul (or questioner) and Carole (or responder). Carole chooses a number x^*∈Sn={1,2,…,n}, Paul has to find the number x^* by asking q-ary bi-interval queries and Carole is allowed to lie at most once throughout the game. The minimum worst-case number LB(n,q,1) of q-ary bi-interval queries necessary to guess the number x^* is determined exactly for all integers n?1 and q?2. It turns out that LB(n,q,1) coincides with the minimum worst-case number L(n,q,1) of arbitrary q-ary queries.     

The rotation graph of k-ary trees is Hamiltonian

In this paper we show that the graph of k-ary trees, connected by rotations, contains a Hamilton cycle. Our proof is constructive and thus provides a cyclic Gray code for k-ary trees. Furthermore, we identify a basic building block of this graph as the 1-skeleton of the polytopal complex dual to the lower faces of a certain cyclic polytope.     

On the linear complexity of some new q-ary sequences

Some new q-ary sequences with period q^3ek-1 (q=p^m, p an odd prime, m, e, k integers) are first constructed and then, inspired by Antweiler’s method, their linear complexity is examined. The exact value of linear complexity k(6e)^w is determined when . Furthermore, an upper bound of the linear complexity is given for the other values of r. Our results show that this sequence has larger linear span than GMW sequence with the same parameters. Finally, the results of a Maple program are included to illustrate the validity of the results.     

A local approach for 3D object recognition through a set of size functions

In this paper, a local approach for 3D object recognition is presented. It is based on the topological invariants provided by the critical points of the 3D object. The critical points and the links between them are represented by a set of size functions obtained after splitting the 3D object into portions. A suitable similarity measure is used to compare the sets of size functions associated with the 3D objects. In order to validate our approach's recognition performance, we used different collections of 3D objects. The obtained scores are favourably comparable to the related work.     

A new type of fuzzy n-ary hyperstructures

The aim of this paper is to consider and study a new kind of fuzzy n-ary hyperstructures, such as fuzzy n-ary hypergroups and fuzzy (m,n)-ary hyperrings.     

Characterizing r-perfect codes in direct products of two and three cycles

An r-perfect code of a graph G=(V,E) is a set C⊆V such that the r-balls centered at vertices of C form a partition of V. It is proved that the direct product of Cm and Cn (r?1, m,n?2r+1) contains an r-perfect code if and only if m and n are each a multiple of ²(r+1)+r² and that the direct product of Cm, Cn, and C? (r?1, m,n,??2r+1) contains an r-perfect code if and only if m, n, and ? are each a multiple of r³+³(r+1). The corresponding r-codes are essentially unique. Also, r-perfect codes in C2r×Cn (r?2, n?2r) are characterized.     

Monte Carlo TD(λ)-methods for the optimal control of discrete-time Markovian jump linear systems

In this paper, we present an iterative technique based on Monte Carlo simulations for deriving the optimal control of the infinite horizon linear regulator problem of discrete-time Markovian jump linear systems for the case in which the transition probability matrix of the Markov chain is not known. We trace a parallel with the theory of TD(λ) algorithms for Markovian decision processes to develop a TD(λ) like algorithm for the optimal control associated to the maximal solution of a set of coupled algebraic Riccati equations (CARE). It is assumed that either there is a sample of past observations of the Markov chain that can be used for the iterative algorithm, or it can be generated through a computer program. Our proofs rely on the spectral radius of the closed loop operators associated to the mean square stability of the system being less than 1.     

New relaxation-based algorithms for the optimal solution of the continuous and discrete p-center problems

We present new relaxation algorithms for the uncapacitated continuous and discrete p-center problems. We have conducted an experimental study that demonstrated that these new algorithms are extremely efficient.     

Reducing non-determinism of k-NN searching in non-ordered discrete data spaces

We propose a generalized version of the Granularity-Enhanced Hamming (GEH) distance for use in k-NN queries in non-ordered discrete data spaces (NDDS). The use of the GEH distance metric improves search semantics by reducing the degree of non-determinism of k-NN queries in NDDSs. The generalized form presented here enables the GEH distance to be used for a much greater variety of scenarios than was possible with the original form.     

New results on H∞ filtering for fuzzy systems with interval time-varying delays

This paper investigates the problem of H_∞ filtering for continuous Takagi-Sugeno (T-S) fuzzy systems with an interval time-varying delay in the state. Based on the delay partitioning idea, a new approach is proposed for solving this problem, which can achieve much less conservative feasibility conditions. The attention is focused on the design of an H_∞ filter via the parallel distributed compensation scheme such that the filter error system is asymptotically stable and the H_∞ attenuation level from disturbance to estimation error is below a prescribed scalar. The constructed Lyapunov-Krasovskii functional, by applying the delay partitioning method, can potentially guarantee the obtained delay-dependent conditions to be less conservative than those in the literature. The obtained results are formulated in the form of linear matrix inequalities (LMIs), which can be readily solved via standard numerical software. Finally, an example is illustrated to show the reduction in conservatism of the proposed filter design method.     

New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI

The problems of relaxed quadratic stability conditions, fuzzy observer designs and H_∞ controller designs for T-S fuzzy systems have been studied. First new stability conditions are obtained by relaxing the stability conditions derived in previous papers. Secondly, new fuzzy observers based on the relaxed stability conditions for the T-S fuzzy systems have been proposed. Thirdly two sufficient LMI conditions, which guarantee the existence of the H_∞ controllers based on fuzzy observers for the T-S fuzzy systems have been proposed. The conditions are not only simple, but also consider the interactions among the fuzzy subsystems. Finally by some examples, using the LMI technique, we show that the regulators, the fuzzy observers and the H_∞ controller designs based on new observers for the T-S fuzzy systems are very practical and efficient.     

The effect of an information ethics course on the information ethics values of students - A Chinese guanxi culture perspective

The development of information technology has a significant influence on social structure and norms, and also impacts upon human behavior. In order to achieve stability and social harmony, people need to respect various norms, and have their rights protected. Students’ information ethics values are of critical and radical importance in achieving this goal. Using qualitative approach, the present study utilizes Kohlberg’s CMD model to measure improvement in students’ “information ethics values” through “technology mediated learning (TML)” models, and to assess the extent to which it is influenced by gender and Chinese guanxi culture. We find that while e-learning improves female students’ “respect rules,” “privacy,” “accessibility” and “intellectual property” values more than male students, the percentages relating to “intellectual property” for females in the higher stages remain lower than for males. Moreover, these results are interpreted from a Chinese guanxi culture perspective. In light of these results, educators should take account of such improvements when designing effective teaching methods and incentives.     

A new approach to solve the k-server problem based on network flows and flow cost reduction

This paper is concerned with two algorithms for solving the k-server problem: the optimal off-line algorithm (OPT) and the on-line work function algorithm (WFA). Both algorithms are usually implemented by network flow techniques including the flow augmentation method. In the paper a new implementation approach is proposed, which is again based on network flows, but uses simpler networks and the cost reduction method. The paper describes in detail the corresponding new implementations of OPT and WFA, respectively. All necessary correctness proofs are given. Also, experiments are presented, which confirm that the new approach assures faster execution of both algorithms.     

Design of experiments for bivariate binary responses modelled by Copula functions

Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting.