A rapid single-flux-quantum (RSFQ) 4-bit bit-slice multiplier is proposed. A new systolic-like multiplication algorithm suitable for RSFQ implementation is developed. The multiplier is designed using the cell library for AIST 10-kA/cm2 1.0-µm fabrication technology (ADP2). Concurrent flow clocking is used to design a fully pipelined RSFQ logic design. A 4n×4n-bit multiplier consists of 2n+17 stages. For verifying the algorithm and the logic design, a physical layout of the 8×8-bit multiplier has been designed with target operating frequency of 50GHz and simulated. It consists of 21 stages and 11,488 Josephson junctions. The simulation results show correct operation up to 62.5GHz.

Let T1,T2,...,Tk be spanning trees in a graph G. If, for any two vertices u,v of G, the paths joining u and v on the k trees are mutually vertex-disjoint, then T1,T2,...,Tk are called completely independent spanning trees (CISTs for short) of G. The construction of CISTs can be applied in fault-tolerant broadcasting and secure message distribution on interconnection networks. Hasunuma (2001) first introduced the concept of CISTs and conjectured that there are k CISTs in any 2k-connected graph. Unfortunately, this conjecture was disproved by Péterfalvi recently. In this note, we give a necessary condition for k-connected k-regular graphs with ⌊k/2⌋ CISTs. Based on this condition, we provide more counterexamples for Hasunuma's conjecture. By contrast, we show that there are two CISTs in 4-regular chordal rings CR(N,d) with N=k(d-1)+j under the condition that k ≥ 4 is even and 0 ≤ j ≤ 4. In particular, the diameter of each constructed CIST is derived.

As an optimal combinatorial object, cyclic perfect Mendelsohn difference family (CPMDF) was introduced by Fuji-Hara and Miao to construct optimal optical orthogonal codes. In this paper, we propose a direct construction of disjoint CPMDFs from the Zeng-Cai-Tang-Yang cyclotomy. Compared with a recent work of Fan, Cai, and Tang, our construction doesn't need to depend on a cyclic difference matrix. Furthermore, strictly optimal frequency-hopping sequences (FHSs) are a kind of optimal FHSs which has optimal Hamming auto-correlation for any correlation window. As an application of our disjoint CPMDFs, we present more flexible combinatorial constructions of strictly optimal FHSs, which interpret the previous construction proposed by Cai, Zhou, Yang, and Tang.

For any positive integer n, define an iterated function $f(n)=left{ egin{array}{ll} n/2, & mbox{ $n$ even, } 3n+1, & mbox{ $n$ odd. } end{array} ight.$ Suppose k (if it exists) is the lowest number such that fk(n)

The technique of replica placement has been extensively employed to improve client perceived performance and disperse server workload. In this paper, we study some well-known algorithms of replica placement on the network and observe the logarithmic relationship between replica number and total access cost. Numerous simulations are done and it is found that some replica algorithms obey the logarithmic relationship with high correlation coefficients. A logrithmic function is proposed about replica number and total access cost. The logarithmic relationship is applied to the minimum facility problem and a function is deduced to get the optimal replica number.

To detect the natural clusters for irregularly shaped data distribution is a difficult task in pattern recognition. In this study, we propose an efficient clustering algorithm for irregularly shaped clusters based on the advantages of spectral clustering and Affinity Propagation (AP) algorithm. We give a new similarity measure based on neighborhood dispersion analysis. The proposed algorithm is a simple but effective method. The experimental results on several data sets show that the algorithm can detect the natural clusters of input data sets, and the clustering results agree well with that of human judgment.

Notes on two constructions of zero-difference balanced (ZDB) functions are made in this letter. Then ZDB functions over Ze×∏ki=0 Fqi are obtained. And it shows that all the known ZDB functions using cyclotomic cosets over Zn are special cases of a generic construction. Moreover, applications of these ZDB functions are presented.

Generalized recursive circulant graphs (GRCGs for short) are a generalization of recursive circulant graphs and provide a new type of topology for interconnection networks. A graph of n vertices is said to be s-pancyclic for some $3leqslant sleqslant n$ if it contains cycles of every length t for $sleqslant tleqslant n$. The pancyclicity of recursive circulant graphs was investigated by Araki and Shibata (Inf. Process. Lett. vol.81, no.4, pp.187-190, 2002). In this paper, we are concerned with the s-pancyclicity of GRCGs.