Fuzzy cellular automata are dynamical systems that are continuous counterparts of the usual cellular automata (CA). Compared with the binary case, defining a fuzzy CA with three or more states is challenging because defining mixed states is difficult. Recently, this difficulty was resolved by representing multiple states as independent vectors in higher dimensions, and the concept of vector-valued fuzzy CA (VFCA) was introduced. In this study, we theoretically analyze and discuss the asymptotic behavior of three-neighbor VFCA. First, we define the weighted-averaging rules of VFCA and show how many rules exist up to the equivalence relations. According to these rules, each state vector in the next step is determined by the weighted average of the vectors in its neighboring cells. Next, we prove that three-state VFCA with weighted-averaging rules converge to a periodic configuration characterized by the symmetric group of order 3. In particular, the non-commutativity of the group action provides an interesting behavior that is not observed in fuzzy CA arising from binary states. Finally, we extend the results to VFCA with more than three states.

Software Defined Network (SDN) is revolutionizing the networking industry by a potential of enabling flexible and uniform management by decoupling the control plane and forwarding plane. However, there are several issues on scalability and adaption against conventional network protocols to implement on the large scaled network. To address these issues, we propose an implementation method which runs SDN controller and Quagga on SDN switch in this paper. By controlling information of each SDN controller uniformly with the upper layer controller, it could be able to handle each problems of implementing SDN without missing the advantage of SDN. Furthermore, by implementing prototype of our model, we will discuss some issues on the implementation of SDN system.

MOTIVATION: Considerable attention has been focused on predicting RNA-RNA interaction since it is a key to identifying possible targets of non-coding small RNAs that regulate gene expression post-transcriptionally. A number of computational studies have so far been devoted to predicting joint secondary structures or binding sites under a specific class of interactions. In general, there is a trade-off between range of interaction type and efficiency of a prediction algorithm, and thus efficient computational methods for predicting comprehensive type of interaction are still awaited. RESULTS: We present RactIP, a fast and accurate prediction method for RNA-RNA interaction of general type using integer programming. RactIP can integrate approximate information on an ensemble of equilibrium joint structures into the objective function of integer programming using posterior internal and external base-paring probabilities. Experimental results on real interaction data show that prediction accuracy of RactIP is at least comparable to that of several state-of-the-art methods for RNA-RNA interaction prediction. Moreover, we demonstrate that RactIP can run incomparably faster than competitive methods for predicting joint secondary structures. AVAILABILITY: RactIP is implemented in C++, and the source code is available at http://www.ncrna.org/software/ractip/.