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The twisted crossed cube is a variant of the hypercube. It is promising as a topology of interconnection networks for massively parallel systems. In this paper, we propose an algorithm that constructs n disjoint paths between an arbitrary pair of nodes in an n-dimensional twisted crossed cube. We also prove that the algorithm is correct, its time complexity is O(n2), and the lengths of the paths constructed are at most 4n --- 8. In addition, we conducted a computer experiment to evaluate our algorithm. Experimental results showed that the maximum path lengths are at most 3n + 1.

In this study, we propose two methods for fault-tolerant routing in the crossed cube. The first method, Method 1, at each node that has the message to the destination node, its neighbor nodes into the set of the forward neighbor nodes, the set of the sideward neighbor nodes, and the set of the backward neighbor nodes by calculating the distances from the neighbor nodes to the destination node. Then, Method 1 chooses one of the neighbor nodes and forwards the message to the node. Based on the observation of the execution of Method 1, we found that the routing tends to fail at the nodes with 3 hops to the destination node. Hence, we have introduced another method, Method 2, that executes the depth-first search at the nodes that are at 3 hops to the destination node. By adopting a simple fault-tolerant routing method, Simple, as the baseline, we conducted a computer experiment in 11-, 12-, and 13-dimensional crossed cubes, CQ11, CQ12, and CQ13. As a result, Method 1 showed better ratios of successful routings than a baseline method by at most 0.0973 in CQ11, 0.2082 in CQ12, and 0.139 in CQ13, respectively. Also, Method 2 showed better ratios than a baseline method by at most 0.1195 in CQ11, 0.2366 in CQ12, and 0.674 in CQ13, respectively. The average path lengths were also improved by Method 1 compared to the baseline method by at most 2.35 in CQ11, 2.07 in CQ12, and 3.63 in CQ13, respectively. Moreover, Method 2 improved them by 1.89 in CQ11, 1.61 in CQ12, and 3.12 in CQ13, respectively.

This paper describes seamless learning analytics methods of VASCORLL (Visualization and Analysis System for COnnecting Relationships of Learning Logs). VASCORLL is a system for visualizing and analyzing the learning logs collected by the seamless learning system, which supports language learning in the real-world. As far, several studies have been made in the seamless learning environments in order to bridge formal learning over informal learning. However, their focus was the implementation of the seamless learning environment in education. This study focuses on visualizing and analyzing learning logs collected in the seamless learning environment. This paper describes how our analytics could contribute to bridging the gap between formal and informal learning. An experiment was conducted to evaluate 1) whether our developed VASCORLL is effective in connecting the words learned in formal learning to the ones learned in informal learning, 2) which social network algorithm is effective to enhance learning in the seamless learning environment. Twenty international students participated in the evaluation experiment, and they were able to increase their learning opportunities by using VASCORLL. In addition, it was found that the betweenness centrality is useful in finding central words bridging formal and informal learning.1

This paper describes a method of the visualization and analysis for mining useful learning logs from numerous learning experiences that learners have accumulated in the real world as the ubiquitous learning logs. Ubiquitous Learning Log (ULL) is defined as a digital record of what learners have learned in the daily life using ubiquitous technologies. It allows learners to log their learning experiences with photos, audios, videos, location, RFID tag and sensor data, and to share and reuse ULL with others. By constructing real-world corpora which comprise of accumulated ULLs with information such as what, when, where, and how learners have learned in the real world and by analyzing them, we can support learners to learn more effectively. The proposed system will predict their future learning opportunities including their learning patterns and trends by analyzing their past ULLs. The prediction is made possible both by network analysis based on ULL information such as learners, knowledge, place and time and by learners' self-analysis using time-map. By predicting what they tend to learn next in their learning paths, it provides them with more learning opportunities. Accumulated data are so big and the relationships among the data are so complicated that it is difficult to grasp how closely the ULLs are related each other. Therefore, this paper proposes a system to help learners to grasp relationships among learners, knowledge, place and time, using network graphs and network analysis.