In the information-spectrum methods proposed by Han and Verd´u, quantities defined using the ordinary limits superior/inferior in probability correspond to the optimal achievable rates in basic information-theoretic problems such as source coding and channel coding. In this paper, we introduce two more nonconventional limits in probability and apply all four limits to the fixed-length coding of a general source. In this paper, we first define four quantities for a source using the four limits in probability. It is shown that the four quantities satisfy a natural inequality if and only if the source is canonical. Next, we give operational meanings for the four quantities in fixed-length source coding. As one of the by-products, we can formulate nonconventional strong converse properties and obtain necessary and sufficient conditions. Finally, we explain a result for the achievable rate region in the optimistic sense of separately coding two correlated general sources. These results suggest the importance of the four quantities as new terminology for characterizing the performance of coding in more detail.

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Classical signal processing focuses on extracting frequency characteristics of time or spatial-domain data. For example, Fourier transform can be defined as the inner product of the signal and eigenfunctions of the one-dimensional Laplacian operator. Graph signal is defined as discrete signal located on vertices of a graph. Analogous to classical signal processing, graph Fourier transform is defined as the inner product of the graph signal and eigenfunctions of graph Laplacian matrix. In this paper, we describe fundamentals and recent advances of graph signal processing, which include; graph Fourier/wavelet transforms, filtering/sampling of graph signal, theoretical progress, and applications of graph signal processing.

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Nanocircuits consisting of materials such as carbon nanotubes have been extensively investigated as promising architechures, since they are relatively easily manufactured. Owing to their small scale, however, nanocircuits are likely to contain many defects, and defect tolerance is an essential issue in their design. We introduce two fundamental problems in the defect-tolerant design of nanocircuits and survey the graph theory associated with the problems.

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This paper introduces an inner-body positioning method using RFID (radio frequency identification) technology. Although small tumors can be detected using the latest medical imaging technologies such as CT (computerized tomography) and MRI (magnetic resonance imaging), it is difficult to find tumors during the surgical operation owing to the variation of the organism. Furthermore, small tumors are not visible from outside the organism in some cases. An RFID-based tumor marker for identifying the position and size of tumors is proposed in this paper. In this scheme, miniature RFID tags are implanted in the vicinity of a tumor during the diagnosis. Then positioning using the RFID technique is carried out during the surgery. In this paper, the validity of the RFID-based inner-body positioning method is shown through some experiments.

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