We propose a K-sparse exhaustive search (ES-K) method and a K-sparse approximate exhaustive search method (AES-K) for selecting variables in linear regression. With these methods, K-sparse combinations of variables are tested exhaustively assuming that the optimal combination of explanatory variables is K-sparse. By collecting the results of exhaustively computing ES-K, various approximate methods for selecting sparse variables can be summarized as density of states. With this density of states, we can compare different methods for selecting sparse variables such as relaxation and sampling. For large problems where the combinatorial explosion of explanatory variables is crucial, the AES-K method enables density of states to be effectively reconstructed by using the replica-exchange Monte Carlo method and the multiple histogram method. Applying the ES-K and AES-K methods * okada@k.u-tokyo.ac.jp

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The recent success with small fish as an animal model of cancer with the aid of fluorescence technique has attracted cancer modelers' attention because it would be possible to directly visualize tumor cells in vivo in real time. Here, we report a medaka model capable of allowing the observation of various cell behaviors of transplanted tumor cells, such as cell proliferation and metastasis, which were visualized easily in vivo. We established medaka melanoma (MM) cells stably expressing GFP and transplanted them into nonirradiated and irradiated medaka. The tumor cells were grown at the injection sites in medaka, and the spatiotemporal changes were visualized under a fluorescence stereoscopic microscope at a cellular-level resolution, and even at a single-cell level. Tumor dormancy and metastasis were also observed. Interestingly, in irradiated medaka, accelerated tumor growth and metastasis of the transplanted tumor cells were directly visualized. Our medaka model provides an opportunity to visualize in vivo tumor cells ''as seen in a culture dish'' and would be useful for in vivo tumor cell biology.animal model ͉ fluorescence imaging ͉ radiation biology M odeling cancer in laboratory animals is important for elucidating molecular mechanisms of tumor formation and is critical for the development of effective strategies for diagnosis and therapy. Among cancer animal models established so far, mouse is widely used because it is closely related to human genetically, and genetic manipulation and engineering for the mouse embryo are sophisticated (1). Mouse xenograft models have been used routinely for evaluation of anticancer drugs, and genetically engineered mice such as transgenic and knockout mice have provided strong evidence that oncogenes and tumor suppressor genes have various biological functions and play crucial roles in tumor formation in vivo (2, 3).Recent advances in fluorescence imaging, coupled with newly developed fluorescence proteins, have revolutionized modern biology (4). The technique has been used in a wide range of biology (5, 6) and has been applied to mouse cancer models, allowing us to visualize tumor cells and trace the dynamics of cell growth in vivo (7). These studies have contributed to a better understanding of tumor cell growth, tumor dormancy, invasiveness and metastasis, microenvironment of cancer cells, to cancer therapeutics (8). However, because mouse skin is not transparent, there are some obstacles such as the difficulty of visualizing a single or a few cancer cells directly through mouse skin and the necessity of expensive imaging modalities or specialized techniques.To overcome such limitations and to further the comprehensive understanding of cancer, alternative animal models are being proposed for development, and they are expected to have advantages over mouse models in certain aspects. Teleost fish such as zebrafish (Danio rerio) and medaka (Oryzias latipes) represent such an alternative vertebrate model. Zebrafish has recently received attention as a cancer model because...

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