DAIHINMIN, which means Grand Pauper, is a popular playing-card game in Japan. TANHINMIN is a simplified variant of DAIHINMIN, which was proposed by Nishino in 2007 in order to investigate the mathematical properties of DAIHINMIN. In this paper, we consider a 2-player generalized TANHINMIN, where the deck size is arbitrary n. We present a linear-time algorithm that determines which player has a winning strategy after all cards are distributed to the players.

In this letter, we present a new lower bound for the treewidth of a graph in terms of the second smallest eigenvalue of its Laplacian matrix. Our bound slightly improves the lower bound given by Chandran and Subramanian [Inf. Process. Lett., 87 (2003)].

In this paper, we study BALL COLLECTING WITH LIMITED ENERGY, which is a problem of scheduling robots with limited energy confined to a line to catch moving balls that eventually cross the line. For this problem, we show the NP-completeness of the general case and some algorithmic results for some cases with a small number of robots.

BLOCKSUM, also known as KEISANBLOCK in Japanese, is a Latin square filling type puzzle, such as Sudoku. In this paper, we prove that the decision problem whether a given instance of BLOCKSUM has a solution or not is NP-complete.

Decision trees are used as a convenient means to explain given positive examples and negative examples, which is a form of data mining and knowledge discovery. Standard methods such as ID3 may provide non-monotonic decision trees in the sense that data with larger values in all attributes are sometimes classified into a class with a smaller output value. (In the case of binary data, this is equivalent to saying that the discriminant Boolean function that the decision tree represents is not positive. ) A motivation of this study comes from an observation that real world data are often positive, and in such cases it is natural to build decision trees which represent positive (i. e. , monotone) discriminant functions. For this, we propose how to modify the existing procedures such as ID3, so that the resulting decision tree represents a positive discriminant function. In this procedure, we add some new data to recover the positivity of data, which the original data had but was lost in the process of decomposing data sets by such methods as ID3. To compare the performance of our method with existing methods, we test (1) positive data, which are randomly generated from a hidden positive Boolean function after adding dummy attributes, and (2) breast cancer data as an example of the real-world data. The experimental results on (1) tell that, although the sizes of positive decision trees are relatively larger than those without positivity assumption, positive decision trees exhibit higher accuracy and tend to choose correct attributes, on which the hidden positive Boolean function is defined. For the breast cancer data set, we also observe a similar tendency; i. e. , positive decision trees are larger but give higher accuracy.

We propose a new configuration for a parallel fiber amplifier that can amplify both the C- and L-bands simultaneously by employing bundled Er3+-doped fiber (EDF). The bundled EDF is a candidate amplification medium for multi-core optical fiber amplifiers. Our parallel fiber amplifier is another application of the multi-core amplification medium. The amplifier achieves almost the same signal gain of 20 dB for both the C- and L-bands by using a bundled EDF, which is realized by bundling seven identical single-core EDFs.