In this paper, we study the problems in the discrete Fourier transform (DFT) test included in NIST SP 800-22 released by the National Institute of Standards and Technology (NIST), which is a collection of tests for evaluating both physical and pseudorandom number generators for cryptographic applications. The most crucial problem in the DFT test is that its reference distribution of the test statistic is not derived mathematically but rather numerically estimated; the DFT test for randomness is based on a pseudo-random number generator (PRNG). Therefore, the present DFT test should not be used unless the reference distribution is mathematically derived. Here, we prove that a power spectrum, which is a component of the test statistic, follows a chi-squared distribution with 2 degrees of freedom. Based on this fact, we propose a test whose reference distribution of the test statistic is mathematically derived. Furthermore, the results of testing non-random sequences and several PRNGs showed that the proposed test is more reliable and definitely more sensitive than the present DFT test.
Recently, it has been suggested that macrolide antibiotics act as immunomodulators. In this study, we evaluated the effect of clarithromycin (CAM) on macrophage function. We used the mouse macrophage cell line, J774.1. The following direct effects of CAM on macrophage function were evaluated: chemotaxis to CAM, chemokinetic effect of CAM, and the effect of CAM on macrophage growth. In order to examine the indirect effects of CAM on macrophage functions, we preincubated macrophages with several concentrations of CAM and then removed the CAM. Thereafter, the phagocytosis of beads, cytocidal activity against Candida albicans, and chemotaxis to lipopolysaccharide were evaluated. In addition, the indirect effects of CAM on endoxan (4 mg/ml) treated macrophage phagocytosis, cytocidal activity, and chemotaxis were evaluated. CAM (at the concentration between 0.04 and 0.2 microgram/ml) directly stimulated macrophage chemotaxis and chemokinesis. In addition, CAM dose-dependently stimulated the growth of macrophages. CAM pretreatment (for 4 hours at the concentrations between 0.04 and 0.2 microgram/ml) stimulated macrophage phagocytosis, cytocidal activity against Candida albicans, and chemotaxis to lipopolysaccharide. In addition, CAM recovered macrophage phagocytosis, cytocidal activity, and chemotaxis which were decreased after endoxan exposure. These results suggest that CAM has direct and indirect effects on macrophage functions.
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