Kolmogorov's goodness-of-fit measure, Dn, for a sample CDF has consistently been set aside for methods such as the D + n or D − n of Smirnov, primarily, it seems, because of the difficulty of computing the distribution of Dn. As far as we know, no easy way to compute that distribution has ever been provided in the 70+ years since Kolmogorov's fundamental paper. We provide one here, a C procedure that provides Pr(Dn < d) with 13-15 digit accuracy for n ranging from 2 to at least 16000. We assess the (rather slow) approach to limiting form, and because computing time can become excessive for probabilities>.999 with n's of several thousand, we provide a quick approximation that gives accuracy to the 7th digit for such cases.
H19 is an imprinted oncofetal non-coding RNA recently shown to be the precursor of miR-675. The pathophysiological roles of H19 and its mature product miR-675 to carcinogenesis have, however, not been defined. By quantitative reverse transcription-polymerase chain reaction, both H19 and miR-675 were found to be upregulated in human colon cancer cell lines and primary human colorectal cancer (CRC) tissues compared with adjacent non-cancerous tissues. Subsequently, the tumor suppressor retinoblastoma (RB) was confirmed to be a direct target of miR-675 as the microRNA suppressed the activity of the luciferase reporter carrying the 3'-untranslated region of RB messenger RNA that contains the miR-675-binding site. Suppression of miR-675 by transfection with anti-miR-675 increased RB expression and at the same time, decreased cell growth and soft agar colony formation in human colon cancer cells. Reciprocally, enhanced miR-675 expression by transfection with miR-675 precursor decreased RB expression, increased tumor cell growth and soft agar colony formation. Moreover, the inverse relationship between the expressions of RB and H19/miR-675 was also revealed in human CRC tissues and colon cancer cell lines. Our findings demonstrate that H19-derived miR-675, through downregulation of its target RB, regulates the CRC development and thus may serve as a potential target for CRC therapy.
We provide a new version of our ziggurat method for generating a random variable from a given decreasing density. It is faster and simpler than the original, and will produce, for example, normal or exponential variates at the rate of 15 million per second with a C version on a 400MHz PC. It uses two tables, integers ki and reals wi. Some 99% of the time, the required x is produced by: Generate a random 32-bit integer j and let i be the index formed from the rightmost 8 bits of j. If j < k i return x = j wi.We illustrate with C code that provides for inline generation of both normal and exponential variables, with a short procedure for setting up the necessary tables.
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