1st 國立交通大學、清華大學 統計學研究所 專題演講 題　目：Issues on Computer Search for Large Order Multiple Recursive Generators 主講人：鄧利源教授 Department of Mathematical Sciences The University of Memphis 時　間：96年12月14日(星期五)上午11:10-12:00 (上午10:50-11:10茶會於交大統計所428室舉行) 地　點：交大綜合一館427室 Abstract Multiple Recursive Generators (MRGs) have become the most popular random number generators recently. They compute the next value iteratively from the previous k values using a k-th order recurrence equation which, in turn, corresponds to a k-th degree primitive polynomial under a prime modulus p. In general, when k and p are large, checking if a k-th degree polynomial is primitive under a prime modulus p is known to be a hard problem. A common approach is to check the conditions given in Alanen and Knuth [1964] and Knuth [1998]. However, as mentioned in Deng [2004], this approach has two obvious problems: (a) it requires the complete factorization of pk-1, which can be difficult; (b) it does not provide any early exit strategy for non-primitive polynomials. To avoid (a), one can consider a prime order k and prime modulus p such that (pk-1)/(p-1) is also a prime number as considered in L'Ecuyer [1999] and Deng [2004]. To avoid (b), one can use a more efficient iterative irreducibility test proposed in Deng [2004]. In this talk, we survey several leading probabilistic and deterministic methods for the problems of primality testing and irreducibility testing. To test primality of a large number, it is known that probabilistic methods are much faster than deterministic methods. On the other hand, a probabilistic algorithm in fact has a very tiny probability of, say, 10-200 to commit a false positive error in the test result. Moreover, even when such an unlikely event had happened, for a specific choice of k and p, it can be argued that such an error has a negligible effect on the successful search of a primitive polynomial. We perform a computer search for large-order DX generators proposed in Deng and Xu [2003] and present many such generators in the talk for ready implementation. An extensive empirical study shows that these large-order DX generators have passed the stringent Crush battery of the TestU01 package. 2nd 國立交通大學、清華大學 統計學研究所 專題演講 題　目：Evolution, Condition-Specificity, and Regulatory Impact of Untranslated RNA and Transcriptional Dark Matter 主講人：Dr. Joshua Rest（Department of Ecology and Evolution, University of Chicago） 時　間：96年12月14日(星期五)上午10:00-10:50 (上午10:50-11:10茶會於交大統計所428室舉行) 地　點：交大綜合一館427室 Abstract Expressed but untranslated regions (UTRs) of genes are now known to participate in gene regulation. Using a tiling microarray assay of genome-wide expression levels, we identify length variation of UTRs among different stress conditions in four yeast strains. We characterize the evolution of these condition-dependent length differences between strains, assess their potential impact on the regulatory evolution of stress response, and look for associations with nucleotide changes. It has also been observed that there is widespread transcription in the intergenic regions of eukaryotes, leading to the idea of transcriptional dark matter. We characterize the evolution of condition-specific intergenic expression, and assess the hypothesis that it represents neutral change due to gain and loss of spurious binding sites. --

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