演講
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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