SMAD1 inactivation caused by decreased expression of bone morphogenetic protein receptor ib contributes to glioma aggravation
- 作者：Shuang Liu ; Zeng Min Tian ; Feng Yin ; Xin Ru Guo ; Hai Tao Wu ; Yan Rui Wu ; Xue Feng Ding ; Yan Wu ; Shu Hong Liu ; Wu Ju Li ; Xiao Zhong Pan ; Jian Gang Yuan ; Bo Qin Qiang ; Wen Hong Fan ; Ming Fan
- 关键词：Clique function ; Monotone circuits ; Perfect hashing ; Vertex cover ; Critical graphs
- 刊名：Cell Biology International
- 出版年：2008
- 期刊代码：164_10656995
- 类别：bio
- 出版时间：March 2008
- 卷：32
- 期：3
- 页码：S32
- 文件大小：50 K
摘要
It is known that, for every constant MathURL&_method=retrieve&_udi=B6V00-4PG2S0T-3&_mathId=mml1&_user=1067359&_cdi=5632&_rdoc=27&_acct=C000050221&_version=1&_userid=10&md5=c88c08611bf1220a453ff55ab9fdfdcc" title="Click to view the MathML source" alt="Click to view the MathML source">k
3, the presence of a k-clique (a complete sub-graph on k vertices) in an n-vertex graph cannot be detected by a monotone boolean circuit using much fewer than mathId=mml2&_user=1067359&_cdi=5632&_rdoc=27&_acct=C000050221&_version=1&_userid=10&md5=b1acdfa974b82183d552f6656f1ed5b2" title="Click to view the MathML source" alt="Click to view the MathML source">nk gates. We show that, for every constant k, the presence of an mathId=mml3&_user=1067359&_cdi=5632&_rdoc=27&_acct=C000050221&_version=1&_userid=10&md5=7b93c7750b998e41364b730947e7e84a" title="Click to view the MathML source" alt="Click to view the MathML source">(n-k)-clique in an n-vertex graph can be detected by a monotone circuit using only a logarithmic number of fanin-2 OR gates; the total number of gates does not exceed mathId=mml4&_user=1067359&_cdi=5632&_rdoc=27&_acct=C000050221&_version=1&_userid=10&md5=093ca61fa9d484cb3275f0aa11afe92a" title="Click to view the MathML source" alt="Click to view the MathML source">O(n2logn). Moreover, if we allow unbounded fanin, then a logarithmic number of gates is enough.
3, the presence of a k-clique (a complete sub-graph on k vertices) in an n-vertex graph cannot be detected by a monotone boolean circuit using much fewer than mathId=mml2&_user=1067359&_cdi=5632&_rdoc=27&_acct=C000050221&_version=1&_userid=10&md5=b1acdfa974b82183d552f6656f1ed5b2" title="Click to view the MathML source" alt="Click to view the MathML source">nk gates. We show that, for every constant k, the presence of an mathId=mml3&_user=1067359&_cdi=5632&_rdoc=27&_acct=C000050221&_version=1&_userid=10&md5=7b93c7750b998e41364b730947e7e84a" title="Click to view the MathML source" alt="Click to view the MathML source">(n-k)-clique in an n-vertex graph can be detected by a monotone circuit using only a logarithmic number of fanin-2 OR gates; the total number of gates does not exceed mathId=mml4&_user=1067359&_cdi=5632&_rdoc=27&_acct=C000050221&_version=1&_userid=10&md5=093ca61fa9d484cb3275f0aa11afe92a" title="Click to view the MathML source" alt="Click to view the MathML source">O(n2logn). Moreover, if we allow unbounded fanin, then a logarithmic number of gates is enough.