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<P align=center class=MsoNormal
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style="FONT-FAMILY: 宋体; FONT-SIZE: 14pt; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 'Times New Roman'">2000网易杯全国大学生数学建模竞赛题目<O:P>
</O:P></SPAN></B></P>
<P class=MsoNormal style="LINE-HEIGHT: 18pt; mso-line-height-rule: exactly"><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-FAMILY: 宋体; FONT-SIZE: 12pt; mso-bidi-font-size: 10.0pt; mso-hansi-font-family: 'Times New Roman'">A题<SPAN
style="mso-spacerun: yes"> </SPAN>DNA序列分类<SPAN
style="mso-spacerun: yes"> </SPAN><O:P></O:P></SPAN></B></P>
<P class=MsoNormal
style="LINE-HEIGHT: 18pt; TEXT-INDENT: 24pt; mso-line-height-rule: exactly"><SPAN
lang=EN-US
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'">2000年6月，人类基因组计划中DNA全序列草图完成，预计2001年可以完成精确的全序列图，此后人类将拥有一本记录着自身生老病死及遗传进化的全部信息的“天书”。这本大自然写成的“天书”是由4个字符A，T，C，G按一定顺序排成的长约30亿的序列，其中没有“断句”也没有标点符号，除了这4个字符表示4种碱基以外，人们对它包含的“内容”知之甚少，难以读懂。破译这部世界上最巨量信息的“天书”是二十一世纪最重要的任务之一。在这个目标中，研究DNA全序列具有什么结构，由这4个字符排成的看似随机的序列中隐藏着什么规律，又是解读这部天书的基础，是生物信息学（Bioinformatics）最重要的课题之一。<O:P>
</O:P></SPAN></P>
<P class=MsoNormal
style="LINE-HEIGHT: 18pt; TEXT-INDENT: 24.1pt; mso-line-height-rule: exactly"><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'">虽然人类对这部“天书”知之甚少，但也发现了<SPAN
lang=EN-US>DNA序列中的一些规律性和结构。例如，在全序列中有一些是用于编码蛋白质的序列片段，即由这4个字符组成的64种不同的3字符串，其中大多数用于编码构成蛋白质的20种氨基酸。又例如，在不用于编码蛋白质的序列片段中，A和T的含量特别多些，于是以某些碱基特别丰富作为特征去研究DNA序列的结构也取得了一些结果。此外，利用统计的方法还发现序列的某些片段之间具有相关性，等等。这些发现让人们相信，DNA序列中存在着局部的和全局性的结构，充分发掘序列的结构对理解DNA全序列是十分有意义的。目前在这项研究中最普通的思想是省略序列的某些细节，突出特征，然后将其表示成适当的数学对象。这种被称为粗粒化和模型化的方法往往有助于研究规律性和结构。<O:P>
</O:P></SPAN></SPAN></P>
<P class=MsoNormal
style="LINE-HEIGHT: 18pt; TEXT-INDENT: 24pt; mso-line-height-rule: exactly"><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'">作为研究<SPAN
lang=EN-US>DNA序列的结构的尝试，提出以下对序列集合进行分类的问题：<O:P> </O:P></SPAN></SPAN></P>
<P class=MsoNormal
style="LINE-HEIGHT: 18pt; mso-line-height-rule: exactly"><SPAN lang=EN-US
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'"><SPAN
style="mso-spacerun: yes">
</SPAN>1）下面有20个已知类别的人工制造的序列（见下页），其中序列标号1—10
为A类，11-20为B类。请从中提取特征，构造分类方法，并用这些已知类别的序列，衡量你的方法是否足够好。然后用你认为满意的方法，对另外20个未标明类别的人工序列（标号21—40）进行分类，把结果用序号（按从小到大的顺序）标明它们的类别（无法分类的不写入）：<O:P>
</O:P></SPAN></P>
<P class=MsoNormal
style="LINE-HEIGHT: 18pt; mso-line-height-rule: exactly"><SPAN lang=EN-US
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'"><SPAN
style="mso-spacerun: yes"> </SPAN>A类 <U><SPAN
style="mso-spacerun: yes"> </SPAN></U><SPAN
style="mso-spacerun: yes"> </SPAN>；<SPAN style="mso-spacerun: yes">
</SPAN>B类 <U><SPAN
style="mso-spacerun: yes"> </SPAN></U>。<O:P>
</O:P></SPAN></P>
<P class=MsoNormal
style="LINE-HEIGHT: 18pt; mso-line-height-rule: exactly"><SPAN lang=EN-US
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'"><SPAN
style="mso-spacerun: yes">
</SPAN>请详细描述你的方法，给出计算程序。如果你部分地使用了现成的分类方法，也要将方法名称准确注明。<O:P> </O:P></SPAN></P>
<P class=MsoNormal
style="LINE-HEIGHT: 18pt; TEXT-INDENT: 21pt; mso-line-height-rule: exactly"><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'">这<SPAN
lang=EN-US>40个序列也放在如下地址的网页上，用数据文件Art-model-data 标识，供下载：<O:P>
</O:P></SPAN></SPAN></P>
<P class=MsoNormal
style="LINE-HEIGHT: 18pt; TEXT-INDENT: 21pt; mso-line-height-rule: exactly"><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'">网易网址：<SPAN
lang=EN-US><A href="http://www.163.com/"><SPAN
style="FONT-FAMILY: 'Times New Roman'">www.163.com</SPAN></A><SPAN
style="mso-spacerun: yes"> </SPAN>教育频道<SPAN
style="mso-spacerun: yes"> </SPAN>在线试题；<O:P> </O:P></SPAN></SPAN></P>
<P class=MsoNormal
style="LINE-HEIGHT: 18pt; TEXT-INDENT: 21pt; mso-line-height-rule: exactly"><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'">教育网：<SPAN
lang=EN-US><SPAN style="mso-spacerun: yes"> </SPAN><A
href="http://www.cbi.pku.edu.cn/"><SPAN
style="FONT-FAMILY: 'Times New Roman'">www.cbi.pku.edu.cn</SPAN></A><SPAN
style="mso-spacerun: yes"> </SPAN>News<SPAN
style="mso-spacerun: yes"> </SPAN>mcm2000<O:P> </O:P></SPAN></SPAN></P>
<P class=MsoNormal
style="LINE-HEIGHT: 18pt; TEXT-INDENT: 21pt; mso-line-height-rule: exactly"><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'">教育网：<SPAN
lang=EN-US><SPAN style="mso-spacerun: yes">
</SPAN>www.csiam.edu.cn/mcm<O:P> </O:P></SPAN></SPAN></P>
<P class=MsoNormal
style="LINE-HEIGHT: 18pt; TEXT-INDENT: 24pt; mso-line-height-rule: exactly"><SPAN
lang=EN-US
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'">2）在同样网址的数据文件Nat-model-data
中给出了182个自然DNA序列，它们都较长。用你的分类方法对它们进行分类，像1）一样地给出分类结果。<O:P> </O:P></SPAN></P>
<P class=MsoNormal
style="LINE-HEIGHT: 18pt; TEXT-INDENT: 24pt; mso-line-height-rule: exactly"><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'">提示</SPAN></B><SPAN
style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'">：衡量分类方法优劣的标准是分类的正确率，构造分类方法有许多途径，例如提取序列的某些特征，给出它们的数学表示：几何空间或向量空间的元素等，然后再选择或构造适合这种数学表示的分类方法；又例如构造概率统计模型，然后用统计方法分类等。<SPAN
lang=EN-US><O:P> </O:P></SPAN></SPAN></P>
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style="FONT-FAMILY: 宋体; mso-hansi-font-family: 'Times New Roman'"> </SPAN><SPAN
lang=EN-US>Art-model-data</SPAN><SPAN lang=EN-US
style="mso-fareast-font-family: 楷体_GB2312"><O:P> </O:P></SPAN></P>
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