二年级以上本科可以做的一个小项目

1、收集“网络科学”的文章，做文章之间的引文网络，然后从引文网络建立共被引网络和共引网络，分析共被引网络和共引网络的集团结构，从而描述“网络科学”各个分支各个主题的提出时间、发展阶段，找出关键文章，关键作者。可以参考CiteSpace软件。

2、可以相应地做一个中国期刊发表的网络科学的文章的完全相同的研究，做一个对比，以及中国学者在上面的国际“网络科学”发展历史中的表现。

3、更一般地，可以画出来每一个时间点，整个“网络科学”的主题在全世界的分布（把属于这个主题的文章的地址作为在全世界上的一个点）。然后这个主题在世界的分布随着时间的演化，会告诉大家，这个学科的研究中心的发展历史。

需要：编程（C、Python、R或者其他），阅读一定量的“网络科学”的文献。

Learned something new about Bayesian formula last night and learned the hard way

Bayesian formula,
[P(A|B)=\frac{P(B|A)P(A)}{P(B|A)P(A)+P(B|\bar{A})P(\bar{A})}]
is conceptually straightforward, but amazingly useful in statistics. It turns calculation of (P(A|B)) into finding out (P(B|A)) by simply making use of the rule of total probability,
[P(A\cap B) = P(A|B)P(B) = P(B|A)P(A)]
and
[P(A) = P(A\cap B) + P(A\cap \bar{B}). ]

This seems rather trivial to me. Here comes the surprising part. Let us now add another set (C) in the following way,
[P\left(A|B\right) = P\left(\left(A|C\right)|B\right)P\left(C|B\right) + P\left(\left(A|\bar{C}\right)|B\right)P\left(\bar{C}|B\right), \hspace{2cm} (1)]
or in this way,
[P\left(A|B\right) = P\left(\left(A|B\right)|C\right)P\left(C\right) + P\left(\left(A|B\right)|\bar{C}\right)P\left(\bar{C}\right). \hspace{2cm} (2)]

Now let us ask which one of the above two formulae is the proper one, or both, or none?

It is easy to verify the first one: Assuming
[P\left(\left(A|C\right)|B\right) = P\left(A|\left(C,B\right)\right) = \frac{A\cap B \cap C}{B \cap C}, \hspace{2cm} (3)]
then right-hand side of Equ(1) becomes
[\frac{A\cap B \cap C}{B \cap C}\frac{B\cap C}{B} + \frac{A\cap B \cap \bar{C}}{B \cap \bar{C}}\frac{B\cap \bar{C}}{B} = \frac{A\cap B \cap C}{B} + \frac{A\cap B \cap \bar{C}}{B} = \frac{A\cap B}{B}, \hspace{1cm} (4)]
which is exactly the left-hand side of Equ(1).

Verifying Equ(2) is however not easy. If the assumption in Equ(3) is right, then Equ(2) becomes
[\frac{A\cap B \cap C}{B \cap C}\frac{C}{\Omega} + \frac{A\cap B \cap \bar{C}}{B \cap \bar{C}}\frac{\bar{C}}{\Omega}. \hspace{1cm} (4)]
I can see no clue that this expression should be (\frac{A\cap B}{B}).

However, if (P\left(A|B\right)) is the probability of a set of events, then the second one should be correct too. So what is the problem? It seems to me that when discussing (P\left(A|B\right)), we have implicitly limited the whole set, which originally is (\Omega), to be (B), therefore, all the expressions derived from there should have carried the condition (B) forever. So lesson one: Keeping the condition (B) as the condition for all other events. Therefore, Equ(1), not Equ(2), should be used in our case.

Another lesson learned is that conditional probability is a tricky concept and one has to deal it with extra attention.

神书推荐（Recommending The Princeton Companion to Mathematics）

最近读了一点点《普林斯顿数学指南》（The Princeton Companion to Mathematics），实在是精品，強烈推荐每一个数学家、物理学家、数学和物理系的学生，都看一看。

这本书把数学的主要分支的研究问题、主要思想、学习材料都做了介绍，而且是深入浅出，又不牺牲准确性、科学性的介绍。

这样的书，高中生、本科生、研究生、教授读了以后都会有收获。

什么时候，物理学也应该整出这样一本书来，系统科学也是。

Recently, I found a great book on mathematics, The Princeton Companion to Mathematics. It is like a guide or a big-picture introduction to almost every subfields of mathematics, without losing any accuracy and attractiveness.

All mathematicians, physicists, and students in math, physics, or even other fields related to appplied math, should read at least certain parts of this great book.

I think physicists should produce a similar book on physics too. Or maybe every discpline should have a simiar one.

ownCloud管理多个目录

我们自己的ownCloud服务器已经能够使用。一部分老师有同步多个目录的需求，而且不希望单独设立一个叫做owncloud的目录（浪费本地硬盘空间）。其实这些功能ownCloud都能实现。

下载并安装客户端。
然后，在客户端第一次启动之后，不要直接点下一步，注意，选择目标目录（默认是建立一个owncloud目录，我们不需要这个），然后在下面的别名位置上写上你给这个目录的名字，不要留着默认的owncloud。

接着，点增加目录，就可以把多个目录加进去了。