## Sunday, 13 December 2009

### Duals Duals Duals

Is there a connection between all these "duals" in math?
There seem to be two main classes of duals.
One from linear algebra / functional analysis, and one from optimization theory. (Lagrangian/convex duals)

Well actually there is.

Recall that dual space of a vector space V is simply the set of all linear functionals of V. To put it another way, dual space is simply all the row vectors if the original space is finite dimensional.

Dual norm comes up in convex optimization. Dual norm of z is defined as sup_x { | ||x||<=1}. This is actually the same as the operator norm of the vector z when you think of z as an element of the dual space (row vector). In great generality, we can think of dual norm as INDUCED NORMS ON THE DUAL SPACE.

This really plays a role in Lp duality.  Lp dualtity says that the dual of Lp space is isometric to Lq. Here we are talking about infinite-dimensional spaces. Also the dual norm of an element of the dual space of Lp will be equal to the Lq norm of that linear functional when mapped into Lq. (See any real analysis text)

You can think about the dual cone as one way of generating a INDUCED CONE IN THE DUAL SPACE. (Again, we think of row vectors as elements in the dual space)

I don't see the relation between the Fenchel dual (Legendre transform), Lagrangian dual, and the dual space though.

## Wednesday, 9 December 2009

### Syndicated from another blog.

“男人有 老婆又有情人是男人的本事。请放心，情人不会成为老婆，两个概念不一样。男人的大部分心思还是在你身上，因为你是他老婆，是孩子的妈妈，名正言顺，任何时 候都改变不了。而情人只不是婚姻的一种补充，是成功男人一种精神上的追求和情感上的需要，其实也是挺正常的事情，也不必太认真。”——这是昨天中午我在一 个案宗中看到的，记录着一个成功男人的一段非常有代表性的“经典话语”，这就是他们奉行“家中红旗不倒，外面彩旗飘飘”，今朝有酒今朝醉，自嘲“自己喜新 不厌旧，风流不下流”。

人生 短暂，即使你通过努力拼搏成功了也不要为自己找许多漂亮的借口，而去三番五次的寻找情人当作自己的“标志”。虽然在你的脸上贴上美丽好看的“情人标志”， 但那都啻是你一厢情愿的虚荣心在作怪罢了，人们一定会对你深恶痛绝而讥笑藐视你的，同样你也将会是臭名远洋、遗臭万年的。之所以，你还是做一个洁身自好的 成功男人为好，这样人们就会对你另眼相看而铭记你的忠贞气节，却给以你流芳百世。

现在 和谐的社会需要更多的是老实敦厚、温文尔雅的成功男人，同样也需要更多的是安分守己、贤惠善良的温柔女人。只有男人永远不再做纸醉金迷、拈花惹草的男人， 女人不再做水性扬花、放任自流的女人，那么整个世界将会是更加充满人情味的，而幸福的婚姻家庭就会是永远的牢固不破了。

## Saturday, 28 November 2009

### Why it's hard to be a moderate

I was playing basketball with a group of Chinese students in the other day. It was great and a lot of fun. We were playing half-court basketball and one end of the court was empty.
At the end of one of our match (about 10 people), around six non-Chinese (Lao Wai) students came and asked us whether we wanted to play full court. We got into a debate about playing one full court game vs. playing two half court games. I thought that the opinion among Chinese students might be diverse so I asked everyone to hold their hands up if they want to play full court (which was my preference). The vote didn't pass.
After the night ended, a few Chinese students half-jokingly / half-seriously accused me of siding with the foreigners. I merely tried to reach a democratic consensus without holding onto ethnic divisions. If a game of basketball can lead to ethnic hard-liners speaking out, no wonder racial genocide will still occur in the world. Not only that, I feel sympathy for those people who do not let their ideologies and decisions fall into racial groups. Such as the moderate Hutus. They are perceived to be extremists by the opposing group and traitors by their own group.

## Tuesday, 24 November 2009

### Funny Chinese names

Sorry this is untranslatable to English because the humour lies in all the homonyms.

## Saturday, 14 November 2009

### PhD vs. Undergrad+Masters / 博士 vs. 本科

Xingbo and I were discussing the difference between PhD and Undergrad/Masters. We reached the following analogy.
If you're a undergrad/masters student, and you're given a paper to read, all you're required is to comprehend the technical points in the paper and know how to reuse it. If you're a PhD student, you need to write a significantly improved paper.

### Science vs. Engineering / 科学 vs. 工程

I was discussing with my friend Xingbo today about the difference between engineering and science. He gave a good definition. Engineering research results in immediate added value to society while science research requires engineering efforts before their fruits can be reaped by the society.
IEOR Department joke: "When does engineering become science? When it stops being useful"

Xingbo 和我讨论了一下科学和工程的区别。 他很英明的发表出一对很吻合的定义。 工程研究是可以直接产生社会价值， 而科学研究是须要工程研究的加工才能导致可用产品。 两个都一样重要， 往往科学更加难，名利少很多。

## Thursday, 5 November 2009

### Finite Simple Group

The path of love is never smooth
But mine's continuous for you
You're the upper bound in the chains of my heart
You're my Axiom of Choice, you know it's true

But lately our relation's not so well-defined
And I just can't function without you
I'll prove my proposition and I'm sure you'll find
We're a finite simple group of order two

I'm losing my identity
I'm getting tensor every day
And without loss of generality
I will assume that you feel the same way

Since every time I see you, you just quotient out
The faithful image that I map into
But when we're one-to-one you'll see what I'm about
'Cause we're a finite simple group of order two

Our equivalence was stable,
A principal love bundle sitting deep inside
But then you drove a wedge between our two-forms
Now everything is so complexified

When we first met, we simply connected
My heart was open but too dense
To have a finite limit, in some sense

I'm living in the kernel of a rank-one map
From my domain, its image looks so blue,
'Cause all I see are zeroes, it's a cruel trap
But we're a finite simple group of order two

I'm not the smoothest operator in my class,
But we're a mirror pair, me and you,
So let's apply forgetful functors to the past
And be a finite simple group, a finite simple group,
Let's be a finite simple group of order two
(Oughter: "Why not three?")

I've proved my proposition now, as you can see,
So let's both be associative and free
And by corollary, this shows you and I to be
Purely inseparable. Q. E. D.

## Tuesday, 20 October 2009

### 为什么有些人那么没有正义感？

“有了台湾， 就可以采到南海的石油， 还可以控制南海的运输。 在多了， 可以在台湾建立军事基地。”

## Saturday, 17 October 2009

### 为什么有些人那么物质？ / Why are some people so materialistic?

(English below)

-----------------------------------------------------------------------------------------------------------------------------
Yesterday I was chatting with a young female colleague about life and career goals.

She mentioned that many people worked tireless at getting into Goldman Sachs, only to find out the miserable long work hours after they enter. These people enter GS mainly to earn good money. But they cannot find time to enjoy the material that the money can buy. So I mentioned to her, why don't they just quit and find a different job? She said, how could anyone forgive a life of wearing brand name apparels and living in five-star hotels?

I was shocked. How can the best educated students in China be this materialistic? Could they possibly think that money can bring true happiness? As the current economy of China booms, we must admit to the great contributions that new generation of entrepreneurs made. However, their satisfaction should be based on the accumulation of account balance but rather from a sense of achievement for overcoming obstacles.

If you only know about living in luxury hotels and wearing expensive clothes, isn't that a rather short-sighted view of life? Ask yourself, what impact do you want to leave on society? What do you want your legacy to be? A life time of ostentatious hedonism? My own personal goal is to leave the world seeing that it is better place based on my efforts.

This is why I chose science. I hope to use science and technology to make people's lives better. To discover knowledge that would benefit mankind for years to come and to lay foundations for future generations. Living like this instills meaning in life. A lifetime of self-enjoyment is not for me.

## Sunday, 11 October 2009

### Veteran

I was riding on the train and met this fellow Joe. We chatted a bit about baseball. Soon, he told me he spent five years in the U.S. Marines. You can see that such experience had made the man immensely mature and determined.
Before he got off, he showed me his uniformed services card. With shocking casualness, he mentioned that he's discharged now because he got "blown up a few times". It was hard for me to tell but I think one of his leg was a prosthetic attachment.
Now I feel even worse about Bush. For he sent such brave loyal young souls to die for the rich man's oil.
Joe, take care.

## Thursday, 8 October 2009

### Amazing O.R. Analyst, Officer, and Rhodes Scholar from West Point

Check out the incredible story of Joshua Lospinoso. Top graduate from West Point Operations Research, NSF Scholarship recipient, and Rhodes Scholar. This man is incredibly intelligent with a strong sense of service and duty.

## Thursday, 24 September 2009

### Un-"Gentlemen's Club"

On the way to school the other day, I saw a taxi cab ad advertising "Gentlemen's Club" in New York City. It got me thinking. A gentlemen used to be a man of honour who upheld the values of chivalry which included justice, courage, politeness, civility, loyalty, and duty. A gentleman is supposed to be courteous and loyal to his lady. Under the Oriental interpretation of the word based on Confucianism (君子), similar values are preached. It is ironic and sad that New York City strip joints, which house the anti-gentlemen of the modern age, call themselves by a title that should be reserved for those with the highest level of conduct. Calling a strip club "gentlemen's club" is comparable to calling a biker's pub "intellectual's club", or calling a strip club in China "君子俱乐部".

## Saturday, 22 August 2009

### Going back in time & Crusaders

I was cleaning up my parents' computer today (optimizing all the accumulated electronic junk similar to how people clean out their attic & garage) and came across some of my history essays from high school. Needless to say I was appalled by my unintellectual discourses from my teenagehood.
One essay I read was about the impact of Crusades on Byzantine. The essay was so hollow it was than a joke. Its thesis seems to be that the Crusaders "destroyed?" Byzantine. The essay's body is more a regurgitation of ideas from secondary sources rather than a product of original thinking. It only focused upon the superficial military impacts of the Crusaders on Byzantine but doesn't address more fundamental questions such as
1. Why did the Crusaders, who were supposed to "Reconquista" Jerusalem and Anatolia, decided to ravage Byzantine and sack Constantinople? Especially when Byzantine was supposed to be their Christian brethren?
2. Why did Byzantine, the continuation of the mighty Eastern Roman Empire, not able to fend off a disorganized army of nobles and peasants from Western Europe?
3. Can't the downfall of Byzantine be attributed to the Turks/Muslims more so than the Crusaders?
On the flip side, I'm glad that university education has had an effect on my cerebrum.

## Monday, 22 June 2009

### Taiping Rebellion - Piece of history usually unknown in the West

I've been reading about the Taiping Rebellion recently. This curiosity was stirred by the recent Chinese movie "The Warlords" and a discussion with a friend about Christianity in China. Most people in the world don't know it but it's the largest civil war in the 19th century and the casualty is close to that of the Napoleonic Wars.
To summarize, it is a large scale sectarian rebellion that took place in Southern & coastal China at the end of the Qing dynasty. Number of deaths is around 25 million. The Taiping rebels managed to control Nanjing and certain major Chinese cities for quite a while and established the Taiping Heavenly Kingdom. The leader, Hong Xiuquan, claimed that he was told to be the brother of Jesus through a vision.
This movement lasted about 15 years and took place simultaneously with other ethnic rebellions in Ningxia, Gansu, and Shanxi.

Source: http://en.wikipedia.org/wiki/Taiping_Rebellion

## Friday, 29 May 2009

### Upcoming search engines

Bing from Microsoft
www.bing.com

and this interesting "computational knowledge engine" from Wolfram (maker of Mathematica) called WolframAlpha
http://www.wolframalpha.com/

## Tuesday, 28 April 2009

### Open letter to all gun rights activists.

1) There are basically two functions to gun ownership, self-defense against criminal violence and organized defense against government tyranny. If the 2nd amendment was written to ensure people's ability to defend against tyranny, shouldn't ordinary people be able to own grenades, automatic heavy weapons, artillery, tanks, fighter jets, and gun ships? It's hard to stand up to a US military junta with just semiautomatic M16s.

2) I think the phrase "criminals will ALWAYS get guns" is false. Strict weapon control on "military grade" weapons makes it very hard to criminals to get any heavy firearm, bazooka, or grenades. If we declare all firearms to be in the category of "military grade" weapon and make REAL concerted effort to control them, then we can pretty much make sure that criminals don't get guns.

3) Under the assumption that gun control can keep most guns out of criminal's hands, then the only validity to owning firearms is self-defense against government tyranny. It's true that superseding your right to own firearms makes it easier for government to abuse its power. Shouldn't we weigh this against the risk of big criminals (terrorists & school shooters) getting ahold of dangerous weapons?

The crux of the argument is whether people are willing to reign in some of their personal freedom and transfer that to state control. But isn't that what organized society is about? We relinquish our natural freedoms (like the free ability to kill someone) to establish a set of rules that can maximize everyone's utility.

## Friday, 24 April 2009

### Philosophy of Science, Google, and Machine Learning in Information Age

http://www.wired.com/science/discoveries/magazine/16-07/pb_theory

This is a blog article that argues for the end of deductive science. With the amount of information available on the internet, the author Chris Anderson argues that simple model built upon mountains of information can generalize much better than complex causal relationships. He calls this the Petabyte Age and uses example from TextRunner project, Google AdSense, and Google Translation.
Is this the end of deductive science?
On a related note, check out this notion of "transductive science" pioneered by Vladimir Vapnik.

## Monday, 20 April 2009

It's an awesome channel on YouTube.

### machine learning + computer vision at the Royal Institution Christmas Lecture

Bunch of kids can play a racing game by leaning left and right. Very cool.

Part of the 2008 Royal Institution Christmas Lecture "Hi-Tech Trek"

## Friday, 17 April 2009

### Infinity QX4 audio repair

Been meaning to post these photos.
A while back, the cd changer on my parents' 2001 Infinity QX4 jammed and we decided to get a new GPS audio navigation system. The unit I settled on was Pioneer AVIC-F700BT along with a bunch of accessories from Crutchfield.com.
The process wasn't that hard. The most critical component was this Scosche audio connector adapter (also called a harness). It allows you to connect Nissan audio cables to your Pioneer unit. I guess the overall process is:
0. UNPLUG THE CAR BATTERY!
1. Get rid of your old unit.
2. Hook up the harness. The Nissan cables all have tiny letters written on the plastic to indicate their functionality. Make sure you connect the AMP wire correctly according to the instruction manual.
3. Hook up the microphone to some place convenient.
4. Put the GPS antenna on the dash board.
5. You can leave the parking break and reverse signal wires from your Pioneer unit unconnected. Only connect the reverse signal if you're using a back-up cam.
By the way, I also bought an Audiovox back-up camera but couldn't get it to work :(
Here are some photos.

### Art vs. entertainment

If you look at every form of human expression, writing, music, film, drawing/painting, it is always divided into an "art/independent" stream and a "blockbuster/commercial" stream. You get movies like 007, Air Force One, American Pie against the more "thinking" films such as John Adams, documentaries, Britney Spears vs. Aaron Copland, John Grisham vs. Toni Morrison, and Japanese comic vs. Yoko Ono. Provided there is a small area of intersection.
I think this division comes from the purpose behind expression. Some pieces are created with entertainment as its ultimate objective while others are motivated by inquisition and enlightenment of the human condition.
Good "overlaps" in my humble opinion are films like Munich, Traffic, and Platoon.

### Why not invade another country to rob their money?

Interesting topic came up at a random conversation in school today. Country A will invade country B to rob their art gallery, industry, precious metal, but never their domestic currency? Ever wondered why?
That's because country B's currency would be utterly devalued on the international market during the invasion that the domestic currency would be equivalent to piles of paper.

## Thursday, 26 March 2009

### Rebecca's Painting

Check out my friend Rebecca's painting:

http://rebextrip.deviantart.com/art/Alpine-Glacier-117184602

## Tuesday, 17 March 2009

### Money as allocation of wealth and allocation of labour

Some of the resentment over the distribution of wealth comes from the fact that money has two functions in the society. It is both redistributing wealth and also redistributing labour.
Society's demand for different skills vary as time goes on. In a socialist society, people would not be free to choose what they do, rather they would be told what the state needs. If the state needs an engineer, you would become an engineer, if the state needs a farmer, you become a farmer. Everything happens according to a state-wide schedule.
In a free society, people cannot be assigned to certain types of work, but society still needs to the demand for certain skills. So the market raises wage for skills that are undersupplied while lowers wages for skills that are oversupplied. Should an accountant be paid more than a lawyer? This is why IT workers got paid huge money in the dot-com boom and are now getting paid less due to oversupply. The effect? Fewer students pursue computer science and turn to other fields. This way, the society keeps supply & demand in balance. Further side effect is that some people got incredibly wealthy for performing a task that can now be outsourced to India.

## Tuesday, 3 March 2009

### Human Computation

Luis von Ahn and the concept of "Human Computation"
How do we make use of wasted human computation cycles?