Sunday, December 28, 2008

Atiyah-Singer Index Theorem

這學期會決定修幾何除了排課上的技術問題外
主要的動機應該源於三年前丘成桐的演講
而最後一根稻草則是去年讀到的這篇nature review

如果說我學classical diff geo有什麼實用目的
大概就是弄清楚Gauss-Bonnet Thm的來龍去脈
近日蔡宜洵開始談G.-B.T.時說
G.-B.T.只是Atiyah-Singer Index Thm的special case
才驚覺Gauss-Bonnet Thm的優雅深邃
並不止於其最為人熟知的表象上(幾何與拓樸的橋樑)
其根源於Gauss的測地實務而至管窺宇宙最深層的實在
......
證明了一個定理真的不代表了解該定理背後可能的蘊涵
A.-S.I.T.某些版本的證明手法甚至是受到物理的啟發而來
隱藏在世界繽紛樣貌背後那一以貫之的道啊!

下節錄自Atiyah和Singer獲頒Abel Prize時的prize announcement──
Scientists describe the world by measuring quantities and forces that vary over time and space. The rules of nature are often expressed by formulas, called differential equations, involving their rates of change. Such formulas may have an "index," the number of solutions of the formulas minus the number of restrictions that they impose on the values of the quantities being computed. The Atiyah–Singer index theorem calculated this number in terms of the geometry of the surrounding space.

A simple case is illustrated by a famous paradoxical etching of M. C. Escher, "Ascending and Descending," where the people, going uphill all the time, still manage to circle the castle courtyard. The index theorem would have told them this was impossible.

不得不提一下
title連結的那篇文章寫得十分清晰易懂
沒什麼接觸數學的人看了應該也會大受感動才是XD

BTW,
因為那篇文章我才知道原來theorem跟theater同字源──
theorem: worthy of closer examination and appreciation
僅僅一個字就道盡了數學本質上的真與美!

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posts in this series:
Hairy Ball Theorem
Brouwer Fixed Point Theorem,
Nash Equilibrium

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Saturday, December 27, 2008

Songs from Disney Films

不小心撞見了許多曾經之於我意義重大的片段:)

Circle of Life from The Lion King
original movie clip (English)
original movie clip (French)

Colors of the Wind from Pocahontas
original movie clip (English)
original movie clip (French)

Go the Distance from Hercules
original movie clip (English)
original movie clip (French)

On the Way (Mulan Revisited)

Two inspiring songs from Mulan

Know yourself; 本覺真如

Reflection
[original movie clip by Lea Salonga
pop version by Christina Aguilera
violin by Vanessa-Mae]

Look at me
You may think you see who I really am
But you'll never know me
Every day, is as if I play apart
Now I see if I wear a mask
I can fool the world
But I can not fool my heart

Who is that girl I see
Staring straight back at me?
When will my reflection show
Who I am inside?

I am now in a world
Where I have to hide my heart
And what I believe in
But somehow I will show the world
What's inside my heart
And be loved for who I am

Who is that girl I see
Staring straight back at me?
Why is my reflection
Someone I don't know?

Must I pretend that I'm someone else for all time?
When will my reflection show who I am inside?

There's a heart that must be free to fly
That burns with a need to know the reason why
Why must we all conceal
What we think
How we feel
Must there be a secret me I'm forced to hide?
I won't pretend that I'm someone else for all time
When will my reflections show
Who I am inside?
When will my reflections show
Who I am inside?

Determination & Responsibility; 精進修行

I'll Make a Man Out of You
[original movie clip by Donny Osmond
Chinese movie clip by Jacky Chan
pop version (Mandarin) by Jacky Chan
pop version (Cantonese) by Jacky Chan]

Let's get down to business
To defeat the Huns
Did they send me daughters
When I asked for sons?
You're the saddest bunch I ever met
But you can bet before we're through
Mister, I'll make a man out of you

Tranquil as a forest
But on fire within
Once you find your center you are sure to win
You're a spineless, pale pathetic lot
And you haven't got a clue
Somehow I'll make a man out of you

I'm never gonna catch my breath
Say good-bye to those who knew me
Boy, was I a fool in school for cutting gym
This guy's got 'em scared to death
Hope he doesn't see right through me
Now I really wish that I knew how to swim

(Be a man)
We must be swift as the coursing river
(Be a man)
With all the force of a great typhoon
(Be a man)
With all the strength of a raging fire
Mysterious as the dark side of the moon

Time is racing toward us till the Huns arrive
Heed my every order and you might survive
You're unsuited for the rage of war
So pack up, go home you're through
How could I make a man out of you?

(Be a man)
We must be swift as the coursing river
(Be a man)
With all the force of a great typhoon
(Be a man)
With all the strength of a raging fire
Mysterious as the dark side of the moon

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Saturday, December 20, 2008

Selected Papers 122008

prokaryotic cytoskelton, evolution
Cell Sorting Protein Homologs Reveal an Unusual Diversity in Archaeal Cell Division [commentary]
A Role for the ESCRT System in Cell Division in Archaea
A Unique Cell Division Machinery in the Archaea

comment: Two groups have identified the cell division components in one of the main archaeal phylum, Crenarchaeota. This solves the long-puzzling question that how Crenarchaeotes execute cytokinesis without any known tublin or actin homologs and provides some clue about evolutionary relationship between Bacteria, Archaea and Eukarya.

biophysics
Cell Shape and Cell-Wall Organization in Gram-Negative Bacteria
Membrane Shape as a Reporter for Applied Forces
Receptor Noise Limitations on Chemotactic Sensing

imaging
Characterizing Heterogeneous Cellular Responses to Perturbations

cell biology, theoretical biology
Negative Feedback that Improves Information Transmission in Yeast Signalling

plant developmental biology
Developmental Patterning by Mechanical Signals in Arabidopsis

ecology, theoretical biology
Strong Effect of Dispersal Network Structure on Ecological Dynamics

evolution
Reverse Engineering the Genotype-Phenotype Map with Natural Genetic Variation [review]

theoretical biology
Extinction and Resurrection in Gene Networks
Ordered Cyclic Motifs Contribute to Dynamic Stability in Biological and Engineered Networks

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Thursday, December 18, 2008

Les Misérables

Comment faire un monde sans misère et sans frontières?

看了教官的這篇《土地銀行
心中的難過已經沒法用言語形容了
自認受Victor Hugo影響甚深
自認有人道關懷的襟懷與實踐
自認有在省察世間的幽暗與苦難

進台大後的資源豐富
我也成了一個何不食肉糜的腐儒
對室友鎮日除了睡覺以外就是打電動的生活方式
一直疑惑何以台大學生可以這樣浪費國家資源卻不知反省
但我卻沒有質疑自己為何會對
可以拿國科會的經費報研討會的帳不用自付餐宿這樣的事情
覺得自己賺到了
真是糟糕到了極致

只能坐在電腦前聽Condamnés讓自己更難過

Friday, December 05, 2008

Selected Papers 120508

genetics, biophysics
Stochasticity and Traffic Jams in the Transcription of Ribosomal RNA: Intriguing Role of Termination and Antitermination

cell biology, eukaryotic cytoskeleton, theoretical biology
Regulation of Microtubule Dynamics by Reaction Cascades Around Chromosomes

cytoskeleton
Detection of GTP-Tubulin Conformation in Vivo Reveals a Role for GTP Remnants in Microtubule Rescues

cell biology
Polarity and Differential Inheritance-- Universal Attributes of Life? [review]
Determination of Bacterial Rod Shape by a Novel Cytoskeletal Membrane Protein
Network Hubs Buffer Environmental Variation in Saccharomyces cerevisiae
Real-Time Luminescence Monitoring of Cell-Cycle and Respiratory Oscillations in Yeast

synthetic biology
Design Principles of Biochemical Oscillators [review]
A Fast, Robust and Tunable Synthetic Gene Oscillator

developmental biology, evolution
Evolution Acts on Enhancer Organization to Fine-Tune Gradient Threshold Readouts

ecology
Defined Spatial Structure Stabilizes a Synthetic Multispecies Bacterial Community

theoretical biology
Interaction Stochasticity Supports Cooperation in Spatial Prisoner's Dilemma
Oscillations and Patterns in Interacting Populations of Two Species

imaging
Fluorescent Probes for Super-Resolution Imaging in Living Cells [review]
Whole-Cell 3D STORM Reveals Interactions between Cellular Structures with Nanometer-Scale Resolution

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Monday, December 01, 2008

Song of the Day

挑了很久
決定是......

となりのトトロ My Neighbor Totoro :)
[selected youtube videos 1, 2; mp3]

トトロ トトロ
Totoro, Totoro
トトロ トトロ
Totoro, Totoro

だれかが こっそり
小路に 木の実 うずめて
Someone planted some seeds on the footpath in secret
ちっさな芽 生えたら
And if you find small buds
秘密の暗号 森へのパスポート
It's the secret password; it's the passport to the forest
すてきな冒険はじまる
Now your wonderful adventure starts

となりのトトロ トトロ
My neighbor Totoro, Totoro
トトロ トトロ
Totoro, Totoro
森の中に むかしから住んでる
Living in the forest from ancient days
となりのトトロ トトロ
My neighbor Totoro, Totoro
トトロ トトロ
Totoro, Totoro
子供のときにだけ
You can see them only when you are kid
あなたに訪れる
不思議な出会い
It's an amazing encounter

雨ふり バス停
In a raining day, at a bus stop
ズブヌレ オバケがいたら
If you encounter a soaking giant
あなたの雨ガサ
さしてあげましょ 森へのパスポート
Don't be afraid just pass your umbrella to him;
it's the passport to the forest

魔法の扉 あきます
Now the magical door opens to you

となりのトトロ トトロ
My neighbor Totoro, Totoro
トトロ トトロ
Totoro, Totoro
月夜の晩に オカリナ吹いてる
They play ocarina under the moonlight
となりのトトロ トトロ
My neighbor Totoro, Totoro
トトロ トトロ
Totoro, Totoro
もしも会えたなら
If you can meet them
すてきな しあわせが
あなたに来るわ
A beautiful happiness will fall to you

今天唯一的願望就是希望到老
都能很快樂地唱這首歌
還能用這樣的角度看世界:)

謝謝今天祝福我的人
我沒什麼東西可以送給你們
那就一起聽となりのトトロ吧XD

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