Geometry

學期總分出乎我意料外的高(93/100; rank: 4/57)
雖然分數並不代表什麼也不曾是我所重視的東西
不過連著這學期愉快的修課經驗
這真的是我9.5年來第一次感覺自己還有一點數學天份
而且還能受到別人小小肯定的一段學習歷程:)

謝謝所有這學期修幾何學的過程中陪伴我的課本老師助教朋友QQ

Selected Papers 012108

molecular biology
Quality Control by the Ribosome Following Peptide Bond Formation

biochemistry
Folding Energy Landscape and Network Dynamics of Small Globular Proteins

eukaryotic cytoskeleton
Filament Rigidity Causes F-Actin Depletion from Nonbinding Surfaces
Force Amplification Response of Actin Filaments under Confined Compression

prokaryotic cytoskeleton, biophysics
Force Generation by a Dynamic Z-Ring in Escherichia coli Cell Division
Condensation of FtsZ Filaments can Drive Bacterial Cell Division

neuroscience
Molecular Mechanism for the Umami Taste Synergism
Emergence of Complex Cell Properties by Learning to Generalize in Natural Scenes

developmental biology
Temporal and Spatial Control of Germ-Plasm RNAs

ecology
Simple Prediction of Interaction Strengths in Complex Food Webs
Origin of Pareto-like Spatial Distributions in Ecosystems

evolution
Darwin's Originality [review]
Simpson's Paradox in a Synthetic Microbial System

computational biology
Shape, Size, and Robustness: Feasible Regions in the Parameter Space of Biochemical Networks

dynamical systems
From Networks of Unstable Attractors to Heteroclinic Switching
Coherence versus Reliability of Stochastic Oscillators with Delayed Feedback
Partition of Networks into Basins of Attraction

astronomy
18 Years of Science with the Hubble Space Telescope [review]

Ajahn Chah

在西藏宗教文化的最後一堂課
接觸到了阿姜查的法語
看似樸實的語句
卻處處流露四法印的甘冽

這是我稍做修改後的pps播放檔
很單純的佛學哲思
並不帶有宗教色彩
所以可以放心的點下去看
並願能帶給你一些啟發:)

Selected Papers 011708

biochemistry
Disordered Flanks Prevent Peptide Aggregation
Stabilizing Effect of Knots on Proteins
How Main-Chains of Proteins Explore the Free-Energy Landscape in Native States

biophysics, cell biology
Dynein Pulls Microtubules without Rotating Its Stalk
Real-Time Visualization of Dynamin-Catalyzed Membrane Fission and Vesicle Release
GTPase Cycle of Dynamin Is Coupled to Membrane Squeeze and Release, Leading to Spontaneous Fission

cell biology, immunology
Scaffold Proteins and Immune-Cell Signalling [review]

developmental biology
Properties of Developmental Gene Regulatory Networks [perspective]

developmental biology, plant physiology
A Conserved Molecular Framework for Compound Leaf Development

evolution
The Eocyte Hypothesis and the Origin of Eukaryotic Cells [commentary]
The Archaebacterial Origin of Eukaryotes

computational biology
Dependence of Bacterial Chemotaxis on Gradient Shape and Adaptation Rate

theoretical biology
Self-Organization of Topological Defects due to Applied Constraints

Brouwer Fixed Point Theorem

posts in this series:
Atiyah-Singer Index Theorem,
Hairy Ball Theorem

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果然...
毛球定理是某個固定點定理(Brouwer F. P. T.)的S^2特例
每次讀幾何都會遇到令人驚奇的事情:)
近來有改行研究geometry/topology的衝動
看來蔡宜洵這學期的幾何教學大大的成功啊

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posts in this series:
Nash Equilibrium

Hairy Ball Theorem

posts in this series:
Atiyah-Singer Index Theorem

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順著Gauss-Bonnet Thm的思維
可以得到Poincaré-Hopf Index Theorem
P.-H.I.T.得到的結果是相當令人驚訝的
因為sum of indices竟然與向量場無關而和流形的拓樸有關
從P.-H.I.T.出發
我們又可以得到著名的毛球定理Hairy Ball Thm
毛球定理在大氣動力學上有個相當有趣的推論
而其定理形式與固定點定理Fixed Point Thm又有神似之處
It's really awesome!

do Carmo在他的課本上這樣寫著──
"The Gauss-Bonnet theorem is probably the deepest theorem in the differential geometry of surfaces."

雖然分數應該不會太好看
但這學期修幾何的經驗是相當愉快的
下學期蔡宜洵會開幾何概論
(historical approach on non-Euclidean geometry, I think)
黃武雄會開大域微分幾何
特別是黃武雄的一番話實在深深的感動了我──
"...關於曲面幾何，大域性質通常都是non-trivial。
每一個大域定理，都隱藏某種原創性的想法。
這是大域幾何最吸引人的地方。
欣賞幾何學家的洞察力，便是十分愉快的經驗。..."
寒假時該好好考慮下學期要不要繼續學幾何:)

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