mRNA剪接Splicing 原理 – 施一公

3 Step Splicing : first & last steps are linear, 2nd step 3D syructure (non-linear) .

施一公 returned from USA, established the private 西湖大学 (funded by Alibaba, Baidu, Huawei etc), a first pure research university modeled on Caltech. His team first decoded the COVID19 genetic code sequence just 1 month after the Wuhan outbreak & announced the result FREE to the world.

The Hungarian lady scientist Katalin Karikó jumped on his newly published DNA code to invent the mRNA PfizerBioNTech vaccines.

https://m.toutiaoimg.cn/a6936774993665589790/?app=news_article&is_hit_share_recommend=0&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share

China Covid19 Test 20 millions in 5 days : Use Math!

惊艳世界的大规模检测,凭啥只有中国做的如此完美?详解混检技术

Why Chinese hospitals can test Covid19 at the speed of 20 million people in 5 days ?

Use Math !

Pre-requisite conditions :
1) <= 0.1% infected Covid19 patients in local population, then save 90% testing effort. If 9% infected, then only save 50%.

2) 10-in-1 混检 mixed test samples is the optimum algorithm : safety + accurate + efficient.

https://m.toutiaoimg.cn/a6902367747532194317/?app=news_article&is_hit_share_recommend=0&tt_from=android_share&utm_medium=toutiao_android&utm_campaign=client_share

BioMath: SARS-COV-2 in “A5 Simple Group” Icosahedral Structure

Abstract Algebra is about the study of all structures in the univers (Math, Nature, Physics, Chemistry, Bioscience,… ) : “Group Theory” is the tool invented by a 19CE genius Évariste Galois, originally used to solve the 300-year-old problem since 16CE “No Redical Solution for Polynomial Equations with degree 5 & above.

A5 is unbreakable structure called “Simple Group”, just like Atoms, so are fatal SARS & Covid19 hidden in A5 structure.

Math (Stats) applied in Coronaviruses Pandamic

Math (Stats) applied in Coronaviruses pandamic, by controlling the Reproduction number Ro < 1 via :
1) self protection : frequent wash hands, don’t shake hands / touch face / eyes / nose…
2) wear mask in enclosed environment (meeting room, church, shop, cinema, office… ) eg. SG COVID19 major Clusters in 2 SG churches, Hyatt Hotel Conference room, Wizlearn Technologies, CNY Loy Hei party,…

Malady math: The key statistic that determines your chances of getting coronavirus

Icosahedral Viruses & Galois Group A5

Icosahedral (or 20-sided geometry) is the math of Group Theory which was discovered by Galois why Polynomial equation of degree 5 (& above) have no radical roots (expressed in +-*/ operations & nth root), ie
A5 (the alternating group of degree 5) is not “SOLVABLE“, or A5 a “SIMPLE” Group (like Atom in Physics).

Is it the reason that most fatal viruses (eg. SAR, Zika.. ) hide their proteins in Icosahedral structure which is also not “SOLVABLE”, ie “BREAKABLE” by any modern medical drugs, unless Mathematicians discover more about the Galois Group “A5” Icosahedral structure.

Geometry Goes Viral: Math Used to Solve Virus Puzzle

AI with Advanced Math helps in discovering new drugs

https://theconversation.com/i-build-mathematical-programs-that-could-discover-the-drugs-of-the-future-110689?from=timeline

Advanced Mathematical Methods with AI is a powerful tool:

  • Algebraic Topology (Persistent Homology)
  • Differential Geometry
  • Graph Theory

https://sinews.siam.org/Details-Page/mathematical-molecular-bioscience-and-biophysics-1

Mind over Matter : Bruce Lipton

Key Points:

1. The Foundation of Science has changed since Newtonian Era, except Biology / Medicine and Psychology which don’t keep up:

Math => Fractal Math

Newton Physics (Matter)=> Quantum Physics (Energy)

(Organic) Chemistry => Electro-Chemistry

Energy = Field = 气 Chi / Qi

3. Environment -> Mind -> Perception -> Genetic Control

4. Consciousness (5%), Subconscious-ness (95%)

Examples:

  • Driving car: inexperienced driver (consciousness), experienced driver (subconscious).
  • Dating (conscious behavior)

Note: The successful Deeplearning AI is using the concept of Perception called “Perceptrons” by analysing the Environmental (BIG DATA) pattern with the help of Mathematics (Calculus : Gradient Descent, Statistics : Bayesian Probability, Algebraic Topology, etc).

Math drives Biology

Does it ring a bell to biologists that viruses are mathematically structured objects ? such as the deadly SARS virus with a beautiful icosahedral symmetry.

Icosahedron corresponds to the “Unsolvable Quintic equation (degree 5 and above) with no radical root”, which led the 19 CE young French math genius Evariste Galois to invent “Group Theory” – a revolutionary foundation of the Modern Math.

The problem is few biologists or doctors are good in math, and rare are mathematicians knowledgeable in Biology and Medicine.

https://futurism.com/math-help-treat-diseases-develop-better-vaccines/

Is There a Multi-dimensional Mathematical World Hidden in the Brain’s Computation?

Algebraic Topology” can detect the Multi-dimensional neural network in our brain – by studying the Homology (同调) and co-Homology (上同调) with the help of Linear Algebra (multi-dim Matrix) &  Computers.

Homology = compute the number of “holes” in multi-dim space. 

Neurons formed in the brain can be modeled in Math (Topology) by Simplex 单纯 (plural : Simplices), billions of them interconnected into a complex – “Simplicial Complex” (单纯复体)。

https://singularityhub.com/2017/06/21/is-there-a-multidimensional-mathematical-world-hidden-in-the-brains-computation/?from=timeline#.WUvPNsvmjqD

The Match Algorithm

1962 two American economists David Gale & Lloyd Shipley designed “The Stable Marriage Problem” aka “The Match“.

Note: ‘Stable’ means nobody would be unhappy or breakup after the match.

Applications:
1. Matching couples
2. Matching hospitals & doctor graduates
3. Match schools to students
4. Match HDB houses to families
5. Match Xmas gifts exchange with party participants (each participant puts their gift in a pool for exchange)

Scenario: An island with 4 men (m1, m2, m3, m4) and 4 women (w1, w2, w3, w4). You are to match 4 couples of opposite sex.

Each man would propose to a woman.
However both men and women could list down their preferences with ranking, the higher ranked person would be given the choice.

Suppose the women preferences are (Table 1):

Choices 1st 2nd 3rd 4th
w1 m1 m2 m3 m4
w2 m2 m4 m1 m3
w3 m3 m4 m1 m2
w4 m4 m3 m2 m1

Suppose the men preferences are (Table 2):

Choices 1st 2nd 3rd 4th
m2 w1 w4 w3 w2
m3 w1 w2 w3 w4
m1 w2 w4 w3 w1
m4 w3 w1 w2 w4

Notation:
“->” propose
“♡” prefer

On Day 1
All men pick their 1st choice woman…

Both (m2 & m3) love the same woman w1,
{m2, m3} -> w1 ♡ {m1, m2, m3, m4}
so w1 chooses m2 tentatively (can be changed if better choice in next days)

m1 -> w2 ♡ {m2, m4, m1, m3}
so w2 chooses m1 tentatively.

m4 -> w3♡ {m3, m4, m1, m2}
so w3 chooses m4 tentatively.

Tentative Choice on Day 1:

m1 w2
m2 w1
m3 ?
m4 w3

On Day 2
Rejected in Day 1, now try 2nd choice…

m3 -> w2 ♡ {m2, m4, m1, m3} (w2 prefers m1 over m3)
So w2 committed to m1 (as in Day 1).

On Day 3
Again, try 3rd choice…
m3 -> w3 ♡ {m3, m4, m1, m2}
So w3 ditches m4 (Day 1 choice) and chooses m3.

Tentative Choice on Day 3:

m1 w2
m2 w1
m3 w3
m4 ?

On Day 4
Now m4 rejected, has to choose another (2nd choice) woman…
m4 -> w1 ♡ {m1, m2, m3, m4}
So w1 stays with m2 (as in Day 1 choice).

On Day 5
Poor m4 rejected by w3 & w1…now try his 3rd choice w2,
m4 -> w2 ♡{m2, m4, m1, m3}
So w2 ditches m1 (Day 1 choice) in favor of m4.

Tentative Choice on Day 5:

m1 ?
m2 w1
m3 w3
m4 w2

On Day 6
m1 was rejected in Day 5, now try his luck on his 2nd choice w4…

m1 -> w4 ♡ {m4, m3, m2, m1}
Since w4 has no other proposal, no choice but to accept m1.

Final Choice on Day 6:

m1 w4
m2 w1
m3 w3
m4 w2

Notes:
1. If we let the women propose to men, then by Day 1 would have terminated the Match as in:
image

2. The complexity occurs for men proposing to women, as shown in Table 2, both {m2, m3} choose w1. There is a fight !

3. While it may be possible for some women to get her man of first choice (here only w3 gets 1st choice m3), what if there are 100 or 1000 men and women? No guarantee to get the 1st choice.

Reference:
image

[Available @ AMK National Library #518.1]

See also: Stable Marriage Problem

Math Applied in Today’s Society數學在今日社會的應用–丘成桐教授

Prof ST Yau (Fields Medal, Harvard Math Dean)

OUHK – 數學在今日社會的應用–丘成桐教授 (第一部分):

image

image

1. Wavelet Data Compression Algorithm:

2. RSA Encryption

OUHK – 數學在今日社會的應用–丘成桐教授 (第二部分):
image

OUHK – 數學在今日社會的應用–丘成桐教授 (第三部分):

3. Akamai Network Distribution
image

OUHK – 數學在今日社會的應用–丘成桐教授 (第四部分):

4. Insurance Risks (Actuary)

OUHK – 數學在今日社會的應用–丘成桐教授 (第五部分):

5. GOOGLE Search:
image

OUHK – 數學在今日社會的應用–丘成桐教授 (第六部分):

6 不急功近利走捷径
image

7. 做大数学家成功之道:
– 对数学浓厚的兴趣
– 行则的培养: 不肤浅, 不偷功,不炫耀。
– 打好基本功

See also:

丘成桐谈holistic中学教育, 做大学问的态度…

Applied Math in Medicine

The young Russian doctor Sergei Arutyunyan was working with patients whose immune systems were rejecting transplanted kidneys.

The doctor has to decide whether to keep or remove it. If they kept the kidney, the patient could die, but if they remove it, the patient would need another long wait (or never) for another kidney.

The mathematician Edward Frankel helped him to analyze the collected data with ‘expert rules’ in a decision tree. (Note: this is like the Artificial Intelligence Rule-based Expert System, except no fuzzy math).

The successful diagnosis (with Math): 95%

image

Love and Math by Edward Frenkel http://www.amazon.co.uk/dp/0465050743/ref=cm_sw_r_udp_awd_53swtb16779PY