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PhenotypeExpansion2016Lunchon

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Ryo Yamada

on 13 December 2016

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Transcript of PhenotypeExpansion2016Lunchon

Phenotype
Expansion

2016/04/05
ICHG2016
Lunchon by Macrogen

Unit of Statistical Genetics
Kyoto University
Ryo Yamada
数学 on 医学
http://prezi.com/yosetp4cjsti/rims2013/
Backbone
Projective geometry
Differential equations
Cross-ratio
Cell population migrate as a slime in a high dimensional space

Optimization/Solution finding algorithm
based on genetic evolution-like algorithm.

Good performance for quite any kind of problems.
Tree structure
Trees, anatomical

Trees, functional
Pseudo-periodic
絡まっている
ほどけない
知恵の輪?
Swarm Intelligence
Lives cover land.

Landcover map by Environmental Research and Teaching at the University of Toronto

Biological Strategies

Slime mold is clever enough to find the shortest route in the labyrinth.
Its strategy is being investigated as a new model of parallel computing system.


Food

DNA molecules
4 letters, {A,T,G,C}
L=3 x 109 in length (Homo sapience)

Sequence variations
4L; L=1,2,…

Biological space is far much smaller than chemical space,
But still enormously big.

Biological space is a part of physico-chemical space.

Environmental fluctuations change width of pathways in biological space

Recombination is three-term relation.
But graph is for two-term relation.
A more informational tool is necessary.

Graph distance between sequences is No. mutations.
Recombination’s distance?

Letters are changed : Mutation
Combination of letters are changed : Recombination

制限のあるランダム・ウォーク
Restricted random walk
Self-avoiding walk
くりこみ群
Renormalization group analysis
巨視と微視を大雑把に分ける
Grossly discriminate macro and micro phenomena
Diffusion equation in a closed world
Eaquality~Simplex
Restictions~Complex

Restrictions as fixed marginl counts in table
Geometry, Curvature, Discrete grammar
Simple rules
Complexity

L-system
Song-bird's song
> songs2
[[1]]
[1] "ピ"

[[2]]
[1] "ピピチ"

[[3]]
[1] "ピピチピピチチピ "

[[4]]
[1] "ピピチピピチチピ ピピチピピチチピ チピ ピピチ "

[[5]]
[1] "ピピチピピチチピ ピピチピピチチピ チピ ピピチ ピピチピピチチピ ピピチピピチチピ チピ ピピチ チピ ピピチ ピピチピピチチピ "
Many switches
Rules but a bit irregular
Waves in neural network
Visual and Auditory Senses
1 dimensional but time-series
2D static
Patterns of cellular growth and curvature measure and discrete language
周期
素数ゼミ
Self-avoiding path with simple rule on a football
Search in Space
イントロA
「数学」とどういう関係にあるのか
Data Analysis
Statistics
Applied Mathematics
Biological rules have piled up through "Genetic Algorithm" for years.
Ways to understand the rules are based on visual/auditory information digestion.
ゲーム理論

あなた
複雑で高次元な仕組みを内包
知覚可能なのはその部分・像
知覚情報をそれなりに「解いて?」戦略を決める
単純なものを測って
関連を調べる
「線形回帰」
じゃあ、
一見、単純でないもの(複雑な表現型)から
単純なもの(単純な表現型)を引き出したい
発現状態の枝分かれ
単純化すると
Combinations
vs.
Permutations
Reprogramming ... based on "combination model"

Stable conditions, Attractor
自己改変型多スイッチシステム

格子上のSelf-avoiding path
Self-avoiding pathは
軌道の物理的周囲のエッジを排除しながら
酔歩する仕組み

自己改変型多スイッチシステムは
軌道上のノードが指定したエッジを排除しながら
酔歩する仕組み
Waves
Still have time?
Methods of integrating data to uncover genotype–phenotype interactions


Marylyn D. Ritchie et.al.
Nature Reviews Genetics 16, 85–97 (2015) doi:10.1038/nrg3868
Genetic Epidemiology
GWAS
Many analyzing methods are rooted deeply to these two.
Any extension?
Persons who can observe biological phenomena/phenotypes should translate them into mathematical languages.
Persons who are skilled in math languages should apply their skills into biological phenomena/phenotypes.

Heterogeneity
Stochastic

Undergrads
Grads
Evolution/Genetic Heterogeneity
Discrete Sparse Space Random Wark
Algebra
Pheno-math bilingual education
Bilingual but no completed dictionary
Development/Differentiation
Switch model
Order of events matter.
Cells are walking around on the hypercube of switches.
Almost Unidirectional labyrinth
Wire puzzle of switch labyrinth
Repetition Branching
Simple syntax
Units and repetition
Genetic Algorithm is better at finding these than others
NGS
0 or 1
Quantitative
Combination of Multiple Axes
0 or 1
Diversity
Phenotypes should be written with Math Syntax
BIG DATA
http://www.datanami.com/2012/05/01/picking_the_connectome_data_lock/


http://mathworld.wolfram.com/HypercubeGraph.html
Hypercube
GATAG|フリーイラスト素材集
PRIMITIVE
BILINGAL
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