**Phenotype**

Expansion

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

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

私

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

と

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.

Persons who are skilled in math languages should apply their skills into biological phenomena/phenotypes.

**Heterogeneity**

Stochastic

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

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