Mendel's First Law

2018. 11. 26. 18:07

Problem

Figure 2. The probability of any outcome (leaf) in a probability tree diagram is given by the product of probabilities from the start of the tree to the outcome. For example, the probability that X is blue and Y is blue is equal to (2/5)(1/4), or 1/10.

Probability is the mathematical study of randomly occurring phenomena. We will model such a phenomenon with a random variable, which is simply a variable that can take a number of different distinct outcomes depending on the result of an underlying random process.

For example, say that we have a bag containing 3 red balls and 2 blue balls. If we let $X$ represent the random variable corresponding to the color of a drawn ball, then the probability of each of the two outcomes is given by $P r (X = red) = \frac{3}{5}$ and $P r (X = blue) = \frac{2}{5}$ .

Random variables can be combined to yield new random variables. Returning to the ball example, let $Y$ model the color of a second ball drawn from the bag (without replacing the first ball). The probability of $Y$ being red depends on whether the first ball was red or blue. To represent all outcomes of $X$ and $Y$ , we therefore use a probability tree diagram. This branching diagram represents all possible individual probabilities for $X$ and $Y$ , with outcomes at the endpoints ("leaves") of the tree. The probability of any outcome is given by the product of probabilities along the path from the beginning of the tree; see Figure 2 for an illustrative example.

An event is simply a collection of outcomes. Because outcomes are distinct, the probability of an event can be written as the sum of the probabilities of its constituent outcomes. For our colored ball example, let $A$ be the event " $Y$ is blue." $P r (A)$ is equal to the sum of the probabilities of two different outcomes: $P r (X = blue and Y = blue) + P r (X = red and Y = blue)$ , or $\frac{3}{10} + \frac{1}{10} = \frac{2}{5}$ (see Figure 2 above).

Given: Three positive integers $k$ , $m$ , and $n$ , representing a population containing $k + m + n$ organisms: $k$ individuals are homozygous dominant for a factor, $m$ are heterozygous, and $n$ are homozygous recessive.

Return: The probability that two randomly selected mating organisms will produce an individual possessing a dominant allele (and thus displaying the dominant phenotype). Assume that any two organisms can mate.

num1=29
num2=24
num3=19
case = num1+num2+num3
mendel = []
probability = 0

def combination(n,k):
    numerator = 1
    denominator = 1
    k = min(n-k,k)
    for i in range(1,k+1):
        denominator*=i
        numerator*=n+1-i
    return  numerator/denominator

total = combination(case,2)

for i in range(1,case+1):
    if i <= num1:
        mendel.append("AA")
    elif i <= num1+num2:
        mendel.append("Aa")
    else:
        mendel.append("aa")


for i in range(0,len(mendel)):
    for j in range(i+1,len(mendel)):
        if mendel[i]=="AA":
            probability+=1
        elif mendel[i]=="Aa" and mendel[j]=="Aa":
            probability+=0.75
        elif mendel[i]=="Aa" and mendel[j]=="aa":
            probability+=0.5

print(round(probability/total,5))

Introduction to Mendelian Inheritanceclick to collapse

Figure 1. A Punnett square representing the possible outcomes of crossing a heterozygous organism (Yy) with a homozygous recessive organism (yy); here, the dominant allele Y corresponds to yellow pea pods, and the recessive allele y corresponds to green pea pods.

Modern laws of inheritance were first described by Gregor Mendel (an Augustinian Friar) in 1865. The contemporary hereditary model, called blending inheritance, stated that an organism must exhibit a blend of its parent's traits. This rule is obviously violated both empirically (consider the huge number of people who are taller than both their parents) and statistically (over time, blended traits would simply blend into the average, severely limiting variation).

Mendel, working with thousands of pea plants, believed that rather than viewing traits as continuous processes, they should instead be divided into discrete building blocks called factors. Furthermore, he proposed that every factor possesses distinct forms, called alleles.

In what has come to be known as his first law (also known as the law of segregation), Mendel stated that every organism possesses a pair of alleles for a given factor. If an individual's two alleles for a given factor are the same, then it is homozygous for the factor; if the alleles differ, then the individual is heterozygous. The first law concludes that for any factor, an organism randomly passes one of its two alleles to each offspring, so that an individual receives one allele from each parent.

Mendel also believed that any factor corresponds to only two possible alleles, the dominant and recessive alleles. An organism only needs to possess one copy of the dominant allele to display the trait represented by the dominant allele. In other words, the only way that an organism can display a trait encoded by a recessive allele is if the individual is homozygous recessive for that factor.

We may encode the dominant allele of a factor by a capital letter (e.g., $A$ ) and the recessive allele by a lower case letter (e.g., $a$ ). Because a heterozygous organism can possess a recessive allele without displaying the recessive form of the trait, we henceforth define an organism's genotypeto be its precise genetic makeup and its phenotype as the physical manifestation of its underlying traits.

The different possibilities describing an individual's inheritance of two alleles from its parents can be represented by a Punnett square; see Figure 1 for an example.

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library(openxlsx) sheet 여러개 쓰기

2018. 11. 26. 14:02

openxlsx 패키지

이번 포스팅에서는 openxlsx 패키지를 이용하여 여러개의 데이터프레임을 하나의 엑셀파일에 저장해 보도록하겠습니다.

library(openxlsx)

Workbook을 만들고-sheet를 만들고-쓰고-저장하는 다음 4개의 함수를 기억하시면 됩니다. createWorkbook()-addWorksheet()-writeDataTable()-saveWorkbook()

우리가 사랑하는 iris와 mtcars로 예시 데이터를 만들어 보겠습니다.

a <- iris
b <- mtcars

예제 Workbook을 만들고

example <- createWorkbook("example")
example

## A Workbook object.
##
## Worksheets:
##  No worksheets attached

Worksheet를 추가해줍니다.

addWorksheet(example, "a")
addWorksheet(example, "b")
example

## A Workbook object.
##
## Worksheets:
##  Sheet 1: "a"
##
##
##  Sheet 2: "b"
##
##
##
##  Worksheet write order: 1, 2

다음과 같이 만들어 놓은 Worksheet에 각 데이터를 넣을 수 있습니다.

writeDataTable(example,"a",a)
writeDataTable(example,"b",b)

저장해 줍니다. write.csv()와 비슷하게 사용하면 됩니다.

saveWorkbook(example, file="example.xlsx")

결과물은 다음과 같습니다.

출처 : https://youngjunna.github.io/2018/04/03/openxlsx/

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리눅스 하드 추가

2018. 11. 26. 14:00

1. fdisk -l

드라이브 목록을 확인한다.

# fdisk -l

Device Boot Start End Blocks Id System

/dev/sda1 * 2048 1026047 512000 83 Linux

/dev/sda2 1026048 1469032447 734003200 83 Linux

/dev/sda3 1469032448 1510975487 20971520 83 Linux

/dev/sda4 1510975488 1953523711 221274112 5 Extended

/dev/sda5 1510977536 1531949055 10485760 83 Linux

/dev/sda6 1531951104 1552922623 10485760 83 Linux

/dev/sda7 1552924672 1560788991 3932160 82 Linux swap / Solaris

/dev/sda8 1560791040 1952958463 196083712 83 Linux

Disk /dev/sdb: 4000.8 GB, 4000787030016 bytes, 7814037168 sectors

Units = sectors of 1 * 512 = 512 bytes

Sector size (logical/physical): 512 bytes / 4096 bytes

I/O size (minimum/optimal): 4096 bytes / 4096 bytes

할당되지 않은 4TB 크기의 /dev/sdb 드라이브가 보인다. 이걸 파티션 할당해줘야 한다.

(리눅스는 보통 첫번째 드라이브가 /dev/sda1,2,3...두번째 드라이브가 /dev/sdb1,2,3... 이렇게 설정된다.)

2. fdisk /dev/[디스크명]

새로운 하드디스크를 추가한다.

# fdisk /dev/sdb

Welcome to fdisk (util-linux 2.23.2).

Changes will remain in memory only, until you decide to write them.

Be careful before using the write command.

Device does not contain a recognized partition table

Building a new DOS disklabel with disk identifier 0x6ad31b53.

WARNING: The size of this disk is 4.0 TB (4000787030016 bytes).

DOS partition table format can not be used on drives for volumes

larger than (2199023255040 bytes) for 512-byte sectors. Use parted(1) and GUID

partition table format (GPT).

The device presents a logical sector size that is smaller than

the physical sector size. Aligning to a physical sector (or optimal

I/O) size boundary is recommended, or performance may be impacted.

Command (m for help): m

Command action

a toggle a bootable flag

b edit bsd disklabel

c toggle the dos compatibility flag

d delete a partition

g create a new empty GPT partition table

G create an IRIX (SGI) partition table

l list known partition types

m print this menu

n add a new partition

o create a new empty DOS partition table

p print the partition table

q quit without saving changes

s create a new empty Sun disklabel

t change a partition's system id

u change display/entry units

v verify the partition table

w write table to disk and exit

x extra functionality (experts only)

Command (m for help): n

Partition type:

p primary (0 primary, 0 extended, 4 free)

e extended

Select (default p):p

Partition number (1-4, default 1): 1

First sector (2048-4294967295, default 2048): 2048

Last sector, +sectors or +size{K,M,G} (2048-4294967294, default 4294967294): #Enter를 치면 default로 잡힌다.

Using default value 4294967294

Partition 1 of type Linux and of size 2 TiB is set

#하드디스크의 용량은 4TB이지만, 파티션에 할당할 수 있는 최대 크기는 2TB다.

Command (m for help): w

The partition table has been altered!

Calling ioctl() to re-read partition table.

Syncing disks.

3. mkfs -t [파일시스템] /dev/[디스크명]

파일시스템 만들기.

# mkfs -t ext4 /dev/sdb1

mke2fs 1.42.9 (28-Dec-2013)

Filesystem label=

OS type: Linux

Block size=4096 (log=2)

Fragment size=4096 (log=2)

Stride=0 blocks, Stripe width=0 blocks

134217728 inodes, 536870655 blocks

26843532 blocks (5.00%) reserved for the super user

First data block=0

Maximum filesystem blocks=2684354560

16384 block groups

32768 blocks per group, 32768 fragments per group

8192 inodes per group

Superblock backups stored on blocks:

32768, 98304, 163840, 229376, 294912, 819200, 884736, 1605632, 2654208,

4096000, 7962624, 11239424, 20480000, 23887872, 71663616, 78675968,

102400000, 214990848, 512000000

Allocating group tables: done

Writing inode tables: done

Creating journal (32768 blocks): done

Writing superblocks and filesystem accounting information: done

4. mount -t [파일시스템] /dev/[디스크명]

마운트하기.

# mount -t ext4 /dev/sdb1 /second

# df -h

Filesystem Size Used Avail Use% Mounted on

/dev/sda3 20G 93M 19G 1% /

/dev/sdb1 2.0T 81M 1.9T 1% /second # 새로 마운트한 드라이브가 보일 것이다.

이렇게 하면 4TB의 하드디스크 중에 2TB를 할당해서 사용할 수 있다.

그러나 2TB씩 쪼개서 사용하기 싫고 4TB를 통으로 사용하고 싶다면, 다르게 설정해줘야 한다.

5. 되돌리기

우선, 추가해줬던 파티션을 삭제하고 마운트도 다시 해제하자.

# fdisk /dev/sdb

WARNING: The size of this disk is 4.0 TB (4000787030016 bytes).

DOS partition table format can not be used on drives for volumes

larger than (2199023255040 bytes) for 512-byte sectors. Use parted(1) and GUID

partition table format (GPT).

The device presents a logical sector size that is smaller than

the physical sector size. Aligning to a physical sector (or optimal

I/O) size boundary is recommended, or performance may be impacted.

Welcome to fdisk (util-linux 2.23.2).

Changes will remain in memory only, until you decide to write them.

Be careful before using the write command.

Command (m for help): m

Command action

a toggle a bootable flag

b edit bsd disklabel

c toggle the dos compatibility flag

d delete a partition

g create a new empty GPT partition table

G create an IRIX (SGI) partition table

l list known partition types

m print this menu

n add a new partition

o create a new empty DOS partition table

p print the partition table

q quit without saving changes

s create a new empty Sun disklabel

t change a partition's system id

u change display/entry units

v verify the partition table

w write table to disk and exit

x extra functionality (experts only)

Command (m for help): d

Selected partition 1

Partition 1 is deleted

Command (m for help): w

The partition table has been altered!

Calling ioctl() to re-read partition table.

WARNING: Re-reading the partition table failed with error 16: 장치나 자원이 동작 중.

The kernel still uses the old table. The new table will be used at

the next reboot or after you run partprobe(8) or kpartx(8)

Syncing disks.

# umount /second

df- h로 확인해보면 디스크를 추가하지 전의 원래 상태로 돌아옴을 확인할 수 있다.

6. 2TB를 초과하는 디스크 할당하기.

2TB를 초과하는 파티션을 할당하기 위해선 parted 명령어를 사용해야 한다.

# parted /dev/sdb

GNU Parted 3.1

Using /dev/sdb

Welcome to GNU Parted! Type 'help' to view a list of commands.

(parted) help

align-check TYPE N check partition N for TYPE(min|opt) alignment

help [COMMAND] print general help, or help on COMMAND

mklabel,mktable LABEL-TYPE create a new disklabel (partition table)

mkpart PART-TYPE [FS-TYPE] START END make a partition

name NUMBER NAME name partition NUMBER as NAME

print [devices|free|list,all|NUMBER] display the partition table, available devices, free space, all found partitions, or a

particular partition

quit exit program

rescue START END rescue a lost partition near START and END

rm NUMBER delete partition NUMBER

select DEVICE choose the device to edit

disk_set FLAG STATE change the FLAG on selected device

disk_toggle [FLAG] toggle the state of FLAG on selected device

set NUMBER FLAG STATE change the FLAG on partition NUMBER

toggle [NUMBER [FLAG]] toggle the state of FLAG on partition NUMBER

unit UNIT set the default unit to UNIT

version display the version number and copyright information of GNU Parted

(parted) mklabel gpt

Warning: The existing disk label on /dev/sdb will be destroyed and all data on this disk will be lost. Do you want to continue?

Yes/No? yes

(parted) unit TB # 단위를 설정한다. GB or TB

(parted) mkpart primary 0.00TB 4.00TB # 용량 설정 start end

(parted) print

Model: ATA HGST HDN726040AL (scsi)

Disk /dev/sdb: 4.00TB

Sector size (logical/physical): 512B/4096B

Partition Table: gpt

Disk Flags:

Number Start End Size File system Name Flags

1 0.00TB 4.00TB 4.00TB ext4 primary # 정상적으로 추가됐다.

(parted) quit

Information: You may need to update /etc/fstab.

파일시스템을 만든다.

# mkfs -t ext4 /dev/sdb1

mke2fs 1.42.9 (28-Dec-2013)

Filesystem label=

OS type: Linux

Block size=4096 (log=2)

Fragment size=4096 (log=2)

Stride=0 blocks, Stripe width=0 blocks

244195328 inodes, 976754176 blocks

48837708 blocks (5.00%) reserved for the super user

First data block=0

Maximum filesystem blocks=3124756480

29809 block groups

32768 blocks per group, 32768 fragments per group

8192 inodes per group

Superblock backups stored on blocks:

32768, 98304, 163840, 229376, 294912, 819200, 884736, 1605632, 2654208,

4096000, 7962624, 11239424, 20480000, 23887872, 71663616, 78675968,

102400000, 214990848, 512000000, 550731776, 644972544

Allocating group tables: done

Writing inode tables: done

Creating journal (32768 blocks): done

Writing superblocks and filesystem accounting information: done

마운트한다.

# mount -t ext4 /dev/sdb1 /second

# df -h

Filesystem Size Used Avail Use% Mounted on

/dev/sda3 20G 93M 19G 1% /

/dev/sdb1 3.6T 89M 3.4T 1% /second # 마운트 완료

이 과정을 모두 마쳤다면, /second 폴더에 넣는 파일들은 모두 새로 추가한 디스크에 저장될 것이다.

그러나 재부팅 시 마운트가 자동으로 해제되기 때문에, 부팅할 때 자동으로 마운트를 해주는 설정을 해줘야 한다.

7. fstab 파일 등록

재부팅 시 자동마운트가 되도록 설정한다.

# blkid # 먼저 자동마운트 등록할 디스크의 UUID를 알아내야 한다.

/dev/sda1: UUID="22a87868-322e-4661-af01-93b2062044ce" TYPE="xfs"

/dev/sdb1: UUID="e001a7f9-1154-129e-a916-dad0b54116f2" TYPE="ext4" PARTLABEL="primary" PARTUUID="52412c84-700e-2313-9e2f-c12b1ca1676a"

# vi /etc/fstab

# /etc/fstab

# Created by anaconda on Sat Sep 26 08:52:44 2015

# Accessible filesystems, by reference, are maintained under '/dev/disk'

# See man pages fstab(5), findfs(8), mount(8) and/or blkid(8) for more info

UUID=1c407d96-e43b-4b52-af5f-b191560e8267 / ext4 defaults 1 1

UUID=e001a7f9-1154-129e-a916-dad0b54116f2 /second ext4 defaults 1 2 # 여기에 추가한다.

이렇게 하면 재부팅을 하더라도 자동마운트 된다.

굳이 재부팅을 할 필요없이 자동으로 마운트가 되는지 확인하고 싶다면, 마운트를 해제하고 mount -a 을 해보면 된다.

출처 : http://zero-gravity.tistory.com/297?category=665557

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