Embed Size (px)
Citation preview
CELLULAR AUTOMATA RULES GENERATOR FOR MICROBIAL
COMMUNITIES
CALIFORNIA STATE UNIVERSITY, SAN BERNARDINOSCHOOL OF COMPUTER SCIENCE & ENGINEERING
By Melissa Quintana
Microbial Community
• April 1999– Removal of Microbial Life
• September 2003– Regrowth
Current Research
• Dr. Penelope Boston
• Explorations of extreme environments
• Microbiologist– Studies Microbial
CommunitiesCourtesy of Dr. Penelope Boston
Cellular Automata
11 11 00
11 11
00 00 11
0 = death1 = life
Total sum = 5
Rule : if total sum is 5 or less the cell state lives.
11 11 00
11 11 11
00 00 11
Cellular Automata
• Dr. SchubertSamples
• Cellular Automata• Rules• Radius of
three• Series of 20 to
represent growth over a period of time
Goal – Extract Radius• Use image analysis to produce a visual
representation of cellular automata specifications.
for i=1:prod(size(a1)) if (a1(i)==0 & b1(i)==1) then Live(a2(i)+1)=Live(a2(i)+1)+1 elseif (a1(i) - b1(i)>0) then Die(a2(i)+1)=Die(a2(i)+1)+1 elseif (a1(i)==1 & b1(i)==1) thenStableTwo(a2(i)+1)=StableTwo(a2(i)+1)+1; end end
What is the radius of effect?• The radius of effect of Cellular Automata• Why is it important?
Goal-Estimate the Rules
•Estimated Rules
Program
•Estimated Rules
What are Rules?Game of Life
1 represents a neighbor0 represents no life
•Any live cell with fewer than two live neighbors dies, as if caused by under-population.
<2 = Death
1 0 0
0 1 0
0 0 0
1 0 0
0 0 0
0 0 0
•Any live cell with more than three live neighbors dies, as if by overcrowding.
>3 = Death
1 1 1
0 1 1
0 0 0
1 1 1
0 0 1
0 0 0
•Any live cell with two or three live neighbors lives on to the next generation.
2 or 3 = life
1 0 0
1 1 0
0 0 0
1 0 0
1 1 0
0 0 0
•Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.
Exactly 3 = Life
0 0 0
0 0 0
1 1 1
0 0 0
0 1 0
1 1 1
Importance of the Study
• Discover the rules without knowing the rules.
• Correlate the rules with patterns.
• Overall understanding of what and how much of the environmental factors contribute to the results of the growth.
Visual Identification
1-34 35-50
Life Death
•Water
•Soil
•Biomass
•Weather
•Randomness
•Over-crowding
Correlate the rules with the patterns with an understanding of
the surrounding environmental factors.
•Air •Sediments (animals, plants)•Hot and Cold Temperatures
Thesis Project• Three Phases
– Phase One• Testing Calculations • Identifying the Radius of effect
– Phase Two• Identifying an approximation of the Rules
– Phase Three• Identifying an approximation of the Rules from pictures
• Samples– Cellular Automata– Pictures
• SciLab
First Phase – Predefined Matrix
• Predefined MatrixA = [110100111;100000100;111001001; 110110000;110100110;001011001; 100010011;111100010;000100000];
1 1 0 1 0 0 1 1 1
1 0 0 0 0 0 1 0 0
1 1 1 0 0 1 0 0 1
1 1 0 1 1 0 0 0 0
1 1 0 1 0 0 1 1 0
0 0 1 0 1 1 0 0 1
1 0 0 0 1 0 0 1 1
1 1 1 1 0 0 0 1 0
0 0 0 1 0 0 0 0 0
Calculate and Store1 1 0 1 0 0 0
1 0 0 0 0 1 0
0 0 1 1 0 0 1
1 0 0 1 1 0
0 1 0 0 0 1 0
1 0 0 1 0 0 1
0 1 1 0 1 0 1
= 20
1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0 0 0 0 0 0 0
1 0 0 0 0 1 0
0 0 1 1 0 0 1
1 0 0 1 1 0
0 1 0 0 0 1 0
1 0 0 1 0 0 1
0 1 1 0 1 0 1
= 17
1 1
0 0 0 0 1 1 1
1 0 0 0 0 1 0
0 0 1 1 0 0 1
1 0 0 1 1 0
0 1 0 0 0 1 0
1 0 0 1 0 0 1
0 1 1 0 1 0 1
= 20
1 2
0 0 0 0 1 1 1
1 0 0 0 0 1 0
0 0 1 1 0 0 1
1 0 0 1 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
= 10
1 1 2
0 0 0 0 1 1 1
1 0 0 0 0 1 0
0 0 1 1 0 0 1
1 0 0 1 0 0
0 0 0 0 0 0 0
0 0 0 0 0 1 1
1 1 1 1 1 1 1
= 17
1 2 2
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 1 1 0 0 0 1
1 0 0 1 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
= 5
1 1 2 2
1 1 1 1 1 1 1
0 0 0 0 0 0 0
0 1 1 0 0 0 1
1 0 0 1 0 0
0 0 0 0 0 1 0
0 0 0 0 0 0 0
1 1 1 1 1 1 1
= 20
1 1 2 3
Calculation Output
• Manual Verification 7.12.24.22.10.4.1.0.0.1.
0. 0. 2. 4. 10. 8. 15. 5. 10. 12. 6. 4. 2. 2. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
Program Function
• Cellular Automaton• Was used that had
specific rules assigned to it.
• Series of 20 to represent growth and time.
• Function • First program was
turned into a function.
• The function was called on every time series to produce Histogram Analysis.
Radius 1 Output
• Radius of effect = 1• Calculation area
Radius 2 Output
• Radius of effect = 2• Calculation area
Radius 3 Output
• Radius of effect = 3• Calculation area
Second Phase
• Created to compare against existing estimates from Cellular Automaton of a static image.
Live Center
Dead Center
14 - 34
35 - 45
Cellular Automata
Calculate and Store (1ST Series)
1 2 3 4 5 6 7 …. …. …. 20
1 1 1 1 1 1 1
0 0 0 0 0 0 0
0 1 1 0 0 0 1
1 0 0 1 1 0 0
0 0 0 0 0 1 0
0 0 0 0 0 0 0
1 1 1 1 1 1 1
= 20
20
1 2 3 4 5 6 7 8 9 10 11 12 . . . . . . . .
Center Cell state – Live (1) or dead (0)
1
1 2 3 4 5 6 7 8 9 10 11 12 . . . . . . . .
1 1 1 1 1 1 1
1 1 0 0 1 0 0
0 1 1 0 0 0 1
1 0 0 0 1 0 0
0 0 1 0 0 1 1
1 0 0 0 1 0 1
1 1 1 1 1 1 1
= 28
20 28
1 0
1 1 1 1 1 1 1
1 1 1 1 1 0 0
0 1 1 0 0 0 1
1 0 1 1 1 0 0
0 0 1 0 0 1 1
1 0 1 0 1 0 1
1 1 1 1 1 1 1
= 32
20 28 32
1 0 1
For all Generations(2nd Series)
1 2 3 4 5 6 7 …. …. …. 20
1 1 1 1 1 1 1
0 0 0 0 0 0 0
0 1 1 0 0 0 1
1 0 0 1 1 0 0
0 0 0 0 0 1 0
0 0 0 0 0 0 0
1 1 1 1 1 1 1
= 20
20
1 2 3 4 5 6 7 8 9 10 11 12 . . . . . . . .
Center Cell state – Live (1) or dead (0)
1
1 2 3 4 5 6 7 8 9 10 11 12 . . . . . . . .
1 1 1 1 1 1 1
1 1 0 0 1 0 0
0 1 1 0 0 0 1
1 0 0 0 1 0 0
0 0 1 0 0 1 1
1 0 0 0 1 0 1
1 1 1 1 1 1 1
= 28
20 28
1 0
1 1 1 1 1 1 1
1 1 1 1 1 0 0
0 1 1 0 0 0 1
1 0 1 1 1 0 0
0 0 1 0 0 1 1
1 0 1 0 1 0 1
1 1 1 1 1 1 1
= 32
20 28 32
1 0 1
Comparison of Selected Generations1 2 3 4 5 6 7 …. …. …. 20t = 20If t == ? then 1 2 3 4 5 6 7 …. …. …. 20
2 7 4 6 7 5 ….Vector with radius summed valuesSeries 5 Matrix calculation Results Series 6 Matrix calculation Results
Vector with radius summed values20 28 32 5 11 49 ….
Vector with radius cell states Vector with radius cell states0 1 1 0 1 0 …. 1 1 0 0 1 0 ….
0-1 1-1 1-0 0-0A dead cell
becomes aliveA live cell
remains aliveA live cell
becomes dead A dead cell
Remains dead
1 2 3 4 5 6 7 . 1 2 3 4 5 6 7 . 1 2 3 4 5 6 7 . 1 2 3 4 5 6 7 .
0-1 1-1 1-0 0-0 0-1 1-1 1-0 0-0 0-1 1-1 1-0 0-0 0-1 1-1 1-0 0-0 0-1 1-1 1-0 0-0 0-1 1-1 1-0 0-0
Program OutputLiveState 0-1
DeadState 1-0
StableState 1-1
StableState 0-0
Static Versus DynamicLiveState 0-1
StableState 1-1
DeadState 1-0
StableState 0-0
Dynamic
Stable 1-13
Live 14-35
Die 36-45
Live Center
Dead Center
14 - 34
35 - 45Static
3rd Phase – Using Pictures
Image Preparation• Paint
– Clip and Resize pictures– Resize according to the radius
• Scilab Image Processing toolbox– Converts the image into a matrix– [Apr1999]=imread('C:\program files\scilab-4.1.2\contrib\siptoolbox\images\
April_1999_Color_W106xH103.jpg')0.34 0.21 0.11 0.42 0.12
0.19 0.11 0.13 0.22 0.19
0.11 0.13
0.44 0.12
0.49 0.33
0.29 0.33 0.19 0.21 0.22
0.39 0.21 0.13 0.34 0.46
0.22 0.44
0.36 0.19
0.34 0.17
Thresholding0.34 0.2
10.11 0.42 0.12 0.11 0.42 0.12 0.12
0.19 0.11
0.13 0.22 0.19 0.13 0.22 0.19 0.19
0.22 0.39
0.14 0.11 0.13 0.14 0.11 0.13 0.13
0.23 0.33
0.43 0.44 0.12 0.43 0.44 0.12 0.12
0.12 0.39
0.44 0.49 0.33 0.44 0.49 0.33 0.33
0.22 0.39
0.14 0.11 0.13 0.14 0.11 0.13 0.13
0.23 0.33
0.43 0.44 0.12 0.43 0.44 0.12 0.12
0.12 0.39
0.44 0.49 0.33 0.44 0.49 0.33 0.33
0.12 0.39
0.44 0.49 0.33 0.44 0.49 0.33 0.33
= Summed value of all cells/(max cell value* radius^2)
Round ValueIf < 0.5
Value = 0If > 0.5
Value = 1
11 01 0 0 1 1 1 0 1 0
1 1 1 1 0 1 0 0 0
0 0 1 0 0 1 1 1 0
1 0 0 0 1 1 0 0 0
0 0 0 0 0 1 1 1 0
1 0 1 0 1 0 1 0 1
0 1 1 1 0 0 1 0 1
0 1 1 0 0 1 1 0 1
1 0 0 1 1 0 0 1 1
1 0 1
Calculate and Store•This is completed for both picture matrix
1 1 1 1 1 1 1
0 0 0 0 0 0 0
0 1 1 0 0 0 1
1 0 0 1 1 0 0
0 0 0 0 0 1 0
0 0 0 0 0 0 0
1 1 1 1 1 1 1
= 20
20
1 2 3 4 5 6 7 8 9 10 11 12 . . . . . . . .
Center Cell state – Live (1) or dead (0)
1
1 2 3 4 5 6 7 8 9 10 11 12 . . . . . . . .
1 1 1 1 1 1 1
1 1 0 0 1 0 0
0 1 1 0 0 0 1
1 0 0 0 1 0 0
0 0 1 0 0 1 1
1 0 0 0 1 0 1
1 1 1 1 1 1 1
= 28
20 28
1 0
1 1 1 1 1 1 1
1 1 1 1 1 0 0
0 1 1 0 0 0 1
1 0 1 1 1 0 0
0 0 1 0 0 1 1
1 0 1 0 1 0 1
1 1 1 1 1 1 1
= 32
20 28 32
1 0 1
Compare
2 7 4 6 7 5 ….Vector with radius summed valuesFirst Picture Matrix calculation Results
Second Picture Matrix calculation ResultsVector with radius summed values
20 28 32 5 11 49 ….
Vector with radius cell states Vector with radius cell states0 1 1 0 1 0 …. 1 1 0 0 1 0 ….
0-1 1-1 1-0 0-0A dead cell
becomes aliveA live cell
remains aliveA live cell
becomes dead A dead cell
Remains dead
1 2 3 4 5 6 7 . 1 2 3 4 5 6 7 . 1 2 3 4 5 6 7 . 1 2 3 4 5 6 7 .
0-1 1-1 1-0 0-0 0-1 1-1 1-0 0-0 0-1 1-1 1-0 0-0 0-1 1-1 1-0 0-0 0-1 1-1 1-0 0-0 0-1 1-1 1-0 0-0
April 1999 September 2003
4th Program - OutputLiveState 0-1
DeadState 1-0
StableState 1-1
StableState 0-0
Picture RulesLiveState 0-1
DeadState 1-0
StableState 0-0
Pictures
Live 1 - 49
Die 17-50
StableState 1-1
Picture Results
•Too long of a time period•High value summed range producing life•High value summed ranged producing death
Future Studies
• Future Research– Compare all series comparisons
• Missing rules
– More samples• What should represent a series?
• Long Term Goals– Correlate the rules with patterns– Aid in ongoing efforts
Test for Missing Rules
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
CompareCOMPARE
Identify an Appropriate Time Series
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Approximately 4 years
Goal
•Estimated Rules
Program
•Estimated Rules
Visual Identification
1-34 35-50
Life Death
•Water
•Soil
•Biomass
•Weather
•Randomness
•Over-crowding
Correlate the rules with the patterns with an understanding of
the surrounding environmental factors.
•Air •Sediments (animals, plants)•Hot and Cold Temperatures
Conclusion
Learning more about microbial communities and supporting other’s in their efforts will enable us to equip ourselves with knowledge to be
used when the opportunity for future endeavors arise.
