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Tutorial of Node Schematas - PI & TwoSymbol

Visualization of schematas for simple boolean nodes (automatas)





In [1]:



    


%load_ext autoreload
%autoreload 2
%matplotlib inline



    











In [3]:



    


from __future__ import division
import numpy as np
import pandas as pd
from IPython.display import Image, display
import cana
from cana.datasets.bools import *
from cana.drawing.canalizing_map import draw_canalizing_map_graphviz



    











In [4]:



    


n = OR()
print( n)
print( 'k_r: %.2f - %.2f' % (n.input_redundancy(mode='node',bound='upper',norm=False), n.input_redundancy(mode='node',bound='lower',norm=False)))
print( 'k_e: %.2f - %.2f' % (n.effective_connectivity(mode='node',bound='upper',norm=False), n.effective_connectivity(mode='node',bound='lower',norm=False)))
print( 'k_s: %.2f - %.2f' % (n.input_symmetry(mode='node',bound='upper',norm=False), n.input_symmetry(mode='node',bound='lower',norm=False)))
print()

print( 'k_r: %s (upper)' % n.input_redundancy(mode='input',bound='upper'))
print( 'k_e: %s (upper)' % n.input_redundancy(mode='input',bound='upper'))
print()

dfLUT, dfPI, dfTS = n.look_up_table(), n.schemata_look_up_table(type='pi'), n.schemata_look_up_table(type='ts')
display(pd.concat({'Original LUT':dfLUT,'PI Schema':dfPI,'TS Schema':dfTS}, axis=1).fillna('-'))
draw_canalizing_map_graphviz(n.canalizing_map())



    


















    






<BNode(name='OR', k=2, inputs=[i1,i2], state=0, outputs='[0,1,1,1]' constant=False)>
k_r: 0.75 - 0.75
k_e: 1.25 - 1.25
k_s: 2.00 - 2.00

k_r: [0.5, 0.5] (upper)
k_e: [0.5, 0.5] (upper)











    











  
    

      
      Original LUT
      PI Schema
      TS Schema
    

    

      
      In:
      Out:
      In:
      Out:
      In:
      Out:
    

  
  
    

      0
      00
      0
      00
      0
      00
      0
    

    

      1
      01
      1
      1#
      1
      1̊#̊
      1
    

    

      2
      10
      1
      #1
      1
      -
      -
    

    

      3
      11
      1
      -
      -
      -
      -
    

  













    
Out[4]:













%3


OR-0

OR


OR-1

OR


T-0_OR-0

2


T-0_OR-0->OR-0




i1-0

i1


i1-0->T-0_OR-0




i2-0

i2


i2-0->T-0_OR-0




T-1_OR-1

1


T-1_OR-1->OR-1




F-0_T-1_OR-1



F-0_T-1_OR-1->T-1_OR-1




i1-1

i1


i1-1->F-0_T-1_OR-1



i2-1

i2


i2-1->F-0_T-1_OR-1





















In [5]:



    


n = CONTRADICTION()
n.name = 'Con'
print( n)
print( 'k_r: %.2f - %.2f' % (n.input_redundancy(mode='node',bound='upper',norm=False), n.input_redundancy(mode='node',bound='lower',norm=False)))
print( 'k_e: %.2f - %.2f' % (n.effective_connectivity(mode='node',bound='upper',norm=False), n.effective_connectivity(mode='node',bound='lower',norm=False)))
print( 'k_s: %.2f - %.2f' % (n.input_symmetry(mode='node',bound='upper',norm=False), n.input_symmetry(mode='node',bound='lower',norm=False)))
print()

print( 'k_r: %s (upper)' % n.input_redundancy(mode='input',bound='upper'))
print( 'k_e: %s (upper)' % n.input_redundancy(mode='input',bound='upper'))
print 

dfLUT, dfPI, dfTS = n.look_up_table(), n.schemata_look_up_table(type='pi'), n.schemata_look_up_table(type='ts')
display(pd.concat({'Original LUT':dfLUT,'PI Schema':dfPI,'TS Schema':dfTS}, axis=1).fillna('-'))
draw_canalizing_map_graphviz(n.canalizing_map())



    


















    






<BNode(name='Con', k=2, inputs=[i1,i2], state=0, outputs='[0,0,0,0]' constant=True)>
k_r: 2.00 - 2.00
k_e: 0.00 - 0.00
k_s: 2.00 - 2.00

k_r: [1.0, 1.0] (upper)
k_e: [1.0, 1.0] (upper)










    











  
    

      
      Original LUT
      PI Schema
      TS Schema
    

    

      
      In:
      Out:
      In:
      Out:
      In:
      Out:
    

  
  
    

      0
      00
      0
      ##
      0
      ##
      0
    

    

      1
      01
      0
      -
      -
      -
      -
    

    

      2
      10
      0
      -
      -
      -
      -
    

    

      3
      11
      0
      -
      -
      -
      -
    

  













    
Out[5]:













%3


Con-0

Con


Con-1

Con


T-0_Con-0

0


T-0_Con-0->Con-0






















In [6]:



    


n = XOR()
print( n)
print( 'k_r: %.2f - %.2f' % (n.input_redundancy(mode='node',bound='upper',norm=False), n.input_redundancy(mode='node',bound='lower',norm=False)))
print( 'k_e: %.2f - %.2f' % (n.effective_connectivity(mode='node',bound='upper',norm=False), n.effective_connectivity(mode='node',bound='lower',norm=False)))
print( 'k_s: %.2f - %.2f' % (n.input_symmetry(mode='node',bound='upper',norm=False), n.input_symmetry(mode='node',bound='lower',norm=False)))
print()

print( 'k_r: %s (upper)' % n.input_redundancy(mode='input',bound='upper'))
print( 'k_e: %s (upper)' % n.input_redundancy(mode='input',bound='upper'))
print 
for input in [0,1]:
    for ts,per,sms in n._two_symbols[input]:
        print( 'TS: %s | PermIdx: %s | SameIdx: %s' % (ts, per,sms))
dfLUT, dfPI, dfTS = n.look_up_table(), n.schemata_look_up_table(type='pi'), n.schemata_look_up_table(type='ts')
display(pd.concat({'Original LUT':dfLUT,'PI Schema':dfPI,'TS Schema':dfTS}, axis=1).fillna('-'))
draw_canalizing_map_graphviz(n.canalizing_map())



    


















    






<BNode(name='XOR', k=2, inputs=[i1,i2], state=0, outputs='[0,1,1,0]' constant=False)>
k_r: 0.00 - 0.00
k_e: 2.00 - 2.00
k_s: 2.00 - 2.00

k_r: [0.0, 0.0] (upper)
k_e: [0.0, 0.0] (upper)
TS: 11 | PermIdx: [] | SameIdx: [[0, 1]]
TS: 00 | PermIdx: [] | SameIdx: [[0, 1]]
TS: 10 | PermIdx: [[0, 1]] | SameIdx: []










    











  
    

      
      Original LUT
      PI Schema
      TS Schema
    

    

      
      In:
      Out:
      In:
      Out:
      In:
      Out:
    

  
  
    

      0
      00
      0
      11
      0
      11
      0
    

    

      1
      01
      1
      00
      0
      00
      0
    

    

      2
      10
      1
      10
      1
      1̊0̊
      1
    

    

      3
      11
      0
      01
      1
      -
      -
    

  













    
Out[6]:













%3


XOR-0

XOR


XOR-1

XOR


T-0_XOR-0

2


T-0_XOR-0->XOR-0




i1-1

i1


i1-1->T-0_XOR-0




F-0_T-2_XOR-1



i1-1->F-0_T-2_XOR-1



i2-1

i2


i2-1->T-0_XOR-0




i2-1->F-0_T-2_XOR-1



T-1_XOR-0

2


T-1_XOR-0->XOR-0




i1-0

i1


i1-0->T-1_XOR-0




F-0_T-2_XOR-0



i1-0->F-0_T-2_XOR-0



i2-0

i2


i2-0->T-1_XOR-0




i2-0->F-0_T-2_XOR-0



T-2_XOR-1

2


T-2_XOR-1->XOR-1




F-0_T-2_XOR-0->T-2_XOR-1




F-0_T-2_XOR-1->T-2_XOR-1






















In [7]:



    


n = AND()
print( n)
print( 'k_r: %.2f - %.2f' % (n.input_redundancy(mode='node',bound='upper',norm=False), n.input_redundancy(mode='node',bound='lower',norm=False)))
print( 'k_e: %.2f - %.2f' % (n.effective_connectivity(mode='node',bound='upper',norm=False), n.effective_connectivity(mode='node',bound='lower',norm=False)))
print( 'k_s: %.2f - %.2f' % (n.input_symmetry(mode='node',bound='upper',norm=False), n.input_symmetry(mode='node',bound='lower',norm=False)))
print()

print( 'k_r: %s (upper)' % n.input_redundancy(mode='input',bound='upper'))
print( 'k_e: %s (upper)' % n.input_redundancy(mode='input',bound='upper'))
print 

dfLUT, dfPI, dfTS = n.look_up_table(), n.schemata_look_up_table(type='pi'), n.schemata_look_up_table(type='ts')
display(pd.concat({'Original LUT':dfLUT,'PI Schema':dfPI,'TS Schema':dfTS}, axis=1).fillna('-'))
draw_canalizing_map_graphviz(n.canalizing_map())



    


















    






<BNode(name='AND', k=2, inputs=[i1,i2], state=0, outputs='[0,0,0,1]' constant=False)>
k_r: 0.75 - 0.75
k_e: 1.25 - 1.25
k_s: 2.00 - 2.00

k_r: [0.5, 0.5] (upper)
k_e: [0.5, 0.5] (upper)










    











  
    

      
      Original LUT
      PI Schema
      TS Schema
    

    

      
      In:
      Out:
      In:
      Out:
      In:
      Out:
    

  
  
    

      0
      00
      0
      0#
      0
      0̊#̊
      0
    

    

      1
      01
      0
      #0
      0
      11
      1
    

    

      2
      10
      0
      11
      1
      -
      -
    

    

      3
      11
      1
      -
      -
      -
      -
    

  













    
Out[7]:













%3


AND-0

AND


AND-1

AND


T-0_AND-0

1


T-0_AND-0->AND-0




F-0_T-0_AND-0



F-0_T-0_AND-0->T-0_AND-0




i1-0

i1


i1-0->F-0_T-0_AND-0



i2-0

i2


i2-0->F-0_T-0_AND-0



T-1_AND-1

2


T-1_AND-1->AND-1




i1-1

i1


i1-1->T-1_AND-1




i2-1

i2


i2-1->T-1_AND-1






















In [7]:



    


n = COPYx1()
n.name = 'CPx1'
print( n)
print( 'k_r: %.2f - %.2f' % (n.input_redundancy(mode='node',bound='upper',norm=False), n.input_redundancy(mode='node',bound='lower',norm=False)))
print( 'k_e: %.2f - %.2f' % (n.effective_connectivity(mode='node',bound='upper',norm=False), n.effective_connectivity(mode='node',bound='lower',norm=False)))
print('k_s: %.2f - %.2f' % (n.input_symmetry(mode='node',bound='upper',norm=False), n.input_symmetry(mode='node',bound='lower',norm=False)))
print

print( 'k_r: %s (upper)' % n.input_redundancy(mode='input',bound='upper'))
print( 'k_e: %s (upper)' % n.input_redundancy(mode='input',bound='upper'))
print()

dfLUT, dfPI, dfTS = n.look_up_table(), n.schemata_look_up_table(type='pi'), n.schemata_look_up_table(type='ts')
display(pd.concat({'Original LUT':dfLUT,'PI Schema':dfPI,'TS Schema':dfTS}, axis=1).fillna('-'))
draw_canalizing_map_graphviz(n.canalizing_map())



    


















    






<BNode(name='CPx1', k=2, inputs=[i1,i2], state=0, outputs='[0,0,1,1]' constant=False)>
k_r: 1.00 - 1.00
k_e: 1.00 - 1.00
k_s: 0.00 - 0.00

k_r: [0.0, 1.0] (upper)
k_e: [0.0, 1.0] (upper)











    











  
    

      
      Original LUT
      PI Schema
      TS Schema
    

    

      
      In:
      Out:
      In:
      Out:
      In:
      Out:
    

  
  
    

      0
      00
      0
      0#
      0
      0#
      0
    

    

      1
      01
      0
      1#
      1
      1#
      1
    

    

      2
      10
      1
      -
      -
      -
      -
    

    

      3
      11
      1
      -
      -
      -
      -
    

  













    
Out[7]:













%3


T-1_CPx1-1

1


CPx1-1

CPx1


T-1_CPx1-1->CPx1-1




CPx1-0

CPx1


T-0_CPx1-0

1


T-0_CPx1-0->CPx1-0




i1-1

i1


i1-1->T-1_CPx1-1




i1-0

i1


i1-0->T-0_CPx1-0






















In [8]:



    


n = RULE90()
n.name = 'R90'
print( n)
print( 'k_r: %.2f - %.2f' % (n.input_redundancy(mode='node',bound='upper',norm=False), n.input_redundancy(mode='node',bound='lower',norm=False)))
print( 'k_e: %.2f - %.2f' % (n.effective_connectivity(mode='node',bound='upper',norm=False), n.effective_connectivity(mode='node',bound='lower',norm=False)))
print( 'k_s: %.2f - %.2f' % (n.input_symmetry(mode='node',bound='upper',norm=False), n.input_symmetry(mode='node',bound='lower',norm=False)))
print()

print( 'k_r: %s (upper)' % n.input_redundancy(mode='input',bound='upper'))
print( 'k_e: %s (upper)' % n.input_redundancy(mode='input',bound='upper'))
print()

dfLUT, dfPI, dfTS = n.look_up_table(), n.schemata_look_up_table(type='pi'), n.schemata_look_up_table(type='ts')
display(pd.concat({'Original LUT':dfLUT,'PI Schema':dfPI,'TS Schema':dfTS}, axis=1).fillna('-'))
draw_canalizing_map_graphviz(n.canalizing_map())



    


















    






<BNode(name='R90', k=3, inputs=[i1,i2,i3], state=0, outputs='[0,1,0,1,1,0,1,0]' constant=False)>
k_r: 1.00 - 1.00
k_e: 2.00 - 2.00
k_s: 1.33 - 1.33

k_r: [0.0, 1.0, 0.0] (upper)
k_e: [0.0, 1.0, 0.0] (upper)











    











  
    

      
      Original LUT
      PI Schema
      TS Schema
    

    

      
      In:
      Out:
      In:
      Out:
      In:
      Out:
    

  
  
    

      0
      000
      0
      1#1
      0
      1#1
      0
    

    

      1
      001
      1
      0#0
      0
      0#0
      0
    

    

      2
      010
      0
      0#1
      1
      0̊#1̊
      1
    

    

      3
      011
      1
      1#0
      1
      -
      -
    

    

      4
      100
      1
      -
      -
      -
      -
    

    

      5
      101
      0
      -
      -
      -
      -
    

    

      6
      110
      1
      -
      -
      -
      -
    

    

      7
      111
      0
      -
      -
      -
      -
    

  













    
Out[8]:













%3


R90-0

R90


R90-1

R90


T-0_R90-0

2


T-0_R90-0->R90-0




i1-1

i1


i1-1->T-0_R90-0




F-0_T-2_R90-1



i1-1->F-0_T-2_R90-1



i3-1

i3


i3-1->T-0_R90-0




i3-1->F-0_T-2_R90-1



T-1_R90-0

2


T-1_R90-0->R90-0




i1-0

i1


i1-0->T-1_R90-0




F-0_T-2_R90-0



i1-0->F-0_T-2_R90-0



i3-0

i3


i3-0->T-1_R90-0




i3-0->F-0_T-2_R90-0



T-2_R90-1

2


T-2_R90-1->R90-1




F-0_T-2_R90-0->T-2_R90-1




F-0_T-2_R90-1->T-2_R90-1






















In [9]:



    


n = RULE110()
n.name = 'R110'
print( n)
print( 'k_r: %.2f - %.2f' % (n.input_redundancy(mode='node',bound='upper',norm=False), n.input_redundancy(mode='node',bound='lower',norm=False)))
print( 'k_e: %.2f - %.2f' % (n.effective_connectivity(mode='node',bound='upper',norm=False), n.effective_connectivity(mode='node',bound='lower',norm=False)))
print( 'k_s: %.2f - %.2f' % (n.input_symmetry(mode='node',bound='upper',norm=False), n.input_symmetry(mode='node',bound='lower',norm=False)))
print()

print( 'k_r: %s (upper)' % n.input_redundancy(mode='input',bound='upper'))
print( 'k_e: %s (upper)' % n.input_redundancy(mode='input',bound='upper'))
print()

dfLUT, dfPI, dfTS = n.look_up_table(), n.schemata_look_up_table(type='pi'), n.schemata_look_up_table(type='ts')
display(pd.concat({'Original LUT':dfLUT,'PI Schema':dfPI,'TS Schema':dfTS}, axis=1).fillna('-'))
draw_canalizing_map_graphviz(n.canalizing_map())



    


















    






<BNode(name='R110', k=3, inputs=[i1,i2,i3], state=0, outputs='[0,1,1,1,0,1,1,0]' constant=False)>
k_r: 0.88 - 0.88
k_e: 2.12 - 2.12
k_s: 1.96 - 1.04

k_r: [0.75, 0.25, 0.25] (upper)
k_e: [0.75, 0.25, 0.25] (upper)











    











  
    

      
      Original LUT
      PI Schema
      TS Schema
    

    

      
      In:
      Out:
      In:
      Out:
      In:
      Out:
    

  
  
    

      0
      000
      0
      111
      0
      111
      0
    

    

      1
      001
      1
      #00
      0
      #00
      0
    

    

      2
      010
      1
      #10
      1
      #1̊0̊
      1
    

    

      3
      011
      1
      #01
      1
      #̊0̊1
      1
    

    

      4
      100
      0
      0#1
      1
      #̊10̊
      1
    

    

      5
      101
      1
      01#
      1
      0#̊1̊
      1
    

    

      6
      110
      1
      -
      -
      -
      -
    

    

      7
      111
      0
      -
      -
      -
      -
    

  













    
Out[9]:













%3


R110-0

R110


R110-1

R110


T-0_R110-0

3


T-0_R110-0->R110-0




i1-1

i1


i1-1->T-0_R110-0




i2-1

i2


i2-1->T-0_R110-0




F-0_T-2_R110-1



i2-1->F-0_T-2_R110-1



T-4_R110-1

2


i2-1->T-4_R110-1




F-0_T-5_R110-1



i2-1->F-0_T-5_R110-1



i3-1

i3


i3-1->T-0_R110-0




i3-1->F-0_T-2_R110-1



T-3_R110-1

2


i3-1->T-3_R110-1




i3-1->F-0_T-5_R110-1



T-1_R110-0

2


T-1_R110-0->R110-0




i2-0

i2


i2-0->T-1_R110-0




F-0_T-2_R110-0



i2-0->F-0_T-2_R110-0



F-0_T-3_R110-0



i2-0->F-0_T-3_R110-0



i3-0

i3


i3-0->T-1_R110-0




i3-0->F-0_T-2_R110-0



F-0_T-4_R110-0



i3-0->F-0_T-4_R110-0



T-2_R110-1

2


T-2_R110-1->R110-1




F-0_T-2_R110-0->T-2_R110-1




F-0_T-2_R110-1->T-2_R110-1




T-3_R110-1->R110-1




F-0_T-3_R110-0->T-3_R110-1




i1-0

i1


i1-0->F-0_T-3_R110-0



i1-0->F-0_T-4_R110-0



T-5_R110-1

2


i1-0->T-5_R110-1




T-4_R110-1->R110-1




F-0_T-4_R110-0->T-4_R110-1




T-5_R110-1->R110-1




F-0_T-5_R110-1->T-5_R110-1






















In [ ]:

Content source: rionbr/CANA

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