# Supplementary Data - Bioinformatics

AI and Robotics

Nov 7, 2013 (4 years and 5 months ago)

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1

SUPPLEMENTARY

INFORMATION

Supplementary Figure 1
:
TGF
-
database.

2

Supplementary Figure 2
:
DAG produced from TGF
-
Beta pathway map

KEGG database.

Each node is identified by gen
e symbol
(e.g. DCN for Decorin).

The remainder of this document

is organized as follows:

Part I
: lays out basic concept
s

required to follow BDe scoring function described in Secton 2.3

Part II
: provides
graph

properties

of the networks in KEGG database (which mot
ivates the
choice of synthetic networks) and

-
standard
Bayesian
Networks (
BNs

-

ALARM network and ASIA network) and synthetically generated 8 BNs to
test the reliability of Bayesian Pathway Analysi
s (BPA)
.

Part
II
I
:

sho
ws the
set of Conditional Probability Tables
(CPTs)
of BNs for ideal case and
non
-
ideal case. An ideal case means data is generated according to consistent CPTs of the
given BN und
er consideration.

A non
-
ideal case means that a CPT is produced which is not

consistent with independencies entailed by the DAG part of the BN.

Part IV:

l
ists parameters of networks used in SynTReN to generate synthetic microarray data.

3

PART I
:

BAYESIAN DIRICHLET EQUIVALENT (BDe)

SCORE
CALCULATION

Given
the

gamma function

note that
. The beta
density function with parameters

and

is defined as

We refer to this function as

and a

random variable F with th
is density function is
said to have a beta distribution.

One can show that

which yields
. Suppose F has a beta distribution

and X is a
random variable with two values (1 and 2) such that
,

then
. In a BN setting

(without loss of generality, consider a bina
ry BN)
,
we
view F as the “driving function” for node X, assign a prior set of parameters (a, b) for X
and update the count for a and b, if there is some observed data.

Consider the single node binary BN to the left. Let’s consider X=1 to be
2 to be tails. If initially say, a=b=3, then we say probability of
observing a heads is 3/6 = 1/2. Assume we use a biased coin and one now
observes data d = 11112211111 with 9 1s and 2 2s. Then the distribution
function is updated as a=3+9=12, and b=3+2=5
and we say probability of
observing a heads is 12/17. If one has a valid reason to bias the initial
configuration of a and b, this can be reflected in the prior distribution
definition. For the above example, one could choose a larger value for a
compared
to b, initially.

Now consider binomial data d = (x
1
, x
2
, …, x
M
) with parameter F following

and N=
a+b. Assume we have s 1s and t 2s in d. One now can calculate

=

For example, let a=b=1 and assume we observe d=(1,2), i.e. on
e heads and one tails. Then

Note that if a random variable X
2

in a BN has a parent X
1
, then we would have two
“driving
functions” for X
2
, one for each instance of X
1

(whether X
1

is 1 or 2). Similarly, if a node in a
BN has 2 parents, we would have fou
r beta functions, one for each configuration of the values
the node’s parents assumes

(11, 12, 21
,

22),

and so on.

4

In Section 2.3 of the manuscript, we use Bayesian Dirichlet equivalent (BDe) scoring scheme,
which uses Dirichlet functions driving each
node, which is a generalization of the beta
distribution.
Based on the definitions listed here, first, let’s review the BDe score definition:

where
N

is the number of nodes,
q
i

is the number of different states of node’s parents, and
r
i

is
the set of

values a node can take on.
N
ij

is the sum of corresponding Dirichlet distribution
hyper
-
parameters
a
ijk
.
M
ij

is
the number of times that the parents of node
i

take on
configuration
j

in the

dataset.

Of these
M
ij

cases,
s
ijk

is
the total number of times in

the sample
that node
i

is observed to have value
k

when its parents take on configuration
j
.

Parameters used in this equation are best explained by an example. Consider the BN where
nodes can take on values 1, 2, or 3 and follow Dirichlet distribution
s
.

Note that X
3

has two parents and since each node can take on 3 values, X
3
’s parents can take
on 9 (3x3) different
configurations
.
Following equivalent sample size method
,

sum of the
initial Dirichlet
h
yper
-
parameters
,

a
ijk
, driving each node has the
same total
, 27. Hence,

a
111

= a
11
2

= a
11
3

=

a
2
11

= a
2
1
2

= a
2
1
3

= 3, and

a
3
11

= a
3
1
2

= a
3
1
3

=

1 (X
3
’s parents take on configuration 1, i.e. X
1
=1, X
2
=1)

a
32
1

= a
322

= a
323

=

1 (X
3
’s parents take on configuration 2, i.e. X
1
=1, X
2
=2)

N
i
q
j
r
k
ijk
ijk
ijk
ij
ij
ij
i
i
a
s
a
M
N
N
Model
Data
P
1
1
1
)
(
)
(
)
(
)
(
)
|
(

5

a
33
1

= a
332

= a
333

=

1 (X
3
’s parents take on configuration 3, i.e. X
1
=1, X
2
=3)

a
34
1

= a
342

= a
343

=

1 (X
3
’s parents take on configuration 4, i.e. X
1
=2, X
2
=1)

a
35
1

= a
352

= a
353

=

1 (X
3
’s parents take on configuration 5, i.e. X
1
=2, X
2
=2)

a
36
1

= a
362

= a
363

=

1 (X
3
’s parents take on

configuration 6, i.e. X
1
=2, X
2
=3)

a
37
1

= a
372

= a
373

=

1 (X
3
’s parents take on configuration 7, i.e. X
1
=3, X
2
=1)

a
38
1

= a
382

= a
383

=

1 (X
3
’s parents take on configuration 8, i.e. X
1
=3, X
2
=2)

a
39
1

= a
392

= a
393

=

1 (X
3
’s parents take on configuration 9, i
.e. X
1
=3, X
2
=3)

Now, let’s consider a sample input data and focus on node 3:

Observation

X1

X2

X3

1

3

1

2

2

3

1

1

3

1

2

1

4

2

1

3

5

2

2

1

6

1

3

2

7

1

3

3

8

3

3

2

9

3

2

3

10

2

3

1

Note that

N
31

= N
3
2

=

N
3
3

=

N
3
4

=

N
3
5

=

N
3
6

=

N
3
7

=

N
3
8

=

N
3
9

= 3.

Considering observed data,

M
31

= 0, M
3
2

=

1, M
3
3

= 2, M
3
4

=

1, M
3
5

=

1, M
3
6

=

1, M
3
7

=

2, M
3
8

=

1, M
3
9

= 1.

That is, for example, M
3
7

=

2 means 3
rd

node’s (X
3
’s ) parents assumed configuration 7 (X
1
=3,
X
2
=1) in 2 instances.
Now breaking these
M
ij

cases into

s
ijk
’s for node 3, we have:

s
311

=

0

s
31
2

= 0

s
31
3

= 0

s
3
2
1

=

1

s
3
22

=

0

s
3
23

= 0

s
3
3
1

=

0

s
3
32

= 1

s
3
33

= 1

s
3
4
1

=

0

s
3
42

=

0

s
3
43

= 1

s
3
5
1

=

1

s
3
52

= 0

s
3
53

= 0

s
3
6
1

=

1

s
3
62

=

0

s
3
63

= 0

s
3
7
1

=

1

s
3
72

= 1

s
3
73

= 0

s
3
8
1

=

0

s
3
82

=

0

s
3
83

= 1

s
3
9
1

=

0

s
3
92

=

1

s
3
93

= 0

That is, for example, 7
th

row in this table means when X
3
’s parents assumed configuration 7,
X
3

assumed the value “1” and “2” once (s
3
7
1

=

1,

s
3
72

=

1), and the value “3” zero times (s
3
73

=

0).
We believe the introduction produc
ed here is sufficient

to follow the equation in Section
2.4.

For further details, we refer the reader to “
Neapolitan R.E. (2004) Learning Bayesian
Networks. Prentice Hall

.

6

PART
I
I
:

DAGs

OF SIMULATED BNs

We first calculated following parameters for pa
thways listed in the KEGG database:

Average

Std. Dev.

# of Nodes

24.292

21.466

# of Edges

25.307

34.148

Max Degree

5.714

6.189

Average Degree

2.058

2.211

Density

0.180

0.264

We then created 8 synthetic BNs (in addition to widely used Asia and Ala
rm BNs) following
parametric distribution found in KEGG.
Synthetic BNs have (avg. ± st. dev.) 25.38 ± 13.87
nodes, 24.38 ± 13.87 links, and 1.93 ± 0.08 average degree reflecting a spectrum of typical
biological networks
.

DAG configuration o
f simulated BN
s

Name

Number of nodes

Number of
edges

ALARMNET

37

47

ASIANET

8

8

BN1

19

18

BN2

8

7

BN3

21

20

BN4

36

35

BN5

18

17

BN6

29

28

BN7

19

18

BN8

53

52

7

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37

ALARM network

1
2
3
4
5
6
7
8

ASIA network

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19

BN1

1
2
3
4
5
6
7
8

BN2

8

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21

BN3

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36

BN4

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18

BN5

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29

BN6

9

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19

BN7

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53

BN8

10

PART

I
II
:

CPTs of

S
imulated
BNs

Condi
tional
Probability D
istribution of a node

(i.e. a random variable in a Bayesian network
model)

can be represented in the form of a table
,
called
the Cond
itional Probability Table
(CPT).

A CPT
defines
P(X(i) | X(Pa(i)))
, where
X
(i)

is the
i
th

node, and
X(Pa(i))

are the
parents of node
i
.

Multidimensional arrays are used to store
and
list

CPTs utilizing

B
ayes
N
et
Toolbox
(BNT)
for Matlab

(
http://www.cs.ubc.ca/~murphyk/Software/BNT/bnt.html
)
.
If node
i

takes on
I

values and has
k

p
arents each of which take on
I
k

values, then the dimension of
the array used to store the CPT for node
i

is
I
1

x

I
2

x

x

I
k

x

I
. In our representation below,
and in the arrays holding CPTs, both nodes and nodes’ parents are shown in ascending order
with res
pect to their node numbers. In our representation, v
alues preceding

:

in the
multidimensional array

show possible values a node’s parent can take
and values following

:
” represent conditional probabilities for the values the node can take, all in ascend
ing order.
For example, assume we have a binary node “Node 1” with two binary parents “Node 3” and
“Node 7”. Then
,
the CP
T would have

a form of 2x2x2 array
and we would represent it as
shown in the table below:

Node 1

1 1 : 0.0377 0.9623

2 1 : 0.7766 0.22
34

1 2 : 0.5753 0.4247

2 2 : 0.8009 0.1991

The probability P(Node1 = 1 | Node3 = 1, Node7 = 2) would be 0.5753, and would be indexed
in the multidimensional array holding the CPTs as CPT(1
,2,1
)

=

0.
5753
. Below is the set of
CPTs for each BN used in MATLA
B simulations.

CPTs are listed in the order of nodes in
each BN.

Ideal CPTs (used to generate “data following CPTs”) are chosen from a Dirichlet distribution
and data that follow this CPT is generated using BNT. As for non
-
ideal CPTs (used to
generate “d
ata inconsistent with CPTs”), we have chosen initial Dirichlet hyper
-
parameters
(prior beliefs) to be equal for each node, i.e. we have chosen null model to
generate

random
data

for each node, and generated data using BNT with this CPT.

Therefore, underlyi
ng CPT
calculated from this randomly generated data is considered to be nonideal CPT since the CPT
is not generated according to the structure of given BN.

11

IDEAL CPTs

CPT of ALA
RM network

1 : 0.9600

2 : 0.0400

1 : 0.9200

2 : 0.0300

3 : 0.0500

1

: 0.8000

2 : 0.2000

1 : 0.9500

2 : 0.0500

1 : 0.8000

2 : 0.2000

1 : 0.0100

2 : 0.9800

3 : 0.0100

1 : 0.0100

2 : 0.9900

1 : 0.9500

2 : 0.0500

1 : 0.9500

2 : 0.0500

1 : 0.9000

2 : 0.1000

1 : 0.9900

2 : 0.0100

1 : 0.9900

2 : 0.0100

1 1 : 0.9500 0.0500

2 1 : 0.9500 0.0500

3 1 : 0.0500 0.9500

1 2 : 0.1000 0.9000

2 2 : 0.1000 0.9000

3 2 : 0.0100 0.9900

1 1 : 0.0500 0.9000 0.0500

2 1 : 0.9500 0.0400 0.0100

1 2 : 0.5000 0.4900 0.0100

2 2 : 0.9800 0.0100 0.0100

1 : 0.0100 0.9700 0.0100 0.0100

2 : 0.0100 0.0100 0.9700 0.0100

3 : 0.0100 0.0100 0.0100 0.9700

1 : 0.3000 0.4000 0.3000

2 : 0.9800 0.0100 0.0100

1 : 0.9900 0.0100

2 : 0.1000 0.9000

1 : 0.0500 0.9000 0.0500

2 : 0.0100 0.1900 0.8000

1 1 :
0.0500 0.9000 0.0500

2 1 : 0.9800 0.0100 0.0100

1 2 : 0.0100 0.0900 0.9000

2 2 : 0.9500 0.0400 0.0100

1 : 0.9500 0.0400 0.0100

2 : 0.0400 0.9500 0.0100

3 : 0.0100 0.2900 0.7000

1 1 : 0.9700 0.0100 0.0100 0.0100

2 1 : 0.9700 0.0100 0.0100 0.0100

1 2 : 0.0100 0.9700 0.0100 0.0100

2 2 : 0.9700 0.0100 0.0100 0.0100

1 3 : 0.0100 0.0100 0.9700 0.0100

2 3 : 0.9700 0.0100 0.0100 0.0100

1 4 : 0.0100 0.0100 0.0100 0.9700

2 4 : 0.9700 0.0100 0.0100 0.0100

1 : 0.9500 0.0400 0.0100

2 : 0.0400 0.950
0 0.0100

3 : 0.0100 0.0400 0.9500

1 1 1 : 0.9700 0.0100 0.0100 0.0100

2 1 1 : 0.9700 0.0100 0.0100 0.0100

1 2 1 : 0.9700 0.0100 0.0100 0.0100

2 2 1 : 0.9700 0.0100 0.0100 0.0100

1 3 1 : 0.9700 0.0100 0.0100 0.0100

2 3 1 : 0.9700 0.0100 0.0100 0.01
00

1 1 2 : 0.0100 0.9700 0.0100 0.0100

2 1 2 : 0.9500 0.0300 0.0100 0.0100

1 2 2 : 0.9700 0.0100 0.0100 0.0100

2 2 2 : 0.9700 0.0100 0.0100 0.0100

1 3 2 : 0.0100 0.9700 0.0100 0.0100

2 3 2 : 0.9500 0.0300 0.0100 0.0100

1 1 3 : 0.0100 0.0100 0.9700 0
.0100

2 1 3 : 0.4000 0.5800 0.0100 0.0100

1 2 3 : 0.9700 0.0100 0.0100 0.0100

2 2 3 : 0.9700 0.0100 0.0100 0.0100

1 3 3 : 0.0100 0.0100 0.9700 0.0100

2 3 3 : 0.5000 0.4800 0.0100 0.0100

1 1 4 : 0.0100 0.0100 0.0100 0.9700

2 1 4 : 0.3000 0.6800 0.010
0 0.0100

1 2 4 : 0.9700 0.0100 0.0100 0.0100

2 2 4 : 0.9700 0.0100 0.0100 0.0100

1 3 4 : 0.0100 0.0100 0.0100 0.9700

2 3 4 : 0.3000 0.6800 0.0100 0.0100

1 1 1 : 0.9700 0.0100 0.0100 0.0100

2 1 1 : 0.9700 0.0100 0.0100 0.0100

1 2 1 : 0.9700 0.0100
0.0100 0.0100

2 2 1 : 0.9700 0.0100 0.0100 0.0100

1 3 1 : 0.9700 0.0100 0.0100 0.0100

2 3 1 : 0.9700 0.0100 0.0100 0.0100

1 1 2 : 0.0100 0.9700 0.0100 0.0100

2 1 2 : 0.0100 0.4900 0.3000 0.2000

1 2 2 : 0.4000 0.5800 0.0100 0.0100

2 2 2 : 0.1000 0.84
00 0.0500 0.0100

1 3 2 : 0.0100 0.9000 0.0800 0.0100

2 3 2 : 0.0100 0.2900 0.3000 0.4000

1 1 3 : 0.0100 0.0100 0.9700 0.0100

2 1 3 : 0.0100 0.0100 0.0800 0.9000

1 2 3 : 0.2000 0.7500 0.0400 0.0100

2 2 3 : 0.0500 0.2500 0.2500 0.4500

1 3 3 : 0.0100 0
.0100 0.3800 0.6000

2 3 3 : 0.0100 0.0100 0.0800 0.9000

1 1 4 : 0.0100 0.0100 0.0100 0.9700

2 1 4 : 0.0100 0.0100 0.0100 0.9700

1 2 4 : 0.2000 0.7000 0.0900 0.0100

2 2 4 : 0.0100 0.1500 0.2500 0.5900

1 3 4 : 0.0100 0.0100 0.0100 0.9700

2 3 4 : 0.010
0 0.0100 0.0100 0.9700

1 1 : 0.9700 0.0100 0.0100 0.0100

2 1 : 0.9700 0.0100 0.0100 0.0100

3 1 : 0.9700 0.0100 0.0100 0.0100

1 2 : 0.0100 0.9700 0.0100 0.0100

2 2 : 0.6000 0.3800 0.0100 0.0100

3 2 : 0.0100 0.9700 0.0100 0.0100

1 3 : 0.0100 0.0100
0.9700 0.0100

2 3 : 0.5000 0.4800 0.0100 0.0100

3 3 : 0.0100 0.0100 0.9700 0.0100

1 4 : 0.0100 0.0100 0.0100 0.9700

2 4 : 0.5000 0.4800 0.0100 0.0100

3 4 : 0.0100 0.0100 0.0100 0.9700

1 1 : 0.9700 0.0100 0.0100 0.0100

2 1 : 0.9700 0.0100 0.0100 0.
0100

3 1 : 0.9700 0.0100 0.0100 0.0100

1 2 : 0.0100 0.9700 0.0100 0.0100

2 2 : 0.0100 0.9700 0.0100 0.0100

3 2 : 0.0300 0.9500 0.0100 0.0100

1 3 : 0.0100 0.0100 0.9700 0.0100

2 3 : 0.0100 0.0100 0.9700 0.0100

3 3 : 0.0100 0.9400 0.0400 0.0100

1 4 :

0.9700 0.0100 0.0100 0.9700

2 4 : 0.0100 0.0100 0.0100 0.9700

3 4 : 0.0100 0.8800 0.1000 0.0100

1 1 : 0.9800 0.0100 0.0100

2 1 : 0.9800 0.0100 0.0100

1 2 : 0.9800 0.0100 0.0100

2 2 : 0.9800 0.0100 0.0100

1 3 : 0.9500 0.0400 0.0100

2 3 : 0.0100 0
.9500 0.0400

1 4 : 0.9500 0.0400 0.0100

2 4 : 0.0100 0.0100 0.9800

1 : 0.0100 0.0100 0.9800

2 : 0.0100 0.0100 0.9800

3 : 0.0400 0.9200 0.0400

4 : 0.9000 0.0900 0.0100

1 1 : 0.9700 0.0100 0.0100 0.0100

2 1 : 0.0100 0.9700 0.0100 0.0100

3 1 : 0.
0100 0.9700 0.0100 0.0100

4 1 : 0.0100 0.9700 0.0100 0.0100

1 2 : 0.9700 0.0100 0.0100 0.0100

2 2 : 0.0100 0.0100 0.9700 0.0100

3 2 : 0.0100 0.0100 0.9700 0.0100

4 2 : 0.0100 0.0100 0.9700 0.0100

1 3 : 0.9700 0.0100 0.0100 0.0100

2 3 : 0.0100 0.0100

0.0100 0.9700

3 3 : 0.0100 0.0100 0.0100 0.9700

4 3 : 0.0100 0.0100 0.0100 0.4300

1 1 : 0.9800 0.0100 0.0100

2 1 : 0.9800 0.0100 0.0100

1 2 : 0.0100 0.9800 0.0100

2 2 : 0.9800 0.0100 0.0100

1 3 : 0.0100 0.0100 0.9800

2 3 : 0.6900 0.3000 0.0100

1 1 1 1 : 0.0500 0.9500

2 1 1 1 : 0.0100 0.9900

1 2 1 1 : 0.0500 0.9500

2 2 1 1 : 0.0100 0.9900

1 3 1 1 : 0.0500 0.9500

2 3 1 1 : 0.0100 0.9900

1 1 2 1 : 0.0500 0.9500

2 1 2 1 : 0.0100 0.9900

1 2 2 1 : 0.0500 0.9500

2 2 2 1 : 0.0100 0.9900

1 3
2 1 : 0.0500 0.9500

2 3 2 1 : 0.0100 0.9900

1 1 3 1 : 0.0100 0.9900

2 1 3 1 : 0.0100 0.9900

1 2 3 1 : 0.0100 0.9900

2 2 3 1 : 0.0100 0.9900

1 3 3 1 : 0.0100 0.9900

2 3 3 1 : 0.0100 0.9900

1 1 1 2 : 0.1000 0.9000

2 1 1 2 : 0.0100 0.9900

1 2 1 2 :
0.9500 0.0500

2 2 1 2 : 0.0100 0.9900

1 3 1 2 : 0.9500 0.0500

2 3 1 2 : 0.0500 0.9500

1 1 2 2 : 0.1000 0.9000

2 1 2 2 : 0.0100 0.9900

1 2 2 2 : 0.9500 0.0500

2 2 2 2 : 0.0100 0.9900

1 3 2 2 : 0.9500 0.0500

2 3 2 2 : 0.0500 0.9500

1 1 3 2 : 0.1000

0.9000

2 1 3 2 : 0.0100 0.9900

1 2 3 2 : 0.3000 0.7000

2 2 3 2 : 0.0100 0.9900

1 3 3 2 : 0.3000 0.7000

2 3 3 2 : 0.0100 0.9900

1 1 1 3 : 0.9500 0.0500

2 1 1 3 : 0.0100 0.9900

1 2 1 3 : 0.9900 0.0100

2 2 1 3 : 0.0500 0.9500

1 3 1 3 : 0.9500 0.050
0

2 3 1 3 : 0.0500 0.9500

1 1 2 3 : 0.9500 0.0500

2 1 2 3 : 0.0100 0.9900

1 2 2 3 : 0.9900 0.0100

2 2 2 3 : 0.0500 0.9500

1 3 2 3 : 0.9900 0.0100

2 3 2 3 : 0.0500 0.9500

1 1 3 3 : 0.3000 0.7000

2 1 3 3 : 0.0100 0.9900

1 2 3 3 : 0.9900 0.0100

2 2

3 3 : 0.0100 0.9900

1 3 3 3 : 0.3000 0.7000

2 3 3 3 : 0.0100 0.9900

1 : 0.1000 0.8900 0.0100

2 : 0.0100 0.0900 0.9000

1 1 : 0.9800 0.0100 0.0100

2 1 : 0.3333 0.3333 0.3333

1 2 : 0.0100 0.9800 0.0100

2 2 : 0.3333 0.3333 0.3333

1 3 : 0.0100 0.0
100 0.9800

2 3 : 0.3333 0.3333 0.3333

1 1 : 0.9800 0.0100 0.0100

2 1 : 0.3333 0.3333 0.3333

1 2 : 0.0100 0.9800 0.0100

2 2 : 0.3333 0.3333 0.3333

1 3 : 0.0100 0.0100 0.9800

2 3 : 0.3333 0.3333 0.3333

1 1 : 0.9800 0.0100 0.0100

2 1 : 0.9500 0.0
400 0.0100

3 1 : 0.3000 0.6900 0.0100

1 2 : 0.9500 0.0400 0.0100

2 2 : 0.0400 0.9500 0.0100

3 2 : 0.0100 0.3000 0.6900

1 3 : 0.8000 0.1900 0.0100

2 3 : 0.0100 0.0400 0.9500

3 3 : 0.0100 0.0100 0.9800

1 1 : 0.9800 0.0100 0.0100

2 1 : 0.9800 0.010
0 0.0100

1 2 : 0.0100 0.9800 0.0100

2 2 : 0.4000 0.5900 0.0100

1 3 : 0.0100 0.0100 0.9800

2 3 : 0.3000 0.4000 0.3000

1 1 : 0.9800 0.0100 0.0100

2 1 : 0.9800 0.0100 0.0100

3 1 : 0.3000 0.6000 0.1000

1 2 : 0.9800 0.0100 0.0100

2 2 : 0.1000 0.8500
0.0500

3 2 : 0.0500 0.4000 0.5500

1 3 : 0.9000 0.0900 0.0100

2 3 : 0.0500 0.2000 0.7500

3 3 : 0.0100 0.0900 0.9000

CPT of ASIA

network

1 : 0.0100

2 : 0.9900

1 : 0.5000

2 : 0.5000

1 : 0.0500 0.9500

2 : 0.0100 0.9900

1 : 0.1000 0.9000

2 :
0.0100 0.9900

1 : 0.6000 0.4000

2 : 0.3000 0.7000

1 1 : 1.0000 0.0000

2 1 : 1.0000 0.0000

1 2 : 1.0000 0.0000

2 2 : 0.0000 1.0000

1 : 0.9800 0.0200

2 : 0.0500 0.9500

1 1 : 0.9000 0.1000

2 1 : 0.7000 0.3000

1 2 : 0.8000 0.2000

2 2 : 0.10
00 0.9000

CPT of BN1

1 : 0.0580

2 : 0.9420

1 1 : 0.6387 0.3613

2 1 : 0.3358 0.6642

1 2 : 0.6118 0.3882

2 2 : 0.6977 0.3023

12

1 : 1.0000 0.0000

2 : 0.0329 0.9671

1 : 0.2310

2 : 0.7690

1 1 : 0.8261 0.1739

2 1 : 0.5497 0.4503

1 2 : 0.8889
0.1111

2 2 : 0.0738 0.9262

1 : 0.6460

2 : 0.3540

1 : 0.4483 0.5517

2 : 0.5053 0.4947

1 : 0.0590 0.9410

2 : 0.5969 0.4031

1 : 0.7440

2 : 0.2560

1 : 0.0320

2 : 0.9680

1 1 1 : 0.8333 0.1667

2 1 1 : 1.0000 0.0000

1 2 1 : 0.8519 0.1481

2 2 1 : 0.3811 0.6189

1 1 2 : 0.6250 0.3750

2 1 2 : 0.7813 0.2188

1 2 2 : 0.1765 0.8235

2 2 2 : 0.0479 0.9521

1 : 0.7470

2 : 0.2530

1 : 0.5400 0.4600

2 : 0.4179 0.5821

1 : 0.5968 0.4032

2 : 0.7466 0.2534

1 : 0.0500

2 : 0.9500

1 : 0
.0433 0.9567

2 : 0.0065 0.9935

1 1 1 1 : 0.2500 0.7500

2 1 1 1 : 0.4000 0.6000

1 2 1 1 : 0.6765 0.3235

2 2 1 1 : 0.4684 0.5316

1 1 2 1 : 0.5000 0.5000

2 1 2 1 : 1.0000 0.0000

1 2 2 1 : 0.4762 0.5238

2 2 2 1 : 0.5758 0.4242

1 1 1 2 : 0.6250 0.37
50

2 1 1 2 : 0.5333 0.4667

1 2 1 2 : 0.2566 0.7434

2 2 1 2 : 0.6780 0.3220

1 1 2 2 : 0.4444 0.5556

2 1 2 2 : 0.5000 0.5000

1 2 2 2 : 0.5474 0.4526

2 2 2 2 : 0.6444 0.3556

1 : 0.6667 0.3333

2 : 0.3710 0.6290

1 : 0.2880

2 : 0.7120

CPT of BN
2

1 : 0.5720

2 : 0.4280

1 1 1 : 0.7325 0.2675

2 1 1 : 0.0000 1.0000

1 2 1 : 0.1111 0.8889

2 2 1 : 0.0000 1.0000

1 1 2 : 0.0959 0.9041

2 1 2 : 1.0000 0.0000

1 2 2 : 0.0205 0.9795

2 2 2 : 1.0000 0.0000

1 : 0.9850

2 : 0.0150

1 : 0.7410

2 :
0.2590

1 : 0.9880

2 : 0.0120

1 : 0.4290

2 : 0.5710

1 1 1 : 0.4463 0.5537

2 1 1 : 0.5549 0.4451

1 2 1 : 0.0000 1.0000

2 2 1 : 1.0000 0.0000

1 1 2 : 0.6431 0.3569

2 1 2 : 0.2803 0.7197

1 2 2 : 0.0000 1.0000

2 2 2 : 1.0000 0.0000

1 : 0.88
11 0.1189

2 : 0.8388 0.1612

CPT of BN3

1 : 0.5123 0.4877

2 : 0.5478 0.4522

1 : 0.2113 0.7887

2 : 0.3929 0.6071

1 : 0.4797 0.5203

2 : 0.4359 0.5641

1 : 0.9501 0.0499

2 : 0.6386 0.3614

1 : 0.0000 1.0000

2 : 0.1677 0.8323

1 : 0.6073 0.
3927

2 : 0.9911 0.0089

1 : 0.4860

2 : 0.5140

1 : 0.7505 0.2495

2 : 0.5372 0.4628

1 : 0.4640 0.5360

2 : 0.4153 0.5847

1 : 0.3762 0.6238

2 : 0.3121 0.6879

1 1 : 0.0204 0.9796

2 1 : 0.0124 0.9876

1 2 : 0.9613 0.0387

2 2 : 0.0435 0.9565

1 : 0.5830

2 : 0.4170

1 1 : 0.0377 0.9623

2 1 : 0.7766 0.2234

1 2 : 0.5753 0.4247

2 2 : 0.8009 0.1991

1 : 0.3810 0.6190

2 : 0.4385 0.5615

1 : 0.7440

2 : 0.2560

1 : 0.2520

2 : 0.7480

1 : 0.5780 0.4220

2 : 0.4688 0.5313

1 : 0.961
0

2 : 0.0390

1 : 0.6087 0.3913

2 : 0.6667 0.3333

1 1 1 : 0.8421 0.1579

2 1 1 : 0.0000 1.0000

1 2 1 : 0.6667 0.3333

2 2 1 : 0.8235 0.1765

1 1 2 : 0.0980 0.9020

2 1 2 : 0.6826 0.3174

1 2 2 : 0.3000 0.7000

2 2 2 : 0.8661 0.1339

1 : 0.9962 0.
0038

2 : 0.0021 0.9979

CPT of BN4

1 : 0.5062 0.4938

2 : 0.5772 0.4228

1 : 0.4820

2 : 0.5180

1 : 0.7370 0.2630

2 : 0.4807 0.5193

1 : 0.5740

2 : 0.4260

1 : 0.5183 0.4817

2 : 0.2929 0.7071

1 1 : 0.9941 0.0059

2 1 : 0.7232 0.2768

1 2
: 0.0000 0.0000

2 2 : 0.0000 0.0000

1 : 0.9870

2 : 0.0130

1 : 0.5511 0.4489

2 : 0.5682 0.4318

1 : 0.3980

2 : 0.6020

1 : 0.8720

2 : 0.1280

1 : 0.6256 0.3744

2 : 0.6927 0.3073

1 : 0.5157 0.4843

2 : 0.6174 0.3826

1 1 : 0.8719 0.128
1

2 1 : 0.7917 0.2083

1 2 : 0.0066 0.9934

2 2 : 0.6765 0.3235

1 : 0.5460 0.4540

2 : 0.8799 0.1201

1 1 1 : 0.9110 0.0890

2 1 1 : 0.7613 0.2387

1 2 1 : 0.6468 0.3532

2 2 1 : 0.0000 1.0000

1 1 2 : 0.0000 0.0000

2 1 2 : 0.0000 0.0000

1 2 2 : 0.
0000 0.0000

2 2 2 : 0.0000 0.0000

1 1 : 0.4611 0.5389

2 1 : 0.5810 0.4190

1 2 : 0.3552 0.6448

2 2 : 0.6000 0.4000

1 1 1 : 0.8542 0.1458

2 1 1 : 0.7182 0.2818

1 2 1 : 0.8230 0.1770

2 2 1 : 0.1647 0.8353

1 1 2 : 0.1839 0.8161

2 1 2 : 0.5639 0.
4361

1 2 2 : 0.6224 0.3776

2 2 2 : 0.3878 0.6122

1 : 0.1806 0.8194

2 : 0.1351 0.8649

1 : 0.2158 0.7842

2 : 0.6718 0.3282

1 : 0.3220 0.6780

2 : 0.5351 0.4649

1 : 0.4460

2 : 0.5540

1 : 0.1674 0.8326

2 : 0.8333 0.1667

1 : 0.3710

2 :
0.6290

1 : 0.6809 0.3191

2 : 0.3455 0.6545

1 : 0.5010

2 : 0.4990

1 : 0.8205 0.1795

2 : 0.6755 0.3245

1 : 0.5795 0.4205

2 : 0.5385 0.4615

1 1 : 0.3273 0.6727

2 1 : 0.3490 0.6510

1 2 : 0.6082 0.3918

2 2 : 0.5400 0.4600

1 : 1.0000

2
: 0.0000

1 : 0.2344 0.7656

2 : 0.4633 0.5367

1 : 0.4210

2 : 0.5790

1 : 0.4607 0.5393

2 : 0.4709 0.5291

1 : 1.0000

2 : 0.0000

1 1 : 0.3959 0.6041

2 1 : 0.3613 0.6387

1 2 : 0.4225 0.5775

2 2 : 0.3509 0.6491

1 1 : 0.4843 0.5157

2 1 :

0.3385 0.6615

1 2 : 0.6212 0.3788

2 2 : 0.8027 0.1973

1 : 0.4790 0.5210

2 : 0.4850 0.5150

CPT of BN5

1 1 : 0.6098 0.3902

2 1 : 0.8141 0.1859

1 2 : 0.3821 0.6179

2 2 : 0.4317 0.5683

1 1 1 : 0.4659 0.5341

2 1 1 : 0.4683 0.5317

1 2 1 : 0.607
9 0.3921

2 2 1 : 0.1912 0.8088

1 1 2 : 0.5000 0.5000

2 1 2 : 0.2727 0.7273

1 2 2 : 0.3333 0.6667

2 2 2 : 0.3333 0.6667

1 : 0.4120

2 : 0.5880

13

1 : 0.1220

2 : 0.8780

1 : 0.4502 0.5498

2 : 0.4367 0.5633

1 : 0.3840

2 : 0.6160

1 : 0.0000

2 : 1.0000

1 : 0.5738 0.4262

2 : 0.4966 0.5034

1 : 0.7570

2 : 0.2430

1 1 : 0.4235 0.5765

2 1 : 0.4700 0.5300

1 2 : 0.3048 0.6952

2 2 : 0.4565 0.5435

1 : 0.9740

2 : 0.0260

1 : 0.6335 0.3665

2 : 0.3401 0.6599

1 : 0.2870

2 : 0.7130

1 1 : 0.0000 0.0000

2 1 : 0.4473 0.5527

1 2 : 0.0000 0.0000

2 2 : 0.7869 0.2131

1 : 0.7109 0.2891

2 : 0.4692 0.5308

1 : 0.3689 0.6311

2 : 1.0000 0.0000

1 1 : 0.4820 0.5180

2 1 : 0.4925 0.5075

1 2 : 0.5960 0.4040

2 2 : 0.4479 0.5521

1

: 0.1897 0.8103

2 : 0.7611 0.2389

CPT of BN6

1 1 : 0.7500 0.2500

2 1 : 0.4624 0.5376

1 2 : 0.8333 0.1667

2 2 : 0.7121 0.2879

1 : 0.2349 0.7651

2 : 0.1328 0.8672

1 : 0.0115 0.9885

2 : 0.0280 0.9720

1 : 0.3960

2 : 0.6040

1 : 0.4280

2
: 0.5720

1 : 0.7580

2 : 0.2420

1 1 : 0.5039 0.4961

2 1 : 0.5025 0.4975

1 2 : 0.5357 0.4643

2 2 : 0.3852 0.6148

1 : 0.5934 0.4066

2 : 0.1325 0.8675

1 : 0.4000 0.6000

2 : 0.6173 0.3827

1 : 0.5918 0.4082

2 : 0.6080 0.3920

1 : 0.5574 0
.4426

2 : 0.2687 0.7313

1 : 0.1023 0.8977

2 : 0.2824 0.7176

1 1 : 0.1509 0.8491

2 1 : 0.5918 0.4082

1 2 : 0.8889 0.1111

2 2 : 0.8073 0.1927

1 : 0.4250

2 : 0.5750

1 : 0.9850 0.0150

2 : 1.0000 0.0000

1 : 0.5491 0.4509

2 : 0.3444 0.6556

1 : 0.4974 0.5026

2 : 0.4530 0.5470

1 : 0.0016 0.9984

2 : 0.5725 0.4275

1 : 0.7300

2 : 0.2700

1 : 0.4317 0.5683

2 : 0.7573 0.2427

1 : 0.6042 0.3958

2 : 0.5704 0.4296

1 : 0.8317 0.1683

2 : 0.0964 0.9036

1 1 : 0.6185 0.3815

2 1 :

0.5084 0.4916

1 2 : 0.6364 0.3636

2 2 : 0.5489 0.4511

1 : 0.3369 0.6631

2 : 0.2285 0.7715

1 : 0.3910

2 : 0.6090

1 : 0.1179 0.8821

2 : 0.1447 0.8553

1 : 0.1941 0.8059

2 : 0.3406 0.6594

1 : 0.9591 0.0409

2 : 0.3058 0.6942

1 1 : 0.50
76 0.4924

2 1 : 0.2166 0.7834

1 2 : 0.5700 0.4300

2 2 : 0.8110 0.1890

CPT of BN7

1 : 0.5265 0.4735

2 : 0.6333 0.3667

1 : 0.3810

2 : 0.6190

1 : 0.0000 1.0000

2 : 1.0000 0.0000

1 1 1 : 1.0000 0.0000

2 1 1 : 0.0000 1.0000

1 2 1 : 0.6170 0.
3830

2 2 1 : 0.5754 0.4246

1 1 2 : 0.0000 0.0000

2 1 2 : 0.0000 0.0000

1 2 2 : 0.9036 0.0964

2 2 2 : 0.2100 0.7900

1 : 0.4850

2 : 0.5150

1 : 0.4330

2 : 0.5670

1 1 : 0.4604 0.5396

2 1 : 0.7413 0.2587

1 2 : 0.6816 0.3184

2 2 : 0.3142 0.685
8

1 1 1 : 0.0000 1.0000

2 1 1 : 0.4444 0.5556

1 2 1 : 0.5714 0.4286

2 2 1 : 0.8525 0.1475

1 1 2 : 0.3125 0.6875

2 1 2 : 0.7647 0.2353

1 2 2 : 0.1364 0.8636

2 2 2 : 0.1948 0.8052

1 : 0.2990 0.7010

2 : 0.1243 0.8757

1 : 0.0470

2 : 0.9530

1 : 0.0020

2 : 0.9980

1 : 0.3400

2 : 0.6600

1 1 : 0.6118 0.3882

2 1 : 0.5887 0.4113

1 2 : 0.2297 0.7703

2 2 : 0.5333 0.4667

1 : 0.4458 0.5542

2 : 0.3641 0.6359

1 : 0.4971 0.5029

2 : 0.5489 0.4511

1 : 0.0000

2 : 1.0000

1 : 0.0000
0.0000

2 : 0.4150 0.5850

1 : 0.7002 0.2998

2 : 0.3831 0.6169

1 : 0.6609 0.3391

2 : 0.7238 0.2762

CPT of BN8

1 1 : 0.3949 0.6051

2 1 : 0.4023 0.5977

1 2 : 0.4248 0.5752

2 2 : 0.4385 0.5615

1 : 0.0000

2 : 1.0000

1 : 0.3880 0.6120

2 : 0
.5341 0.4659

1 : 0.3570

2 : 0.6430

1 1 : 0.5556 0.4444

2 1 : 0.4136 0.5864

1 2 : 0.6266 0.3734

2 2 : 0.5369 0.4631

1 : 0.2381 0.7619

2 : 0.2737 0.7263

1 : 0.6360

2 : 0.3640

1 : 0.4564 0.5436

2 : 0.6102 0.3898

1 : 0.1402 0.8598

2 :

0.9364 0.0636

1 : 0.9980

2 : 0.0020

1 : 0.5510

2 : 0.4490

1 : 0.9979 0.0021

2 : 0.0135 0.9865

1 : 0.6283 0.3717

2 : 0.6905 0.3095

1 : 0.3698 0.6302

2 : 0.5325 0.4675

1 : 0.8348 0.1652

2 : 0.5256 0.4744

1 : 0.6603 0.3397

2 : 0.4
783 0.5217

1 : 0.3376 0.6624

2 : 0.6955 0.3045

1 : 0.7730

2 : 0.2270

1 : 0.4550

2 : 0.5450

1 : 0.0990

2 : 0.9010

1 : 0.1736 0.8264

2 : 0.5347 0.4653

1 : 0.6923 0.3077

2 : 0.3091 0.6909

1 : 0.4322 0.5678

2 : 0.3853 0.6147

1 1
1 : 0.6593 0.3407

2 1 1 : 0.4926 0.5074

1 2 1 : 0.4507 0.5493

2 2 1 : 0.7342 0.2658

1 1 2 : 0.2840 0.7160

2 1 2 : 0.4200 0.5800

1 2 2 : 0.4919 0.5081

2 2 2 : 0.4462 0.5538

1 : 0.0573 0.9427

2 : 0.8916 0.1084

1 1 : 0.0000 0.0000

2 1 : 0.4444
0.5556

1 2 : 0.0000 0.0000

2 2 : 0.6712 0.3288

1 : 0.8773 0.1227

2 : 0.6936 0.3064

1 : 0.5171 0.4829

2 : 0.4349 0.5651

1 : 0.7809 0.2191

2 : 0.5086 0.4914

1 : 0.6283 0.3717

2 : 0.5401 0.4599

1 : 0.3563 0.6437

2 : 0.7168 0.2832

1 1
: 0.4375 0.5625

2 1 : 0.4470 0.5530

1 2 : 0.4286 0.5714

2 2 : 0.5369 0.4631

1 : 0.7510

2 : 0.2490

14

1 : 0.6080 0.3920

2 : 0.5551 0.4449

1 : 0.5340

2 : 0.4660

1 1 : 0.5588 0.4412

2 1 : 0.4977 0.5023

1 2 : 0.3951 0.6049

2 2 : 0.3890 0.6110

1 1 : 0.9882 0.0118

2 1 : 0.0000 0.0000

1 2 : 1.0000 0.0000

2 2 : 1.0000 0.0000

1 : 0.4383 0.5617

2 : 0.4393 0.5607

1 1 1 : 0.8304 0.1696

2 1 1 : 0.2561 0.7439

1 2 1 : 0.5652 0.4348

2 2 1 : 0.4800 0.5200

1 1 2 : 0.5932 0.4068

2 1 2 : 0.6
306 0.3694

1 2 2 : 0.6563 0.3438

2 2 2 : 0.4262 0.5738

1 1 : 0.8214 0.1786

2 1 : 0.8076 0.1924

1 2 : 0.2791 0.7209

2 2 : 0.5507 0.4493

1 : 0.3530

2 : 0.6470

1 : 0.0390

2 : 0.9610

1 : 0.3770

2 : 0.6230

1 : 0.9951 0.0049

2 : 0.6057 0.
3943

1 1 : 0.5714 0.4286

2 1 : 0.5228 0.4772

1 2 : 0.9400 0.0600

2 2 : 0.3679 0.6321

1 : 0.4147 0.5853

2 : 0.4775 0.5225

1 1 : 0.4924 0.5076

2 1 : 0.4333 0.5667

1 2 : 0.5040 0.4960

2 2 : 0.7150 0.2850

1 : 0.5062 0.4938

2 : 0.1629 0.8371

1 1 : 0.1978 0.8022

2 1 : 0.7406 0.2594

1 2 : 0.3750 0.6250

2 2 : 0.0526 0.9474

1 : 0.4966 0.5034

2 : 0.3102 0.6898

1 : 0.7480

2 : 0.2520

1 : 0.3490

2 : 0.6510

1 : 0.6340 0.3660

2 : 0.5528 0.4472