diff --git a/TODO.txt b/TODO.txt
index 35ce761..b7b6565 100644
--- a/TODO.txt
+++ b/TODO.txt
@@ -1,5 +1,4 @@
 TODO: 
-chapter10: compute bound terms (entropy) inside each factors
 chapter10/12: prediction functions for VB
 chapter05: MLP
 chapter08: BP, EP
diff --git a/chapter01/condEntropy.m b/chapter01/condEntropy.m
index df8ec94..bc43d52 100644
--- a/chapter01/condEntropy.m
+++ b/chapter01/condEntropy.m
@@ -1,6 +1,9 @@
 function z = condEntropy (x, y)
-% Compute conditional entropy H(x|y) of two discrete variables x and y.
-% x, y: two vectors of integers of the same length
+% Compute conditional entropy z=H(x|y) of two discrete variables x and y.
+% Input:
+%   x, y: two vectors of integers of the same length
+% Output:
+%   z: conditional entropy z=H(x|y)
 % Written by Mo Chen (sth4nth@gmail.com).
 assert(numel(x) == numel(y));
 n = numel(x);
diff --git a/chapter01/entropy.m b/chapter01/entropy.m
index 4ba1596..dbdbc84 100644
--- a/chapter01/entropy.m
+++ b/chapter01/entropy.m
@@ -1,6 +1,9 @@
 function z = entropy(x)
-% Compute entropy H(x) of a discrete variable x.
-% x: a vectors of integers
+% Compute entropy z=H(x) of a discrete variable x.
+% Input:
+%   x: a vectors of integers
+% Output:
+%   z: entropy z=H(x)
 % Written by Mo Chen (sth4nth@gmail.com).
 n = numel(x);
 x = reshape(x,1,n);
diff --git a/chapter01/jointEntropy.m b/chapter01/jointEntropy.m
index 33d58f2..accaa7b 100644
--- a/chapter01/jointEntropy.m
+++ b/chapter01/jointEntropy.m
@@ -1,6 +1,9 @@
 function z = jointEntropy(x, y)
-% Compute joint entropy H(x,y) of two discrete variables x and y.
-% x, y: two vectors of integers of the same length
+% Compute joint entropy z=H(x,y) of two discrete variables x and y.
+% Input:
+%   x, y: two vectors of integers of the same length
+% Output:
+%   z: joint entroy z=H(x,y)
 % Written by Mo Chen (sth4nth@gmail.com).    
 assert(numel(x) == numel(y));
 n = numel(x);
diff --git a/chapter01/mutInfo.m b/chapter01/mutInfo.m
index d3d306d..4d7023b 100644
--- a/chapter01/mutInfo.m
+++ b/chapter01/mutInfo.m
@@ -1,6 +1,9 @@
 function z = mutInfo(x, y)
 % Compute mutual information I(x,y) of two discrete variables x and y.
-% x, y: two vectors of integers of the same length
+% Input:
+%   x, y: two vectors of integers of the same length
+% Output:
+%   z: mutual information z=I(x,y)
 % Written by Mo Chen (sth4nth@gmail.com).
 assert(numel(x) == numel(y));
 n = numel(x);
diff --git a/chapter01/nmi.m b/chapter01/nmi.m
index 45f6538..816fd05 100644
--- a/chapter01/nmi.m
+++ b/chapter01/nmi.m
@@ -1,6 +1,9 @@
 function z = nmi(x, y)
-% Compute normalized mutual information I(x,y)/sqrt(H(x)*H(y)).
-% x, y: two vectors of integers of the same length
+% Compute normalized mutual information I(x,y)/sqrt(H(x)*H(y)) of two discrete variables x and y.
+% Input:
+%   x, y: two vectors of integers of the same length
+% Ouput:
+%   z: normalized mutual information z=I(x,y)/sqrt(H(x)*H(y))
 % Written by Mo Chen (sth4nth@gmail.com).
 assert(numel(x) == numel(y));
 n = numel(x);
diff --git a/chapter01/nvi.m b/chapter01/nvi.m
index 5bfc89b..d8b614b 100644
--- a/chapter01/nvi.m
+++ b/chapter01/nvi.m
@@ -1,6 +1,9 @@
 function z = nvi(x, y)
-% Compute normalized variation information (1-I(x,y)/H(x,y)).
-% x, y: two vectors of integers of the same length
+% Compute normalized variation information z=(1-I(x,y)/H(x,y)) of two discrete variables x and y.
+% Input:
+%   x, y: two vectors of integers of the same length
+% Output:
+%   z: normalized variation information z=(1-I(x,y)/H(x,y))
 % Written by Mo Chen (sth4nth@gmail.com).
 assert(numel(x) == numel(y));
 n = numel(x);
diff --git a/chapter01/relatEntropy.m b/chapter01/relatEntropy.m
index 64e8d60..60b84e6 100644
--- a/chapter01/relatEntropy.m
+++ b/chapter01/relatEntropy.m
@@ -1,6 +1,9 @@
 function z = relatEntropy (x, y)
-% Compute relative entropy (a.k.a KL divergence) KL(p(x)||p(y)) of two discrete variables x and y.
-% x, y: two vectors of integers of the same length
+% Compute relative entropy (a.k.a KL divergence) z=KL(p(x)||p(y)) of two discrete variables x and y.
+% Input:
+%   x, y: two vectors of integers of the same length
+% Output:
+%   z: relative entropy (a.k.a KL divergence) z=KL(p(x)||p(y))
 % Written by Mo Chen (sth4nth@gmail.com).    
 assert(numel(x) == numel(y));
 n = numel(x);