diff --git a/docs/Implementations.md b/docs/Implementations.md
index 078b7d5..4c78a36 100644
--- a/docs/Implementations.md
+++ b/docs/Implementations.md
@@ -25,7 +25,7 @@ The purpose of this function is linearized state-space model for general LCC sys
**General System Model Formula:**
![General System Model Formula](img/General_System_Model_Formula1.jpg)
-where ![F](img/F.png) and ![P](img/P.png) shown in [LCC figure](https://github.com/soc-ucsd/LCC/blob/main/docs/img/LCC.png)
+where and shown in [LCC figure](https://github.com/soc-ucsd/LCC/blob/main/docs/img/LCC.png)
@@ -39,10 +39,12 @@ The purpose of this function is linearized state-space model for Car-following s
**Output:**
- state-space model: [A, B]
-![state_model_formula](img/state_model_formula.png)
+
**Car-following system model formula:**
-![Car-following_system_model_formula](img/Car-following_system_model_formula.png)
+
+
+
> (For more information of how to derive from general formula to car-following formula, please check the [LCC paper](https://arxiv.org/abs/2012.04313))
#### SystemModel_FD[.m](https://github.com/soc-ucsd/LCC/blob/main/_model/SystemModel_FD.m) / [.py](https://github.com/soc-ucsd/LCC/blob/main/Python%20Implementation/_model/SystemModel_FD.py)
@@ -54,11 +56,11 @@ The purpose of this function is linearized state-space model for free-driving sy
**Output:**
- state-space model: [A, B]
-![state_model_formula](img/state_model_formula.png)
+
**Free-driving system model formula:**
-![Free-driving_system_model_formula](img/Free-driving_system_model_formula.png)
+
>(For more information of how to derive from general formula to free-driving formula, please check the [LCC paper](https://arxiv.org/abs/2012.04313))
@@ -238,11 +240,15 @@ The purpose of this file is to find the head-to-tail string stable regions when
When only monitoring one HDV the transfer function is slightly different for each different cases.
Case 1: id < 0 Monitoring the preceding vehicle
-![ID_less_zero](img/ID_less_zero.png)
+
+
+
Case 2: id > 0 Monitoring the following vehicle
-![ID_greater_zero](img/ID_greater_zero.png)
+
+
+
Besides the Gamma function formula, the rest formula stays the same.