diff --git a/tutorial/.ipynb_checkpoints/ex1_simple_ZARC_model-checkpoint.ipynb b/tutorial/.ipynb_checkpoints/ex1_simple_ZARC_model-checkpoint.ipynb
index d9d40c5..2e785a1 100644
--- a/tutorial/.ipynb_checkpoints/ex1_simple_ZARC_model-checkpoint.ipynb
+++ b/tutorial/.ipynb_checkpoints/ex1_simple_ZARC_model-checkpoint.ipynb
@@ -331,7 +331,7 @@
     "\\end{align}\n",
     "$$\n",
     "\n",
-    "The key ingredient is to do Cholesky factorization of $\\mathcal L^2_{\\rm im} \\mathbf K+\\sigma_n^2\\mathbf I$"
+    "The key ingredient is to do Cholesky factorization of $\\mathcal L^2_{\\rm im} \\mathbf K+\\sigma_n^2\\mathbf I$, _i.e._, `K_im_full`"
    ]
   },
   {
@@ -487,20 +487,13 @@
     "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n",
     "plt.show()"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python_pytorch",
+   "display_name": "Python 3",
    "language": "python",
-   "name": "machine_learning"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -512,7 +505,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.7.5"
   }
  },
  "nbformat": 4,
diff --git a/tutorial/.ipynb_checkpoints/ex2_double_ZARC_model-checkpoint.ipynb b/tutorial/.ipynb_checkpoints/ex2_double_ZARC_model-checkpoint.ipynb
index 2653f1b..e411bfe 100644
--- a/tutorial/.ipynb_checkpoints/ex2_double_ZARC_model-checkpoint.ipynb
+++ b/tutorial/.ipynb_checkpoints/ex2_double_ZARC_model-checkpoint.ipynb
@@ -404,20 +404,13 @@
     "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n",
     "plt.show()"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python_pytorch",
+   "display_name": "Python 3",
    "language": "python",
-   "name": "machine_learning"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -429,7 +422,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.7.5"
   }
  },
  "nbformat": 4,
diff --git a/tutorial/.ipynb_checkpoints/ex3_truncated_ZARC_model-checkpoint.ipynb b/tutorial/.ipynb_checkpoints/ex3_truncated_ZARC_model-checkpoint.ipynb
index 4267b6d..65d1539 100644
--- a/tutorial/.ipynb_checkpoints/ex3_truncated_ZARC_model-checkpoint.ipynb
+++ b/tutorial/.ipynb_checkpoints/ex3_truncated_ZARC_model-checkpoint.ipynb
@@ -378,20 +378,13 @@
     "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n",
     "plt.show()"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python_pytorch",
+   "display_name": "Python 3",
    "language": "python",
-   "name": "machine_learning"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -403,7 +396,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.7.5"
   }
  },
  "nbformat": 4,
diff --git a/tutorial/.ipynb_checkpoints/ex4_real_experimental_data-checkpoint.ipynb b/tutorial/.ipynb_checkpoints/ex4_real_experimental_data-checkpoint.ipynb
index a440a76..827ecbc 100644
--- a/tutorial/.ipynb_checkpoints/ex4_real_experimental_data-checkpoint.ipynb
+++ b/tutorial/.ipynb_checkpoints/ex4_real_experimental_data-checkpoint.ipynb
@@ -11,9 +11,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## In this tutorial we will show an example for real experiemntal impedance data\n",
+    "## In this tutorial we will show use the GP-DRT method to analyze actual experimental data\n",
     "\n",
-    "The impedance data obtained by the measurement is stored in the csv file `EIS_experiment.csv`, where the three columns are frequency, the real part of impedance, the imaginary part of impedance, respectively. To run this tutorial smoothly, we recommend the user to write the frequency data ascendingly."
+    "The impedance data in the csv file named `EIS_experiment.csv`. The file has three columns. The first column is the frequency, the second one the real part of the impedance. The third column is the imaginary part of impedance. To use this tutorial for your own data, we recommend the frequencies go are sorted ascendingly."
    ]
   },
   {
@@ -417,7 +417,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.7.5"
   }
  },
  "nbformat": 4,
diff --git a/tutorial/ex1_simple_ZARC_model.ipynb b/tutorial/ex1_simple_ZARC_model.ipynb
index a3c17f6..2e785a1 100644
--- a/tutorial/ex1_simple_ZARC_model.ipynb
+++ b/tutorial/ex1_simple_ZARC_model.ipynb
@@ -487,20 +487,13 @@
     "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n",
     "plt.show()"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python_pytorch",
+   "display_name": "Python 3",
    "language": "python",
-   "name": "machine_learning"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -512,7 +505,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.7.5"
   }
  },
  "nbformat": 4,
diff --git a/tutorial/ex2_double_ZARC_model.ipynb b/tutorial/ex2_double_ZARC_model.ipynb
index 2653f1b..e411bfe 100644
--- a/tutorial/ex2_double_ZARC_model.ipynb
+++ b/tutorial/ex2_double_ZARC_model.ipynb
@@ -404,20 +404,13 @@
     "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n",
     "plt.show()"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python_pytorch",
+   "display_name": "Python 3",
    "language": "python",
-   "name": "machine_learning"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -429,7 +422,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.7.5"
   }
  },
  "nbformat": 4,
diff --git a/tutorial/ex3_truncated_ZARC_model.ipynb b/tutorial/ex3_truncated_ZARC_model.ipynb
index 4267b6d..65d1539 100644
--- a/tutorial/ex3_truncated_ZARC_model.ipynb
+++ b/tutorial/ex3_truncated_ZARC_model.ipynb
@@ -378,20 +378,13 @@
     "plt.ylabel(r'$-Z_{\\rm im}/\\Omega$', fontsize = 20)\n",
     "plt.show()"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python_pytorch",
+   "display_name": "Python 3",
    "language": "python",
-   "name": "machine_learning"
+   "name": "python3"
   },
   "language_info": {
    "codemirror_mode": {
@@ -403,7 +396,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.7.5"
   }
  },
  "nbformat": 4,
diff --git a/tutorial/ex4_real_experimental_data.ipynb b/tutorial/ex4_real_experimental_data.ipynb
index a440a76..827ecbc 100644
--- a/tutorial/ex4_real_experimental_data.ipynb
+++ b/tutorial/ex4_real_experimental_data.ipynb
@@ -11,9 +11,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## In this tutorial we will show an example for real experiemntal impedance data\n",
+    "## In this tutorial we will show use the GP-DRT method to analyze actual experimental data\n",
     "\n",
-    "The impedance data obtained by the measurement is stored in the csv file `EIS_experiment.csv`, where the three columns are frequency, the real part of impedance, the imaginary part of impedance, respectively. To run this tutorial smoothly, we recommend the user to write the frequency data ascendingly."
+    "The impedance data in the csv file named `EIS_experiment.csv`. The file has three columns. The first column is the frequency, the second one the real part of the impedance. The third column is the imaginary part of impedance. To use this tutorial for your own data, we recommend the frequencies go are sorted ascendingly."
    ]
   },
   {
@@ -417,7 +417,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.7.5"
   }
  },
  "nbformat": 4,