diff --git a/.gitignore b/.gitignore
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--- /dev/null
+++ b/.gitignore
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+/.DS_Store
+/.vscode
+/blog/_build/
+/poster/*pptx
+/6s989_proposal.pdf
diff --git a/blog/_config.yml b/blog/_config.yml
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--- /dev/null
+++ b/blog/_config.yml
@@ -0,0 +1,37 @@
+# Book settings
+# Learn more at https://jupyterbook.org/customize/config.html
+
+title: Demistiyfing E(3)-equivariant NN
+author: Killian Sheriff, Yifan Cao
+logo: square.png
+
+# Force re-execution of notebooks on each build.
+# See https://jupyterbook.org/content/execute.html
+execute:
+  execute_notebooks: force
+
+# Define the name of the latex output file for PDF builds
+latex:
+  latex_documents:
+    targetname: book.tex
+
+# Add a bibtex file so that we can create citations
+bibtex_bibfiles:
+  - references.bib
+
+# Information about where the book exists on the web
+repository:
+  url: https://github.com/killiansheriff/blog_e3nn/  # Online location of your book
+  path_to_book: docs  # Optional path to your book, relative to the repository root
+  branch: master  # Which branch of the repository should be used when creating links (optional)
+
+# Add GitHub buttons to your book
+# See https://jupyterbook.org/customize/config.html#add-a-link-to-your-repository
+html:
+  use_issues_button: true
+  use_repository_button: true
+
+sphinx:
+  config:
+    html_js_files:
+    - https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js
diff --git a/blog/_toc.yml b/blog/_toc.yml
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index 0000000..5464c7c
--- /dev/null
+++ b/blog/_toc.yml
@@ -0,0 +1,14 @@
+# Table of contents
+# Learn more at https://jupyterbook.org/customize/toc.html
+
+format: jb-book
+root: index
+chapters:
+- file: notebooks/group_representation
+- file: notebooks/irreducible_representations
+- file: notebooks/transformation_under_e3
+- file: notebooks/spherical_harmonics
+- file: notebooks/equivariance_and_polynomials
+- file: notebooks/tensor_product
+- file: notebooks/data_efficiency
+
diff --git a/blog/equiv.png b/blog/equiv.png
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diff --git a/blog/index.md b/blog/index.md
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@@ -0,0 +1,38 @@
+# Index
+
+## Demistifying E(3)-equivariant neural networks!
+
+Welcome to our blog post on demistifying E(3)-equivariant neural networks! This blog aim to introduces the following concepts, in order to understand the mathematical tools leading to learnable equivariant operations:
+
+```{tableofcontents}
+```
+## Poster 
+
+![poster]('../../../poster/shared/poster.png)
+
+## Disclaimer
+
+This post serves as an explanation of the paper by ``Geiger et al [1]``. It was written as a final project for the ``Fall 2022 Final Project`` section of the ``6.S898: Deep Learning`` course at the ``Massachusetts Institute of Technology``. Needless to say that the intuition presented herein are heavily influenced by the explanations of Geiger et al.
+
+## References 
+
+1. Geiger, M. & Smidt, T. e3nn: Euclidean Neural Networks. Arxiv (2022).
+
+## Citation
+
+If used, please cite: 
+
+```citation
+@software{killian_sheriff_2022_7430281,
+  author       = {Killian Sheriff and
+                  Yifan Cao},
+  title        = {killiansheriff/blog\_e3nn: blog\_e3nn},
+  month        = dec,
+  year         = 2022,
+  publisher    = {Zenodo},
+  version      = {blog\_e3nn},
+  doi          = {10.5281/zenodo.7430281},
+  url          = {https://doi.org/10.5281/zenodo.7430281}
+}
+```
+  
\ No newline at end of file
diff --git a/blog/irrep.png b/blog/irrep.png
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diff --git a/blog/irrep_2.png b/blog/irrep_2.png
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diff --git a/blog/notebooks/.ipynb_checkpoints/Untitled2-checkpoint.ipynb b/blog/notebooks/.ipynb_checkpoints/Untitled2-checkpoint.ipynb
new file mode 100644
index 0000000..363fcab
--- /dev/null
+++ b/blog/notebooks/.ipynb_checkpoints/Untitled2-checkpoint.ipynb
@@ -0,0 +1,6 @@
+{
+ "cells": [],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/blog/notebooks/.ipynb_checkpoints/Untitled3-checkpoint.ipynb b/blog/notebooks/.ipynb_checkpoints/Untitled3-checkpoint.ipynb
new file mode 100644
index 0000000..363fcab
--- /dev/null
+++ b/blog/notebooks/.ipynb_checkpoints/Untitled3-checkpoint.ipynb
@@ -0,0 +1,6 @@
+{
+ "cells": [],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/blog/notebooks/data_efficiency.ipynb b/blog/notebooks/data_efficiency.ipynb
new file mode 100644
index 0000000..aacfbcb
--- /dev/null
+++ b/blog/notebooks/data_efficiency.ipynb
@@ -0,0 +1,138 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# MLIP and data efficiency"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this section we will showcase data efficiency of equivariant neural networks by carrying out a case study of implementing Machine-Learning interatomic potentials (MLIAPs) that are often used to carry out large-scale molecular dynamic simulations in the field of computational material science.  Interatomic potentials (IAPs) are a group of functions $f: \\mathcal{R}^{n_{nbi} \\times m_{in}} \\to \\mathcal{R}^{m_{out}}$ that maps the local information tensor of neighboring atoms in the vicinity of the center atom to a vector of $\\mathcal{R}^{m_{out}}$ that contains the potential energy and forces of the center atom.\n",
+    "\n",
+    "A critical bottleneck of the current field resides not only in the expressiveness of such MLIAPs, but also in the computational cost of generating accurate training and testing datasets using first-principle calculations such as Density-Functional Theory(DFT). The input representations used by status-quo MLIAPs are usually invariant to symmetries and translations of the local environment[1] which are shown to be very data-craving. As described in some prior works[2], MLIAPs with equivariant features have been proven to be more data-efficient than non-equivariant potentials thanks to its features and architectures."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this case study, we will make a direct comparison between en equivariant machine learning inter-atomic potential (Nequip)[2]  and a non-equivariant simple feed-forward Moment Tensor Potentials (MTP)[1]. The complete training dataset consists of $\\sim 1250$ structures of a 3-component alloy system obtained from DFT simulations, and we varied the training dataset size from $10\\%$ to $100\\%$ of the complete training dataset, each time increasing the fraciton by $10\\%$.\n",
+    "\n",
+    "In addition to dataset sizes, we also controlled the number of training epochs for each dataset size such that all potentials are trained using the same amount of computation resources (1 GPU-hour $\\sim$ 10 CPU-hours). We then compared the mean absolute error (MAE) of predicted energies from both potentials and plotted the errors against the dataset size:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt \n",
+    "plt.style.use(['ipynb', 'use_mathtext'])\n",
+    "import numpy as np\n",
+    "import matplotlib as mpl\n",
+    "mpl.rcParams['axes.formatter.limits'] = -10,10\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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yYmJiFBUVpdDQ0MufGampqTpy5IjOnTvncVze4OpuIt9//72ee+453wQDAAGGgjMAAIAJmjVrpsKFC7vcTbphwwavF5yLFCmirl27qkmTJqpfv77q1avn8hbfaWlp2rx5s5YtW6Zp06bp999/dznO+vXr9eSTT+qll17Kc4xNmza94jO+FixY4PSCSd++ffM81p+VLFkyX78vBcbr+3cvvvii9u7d67Jd4cKFNWDAAHXv3l1t2rRRiRIlnLY3DEMHDhzQtm3btG3bNv34449auXKlKbuLMjIy1KtXL7eLzfXr19egQYPUtm1bNW7cWOHh4Vdsd/DgQcXHx+uzzz7T0qVLnfZpGIZGjx6tGjVqqFGjRm7FUbJkySu+b3fs2OF0J2GTJk1UqVIlt8a4kqZNm3r8u2a4cOGC7r33Xrfa1qlTR/3791e3bt1Ur149RUZGOm1//vx57dy5U7/88os2bNig77//3q1zzGrt27d3eY5508GDB7Vu3TpT+k5KSlL37t3dLja3bdtWN998s9q2bav69esrJOTKN1/79ddfFR8fr48//lgbN2502mdmZqb69eun9evX++SLXN7m6nmUbdq0MW3sJUuW6Msvv3TZLjQ0VL169VKPHj3UqVMnVapUyWUR/OTJk9q2bZt++eUXrVy5UvHx8R7faeP666/XiRMn/vJn6enpTguNJUqU8JsvIbzwwgu53oo1NjZWQ4cO1c0336ymTZvm+pm1d+9ezZ07V2+//baZoQYMwzA0YsSIPBWbmzZtqv79++vaa69VvXr1cs0/0sW7Nqxfv17r1q3T/PnztX379jzHmFuunz17dq6/ExUVpeuuuy7PY/1ZdHR0vn4/GGRkZGjo0KG5FowbN26sESNGqHv37rr66quv2CYrK0urVq3S559/rv3797scc+7cuW4XmwsWLKiBAweqS5cuatu2rcqWLXvFdpmZmVq5cqUWLFigjz76yOXjLDZt2qSRI0dq1qxZLmPIzbhx49x6NEqpUqU0aNAgdevWTS1atFCRIkWcts/JydHu3bv1yy+/aMuWLfrhhx/0888/5+mLu/lVvXp1lSxZMtcvTG3ZskVHjx516xFaABB0DAAAgAAxdepUQ5LTn4SEBKvDvOz66693Ge9jjz3mcf9XX3315X5Kly5t3HXXXUZ8fLyRmZmZ79h//PFHo1atWi7jDw0NNbZu3Zrv8S6pVKmS0/F8yS6vb1pamlG4cGGn44SEhBiPPvqokZKSku+5paSkGLNmzTL69u1rhIaGGpKMvn375rvf4cOHu3y9JBnt2rUzFi1a5NEY8fHxRr169VyOUbNmTSMjIyNf8xk/frzTMaZOnZqv/v3N9OnTXb6u5cqVM7799lsjJycn3+Pt2rXLmDhxolG7du3L/c+bN8/j/oYNGxYwnz1XcuLEib/ktNx+Hn744Tz3nZ2dbVx77bVunZ+9e/c2fv755zyPkZOTY8yaNcuIi4tzOca1116b5/79QePGjZ3Oa/HixaaN3blzZ7f+7vbs2ZPvsTIzM41FixYZ99xzz+XPptjYWI/727dvn9O427dvn++Y3eVqDRMREfGPPwsPDzeeeOIJ48yZM3kaKysry7hw4UKux12tmcePH5/P2Trnq7+XZ555xq3cI8no2LGjsXr16nyN98svvxhPPPHEX/6uPX0tncVaqVKlfMXpLru/TxISEvJ8Tkoy4uLijO+++y7P450/f97p8V9++cUoVKiQy/dqdHS0MWHCBOPkyZN5jiEpKcn4z3/+Y4SFhbkc55NPPslz/4ZhGAcOHDBCQkKc9h0ZGWm8+uqrxrlz5zwa489OnDhhTJ061ejatavhcDgMScaDDz6Y736dcbWu+frrr00dHwACFc9wBgAAMEm9evVctsnrrYH/rlatWvroo4904MABvf322+ratWuuu2Ly4tprr9WmTZs0btw4p+2ys7P19NNP53s8f2WH13fu3LlOd5OFhoZqzpw5evbZZ13uOnBHkSJF1L9/f3311Vfau3evxo4dq+LFi+erz6+//lrTpk1z2iY8PFzPP/+8li5dqs6dO3s0TteuXfXTTz/p5ptvdtpu586d3Eovjz755BOnx+vUqaONGzeqZ8+eXrltcPXq1fXggw/ql19+0aJFi3TDDTc43cVmZ+fOnVPPnj21Z88ep+3atm2rCRMm5Ln/1157TYsXL3baJjo6WlOnTtWcOXM82n3vcDjUv39/rVu3Tu3atXPadvHixS7zhb/JzMzUtm3bnLapW7euKWMfOXLE5d/fww8/rDlz5qhKlSr5Hi88PFydO3fWpEmTdPjwYb3xxhu65ppr8t1vIPj7c05Lly6tlStX6umnn1ahQoXy1FdoaKjCwoL7poXr1q1zK2cVKFBAH374oZYsWaKWLVvma8zatWvr6aef1u7duzVt2jTVqFEjX/3BWld69nCvXr20detWXX/99Xnuz9kdWbKysjRkyJAr3uHpzxo2bKiNGzfqySef9OguKMWKFdOLL76oBQsWuFzX//vf/1ZiYmKex5gxY4bTHcfR0dFasWKF/v3vf3vl0UAlS5bU8OHDFR8fr+3bt+uOO+4wfQe/q3/Hm3XHGAAIdMH5L24AAAAfcOfi8IEDBzzu/9NPP9Uvv/yiUaNGubzlrCciIiL0/PPP69lnn3Xabvbs2dq3b5/Xx7eaXV7fRYsWOT3+2GOPqWfPnh7370zFihX10ksv6YMPPvC4j5SUFN11111O2xQsWFCLFi3SuHHj8l2sLFiwoL744gvdfvvtTtu98sorPEvTTRkZGVq+fHmuxyMiIvTll1+qVKlSpozfuXNnzZ8/36OLx4EuJydHgwYN0tq1a522q1GjhubMmZPnXLdnzx498cQTTtuUKFFCP//8s4YPH56nvq8kNjb28hcInHnyySevWEjwV1u2bHEa71VXXeWVR0JcyeLFi53e2rVDhw6mfcEmJiZG9957b663mbazkiVLavny5WrWrJnVoQSk7OxsjRgxQllZWU7bFStWTMuXL9fo0aO9On5YWJiGDRum7du3u1wvIHDcdNNN+vrrr/P8BRB3vPzyy9q0aZPTNjfeeKN++uknVatWLd/jde7cWatXr3ZadE5MTPTo0T2u/m0xadIk0x7tUrNmTb333nsefUEuL+rXr+/0OAVnALgyCs4AAAAmqVq1qss2hw8f9rj/li1bemUnoCuPPvqoBg0alOtxwzBc7l4MRHZ5fZ3too+MjNT999/vcd++8NJLL+n48eO5Hg8NDdXMmTO9+oxOh8OhSZMmqXnz5rm2OXv2rF555RWvjWlnv/32m86fP5/r8d69e7NLzCQPPPCAvvnmG6dtSpcurQULFnh0J4InnnhC586dy/V4VFSU5s+fr1q1auW579xERERo+vTpiouLy7XNoUOHNHXqVK+Nabb169c7PW7W7mbJ9Z1Wxo4dG7R3BzDTjBkzvFJUClZTp051+TzlqKgo/fDDD6YVviQpJCQk1+fqIrBUrVpV06dPV2hoqNf7TkxM1PPPP++0TevWrTVz5kxFRER4bdxatWrp448/dtrm7bffVlJSUp76dfa5UaZMGQ0dOjRP/fkjVzuc169f79ZzuAEg2PCvBgAAAJOUKVPGZZvk5GSlp6f7IJr8efnllxUTE5Pr8a+++sqH0diPma/v/v37cz3WtGlTFStWzOO+zXby5Em9+eabTts88cQT6t27t9fHjoiI0Oeff+50x+eUKVN04cIFr49tN87eg5LUrVs33wQSZF577TW98cYbTttER0dr/vz5qly5cp773759uz7//HOnbd555x2nX9zwVNGiRTVz5kynbd5//32vj2uWzZs3Oz1evXp108Z2dn6GhISoS5cupo0drIYNG8brmg9ZWVluPW7k/fffV5MmTXwQEezggw8+UMGCBU3p+6WXXtKZM2dyPR4bG6u5c+d65fbTf9e7d2+NGTMm1+NpaWmaPn262/2dOXPGaYH62muvNaVo72uuvgiZkpLicn0LAMGIgjMAAIBJrrrqKrd2yJ48edIH0eRPmTJldOutt+Z6/JdffnG6CxXOmfn6OrvAVa5cOY/69JXJkycrLS0t1+MVK1bUf/7zH9PGr1SpktPbAJ84cULff/+9aePbhbP3oOT/78NA9PXXX+uhhx5y2iY0NFSzZs3yuCAzadIkp89wbNasmam7nJo3b+70ywqbNm1yuXvXX7h6bEL58uVNG9vZ+VmyZEmFh4ebNnYwiomJ0auvvmp1GAHt22+/1aFDh5y26dWrlwYPHuyjiBDoBg0apI4dO5rS9/nz5/Xhhx86bfP0008rNjbWlPGli3dTcpbL83JHkGBZ0xUsWNDll3L37t3ro2gAIHBQcAYAADBJeHi4W9+Ud3Y7Un/iahfpypUrfRSJPZn1+oaFheV6zJ/fe4Zh6KOPPnLa5v/+7/9M241yycMPP+z0iyPz5883dXw7cPYelPz7fRiI1qxZo0GDBjktBkvSW2+9pR49eng0Rlpamj777DOnbSZOnGj6YwnGjRvn9HignJ+udkmZeQE/UD8jAlX//v09un09/sdV8S40NJSiPvLkzjvvNK3vL7/8UsnJybker1atmu644w7TxpekChUqaODAgbke37x5s44cOeJWX8G0pnP12csOZwD4JwrOAAAAJnLn1miB8g/zVq1aOT2+bds2H0ViT2a9vs52TGzYsMFvnz+2YcMG7dmzJ9fjMTExuvnmm02PIy4uzunzU+Pj402PIdC52rWzbt06H0Vif7t371avXr2cPjNbuvhFCme32HRlwYIFTnc5Va1aVW3btvW4f3e1a9fO6Q6kQDg/DcPQwYMHnbYxs+Ds7PxMTU3Vb7/9ZtrYwWjUqFFWhxDQUlNTtXjxYqdt+vfvr6uvvtpHESHQVa9eXa1btzatf1ePnhgyZIhPbkHt6out7n5eFi9e3OmXyey0pnN1dxEKzgDwTxScAQAATGSngnOxYsWcPs92+/btPozGfsx6fa+66qpcjx05ckRffPGFR/2azdWtqnv16mX67uZLOnTokOuxQ4cO6ejRoz6JI1A5ew9KF2/lePr0aR9FY1+nTp3Sddddp1OnTjltN2DAAD3//PP5GsvV+dm/f/989e+ukJAQp4XtDRs2uNzpbbVjx44pIyPDaRszC86uzs/XXnvNtLGDTeXKldWiRQurwwho8fHxunDhgtM2FPWRFwMGDDCt7/PnzyshIcFpG2eP1PGm9u3bOy0Ur1271q1+wsLCnH5R6aefftJPP/2U5/j8ETucASDvKDgDAACYKCTE9XLL3y+G/1mJEiVyPeburdiQOzNeX1c7p++++25t2rTJo77N9OOPPzo97umtgD3hqkCwefNm3wQSoGrWrOl0F+qxY8c0cOBAl7tykbtz586pV69e2r17t9N27du319SpU/N9q+tAOT/T09P166+/+iwWTxw7dsxlGzOf7enqM+L999/XtGnTTBs/mDRt2tTqEALesmXLnB4vVaqU0y+JAX9n5nm5evVqpaen53q8evXqqlq1qmnj/1nx4sV1zTXX5Ho8L2tZZ58bhmFo4MCBtijGuvrsdefzGwCCjfMHLwAAACBf3Nm9bPYuzfPnz+v333/X77//roMHD+rkyZNKTEzUuXPnlJmZqaysLLdvq+zsGWTBusvT31/fzp07680338z1eGJiotq2baunnnpKd999t892DTuTk5Pjsghep04dH0Vz8QK2M7t27dJ1113no2gCT0hIiDp27Kivv/461zbff/+9WrRooddee00dO3b0YXSBLycnR4MHD9aaNWuctqtZs6bmzJnj9E4K7jhx4oQOHTrktE3t2rXzNUZeuHN+1qxZ00fR5F1aWprLNmbm5Y4dOyo0NFTZ2dlXPG4YhkaOHKk1a9boqaeeUpkyZUyLxe4aN25sdQgBb8OGDU6Pd+rUya0vewKXmHlerl+/3ulxX65lpYufl7k9JmHXrl1u99O5c2d9++23uR7ft2+fmjVrphdeeEFDhw51+dxnf+Xqs9edz28ACDaBmfEBAAAChKvbZErev5CclZWl5cuXa968eVq5cqW2bNni8vaD3pCSkmL6GP4g0F7fbt26qWLFik6fEZqWlqaxY8fq+eef1+DBgzVgwAA1b94837sgPfX777/r7NmzuR4PCwtTtWrVfBaPqx0O7O537bbbbnNacJakLVu2qFOnTmrYsKGGDx+uvn37mnorYbt48MEHXb62V111lRYsWKCiRYvmezxXXwapUKGCYmJi8j2OuwL9/HTngrU7j+fwVNGiRXXzzTc7fc6oYRj64IMPNG3aNPXp00eDBg1S165d8/3lhWDTsGFDq0MIaIZhaOvWrU7buNqxD/xZmTJlVLp0adP6d/V5WatWLdPGvhJnn5epqak6e/asChUq5LKfAQMG6NFHH3W6Vj958qRGjRqlJ598UsOGDVP//v1Vr149j+K2CgVnAMg7Cs4AAAAmycnJ8ekO52PHjmnSpEmaMmWKJbf4svvtcAP19Y2IiNCjjz6qMWPGuGyblJSkN998U2+++aZKly6trl27qmPHjmrTpo3T2/B5W267Ly4JCwvTwIEDfRSN6wtKwbq7Py+6d++uFi1auPVcv02bNmnTpk26//771aBBA3Xu3FkdOnRQq1atvFIwtZM333xTr7/+utM20dHRmj9/vipVquSVMV2dn2lpabr55pu9MpY7Tpw44fS4v5+fzm63KkmRkZGm79h88skn9eWXX7p8xEdmZqY+//xzff7554qOjlbHjh3VqVMntWvXTvXr1w/YXWy+wu7w/Dl58qTL86Vu3bo+igZ2YPY56erz8rvvvtOOHTtMjeHPXBXAjx496tZ6v0SJErrnnnv0wgsvuGx75MgRPffcc3ruuedUqVKlv/zbokKFCm7HboWoqCinxyk4A8A/8a8BAAAAk5w4cSLXW1T+mbNnm7ojIyNDzz77rF555RWXF+LM5M5u7kBkh9d39OjRmjNnjhYuXOj27xw/flyffvqpPv30U0lSyZIl1aJFC7Vo0UKtW7dWs2bNTLvN6+HDh50eP3/+vGbPnm3K2J7ggpN7pkyZohYtWig1NdWt9oZhXC4+v/zyy3I4HKpRo4Zatmypli1bqnXr1qpRo4ZlO/Gt9s033+jf//630zahoaH64osvvHrLUFfnZ1JSEudnHrj6XPHFYw5q1aqlp59+Wo8//rjbv5OWlqb58+dr/vz5ki5emG/atKlatGihVq1aqVWrVipRooRZIQekIkWKWB1CQHN1K39JiouL80EksAuzz0lXn5cbN27Uxo0bTY0hL/Lyefn4449rwYIF2rJli9u/c+DAAX344Yf68MMPJUnlypVTy5YtL//bonHjxgoPD89z3GZx9flr5b8LAcBfUXAGAAAwiTu7YAsVKpSvHXu//vqr+vbtq+3bt3vch7e4+5ziQGKX1zc0NFQzZ85Uu3bttG3bNo/6OHnypObNm6d58+ZJksLDw9WyZUt169ZNffr08eozUv/44w+v9eUL7tzJABefITxr1iz16dPHoy9QGIahnTt3aufOnZoyZYqki7tsunTpouuuu049e/YMmh3QP/30kwYNGuRyR+o777yj66+/3qtjc376lq8+Wx977DH99ttv+uSTTzz6/fT0dC1btkzLli27/Gd169ZV165d1atXL7Vp0ybon61LwTl/XN3NQGIXOfLGzHMyKytLJ0+eNK1/M+Tl8zI6OlrffvutWrdu7bKwnpsjR47oq6++0ldffSXpYoG3Xbt26t69u/r06eO1O7N4ytXnb7B+4REAnAnu1T4AAICJDhw44LJNfp5P+tNPP6lVq1Z+UQy1I7u9vkWLFtXq1avVr18/r/R34cIFLV++XI899phq1aqlevXq6bXXXlNycnK++3b2TDh/lJmZaXUIAeO6667TihUrvHYbxVOnTmnmzJkaOnSoSpcurT59+ui7776z5RdgLtmzZ4969erl8sLwI488ottvv93r43N+eld0dLTT474smE+bNk3PPfec1wrD27Zt0yuvvKL27durXLly+s9//qPdu3d7pe9A5Mtnm9uRq92EBQoUUEREhI+igR2YeU6mpaUF3Fokr5+XFStW1IYNG9S+fXuvjH/u3DnFx8fr3//+typXrqxWrVrpww8/tGwnsavPX1e33AaAYETBGQAAwCTu7CT1tOjy66+/6oYbblBSUpJHvw/n7Pr6FipUSF988YVmzJihKlWqeLXvbdu26YEHHlDFihX18MMPKyUlxeO+Am1HYqBdULRa06ZNtXnzZv373/9WZGSk1/rNzMzUnDlz1KNHD9WuXVtffvml1/r2F4mJibruuutc7poaOHCgnn32WVNi4Pz0LlcXrDMzM13uZPcWh8OhRx55RKtXr/ZaAeGSY8eO6eWXX1b16tXVv39//f77717tPxAE+w7v/HKVewoUKOCjSGAXZp6TgfZZKXn2eVmqVCn9+OOPmjRpkkqXLu3VeNasWaPbb79dlSpV0gsvvKDz5897tX9XXP0duvrCGAAEI1a7AAAAJnGn4Fy3bt0895uZman+/fvnqRharlw53XjjjXryySc1bdo0LV68WNu2bdOhQ4eUnJys8+fP68KFCzIMw+mP1bc284VgeH0HDhyoXbt26cMPP1Tz5s292vfZs2f10ksv6ZprrvG44HfhwgWvxgT/U7x4cb366qv6/fff9eCDD3r9IuXOnTt1yy23qEOHDtq3b59X+7bK+fPn1atXL5eFug4dOmjq1Kmm3eqR89O73Llg7evCRfPmzbV06VLFx8erV69eXn2mZk5Ojr744gvVrl1b48ePV1ZWltf6BgB/EUyflWFhYbrnnnu0Z88evfLKK6pdu7ZX+z916pQeeeQR1axZUwkJCV7t2xl2OANA3vEMZwAAAJOsXr3aZZvGjRvnud/XX39dW7ZscdmuZMmSGjNmjG699VbVqlUrz+MEq2B5fcPDwzV69GiNHj1av/76q2bOnKkff/xRP//8s1cukp06dUq33HKL/vOf/+jFF1/M0+96c9cr/FuFChU0ceJEvfDCC4qPj9ecOXOUkJCgPXv2eKX/ZcuWqUmTJpo7d67atGnjlT6tYBiGhgwZ4vJzpVatWvrmm29Mva0s56d3uVtwtmInVdeuXdW1a1edOnVKs2bN0sKFC7VixQqlpqbmu+8LFy7o6aef1sqVKzV37lwVKlTICxHDzgoWLOj0uK93PwLOBONnZXR0tB544AE98MAD2rBhgz7//HMtWbJEmzZt8sqdOvbv368uXbrotdde07/+9S8vROwcO5wBIO8oOAMAAJhg165dOnz4sMt2eS04p6en66WXXnLZbvDgwXrvvfe8/g9hb1xk9mfB+vpWr15dTz31lJ566imlp6dr1apVWrFihVatWqWff/45X89sfemll1S0aFE98sgjbv+Oq4vK5cqVc+v8QuAICwvTDTfcoBtuuEGSdOjQIS1dulSrVq3SqlWrtGPHDo8vViYlJalnz55avXq1atas6c2wfebBBx/UV1995bRNmTJltGDBAhUtWtTUWFydn61bt9bKlStNjcFOypQp47LNqVOnVKJECR9Ec2UlSpTQPffco3vuuUfZ2dnasGHD5c+I1atX6/jx4x73vWTJEvXv31/ffvutQkNDvRg17MbVbsLz588rMzOT5zjDL7j6rJSkDz/8UKNHj/ZBNL7XuHHjy//OTUlJ0YoVK7RixQqtXr1a69evV0ZGhkf9Zmdn67777lOJEiU0YMAAb4b8D64eX1K2bFlTxweAQMQttQEAAEywcOFCl21KlCihatWq5anf2bNnKzEx0WmbJ554Qp9++qnXi6E5OTk6ffq0V/v0N7y+Fy/odunSRU8//bQWL16slJQUbdiwQa+//rp69+6twoUL57nPxx57zK1z4pLixYs7Pc4uJvurUKGChgwZovfee0/btm1TUlKSFixYoHHjxqlZs2Z5fu5iSkqKbrjhhoB8puKkSZP02muvOW1TqFAhfffdd6pYsaLp8XB+elfp0qVdFib86Qs2oaGhatasmR588EF9/fXXOnbsmH7//XdNmzZNw4YNU/ny5fPc5/fff6/HH3/chGhhlczMTK/3WapUKZdtjh496vVxYR4z3if+olChQi4fRxAsn5dFixZVz5499dJLL2nlypVKTU3VqlWr9MILL6hbt25uFef/zDAMjRgxQlu3bjUp4ouOHDni9HjlypVNHR8AAhEFZwAAABN88sknLttcf/31eS6auNrh1rZtWz311FN56tNdp0+f9srt0PwZr+8/hYaGqlGjRrrvvvs0Z84cJSYmavHixbrrrrtcFp4uMQxDY8eOdXt+ropmKSkpPPczyBQpUkTdu3fX888/r7Vr1+r48eOaMmWKunfv7nYe3bdvn9566y2TI/Wu/2/vzuOjqNL9j38TQlayAGELCiFAAgYQZQZGBBICIaI3gMoFFVlkXjKImbl4hcFxw2FccBkZLirq1QEcBhFQQQGDigGGJUAE2QYuJCxhiSxJgCxmr98f/mQYSaq6O92dpPm8X6/8dU6f81T1qe5KP1VPrVq1SlOnTjXt4+Pjo+XLl+uWW25xS0xWx6fVHUG4Vvv27U3brX70rmudOnXS+PHjtXDhQp08eVJ79uzRc889p06dOtk8xpw5c3Ty5EkXRgl3ysvLc/qYtlzMcOzYMafPC9dxxTqpL7y8vHTjjTea9rlevy99fX3Vt29fzZgxQ6mpqcrLy9Pq1as1fvx4my/oLS0ttat6kiOsLvYi4QwA1yLhDAAA4GTfffeddu/ebdkvOTnZrnENw9A//vEP0z5/+tOf7E5i26q+/+BdW+xf2/j4+CghIUFvvvmmTp8+rXfffdemH4H379+vTz75xKY5rH7AqaysbDD7C64RHh6uhx56SF988YWOHj2qRx99VD4+1k+Mmj17tsNlHN1tx44deuCBBywv1Jg/f77uuOMON0VlfXyeOXNGlZWV7gnGQ1jt0/p0h7MtevTooZkzZ+rIkSNKTU1Vnz59LF9TWlqql19+2Q3RXR+sPg+Li4tdOr8rEoktW7a0LKu9b98+p8/ryTxxndQnVp/t2dnZ7gmknvP399ddd92lhQsX6syZM3r11Vdtuqh17dq1ysjIcFlc3OEMAPYj4QwAAOBkL774omWfoKAgJSUl2TVudna28vPza2yPiIhQ//797RrTHlu3bnXZ2PUB+9d+/v7+evjhh3XgwAElJCRY9v/ss89sGrd79+7y8vIy7cOPyvhJ+/bt9cYbb2jDhg0KDQ017ZuXl6ctW7a4KTLHHT16VMnJyZY/9j/11FNuf/5jjx49TNsrKip08OBBN0XjGaKiokzbG1rC+WpJSUnaunWrfv/731v2tfU7Atb8/PxM2wsKClw6f22e610TLy8v3XzzzaZ9tm3b5vR5PZknrpP6xOr7knPZa4WEhGjatGnav3+/unfvbtnfVd8bhYWFlo866tChg0vmBoCGjIQzAACAE+3du9eyLLMkjRs3TsHBwXaNffToUdP2Pn36uOzuW0kNIklTG+xfx4WEhOjzzz+3/OHlq6++smm8sLAwde7c2bRPenq6zfHh+nD77bfrww8/tOz35ZdfuiEax+Xm5mro0KE6d+6cab+xY8fq+eefd1NU/9KtWzfLuww5Pu1jVQ790KFDborENby9vfXyyy9r9OjRpv1OnjzZ4Le1vrAqS+vqRKKrPgN69epl2r5+/XoZhuGSuT2Rp66T+qJ3796m7fv27XP5XeQNVZs2bfTll19aXkjoqnM6q++iZs2acYczAFSDhDMAAICTVFZWatKkSTb90JWSkmL3+FZl51q3bm33mLYyDEMbN2502fg/sbqr1ZU/Il4P+9eVAgMDLZ9v/f3339tcPnHAgAGm7WvWrLE1tHqpLte6Jxs6dKgGDhxo2uef//ynm6KxX0lJiYYPH67Dhw+b9ktISND777/vpqj+XaNGjdS3b1/TPg39+HS3X/ziF6btnnIXnC0ls+09PvksrV7Lli1N2139rGNXXUQXHx9v2n7u3Dlt2LDBJXO7k7vWraeuk/rCqjJSWVmZzRdjXo9at26t//7v/zbt46pzur1795q2W31vA8D1ioQzAACAk7z00kvavn27Zb/k5GTddNNNdo9vdQV806ZN7R7TVmvXrtWJEydcNv5PGjdubNpeUVHhsrmvh/3rarY8l/z8+fM2jTVixAjT9u+++0779++3aaz6qC7XuqcbNmyYabuta9DdDMPQuHHjLH+A79atmz755BPLNeRKVsfnF198oQsXLrgnGA/QrVs3+fv719iem5vrEc+tb9++vWVJZHuPTz5Lq9emTRvT9v3797ssqZmTk+OyJNCQIUPk6+tr2qeuLsaxl9nadde69dR1Ul/ccMMNlonJv/3tb26KpmGyOqcrKChQaWmp0+e1Sjj/8pe/dPqcAOAJSDgDAAA4wfLly/Xss89a9mvcuLFee+01h+bw8fExbc/NzXVoXFvMnTvXZWNfLSAgwLTdlaX9rof962pNmzZVWFiYaR9b9+PgwYMtx5ozZ46NkdU/dbnWPZ1VaXdXHsu1MX36dC1fvty0T0REhNauXWtZYtLV7r77bjVq1KjG9tLSUs2fP9+NETVsPj4+lolYT7nL2dnHJ5+l1YuIiDAtl3z58mXLR4k46o033nBZkjI4OFiJiYmmfT766COXbZszma1dd61bT10n9cnIkSNN21etWuXyO8kbMluek+yK8zrucAYAx5BwBgAAqKWVK1dq7NixNpfSjo6OdmgeqwSDq36sSE9Pd1u5t+bNm5u2nz171mVzXw/71x3MklCSLO9M+omfn58mTpxo2mfRokUNNglTl2vd0zlrDbrTm2++qT//+c+mfYKDg7VmzRrdeOONboqqZhERERo+fLhpn1dffZV1bIfbbrvNtH3Pnj1uisS1nH18hoWFmY55va5BLy8vde3a1bTPp59+6vR5i4uL9fbbbzt93KtNmjTJtL2iokKPP/64S2NwBrPzgIKCAv3www8uj8GT10l9MXHiRPn5+dXYXlFRoRkzZrgxoobF6jtDcs15nVXC+Ve/+pXT5wQAT0DCGQAAwEGGYejPf/6z7r33XptKecXGxur55593eD6rJMOmTZssy0Lbq6ioSGPHjnXqmGasnpN85MgRl819PexfVyssLLS8y6BFixY2j5eSkmL6Q1NlZaXGjRvnklJ6rlaXa93TWZWnt2cNusNnn32m3/3ud6Z9fHx8tGLFCvXs2dM9Qdlg6tSppu0FBQWaOHHidXEHmzMkJSWZtm/evNlNkbiWs49PLy8v0+fQnjt3TpcuXbJrTE9hdRHDkiVLnD7nzJkzlZeX5/Rxr3bXXXcpMjLStM/KlSv14YcfujSO2qov5wGeuk7qixYtWmjMmDGmfZYvX65ly5a5KaKGxeo7w8fHx7Iikr0OHjxo+v9Mz549LY9fALhekXAGAABwwNGjRzVo0CBNmzZNVVVVlv2DgoK0fPlyBQYGOjxndHS06RXcJSUlWrhwocPjV+e//uu/lJmZ6dQxzXTq1Mm0fdu2bS6b2xP3b3l5ucvGrs7KlStN2wMDA9WuXTubx+vQoYPlnUzfffedJkyYYNNxWJ9YrfX09HQ3ReJ67l6HVndjdenSxU2RWNuxY4fuv/9+y/X7zjvvaMiQIW6Kyjb9+/fX0KFDTfusXbtWTzzxhJsiatji4+NNS+xu2rRJlZWVTp2zqqrK6WOayc7O1q5du0z7OHJ8Xk+fp/YYOHCgafvu3bu1bt06p823bt06y0oNztCoUSPNnDnTst/DDz+s3bt3uzweR9XlOe/VPHWd1CczZ86Uv7+/aZ9f//rX2rFjh5siclx9O6fr1KmT5WOR7JWWlmbabnXuAwDXMxLOAAAAdjh58qSmTJmirl27Wv4z+pPGjRtryZIlliXrrPj5+alXr16mfWbOnKlz587Vap6fzJo1S++//75TxrJV9+7dTduXL1/ush/HPXH/rl27VgkJCfrmm29cOo/0Y3nEl156ybRP//795eXlZde4s2bNUtOmTU37LF26VGPGjFFJSYldYzuqqqpKy5YtU0JCgsNjREZGKjg4uMb2nJwcbdy40eHx65Px48dr6tSpOn36tMvnSktLs1zvcXFxLo/DFseOHVNycrJl5YRnnnnGsrx8XXn99dfVuHFj0z6vvPKKHn/8cbddFFJWVqZ3331Xo0aNcst8zuLv72+a+Ll8+bJlstZely9fVteuXbVgwQK3JBFmzpxpug6Cg4N166232j2u1bnD0qVL7R7TEyQlJVle6JiSkuKUKiEHDx60+fEyzjBu3Dj16NHDtE9RUZESExOdftxcraqqSmfOnHHotfVl3XryOqkv2rVrp+nTp5v2KSwsVFJSkjZs2OCeoPTjRUCPPvqo3nvvPZtfM3/+fN1999369ttvXRjZj86ePas33njDtI8rzums3oM777zT6XMCgKcg4QwAAGChsLBQy5cvV3JysqKiojR//nyVlZXZ9FofHx8tXbpUw4YNc0osI0aMMG2/cOGC7rjjDl2+fNnhOcrKyvTII4/YdPeIs/Xr18+0PSsrSy+88ILL5ve0/WsYhtLS0jRo0CD17NlT7733noqKipw+T0lJicaNG6d//vOfpv1Gjhxp99jh4eE2Pedv6dKl6tu3r0uf6Zybm6vXXntNnTt31ujRoy2f72bG29vbsozlY489posXLzo8R31RXFysuXPnqkOHDrrvvvv0j3/8wyXz7Nu3Tw888IDpD9mBgYH14s6UvLw8DR061PIClvHjx2vWrFluisp+Xbp0selREa+//rqGDBliWRqzNk6dOqVnn31W7du3129+8xsdPXrUZXO5itWP2K5IRBw5ckQTJ05U+/bt9cc//tHh5JmV1157zbJKyLBhwywvYKiO1bnD4sWL3XLhVX0TGBhoeV6TmZmpUaNG2XxeW51NmzYpPj5e58+fd3gMe3l7e2vBggWWdzbm5uaqX79+Tq9QU1FRoQ8++EDdunXTu+++69AYVut2w4YN+uCDDxwa2x6evE7qk6efftrysRgXL17UkCFD9Pzzz6uiosJlsWzcuFGjRo1Sx44d9dZbb9l1wWZVVZVWrlypX/ziF+rfv78++uijWq2LmuTn52vkyJE6e/asaT9H/rewYvZdGxYWZnn+DgDXNQMAAKCBWLBggSHJ9C8tLa1Wc5SWlhoHDhwwPvroI+Opp54y+vXrZzRu3Nhy3ur+QkNDjc8//9w5G///5eTkGL6+vpZzd+7c2di+fbvd43/zzTdGbGxstWMGBwcboaGhpvM6wy233GK5fXfddZeRmppqlJaWOmXOn3ja/v3000+vGSMoKMh48MEHjc8//9woLi62e8yf27Jli3Hrrbda7rPw8HCjqKjI4Xkefvhhm447Hx8fY9KkSUZmZmatt80wDCM3N9f4+9//biQnJ1/zWdC8efNajT137lzL7WnXrp3x1ltvGWfPnnXK9tSF4cOHX7NdHTt2NJ599llj9+7dtR6/pKTEmDdvnhEUFGS5P6dMmeLQHOPHj3fqd8+oUaMsYx08eLBRVlbmULzuVFVVZSQlJdl0fAYGBhozZswwzpw545S5z5w5Y/zv//6vkZCQYHh7e//bXL169XLKHO6UnZ1teHl51bj/kpKSnDpffn7+NXN4e3sbiYmJxl//+lenfO4cP37cGD16tE3rw5HvVcP48XPax8fHdOxGjRoZv/3tb41du3YZVVVVtd6u6rRv396p3+HOsH37dpv2/ZAhQ4wTJ07YNXZ+fr7x+OOPV7vvmzZtajpfXFycU7bvhRdesGn7JBmDBg0y0tPTazXfoUOHjOeee86IjIy8Mu7MmTMdGquiosJo0aKFZdxjx441Nm/ebFRUVNQqdjOeuk7S0tJMxx8/fnytxrfXoUOHjODgYJv2dUxMjLFkyRKnnAdUVVUZGRkZxlNPPWV06NDhmrnmzZtn81hz5sy55vXNmjUzJk+ebHz99ddOiXfNmjVGVFSU5T6KjY11+uf53r17Ted88MEHnTofAHgaL8O4zuqYAACABmvhwoV66KGHTPsMGDBALVq0sGm8srIylZaWqqSkRHl5ecrJyVFeXp5Tyrz16NFDH3/8seXz2RwxZcoUzZ8/37Kft7e37rzzTk2ePFkDBgyosXxvdna2UlNTtXDhQtPnxb3//vuaNWuW6R1qzth3f/nLX/TYY4/Z1NfHx0edO3dW69atFRQUJD8/P9P+f/zjHxUbG2vax5P278qVK3X33XfX2B4QEKD+/furX79+6tOnj2JjY9W2bVvTMSsrK5WZmal169bp448/1qZNm2yK5Z133rF8HrOZiooKJScnKzU11ab+Xl5eiouL07BhwzRw4EDFxsZa3jlXXl6urKws7d+/X+np6dqyZYt27txZYxn35s2b68KFC3Zvy0/Onj2r9u3b21ymsk2bNoqKilJwcLACAwNNy5MPHDhQjz76qMOxOdOIESO0atWqGttvuOEGDRw4ULfffrtuvfVWde3aVU2aNDEds6ioSBkZGVq9erU+/PBDm8p1h4aG6vDhw2rZsqXd2zBhwgQtWrSoxva0tDTFx8fbPF58fLxlyfTExESFhITYPKYzOLpuCgoKFBcXZ/PzUn18fJSUlKT/+I//UFxcnKKjo9WoUSPT15SUlOjIkSPau3ev0tPTtXnzZu3Zs6fGz8VevXopIyPD7m2pawMHDqzx7ipfX1+dO3dOoaGhTpnr4sWLpo8s8Pb2vnIXW9++fdW9e3dFRUVZvldnzpxRWlqaPvvsM3366ac2leu+//77tWTJEru34SdWnzNXCwoKUkxMjJo1a6agoCDLu2RXrFhh07iRkZEuP0dyRHJyslavXm3ZLyAgQCkpKRo5cqR++ctfVvsdU1JSovT0dK1YsUIffPCBCgoKrunTuHFj/f3vfzctax8XF+e0O/YfeOABffjhhzb379Onj0aPHq1BgwapW7du8vauufjjqVOnlJGRceX7Zs+ePdf0mTlzpp577jlHQtfUqVM1d+5cm/r6+fkpJiZG4eHhatKkieU5zfz5823+n0jyzHWyYcMG00cVjB8/3ul3v1tZv3697rzzTpvvCm7ZsqXuvfdeDR06VL1791arVq0sX3P+/HkdOnRI3377rdLT07VhwwbTO4XnzZunlJQUm+Kx+j8tJCRE8fHxuv3229WnTx/ddNNNluuwvLxcBw8e1Nq1a7Vs2TKbzyVSU1OVlJRkU19bzZo1y7QK1bp16zRkyBCnzgkAnoSEMwAAaDBsSTjXNX9/f02bNk1PPvmkAgICXDJHbm6uunbtaldJOm9vb8XExKhly5YKCwtTRUWF8vPzlZWVZVmqTJJGjRqljz76yC0/phYWFioqKsolJfdsSQp50v61SjhXJzg4WG3btlXr1q0VGBgoPz8/lZaWqrCwUBcuXFBWVpbdz/FLTk7WqlWr7H5+888VFRVp2LBhDpVG9fX1Vbt27RQREaHg4GD5+fmpvLz8ygUnZ8+eVU5Ojl3PCK9twlmSHnnkEZtKhturLn5ErYk9iSDpx4sFWrZsqYiICIWHhysgIEDe3t4qKipSYWGhTp48qdOnT9t9PCxfvtzh0ot1kXCuC7VZN+fOnVNiYqJDpeYDAgKuHJ9BQUHy9fVVWVmZSkpKlJubq++//15nz5616znQDTXhvGDBAtNndv/tb3/Tgw8+6JS5rBLO1fHz81NERMSVz1J/f39VVFSoqKhIly5dUmZmpt2PnWjfvr127dqlZs2a2fW6q6Wnp7uszKmtnzX1NeGcmZmpm2++2fJ58Vdr3ry52rVrpxYtWiggIEBFRUU6deqUsrKyLC8gmDt3roYNG6YOHTrU2MeZCefS0lKNGDHC5gvSrhYYGKgOHTqoTZs2CgwMVFVVlfLz85Wfn6+zZ88qNzfXcozaJJxPnDihmJgYpzwf+eeOHTumyMhIm/t74jqpjwln6cfz8/vuu8+h9z08PFw33nijWrZsKX9/f3l7e6ukpERFRUU6d+6ccnJydOnSJbvGdGbCuTphYWFq27atWrVqpcDAQDVu3Fg//PCDioqKdPbsWR09etTuEuIpKSmaN2+eXa+xRY8ePWp8PE9ERIROnjxpepEKAFz36uK2agAAAEfYUlK7rv68vb2Ne++918jKynLLvkhNTb2mfKir/uLi4oySkhLDMNxXLnLJkiUu2RZby956yv6trqS2u/969+5tXLp0ye7Ya1JaWmrcf//9db5dUu1LahvGj6Vg27Rp4/TY3F0m0kx1JbXd/Td79uxabYOzS2rHxcXV+T5xxbq5ePGikZCQUOfbITXMktqGYRiXL182AgICatyu4cOHO22u6kpqu/svPDzc2Ldvn1O2Z9KkSS6J0Vb1saT2T95//323vJ8zZswwDMMwjh07ZtrPWSW1f1JaWmrcc889dbKGHS2p/ZMXX3zRJXEdO3bM7lg8bZ3Ut5LaV9u4caNlSXF3/dW2pLa7/4YNG+aSR44cPnzYdN7p06c7fU4A8DRckgMAAFALAQEB+s1vfqODBw9qxYoVioqKcsu8SUlJevfdd2t9x6iVgQMHatWqVZalqp3t/vvv1zPPPOPWOa/m6fvXXYYOHaovv/zSqWWBfX19tWTJEs2bN89lVQTcqVmzZvr888/tvssQtvHx8dGbb76pGTNm1HUo14XQ0FCtW7dOzzzzjGXZZVQvODhYI0aMqLF93bp1KiwsdF9ALtSxY0dt3LhR3bp1c8p4//M//6PBgwc7ZSxPM3HiRD355JMunWP69OmaPXu2S+eoia+vr1asWKE//elPDe6z54knntC4cePqOgxJnr9O6pMBAwZo165d6tevX12H0qBMmDBBy5cvtywp7wirxyfUl+MUAOozEs4AAAB28vPzU3Jysj744AN9//33evvttxUdHe32OH79619r6dKlLku6TZ48WevWrXPasyLtNWvWLC1atKhWJTZrwxP2r6sT5jUJCwvT3LlztXr1apdtX0pKinbv3q077rjDJeNbiY6OdloSs1evXtq+fbvLysHWtbpah71799aWLVs0ZcqUOpn/euXj46NZs2Zpy5Yt6tOnT53E0LNnz3rzDHNHmD3vvqSkRJ999plT5qmrY7NRo0Z69NFHlZGRoZtuuslp4/r5+Wnt2rWaNm2a5XOZr0cvvPCCXnzxRae/7/7+/nrvvff0yiuvOHVce3l5eenpp5/Wxo0b1aNHD7fNW9vyul5eXlq4cKFeeeUVBQYGOikqx3n6OqlPIiMjtXHjRs2dO7dO/t/x8/PTyJEjTcuO/1xdfW9ERERo8eLFWrBggXx9fV0yx7Jly2psu+2225x2cRQAeLS6vsUaAADAVnVVUjswMNDo37+/8eSTTxpffPGFcfny5breFf/m4MGDRt++fZ22vTExMcY333xT7Vx1US4yLy/PeOGFF4xOnTrVetvsLXtrGA17/1ZVVRnp6enG008/bfTs2dPlx4qvr68xadIk4/z583bHWhtfffWVMXjwYJdvX7NmzYzJkycbW7dudcl2VFVVGStXrjQSExMNHx+fWsVan0pqX7582VixYoUxYcIEo1WrVi5/n9q2bWv89a9/Naqqqpy2DZTUdtyyZcuM3r17uzz2iIgIY9q0aU4rz1zXbrnllhq3NT4+3mnzZGZmGnPmzDEGDRpk+Pr6uvx9Gjx4sFveo8OHDxtTpkwxwsPDax2zrepzSe2rrV+/3ujYsaNT3s+4uDjj//7v/66Zw90ltX+uoqLCePvtt522nT//8/LyMhITE40VK1YY5eXlTov71KlTxowZM4wbbrih1jE6UlL7ap6wTupzSe2fy8vLM55++mmjRYsWLlmzV6/d2267zZg/f76Rl5dnd5zl5eVGWlqa8fjjjxsxMTEujVX68f/wJ554wigsLHTBXv+XHTt2mMaxbNkyl84PAJ7CyzAMQwAAAA3AwoUL9dBDD9V6HC8vL/n6+srX11d+fn7y8/NT06ZN1bJlS7Vq1UqtWrVSu3bt1KVLF3Xp0kWRkZF1djW3PVatWqW//OUv2rBhg92vbdSokQYMGKCUlBQNHz68xnKE9913n77//vsax3FkbnscOnRImzdv1u7du3XkyBGdOnVKubm5unz5ssrLy1VZWWn6+rS0NMXHxzs0tyfs39OnT+vrr7/W1q1btW3bNh04cEBVVVW1GtPLy0v9+vXTmDFj9J//+Z91dke69OP6WLx4sVatWqX9+/fXeryAgADdfvvtGjRokAYNGqRevXrV+k4mW+Xn52vTpk3asWOHDh06pOPHj+v8+fPKz89XaWmpysvLTV8/fvx4LVy40C2x2sMwDO3cuVMbN27Utm3blJ6erpycnFqPGxwcrHvuuUdjxoxRQkKC00uqTpgwQYsWLaqx3d7Plvj4eG3cuNEJkTmXK9dNRkaGlixZolWrVuno0aO1Hi8kJEQDBgy4cnx2797dCVHWH4sXL9bYsWNrbD98+LA6d+7s1DkLCgq0fv16bdmyRenp6fr222/1ww8/1HrcmJgYPfDAAxozZow6duzohEhtV1lZqZ07d2rr1q3at2+fsrKylJOTo9zcXBUXF6u8vNzye9DWn80iIyN14sSJWo/jDqWlpVq4cKHmzZunAwcO2PVab29vJSYmatq0aTWWMD9+/Lg6dOhQ4xhxcXEuP2eUpKqqKq1evVpLlizRmjVralWO3t/fX/3799eQIUN0zz33uPQxOoZhaM+ePdqyZYv27NmjzMxMnTlzRrm5uSosLFRZWZnluj127JgiIyNrFUdDXycbNmwwvXu3Pp4rlZaW6pNPPtEnn3yi1NRUpzxCISoq6sp35aBBgxQeHu6ESH+UlZWlr7/+Wtu2bdO2bdt05MiRWn/W+fj4aPDgwRozZozuvvtuBQUFOSnamj388MN67733qm2LjIxUZmZmgyvXDwB1gYQzAACAhzl16pTWrl2r7du368CBA8rOztbFixdVWloqPz8/NWnSRE2bNlXnzp0VExOjPn36KDExkWfI2siT9m9BQYF27dqlw4cPKysrS1lZWTp27JguXryowsJCFRQUqLS0VIGBgQoJCVFISIhCQ0PVsWNH9ezZUz179tQtt9yi5s2b1/WmXOPUqVPasWOHMjIydPjwYWVnZ+v06dMqKirSDz/8oKqqKjVp0kTBwcEKDg5WSEiIIiMj1bVr1ysXm3Tp0sVlZfvwL8ePH9eePXuurMHMzEydPn1aBQUFKiwsVGFhoQzDuPI+hYSEKDw8XLGxsVfWYbdu3Vz6Xjk74Xy9y8rK0s6dO5WRkaHMzExlZ2crJydHxcXFKi4ulqQr73dwcLBCQ0MVFRX1b8dndHS0R//4W15erg4dOuj06dPVtk+bNk2vvvqqy2PYu3evDh48eOXYPHr0qC5cuHDl2CwqKpKvr++VYzMkJEQ33nijbr755ivHZ22TXnCtffv26auvvtL27duvXMxXUFCgsrIyBQUFKTQ0VJGRkYqNjdVtt92mu+66y6kJK3cpLS1VRkbGlYsPjh07puzsbF2+fFnFxcVXzgt+OjeIiIi48nkTGxurX/3qVy57zEpDcL2sk/qkrKxMu3fv1s6dO7Vnzx4dP35c2dnZysvLU3FxsUpKSuTn5/dv35ctWrRQdHT0le/Lm266Sa1bt3ZbzHl5efr222+VmZmpzMxMZWVl6cSJE7p06dKV742ysjI1adLkyndGWFiYoqOjr3xn9OzZUyEhIW6LuaCgQBERETUm919//XU99thjbosHABoyEs4AAAAAAAD1zOzZs/WHP/yh2rYWLVro1KlTXBQDAEAtvPPOO5o8eXK1bSEhITp58qRbE+AA0JC5px4cAAAAAAAAbPbII4/U+JiC8+fPa9myZW6OCAAAz/LWW2/V2JaSkkKyGQDsQMIZAAAAAACgngkNDdXvf//7GttffvnlevVcYAAAGpI1a9Zo79691bY1bdpU06dPd3NEANCwkXAGAAAAAACoh37729/W+PzN/fv3a/Xq1W6OCAAAzzB79uwa26ZPn66wsDD3BQMAHoCEMwAAAAAAQD0UGBiop556qsZ2sx/LAQBA9TZv3qzNmzdX29aqVSv97ne/c3NEANDwkXAGAAAAAACopyZNmqTIyMhq27Zu3apNmza5NyAAABq4l156qca2J598UkFBQW6MBgA8g5fBA38AAAAAAADqrWXLlmn06NHVtiUkJGj9+vVujggAgIZpx44d6tOnT7Vt0dHR2rdvn3x9fd0cFQA0fNzhDAAAAAAAUI+NGjVKCQkJ1bZ98803Sk1NdXNEAAA0TNOnT6+xbd68eSSbAcBB3OEMAAAAAABQzx08eFA333yzysvLr2nr0aOHdu/eLW9v7isAAKAmq1evVnJycrVt99xzjz7++GM3RwQAnoP/RAAAAAAAAOq5rl27aurUqdW27d27V4sXL3ZvQAAANCCVlZV64oknqm0LDAzUnDlz3BwRAHgWEs4AAAAAAAANwLPPPqu2bdtW2/bMM8+opKTEzREBANAwLFq0SAcOHKi27Q9/+IPatWvn5ogAwLNQUhsAAAAAAAAAAAAA4BDucAYAAAAAAAAAAAAAOISEMwAAAAAAAAAAAADAISScAQAAAAAAAAAAAAAOIeEMAAAAAAAAAAAAAHAICWcAAAAAAAAAAAAAgENIOAMAAAAAAAAAAAAAHELCGQAAAAAAAAAAAADgEBLOAAAAAAAAAAAAAACHkHAGAAAAAAAAAAAAADiEhDMAAAAAAAAAAAAAwCEknAEAAAAAAAAAAAAADiHhDAAAAAAAAAAAAABwCAlnAAAAAAAAAAAAAIBDSDgDAAAAAAAAAAAAABxCwhkAAAAAAAAAAAAA4BASzgAAAAAAAAAAAAAAh5BwBgAAAAAAAAAAAAA4hIQzAAAAAAAAAAAAAMAhJJwBAAAAAAAAAAAAAA4h4QwAAAAAAAAAAAAAcAgJZwAAAAAAAAAAAACAQ0g4AwAAAAAAAAAAAAAcQsIZAAAAAAAAAAAAAOAQEs4AAAAAAAAAAAAAAIeQcAYAAAAAAAAAAAAAOISEMwAAAAAAAAAAAADAISScAQAAAAAAAAAAAAAOIeEMAAAAAAAAAAAAAHAICWcAAAAAAAAAAAAAgENIOAMAAAAAAAAAAAAAHELCGQAAAAAAAAAAAADgEBLOAAAAAAAAAAAAAACHkHAGAAAAAAAAAAAAADiEhDMAAAAAAAAAAAAAwCEknAEAAAAAAAAAAAAADiHhDAAAAAAAAAAAAABwCAlnAAAAAAAAAAAAAIBDSDgDAAAAAAAAAAAAABxCwhkAAAAAAAAAAAAA4BASzgAAAAAAAAAAAAAAh5BwBgAAAAAAAAAAAAA4hIQzAAAAAAAAAAAAAMAhJJwBAAAAAAAAAAAAAA4h4QwAAAAAAAAAAAAAcAgJZwAAAAAAAAAAAACAQ0g4AwAAAAAAAAAAAAAcQsIZAAAAAAAAAAAAAOAQEs4AAAAAAAAAAAAAAIeQcAYAAAAAAAAAAAAAOOT/ASlniori8bHCAAAAAElFTkSuQmCC",
+      "text/plain": [
+       "<Figure size 2025x1557 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig,ax = plt.subplots()\n",
+    "\n",
+    "x = [125,251,378,503,628,754,880,1006,1131,1257]\n",
+    "y = np.array([0.00403113, 0.00445634, 0.0054036, 0.00676608, 0.00752462, 0.00676533, 0.00675098, 0.00646613, 0.00641488, 0.00650355])*1000\n",
+    "y2 = np.array([0.0201, 0.0233, 0.0191, 0.00784, 0.0186, 0.00759, 0.0272, 0.0247, 0.0225, 0.0179])*1000\n",
+    "\n",
+    "# ax.plot(x,y4,label = 'SNAP - Feed forward')\n",
+    "# ax.plot(x,y3,label = 'Schnet - GCNN')\n",
+    "ax.plot(x,y,label = 'MTP - Feed forward (optimized)')\n",
+    "ax.plot(x,y2,label = 'Nequip - E(3)-equivariant')\n",
+    "\n",
+    "ax.set_xlabel('Dataset size (structures)')\n",
+    "ax.set_ylabel('Energy MAE (meV/atom)')\n",
+    "ax.legend(title='MLIAP', fontsize=5, loc='upper left')\n",
+    "plt.rcParams['legend.title_fontsize'] = 10\n",
+    "fig.savefig('figs/data_efficiency_schematic.pdf')"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Disclaimer\n",
+    "\n",
+    "This data is not to be trusted and is just there as a rough metric to compare. For data extraction, we used the default energy MAE values from the full.yaml config file (nequip) and the standard training output files (MTP). Note that the hyper-parameters implemented for MTPs are already optimized during our previous researches and uses a complex architecture with lots of parameters, whereas ,due to the limit of time, we did not perform hyper-parameter optimization for the nequip potential nor did we get the change to compare the number of parameters used in nequip or implement a nequip potential with more complex structures. But the fact that a very rough model of equivariant nequip potential can obtian similar levels of energy errors with respect to a well-estabilished potential is very exciting."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## References"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "1. Shapeev, Alexander V. \"Moment tensor potentials: A class of systematically improvable interatomic potentials.\" Multiscale Modeling & Simulation 14.3 (2016): 1153-1173.\n",
+    "2. Batzner, Simon, et al. \"E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials.\" Nature communications 13.1 (2022): 1-11."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.12 (main, Mar 26 2022, 15:44:31) \n[Clang 13.1.6 (clang-1316.0.21.2)]"
+  },
+  "orig_nbformat": 4,
+  "vscode": {
+   "interpreter": {
+    "hash": "b0fa6594d8f4cbf19f97940f81e996739fb7646882a419484c72d19e05852a7e"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/blog/notebooks/equivariance_and_polynomials.ipynb b/blog/notebooks/equivariance_and_polynomials.ipynb
new file mode 100644
index 0000000..d6085cf
--- /dev/null
+++ b/blog/notebooks/equivariance_and_polynomials.ipynb
@@ -0,0 +1,167 @@
+{
+ "cells": [
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Equivariance and Polynomials\n",
+    "\n",
+    "In this section we will define what it means for a function to be ``equivariant``, and what tools are available to create ``equivariant polynomials``. This latter is of great importance as almost any functions can be approximated by polynomials, and that the role of our neural network is to estimate an (equivariant) function."
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Equivariance\n",
+    "We say that a function $f: V \\rightarrow V'$ is equivariant to the action of the symmetry element $g$, represented by $D(g)$ on it's input $x$, if it gives rise to a similar action $D'(g)$ of its output, i.e:\n",
+    "\n",
+    "$$\n",
+    "f(D(g)x) = D'(g)f(x).\n",
+    "$$\n",
+    "\n",
+    "This principle is illustrated in figure 1.\n",
+    "\n",
+    "For a concreate example, consider a 3D rotation of $\\theta$ degrees around the x axis:\n",
+    "\n",
+    "$$\n",
+    "R_{x}(\\theta )=\\begin{bmatrix}1&0&0\\\\0&\\cos \\theta &-\\sin \\theta \\\\[3pt]0&\\sin \\theta &\\cos \\theta \\\\[3pt]\\end{bmatrix},\n",
+    "$$\n",
+    "\n",
+    "and the following functions function:\n",
+    "\n",
+    "$$\n",
+    "f: \\begin{bmatrix}\n",
+    "           x \\\\\n",
+    "           y \\\\\n",
+    "           z\n",
+    "         \\end{bmatrix} \n",
+    "\\rightarrow\n",
+    "\\begin{bmatrix}\n",
+    "           x^2+y^2+z^2\n",
+    "        \n",
+    "         \\end{bmatrix} \n",
+    "$$\n",
+    "\n",
+    "Then $f$ is equivariant to rotation as:\n",
+    "\n",
+    "$$\n",
+    "f(R_x(\\theta) \\vec{x}) = f(\\begin{bmatrix}\n",
+    "           x \\\\\n",
+    "           cos(\\theta)y-sin(\\theta)z \\\\\n",
+    "           sin(\\theta)y+cos(\\theta)z\n",
+    "         \\end{bmatrix} ) = \\begin{bmatrix}\n",
+    "           x^2+y^2+z^2\n",
+    "        \n",
+    "         \\end{bmatrix}  = R'_x(\\theta) f(x) = f(x).\n",
+    "$$\n",
+    "\n",
+    "especialy in this case the function is actually invariant to rotations: $R'_x(\\theta) =1  \\space \\forall \\theta \\in \\mathcal{R}$.\n",
+    "\n",
+    "An example of a non equivariant polynomials would be $p$:\n",
+    "\n",
+    "$$\n",
+    "p : \\begin{bmatrix}\n",
+    "           x \\\\\n",
+    "           y \\\\\n",
+    "           z\n",
+    "         \\end{bmatrix} \n",
+    "\\rightarrow\n",
+    "\\begin{bmatrix}\n",
+    "           x^2+2(y-3z) \\\\\n",
+    "           y^2x \\\\\n",
+    "        \n",
+    "         \\end{bmatrix}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "\n",
+    "| ![square](../equiv.png) |\n",
+    "|:--:|\n",
+    "| <b>Fig.1 - Principle of equivariance.</b>|"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Equivariant polynomials\n",
+    "\n",
+    "In this section we will discuss the tools to create equivariant polynomials.\n",
+    "\n",
+    "We will first show that the compositon of 2 equivariant polynomial is equivariant: \n",
+    "\n",
+    "Consider two equivariant function:\n",
+    "\n",
+    "$$ \n",
+    "f: V_1 \\rightarrow V_3,\n",
+    "$$ \n",
+    "\n",
+    "$$ \n",
+    "g: V_2 \\rightarrow V_3,\n",
+    "$$ \n",
+    "\n",
+    "then: \n",
+    "\n",
+    "### ``Addition`` of equivariant polynomials is equivariant:\n",
+    "\n",
+    "Indeed, $f+g$ is equivariant as:\n",
+    "\n",
+    "$$\n",
+    "D_3(g)(f(x)+g(x)) = D_1(g)f(x)+D_2(g)g(x) = f(D_1(g)x)+g(D_2(g)x).\n",
+    "$$\n",
+    "\n",
+    "\n",
+    "### ``Composition`` of equivariant polynomials is equivariant:\n",
+    "\n",
+    "Indeed, $f \\circ g$ is equivariant as:\n",
+    "\n",
+    "$$\n",
+    "D_3(g)(f(g(x))) =f( D_2(g) g(x)) = f(g(D_1(g)x)).\n",
+    "$$\n",
+    "\n",
+    "### The ``Tensor Product`` of two polynomial is equivariant:\n",
+    "It is denoted $f \\otimes g$. The ``Tensor Product`` section is dedicated to it."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "base",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.5 (default, May 18 2021, 12:31:01) \n[Clang 10.0.0 ]"
+  },
+  "orig_nbformat": 4,
+  "vscode": {
+   "interpreter": {
+    "hash": "a429a41e61deb9ee9f43170a4271c5d42eef99359a9088d8c58f4b96e2ffedc5"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Group representation"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this section, we will show how symmetry elements can be represented as matrices, and how we can represent their action as simple matrix multiplication, which in turns allow for symmetry operations to be implemented on a computer.\n",
+    "\n",
+    "We will use the example of the group of symmetries of a $n$ vertices regular polyhedron $D_n$. We can think of this polygon as having vertices on the unit circle, each labeled from $0$ to $n-1$.\n",
+    "\n",
+    "An illustration of a square (4 vertices regular polygon) is presented is Fig. 1. Its set of symmetry element constitute the group element of \n",
+    "\n",
+    "$$D_4 = \\{R_0, R_{90}, R_{180}, R_{270}, H, V , D, D'\\},$$ \n",
+    "\n",
+    "where the $R_{\\theta}$ are $\\theta$ counter-clockwise degrees rotations with respect to the center of the square, $H$ a flips with respect to the horizontal line going through the middle of the upper and bottom edges, $V$ a flip with respect to the vertical line going through the middle of the left and right edges, $D$ a flip with respect to the diagonal through the upper right corner and the lower left corner, and $D'$ a flip with respect to the other diagonal.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "<!-- ![square](../square.png)\n",
+    "<figcaption align = \"center\"><b>Fig.1 - A square and its symmetry elements.</b></figcaption>\n",
+    "<!-- <p align=\"center\">\n",
+    "  <img src=\"../square.png\"  />\n",
+    "</p> --> \n",
+    "\n",
+    "| ![square](../square.png) |\n",
+    "|:--:|\n",
+    "| <b>Fig.1 - A square and its symmetry elements.</b>|\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Representing each vertex by its 2D vector coordinates $\\vec{x}$, the action of a symmetry element $s \\in D_4$ displacement the vertex to its new set of coordinates $\\vec{\\hat{x}}$ is defined by the matrix multiplication: \n",
+    "\n",
+    "$$\\vec{\\hat{x}}=\\hat{s}\\vec{x},$$ \n",
+    "\n",
+    "where $\\hat{s}$ is the matrix representation of the symmetry element $s \\in D_4$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "More generally, each rotation can have the following matrix representation:\n",
+    "\n",
+    "$$\n",
+    "R_{\\theta} =\n",
+    "\\begin{pmatrix} \n",
+    "cos(\\theta) & -sin(\\theta) \\\\ \n",
+    "sin(\\theta) & cos(\\theta)\n",
+    "\\end{pmatrix},\n",
+    "$$\n",
+    "\n",
+    "leading to:\n",
+    "\n",
+    "$$\n",
+    "R_{0} = \n",
+    "\\begin{pmatrix}\n",
+    "1 & 0 \\\\\n",
+    "0& 1\n",
+    "\\end{pmatrix}\n",
+    "\\text{, }\n",
+    "R_{90} = \n",
+    "\\begin{pmatrix}\n",
+    "0 & -1 \\\\\n",
+    "1& 0\n",
+    "\\end{pmatrix}\n",
+    "\\text{, }\n",
+    "R_{180} = \n",
+    "\\begin{pmatrix}\n",
+    "-1 & 0 \\\\\n",
+    "0& -1\n",
+    "\\end{pmatrix}\n",
+    "\\text{ and }\n",
+    "R_{270} = \n",
+    "\\begin{pmatrix}\n",
+    "0 & 1 \\\\\n",
+    "-1& 0\n",
+    "\\end{pmatrix}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "On the other hand, $H, V , D, D'$ are special cases of reflections about the line through the\n",
+    "origin and making an angle of $\\theta$ with the horizontal axis, such that:\n",
+    "\n",
+    "$$\n",
+    "S_{\\theta} = \\begin{pmatrix}\n",
+    " cos(2 \\pi k/n) & sin(2 \\pi k/n) \\\\\n",
+    "sin(2 \\pi k/n) & -cos(2 \\pi k/n) \n",
+    "\\end{pmatrix},\n",
+    "$$\n",
+    "\n",
+    "and so:\n",
+    "\n",
+    "$$\n",
+    "H = S_{0} = \n",
+    "\\begin{pmatrix}\n",
+    "1 & 0 \\\\\n",
+    "0& -1\n",
+    "\\end{pmatrix}\n",
+    "\\text{, }\n",
+    "D = S_{90} = \n",
+    "\\begin{pmatrix}\n",
+    "0 & 1 \\\\\n",
+    "1& 0\n",
+    "\\end{pmatrix}\n",
+    "\\text{, }\n",
+    "V = S_{180} = \n",
+    "\\begin{pmatrix}\n",
+    "-1 & 0 \\\\\n",
+    "0& 1\n",
+    "\\end{pmatrix}\n",
+    "\\text{ and }\n",
+    "D' = S_{270} = \n",
+    "\\begin{pmatrix}\n",
+    "0 & -1 \\\\\n",
+    "-1& 0\n",
+    "\\end{pmatrix}.\n",
+    "$$"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## References\n",
+    "1. https://web.northeastern.edu/suciu/MATH3175/DihedralGroups.pdf"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3.9.5 ('base')",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "name": "python",
+   "version": "3.9.5 (default, May 18 2021, 12:31:01) \n[Clang 10.0.0 ]"
+  },
+  "orig_nbformat": 4,
+  "vscode": {
+   "interpreter": {
+    "hash": "a429a41e61deb9ee9f43170a4271c5d42eef99359a9088d8c58f4b96e2ffedc5"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/blog/notebooks/irreducible_representations.ipynb b/blog/notebooks/irreducible_representations.ipynb
new file mode 100644
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--- /dev/null
+++ b/blog/notebooks/irreducible_representations.ipynb
@@ -0,0 +1,134 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Irreducible representations"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "| ![square](../irrep_2.png) |\n",
+    "|:--:|\n",
+    "| <b>Fig.1 - Transformation to irreducible representations.</b>|"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this section, we will give the definition of irreducible representations and showcase how the reducible and irreducible representations of the same mathematical object can be transfered interchangably in the context of E(3)-equivariant neural networks.\n",
+    "\n",
+    "By definition, an irreducible representation is a representation that does not contain a smaller representation in it. For example, there is no nontrivial projector $P \\in \\mathcal{R}^{q\\times d}$ such that the function $g \\to PD(g)P^t$ is a representation. The irreducible representations of $SO(3)$ are indexed by the integers $l=0,1,2,\\dots$, and the $l$-irrep is of dimension $2l+1$. For example, $irrep(l=0) \\in \\mathcal{R}^1$ corresponds to $\\textit{scalars}$, $irrep(l=1) \\in \\mathcal{R}^3$ corresponds to $\\textit{vectors}$, and $irrep(l=2) \\in \\mathcal{R}^5$ is the decomposition of a trace-less symmetric rank 2 tensor. A more detailed discussion of irreducible representations can be found here [\\cite{E3NN paper + ref.21}].\n",
+    "\n",
+    "Here, we will use the example of a random rank-2 tensor $A \\in \\mathcal{R}^{3\\times 3}$, and show how we can decompose tensor $A$ into irreducible representations of $l=0,1,2$: namely, a scalar corresponding to the tensor trace $tr(A)$, a pseudovector corresponding to the anti-symmetric component, and a 5 component irrep corresponding to the trace-less component of the symmetric component of tensor $A$.\n",
+    "\n",
+    "First, we can decompose tensor $A$ into a symmetric part $A_{sym}$ and a trace-less anti-symmetric part $A_{anti-sym}$:\n",
+    "\n",
+    "$$A = A_{sym} + A_{anti-sym} = \\frac{A+A^T}{2} + \\frac{A-A^T}{2}$$\n",
+    "\n",
+    "where,\n",
+    "\n",
+    "$$\n",
+    "A_{sym}=\\begin{bmatrix}\n",
+    "   a_{11} & \\frac{1}{2}(a_{12}+a_{21}) & \\frac{1}{2}(a_{13}+a_{31}) \\\\\n",
+    "   \\frac{1}{2}(a_{12}+a_{21}) & a_{22} & \\frac{1}{2}(a_{23}+a_{32}) \\\\\n",
+    "   \\frac{1}{2}(a_{13}+a_{31}) & \\frac{1}{2}(a_{23}+a_{32}) & a_{33}\n",
+    "   \\end{bmatrix}\n",
+    "$$\n",
+    "\n",
+    "$$\n",
+    "A_{anti-sym}=\\begin{bmatrix}\n",
+    "   0 & \\frac{1}{2}(a_{12}-a_{21}) & \\frac{1}{2}(a_{13}-_{31}) \\\\\n",
+    "   \\frac{1}{2}(a_{21}-a_{12}) & 0 & \\frac{1}{2}(a_{23}-a_{32}) \\\\\n",
+    "   \\frac{1}{2}(a_{31}-a_{13}) & \\frac{1}{2}(a_{32}-a_{23}) & 0\n",
+    "   \\end{bmatrix}\n",
+    "$$\n",
+    "\n",
+    "and we can further decouple the symmetric part $A_{sym}$ into a identity matrix multiplied by the trace $tr(A)$ and a traceless symmetric matrix $A^\\prime_{sym}$:\n",
+    "\n",
+    "$$\n",
+    "A_{sym}= \\frac{1}{3}tr(A)\\cdot \\textbf{I} + A^\\prime_{sym} = \\frac{a_{11}+a_{22}+a_{33}}{3}\\cdot \\textbf{I} + \\begin{bmatrix}\n",
+    "   \\frac{2}{3}a_{11}-\\frac{1}{3}a_{22}-\\frac{1}{3}a_{33} & \\frac{1}{2}(a_{12}+a_{21}) & \\frac{1}{2}(a_{13}+a_{31}) \\\\\n",
+    "   \\frac{1}{2}(a_{12}+a_{21}) & \\frac{2}{3}a_{22}-\\frac{1}{3}a_{11}-\\frac{1}{3}a_{33} & \\frac{1}{2}(a_{23}+a_{32}) \\\\\n",
+    "   \\frac{1}{2}(a_{13}+a_{31}) & \\frac{1}{2}(a_{23}+a_{32}) & \\frac{2}{3}a_{33}-\\frac{1}{3}a_{11}-\\frac{1}{3}a_{22}\n",
+    "   \\end{bmatrix}\n",
+    "$$\n",
+    "\n",
+    "Such that overall, tensor $A$ can be decomposed into the following terms:\n",
+    "\n",
+    "$$A = tr(A)\\cdot \\textbf{I} + A_{anti-sym} + A^\\prime_{sym} $$\n",
+    "\n",
+    "and if we write it element-wise:\n",
+    "\n",
+    "$$A_{ij} = \\frac{1}{3}tr(A)\\delta_{ij} + \\frac{1}{2}(a_{ij}-a_{ji}) + \\frac{1}{2}(a_{ij}+a_{ji}-\\frac{2}{3}\\delta_{ij}tr(A))$$\n",
+    "\n",
+    "Notice that each of the three parts of the two equations above are preserved by rotations, and thus we have successfully decomposed a rank-2 tensor into irreducible representations of $l=0,1,2$, in the sense that:\n",
+    "\n",
+    "$$tr(A) = a_{11}+a_{22}+a_{33} \\to irrep^{l=0} \\quad \\text{is a scalar with DOF=1}$$\n",
+    "$$A_{anti-sym} = \\begin{bmatrix}\n",
+    "   0 & v_1 & v_2 \\\\\n",
+    "   -v_1 & 0 & v_3 \\\\\n",
+    "   -v_2 & -v_3 & 0\n",
+    "   \\end{bmatrix} \\to irrep^{l=1} = \\begin{bmatrix} v_1\\\\ v_2\\\\ v_3\\end{bmatrix} \\quad \\text{is a vector with DOF=3}$$\n",
+    "$$A^\\prime_{sym} = \\begin{bmatrix}\n",
+    "   l_1 & l_3 & l_4 \\\\\n",
+    "   l_3 & l_2 & l_5 \\\\\n",
+    "   l_4 & l_5 & 0-l_1-l_2\n",
+    "   \\end{bmatrix} \\to irrep^{l=2} = \\begin{bmatrix} l_1\\\\ l_2\\\\ l_3\\\\ l_4\\\\ l_5\\end{bmatrix} \\quad \\text{is a l=2 irreducible representation with DOF=5}$$\n",
+    "\n",
+    "In e3nn, the irreducible representation of a rank-2 tensor can be written in simplified format as \"1x0e + 1x1o + 1x2o\". Similar to the example of rank-2 tensor shown above, higher-order mathematical objects can also be decomposed into irreducible representations, as shown in the e3nn paper [\\cite].\n",
+    "\n",
+    "The fact that irreducible representations can be obtained by decomposing arbitrary mathematical objects sets the foundation of E(3)-equivariant neural networks, where all input and output data are used in the form of irreducible representation class called ``Irrep``.\n",
+    "\n"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## References\n",
+    "1. https://math.stackexchange.com/questions/1425825/two-notions-of-so3s-irreps-whats-the-connection-between-them\n",
+    "2. https://pcgschool2018.files.wordpress.com/2018/06/pcgschool_irrep_analysis_l1_version2.pdf\n",
+    "3. http://www.physics.usu.edu/Wheeler/QuantumMechanics/QMWignerEckartTheorem.pdf"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "base",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.5 (default, May 18 2021, 12:31:01) \n[Clang 10.0.0 ]"
+  },
+  "orig_nbformat": 4,
+  "vscode": {
+   "interpreter": {
+    "hash": "a429a41e61deb9ee9f43170a4271c5d42eef99359a9088d8c58f4b96e2ffedc5"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/blog/notebooks/spherical_harmonics.ipynb b/blog/notebooks/spherical_harmonics.ipynb
new file mode 100644
index 0000000..7acc093
--- /dev/null
+++ b/blog/notebooks/spherical_harmonics.ipynb
@@ -0,0 +1,121570 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Spherical Harmonics"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In E(3)-equivariant NN, mathematical objects are further decomposed into ``irreps``, approximated by ``spherical harmonics`` which are equivariant. The spherical harmonics $Y^l$ are a family of $2l+1$ functions from $R^3$ to $D^l$, the set of l-ireps, such that:\n",
+    "\n",
+    "$$ \n",
+    "Y^l\\left(\\vec{x}\\right) = \\left[ Y_{-l}^{l}\\left(\\vec{x}\\right), Y_{-l+1}^{l}\\left(\\vec{x}\\right), ... , Y_{l}^{l}\\left(\\vec{x}\\right) \\right], \n",
+    "$$\n",
+    "\n",
+    "and $Y^l_m$ are real (normalized) spherical harmonics defined by:\n",
+    "\n",
+    "$$\n",
+    "Y^l_m = \n",
+    "\\begin{cases}\n",
+    "  \\sqrt{2}(-1)^m\\mathcal{I}[\\hat{Y}^l_{|m|}] & \\text{if $m<0$} \\\\\n",
+    "  \\hat{Y}^l_{|m|} & \\text{if $m=0$} \\\\\n",
+    "  \\sqrt{2}(-1)^m\\mathcal{R}[\\hat{Y}^l_{m}] & \\text{if $m>0$} \\\\\n",
+    "\\end{cases}\n",
+    "$$\n",
+    "\n",
+    "with: \n",
+    "\n",
+    "$$\n",
+    "\\hat{Y}^l_{m} = (-1)^m \\sqrt{\\frac{(2l+1)}{4\\pi} \\frac{(l-m)!}{(l+m)!} }P_m^l(cos(\\theta))e^{im\\phi},\n",
+    "$$\n",
+    "\n",
+    "where $P_m^l$ are Legendre polynomials without the Condon–Shortley phase, and $\\theta, \\phi$ spherical coordinates and $m \\in \\{-l, -l+1, ..., l+1\\}$.\n",
+    "\n",
+    "It is to be noted that each $Y^l$ is equivariant to $SO(3)$ with respect to the irrep of the same order. For example, consider any rotation matrix $R$, then:\n",
+    "\n",
+    "$$\n",
+    "Y^l(R\\vec{x}) = D^l(R)Y^l(g)\n",
+    "$$\n",
+    "\n",
+    "i.e, \n",
+    "\n",
+    "$$\n",
+    "Y^l_m(R\\vec{x}) = \\sum_{n=-l}^{n=l} D^l_{mn}(R)Y^l_n(\\vec{x}) = D^l_m(R) \\cdot Y^l,\n",
+    "$$\n",
+    "\n",
+    "where $D^l$ are the irreducible representations of $SO(3)$.\n",
+    "\n"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "``e3nn`` provides utilities functions to compute spherical harmonics:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "tags": [
+     "hide_cell",
+     "hidden_cell"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "import torch\n",
+    "import math\n",
+    "from e3nn import o3\n",
+    "import plotly.graph_objects as go\n",
+    "\n",
+    "axis = dict(\n",
+    "    showbackground=False,\n",
+    "    showticklabels=False,\n",
+    "    showgrid=False,\n",
+    "    zeroline=False,\n",
+    "    title='',\n",
+    "    nticks=3,\n",
+    ")\n",
+    "\n",
+    "layout = dict(\n",
+    "    width=690,\n",
+    "    height=160,\n",
+    "    scene=dict(\n",
+    "        xaxis=dict(\n",
+    "            **axis,\n",
+    "            range=[-8, 8]\n",
+    "        ),\n",
+    "        yaxis=dict(\n",
+    "            **axis,\n",
+    "            range=[-2, 2]\n",
+    "        ),\n",
+    "        zaxis=dict(\n",
+    "            **axis,\n",
+    "            range=[-2, 2]\n",
+    "        ),\n",
+    "        aspectmode='manual',\n",
+    "        aspectratio=dict(x=8, y=2, z=2),\n",
+    "        camera=dict(\n",
+    "            up=dict(x=0, y=0, z=1),\n",
+    "            center=dict(x=0, y=0, z=0),\n",
+    "            eye=dict(x=0, y=-5, z=5),\n",
+    "            projection=dict(type='orthographic'),\n",
+    "        ),\n",
+    "    ),\n",
+    "    paper_bgcolor=\"rgba(0,0,0,0)\",\n",
+    "    plot_bgcolor=\"rgba(0,0,0,0)\",\n",
+    "    margin=dict(l=0, r=0, t=0, b=0)\n",
+    ")\n",
+    "\n",
+    "\n",
+    "def s2_grid():\n",
+    "    betas = torch.linspace(0, math.pi, 40)\n",
+    "    alphas = torch.linspace(0, 2 * math.pi, 80)\n",
+    "    beta, alpha = torch.meshgrid(betas, alphas, indexing='ij')\n",
+    "    return o3.angles_to_xyz(alpha, beta)\n",
+    "\n",
+    "def trace(r, f, c, radial_abs=True):\n",
+    "    if radial_abs:\n",
+    "        a = f.abs()\n",
+    "    else:\n",
+    "        a = 1\n",
+    "    return dict(\n",
+    "        x=a * r[..., 0] + c[0],\n",
+    "        y=a * r[..., 1] + c[1],\n",
+    "        z=a * r[..., 2] + c[2],\n",
+    "        surfacecolor=f\n",
+    "    )\n",
+    "\n",
+    "def plot(data, radial_abs=True):\n",
+    "    r = s2_grid()\n",
+    "    n = data.shape[-1]\n",
+    "    traces = [\n",
+    "        trace(r, data[..., i], torch.tensor([2.0 * i - (n - 1.0), 0.0, 0.0]), radial_abs=radial_abs)\n",
+    "        for i in range(n)\n",
+    "    ]\n",
+    "    cmax = max(d['surfacecolor'].abs().max().item() for d in traces)\n",
+    "    traces = [go.Surface(**d, colorscale='RdYlBu', cmin=-cmax, cmax=cmax) for d in traces]\n",
+    "    fig = go.Figure(data=traces, layout=layout)\n",
+    "    fig.show()\n",
+    "    return fig"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.plotly.v1+json": {
+       "config": {
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+            "gridcolor": "white",
+            "linecolor": "white",
+            "ticks": ""
+           },
+           "bgcolor": "#E5ECF6",
+           "caxis": {
+            "gridcolor": "white",
+            "linecolor": "white",
+            "ticks": ""
+           }
+          },
+          "title": {
+           "x": 0.05
+          },
+          "xaxis": {
+           "automargin": true,
+           "gridcolor": "white",
+           "linecolor": "white",
+           "ticks": "",
+           "title": {
+            "standoff": 15
+           },
+           "zerolinecolor": "white",
+           "zerolinewidth": 2
+          },
+          "yaxis": {
+           "automargin": true,
+           "gridcolor": "white",
+           "linecolor": "white",
+           "ticks": "",
+           "title": {
+            "standoff": 15
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+           "zerolinecolor": "white",
+           "zerolinewidth": 2
+          }
+         }
+        },
+        "width": 690
+       }
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "r = s2_grid()\n",
+    "lmax = 2\n",
+    "\n",
+    "for l in range(lmax+1):\n",
+    "    yl = o3.spherical_harmonics(l,r, 'norm')\n",
+    "    fig = plot(yl)"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Disclaimer\n",
+    "\n",
+    "Conventions between field varies on how to define spherical harmonics and thus their transformation to real space formula varies depending on which field you are in. ``e3nn`` might adopt a different conventions then the formula proposed here, but the ideas are similar."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## References"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "1. Geiger, M. & Smidt, T. e3nn: Euclidean Neural Networks. Arxiv (2022).\n",
+    "2. https://docs.e3nn.org/en/stable/api/o3/o3_sh.html"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": []
+  }
+ ],
+ "metadata": {
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+    "name": "ipython",
+    "version": 3
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+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.5 (default, May 18 2021, 12:31:01) \n[Clang 10.0.0 ]"
+  },
+  "orig_nbformat": 4,
+  "vscode": {
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+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/blog/notebooks/tensor_product.ipynb b/blog/notebooks/tensor_product.ipynb
new file mode 100644
index 0000000..67c7d00
--- /dev/null
+++ b/blog/notebooks/tensor_product.ipynb
@@ -0,0 +1,160375 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Tensor Product"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this section, we will first define tensor product in the scope of ``e3nn``, introduce some rules tensor products must abide by, and visualize how each tensor product pathway can be parameterized by weights, which allows for the learning process to happen for a equivariant-NN."
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Tensor product is the equivariant multiplication operation of two representations denoted by:\n",
+    "\n",
+    "$$\n",
+    "x\\otimes y\n",
+    "$$\n",
+    "\n",
+    "In all cases, tensor products must satisfy the two conditions of being: 1). ``bilinear`` and 2). ``equivariant``. Depending on the irrep type of $x$ and $y$ this operation can take different forms. For instance if $x$ and $y$ are two scalars it will simply be the product $xy$ up to a multiplicative constant. If $x$ is a scalar and $y$ is a vector, $x\\otimes y$ will be the vector made of the product of $x$ with $y$.\n",
+    "\n",
+    "In the case of two vectors, $x\\otimes y$ is an element of $\\mathcal{R}^9$ or a rank-2 tensor. As shown in the ``irreducible representations`` section, via a change of basis $x\\otimes y$ can be decomposed into irrep of the form \"1x0e + 1x1o + 1x2o\" (a scalar, a pseudovector, and a trace-less symmetric matrix). Thus this tensor product can be written as:\n",
+    "\n",
+    "$$\n",
+    "1o\\otimes 1o \\to 0e + 1e + 2e\n",
+    "$$\n",
+    "\n",
+    "Notice that there are three branching operations in this tensor product that are each bilinear and equivariant. A e3nn implementation of this tensor product and a visuallization of this branching operation is given below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "import e3nn\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(<Figure size 432x288 with 1 Axes>, <AxesSubplot:>)"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": "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",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Here is the e3nn way of computing: \"3 x 3 = 1 + 3 + 5\"\n",
+    "\n",
+    "tp = e3nn.o3.FullTensorProduct(\"1o\", \"1o\")\n",
+    "\n",
+    "tp.visualize()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "When computing the tensor product of representations of higher order $l$ we can obtain more independent operations. These independent operations are called ``paths``. Each path from the tensor product of an irrep ($l_1$, $p_1$) with an irrep ($l_2$ , $p_2$) will yield an irrep of order $l_3$ and parity $p_3$ following the underlying rules:\n",
+    "\n",
+    "$$\n",
+    "\\begin{cases} |l_1-l_2|\\leq l_3 \\leq l_1 + l_2\\\\\n",
+    "p_1p_2=p_3\n",
+    "\\end{cases}\n",
+    "$$\n",
+    "\n",
+    "Since there is one path for each allowed value of $l_3$, this formula would yield a total of $l_1+l_2-|l_1-l_2|+1$ paths for tensor products.\n",
+    "\n",
+    "The distributive law also applies for tensor products. For example, we can work out the the tensor product of \"$5\\times 1o$\" with \"$3\\times 0e + 2\\times 1o$\" manually:\n",
+    "\n",
+    "$$\n",
+    "5\\times 1o\\otimes 3\\times 0e \\to 15\\times 1o\n",
+    "$$\n",
+    "\n",
+    "$$\n",
+    "5\\times 1o\\otimes 2\\times 1o \\to 10\\times 0e + 10\\times 1e + 10\\times 2e\n",
+    "$$\n",
+    "\n",
+    "Thus the final tensor product:\n",
+    "\n",
+    "$$\n",
+    "5\\times 1o\\otimes (3\\times 0e + 2\\times 1o) \\to 10\\times 0e + 15\\times 1o + 10\\times 1e + 10\\times 2e\n",
+    "$$\n",
+    "\n",
+    "A visualization of this tensor product is given below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(<Figure size 432x288 with 1 Axes>, <AxesSubplot:>)"
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "t = e3nn.o3.FullTensorProduct(\"5x1o\", \"3x0e + 2x1o\")\n",
+    "\n",
+    "t.visualize()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "After tensor product the resulting irreducible representations will again be stored in vector format which makes it easier for subsequent operations such as symmetric transformations or tensor products:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Irrep 0e: tensor([0.])\n",
+      "Irrep 1e: tensor([0.0000, 0.0000, 0.7071])\n",
+      "Irrep 2e: tensor([0.0000, 0.7071, 0.0000, 0.0000, 0.0000])\n",
+      "Final irrep vector 0e + 1e + 2e: tensor([0.0000, 0.0000, 0.0000, 0.7071, 0.0000, 0.7071, 0.0000, 0.0000, 0.0000])\n"
+     ]
+    }
+   ],
+   "source": [
+    "import torch\n",
+    "\n",
+    "# Feed tp with some data\n",
+    "for ireps in ['0e', '1e', '2e']:\n",
+    "    tp = e3nn.o3.FullTensorProduct(\"1o\", \"1o\",[ireps])\n",
+    "    x1 = torch.tensor([1.0, 0.0, 0.0])\n",
+    "    x2 = torch.tensor([0.0, 1.0, 0.0])\n",
+    "\n",
+    "    print(\"Irrep {}: {}\".format(ireps, tp(x1, x2)))\n",
+    "    \n",
+    "tp = e3nn.o3.FullTensorProduct(\"1o\", \"1o\")\n",
+    "print(\"Final irrep vector 0e + 1e + 2e: {}\".format(tp(x1, x2)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Next, we will explore how tensor product with weights can be implemented in e3nn as the parallel of a linear layer in MLPs.\n",
+    "\n",
+    "As mentioned earlier, each independent ``paths`` inside a tensor product can be parametrized by constants, thus these parameters can be updated through back-propagation during training process in the similar fashion as those in MLPs.\n",
+    "\n",
+    "An example of the weighted tensor product (or fully connected tensor product layer) with random initial weights is shown below:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Parameter containing:\n",
+       "tensor([ 1.4761, -0.6806, -0.1231, -0.4660,  0.8056, -0.6972,  0.0231, -0.8141,\n",
+       "         0.1462, -1.1039, -1.0309,  0.4627], requires_grad=True)"
+      ]
+     },
+     "execution_count": 15,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Tensor product with weights\n",
+    "tp1 = e3nn.o3.FullyConnectedTensorProduct(\"1o + 1o + 1o\", \"1o + 1o\", \"1e + 1e + 3e\")\n",
+    "tp1.visualize(plot_weight=True)\n",
+    "tp1.weight"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "As discussed in section ``Irreducible representations``, a 3x3 matrix (tensor product between two $l=1$ representations) decomposes in $l=0$, $l=1$ and $l=2$ representations which can be represented by spherical harmonics. \n",
+    "\n",
+    "More generally, spherical harmonics can be obtained from the sucessive application of tensor products as seen in Fig. 1:\n",
+    "\n",
+    "| ![square](figs/tp.png) |\n",
+    "|:--:|\n",
+    "| <b>Fig.1 - Successive application of tensor products.</b>|\n"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "``e3nn`` allows you to select the l-order output of the tensor product. We can thus recover the spherical harmonics:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {
+    "tags": [
+     "hidden_cell",
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "import torch\n",
+    "import math\n",
+    "from e3nn import o3\n",
+    "import plotly.graph_objects as go\n",
+    "\n",
+    "axis = dict(\n",
+    "    showbackground=False,\n",
+    "    showticklabels=False,\n",
+    "    showgrid=False,\n",
+    "    zeroline=False,\n",
+    "    title='',\n",
+    "    nticks=3,\n",
+    ")\n",
+    "\n",
+    "layout = dict(\n",
+    "    width=690,\n",
+    "    height=160,\n",
+    "    scene=dict(\n",
+    "        xaxis=dict(\n",
+    "            **axis,\n",
+    "            range=[-8, 8]\n",
+    "        ),\n",
+    "        yaxis=dict(\n",
+    "            **axis,\n",
+    "            range=[-2, 2]\n",
+    "        ),\n",
+    "        zaxis=dict(\n",
+    "            **axis,\n",
+    "            range=[-2, 2]\n",
+    "        ),\n",
+    "        aspectmode='manual',\n",
+    "        aspectratio=dict(x=8, y=2, z=2),\n",
+    "        camera=dict(\n",
+    "            up=dict(x=0, y=0, z=1),\n",
+    "            center=dict(x=0, y=0, z=0),\n",
+    "            eye=dict(x=0, y=-5, z=5),\n",
+    "            projection=dict(type='orthographic'),\n",
+    "        ),\n",
+    "    ),\n",
+    "    paper_bgcolor=\"rgba(0,0,0,0)\",\n",
+    "    plot_bgcolor=\"rgba(0,0,0,0)\",\n",
+    "    margin=dict(l=0, r=0, t=0, b=0)\n",
+    ")\n",
+    "\n",
+    "\n",
+    "def s2_grid():\n",
+    "    betas = torch.linspace(0, math.pi, 40)\n",
+    "    alphas = torch.linspace(0, 2 * math.pi, 80)\n",
+    "    beta, alpha = torch.meshgrid(betas, alphas, indexing='ij')\n",
+    "    return o3.angles_to_xyz(alpha, beta)\n",
+    "\n",
+    "def trace(r, f, c, radial_abs=True):\n",
+    "    if radial_abs:\n",
+    "        a = f.abs()\n",
+    "    else:\n",
+    "        a = 1\n",
+    "    return dict(\n",
+    "        x=a * r[..., 0] + c[0],\n",
+    "        y=a * r[..., 1] + c[1],\n",
+    "        z=a * r[..., 2] + c[2],\n",
+    "        surfacecolor=f\n",
+    "    )\n",
+    "\n",
+    "def plot(data, radial_abs=True):\n",
+    "    r = s2_grid()\n",
+    "    n = data.shape[-1]\n",
+    "    traces = [\n",
+    "        trace(r, data[..., i], torch.tensor([2.0 * i - (n - 1.0), 0.0, 0.0]), radial_abs=radial_abs)\n",
+    "        for i in range(n)\n",
+    "    ]\n",
+    "    cmax = max(d['surfacecolor'].abs().max().item() for d in traces)\n",
+    "    traces = [go.Surface(**d, colorscale='RdYlBu', cmin=-cmax, cmax=cmax) for d in traces]\n",
+    "    fig = go.Figure(data=traces, layout=layout)\n",
+    "    fig.show()\n",
+    "    return fig"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.plotly.v1+json": {
+       "config": {
+        "plotlyServerURL": "https://plot.ly"
+       },
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+     "output_type": "display_data"
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+   "source": [
+    "tp = o3.ElementwiseTensorProduct(\"2e\", \"1o\", ['3o'], irrep_normalization='norm')\n",
+    "y3 = tp(y2, r)\n",
+    "fig = plot(y3)"
+   ]
+  }
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diff --git a/blog/notebooks/transformation_under_e3.ipynb b/blog/notebooks/transformation_under_e3.ipynb
new file mode 100644
index 0000000..9353456
--- /dev/null
+++ b/blog/notebooks/transformation_under_e3.ipynb
@@ -0,0 +1,162020 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Transformation under Euclidean symmetries"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In this section, we will show how the action of a symmetry element denoted by $g$ can be tailored to respect symmetries when knowing the irreducible representation type ``Irrep`` of the input data.\n",
+    "\n",
+    "For example, we take the irreducible representation obtained through decomposing an arbitrary rank-2 tensor: \"1x0e + 1x1o + 1x2o\" from the previous section. Irrep objects are represented as a vector by concatenating irreducible componentes of increasing order $l$. Remember that a $l$-irrep is of dimension $\\mathcal{R}^{2l+1}$, the irrep \"1x0e + 1x1o + 1x2o\" can be expressed as a vector of $\\mathcal{R}^9$:\n",
+    "\n",
+    "$$\n",
+    "Irrep = \\begin{bmatrix} \\vec{I^0} & \\vec{I^1} & \\vec{I^2} \\end{bmatrix} =\\begin{bmatrix}\n",
+    "   c_1 & v_1 & v_2 & v_3 & l_1 & l_2 & l_3 & l_4 & l_5\n",
+    "   \\end{bmatrix} \\in \\mathcal{R}^9\n",
+    "$$\n",
+    "\n",
+    "Under this definition, any symmetry elements $g$ such as rotations can be represented as a ``block diagonal square matrix`` $D(g)$ that can be constructed based on the irreducible representation type. For the irrep \"1x0e + 1x1o + 1x2o\", $D(g)$ will be a square matrix of $\\mathcal{R}^{9\\times 9}$:\n",
+    "\n",
+    "$$\n",
+    "D(g) = \\begin{bmatrix}\n",
+    "   1 & & \\\\\n",
+    "    & D(g)^{l=1} & \\\\\n",
+    "    & & D(g)^{l=2}\n",
+    "   \\end{bmatrix} \\text{ where } D(g)^{l} \\in \\mathcal{R}^{(2l+1)\\times (2l+1)} \\text{ is the transformation matrix for $l$-irrep}\n",
+    "$$\n",
+    "\n",
+    "Notice that $D(g)^{l=0}$ for irrep \"$n\\times$ 0e\" of n scalars will be $I_{n\\times n}$ since scalar values do not change under rotation.\n",
+    "\n",
+    "For the illustration below we will use the example of a particle sitting at location $(x, y, z)$ with four vector properties $v_0, v_1, v_2, v_3 \\in \\mathcal{R}^3$ (velocity, acceleration, spin etc.) This particle and all of its properties can be represented by an Irrep of \"3x0e + 4x1o\" expressed as a vector of $\\mathcal{R}^{15}$. Its corresponding transformation matrix $D(g)$ given an arbitrary symmetry opertation $g$ will be of $\\mathcal{R}^{15\\times 15}$.\n",
+    "\n",
+    "The illustration plotted here showcases how the block diagonal matrix $D(g)$ and the particle properties transforms under a rotation operation with $\\alpha = \\beta = \\theta$ varing from $0$ to $2\\pi$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "from numpy import *\n",
+    "import numpy as np\n",
+    "\n",
+    "n_vec = 4\n",
+    "x = np.zeros(n_vec)\n",
+    "y = np.zeros(n_vec)\n",
+    "z = np.zeros(n_vec)\n",
+    "\n",
+    "# phi = 2*np.pi*(np.random.random(n_vec)*0.05+0.125)\n",
+    "phi = 2*np.pi*(0.125)\n",
+    "# theta = np.arccos(-1 + 2*(np.random.random(n_vec)*0.05+sqrt(2)/2))\n",
+    "theta = np.arccos(-1 + 2*(sqrt(2)/2))\n",
+    "R = np.ones(n_vec)\n",
+    "u = np.abs(R * sin(theta) * cos(phi)) * np.array([-1,1,-1,1])\n",
+    "v = np.abs(R * sin(theta) * sin(phi)) * np.array([1,-1,-1,1])\n",
+    "w = np.abs(R * cos(theta)) * np.array([1,1,-1,-1])"
+   ]
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+           "landcolor": "#E5ECF6",
+           "showlakes": true,
+           "showland": true,
+           "subunitcolor": "white"
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+          "hoverlabel": {
+           "align": "left"
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+          "hovermode": "closest",
+          "mapbox": {
+           "style": "light"
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+          "paper_bgcolor": "white",
+          "plot_bgcolor": "#E5ECF6",
+          "polar": {
+           "angularaxis": {
+            "gridcolor": "white",
+            "linecolor": "white",
+            "ticks": ""
+           },
+           "bgcolor": "#E5ECF6",
+           "radialaxis": {
+            "gridcolor": "white",
+            "linecolor": "white",
+            "ticks": ""
+           }
+          },
+          "scene": {
+           "xaxis": {
+            "backgroundcolor": "#E5ECF6",
+            "gridcolor": "white",
+            "gridwidth": 2,
+            "linecolor": "white",
+            "showbackground": true,
+            "ticks": "",
+            "zerolinecolor": "white"
+           },
+           "yaxis": {
+            "backgroundcolor": "#E5ECF6",
+            "gridcolor": "white",
+            "gridwidth": 2,
+            "linecolor": "white",
+            "showbackground": true,
+            "ticks": "",
+            "zerolinecolor": "white"
+           },
+           "zaxis": {
+            "backgroundcolor": "#E5ECF6",
+            "gridcolor": "white",
+            "gridwidth": 2,
+            "linecolor": "white",
+            "showbackground": true,
+            "ticks": "",
+            "zerolinecolor": "white"
+           }
+          },
+          "shapedefaults": {
+           "line": {
+            "color": "#2a3f5f"
+           }
+          },
+          "ternary": {
+           "aaxis": {
+            "gridcolor": "white",
+            "linecolor": "white",
+            "ticks": ""
+           },
+           "baxis": {
+            "gridcolor": "white",
+            "linecolor": "white",
+            "ticks": ""
+           },
+           "bgcolor": "#E5ECF6",
+           "caxis": {
+            "gridcolor": "white",
+            "linecolor": "white",
+            "ticks": ""
+           }
+          },
+          "title": {
+           "x": 0.05
+          },
+          "xaxis": {
+           "automargin": true,
+           "gridcolor": "white",
+           "linecolor": "white",
+           "ticks": "",
+           "title": {
+            "standoff": 15
+           },
+           "zerolinecolor": "white",
+           "zerolinewidth": 2
+          },
+          "yaxis": {
+           "automargin": true,
+           "gridcolor": "white",
+           "linecolor": "white",
+           "ticks": "",
+           "title": {
+            "standoff": 15
+           },
+           "zerolinecolor": "white",
+           "zerolinewidth": 2
+          }
+         }
+        },
+        "title": {
+         "text": "Rotation with angle &#945; = &#946; = &#947; = 0&#960;"
+        },
+        "width": 1000,
+        "xaxis": {
+         "anchor": "y",
+         "domain": [
+          0,
+          0.405
+         ]
+        },
+        "yaxis": {
+         "anchor": "x",
+         "autorange": "reversed",
+         "domain": [
+          0,
+          1
+         ]
+        }
+       }
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import plotly.figure_factory as ff\n",
+    "import plotly.graph_objects as go\n",
+    "import plotly.express as px\n",
+    "from plotly.express.colors import sample_colorscale\n",
+    "\n",
+    "c = px.colors.qualitative.Plotly\n",
+    "# c = sample_colorscale('Viridis', np.linspace(0,1,4))\n",
+    "\n",
+    "vector_flattened = np.concatenate((u[None,:],v[None,:],w[None,:]), axis=0).flatten(\"F\")\n",
+    "vector_in = np.concatenate(([0,0,0], vector_flattened))\n",
+    "\n",
+    "from e3nn.o3 import Irreps\n",
+    "\n",
+    "irreps = Irreps(\"3x0e + 4x1o\")\n",
+    "\n",
+    "import plotly.graph_objects as go\n",
+    "import numpy as np\n",
+    "from plotly.subplots import make_subplots\n",
+    "import torch\n",
+    "t = torch.tensor\n",
+    "\n",
+    "# Create figure\n",
+    "fig = make_subplots(rows=1, cols=2,\n",
+    "    specs=[[{\"type\": \"xy\"}, {\"type\": \"scene\"}]],\n",
+    "    column_widths=[0.45, 0.55])\n",
+    "\n",
+    "# Add traces, one for each slider step\n",
+    "rotations = np.linspace(0, 2*np.pi, 101)\n",
+    "for step in rotations:\n",
+    "    # a small rotation around the y axis\n",
+    "    D = irreps.D_from_angles(alpha=t(float(step)), beta=t(float(step)), gamma=t(float(step)), k=t(0))\n",
+    "\n",
+    "    # Display Heatmap\n",
+    "    fig.add_trace(\n",
+    "        go.Heatmap(visible=False, z=D, colorscale=\"RdYlBu\", zmin=-1, zmax=1, \n",
+    "        colorbar=dict(x=0.40, \n",
+    "            y=0, \n",
+    "            xanchor='left', \n",
+    "            yanchor='bottom',\n",
+    "            len=1, \n",
+    "            thickness=20)),\n",
+    "        row=1, col=1)\n",
+    "\n",
+    "    # Calculate vector after rotation\n",
+    "    v_out = vector_in @ np.array(D)\n",
+    "\n",
+    "    # Plot Points and Vectors after rotation\n",
+    "    fig = fig.add_trace(go.Scatter3d(\n",
+    "        x=v_out[0:1], y=v_out[1:2], z=v_out[2:3],\n",
+    "        mode='markers',\n",
+    "        name='point (3x0e)',\n",
+    "        marker=dict(\n",
+    "            size=12,\n",
+    "            color=c[0]),\n",
+    "        visible=False),\n",
+    "        row=1,\n",
+    "        col=2\n",
+    "    )\n",
+    "    for idx in range(n_vec):\n",
+    "        x_vec = np.array([v_out[0], v_out[3*idx+3]])\n",
+    "        y_vec = np.array([v_out[1], v_out[3*idx+4]])\n",
+    "        z_vec = np.array([v_out[2], v_out[3*idx+5]])\n",
+    "        fig.add_trace(go.Scatter3d(\n",
+    "            visible=False,\n",
+    "            x=x_vec, y=y_vec, z=z_vec,\n",
+    "            mode='lines', name='vector {} (1x1o)'.format(idx),\n",
+    "            line=dict(color=c[idx],width=2)\n",
+    "        ), row=1, col=2)\n",
+    "        x_cone = [v_out[3*idx+3]*0.9]\n",
+    "        y_cone = [v_out[3*idx+4]*0.9]\n",
+    "        z_cone = [v_out[3*idx+5]*0.9]\n",
+    "        u_cone = [v_out[3*idx+3]*0.3]\n",
+    "        v_cone = [v_out[3*idx+4]*0.3]\n",
+    "        w_cone = [v_out[3*idx+5]*0.3]\n",
+    "        fig.add_trace(go.Cone(\n",
+    "            x=x_cone, y=y_cone, z=z_cone, u=u_cone, v=v_cone, w=w_cone,\n",
+    "            showscale=False, colorscale=[[0, c[idx]], [1, c[idx]]], sizemode=\"absolute\", visible=False\n",
+    "        ), row=1, col=2)\n",
+    "\n",
+    "# Make first set of traces visible\n",
+    "# for idx in range(410, 420):\n",
+    "for idx in range(10):\n",
+    "    fig.data[idx].visible = True\n",
+    "\n",
+    "# Create and add slider\n",
+    "steps = []\n",
+    "for i in range(len(rotations)):\n",
+    "    step = dict(\n",
+    "        method=\"update\",\n",
+    "        args=[{\"visible\": [False] * len(fig.data)},\n",
+    "              {\"title\": 'Rotation with angle &#945; = &#946; = &#947; = {:.2f}&#960;'.format(0.02*i)}],  # layout attribute\n",
+    "            # {\"title\":  '&#945; =&#946;=&#947;=&#960;'}]\n",
+    "    )\n",
+    "    for idx in range(10):\n",
+    "        step[\"args\"][0][\"visible\"][10*i+idx] = True  # Toggle i'th trace to \"visible\"\n",
+    "    steps.append(step)\n",
+    "\n",
+    "sliders = [dict(\n",
+    "    active=0,\n",
+    "    currentvalue={\"prefix\": \"Rotation \"},\n",
+    "    steps=steps\n",
+    ")]\n",
+    "\n",
+    "fig.update_layout(\n",
+    "    sliders=sliders, \n",
+    "    title_text='Rotation with angle &#945; = &#946; = &#947; = 0&#960;'\n",
+    ")\n",
+    "fig.update_yaxes(autorange=\"reversed\")\n",
+    "fig.update_layout(\n",
+    "    scene = dict(\n",
+    "        xaxis = dict(nticks=4, range=[-1,1]),\n",
+    "        yaxis = dict(nticks=4, range=[-1,1]),\n",
+    "        zaxis = dict(nticks=4, range=[-1,1]),\n",
+    "    ),\n",
+    "    scene_aspectmode='cube',\n",
+    "    autosize=False,\n",
+    "    width=1000,\n",
+    "    height=500)\n",
+    "\n",
+    "fig.show()\n",
+    "# fig.write_image('figs/transformation.pdf')"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "base",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.5 (default, May 18 2021, 12:31:01) \n[Clang 10.0.0 ]"
+  },
+  "orig_nbformat": 4,
+  "vscode": {
+   "interpreter": {
+    "hash": "a429a41e61deb9ee9f43170a4271c5d42eef99359a9088d8c58f4b96e2ffedc5"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/blog/references.bib b/blog/references.bib
new file mode 100644
index 0000000..783ec6a
--- /dev/null
+++ b/blog/references.bib
@@ -0,0 +1,56 @@
+---
+---
+
+@inproceedings{holdgraf_evidence_2014,
+	address = {Brisbane, Australia, Australia},
+	title = {Evidence for {Predictive} {Coding} in {Human} {Auditory} {Cortex}},
+	booktitle = {International {Conference} on {Cognitive} {Neuroscience}},
+	publisher = {Frontiers in Neuroscience},
+	author = {Holdgraf, Christopher Ramsay and de Heer, Wendy and Pasley, Brian N. and Knight, Robert T.},
+	year = {2014}
+}
+
+@article{holdgraf_rapid_2016,
+	title = {Rapid tuning shifts in human auditory cortex enhance speech intelligibility},
+	volume = {7},
+	issn = {2041-1723},
+	url = {http://www.nature.com/doifinder/10.1038/ncomms13654},
+	doi = {10.1038/ncomms13654},
+	number = {May},
+	journal = {Nature Communications},
+	author = {Holdgraf, Christopher Ramsay and de Heer, Wendy and Pasley, Brian N. and Rieger, Jochem W. and Crone, Nathan and Lin, Jack J. and Knight, Robert T. and Theunissen, Frédéric E.},
+	year = {2016},
+	pages = {13654},
+	file = {Holdgraf et al. - 2016 - Rapid tuning shifts in human auditory cortex enhance speech intelligibility.pdf:C\:\\Users\\chold\\Zotero\\storage\\MDQP3JWE\\Holdgraf et al. - 2016 - Rapid tuning shifts in human auditory cortex enhance speech intelligibility.pdf:application/pdf}
+}
+
+@inproceedings{holdgraf_portable_2017,
+	title = {Portable learning environments for hands-on computational instruction using container-and cloud-based technology to teach data science},
+	volume = {Part F1287},
+	isbn = {978-1-4503-5272-7},
+	doi = {10.1145/3093338.3093370},
+	abstract = {© 2017 ACM. There is an increasing interest in learning outside of the traditional classroom setting. This is especially true for topics covering computational tools and data science, as both are challenging to incorporate in the standard curriculum. These atypical learning environments offer new opportunities for teaching, particularly when it comes to combining conceptual knowledge with hands-on experience/expertise with methods and skills. Advances in cloud computing and containerized environments provide an attractive opportunity to improve the effciency and ease with which students can learn. This manuscript details recent advances towards using commonly-Available cloud computing services and advanced cyberinfrastructure support for improving the learning experience in bootcamp-style events. We cover the benets (and challenges) of using a server hosted remotely instead of relying on student laptops, discuss the technology that was used in order to make this possible, and give suggestions for how others could implement and improve upon this model for pedagogy and reproducibility.},
+	booktitle = {{ACM} {International} {Conference} {Proceeding} {Series}},
+	author = {Holdgraf, Christopher Ramsay and Culich, A. and Rokem, A. and Deniz, F. and Alegro, M. and Ushizima, D.},
+	year = {2017},
+	keywords = {Teaching, Bootcamps, Cloud computing, Data science, Docker, Pedagogy}
+}
+
+@article{holdgraf_encoding_2017,
+	title = {Encoding and decoding models in cognitive electrophysiology},
+	volume = {11},
+	issn = {16625137},
+	doi = {10.3389/fnsys.2017.00061},
+	abstract = {© 2017 Holdgraf, Rieger, Micheli, Martin, Knight and Theunissen. Cognitive neuroscience has seen rapid growth in the size and complexity of data recorded from the human brain as well as in the computational tools available to analyze this data. This data explosion has resulted in an increased use of multivariate, model-based methods for asking neuroscience questions, allowing scientists to investigate multiple hypotheses with a single dataset, to use complex, time-varying stimuli, and to study the human brain under more naturalistic conditions. These tools come in the form of “Encoding” models, in which stimulus features are used to model brain activity, and “Decoding” models, in which neural features are used to generated a stimulus output. Here we review the current state of encoding and decoding models in cognitive electrophysiology and provide a practical guide toward conducting experiments and analyses in this emerging field. Our examples focus on using linear models in the study of human language and audition. We show how to calculate auditory receptive fields from natural sounds as well as how to decode neural recordings to predict speech. The paper aims to be a useful tutorial to these approaches, and a practical introduction to using machine learning and applied statistics to build models of neural activity. The data analytic approaches we discuss may also be applied to other sensory modalities, motor systems, and cognitive systems, and we cover some examples in these areas. In addition, a collection of Jupyter notebooks is publicly available as a complement to the material covered in this paper, providing code examples and tutorials for predictive modeling in python. The aimis to provide a practical understanding of predictivemodeling of human brain data and to propose best-practices in conducting these analyses.},
+	journal = {Frontiers in Systems Neuroscience},
+	author = {Holdgraf, Christopher Ramsay and Rieger, J.W. and Micheli, C. and Martin, S. and Knight, R.T. and Theunissen, F.E.},
+	year = {2017},
+	keywords = {Decoding models, Encoding models, Electrocorticography (ECoG), Electrophysiology/evoked potentials, Machine learning applied to neuroscience, Natural stimuli, Predictive modeling, Tutorials}
+}
+
+@book{ruby,
+  title     = {The Ruby Programming Language},
+  author    = {Flanagan, David and Matsumoto, Yukihiro},
+  year      = {2008},
+  publisher = {O'Reilly Media}
+}
diff --git a/blog/requirements.txt b/blog/requirements.txt
new file mode 100644
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--- /dev/null
+++ b/blog/requirements.txt
@@ -0,0 +1,3 @@
+jupyter-book
+matplotlib
+numpy
diff --git a/blog/square.png b/blog/square.png
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diff --git a/poster/shared/poster.pdf b/poster/shared/poster.pdf
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diff --git a/readme.md b/readme.md
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--- /dev/null
+++ b/readme.md
@@ -0,0 +1,46 @@
+# Index
+
+## Demistifying E(3)-equivariant neural networks!
+
+Check out the website: https://killiansheriff.github.io/blog_e3nn/index.html
+
+Welcome to our blog post on demistifying E(3)-equivariant neural networks! This blog aim to introduces the following concepts, in order to understand the mathematical tools leading to learnable equivariant operations:
+
+1. Group_representation
+1. Irreducible Representations
+1. Transformation under Euclidean Symmetries
+1. Spherical Harmonics
+1. Principle of Equivariance and Polynomials
+1. Learnable Tensor Products
+1. MLIAP and Data Efficiency
+
+## Disclaimer
+
+This post serves as an explanation of the paper by ``Geiger et al [1]``. It was written as a final project for the ``Fall 2022 Final Project`` section of the ``6.S898: Deep Learning`` course at the ``Massachusetts Institute of Technology``. Needless to say that the intuition presented herein are heavily influenced by the explanations of Geiger et al.
+
+## References 
+1. Geiger, M. & Smidt, T. e3nn: Euclidean Neural Networks. Arxiv (2022).
+
+## JupyterBook
+```bash
+jupyter-book create blog/
+jupyter-book build blog/
+```
+<!-- Inside blog directory to publish online ghp-import -n -p -f _build/html -->
+
+## Citation
+If used, please cite: 
+
+```citation
+@software{killian_sheriff_2022_7430281,
+  author       = {Killian Sheriff and
+                  Yifan Cao},
+  title        = {killiansheriff/blog\_e3nn: blog\_e3nn},
+  month        = dec,
+  year         = 2022,
+  publisher    = {Zenodo},
+  version      = {blog\_e3nn},
+  doi          = {10.5281/zenodo.7430281},
+  url          = {https://doi.org/10.5281/zenodo.7430281}
+}
+```