diff --git a/Code/ThoughtsOnUsingPytorch.ipynb b/Code/ThoughtsOnUsingPytorch.ipynb
index a0430fa..a85c5ee 100644
--- a/Code/ThoughtsOnUsingPytorch.ipynb
+++ b/Code/ThoughtsOnUsingPytorch.ipynb
@@ -2,19 +2,20 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
-   "id": "dense-italic",
+   "execution_count": 25,
+   "id": "meaningful-piece",
    "metadata": {},
    "outputs": [],
    "source": [
     "import torch\n",
-    "import numpy\n"
+    "import numpy\n",
+    "from torch.autograd.functional import jacobian"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "adult-cargo",
+   "id": "prescribed-roller",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -27,7 +28,7 @@
   {
    "cell_type": "code",
    "execution_count": 3,
-   "id": "photographic-miniature",
+   "id": "amateur-taste",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -38,7 +39,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "charming-plate",
+   "id": "accepted-bonus",
    "metadata": {},
    "outputs": [],
    "source": []
@@ -46,7 +47,7 @@
   {
    "cell_type": "code",
    "execution_count": 4,
-   "id": "fitting-horizontal",
+   "id": "burning-peeing",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -56,7 +57,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "secret-oasis",
+   "id": "special-hydrogen",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -66,7 +67,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "comic-context",
+   "id": "played-fairy",
    "metadata": {},
    "outputs": [
     {
@@ -121,7 +122,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "chinese-family",
+   "id": "scientific-egypt",
    "metadata": {},
    "source": [
     "# Try this\n",
@@ -163,7 +164,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "exceptional-amount",
+   "id": "flexible-hotel",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -174,7 +175,7 @@
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "biblical-convertible",
+   "id": "floating-alert",
    "metadata": {},
    "outputs": [
     {
@@ -198,7 +199,7 @@
   {
    "cell_type": "code",
    "execution_count": 9,
-   "id": "classified-crisis",
+   "id": "historical-elevation",
    "metadata": {},
    "outputs": [
     {
@@ -222,7 +223,7 @@
   {
    "cell_type": "code",
    "execution_count": 10,
-   "id": "charged-locator",
+   "id": "proud-brake",
    "metadata": {},
    "outputs": [
     {
@@ -244,7 +245,7 @@
   {
    "cell_type": "code",
    "execution_count": 11,
-   "id": "cheap-necessity",
+   "id": "protective-grave",
    "metadata": {},
    "outputs": [
     {
@@ -267,7 +268,7 @@
   {
    "cell_type": "code",
    "execution_count": 12,
-   "id": "flexible-nightlife",
+   "id": "coated-guard",
    "metadata": {},
    "outputs": [
     {
@@ -292,7 +293,7 @@
   {
    "cell_type": "code",
    "execution_count": 13,
-   "id": "heavy-duration",
+   "id": "competitive-acting",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -303,7 +304,7 @@
   {
    "cell_type": "code",
    "execution_count": 14,
-   "id": "quantitative-organ",
+   "id": "statutory-starter",
    "metadata": {},
    "outputs": [
     {
@@ -324,7 +325,7 @@
   {
    "cell_type": "code",
    "execution_count": 16,
-   "id": "transparent-cartridge",
+   "id": "engaged-teddy",
    "metadata": {},
    "outputs": [
     {
@@ -351,16 +352,124 @@
   },
   {
    "cell_type": "markdown",
-   "id": "adjusted-saskatchewan",
+   "id": "stretch-mercury",
    "metadata": {},
    "source": [
     "So, I think I can construct a gradient, and possibly invert it/choose some other solution method."
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "disciplinary-opposition",
+   "metadata": {},
+   "source": [
+    "basic transition functions\n",
+    "$$\n",
+    "s^i(s,D)\\prime = (1-D^{\\sum s}) s^i + x\\\\\n",
+    "D\\prime = (1-\\delta)D + D^{\\alpha} +\\gamma D^{\\sum s} +\\Gamma x\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 54,
+   "id": "missing-robinson",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def satellite_loss(d,s):\n",
+    "    return d**(s.sum())\n",
+    "\n",
+    "def gs(d,s,x):\n",
+    "    return (1-d**(s.sum()))*s + x\n",
+    "\n",
+    "#Parameters\n",
+    "gamma, alpah, Gamma, delta = 0.1, 4000, 0.001, 0.1\n",
+    "\n",
+    "def gd(d,s,x):\n",
+    "    return d*(1-delta) + gamma *s.sum()*d**(s.sum()) + Gamma*x"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "id": "driving-wright",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(tensor([7.9941, 6.9961], grad_fn=<AddBackward0>),\n",
+       " tensor([6., 4.], requires_grad=True),\n",
+       " tensor([2., 3.], requires_grad=True))"
+      ]
+     },
+     "execution_count": 51,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "D = torch.Tensor([0.5])\n",
+    "gs(D,b,a),b,a"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 52,
+   "id": "infectious-plaintiff",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(tensor([[-0.1172],\n",
+       "         [-0.0781]]),\n",
+       " tensor([[1.0031, 0.0041],\n",
+       "         [0.0027, 1.0017]]),\n",
+       " tensor([[1., 0.],\n",
+       "         [0., 1.]]))"
+      ]
+     },
+     "execution_count": 52,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "jacobian(gs,(D,b,a))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 53,
+   "id": "proud-dance",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(tensor([[0.9195],\n",
+       "         [0.9195]]),\n",
+       " tensor([[-0.0006, -0.0006],\n",
+       "         [-0.0006, -0.0006]]),\n",
+       " tensor([[0.0010, 0.0000],\n",
+       "         [0.0000, 0.0010]]))"
+      ]
+     },
+     "execution_count": 53,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "jacobian(gd,(D,b,a))"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "outdoor-functionality",
+   "id": "satisfied-briefs",
    "metadata": {},
    "outputs": [],
    "source": []