{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "98fcc019707df7b5",
   "metadata": {},
   "source": [
    "# Constructing LIF neuron model with ``brainstate``\n",
    "\n",
    "[![Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/chaobrain/brain-modeling-ecosystem/blob/main/docs/brainstate_LIF_neuron.ipynb)\n",
    "[![Open in Kaggle](https://kaggle.com/static/images/open-in-kaggle.svg)](https://kaggle.com/kernels/welcome?src=https://github.com/chaobrain/brain-modeling-ecosystem/blob/main/docs/brainstate_LIF_neuron.ipynb)\n",
    "\n",
    "Welcome! This beginner-friendly tutorial will guide you through:\n",
    "\n",
    "- Understanding the Leaky Integrate-and-Fire (LIF) neuron.\n",
    "- Implementing LIF with `brainstate.nn.Dynamics`.\n",
    "- Simulating with `brainstate.transform.for_loop`.\n",
    "- Running small experiments (step response, tonic spiking, F–I curve).\n",
    "\n",
    "Prerequisites:\n",
    "- Basic Python. Some calculus intuition helps but is optional.\n",
    "- `brainstate` and `brainunit` installed; this notebook uses unit-aware quantities (ms, mV, mA)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7c5798579d236459",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-16T02:57:35.587846Z",
     "start_time": "2025-09-16T02:57:33.658024Z"
    }
   },
   "outputs": [],
   "source": [
    "# Imports and environment setup\n",
    "import braintools\n",
    "import brainstate\n",
    "import brainunit as u\n",
    "import jax\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Global simulation step (time resolution)\n",
    "brainstate.environ.set(dt=0.1 * u.ms)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa82d5981c946e9e",
   "metadata": {},
   "source": [
    "## LIF Basics\n",
    "\n",
    "The LIF neuron approximates a neuron's membrane as a leaky RC circuit. Its membrane potential `V(t)` obeys:\n",
    "\n",
    "- ODE: `dV/dt = (-(V - V_rest) + R I_in)/tau`\n",
    "- Parameters:\n",
    "  - `V_rest`: resting potential (e.g., 0 mV here for simplicity).\n",
    "  - `R`: membrane resistance (maps input current to a steady-state voltage).\n",
    "  - `tau`: membrane time constant (how fast `V` relaxes).\n",
    "  - `I_in`: input current.\n",
    "\n",
    "Spiking and reset:\n",
    "- When `V` crosses a threshold `V_th`, the neuron emits a spike.\n",
    "- After spiking, `V` is reset (commonly to `V_reset`).\n",
    "\n",
    "Discrete-time integration:\n",
    "- We integrate with an exponential Euler step (`brainstate.nn.exp_euler_step`),\n",
    "  equivalent to the exact solution for this linear ODE over one small time step `dt`.\n",
    "- For constant input, the steady state is `V_inf = V_rest + R I_in`, and\n",
    "  `V(t + dt) = V_inf + (V(t) - V_inf) * exp(-dt/tau)`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6663cdf945acd111",
   "metadata": {},
   "source": [
    "## Implementing LIF with `brainstate.nn.Dynamics`\n",
    "\n",
    "We implement a single-compartment LIF neuron. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "69554be12be88022",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-16T02:57:35.710573Z",
     "start_time": "2025-09-16T02:57:35.592880Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LIFDynamics(\n",
       "  in_size=(1,),\n",
       "  out_size=(1,),\n",
       "  R=1. * ohm,\n",
       "  tau=5. * msecond,\n",
       "  V_th=1. * mvolt,\n",
       "  V_reset=0. * mvolt,\n",
       "  V_rest=0. * mvolt,\n",
       "  V_initializer=Constant(value=0.0 * mvolt),\n",
       "  spk_fun=ReluGrad(alpha=0.3, width=1.0),\n",
       "  spk_reset=soft,\n",
       "  V=HiddenState(\n",
       "    value=~float32[1] * mvolt\n",
       "  )\n",
       ")"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from typing import Callable\n",
    "\n",
    "class LIFDynamics(brainstate.nn.Dynamics):\n",
    "    \"\"\"\n",
    "    A leaky integrate-and-fire neuron implemented as a Dynamics module.\n",
    "\n",
    "    Parameters: R, tau, V_th, V_reset, V_rest, and a spike function.\n",
    "    Soft reset subtracts (V_th - V_reset) when a spike occurs;\n",
    "    Hard reset uses (V - V_reset), which resets exactly to V_reset.\n",
    "    \"\"\"\n",
    "    def __init__(\n",
    "        self,\n",
    "        in_size: brainstate.typing.Size,\n",
    "        R: brainstate.typing.ArrayLike = 1.0 * u.ohm,\n",
    "        tau: brainstate.typing.ArrayLike = 5.0 * u.ms,\n",
    "        V_th: brainstate.typing.ArrayLike = 1.0 * u.mV,\n",
    "        V_reset: brainstate.typing.ArrayLike = 0.0 * u.mV,\n",
    "        V_rest: brainstate.typing.ArrayLike = 0.0 * u.mV,\n",
    "        V_initializer: Callable = braintools.init.Constant(0.0 * u.mV),\n",
    "        spk_fun: Callable = braintools.surrogate.ReluGrad(),\n",
    "        spk_reset: str = \"soft\",\n",
    "        name: str | None = None,\n",
    "    ):\n",
    "        super().__init__(in_size, name=name)\n",
    "        # Parameters (unit-aware)\n",
    "        self.R = braintools.init.param(R, self.varshape)\n",
    "        self.tau = braintools.init.param(tau, self.varshape)\n",
    "        self.V_th = braintools.init.param(V_th, self.varshape)\n",
    "        self.V_reset = braintools.init.param(V_reset, self.varshape)\n",
    "        self.V_rest = braintools.init.param(V_rest, self.varshape)\n",
    "        self.V_initializer = V_initializer\n",
    "        # Spiking\n",
    "        self.spk_fun = spk_fun\n",
    "        self.spk_reset = spk_reset\n",
    "\n",
    "    def init_state(self, batch_size: int | None = None, **kwargs):\n",
    "        self.V = brainstate.HiddenState(\n",
    "            braintools.init.param(self.V_initializer, self.varshape, batch_size)\n",
    "        )\n",
    "\n",
    "    def reset_state(self, batch_size: int | None = None, **kwargs):\n",
    "        self.V.value = braintools.init.param(self.V_initializer, self.varshape, batch_size)\n",
    "\n",
    "    def get_spike(self, V=None):\n",
    "        V = self.V.value if V is None else V\n",
    "        v_scaled = (V - self.V_th) / (self.V_th - self.V_reset)\n",
    "        return self.spk_fun(v_scaled)\n",
    "\n",
    "    def update(self, x=0.0 * u.mA):\n",
    "        last_v = self.V.value\n",
    "        spk = self.get_spike(last_v)\n",
    "        # Reset policy\n",
    "        V_th_or_v = self.V_th if self.spk_reset == 'soft' else jax.lax.stop_gradient(last_v)\n",
    "        V = last_v - (V_th_or_v - self.V_reset) * spk\n",
    "        # Dynamics integration by exponential Euler\n",
    "        dv = lambda v: (-(v - self.V_rest) + self.R * x) / self.tau\n",
    "        V = brainstate.nn.exp_euler_step(dv, V)\n",
    "        self.V.value = V\n",
    "        return self.get_spike(V)\n",
    "\n",
    "# Create and initialize a neuron\n",
    "lif = LIFDynamics(1)\n",
    "brainstate.nn.init_all_states(lif)\n",
    "lif"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1cc893ce3353ed5",
   "metadata": {},
   "source": [
    "### Code Walkthrough\n",
    "- Parameters are registered with `braintools.init.param` to track shapes and units.\n",
    "- Hidden state `V` holds the membrane potential and updates each step.\n",
    "- `get_spike(V)`: rescales `(V - V_th)` by `(V_th - V_reset)` and applies a surrogate spike function (here `ReluGrad`), enabling differentiable spikes for learning.\n",
    "- Reset: `soft` subtracts `(V_th - V_reset) * spk`; `hard` subtracts `(V - V_reset) * spk` (i.e., set to `V_reset` when spiking).\n",
    "- Integration: `exp_euler_step` advances `V` one `dt` under the environment's time step."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7233f7df473e261",
   "metadata": {},
   "source": [
    "## Simulating with `brainstate.transform.for_loop`\n",
    "\n",
    "We'll write a small helper to run the neuron over a sequence of input currents,\n",
    "use indexing pattern with `brainstate.environ.context(i=i)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "56fb1cdd4b716490",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-16T02:57:35.730992Z",
     "start_time": "2025-09-16T02:57:35.724895Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1 * msecond"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def run_lif(lif_module, inputs):\n",
    "    \"\"\"Run the LIF over a 1D array of input currents.\n",
    "    Returns membrane potentials and spikes over time.\n",
    "    \"\"\"\n",
    "    lif_module.reset_state()\n",
    "    idx = np.arange(len(inputs))\n",
    "\n",
    "    def step(i, x):\n",
    "        with brainstate.environ.context(i=i):\n",
    "            s = lif_module(x)\n",
    "            return lif_module.V.value, s\n",
    "\n",
    "    V_seq, S_seq = brainstate.transform.for_loop(step, idx, inputs)\n",
    "    return V_seq, S_seq\n",
    "\n",
    "dt = brainstate.environ.get_dt()\n",
    "dt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68ad539b7238ffca",
   "metadata": {},
   "source": [
    "## Experiment 1: Subthreshold Step Response\n",
    "\n",
    "Use a constant current that keeps `V_inf = V_rest + R I` below `V_th`. We should see a smooth approach to `V_inf` without spiking."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "120203d7718fd12f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-16T02:57:36.046072Z",
     "start_time": "2025-09-16T02:57:35.759749Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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b0b/99psKPAqqEbwV5DYiOEH3VvkNuaqdr8Lup9YNGoIrDX6gYB6BnJbfi2OO2/7ogcHwdbhWUVuHW9OmwPky7GIOsF8IxLTyIUcbnycMBpLf9XW71AyUHdcoWvHfCZwfnCecL8Nb/PixhSAPPSegfAXJ/XlB4Kvd3ch9DnDtGu4jglEc38LWnKOWF70uoNs0pAAZXq+4FtD7RW7YvvZ/CmpZc///ptX45y4r8qaRd5s7jYGouLFGluguoAEWvnx79uypanrwZY9+GvHFjlorLZ8UUHuB23z4ixpbBLVaDVd+UMOBRmTolgmBD2qj0JgE/XQafimjZgWBHoIR1ODequsfU6CsCNSxPYxahuA0NjZWBWB4TzwGfKnjFi9qd5DXiK6E0I0Pgk4EIKbAviGVAV/g+DJFIIS8Y9xyRQ2TYe1UbtrIavjyxpcqah1x+xm1Z7eDnGbcZkZeM8qAIAz7iBxD1AQaHm+cWzRGQwoJ1kOt2jPPPKO6p0JjNhwzHAsECqihw3LcktVq6QHdEyEgM+x+C3KnYhQWgiHkwiLAQSCB6w4NDhFcozwIrHBruLD7CbiekHKAYA2pMthv3BLHudEaIKExEoJb1PrhmOOaxw8J5Ejjx4ip5x+fB9RqI9DC9YY0AaRAIEh88skn1TrYFwR0OOaoScZyBNfoHguNAXHscR0UBHcIcM1iv6dMmXJHx/vdd99VjbUQtKI2FeXEcUBwh5zeW8HnH58d5PjiXOCuDAJ/BIi5azPx/4l2PFADjOsE74n/FwoLXXih8Rm6j0OgiT6Z8blCwz2kbOCc4njgnKIGGOlQ6NMW1wg+d3hP/P+GHxS4fvBjDecgd60wjgc+C8yRpXuuSPtAICpl/vzzT9WlVK1atVR3Q+iSB909jRw5UhcZGWm0LrpCQpdW6CII3fT07dtXFxUVVWD3W8eOHdP16dNHrVumTBndiBEjdDdu3DDa5okTJ1R3Py4uLuo1Wldc2jaio6Pz7dYH3SFpMF9Qd0zYBzxXoUIFnYODgy4gIEDXsWNH3Zdffqlf54svvlBlQNdKTk5OumrVquleffVVXXx8fJ59Kkx5MjIydJMnT1bdRuE98d4TJkzQpaamGr02d7dDWjdW6LbM1dVVdTmEro60LoVu1f0WupZCmRs2bKiON7o1w+PPPvvMaL2kpCTdU089pbp/wjYNu+JCN0kffPCB6ooMxwHnDN0nYV8Mj4V2vNFlFbrMwrqNGze+bfdgubtWyg+6WOrVq5f+XKB8uM42btxo0n7iuGI/0EUYutJC12DY1pw5c/K9RoYMGaKON67/+vXr5+lmTut+K79utQyvf3T1hmODzxPKhs9KixYtjLpUMzwW6G4M66B8uO4GDx5s1K1ZQZYvX66zsbHRhYWF5SlLfp8F7Hvubu7279+v3h+fe1xvHTp0UF1Q3c7PP/+s69y5s+rGDMerYsWKuv/973+68PDwPJ+LzZs3655//nl1LeF9BgwYoLt27ZrR9m7V/ZYhdA2I5YbnEJ9jXKP4/wPXA84d1kNXYto+9u/fX5UR1xPK/Nhjj+U5xsePH1fb3rBhw233n6io2eCfex8+ExGVTqixQs8Ot6o1NDd07I9ulPJLKykJUFuOGl/UdOZ3e93ctIEKUFNuWJNvqdBAD3eYUCvPGlm615gjS0REpQryXJFWgDz0/HKKqfCQ84u0FqRbMIglc2COLBERlTpaLxt0d9CdGX8MkDmxRpaIiIiIrBJzZImIiIjIKrFGloiIiIisEgNZIiIiIrJKpa6xF4YDxOg/6KibLSyJiIiILAuyXjEABwZmMRz+Oj+lLpBFEHu7cbCJiIiIyLwwfDdGwLuVUhfIakMm4uDcajxsIiIiIrr3MKwyKh0LM8x1qQtktXQCBLEMZImIiIgsU2FSQNnYi4iIiIisEgNZIiIiIrJKZg1kt2zZIo8//rhqlYbq419//fW2r/n777+lSZMm4uTkJNWrV5dvv/32npSViIiIiCyLWXNkk5OTpWHDhjJ06FDp1avXbdc/f/68dO3aVV544QX58ccfZePGjfLss89KYGCgdOnS5Z6UmYiIiEqurKwsycjIMHcxSjQHBwexs7Oz/kD2kUceUVNhzZs3T6pUqSIzZ85U87Vr15Z//vlHPvroIwayREREdFd9l0ZEREhcXJy5i1IqeHt7S0BAwF336W9VvRbs2LFDOnXqZLQMAezLL79stjIRERGR9dOCWD8/P3F1deWgScX4gyElJUWioqLUPO6ql5pAFheZv7+/0TLMo7+xGzduiIuLS57XpKWlqUmDdW8++G8lBwcRvPbGDRHD2wlOTjlTcjLuNfy33NlZxNFRJCkJQ4X9t9zVVcTe3njb4OYmgpEpEhONl6N/NLwe2zeEbsEyM0VSUv5bhte7u4ukp4ukpv63HFXz2D720WA/uU/cJ+4T94n7xH3iPhVun7LS0iQuNlYFseW8vf8rP9bX6YzXz285gl68Z0HLDffnVsuxDM/ltxwM9/9Wy+3scsqR33IL2CcXnE+dTqKio8XPxUXsDEfvwnnKvY1b0VkIFGXFihW3XCckJEQ3depUo2WrVq1Sr01JScn3NZMmTVLP557ic05LzhQamrMy/hounzQpZ3nnzsbLv/oqZ3mdOsbL16zJWe7hYbz8yBGdLj7eeBkmLMNzhsvwWsC2DJfjvQDvbbgcZcvZUePl3CfuE/eJ+8R94j5xnwq1TzfWrdMdW71al7Jnj06H6fDhnG1HReXMa9PJkznLr1wxXn7+fM5y/DVcjvUArzNcju0C3sdweVxczvJ9+4yXI8bJzDRehikzM+c5w2V4LWBbhsstbJ9SYmN1x44c0d2oWDHPeYrfuTMnVsM5uw0b/CMWAFX4K1askB49ehS4Trt27VSPBbNnz9YvW7BggUotiI+Pz/c1+dXIYrSIeMORvSzw12FJ/MXLfeI+cZ+4T9wn7pMl7lNqUpKcv3hRqlSuLM54PwuqvdQvL0E1spCani7nL1yQKr6+4ozzq/HwkIS4OPEqW1bFdrcbvMqqAtnXXntNVq9eLYcPH9Yve+qppyQ2NlbWrFlTqPdBIOvl5VWog0NEREQlX2pqquoZCQ3K9YEsme2YmxKrmbUf2aSkJDl48KCaADuEx2FhYWp+woQJMnDgQP366Hbr3LlzMm7cODlx4oR89tlnsnTpUhk9erTZ9oGIiIjIkr311lvy/PPP33KdY8eOSfny5VXXqNbErIHs3r17pXHjxmqCMWPGqMcTJ05U8+Hh4fqgFhC1r1q1StavX6/6n0U3XF9//TW73iIiIqJSBQNKPfzww/k+t3XrVnWn+9ChQ6qh/McffyxvvPGG/vkHHnggT49PderUkZYtW8qsWbPEmpi11wIcyFtlNuQ3ahdec+DAgWIuGREREZHlCg0Nld69e8vly5dVTaohtB9q1qyZNGjQQN59911p3bq1VKpU6bbbHDJkiDz33HPqjrg98o+tgFlrZImIiIjIdI899pj4+vrmqfRD2uayZctUoAuLFy9WtbeawYMHy+bNm1UtLWptMV24cEE999BDD6l2R3jeWlhHuE1ERER0j+Bu8Y0ME/oyLUIuDnaFGowBNaYDBw5UgSzSBrTXIIjFMLv9+/dXQSlyX1E7q0EAe+rUKalXr55MmTJFLUNADI6OjtKoUSOVmtCxY0exBgxkiYiIiAwgiK0zca1Z3vvYlC7i6li48Gzo0KEyY8YMVYOK1EstrQApB2j1jwb0CMqDgoL0r8FyBKwYvQxDxOaGdS9evCjWgqkFRERERFaoVq1aKv91/vz5av7MmTOqNlVLK8Cop2BKl2IYJRVDyFoL1sgSERER5bq9j5pRc723KUJDQ2XkyJEyd+5cVRtbrVo1ad++vXrOx8dH/b1+/bo+feB2kI6AbVgLBrJEREREBpBvWtjb++bWt29fGTVqlCxatEgWLlwow4YN0+fLIiDFgALIk61Ro4b+NUgtQB5tfo4cOSJ9+vQRa8HUAiIiIiIr5e7uLv369VNdZqH/ffRKoLG1tZVOnTrJP//8Y/SaypUry65du1RvBTExMZJ9cyhbzF+5ckW9xlowkCUiIiKyYqGhoSp9AANEGTbsgmeffVZ1waUFqzB27Fixs7NTgyAg5UAbfOqnn36Szp07F6rPWUthHfXmRERERJSvVq1aFTjAFEb/QnC7ZMkS1SUXIM1gx44dRuulp6fLvHnzVIqCNSl0jWxBuRREREREZJlsbGzkyy+/lMzMzFuuh1rZ119/Xdq0aSPWpNA1ssHBwSrvAn2WGSYMExEREZHlatSokZpupXr16mqyNoWukR0+fLj8/PPPUrt2bWnbtq0aScKa+hkjIiIiopKl0IHsW2+9pTra3bhxo1StWlVGjBghgYGB8txzz6mWb0REREREFt1rAYZA++677yQiIkJmzpwpx48fV0nGdevWlVmzZhVPKYmIiIiIiqr7LfRbhi4d0DfZypUrVWD76quv3unmiIiIiIjuTSCL/FjkyWIYtG7dukm5cuXkvffeu9PNEREREREVbz+y27dvl/nz58uyZctUVw4Yxuydd96Rdu3ambopIiIiIqLiD2SnT58uCxYskFOnTkmzZs1kxowZqmNdDw+PO393IiIiIqLiDmQRuD799NOqJrZevXp3+n5ERERERPc2R/bq1avy0UcfMYglIiIiMrPHH39cDT+bn61bt6oRvQ4dOnRPy3ThwgX1vgcPHrS8QNbBwaF4S0JEREREhRIaGirr16+Xy5cv53kOqaBIA23QoEGht6fT6W47jG2J6rWAiIiIiMzjscceE19fX9WDlKGkpCSVBopA91b+/vtvVXv6559/StOmTcXJyUl1qZqdnS3Tpk2TKlWqiIuLizRs2FCN7Kq5fv26DBgwQL03ng8JCVGBM+A10LhxY7VtjD1gcb0WEBEREZF52dvby8CBA1Ug+8Ybb6jAERDEZmVlqQb5hTF+/Hj58MMP1aitZcqUUUHsDz/8IPPmzVNB6pYtW1QbKQSu6HIVI70eO3ZMBcA+Pj5q1NcbN26obe3evVuaN28uGzZsUANlOTo6SnFjIEtERESUj7S0NDUZplmiFhKBW0ZGhn45ajMxJScnqyBS4+zsrII51JKiplPj6uqqAtGEhASj93NzcxM7O7tCl2/o0KGqMf7mzZv1tZ+oHe3du7d4eXkVahtTpkyRhx56SL+/U6dOVYEoRm0FBLioqf3iiy9UIBsWFqZqXJG6AJUrV9ZvC8EuYGyBgIAAsZjUAhzowk5EREREJQFqJxEQatPIkSPVcvw1XI71oFevXkbLFy5cqJa3aNHCaPnGjRvV8vLlyxstP3HihEnlq1WrlrRu3Vr17w+oHUVDr9ulFRjSAlLt9RjwCoEtRnDVJuzH2bNn1TrDhg2TxYsXS6NGjWTcuHFqfAFzKlSNrLe3t77K+lZJwljH8JcIERERkbWaMGGCjBkzJk/D908//VRmzZqlX47aWFi+fHmeGlnYtWtXnhpZyN1QCzWypgoNDVWB9dy5c1VtbLVq1VTNaWEZvidqjmHVqlUSHBxstJ62j4888ohcvHhRVq9erRqbdezYUYYPH67SEyw2kN20aVOxFQAHHtXiERERKqEYFwfyKwoye/Zs+fzzz1XVNnIzMLIYfglpFwsRERFRUdBSBnJDegGm3AoKRFGrmR9PT8+7LmPfvn1l1KhRsmjRIlVzihrT21U+FqROnTpqfxFj3SoYRgrBoEGD1NS2bVt59dVXVSCr5cTey0rNQgWypkT2pliyZIn6pYOEYlS7I0jt0qWLnDx5Uvz8/PKsj5OEpGRUoaMqHaOMDR48WJ0ww19GRERERKWBu7u79OvXT9UeI8UTcdGdwmitY8eOldGjR6sa5Pvvv1/i4+Nl27ZtKuhG4Dpx4kTVywEacyGn9o8//pDatWur1yN2Q4C/Zs0alTaBSsbC5ure8+63kEOBXA50tms4mQLB53PPPSdDhgxRvwIQ0KK6Xcv1yA15GG3atJGnnnpKJRd37txZtcpDKzkiIiKi0ig0NFR1i4XKwKCgoLva1jvvvKN6JsDdbgSoGHQBqQZa11qodUXQjD5q27VrpxqnIWcW0IDtk08+UQ3DUI7u3btLcbPRIbnVBNHR0SrwRLcL+SlsdXJ6eroKWtE3WY8ePfTLEe3HxcXJb7/9lm+N7Isvvijr1q1T6Qfnzp2Trl27yjPPPCOvv/56od4Xv1bw6wC/MIqiSp+IiIisW2pqqpw/f14Fa0xVNP8xNyVWM7n7rZdfflkFmkhcRlcPK1askMjISHn33Xdl5syZhd5OTEyMCnr9/f2NlmO+oFZ7qInF61DVrY1A8cILL9wyiM3ddQZ7ViAiIiIqGUxOLfjrr79USgC6a7C1tZVKlSqpjnKnT5+u736iuGAUCvRv9tlnn8n+/ftV60BUd6MavLBdZ1SoUKFYy0hERERkbi+88IJRF1qGE54rKUyukUVnv1pDLIwAgVSDGjVqSP369VVwWVjocQB5FajNNYT5gjrRRc4G0gieffZZNY/3RHmef/55NaoFAuvbdZ2BGlkGs0RERFSSTZkyRTXcyk9JSq00OZCtWbOm6lUAja3QXRYSevEYDbUCAwMLvR0kC6PVGzoF1nJk0UIO8yNGjCiwgVnuYFUbAaOgVN+Cus4gIiIiKqn8/Pzy7QGqpDE5kEVfZeHh4erxpEmTVGu2H3/8UQWmGO/XFKgpReMupCmg8Ra630INKxqTAcYQRoe8WsrC448/rtIaMDQauuvCCBSopcVyU4Z0IyIiIiLrZ3Igi3xYDWpUMboDGmdVrFhRpQuYAv2eITUBfZJhQAQMd4a+x7QGYOiQ17AG9s0331R9xuLvlStXVIe8CGLfe+89U3eDiIiIiKycyd1vWTt2v0VERESG2P1WCe9+CykA6BkAQ68ZNpzKD0fYIiIiIqJ7oVCB7IEDByQjI0P/mIiIiIjIKgLZTZs25fuYiIiIiEqOBx54QLVZQgP8EjkgwtChQyUxMTHPcvQ2gOeIiIiIqHihsfvDDz+c73Nbt25VjeMPHTp0y0GmsA5Ga7VmJgey3333ndy4cSPPcixbuHBhUZWLiIiIiAoQGhoq69evl8uXL+d5bsGCBapr0wYNGkhJV+hAFi3I0HoMnRygRhbz2nT9+nVZvXp1qeh4l4iIiMjcHnvsMdUNae4+/JOSkmTZsmUq0C3IhQsXpEOHDvpRWlEzO3jwYP3zGKBq3LhxUrZsWTXa6ttvvy1W34+st7e32lFMGJI2NyyfPHlyUZePiIiIiHKxt7dXA0chkH3jjTdUHAYIYrOysqR///4FvrZChQryyy+/SO/evdVorejiysXFxejuO3qp2rVrl+zYsUMFuW3atJGHHnpIrDaQRSMv1MY++OCDaucRpWswqlelSpUkKCiouMpJREREdG+lpeVMGgcHEQR8SLG82ZuT4uSUMyUni2Rl/bcc/aM6OqKaFNWc/y13dUUkitvdxu/n5iZiwkilQ4cOlRkzZsjmzZtVIy0trQABKvphLQhGQ9XiONxNR2WlIaQkYPRWCAkJkTlz5sjGjRstMpAtdGpB+/bt1UFC57Xdu3dX89rUqlUrBrFERERUskybJoKAUJtGjsxZjr+Gy7Ee9OplvFxrO9SihfHyjRtzlpcvb7z8xAmTilerVi1p3bq1zJ8/X82fOXNGNfS6VVpBYeTOrQ0MDJSoqCgpEUPUouYVLdx2796tdgp5FIZQzU1ERERk9SZMwKhQ/82jRhY+/RQjQP23HLWxsHx53hpZ2LUrb40s5G6ohRpZE4WGhsrIkSNl7ty5qja2WrVqqpLxbjho+3kT0hZyx3tWG8iuXLlSBgwYoJKJkVOh5WQAHjOQJSIiohJBSxnIDekFBjmltw1E3d3zX36b4VcLo2/fvjJq1ChZtGiR6j1q2LBhRrFZQZAWCsinLVXdb73yyisqJwOBLGpm0WOBNsXGxhZPKYmIiIgoD3d3d+nXr59MmDBBwsPDjXofuN0ddgS8f/zxh0RHR6u4rlQEsleuXJGXXnpJXLVqcSIiIiIym9DQUFWh2KVLl0K3WQoODla9TY0fP178/f1lxIgRYo1sdOiKwAS9evWSJ598UlVlWyP0e4uWfOgTF6kRREREVLqlpqaqxuxVqlQRZy2vlcx2zE2J1UzOke3atau8+uqrcuzYMalfv36ehOBu3bqZukkiIiIiIpOZHMg+99xz6u+UKVPyPIdcC2tPGiYiIiKydi+88IL88MMP+T739NNPy7x586RUBrKW2v0CEREREYm+wnHs2LGSn5KUWmlyIJs7v4G5JERERESWxc/PT00lncm9FiB14J133lGt3dDlw7lz59Tyt956S7755pviKCMRERER0d0Hsu+99558++23Mn36dH1nulCvXj35+uuvTd0cEREREdG9CWQxasSXX36pRveys7PTL2/YsKGcMHGMYCIiIiKiezogQvXq1fNtBJaRkXHHBSEiIiIiKtZAtk6dOrJ169Y8y3/++Wdp3LixqZsjIiIiIro3gezEiRPVMGYffPCBqoVdvny56lsWubN4joiIiIgs299//636/4+LizPpdW+//bYa0hav/fXXX8XqAtnu3bvLypUrZcOGDeLm5qaC1+PHj6tlDz30UPGUkoiIiIj0Hn/8cXn44YfzfQ53zhFoHjp0qMDXt27dWsLDw9VQsIWFeG/y5MnyxRdfqNc+8sgjYpX9yLZt21bWr19f9KUhIiIiotsKDQ2V3r17y+XLl6V8+fJGzy1YsECaNWsmDRo0KPD16HkqICDApPc8e/asvlITgbIlMLlGtmrVqnLt2rU8y1E1jedMNXfuXKlcubIaWKFFixaye/fuW66P9xk+fLgEBgaKk5OT1KhRQ1avXm3y+xIRERFZq8cee0x8fX1Vl6iGkpKSZNmyZSrQNSW1ANvx9vaWtWvXSu3atdVYAajxRc2rllKAWmCwtbW13kD2woULalCE3NLS0lSPBqZYsmSJjBkzRiZNmiT79+9XXXh16dJFoqKi8l0/PT1dpS+gDGhcdvLkSfnqq6/U4AxEREREpYW9vb0MHDhQBaA6nU6/HEEs4rT+/fubvM2UlBT58MMP5fvvv5ctW7ZIWFiYfphb/EVNLyC41QJcq0kt+P333/WPEa0b5lTggG3cuFHVrJpi1qxZqqHYkCFD1Py8efNk1apVMn/+fBk/fnye9bE8NjZWtm/fLg4ODmqZqe9JREREVBjhieESkxIj9f3rq/lj0cfEw9FDKnhVkNTMVDUfUjZEPJw8JDIpUiKSIqRhQEO17smYk+Js7yyVvCtJRlaGHI46LNXKVBMvZy+JTo6WywmXpXFgTm9Pp6+dFntbe6lSpopJ5Rs6dKjMmDFDNm/eLA888IBahmATKQem5L5q0I0qYrFq1aqpeTTunzJlinqMGlrU2IKpKQkWUSPbo0cPNaEqedCgQfp5TE8++aTKmZ05c2ah3xi1q/v27ZNOnTr9VxhbWzW/Y8eOAoPpVq1aqdQCtJjDaGJTp07Nt4aYiIiI6G58se8LeeTH/xo0PfnzkzJj+wz1GIFo0y+byr7wfWp+4b8LpcN3HfTrDv5tsLyz5R31GMEw1v0n7B81v/ToUmn5TUv9usNWDZPX/3rd5PLVqlVLNdpCRR+cOXNGNfS6XVpBQVxdXfVBLCCNs6C75Jai0DWy6GoLqlSpInv27BEfH5+7euOYmBgVgCIgNYT5gkYIO3funPz1119qVDHkxeKEvfjii+oXBNIT8oOUB0yahISEuyo3ERERlQ7/a/o/6V27t35+cZ/FqkYWynuWl33P71M1sjCw4UDpXK2zft1vu3+ramTBx9VHrYsaWehbt6+0rtBav+7nXT9XNbJ3IjQ0VEaOHKnaHKE2FoFo+/bt72hb2t1uDSovDdMWLJHJR+38+fNiLgim/fz81BC5GB63adOmKi8X1eoFBbLTpk1TXUUQERERmSLQI1BNmjq+dfSPEaQ2CWyin/d391eTpqZPTf1jBzsHo3V93XzVpAkplxMM34m+ffvKqFGjZNGiRbJw4UIZNmyYxTTEssjGXoBcDLRcw1C1mLp165bvaF+3ghpdBKORkZFGyzFfUO4FqrjRSwFep0HLuoiICJWqkJ8JEyZIfHy8frp06ZJJ5SQiIiKyVO7u7tKvXz8V76AB1uDBg6U0MTmQ/eGHH1QeK/IoXnrpJTW5uLhIx44d1a+BwkL/ZahRRSMxwxpXzCMPNj9t2rRR6QRamgOcOnVKBbjYXn7QRZenp6fRRERERFRShIaGyvXr11XPT0FBQVKa2OhMTH5ADejzzz8vo0ePztMDAbrCwqgPpnS/hYZjGCGiefPmMnv2bFm6dKnKkUWuLLqVQNdaSA8A1KbWrVtXvQb5IKdPn1Yt9hBMv/HGG4V6T+TIoiUfamcZ1BIREVFqaqpKnUQ7IPRrT+Y95qbEaibnyKLBldYhriGkF7z+umkt7lAVHh0drYa5RXpAo0aNZM2aNfoGYOi/DD0ZaCpUqKC6/kIQjdEqEOQiL+S1114zdTeIiIiIyMqZHMgimMTtf+TGGtqwYYN6zlToowxTQaNO5Ia0g507d5r8PkRERESlxQsvvKDSQfPz9NNPq/5iS2Ug+8orr6hb+QcPHlR9l8G2bdvUyBIff/xxcZSRiIiIiEwwZcoU/ahcuZWk1EqTA1l064BeBTD4AfJZtbxZ5Lt27969OMpIRERERCbw8/NTU0l3R73v9uzZU01EREREROZyZ8NIiMjevXv1PRTUqVNHdaVFREREZK0sfRSrkkRXRMfa5ED28uXL0r9/f5UX6+3trZbFxcWpfNnFixdL+fLli6RgRERERPeCNjRrSkqK6hufih+OdX7D4hZ7IPvss89KRkaGqo2tWTNn+LWTJ0/KkCFD1HPoPouIiIjIWmDEUFTORUVFqXkM+lSahnm91zWxCGJxrHHMDUdrvScDIuCXyvbt26Vx48ZGy/ft2ydt27bVR9iWigMiEBERUW4Ih9CnPe4yU/FDEIvOA/L7wVCsAyKgr1jUyOaWlZVV6oZFIyIiopIBARWGvEdL//ziHCo6SCe425rYOw5kZ8yYoYaHnTt3rjRr1kzf8AsjbH344YdFUigiIiIic0CAVVRBFhU/k1MLypQpo9IHMjMzxd4+Jw7WHru5uRmtGxsbK5aGqQVERERElqtYUwtmz559N2UjIiIiIioSJgeygwYNKpp3JiIis8CNONyLy9LpJCvb+HE2Jjwvov7igfb45qxaJ2c7N5ff3GbO4pz18BjPZGfn/FWvvbnM+HU3y2O4PYP1tMdqewbvpT2Xezs5JdD28+bfm0v+m//vOOQ9NgW8poDX6rdw2/fK/3njbRRQ/gL3K//9uP1+S6Fp2yjUusXUBaspN45N2zcppu2av7xSyA2bsk1nBzsZ3qG6lJgBEazd0aij0sqzlXp8LPqYeDh6SAWvCpKamarmQ8qGiIeTh0QmRUpEUoQ0DGio1j0Zc1Kc7Z2lknclycjKkMNRh6VamWri5ewl0cnRcjnhsjQOzOnR4fS102Jvay9VylSRrOws+TfyX6niXUXKuJSRaynX5GL8RWkc0FglmJ+NPateU61sNfWhPRBxQCp5VZJyruXk+o3rcj7uvDT0byh2tnZy/vp5yczOlJByIeo1B8IPSHnP8uLr5ivxqfFy9vpZqe9XXxzsHORi3EW1TzV9crpK+zfiXwlwDxB/d39JTEuU07GnpY5vHbVPl+IvSWJ6opqHw5GHxcfVRwI9AiU5PVlOXjsptX1qi4uDi1xJuCJxqXFS16+u/njiGKAcNzJuyPGY41KjXA1xd3SX8MRwiU6Jlgb+DdS6x6OPi5ujm1T0qihpmWlyNPqoVC9bXTydPNXxDk8Kl0YBjfTH28neSSp7V9Yf76plqoq3s7c63pcSLkmTwCb6443jg+e1443XlXUpK7E3YuVC3AW1XVsbWzl3/Zxk67LV+8L+8P2qPNhf7XijvDh/ON4Z2Rlqf+BgxEEJ8ggSPzc/SUhLkDOxZ6SeXz1xtHOUsPgwSclIkVo+tdS6hyIPqfVwzJPSk+TUtVP6441rBa/XjveRqCOqrNg2tnEi5oTajquDq1xNvKr2Ae+jXbM4Xjje2jWrHW9cr1HJUfrjje1gG9i/9Kx09T7a8cZ62LZ2vFE+B1sHdc3iGkP5tWs2JiVG7Z92vLHfOJY43jiWOC65j7d2zeJ445xo1yyOdwXPCuqaxXWE57VrFq/DdaFds9huoHuguma1413Xt666LlAeXJu1fWvrj7evq6+6ZrXjrV2zON74fBhes7iOAt2DJD41WQ5FHpNKXtXF0dZFLsdflcjkaKniVVvSMrPlZMxxcbR1lbIu+CzckPNxJ8XPpbI42rlJTEqUXLsRJcHutSQzSyeXk86IjTiKl0OQpGWmy+WkE+LtUEHsbNwlIT1GYtMixNexlmRkZ8u11IuSnW0rrnaBkp6ZKVFpp8TVNkDsxENuZMZLUma4eNiFqO+khMzLKih0sQ2SzKxsScg6JY42/mKr85T07ARJyQoXZ6kiOrGTG1lXJUuXJfa6IPXa5OzTYqPzETudp2RkJ0mahIujrrLYiL1k2kSJTtLFQZfTB3i6zTmx05UROykj2ZIiGTZXxVFXUe1Tpk20ZMsNNZ+z7gX1/vZSVrIlVTJsLouDroLYipNkSoxk2ySLo67SzXUviq3OTezFR7IlTTJsLomDLlhsxUUyJVaybeLFUVdFrYvnbMRJ7HV+opMM9VoHXZDYiqtkyXXJsrkujrqqN9e9LDbiIPY6f9FJpiqTgy5AbMVdsiReldlJl/M5z7C5ggxI9bxOsiTd5rx6HY53liRKpk2k2q6N2EqGTQRCdvW+kGZzRux1vmInXpIlSZJpE6HKayN2N9fNUvvz3zEsK3bibXAMK6ly5hzvNHWcctY9L3Y675vH+4Yqo/54q2OYkut4e4i9lDM43uXFVpwlU65Jtk2iOq8564aJrc5VHW+cX8xrxzvnGMYV8njHSZZNrMHxzu8Y4prN73hfFRHbm+tmq+OS93jnfwwNj3e2JKnn/7tmI1U5b33NFny8bXVeN6/ZnONt2jWrHW9cswnGx1tcVJn/O963umYdbx5v7ZoNFFtxU8cwyyZGHHXVCnG8E9T+YV0bsZEMm3D1GmwLwXS6zVn1HnbiWYhr9qzY4f8IdbyT1bZy/x/h71pVBbL3Ko4oLFsppXov7a1//OTPT8qM7TPUY3zZNf2yqewL36fmF/67UDp810G/7uDfBss7W95Rj/HFjnX/CftHzS89ulRaftNSv+6wVcPk9b9eV4+TM5LVuhvObVDzK0+tVPP4soHRa0erCbAMz2EdwGswj20Atolta/CeeG9AWbAuygYoK8qswb5gnwD7iHWxz4BjgGOheeTHR+SLfV+oxwiUsC4uWJize450X9xdv26vpb3k450fq8cISrAuLmD45sA30uWHLvp1BywfIB/884F6jKAV6+6+slvN/3j4R2m3oJ1+3dDfQ+Xtv99Wj3HBY90tF7eo+eXHl0vzr5rr1x3x5wh5bcNr6jGCO6y79sxaNb/69Go1j2AYxq4bK6PWjNK/Fs/9euJX9XjThU1qHkETvLXpLXl+5fP6ddvMbyOLjyxWj3dc2qHWRUAI7215T55Z8Yx+3Y4LO8qCAwv0ARnWxY8LmLVjljyx7An9uo8tekw+2/OZPvjEuvgLWI7nNXgdXg/YHtbF9gHvh/fVoDwoF6CcWBflBuwH9keD/cT+AvYf6+J4AI4P5jU4fjiOgOOK53CcAccd8zgPgPOC86PBecP5A5xPrIsfEKkZWfL6honyzIohci46SY5ejZf757eVdzd9KRuORcrHW3LO49wte+TLLWdlwJIJ0unb3vL270dlwvJD0uqrjtJtwRQZNH+39PzyJ7XuI3N+li4fbZHWc8ZKs3kPy33vbZCGk9dJ488eknozRkvV11dL3Xe+lQcWtpBWM76T1u//JZ2/ekt6Ln1MHvv0H+n9+XYZ/PsAGbp8ogz9dq+88NN6GbXpYXl5xXIZs/RfeW3NHHlz2xMy8bejMuWPY/LejpEyfdtUmbX+lHy8ab98cqSPfL5ztczfdl4W7P9JFpwaIEv2XpLl+6/I0jOTZPnZD2Xt0UjZePKSrI4cJH9f2CQ7z8XKtitr5a/rQ+XApVj593K87Ir9SPbEfSQnIhLldHSC7LnxPzkR97eExabI2YSdcjhzmEQkJkh0Ypqcz/hGLmR9LImpmZKUlikX7EZLvG6zZGTpJMXmmEQ4v6y+BCHefrHEOH6kPzeRTq9Lkv1f6nG67Rm1rs72mtjb2kiSwwq55jRdnOxtxcXBTqKdJkma01rxcLIXB+cral0Xlygp4+ogmS5/Sqzze+Lj7iR+Hk5y3XmaZLutkiAvZynnGafWLeMVLhXLuoqD5ya55jJJqvq4STVfN0l0nSU2Hr9LTX8PqeyXptYN8LksdYM8xbPsTol2GS8Ny3tJowrekuo+V+y8fpZmlcpIw4r2at2KAReleZWy4uf/r0Q6vyItqpSVllXLSrbnN2Ln/aO0qlpOWlTxyFk36JS0qV5OKgSdUPOtq3lL2xAfsfP+XsT7W/W4XQ1f9VyFoKPSvoavVK9wQc23qe4iHWr6inO5nyXb6wvpWMtPTdEu46R88AHpVNtf6lSOyFm3hoN0ruMvHr4rJcPrE+lS118erhsg113fkqCgnfJIvQBpUi0+pww1s6Vr/UDxCVgvqZ4fStcGgfJYg0BJcn9PAoO3yOMNg6R1zZzj0qZWmnRvFCRBwVvU8z0bB6spzfND8Q9aL72aBEuHujY5262VJH2alpfKlXZLnNtEeaJpeTVleX8q5QJWqcePNHBV6zavGaPma1Q+pPanb7PyarIr+6V4+S9Xj7s18lbrNq1xRc3XrXZSzeNxv2YVxNnne3HzXaQe92kSqJ5rWP2cmm8UclHN92rip+Y9/JaIo8+38uR9FdSE81a32nH1+L6akWrd7o291HyZgN/Etuw86d+8gpquuU6QGlUOqsdt6lxX6z7ayEnN+wetlSzvj6V/84pqSnCfLFUr71aPH6ibqtbt3MBGzQdX2CRpntPlqRYV1XTD832pWHGrety5gU6t+2D9dDVfpdJ2SfKYoh4PaFFRMr0/ksDg9erxo40c1brt6iaq+RpV9st1tzfVY0w2ZT8Tn6CV8nTLitKjac512KpOtJqvW/2oRLmMVY8xOfrMF++AX+SZlpWk331+Oeem1mU137jGWTX/dIvyat7N70c1DWxVSZ5pWV4916TGWTXfovZlNf9kcz81XybgF3Hyma8eD2pVSb1n/epH1eM2dWLUur2beap5v6A/VJn73VfhnsURqNAotsZeJSWBePvp7dKqOmtkWSPLGtm7rZEN9qgk11PSZNelfeLhEKxqWyISo+V83AXxdaohN9J1EhZ/QZLT08VJglVgdSnpqOiyyklmhofEp8bJ9fRLkpVWQXQ689e2ONu5io39dbG1SxIv+2riaG+r1nW2dxcvhwARm3RJ0YWpWlYXBw/J0MVKenas+LvWFHtbW0nIuKiu2bLO5cXWNlNi0s6Iv0slcXP0lLSs65KYESWVveqqwPBa2kVxtHOQQPeKYmuTrWpvg9wriqdTGUnOuC4xN65ISJn6Ym9nK+HJF8XWRqSiZ1WxsdHJmeuHJcijopR1KSdJ6XESkRwmtcrhc28v4UkXVU1PlTIhYmdjI8ev/StB7sHi5+4nyekJcjH+vNTzqy/O9o5yKfGiZGSlSW3fWoLuHI9EHZIg90AJ8PBX1yz/j+D/EaX9rk2wZ7D+mq1Zrqa6NnHNYn/r+9dnHBFb9P9HRF6LlACfgEI19iq1gSx7LSAylpKeKdeS0uVacrrEJqfJ9eQMib/x35SAKdV4GabUjOwiL4uDnY3Kx0Ktn/6vI/7a6ucxOWmPHXNqCJ0NJgSgjna24mhvI452N+f1ywz+GizH+3I0HyKiEtxrgebMmTNy9uxZadeunRrtC/EwvwCILAca5CAojUxIlajEVIlJQoCaLteS0m4Gq3h8829y2l0FpPjoezo7iKeLvbg7OYi7k524Odmryd3x5l/DZTf/ujnZ6R/jr6sKVu1UDSQREdHtmBzIXrt2Tfr16yd//fWXClxPnz4tVatWldDQUNXH7MyZM03dJBGZKDE1Q8LjUyUiPvVmoJqm/mKKSEiTqIRUlSuZebN1eWEh9xE5jWXdHMXb1UG8XAqePA3+IkfSFve9iYiILDmQHT16tBr8ICwsTGrXzsk5AQS3Y8aMYSBLVARwy/7y9RS5cv2GXL45XYlL0T/G84WtKdUa2+BvOXdHKefmKGXdDB876oNX1IjyzgoREZXYQHbdunWydu1aKV8+pyGGJiQkRC5ezGmNTUS3F5eSLudjktV0ISZZzt18jFboaG1+O6gNDfB0Fj9PJ/XXX01O4ufprJ/3cXfkbXoiIiqxTA5kk5OTxdXVNc9yDEfr5ORUVOUiKjF5qlfibsipyEQ5GZkoZ6KSVNCKgPV6yq1rVVFbGlzGRcqryVX9DfbOeYzlyCklIiIqzUz+Jmzbtq0sXLhQ3nknpy9V3IbMzs6W6dOnS4cO//W3SlSaoLFjdFKanIpIUgHrqYicwPV0ZKIkp+f0FZwf1JxW9nGVKj7uUuXm30rlcoJWV0cGqkRERLdi8jclAtaOHTvK3r17JT09XcaNGydHjx5VNbLbtm0zdXNEVhm0RiSkyuHL8XLkSrwcupLzF70C5AddOlXzdZeaAR4S4oeAFZObCmAZrBIREd05k79F69WrJ6dOnZI5c+aIh4eHJCUlSa9evWT48OESGBh4F0UhskzxKRmyLyxWDobFyeEr8WrKL2hFG6nK5dykhr+7GpGoZoCn1AxADaubODBPlYiIqMhxQAQiA/g4XLiWIvsuXpd9F2Nl74XrcjoqKc96drY2qna1XrCX1MdU3ktqB3iKi6OdWcpNRERUUhT7gAhxcXGye/duiYqKUvmxhgYOHHgnmyQyW+B6KjJJtp2JkZ3nrsn+sOv51rZiDPgmlcpIg/JeKnitE+ipRo8iIiIi8zE5kF25cqUMGDBApRQgSjbscxKPGciSpbsUmyLbz8bItjPXZPvZaxKTlGb0PIYqRQ1rs0plpOnNqZw7e+QgIiKy+kD2lVdekaFDh8rUqVPz7YbrTsydO1dmzJghERER0rBhQ/n000+lefPmt33d4sWLpX///tK9e3f59ddfi6QsVPKkZWbJrnOx8teJKNl0MkouXksxet7ZwVbuq1xWWlfzkeZVykjdIC/WthIREZXEQPbKlSvy0ksvFVkQu2TJEjUi2Lx586RFixYye/Zs6dKli5w8eVL8/PwKfN2FCxdk7NixqjswotwwVOumE1EqeP3nTIykGHSBhfzWhuW9pE11HzU1rugtTvYMXImIiEp8IIsgE11vVa1atUgKMGvWLHnuuedkyJAhah4B7apVq2T+/Pkyfvz4fF+TlZWl0hsmT54sW7duVTm7RGHXUmTV4XD580i4HLocb/Qchmh9sJafdKjlJ62rlRMPZwezlZOIiIjMFMh27dpVXn31VTl27JjUr19fHByMA4Ju3boVelvoh3bfvn0yYcIE/TJbW1vp1KmT7Nixo8DXTZkyRdXWhoaGqkD2VtLS0tRk2BKOSo6L15JV8Lr6cLgcuWJ8bhtW8JaOtfxUAFs3yDifm4iIiEphIIvaUy2YzA2BAmpLCysmJkat7+/vb7Qc8ydOnMj3Nf/884988803cvDgwUK9x7Rp01TNLZWstIFfD1yRlYeuGgWvtjYiraqVk0frB0rnOgHi68EGWkRERCWZyYFs7u627qXExER55pln5KuvvhIfH59CvQa1vcjBNayRrVChQjGWkopDakaWrDsWKb/suyxbT0dLtu6/fNdWVXOC1y51/dm7ABERUSli1vExEYza2dlJZGSk0XLMBwQE5Fn/7NmzqpHX448/niewtre3Vw3EqlWrZvQaJycnNZF1+vdSnCzec0n+OHRVElMz9cvRNVbPJsHycN0ABq9ERESl1B0FssnJybJ582YJCwtTea6G0KNBYTk6OkrTpk1l48aN0qNHD31givkRI0bkWb9WrVpy+PBho2Vvvvmmqqn9+OOPWdNaQtxIz5Lf/70iP+wMU8PBaoK9XaR3k2Dp1aS8VPZxM2sZiYiIyAoD2QMHDsijjz4qKSkpKqAtW7asynVFd1xogGVKIAu47T9o0CBp1qyZ6jsW3W9hu1ovBhhgITg4WOW6Ojs7S7169Yxe7+3trf7mXk7W50xUkvy466L8vO+yvvYVgxN0bRAofZtVkBZVyootEmGJiIiI7iSQHT16tLq1j26yMA7uzp07Vc8FTz/9tIwaNcrkAvTr10+io6Nl4sSJakCERo0ayZo1a/QNwFDri54MqOQOEbvzXKx8tfWc6vNVU7GsqwxoUVGeaFZByro5mrWMREREZJlsdIgkTIAa0F27dknNmjXVY3STVbt2bbUMNasF9TZgKdDYCwF4fHy8GmKXzCMzK1tWH4mQr7ac06cPoHcsdJf1dMtK0i7El7WvREREpVCCCbGayTWyqH3VakiRSoAaUwSyeMNLly7deamp1PQ+sGTPJflyyzm5EndDLXOyt5UnmpWX0PurShXmvhIREVEhmRzINm7cWPbs2SMhISHSvn17lRKAHNnvv/+eeap02wD2s7/PSGRCzgAV5dwcZWCryvJ0y4rseYCIiIiKP5CdOnWq6iUA3nvvPdUYa9iwYSqwxbCyRIbSMm8GsJvOSkRCqloW5OUswzpUlyealhdnBztzF5GIiIhKQyCLdFqkE2g1r3iMhllEuWVl69TgBR9tOCXh8TkBbKCXswxHANusvDjZM4AlIiKiexzIVq9eXY4ePapqYInys+VUtExdfVxORCTqA9gXO1SXvgxgiYiIyFyBLBp5IYC9du0aA1nK43h4ggpgt56OUfNeLg4y8sHq8kyrSgxgiYiIyPw5su+//768+uqr8vnnn7NxFykxSWkyY81JWbrvkqAzNwc7GxnUqrKMeLC6eLuyD1giIiKykH5ky5Qpo0b1yszMVEPMuri4GD0fGxsrloz9yBZtHuyi3WEyY80JSbg5EhdG4XqtSy2pWM7V3MUjIiIiK1Ss/chiCFmiQ5fj5M1fj8ihyzmDGdQN8pQp3etK00plzV00IiIiKiVMDmQxeheVXslpmTJj7Un5bscFlUbg4WQvY7vUVKNx2XEkLiIiIrLkQBaysrJkxYoVcvz4cTVfp04d6d69u9jb39HmyEpsOxMjr/1ySC5fzxmRq2fjYJnwaC3x83A2d9GIiIioFDI58kTXW926dZOIiAipWbOmWvbBBx+Ir6+vrFy5kg3ASqCE1AyZtvq4/LQ7ZwjiYG8Xeb93fWkb4mvuohEREVEpZnIg++yzz0rdunVl7969quEXXL9+XQYPHizPP/+8bN++vTjKSWay/WyMvLL0X/2gBgNbVZJxD9cSdyfWvhMREZF5mRyNHDx40CiIBTzGcLX33XdfUZePzCQ9M1tmrT8lX2w5q3JhK5VzlQ96N5CWVcuZu2hEREREdxbI1qhRQyIjI1WtrKGoqCg16hdZv7PRSTJq8QE5ciVBzT95XwWZ+HgdcXVkLSwRERFZDvvC9uelmTZtmrz00kvy9ttvS8uWLdWynTt3ypQpU1SuLFm3pXsvycTfjkhqRrZ4uzrI+73qy8P1As1dLCIiIqI7GxABQ9Pa2PzXtZL2Em2Z4Tx6NLBkHBAhf6kZWSqAXbr3sppvU72czHyikQR4sUcCIiIisuIBETZt2lRUZSMLFHYtRV74YZ8cC08Q/DYZ06mGDO9QXWzZLywRERFZsEIFsu3bty/+kpBZbDgWKaOXHpTE1Ewp6+YonzzZWO4P8TF3sYiIiIhu645a76SmpsqhQ4dUA6/s7Gyj59DHLFk+pIPM3XRGPlx3Ss03qegtcwc0kUAvF3MXjYiIiKh4Atk1a9bIwIEDJSYmJs9z1pAjSzn5sON/OSS/Hryq5ge1qiRvdK0jjva25i4aERERUaGZHLmMHDlSnnjiCQkPD1e1sYYTg1jLF5WYKk9+uVMFsfa2NvJez3oyuXs9BrFERERU8mtk0YfsmDFjxN/fv3hKRMXm2NUEefa7PXI1PlW8XBzk86ebSOtqzIclIiIi62RyNVyfPn3k77//Lp7SULEONdv3ix0qiK3q6ya/Dm/DIJaIiIhKfj+yhlJSUlRqga+vr9SvX18cHByMnsdgCZasNPYju+pQuIxeclDSs7KlRZWy8uUzzcTL1fi8EREREZXIfmQN/fTTT7Ju3TpxdnZWNbOGAyXgsaUHsqXNwh0XZNLvRwU/Vx6pFyAf9Wskzg525i4WERER0b1PLXjjjTdk8uTJKkq+cOGCnD9/Xj+dO3fujgoxd+5cqVy5sgqOW7RoIbt37y5w3a+++kratm0rZcqUUVOnTp1uuX5phYr2metOysTfcoLYAS0qypynmjCIJSIiotIbyKanp0u/fv3UsLVFYcmSJarx2KRJk2T//v3SsGFD6dKli+qjNj+oBe7fv78abWzHjh1SoUIF6dy5s1y5cqVIylNSgth3/jgun/51Rs2P7lRD3u1RT+w4UhcRERGV5hzZ0aNHq/zY119/vUgKgBrY++67T+bMmaPm0Y0XglN08zV+/Pjbvh5dfqFmFq9H/7alPUc2O1snb688Kgt3XFTz73SvK8+0qmzuYhERERGZP0cWgeP06dNl7dq10qBBgzyNvWbNmmVS7e6+fftkwoQJ+mWo6UW6AGpbC9v4LCMjQ8qWLZvv82lpaWoyPDglFYLYN349Ij/tDhOkLk/rWV+ebF7R3MUiIiIiKhYmB7KHDx+Wxo0bq8dHjhwxes6w4VdhYHQwBMa5+6TF/IkTJwq1jddee02CgoJU8JufadOmqZzeki4rWycTlh+SpXsvqyB2Rp+G0qdpeXMXi4iIiMhyAlnkplqK999/XxYvXqzyZtFQLD+o7UUOrmGNLFIXSlpNLIacXbbvsiANdlbfRtKjcbC5i0VERERkWYGs5syZM3L27Flp166duLi4qAZGptbI+vj4iJ2dnRotzBDmAwICbvnaDz/8UAWyGzZsUCkOBXFyclJTSYXjPuWPYyqIRWOu2f0ayeMNg8xdLCIiIqJiZ3LXA9euXZOOHTtKjRo15NFHH5Xw8HC1PDQ0VF555RWTtuXo6ChNmzaVjRs36pehsRfmW7VqVeDrkKP7zjvvyJo1a6RZs2ZSmn204bR8u/2Cejy9dwMGsURERFRqmBzIotcCNPAKCwsTV1dX/XJ0yYXA0lS47Y++Yb/77js5fvy4DBs2TJKTk2XIkCHqefREYNgY7IMPPpC33npL5s+fr/qejYiIUFNSUpKUNl9vPSefbDytHk/pXld6MyeWiIiIShGTUwswqhd6LChf3jhoCgkJkYsXc7p8MgUC4OjoaJk4caIKSBs1aqQCYq0BGAJmwz5rP//8c9XbQZ8+fYy2g35o3377bSktFu8Ok3dXHVePX+1SUwayiy0iIiIqZUwOZFFbalgTq4mNjb3jXNQRI0aoKT9oyGUIo4mVdmuPRsiEFYfV4/+1ryovPlDN3EUiIiIisvzUAgwPu3DhQv08GnghrxV5qx06dCjq8lEuBy/FyajFB9Sws/2bV5DxD9cyuZEdERERUamskUXAisZee/fuVbf4x40bJ0ePHlU1stu2bSueUpJyKTZFnv1uj6RmZEuHmr7yTvd6DGKJiIio1DK5RrZevXpy6tQpuf/++6V79+4q1aBXr15y4MABqVaNt7iLS1xKugxasFtiktKlbpCnzHmqidjbmXz6iIiIiEoMGx06Ii1FTBm/11KkZWbJM9/slt3nYyXIy1lWDG8j/p75DwBBREREVFpitTsaECE1NVUOHTokUVFRKj/WULdu3e5kk1QA/M6Y8MthFcR6ONnL/CH3MYglIiIiupNAFl1joW/XmJiYPM8hXzMrK6uoykYiMn/bBVl+4Ioateuzp5tIrQDrqEUmIiIiKm4mJ1mOHDlSnnjiCTWiF2pjDScGsUVr+5kYmbo6p6/YNx6tLW1DfM1dJCIiIiLrDWQjIyPVaFzagAVUfD0UDF+0X7KyddKrSbAMacMBD4iIiIjuKpDFiFq5BymgonUjPUv+9/0+uZ6SIfWDvWRqz/rsZouIiIjobnNk58yZo1ILtm7dKvXr1xcHBwej51966SVTN0m5Gne99sshORaeIOXcHOWLZ5qKs4OduYtFREREZP2B7E8//STr1q0TZ2dnVTNrWFOIxwxk7873Oy/K7/9eFXs07hrQRIK8XcxdJCIiIqKSEci+8cYbMnnyZBk/frzY2rJD/qJ09Gq8vPtHTuOu8Y/UkhZVy5m7SEREREQWy+RIFMPS9uvXj0FsEUtKy5QRiw5Iela2dKrtL6H3VzF3kYiIiIgsmsnR6KBBg2TJkiXFU5pSnBf7xorDcj4mWY3c9eETDdi4i4iIiKioUwvQV+z06dNl7dq10qBBgzyNvWbNmmXqJku9ZXsvy28Hr6pBDz7p31i8XR3NXSQiIiKikhfIHj58WBo3bqweHzlyxOg51iKa7lRkokz8Pec4jnmohjSrXNbcRSIiIiIqmYHspk2biqckpVBaZpa89NMBSc3IlrYhPjKsfTVzF4mIiIjIarDFlhnN3nBaTkQkSlk3R5nZt6HY2rJGm4iIiKiwGMiayb6LsfLF5rPq8dSe9cTPw9ncRSIiIiKyKgxkzSAlPVNeWfqvZOtEejYOlofrBZq7SERERERWh4GsGXzw5wm5cC1FAjyd5e1udc1dHCIiIiKrxED2Htt2Jka+23FRPZ7ep4F4uRh3X0ZEREREhcNA9h5KSM2QV5f9qx4/3bKitKvha+4iEREREVktBrL3OKXganyqVCrnKq8/WtvcxSEiIiKyagxk75E9F2Llx11h6vH7vRqIq6PJXfgSERERkQEGsvdo4IPxvxxSj/s1qyCtqpUzd5GIiIiIrJ5FBLJz586VypUri7Ozs7Ro0UJ27959y/WXLVsmtWrVUuvXr19fVq9eLZZs7qazcjY6WXzcnZhSQERERFRSAtklS5bImDFjZNKkSbJ//35p2LChdOnSRaKiovJdf/v27dK/f38JDQ2VAwcOSI8ePdR05MgRsUSnIhPl87/PqMeTu9UVL1f2UkBERERUFGx0Op1OzAg1sPfdd5/MmTNHzWdnZ0uFChVk5MiRMn78+Dzr9+vXT5KTk+WPP/7QL2vZsqU0atRI5s2bd9v3S0hIEC8vL4mPjxdPT08pTji0T8zbIXsvXpdOtf3kq4HNxMaGw9ASERERFUWsZtYWR+np6bJv3z6ZMGGCfpmtra106tRJduzYke9rsBw1uIZQg/vrr7/mu35aWpqaDA+O4V9wcHAQFxcXuXHjhmRkZOiXOzk5qQmBc1ZWln45UhocHR0lKSlJBd4aV1dXsbe3N9r2/1oGSkpauqqNTUxMNCqbh4eHej22bwgnLTMzU1JSUoyOi7u7uzpmqamp+uV2dnbi5uaWZz+Lc58A74kycZ+4T9wn7hP3ifvEfeI+ORfhPhlu97Z0ZnTlyhXUBuu2b99utPzVV1/VNW/ePN/XODg46BYtWmS0bO7cuTo/P7981580aZJ6j1tNoaGhal38NVyO10Lnzp2Nln/11VdqeZ06dYyWr1mzRi338PAwWn748GFdfHx8nvfFsiNHjhgtw2sB2zJcjvcCvLfhcpQtv/0s7n1CublP3CfuE/eJ+8R94j5xn6SI92nnzp36x7dj1tSCq1evSnBwsMp7bdWqlX75uHHjZPPmzbJr1648r0G0/91336k8Wc1nn30mkydPlsjIyELVyCJ14dKlS/rqav6S4j5xn7hP3CfuE/eJ+8R9SrOIfYqLi5OyZcsWKrXArIEsDiZ28Oeff1YNtjSDBg1SO/Hbb7/leU3FihVVasHLL7+sX4aGYkgt+PffnFGzLCVHloiIiIhMY0qsZtZeCxC5N23aVDZu3Khfhige84Y1tIaw3HB9WL9+fYHrExEREVHJZPbhpVC7ihrYZs2aSfPmzWX27NmqunrIkCHq+YEDB6r0g2nTpqn5UaNGSfv27WXmzJnStWtXWbx4sezdu1e+/PJLM+8JEREREZWqQBbdaUVHR8vEiRMlIiJCdaO1Zs0a8ff3V8+HhYWpHApN69atZdGiRfLmm2/K66+/LiEhISqtoF69embcCyIiIiIqdf3I3mvMkSUiIiKyXFaTI0tEREREdKcYyBIRERGRVTJ7juy9pmVS5O7PjIiIiIjMT4vRCpP9WuoCWa3jXQyKQERERESWG7MhV/ZWSl1jL/RTixHFMHKEjY1Nsb9ffiOJkXXhObR+PIfWj+fQuvH8Wb+Ee3gOEZoiiA0KCjLquSo/pa5GFgekfPny9/x9cdL54bVuPIfWj+fQ+vEcWjeeP+vneY/O4e1qYjVs7EVEREREVomBLBERERFZJQayxczJyUkmTZqk/pJ14jm0fjyH1o/n0Lrx/Fk/Jws9h6WusRcRERERlQyskSUiIiIiq8RAloiIiIisEgNZIiIiIrJKDGSL2dy5c6Vy5cri7OwsLVq0kN27d5u7SFSALVu2yOOPP646YMZgGb/++qvR80gnnzhxogQGBoqLi4t06tRJTp8+bbbykrFp06bJfffdpwY78fPzkx49esjJkyeN1klNTZXhw4dLuXLlxN3dXXr37i2RkZFmKzMZ+/zzz6VBgwb6fipbtWolf/75p/55nj/r8v7776v/S19++WX9Mp5Dy/b222+rc2Y41apVy6LPHwPZYrRkyRIZM2aMauW3f/9+adiwoXTp0kWioqLMXTTKR3JysjpH+PGRn+nTp8snn3wi8+bNk127dombm5s6n/hgk/lt3rxZ/Qe7c+dOWb9+vWRkZEjnzp3VedWMHj1aVq5cKcuWLVPrY5S/Xr16mbXc9B8MVoPgZ9++fbJ371558MEHpXv37nL06FH1PM+f9dizZ4988cUX6oeJIZ5Dy1e3bl0JDw/XT//8849lnz/0WkDFo3nz5rrhw4fr57OysnRBQUG6adOmmbVcdHv4aKxYsUI/n52drQsICNDNmDFDvywuLk7n5OSk++mnn8xUSrqVqKgodR43b96sP18ODg66ZcuW6dc5fvy4WmfHjh1mLCndSpkyZXRff/01z58VSUxM1IWEhOjWr1+va9++vW7UqFFqOc+h5Zs0aZKuYcOG+T5nqeePNbLFJD09XdUq4Paz4fC4mN+xY4dZy0amO3/+vERERBidTwyfh3QRnk/LFB8fr/6WLVtW/cXnEbW0hucQt8wqVqzIc2iBsrKyZPHixapGHSkGPH/WA3dGunbtanSugOfQOpw+fVql2FWtWlUGDBggYWFhFn3+7M32ziVcTEyM+o/Y39/faDnmT5w4YbZy0Z1BEAv5nU/tObIc2dnZKi+vTZs2Uq9ePbUM58nR0VG8vb2N1uU5tCyHDx9WgStSdpCDt2LFCqlTp44cPHiQ588K4McHUumQWpAbP4OWr0WLFvLtt99KzZo1VVrB5MmTpW3btnLkyBGLPX8MZImoRNYI4T9ew9wusg74AkXQihr1n3/+WQYNGqRy8cjyXbp0SUaNGqVy1NHAmazPI488on+M/GYEtpUqVZKlS5eqRs6WiKkFxcTHx0fs7OzytObDfEBAgNnKRXdGO2c8n5ZvxIgR8scff8imTZtU4yENzhNSfuLi4ozW5zm0LKjxqV69ujRt2lT1RIEGmB9//DHPnxXArWc0Zm7SpInY29urCT9C0EgWj1Fzx3NoXby9vaVGjRpy5swZi/0MMpAtxv+M8R/xxo0bjW53Yh63zci6VKlSRX1QDc9nQkKC6r2A59MyoI0egljciv7rr7/UOTOEz6ODg4PROUT3XMj/4jm0XPh/My0tjefPCnTs2FGlhqBGXZuaNWum8iy1xzyH1iUpKUnOnj2rup201M8gUwuKEbrewm0xfHibN28us2fPVg0XhgwZYu6iUQEfWPzqNGzghf980VgIyezIuXz33XclJCREBUlvvfWWSohHf6VkGekEixYtkt9++031JavlbKFRHm6J4W9oaKj6XOKcop/SkSNHqv+AW7Zsae7ik4hMmDBB3drE5y0xMVGdz7///lvWrl3L82cF8LnTctI16KYQfY5qy3kOLdvYsWNVf+pIJ0DXWug+FHeX+/fvb7mfQbP1l1BKfPrpp7qKFSvqHB0dVXdcO3fuNHeRqACbNm1S3YjkngYNGqTvguutt97S+fv7q263OnbsqDt58qS5i0035XfuMC1YsEC/zo0bN3Qvvvii6tLJ1dVV17NnT114eLhZy03/GTp0qK5SpUrq/0tfX1/1GVu3bp3+eZ4/62PY/RbwHFq2fv366QIDA9VnMDg4WM2fOXPGos+fDf4xXxhNRERERHRnmCNLRERERFaJgSwRERERWSUGskRERERklRjIEhEREZFVYiBLRERERFaJgSwRERERWSUGskRERERklRjIEhEREZFVYiBLRGShMDyrjY2NxMXFmbsoREQWiSN7ERFZiAceeEAaNWoks2fPVvPp6ekSGxsr/v7+KqAlIiJj9rnmiYjIQjg6OkpAQIC5i0FEZLGYWkBEZAEGDx4smzdvlo8//ljVvmL69ttvjVILMO/t7S1//PGH1KxZU1xdXaVPnz6SkpIi3333nVSuXFnKlCkjL730kmRlZem3nZaWJmPHjpXg4GBxc3OTFi1aqLQFIiJrxxpZIiILgAD21KlTUq9ePZkyZYpadvTo0TzrIWj95JNPZPHixZKYmCi9evWSnj17qgB39erVcu7cOendu7e0adNG+vXrp14zYsQIOXbsmHpNUFCQrFixQh5++GE5fPiwhISE3PN9JSIqKgxkiYgsgJeXl0olQC2rlk5w4sSJPOtlZGTI559/LtWqVVPzqJH9/vvvJTIyUtzd3aVOnTrSoUMH2bRpkwpkw8LCZMGCBeovglhA7eyaNWvU8qlTp97jPSUiKjoMZImIrAgCXS2IBTQEQ0oBgljDZVFRUeoxal2RZlCjRg2j7SDdoFy5cvew5ERERY+BLBGRFXFwcDCaRw5tfsuys7PV46SkJLGzs5N9+/apv4YMg18iImvEQJaIyEIgtcCwkVZRaNy4sdomamjbtm1bpNsmIjI39lpARGQhkCKwa9cuuXDhgsTExOhrVe8GUgoGDBggAwcOlOXLl8v58+dl9+7dMm3aNFm1alWRlJuIyFwYyBIRWQg0wsLtfzTY8vX1VQ20igIadSGQfeWVV1S3XT169JA9e/ZIxYoVi2T7RETmwpG9iIiIiMgqsUaWiIiIiKwSA1kiIiIiskoMZImIiIjIKjGQJSIiIiKrxECWiIiIiKwSA1kiIiIiskoMZImIiIjIKjGQJSIiIiKrxECWiIiIiKwSA1kiIiIiskoMZImIiIjIKjGQJSIiIiKxRv8HfOr2CMt8+FUAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_time = 500\n",
    "I_sub = 0.5 * u.mA  # V_inf = 0.5 mV < V_th = 1.0 mV\n",
    "inputs = np.ones(n_time) * I_sub\n",
    "V_sub, S_sub = run_lif(lif, inputs)\n",
    "t = np.arange(n_time) * dt\n",
    "\n",
    "plt.figure(figsize=(7, 3))\n",
    "plt.plot(t, V_sub, label='V(t)')\n",
    "plt.axhline(0.0 * u.mV, ls='--', c='k', lw=0.8, label='V_rest')\n",
    "plt.axhline(1.0 * u.mV, ls='--', c='r', lw=0.8, label='V_th')\n",
    "plt.axhline(0.5 * u.mV, ls=':', c='g', lw=1.0, label='V_inf')\n",
    "plt.title('Subthreshold step response (no spikes)')\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('membrane potential V')\n",
    "plt.legend(loc='best')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cbe59fcf543f7ce1",
   "metadata": {},
   "source": [
    "## Experiment 2: Suprathreshold Constant Current (Tonic Spiking)\n",
    "\n",
    "Now choose a current with `V_inf > V_th`. The neuron should emit regular spikes.\n",
    "We'll also estimate the firing rate from the simulated spikes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "82cec9da03b7eb42",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-16T03:03:56.800357Z",
     "start_time": "2025-09-16T03:03:56.643302Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean ISI: 5.5 * msecond\n",
      "Estimated firing rate: 181.81819 * hertz\n"
     ]
    }
   ],
   "source": [
    "n_time = 1500\n",
    "I_sup = 1.5 * u.mA  # V_inf = 1.5 mV > V_th\n",
    "inputs = np.ones(n_time) * I_sup\n",
    "V_sup, S_sup = run_lif(lif, inputs)\n",
    "t = np.arange(n_time) * dt\n",
    "\n",
    "# Basic spike detection from surrogate output (>= 0.5 as spike)\n",
    "spk_mask = np.asarray(S_sup) >= 0.5\n",
    "spk_time, spk_indices = np.where(spk_mask)\n",
    "spike_times = t[spk_time]\n",
    "\n",
    "plt.figure(figsize=(8, 3))\n",
    "plt.plot(t, V_sup, label='V(t)')\n",
    "plt.plot(spike_times, V_sup[spk_time], 'rx', label='spikes')\n",
    "plt.axhline(1.0 * u.mV, ls='--', c='r', lw=0.8, label='V_th')\n",
    "plt.title('Suprathreshold input: tonic spiking')\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('membrane potential V')\n",
    "plt.legend(loc='best')\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "# Estimate firing rate from inter-spike intervals (ISI)\n",
    "if spike_times.size > 1:\n",
    "    isi = u.math.diff(spike_times)\n",
    "    mean_isi = u.math.mean(isi)\n",
    "    firing_rate = (1.0 / mean_isi).to(u.Hz)\n",
    "    print('Mean ISI:', mean_isi)\n",
    "    print('Estimated firing rate:', firing_rate)\n",
    "else:\n",
    "    print('No spikes detected — increase I_sup or duration.')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f78d857408ccf1b8",
   "metadata": {},
   "source": [
    "## Experiment 3: Soft vs Hard Reset\n",
    "\n",
    "`soft` decreases `V` by `(V_th - V_reset)`; `hard` resets directly to `V_reset`.\n",
    "Below we run both with the same current to compare trajectories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6052caeb648f155b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-16T02:58:43.030069Z",
     "start_time": "2025-09-16T02:58:42.778548Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lif_soft = LIFDynamics(1, spk_reset='soft')\n",
    "lif_hard = LIFDynamics(1, spk_reset='hard')\n",
    "brainstate.nn.init_all_states(lif_soft)\n",
    "brainstate.nn.init_all_states(lif_hard)\n",
    "\n",
    "n_time = 1000\n",
    "inputs = np.ones(n_time) * (1.5 * u.mA)\n",
    "V_soft, _ = run_lif(lif_soft, inputs)\n",
    "V_hard, _ = run_lif(lif_hard, inputs)\n",
    "t = np.arange(n_time) * dt\n",
    "\n",
    "plt.figure(figsize=(8, 3))\n",
    "plt.plot(t, V_soft, label='soft reset')\n",
    "plt.plot(t, V_hard, label='hard reset', alpha=0.75)\n",
    "plt.axhline(1.0 * u.mV, ls='--', c='r', lw=0.8, label='V_th')\n",
    "plt.title('Soft vs hard reset under the same input')\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('membrane potential V')\n",
    "plt.legend(loc='best')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f52704c4ea2f63bd",
   "metadata": {},
   "source": [
    "## Experiment 4: F–I Curve (Firing Rate vs Current)\n",
    "\n",
    "We sweep constant inputs and estimate the stationary firing rate at each level.\n",
    "This is a classic characterization for LIF neurons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "21a28dfca66c8359",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-09-16T03:04:48.110406Z",
     "start_time": "2025-09-16T03:04:47.475510Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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o6+WGSd3C0D7UF7aGgRMREREV2J6ztzBy2XFcvvNALfeqXxFjO4fAu5gLbBEDJyIiIsq3hOQ0TF53GosOXFLL/t7umNwzHC1qlIUtY+BERERE+bL19A2MWXYC1xMeTrzbp0llNZill7tt1jLpY+BERERERvn7fiomronCsiNX1XJA6WJqupQmQZYxj1xRYOBEREREj7Q+MhZjV57ArXupkBlSZELe4W1rwsPVCfaEgRMRERHl6mZiCj5eeQLrT1xXy9XKeWJqr3DUq1wK9oiBExEREWWj0Wiw4uhVRKyOwt2kNDg5OuBfLati6DPV4OZsX7VM+hg4ERERkYHY+AcYsywS26JvquVQ/xKqlinU3xv2ztGcbz558mQ0bNgQXl5eKFeuHLp164bo6GiDfVq2bKmGaNe/vfXWWwb7XLp0CZ07d0axYsXU63zwwQdIT08v4qMhIiKy/lqmhfsvod2XO1XQ5OrkiA/a18SKIU8xaLKEGqcdO3ZgyJAhKniSQGfMmDFo164doqKiULx4cd1+gwYNwoQJE3TLEiBpZWRkqKDJ19cXe/bsQWxsLF599VW4uLjg008/LfJjIiIiskaXbidh1LLj2HPutlp+onJJfN4rHNXKeZm7aBbFQSPhpYW4efOmqjGSgKp58+a6Gqe6deviq6++yvE569evx7PPPotr166hfPnyat3s2bMxcuRI9Xqurq6PfN+EhAR4e3sjPj4eJUqUMPFRERERWS6ZiHfengtqypQHaRlwd5FapmD0f7KKymuyBwn5iAPM2lSXlRRY+Pj4GKxfsGABypQpg7CwMIwePRpJSUm6bXv37kXt2rV1QZNo3769OgknT57M8X1SUlLUdv0bERGRvTkbdw8vfL8XE9ZEqaCpSZAPNg5rroYasJegyWqTwzMzMzFs2DA89dRTKkDSevnllxEQEAB/f38cP35c1SRJHtSyZcvU9uvXrxsETUK7LNtyy62KiIgo1OMhIiKyVOkZmfh+53l8veUMUtMz4enmjNGdgvFSw8pwZMBkHYGT5DqdOHECu3btMlj/xhtv6B5LzZKfnx9at26Nc+fOoWrVqgV6L6m1Gj58uG5ZapwqVar0GKUnIiKyDlHXEvDh0mM4cfVha0vLmmXxaffa8C/pYe6iWQWLCJyGDh2KNWvWYOfOnahYsWKe+zZu3Fjdnz17VgVOkhR+4MABg31u3Lih7mVbTtzc3NSNiIjIVvOWDsTcQVxiMsp5uaNRoA/SMzPx7daz+G77OaRnauDt4YKPnw1Bj3oVVI91soLASfLS3377bSxfvhzbt29HYGDgI59z9OhRdS81T6Jp06b45JNPEBcXpxLLxebNm1VyV0hISCEfARERkWXZcCJWDVoZG/9wAl5RurgrXJ0ddevah5bHxG5hKqgiKwqcpHlu4cKFWLlypRrLSZuTJJntHh4eqjlOtnfq1AmlS5dWOU7vvfee6nEXHh6u9pXhCyRA6tu3L6ZOnape46OPPlKvzVolIiKyt6Bp8PzDyNpd/vb9VHUvuUwyKW+n2r6sZbLG4Qhy+6PNmTMH/fv3x+XLl9GnTx+V+3T//n2Vh9S9e3cVGOl3F7x48SIGDx6saq1k/Kd+/frhs88+g7OzcXEhhyMgIiJbaJ5rNmWrQU1TVuVLuGHPqNbsMfcYcYDZm+ryIoGSjOn0KNLrbt26dSYsGRERkXWRnKa8giZxIyFF7de0aukiK5etsahxnIiIiKhgJBHclPtRzhg4ERERWbn4B2lYfviKUfsyIdwGhiMgIiKigtkcdQP/Xh6JuMSUPPeTrCZf74dDE1DBscaJiIjICt2+l4J3Fh3BoP8eVEFTUJniGNGuhgqQsqZ+a5fHdQlhYvhjYo0TERGRFZGOVWuOx2LcqpO4cz8VEge90bwqhrWpDncXJ1Qr55ltHCepaZKgqUPYwzEQqeAYOBEREVmJGwnJ+GjFCdU8J4J9vTC1VzjCK5bU7SPBUdsQ32wjh7OmyTQYOBEREVlBLdPvh65g4pooJCanw8XJAUNaVcO/WlZTI4JnJUEShxwoHAyciIiILNiVv5Mwelkk/jhzSy2HV/RWtUzBvhyw2RwYOBEREVmgzEwNFuy/iM/Wn8b91Ay4OTtieNsaGNgsEM5O7NtlLgyciIiILEzMrfsYufS4ylMSDauUUnPMBZX1NHfR7B4DJyIiIguab+7nXTGYtikaKemZKObqhJEdgtG3SQAcmdxtERg4ERERWYC/biTigyXHcezyXbXcrFoZTO5RG5V8ipm7aKSHgRMREZEZpWVkYvb2c5ix9QzSMjTwcnfGR51r4YUGleDgwFomS8PAiYiIyExOXI1XtUynYhPUcpta5TCpW201YCVZJgZORERERSw5LQMztpzB9zvPq7ymUsVcML5rKLrW8Wctk4Vj4ERERFSEDl28gw+XHMe5m/fVcudwP0R0DUUZTzdzF42MwMCJiIioCCSlpmPaxr8wZ08MNBqgrJcbJj4Xhg5hvuYuGuUDAyciIqJCtufsLYxaFolLd5LUcq/6FTG2cwi8i7mYu2iUTwyciIiICklCchomrzuNRQcuqWV/b3dM7hmOFjXKmrtoVEAMnIiIiArBttNxGLM8ErHxyWq5T5PKajBLL3fWMlkzBk5EREQmdDcpFRNWR2HZkatqOaB0MTVdSpOg0uYuGpkAAyciIiITWR8Zi7ErT+LWvRTIDCkyIe/wtjXh4epk7qKRiTBwIiIiekw3E1MwbtUJrIu8rparlfPE1F7hqFe5lLmLRibGwImIiKiANBoNVhy9iojVUbiblAYnRwf8q2VVDH2mGtycWctkixg4ERERFUBs/AOMWRaJbdE31XKIXwlVyxRWwdvcRaNCxMCJiIgon7VMiw5cxuR1p5CYkg5XJ0e826Y63mgeBBcnR3MXjwoZAyciIiIjXbqdhFHLjmPPudtq+YnKJTG1Zziql/cyd9GoiDBwIiIiegSZiHfengv4fGM0HqRlwN3FER+0D0b/J6uovCayHwyciIiI8nA27h5GLj2OQxf/VstNgnzUuEwBpYubu2hkBmZtjJ08eTIaNmwILy8vlCtXDt26dUN0dLTBPsnJyRgyZAhKly4NT09P9OzZEzdu3DDY59KlS+jcuTOKFSumXueDDz5Aenp6ER8NERFZc43S3nO3sfLoVXUvy+kZmfhu+1l0mvGHCpo83ZzxSfcwLHy9CYMmO2bWGqcdO3aooEiCJwl0xowZg3bt2iEqKgrFiz+8KN977z2sXbsWv//+O7y9vTF06FD06NEDu3fvVtszMjJU0OTr64s9e/YgNjYWr776KlxcXPDpp5+a8/CIiMgKbDgRq4YT0E6NIsp4uqKYq7NuUt6WNcvi0+614V/Sw4wlJUvgoJHuAUbKzMxUwc4ff/yBixcvIikpCWXLlsUTTzyBNm3aoFKlSo9VmJs3b6oaI3mP5s2bIz4+Xr3+woUL0atXL7XP6dOnUatWLezduxdNmjTB+vXr8eyzz+LatWsoX7682mf27NkYOXKkej1XV9dHvm9CQoIKyuT9SpQo8VjHQERE1hU0DZ5/GLl9ERZzdcLE58LQo14FODgwl8lW5ScOMKqp7sGDB5g0aZIKjDp16qSClbt378LJyQlnz57FuHHjEBgYqLbt27evwAWXAgsfHx91f+jQIaSlpamgTCs4OBiVK1dWgZOQ+9q1a+uCJtG+fXt1Ek6ePFngshARkW2T5jipacqr9sDL3RndnmDQRPlsqqtRowaaNm2KH3/8EW3btlXNYFlJDZTUDPXu3Rv//ve/MWjQoHwVRGqzhg0bhqeeegphYWFq3fXr11WNUcmSJQ32lSBJtmn30Q+atNu123KSkpKibloSZBERkX05EHPHoHkuJzcSUtR+Tatygl7KR+C0adMm1TyWl4CAAIwePRojRoxQydr5JblOJ06cwK5du1AUSekRERGF/j5ERGS54hKTTbof2QejmuoeFTTpk9qoqlWr5qsQkvC9Zs0abNu2DRUrVtStl4Tv1NRU1SyoT3rVyTbtPll72WmXtftkJQGeNAtqb5cvX85XeYmIyLrdS0nH2uOxRu1bzsu90MtDNjwcQVBQEAYMGGDQ1CVu3bqltuWH5KVL0LR8+XJs3bpV5Unpq1+/vgrEtmzZolsnwxVIjZY0HQq5j4yMRFxcnG6fzZs3q+SukJCQHN/Xzc1Nbde/ERGRffjjzE20n74Tm6IMf3RnJVlNft7uaBT4MO+WqEDDEVy4cAHOzs54+umnsWrVKl2tjgwLIHlO+W2ek7yolStXqrGctDlJktnu4eGh7gcOHIjhw4erhHEJcN5++20VLEmPOiHDF0iA1LdvX0ydOlW9xkcffaReWwIkIiIiEf8gDZ+sjcJvB6+o5YqlPNCrXkV8veWMWtZPEtemgo/rEsKRwenxapykZ8GGDRtUk5rUCP35558oqFmzZqmmspYtW8LPz093W7x4sW6f6dOnq+EGZOBLGaJAArVly5bptkvPPmnmk3sJqPr06aPGcZowYUKBy0VERLZlc9QNtP1yhwqapIOcTJWycVhzDGtbA7P61IOvt2FznCzL+g5hfmYrM9nAOE7C0dFR1erIeEuSK/T111/jhx9+UL3t/P39Vc2TteE4TkREtun2vRQ15MCqY9fUclCZ4pjaKxwNqvhkG5pAes9JIrjkNEnzHGua7EdCPuKAfDfV6Y9lIb3TQkND1dADL730UsFKS0REZGJSJ7DmeCzGrTqJO/dTITHQG82rYlib6nB3ccq2vwRJHHKAjJHvwClrBZU0jUkvuu7du+f3pYiIiEwuLiEZ/15xQjXPiWBfL1XLFF7RcExAoiIJnGSgyqwkt+jYsWNqOhQiIiJzkB/2Sw5dwcQ1UUhIToeLkwOGtKqGf7WsBldns85pTzbEZJP8ymjdWUfwJiIiKgpX/k7CmOUnsPOvm2o5vKK3qmUK9mXeKpkpcJKJfI2Zq+fw4cOPWyYiIiKjZGZqsODAJXy27hTup2aomqXhbWvg9WaBcHZiLROZMXDq1q2bQXWoJIa/9dZbugl5iYiIilLMrfsYufS46g0nGgSUwpRe4aha1tPcRSMblu/hCLRkwErJa8rvaOGWiMMREBFZDxk64OddMZi2KRop6Zko5uqEkR2C0bdJABw5hABZ2nAERERE5vLXjUR8sOQ4jl1+OIfpU9VK47Me4ajkU8zcRSM7wcCJiIgsXlpGJmZvP4cZW88gLUMDLzdnfPRsLbzQoJJR+bdEpsLAiYiILNqJq/GqlulUbIJabh1cDp90r51tmhQiiwqcZsyYYbCcnp6OuXPnokyZMgbr33nnHdOVjoiI7FZyWgZmbDmD73eeV3lNpYq5YHzXUHSt489aJrL85PDAwMBHv5iDA86fPw9rw+RwIiLLcuji3/hwyTGcu3lfLXcO90NE11CU8XQzd9HIBhVKcnhMTIwpykZERJSrpNR0TNv4F+bsiYH8rC/r5YaJz4WhQ5ivuYtGpDDHiYiILMKec7cwamkkLt1JUsu96lfE2M4h8C7mYu6iEekYNazqr7/+CmNdvnwZu3fvNnp/IiKyb4nJaRizPBIv/7hfBU3+3u6YO6Ahpj1fh0ETWWfgNGvWLNSqVQtTp07FqVOnsm2XNsF169bh5ZdfRr169XD79u3CKCsREdmYbdFxaDd9Jxbuv6SW+zSpjI3vNUfLmuXMXTSigjfV7dixA6tWrcLMmTMxevRoFC9eXE3o6+7ujr///hvXr19Xvev69++PEydOcLJfIiLK092kVExYE4Vlh6+q5YDSxdRAlk2rljZ30YhMO+XKrVu3sGvXLly8eBEPHjxQAZNMACw3R0frnFCRveqIiIrOhhOx+GjFSdy6lwIZVWDgU4F4v11NeLg6mbtoZKcSCnPKFQmU9Cf8JSIiMsbNxBSMX3USayNj1XK1cp6Y2isc9SqXMnfRiIzGXnVERFSopGFj5dFrGL/6JO4mpcHJ0QGDW1TF262rwc2ZtUxkXRg4ERFRoYmNf4B/Lz+Brafj1HKIXwlVyxRWwdvcRSMqEAZORERUKLVMv/55GZ+uPYXElHS4OjnindbV8GaLqnBxss58WCLBwImIiEzq8p0kjFp2HLvPPhyapm6lkvi8Vziql/cyd9GIzBc4paamqmlYqlatCmdnxl9ERPZEJt09EHMHcYnJKOfljkaBPpBpd+ftvYCpG6LxIC0D7i6OGNGuJgY8FajymohsQb4jnqSkJLz99tuYN2+eWv7rr78QFBSk1lWoUAGjRo0qjHISEZEFDScQsToKsfHJunVlPV1RwsNFNylv40AfTOkZjiplipuxpESml++GZhkA89ixY9i+fbsaAFOrTZs2WLx4sanLR0REFhY0DZ5/2CBoEjfvpaqgyc3ZEZO6hWHRoCYMmsgm5bvGacWKFSpAatKkCRxk5LJ/hIaG4ty5c6YuHxERWVDznNQ05TVqsreHC15qVBmObJojG5XvGqebN2+iXLnscwjdv3/fIJAiIiLbIjlNWWuasopLTFH7EdmqfAdODRo0wNq1a3XL2mDpp59+QtOmTU1bOiIishiSCG7K/Yjsoqnu008/RceOHREVFYX09HR8/fXX6vGePXvUZMBERGSjjJzZVHrZEdmqfNc4NWvWDEePHlVBU+3atbFp0ybVdLd3717Ur18/X6+1c+dOdOnSBf7+/qrmSvKn9PXv31+t17916NDBYJ87d+7glVdeUZPylSxZEgMHDsS9e/fye1hERJSHbdFxGLvyRJ77SPuDn/fDoQmIbFWBBmCSsZt+/PHHx35zyYuqU6cOXnvtNfTo0SPHfSRQmjNnjm7Zzc3NYLsETbGxsdi8eTPS0tIwYMAAvPHGG1i4cOFjl4+IyN5lZmowc+tZfLXlL2g0QEDpYrh4O0kFSfoVUNoM13FdQjhmE9m0fAdOTk5OKlDJmiB++/ZttS4jI8Po15ImP7nlRQIlX1/fHLedOnUKGzZswJ9//qlyr8TMmTPRqVMnTJs2TdVkERFRwcQ/SMPwxUex5Z955l5uXFkFRttOx2Ubx8nX211t6xDmZ8YSE1lg4CTzD+UkJSUFrq6uMDUZL0oCslKlSuGZZ57BpEmTULp0abVNmgeleU4bNGnHk3J0dMT+/fvRvXt3k5eHiMgenL6egDd/OaRql1z/GZvphQaV1DYJjtqG+GYbOZw1TWQPjA6cZsyYoe4lz0h60Hl6euq2SS2T5CsFBwebtHDSTCdNeIGBgWqMqDFjxqgaKgmYpObr+vXr2Wq+ZPoXHx8ftS03EuTJTSshIcGk5SYismYrj17FqKWRatqUCiU9MLtPfdSu6G2wjwRJTas+/BFLZE+MDpymT5+uq3GaPXu2Cly0pKapSpUqar0p9e7dW/dYEtHDw8NVfpXUQrVu3brArzt58mRERESYqJRERLYhLSMTn647hTm7L6jlp6uXwYzeT6BUcdO3JhDZfOAkE/qKVq1aYdmyZarprKjJnHhlypTB2bNnVeAkuU9xcQ/b3rWkt5/0tMstL0o7bczw4cMNapwqVXpYBU1EZI+kyW3ogiM4cOHh4JVDWlXF8LY12fxG9Lg5Ttu2bYO5XLlyRSWh+/k9TD6UATfv3r2LQ4cO6YZC2Lp1KzIzM9G4ceM8E86z9s4jIrJXhy7eUfPPyajfXm7O+OKFOmgXmvuPTyJ75lzQAGbVqlW4dOkSUlNTDbZ9+eWXRr+OjLcktUf6tVoyRpTkKMlNmtN69uypao8kx+nDDz9EtWrV0L59e7V/rVq1VB7UoEGDVDOhDEcwdOhQ1cTHHnVERHmT1Iv/7r2IiWuikJ6pQfVynvi+b30Elf3/HFYieszAacuWLejatatqNjt9+jTCwsJw4cIF9R+wXr16+XqtgwcPqqY/LW3zWb9+/TBr1iwcP34c8+bNU7VKEgi1a9cOEydONKgtWrBggQqWpOlOetNJoKVNZCciopw9SM3AmOWRWH7kqlruHO6HqT3DUdytQL+nieyGgya38QVy0ahRI9WzTWqDvLy8cOzYMdWzTQailNqfwYMHw9pIjpO3tzfi4+PVCORERLbs0u0kvDn/EE7FJqgcplEdgvH604GcqJ3sVkI+4oB8T7kig06++uqruq7/Dx48UEMTTJgwAVOmTCl4qYmIqNDJ4JXPzvxDBU2li7ti/sDGGNQ8iEETkZHyHTgVL15cl9ckSdqSe6R169at/L4cEREV0dQpX/3vL7w2708kJKejbqWSWPNOM47FRJRP+W7MbtKkCXbt2qUSs2Vqk/fffx+RkZFqiALZRkREliU+KQ3v/XYUW/+ZOuWVxpXxcZcQuDn//3h8RFRIgZP0mpPecELynOTx4sWLUb169Xz1qCMiosInTXJvzf//qVM+6RaG5/+ZOoWICjlwkqlVZCgCGcFb22xn6tHCiYjIdFOnjFx6HMlpmWrqFBlqIKyC4dQpRFSIgZNMsyJDAkiCuEyuS0REljl1yidrT2HuHk6dQmT2pjoZt+n8+fNq4l0iIrIscQnJGLLwMP688LdaHtqqGt5rW4NTpxCZK3CaNGkSRowYoQailGlOpLlOH8dBIiIyj4MX7uBfCzh1CpFFDYApo3Prnqw37oe8jCxLHpS14QCYRGTN5PN33p4LmLT2FKdOISrkOMCqJvklIiJDnDqFqGjl+39WixYtCqckRESULxdv38ebvxzC6euJKodpdMdgDGzGqVOIChN/khARWenUKe/+ekSNAl7G0xUzX6rHUcCJigADJyIiK5s6ZcbWM/h6yxlIhuoTlUviu1fqwc/bw9xFI7ILDJyIiKx06pQ+TSpj7LOcOoWoKDFwIiKykqlTJJ/p0p0kuMnUKd1ro1f9iuYuFpHdYeBERGThVhy5ilHLHk6dUrGUB2b34dQpRFYTOD3xxBM59tiQde7u7qhWrRr69++PVq1amaqMRER2KevUKc1rlMXXL9bl1ClEZvT/o1kaqUOHDmrKFRkxXIIjuXl6euLcuXNo2LAhYmNj0aZNG6xcubJwSkxEZCdTp7z84z5d0CRTp8zp35BBE5G11TjdunUL77//PsaOHZttKpaLFy9i06ZNGDdunJqS5bnnnjNlWYmI7GbqlMELDuMmp04hsv4pV2RI8kOHDqkmOX1nz55Vc9fJcOWnT59WtU+JiYmwBpxyhYgsceqUGuU9VT4Tp04hsuIpVySPac+ePdkCJ1kn20RmZqbuMRERGTd1yuhlx7Hi6DW1/Gy4H6Zw6hQii5Pv/5Fvv/023nrrLVXrJLVK4s8//8RPP/2EMWPGqOWNGzeibt26pi8tEZEN4tQpRDbcVCcWLFiAb775BtHR0Wq5Zs2aKqB6+eWX1fKDBw90veysAZvqiMhctp6+gWG/HtVNnfLNy/XQJIhTpxBZahxQoMDJ1jBwIqLClpGpwYGYO4hLTEY5L3c0CCiFb7adVVOnCJk6ZdYr9eHrbR0/OIlsSaHmOGmlpqYiLi5O5TPpq1y5ckFfkojIJm04EYuI1VGIjU/WrZPRv1PSH35+9m0SoKZOcXXO9wgxRFTE8h04nTlzBq+99ppKBtcnFVfSPJeRkWHK8hERWX3QNHj+YWSt2tcGTf2aBiDiuTCzlI2IiiBwklHBnZ2dsWbNGvj5+TF5kYgoj+Y5qWnKKx9iU9QNfNwlVCWFE5ENBk5Hjx5VPeqCg4MLp0RERDZCcpr0m+dyIttlv6ZVmRBOZA3y3aAeEhKiRg8nIqK8SSK4KfcjIisMnKZMmYIPP/wQ27dvx+3bt1Umuv6NiIgekt5zptyPiKwwcJIJfPft24fWrVujXLlyKFWqlLqVLFlS3efHzp070aVLF/j7+6tcqRUrVmRLOP/4449VLpWHh4d6b0lO13fnzh288sorqvuglGHgwIG4d+9efg+LiMjkGgX6oJyXW67bJavJz9td7UdENprjtG3bNpO9+f3791GnTh3VS69Hjx7Ztk+dOhUzZszAvHnzEBgYqCYWbt++PaKionSDa0rQFBsbi82bNyMtLQ0DBgzAG2+8gYULF5qsnEREBSEJ31XLeiIuMSXbNm0q+LguIUwMJ7IiFjMAptQ4LV++HN26dVPLUiypiXr//fcxYsQItU4Gpipfvjzmzp2L3r1749SpUyrnSqZ8adCggdpnw4YN6NSpE65cuaKebwwOgElEheHIpb/R/buHQ7eULu6K2/dTddukpkmCpg5hfmYsIREVygCYx48fR1hYGBwdHdXjvISHh8MUYmJicP36ddU8pyUH1bhxY+zdu1cFTnIvzXPaoEnI/lLO/fv3o3v37iYpCxFRfmVmajB+1Un1uGe9ipjaK9xg5HBpnmNNE5H1MSpwkgl7JYiRnCZ5LLVDOVVUmXIATHk/ITVM+mRZu01bJn0yxpSPj49un5ykpKSomxaT2onI1JYcuoJjV+Lh6eaMkR1rqiCJQw4Q2UngJLU/ZcuW1T22dpMnT0ZERIS5i0FENir+QRqmbDitHr/bujp7zRHZW6+6gIAAVZskydcScMj8dLIup5up+Pr6qvsbN24YrJdl7Ta5l/ny9KWnp6uedtp9cjJ69GjVjqm9Xb582WTlJiL6+n9nVD5T1bLF0e/JKuYuDhGZazgCFxcXLF26FEVBetFJ8LNlyxaDJjXJXWratKlalvu7d++qkcy1tm7dqgI7yYXKjZubm0r+0r8REZnCmRuJmLf3gno8rksoJ+4lsjH5/h8tvd6yjrdUUDLekkzhIjdtM6A8vnTpkqrhGjZsGCZNmoRVq1YhMjISr776quopp+15V6tWLXTo0AGDBg3CgQMHsHv3bgwdOlQljhvbo46IyFQk93P86pNqjrq2IeXRvMbDFAcisuNxnKpXr44JEyaoIKV+/fooXry4wfZ33nnH6Nc6ePAgWrVqpVsePny4uu/Xr58ackBGKJexnmRcJqlZatasmRpuQDuGk1iwYIEKlmRATulN17NnTzX2ExFRUdt48jp2n72tapnGdg4xd3GIyBLGcZImtFxfzMEB58+fh7XhOE5E9LiS0zLQ+osduHr3Ad5+phreb1fT3EUiInON46TPFnrVERGZ2uwd51TQ5O/tjn+1rGbu4hBRIWHWIhHRY7rydxJmbT+nHo/pXAserk7mLhIRFRKjapwk92jixIkqn0mbh5SbL7/80lRlIyKyCp+uO4WU9Ew0CfJB59qcQoUI9h44HTlyRI3hpH2cV44TEZE92X32FtZFXofMnjK+ayg/B4lsnFGB07Zt21TStyROyWMiIgLSMjIRsfrhfHR9mwQg2JedS4hsnWN+hiG4efOmbvnFF1/MNqo3EZE9+WXvRfx14x5KFXPB8LbsRUdkD4wOnLKOWrBu3To1xhIRkT26dS8F0//3l3r8QftgeBdzMXeRiKgIsFcdEVEBTNsYjcTkdIRVKIEXG1Yyd3GIyNICJ0l4zJr0yCRIIrJHx6/cxeKDDycHH98lFE6SGU5EdsE5P011/fv3VxPkiuTkZLz11lvZplxZtmyZ6UtJRGQhMjM1GLfqJCR7ofsTFdCgio+5i0RElhg4yfxx+vr06VMY5SEismjLjlzFkUt3UdzVCaM6Bpu7OERkqYHTnDlzCrckREQWLjE5DZ+tP60ev926OsqX+P8Jx4nIPjA5nIjISDO2nFG96YLKFMdrT+U+4TkR2S4GTkRERjgbdw9zdl9Qj8d2CYGrMz8+iewR/+cTERnROUZGCE/P1KBNrXJoVbOcuYtERGbCwImI6BE2R93AH2duwdXJER91DjF3cYjIjBg4ERHlITktAxPXRqnHrz8diCplDIdgISL7wsCJiCgPP+48j8t3HsC3hDuGtKpm7uIQkZkxcCIiysW1uw/w7faz6vHoTsEo7mb0CC5EZKMYOBER5eLTdaeQnJaJRlV80LWOv7mLQ0QWgIETEVEO9p67jTXHYyHT0I3vGsq5OYlIYeBERJRFekamGn5AvNI4ACH+JcxdJCKyEAyciIiyWLD/Ek5fT0TJYi4Y3raGuYtDRBaEgRMRkZ4791PxxaZo9fj9djVRqriruYtERBaEgRMRkZ7PN0YjITkdtfxK4OVGlc1dHCKyMAyciIj+ceJqPH7985J6HNE1FE6SGU5EpIeBExHRP/PRjVt1EhoN8FxdfzQK9DF3kYjIAjFwIiICsOLoVRy6+DeKuTphdMda5i4OEVkoBk5EZPfupaRj8rrT6rFMq+Lr7W7uIhGRhWLgRER2b+bWM4hLTEFA6WJqIl8iIqsMnMaPH69G69W/BQcH67YnJydjyJAhKF26NDw9PdGzZ0/cuHHDrGUmIuty/uY9/LwrRj3++NkQuDk7mbtIRGTBLDpwEqGhoYiNjdXddu3apdv23nvvYfXq1fj999+xY8cOXLt2DT169DBreYnIukxcE4W0DA1a1SyL1rXKm7s4RGThLH6qb2dnZ/j6+mZbHx8fj//85z9YuHAhnnnmGbVuzpw5qFWrFvbt24cmTZqYobREZE22nLqBbdE34eLkgLHPhpi7OERkBSy+xunMmTPw9/dHUFAQXnnlFVy69HCMlUOHDiEtLQ1t2rTR7SvNeJUrV8bevXvzfM2UlBQkJCQY3IjIvqSkZ2DCmij1eGCzIASV9TR3kYjIClh04NS4cWPMnTsXGzZswKxZsxATE4Onn34aiYmJuH79OlxdXVGyZEmD55QvX15ty8vkyZPh7e2tu1WqVKmQj4SILM1Pf8Tg4u0klPNyw9Bnqpm7OERkJSy6qa5jx466x+Hh4SqQCggIwG+//QYPD48Cv+7o0aMxfPhw3bLUODF4IrIfsfEP8M3Ws+rx6E7B8HSz6I9CIrIgFl3jlJXULtWoUQNnz55VeU+pqam4e/euwT7Sqy6nnCh9bm5uKFGihMGNiOyHjNn0IC0D9QNKoVvdCuYuDhFZEasKnO7du4dz587Bz88P9evXh4uLC7Zs2aLbHh0drXKgmjZtatZyEpHlOhBzB6uOXYODw8P56GSYEyIiY1l0/fSIESPQpUsX1TwnQw2MGzcOTk5OeOmll1Ru0sCBA1WTm4+Pj6o1evvtt1XQxB51RJSTjMyH89GJlxpVRlgFb3MXiYisjEUHTleuXFFB0u3bt1G2bFk0a9ZMDTUgj8X06dPh6OioBr6UnnLt27fHd999Z+5iE5GFWnjgEk7FJqCEuzNGtKtp7uIQkRVy0MiU4HZOksOlBkvGhmK+E5Ft+vt+Klp9sR13k9JUE12/J6uYu0hEZIVxgFXlOBERFdQXm6NV0BTs64VXGlc2d3GIyEoxcCIim3fyWjwW7n84eO74rqFwduJHHxEVDD89iMimSTZCxKooZGqAZ8P90CSotLmLRERWjIETEdk0GXrgwIU78HBxwphOtcxdHCKycgyciMhm3U9JV4NdiiGtqsK/ZMFnHCAiEgyciMhmfbvtLK4nJKOSjwdefzrI3MUhIhvAwImIbNKFW/fVRL5ibOcQuLs4mbtIRGQDGDgRkU2atDYKqRmZaF6jLNqGlDd3cYjIRjBwIiKbsy06Dv87FQdnRwd8/GwI56MjIpNh4ERENiU1PRMTVkepx681C0S1cp7mLhIR2RAGTkRkU37eHYOYW/dRxtMNbz9TzdzFISIbw8CJiGzGjYRkzNxyRj0e1TEYXu4u5i4SEdkYBk5EZDM+W38a91Mz8ETlkujxRAVzF4eIbBADJyKyCQcv3MHyI1cheeARXUPh6MiEcCIyPQZORGT1MjI1GL/6pHr8YoNKCK9Y0txFIiIbxcCJiKze4j8v48TVBHi5O2NE+5rmLg4R2TAGTkRk1eKT0vD5xofz0Q1vW0P1piMiKiwMnIjIqn25ORp/J6WhRnlP9GkSYO7iEJGNY+BERFbr9PUE/LLvono8vksoXJz4kUZEhYufMkRklTQaDcavOolMDdCpti+erFbG3EUiIjvAwImIrNLayFjsO38H7i6OGNOplrmLQ0R2goETEVmdpNR0fLr2lHo8uEU1VCxVzNxFIiI7wcCJiKzOrO3ncC0+GRVKeuDNFkHmLg4R2REGTkRkVS7dTsL3O8+rx2OfrQV3FydzF4mI7AgDJyKyKhPXRiE1PRPNqpVB+1BfcxeHiOwMAycisho7/rqJzVE34OzogHFdQuAgE9MRERUhBk5EZBWklinin/no+j1ZBdXLe5m7SERkhxg4EZFVmLfnAs7fvI8ynq54t011cxeHiOwUAycisnhxicn4essZ9fjDDsEo4e5i7iIRkZ1yNncBbFlGpgYHYu6oD/1yXu5oFOgDJ0frzcng8Vg2Wz6epYeu4F5KOupU9EavehXNXTQismM2Ezh9++23+Pzzz3H9+nXUqVMHM2fORKNGjcxWng0nYhGxOgqx8cm6dX7e7iqhtUOYH6wNj8ey2cPxCOlF52jFwSARWT+baKpbvHgxhg8fjnHjxuHw4cMqcGrfvj3i4uLM9qE/eP7hbB/61+OT1XrZbk14PJbNXo5HfL4x2uqOh4hsi00ETl9++SUGDRqEAQMGICQkBLNnz0axYsXw888/m6V5QX4pa3LYpl0n22U/a8DjsWz2dDywwuMhItvjoJEpxq1YamqqCpKWLFmCbt266db369cPd+/excqVK7M9JyUlRd20EhISUKlSJcTHx6NEiRKPVZ69527jpR/3PXK/0sVd4OZs+SMep6Rn4Pb9tEfux+MxD3s9nkWDmqBp1dJFUiYisn0JCQnw9vY2Kg6w+hynW7duISMjA+XLlzdYL8unT5/O8TmTJ09GREREoZRHElmN8fDL4dFfENaCx2PZbO14jP1/RkRkalYfOBXE6NGjVU5U1honU5DeTMb4tFsYalcsCUsXeeUuxqw48cj9eDzmYa/HY+z/MyIiU7P6wKlMmTJwcnLCjRs3DNbLsq9vzvNYubm5qVthkC7g0ptJEnNzagOV/kC+3u54sVFlq+gqHuJfAjO3neXxWCh7PR75f0ZEZA5Wnxzu6uqK+vXrY8uWLbp1mZmZarlp06ZFXh75cpIu4CLr15R2WbZbw5eY4PFYNh4PEVHRsvrASUiz248//oh58+bh1KlTGDx4MO7fv6962ZmDjJszq0899ctYnyzLemsbV4fHY9l4PERERcfqe9VpffPNN7oBMOvWrYsZM2agcePGJs+mzw9bHsmZx2N5eDxERAWTnzjAZgKnx1FYgRMRERHZVhxgE011REREREWBgRMRERGRkRg4ERERERmJgRMRERGRvQyAaQra/HhJDiMiIiL7kvDP978x/eUYOAFITExU96aadoWIiIisMx6Q3nV54XAE/4w0fu3aNXh5ecHBwfzjxGjnzrt8+bLdDo/Ac8BzIHgOeA4EzwHPQWGfAwmFJGjy9/eHo2PeWUyscZJEL0dHVKxYEZZGLgx7/Q+ixXPAcyB4DngOBM8Bz0FhnoNH1TRpMTmciIiIyEgMnIiIiIiMxMDJArm5uWHcuHHq3l7xHPAcCJ4DngPBc8BzYEnngMnhREREREZijRMRERGRkRg4ERERERmJgRMRERGRkRg4FZFvv/0WVapUgbu7Oxo3bowDBw7kuu+PP/6Ip59+GqVKlVK3Nm3aZNu/f//+arBO/VuHDh1gK+dg7ty52Y5PnqdP0vM+/vhj+Pn5wcPDQ52nM2fOwBaOv2XLltmOX26dO3e22mtg586d6NKlixpgTsq6YsWKRz5n+/btqFevnkoGrVatmrouHue8Wts5WLZsGdq2bYuyZcuqcWuaNm2KjRs3Guwzfvz4bNdBcHAwbOUcyDWQ0/+F69ev2811kNP/dbmFhoZa5XUwefJkNGzYUA06Xa5cOXTr1g3R0dGPfN7vv/+ujkn+xrVr18a6devM8p3AwKkILF68GMOHD1e9AQ4fPow6deqgffv2iIuLy/WD4qWXXsK2bduwd+9eNVJqu3btcPXqVYP95EsyNjZWd1u0aBFs5RwI+aLQP76LFy8abJ86dSpmzJiB2bNnY//+/ShevLh6zeTkZFj78csXpv6xnzhxAk5OTnj++eet9hq4f/++Om75gjNGTEyMChRbtWqFo0ePYtiwYXj99dcNAoeCXFfWdA7kC1YCJ/mCOHTokDoX8oV75MgRg/3kC1T/Oti1axcsVX7PgZZ8seofo3zh2st18PXXXxscu4yc7ePjk+3zwFqugx07dmDIkCHYt28fNm/ejLS0NPUdJ+clN3v27FHfiwMHDlTXvwRbcpPPxiL/TpBedVS4GjVqpBkyZIhuOSMjQ+Pv76+ZPHmyUc9PT0/XeHl5aebNm6db169fP81zzz2nsdVzMGfOHI23t3eur5eZmanx9fXVfP7557p1d+/e1bi5uWkWLVqksbVrYPr06eoauHfvntVeA/rko2f58uV57vPhhx9qQkNDDda9+OKLmvbt25vsvFr6OchJSEiIJiIiQrc8btw4TZ06dTTWyJhzsG3bNrXf33//nes+9nYdyP4ODg6aCxcu2MR1EBcXp87Djh07ct3nhRde0HTu3NlgXePGjTVvvvlmkX8nsMapkKWmpqpfilJlqD/FiyxLbZIxkpKSVEQuvzCy1kzJr66aNWti8ODBuH37NmzpHNy7dw8BAQGqxu25557DyZMnDWojpKpe/zVluHypojf2vFrTNfCf//wHvXv3Vr+grPEaKAg5N/rnTMivR+05M8V5tcZ5NWU+rayfBdIcIc0+QUFBeOWVV3Dp0iXYmrp166omGKmB2717t269PV4H8nkgxyefj7ZwHcTHx6v7rNd1fj4PivI7gYFTIbt16xYyMjJQvnx5g/WynLWNPjcjR45U/xn0Lwhpovnvf/+LLVu2YMqUKarqs2PHjuq9bOEcSCDw888/Y+XKlZg/f776wnjyySdx5coVtV37vMc5r9ZyDUiuhlRHSzOVPmu6BgpCzk1O50wm+nzw4IFJ/m9Zm2nTpqkfFC+88IJunXwxSO7Xhg0bMGvWLPUFIjmSEmDZAgmWpOll6dKl6iY/pCQHUJrkhL1dBzIh/fr167N9HljrdZCZmama4Z966imEhYXl+/NA+zcuyu8ETvJr4T777DP8+uuvqmZBPzlaah+0JEkuPDwcVatWVfu1bt0a1k6SYOWmJUFTrVq18P3332PixImwJ/LrUv7GjRo1Mlhv69cAGVq4cCEiIiLUjwn9/B4JlrXkGpAvUKmJ+O2331Q+iLWTH1Fy0/8sOHfuHKZPn45ffvkF9mbevHkoWbKkyu/RZ63XwZAhQ9QPQ0vNx8oJa5wKWZkyZVRS740bNwzWy7Kvr+8jf11K4LRp0yb1HyEvUjUr73X27FnY0jnQcnFxwRNPPKE7Pu3zHuc1reH4JVlSAmdjPvgs+RooCDk3OZ0z6TQgPWZMcV1ZC7kGpIZBvgSzNldkJV+qNWrUsJnrICfyI0J7fPZ0HUhKlNTE9+3bF66urlZ/HQwdOhRr1qxRHaEqVqxYoM8D7d+4KL8TGDgVMrm469evr5pT9KsmZVm/RiUr6R0gNStS7dqgQYNHvo80YUl+i1Rr28o50CdV8ZGRkbrjCwwMVP8Z9F9TmnCkJ4Wxr2kNxy/db1NSUtCnTx+rvgYKQs6N/jkT0gNHe85McV1ZA+kpOWDAAHWvPxxFbqQpT2pkbOU6yIn0stQen71cB0Ka4yUQMuaHlCVfBxqNRgVNy5cvx9atW9Xn+eN+HhTpd4JJU80pR7/++qvK7J87d64mKipK88Ybb2hKliypuX79utret29fzahRo3T7f/bZZxpXV1fNkiVLNLGxsbpbYmKi2i73I0aM0Ozdu1cTExOj+d///qepV6+epnr16prk5GSzHacpz4H0Gtq4caPm3LlzmkOHDml69+6tcXd315w8edLgPMlrrFy5UnP8+HHVwywwMFDz4MEDjbUfv1azZs1UT7KsrPEakDIfOXJE3eSj58svv1SPL168qLbL8ct50Dp//rymWLFimg8++EBz6tQpzbfffqtxcnLSbNiwwejzau3nYMGCBRpnZ2d17PqfBdJbSOv999/XbN++XV0Hu3fv1rRp00ZTpkwZ1VPJFs6B9ChdsWKF5syZM5rIyEjNu+++q3F0dFTXvL1cB1p9+vRRPclyYk3XweDBg1WvaSmv/nWdlJSk2yfrZ6Ick/xfmDZtmvo8kF6ELi4u6poo6u8EBk5FZObMmZrKlSurgEi6zu7bt0+3rUWLFqpruVZAQID6z5T1JheKkIurXbt2mrJly6oLR/YfNGiQxX5IFOQcDBs2TLdv+fLlNZ06ddIcPnzY4PWk++nYsWPVdvnQbN26tSY6OlpjC8cvTp8+rf7umzZtyvZa1ngNaLuVZ71pj1vu5TxkfU7dunXVOQsKClLDVOTnvFr7OZDHee0vJLD28/NTx1+hQgW1fPbsWY2tnIMpU6Zoqlatqn44+fj4aFq2bKnZunWrXV0HQoJlDw8PzQ8//JDja1rTdYAcjl1u+v+/c/pM/O233zQ1atRQxyhDlaxdu9Ys3wkO/xwEERERET0Cc5yIiIiIjMTAiYiIiMhIDJyIiIiIjMTAiYiIiMhIDJyIiIiIjMTAiYiIiMhIDJyIiIiIjMTAiYiIiMhIDJyIiIiIjMTAiYgeW//+/dGtW7cif9+5c+eqWeBtUZUqVfDVV1+ZbD8iMg0GTkREBZCWlpZtXWpqqlnKQkRFh4ETEZlcy5Yt8c477+DDDz+Ej48PfH19MX78eIN9HBwcMGvWLHTs2BEeHh4ICgrCkiVLdNu3b9+u9rl7965u3dGjR9W6CxcuqO0DBgxAfHy8Wie3rO+hb/Xq1WjYsCHc3d1RpkwZdO/e3aAsK1asMNhfarKkRkvI+8k+ixcvRosWLdRrLFiwQFfT9sknn8Df3x81a9ZU+1++fBkvvPCCeg05/ueee069hpb2edOmTYOfnx9Kly6NIUOG6IIxOX8XL17Ee++9pzs2IrIMDJyIqFDMmzcPxYsXx/79+zF16lRMmDABmzdvNthn7Nix6NmzJ44dO4ZXXnkFvXv3xqlTp4x6/SeffFI1UZUoUQKxsbHqNmLEiBz3Xbt2rQqUOnXqhCNHjmDLli1o1KhRvo9p1KhRePfdd1UZ27dvr9bJa0VHR6tjW7NmjQp+ZJuXlxf++OMP7N69G56enujQoYNBjdS2bdtw7tw5dS/nSoI0baC2bNkyVKxYUZ0z7bERkWVwNncBiMg2hYeHY9y4cepx9erV8c0336ggo23btrp9nn/+ebz++uvq8cSJE1XwMXPmTHz33XePfH1XV1d4e3ur2hip0cqL1AhJUBYREaFbV6dOnXwf07Bhw9CjRw+DdRIc/vTTT6o8Yv78+cjMzFTrtDVFc+bMUbVPUkvWrl07ta5UqVLqnDg5OSE4OBidO3dW52fQoEGqlkrWS/D1qGMjoqLFGiciKrTASZ80ScXFxRmsa9q0abZlY2uc8kOa+Fq3bv3Yr9OgQYNs62rXrq0LmoTUnp09e1YFPVLTJDcJhJKTk1UNk1ZoaKgKjvI6P0RkeVjjRESFwsXFxWBZal+kJsZYjo4Pf9dpNJo8E7KNITlUeZGy6b9Pbu8ltUuPWnfv3j3Ur19f5UBlVbZsWZOdHyIyD9Y4EZHZ7Nu3L9tyrVq1DIIM/fweqTnSJzU9GRkZRtV+STNYbuS99N/nzJkzSEpKQkHUq1dPPb9cuXKoVq2awU2aFo1l7LERUdFi4EREZvP777/j559/xl9//aXyoQ4cOIChQ4eqbRJoVKpUSfWUk0BEEry/+OKLbGMYSQ2PBEW3bt3KNdiR1160aJG6l6bAyMhITJkyRbf9mWeeUflGkjh+8OBBvPXWW9lqhIwlSe7Sa0960klyeExMjMptkl6GV65cMfp15Nh27tyJq1evqmMjIsvAwImIzEaStX/99VdVI/Tf//5XBTchISFqmwQusnz69Gm1XQKdSZMmZetZJ0HOiy++qGqNpPdeTqR7vwRpq1atQt26dVWgJEGalgRkEqQ9/fTTePnll1XvvGLFihXomOR5EvBUrlxZJZJLDdrAgQNVjpP0ADSW9KiTIQyqVq1q0MRHRObloMnasE9EVAQkp2f58uVmGXGciKigWONEREREZCQGTkRERERG4nAERGQWzBIgImvEGiciIiIiIzFwIiIiIjISAyciIiIiIzFwIiIiIjISAyciIiIiIzFwIiIiIjISAyciIiIiIzFwIiIiIjISAyciIiIiGOf/AJD+/lo6oP1mAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 600x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lif_fi = LIFDynamics(1)\n",
    "brainstate.nn.init_all_states(lif_fi)\n",
    "\n",
    "def estimate_rate(I_const, n_burn=300, n_eval=1200):\n",
    "    # Simulate, drop initial transients (burn), then count spikes\n",
    "    n_time = n_burn + n_eval\n",
    "    inputs = np.ones(n_time) * I_const\n",
    "    V, S = run_lif(lif_fi, inputs)\n",
    "    spk = np.asarray(S[n_burn:]) >= 0.5\n",
    "    n_spikes = spk.sum()\n",
    "    T = n_eval * brainstate.environ.get_dt()\n",
    "    rate = (n_spikes / (T / u.second)) * u.Hz\n",
    "    return rate\n",
    "\n",
    "curr_levels = np.linspace(0.2, 2.0, 10) * u.mA\n",
    "rates = u.math.asarray([estimate_rate(I) for I in curr_levels])\n",
    "\n",
    "plt.figure(figsize=(6, 3.5))\n",
    "plt.plot(curr_levels, rates, 'o-')\n",
    "plt.xlabel('Input current I')\n",
    "plt.ylabel('Firing rate (Hz)')\n",
    "plt.title('LIF F–I curve (simulated)')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1db122d67991551",
   "metadata": {},
   "source": [
    "## Tips and Common Pitfalls\n",
    "- Units matter: keep `R`, `tau`, `V_*`, and `I` consistent. `brainunit` helps track them.\n",
    "- Time step `dt`: too large can distort dynamics or miss spikes; start with `0.1 ms`.\n",
    "- Always re-initialize or reset states before a new run (`init_all_states` once, `reset_state` per run).\n",
    "- Surrogate spikes are differentiable; when just simulating, treat values `>= 0.5` as spikes.\n",
    "- Soft vs hard reset changes spike waveform and ISI slightly; both are common in literature."
   ]
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    "## Where To Go Next\n",
    "- Add synaptic inputs and build small networks (`brainstate.nn` projections).\n",
    "- Explore noise currents and refractory periods.\n",
    "- Compare with conductance-based models (e.g., Hodgkin–Huxley) in the docs."
   ]
  }
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