fix equantion show

docs/quickstart/snn_simulation-en.ipynb

@@ -34,8 +34,16 @@
     "\n",
     "The **Hodgkin-Huxley (HH) model** is a mathematical model proposed in 1952 by neurophysiologists Allen Hodgkin (1914-1998) and Andrew Huxley (1917-2012) to describe the generation and propagation of action potentials in neurons. The HH model is based on the classical electrical circuit model and links the dynamic changes of the neuron membrane potential with the biophysical properties of the membrane ion channels. It is one of the most important theoretical models in neuroscience and earned the two researchers the Nobel Prize in Physiology or Medicine in 1963. The mathematical definition of the HH model is:\n",
     "\n",
-    "\\begin{aligned}C \\frac {dV} {dt} = -(\\bar{g}_{Na} m^3 h (V &-E_{Na})\n",
-    "+ \\bar{g}_K n^4 (V-E_K) + g_{leak} (V - E_{leak})) + I(t)\\\\\\frac {dx} {dt} &= \\alpha_x (1-x)  - \\beta_x, \\quad x\\in {\\rm{\\{m, h, n\\}}}\\\\&\\alpha_m(V) = \\frac {0.1(V+40)}{1-\\exp(\\frac{-(V + 40)} {10})}\\\\&\\beta_m(V) = 4.0 \\exp(\\frac{-(V + 65)} {18})\\\\&\\alpha_h(V) = 0.07 \\exp(\\frac{-(V+65)}{20})\\\\&\\beta_h(V) = \\frac 1 {1 + \\exp(\\frac{-(V + 35)} {10})}\\\\&\\alpha_n(V) = \\frac {0.01(V+55)}{1-\\exp(-(V+55)/10)}\\\\&\\beta_n(V) = 0.125 \\exp(\\frac{-(V + 65)} {80})\\end{aligned}\n",
+    "$$\n",
+    "\\begin{aligned}C \\frac {dV} {dt} = -(\\bar{g}_{Na} m^3 h (V &-E_{Na}) + \\bar{g}_K n^4 (V-E_K) + g_{leak} (V - E_{leak})) + I(t)\\\\\n",
+    "\\frac {dx} {dt} &= \\alpha_x (1-x)  - \\beta_x, \\quad x\\in {\\rm{\\{m, h, n\\}}}\\\\\n",
+    "&\\alpha_m(V) = \\frac {0.1(V+40)}{1-\\exp(\\frac{-(V + 40)} {10})}\\\\\n",
+    "&\\beta_m(V) = 4.0 \\exp(\\frac{-(V + 65)} {18})\\\\\n",
+    "&\\alpha_h(V) = 0.07 \\exp(\\frac{-(V+65)}{20})\\\\\n",
+    "&\\beta_h(V) = \\frac 1 {1 + \\exp(\\frac{-(V + 35)} {10})}\\\\\n",
+    "&\\alpha_n(V) = \\frac {0.01(V+55)}{1-\\exp(-(V+55)/10)}\\\\\n",
+    "&\\beta_n(V) = 0.125 \\exp(\\frac{-(V + 65)} {80})\\end{aligned}\n",
+    "$$\n",
     "\n",
     "In this tutorial, we simulate the HH model as an example of a single neuron model.``brainstate`` can run multiple neuron models in parallel, which saves time. We will simulate a group of HH neurons."
    ]

docs/quickstart/snn_simulation-zh.ipynb

@@ -34,8 +34,15 @@
     "\n",
     "**Hodgkin-Huxley模型（HH模型）** 是由神经生理学家艾伦·霍奇金（Allen Hodgkin，1914-1998）和安德鲁·赫胥黎（Andrew Huxley，1917-2012）于1952年提出的数学模型，用以描述神经元动作电位的产生和传播过程。HH模型以经典电路模型为基础，将神经元膜电位的动态变化与膜离子通道的生物物理特性联系起来，是神经科学中最重要的理论模型之一，曾为二人赢得1963年的诺贝尔生理学或医学奖。HH模型的数学定义是：\n",
     "\n",
-    "\\begin{aligned}C \\frac {dV} {dt} = -(\\bar{g}_{Na} m^3 h (V &-E_{Na})\n",
-    "+ \\bar{g}_K n^4 (V-E_K) + g_{leak} (V - E_{leak})) + I(t)\\\\\\frac {dx} {dt} &= \\alpha_x (1-x)  - \\beta_x, \\quad x\\in {\\rm{\\{m, h, n\\}}}\\\\&\\alpha_m(V) = \\frac {0.1(V+40)}{1-\\exp(\\frac{-(V + 40)} {10})}\\\\&\\beta_m(V) = 4.0 \\exp(\\frac{-(V + 65)} {18})\\\\&\\alpha_h(V) = 0.07 \\exp(\\frac{-(V+65)}{20})\\\\&\\beta_h(V) = \\frac 1 {1 + \\exp(\\frac{-(V + 35)} {10})}\\\\&\\alpha_n(V) = \\frac {0.01(V+55)}{1-\\exp(-(V+55)/10)}\\\\&\\beta_n(V) = 0.125 \\exp(\\frac{-(V + 65)} {80})\\end{aligned}\n",
+    "$$\n",
+    "\\begin{aligned}C \\frac {dV} {dt} = -(\\bar{g}_{Na} m^3 h (V &-E_{Na}) + \\bar{g}_K n^4 (V-E_K) + g_{leak} (V - E_{leak})) + I(t)\\\\\n",
+    "\\frac {dx} {dt} &= \\alpha_x (1-x)  - \\beta_x, \\quad x\\in {\\rm{\\{m, h, n\\}}}\\\\\n",
+    "&\\alpha_m(V) = \\frac {0.1(V+40)}{1-\\exp(\\frac{-(V + 40)} {10})}\\\\\n",
+    "&\\beta_m(V) = 4.0 \\exp(\\frac{-(V + 65)} {18})\\\\\n",
+    "&\\alpha_h(V) = 0.07 \\exp(\\frac{-(V+65)}{20})\\\\\n",
+    "&\\beta_h(V) = \\frac 1 {1 + \\exp(\\frac{-(V + 35)} {10})}\\\\&\\alpha_n(V) = \\frac {0.01(V+55)}{1-\\exp(-(V+55)/10)}\\\\\n",
+    "&\\beta_n(V) = 0.125 \\exp(\\frac{-(V + 65)} {80})\\end{aligned}\n",
+    "$$\n",
     "\n",
     "在这里我们对HH模型进行仿真，作为单个脉冲神经元模型仿真的示例。``brainstate``可以同时运行多个神经元模型，并行运行节省时间。我们对一群HH神经元进行仿真。"
    ]