code: def sigma_star_plot(g, label, fig):
      norm_list = np.linspace(0.01, 8, 100)
      sigma_list = np.zeros_like(norm_list)
      for i, norm in enumerate(norm_list):
          root = sigma_star(g, norm)
          sigma_list[i] = root
      if fig is None:
          fig = plt.figure(figsize=(7, 7))
      else:
          plt.figure(fig.number)
      plt.plot(norm_list, sigma_list, label=label)
      plt.ylabel(r"$\sigma^*$", fontsize=40)
      plt.xlabel(r"$\Vert \mathbf{x} \Vert$", fontsize=40)
      plt.legend(prop={"size": 30})
      ax = plt.gca()
      ax.tick_params(axis="both", which="major", labelsize=30)
      plt.savefig("code/dynamics/g_roots.pdf")
  
      return fig
  
file_path: elu-gelu-kernels/code/dynamics/dynamics.py
imports: from ..kernels.nn_kernel_elu import NNKernelElu
  from ..kernels.nn_kernel_gelu import NNKernelGelu
  from ..kernels.nn_kernel_relu import NNKernelRelu
  import matplotlib
  import matplotlib.pyplot
  from matplotlib import rc
  import numpy
  import scipy.optimize
  from scipy.stats import multivariate_normal
label_desc: Use image node_id 1 for calling a global function with example usage: sigma_star_plot(g, label, fig) and returns: fig