input: 
  def is_numeric_string(string: str) -> bool:
      """Check if the given string is a valid numeric string using a regular expression.
      >>> is_numeric_string('123456789')
      True
      >>> is_numeric_string('abc123')
      False
      """
  
output:     import re
      return bool(re.match(r'^-?\d+(\.\d+)?$', string))