autocomplete path callback with extra parameters ?

We see
in ajax_example_autocomplete.inc the $autocomplete_path = 'examples/ajax_example/node_by_author_autocomplete/' . $author->uid; as below:

  // When the author changes in the author field, we'll change the
  // autocomplete_path to match.
  if (!empty($form_state['values']['author'])) {
    $author = user_load_by_name($form_state['values']['author']);
    if (!empty($author)) {
      $autocomplete_path = 'examples/ajax_example/node_by_author_autocomplete/' . $author->uid;
      $form['node']['#autocomplete_path'] = $autocomplete_path;
      $form['node']['#title'] = t('Choose a node title authored by %author', array('%author' => $author->name));
      $form['node']['#disabled'] = FALSE;
    }
  }

Then the hook menu is:

  $items['examples/ajax_example/node_by_author_autocomplete'] = array(
    'page callback' => 'ajax_example_node_by_author_node_autocomplete_callback',
    'file' => 'ajax_example_autocomplete.inc',
    'type' => MENU_CALLBACK,
    'access arguments' => array('access content'),
  );

Then again , the callback is

function ajax_example_node_by_author_node_autocomplete_callback($author_uid, $string = "") {
  $matches = array();
  if ($author_uid > 0 && trim($string)) {
    $result = db_select('node')
      ->fields('node', array('nid', 'title'))
      ->condition('uid', $author_uid)
      ->condition('title', db_like($string) . '%', 'LIKE')
      ->range(0, 10)
      ->execute();
    foreach ($result as $node) {
      $matches[$node->title . " [$node->nid]"] = check_plain($node->title);
    }
  }

  drupal_json_output($matches);
}

Can some one help us make it clear about when and how author id and string become parameters of the callbackback function?

Thank you in advance.