Using Advanced Search on a list does not indicate that a search has been performed when the results are displayed (unless you also show the basic search on the list - which will then display the "Show all" cross icon). To make it clear that an advanced search has been applied use the following code snippet on the list page:
if($_SERVER['QUERY_STRING']!="")
{
// get query parameters
$urlQueries = explode("&",$_SERVER['QUERY_STRING']);
$urlParams = array();
foreach($urlQueries as $urlQuery)
{
$queryParts = explode("=",$urlQuery);
$urlParams[] = $queryParts[0];
}
// check for advanced search parameter
if(in_array("q", $urlParams))
echo "Displaying search results..";
}