Only display authors who have posts

The default version of the WordPress function provides the count of the default post type ‘POST’ as stated below:

<?php
    $post_count = count_user_posts($userid);
?>

For retrieving the post count based on a post type a custom function as below is required:

<?php
    function count_user_posts_by_type( $userid, $post_type="post" ) {

        global $wpdb;

        $where = get_posts_by_author_sql( $post_type, true, $userid );

        $count = $wpdb->get_var( "SELECT COUNT(*) FROM $wpdb->posts $where" );

        return $count;
    }
?>

Usage of the above function:

<?php
    $post_count = count_user_posts_by_type($userid, $post_type);
?>

Now as you have got the post count wrap your code in a conditional loop.

How to use in your function:

<?php
// count number of Articles (CPT) written by a user
function count_user_posts_by_type( $userid, $post_type="publication" ) {
    global $wpdb;
    $where = get_posts_by_author_sql( $post_type, true, $userid );
    $count = $wpdb->get_var( "SELECT COUNT(*) FROM $wpdb->posts $where" );
    return $count;
}
$allUsers = get_users('orderby=title&order=ASC&post_type=publication');
$users = array();
// Remove subscribers from the list as they won't write any articles
foreach($allUsers as $currentUser)
{
    if(!in_array( 'subscriber', $currentUser->roles ))
    {
        $users[] = $currentUser;
    }
}

foreach($users as $user) { 

    $post_count = count_user_posts_by_type($user->id);

        if ($post_count > 0 { ?>

        <div class="authorInfo">
        <h2 class="authorName"><?php echo $user->display_name; ?></h2>

         <?php query_posts( array( 'post_type' => 'publication', 'showposts' => -1, 'author'=>$user->ID ) );
            while (have_posts()) : the_post();
                the_content(); 
            endwhile; ?>
        </div>

    <?php }
} 
?>

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