3 loops, no duplicates

FIRST LOOP

<?php $do_not_duplicate = array();
	$my_query = new WP_Query(array('posts_per_page' => 3, 'post__in' => get_option( 'sticky_posts' ), 'caller_get_posts' => 1 ) );
	while ($my_query->have_posts()) : $my_query->the_post();
	$do_not_duplicate[] = $post->ID; ?>

<?php
$category = get_the_category();
if ($category) {
  echo '<a href="' . get_category_link( $category[0]->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category[0]->name ) . '" ' . '>' . $category[0]->name.'</a>';
}
?>

<br>

<a href="<?php the_permalink() ?>" rel="bookmark" title="Read: <?php the_title(); ?>"><?php the_title(); ?></a>

<br>

<?php endwhile;?>
<?php wp_reset_query(); ?>

SECOND LOOP

<?php
  $my_query = new WP_Query(array('posts_per_page' => 4, 'post__not_in' => array_merge($do_not_duplicate, get_option( 'sticky_posts' )) ) );
  while ($my_query->have_posts()) : $my_query->the_post();
  $do_not_duplicate[] = $post->ID; ?>

<a href="<?php the_permalink() ?>" title="Read: <?php the_title(); ?>"><?php the_title(); ?></a><br>
<br>

<?php endwhile;?>
<?php wp_reset_query(); ?>

THIRD LOOP

<?php
//for each category, show 1 post
$cat_args=array(
  'orderby' => 'name',
  'order' => 'ASC'
   );

$categories=get_categories($cat_args);
	foreach($categories as $category) {
    $args=array(
    'numberposts' => 1,
    'post__not_in' => array_merge($do_not_duplicate,get_option( 'sticky_posts' )),
	'category__in' => array($category->term_id)
    );

    $posts=get_posts($args);
      if ($posts) {
        $ncat = '<a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name.'</a>';
        foreach($posts as $post) {
          setup_postdata($post);
		  $do_not_duplicate[] = $post->ID; ?>

<a href="<?php the_permalink() ?>" title="Read: <?php the_title(); ?>"><?php the_title(); ?></a><br>
<br>
<?php the_excerpt(); ?><br>
<br>
By <?php the_author_link(); ?>, <?php the_time('F j, Y'); ?> | In: <?php echo $ncat ?><?php comments_popup_link('<b>No Comments</b>', '<b>1 Comment</b>', '<b>% Comments</b>', '', '<b>Comments off</b>'); ?><br>
<br>

          <?php
        } // foreach($posts
      } // if ($posts
    } // foreach($categories
?>

<?php wp_reset_query(); ?>