Exclude a Category from PHP Widget

Hi, I’m building a child theme in Genesis, trying to modify code placed into the PHP Widget plugin to display posts titles from categories in a sidebar, but I need to exclude one category. I am new to PHP so although I can read about how its done in threads ,I don’t have enough general bearings on it to implement the exclude into what I pasted into my PHP widget and get anything working yet. (The rest is working fine) So…would much appreciate if anyone can take a look.

Below I will paste the code I am using. My question: where to add in the exclude function (for category 1)?

Basically I am trying to add something like this to my whole query:
http://wordpress.org/support/topic/exclude-category-name-from-the-get_the_category-function?replies=10

Here is my code: Thanks.

<?php
if ( is_single() ) {

$categories = get_the_category();
$currentID = get_the_ID();
$parent = get_cat_name($category[0]->category_parent);

  if ($categories) {
    foreach ($categories as $category) {
      // echo "<pre>"; print_r($category); echo "</pre>";

      $cat = $category->cat_ID;
      $args=array(
        'cat' => $cat,
        'post__not_in' => array($post->ID),
'post__not_in' => array($currentID),

        'posts_per_page'=>7,
        'caller_get_posts'=>1
      );

      $my_query = null;
      $my_query = new WP_Query($args);
      if( $my_query->have_posts() ) {

 echo '<h4>more projects from</h3>';
echo  $categories[0]->cat_name ;

        while ($my_query->have_posts()) : $my_query->the_post(); ?>
          <p><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php  the_title_attribute(); ?>"><?php the_title();?></a></p>
         <?php
        endwhile;
      } //if ($my_query)
    } //foreach ($categories
  } //if ($categories)

  wp_reset_query();  // Restore global post data stomped by the_post().
} //if (is_single())
?>