How to highlight 1st level menu item based on actual page

Yes, very much possible and you don’t even have to add classes yourself. If you’re using wp_nav_menu, WordPress adds classes for every case the specific nav item is in. I’ll name the important classes for Publications (amongst others), based on where you clicked hypothetically:

1. Publications – This is now the selected item, and will get (amongst others) the classes: current-menu-item because it’s selected

2. Computers – Publications is not the selected item, but will get the classes: current-page-parent and current-menu-parent because it’s direct child is the selected item, and current-page-ancestor and current-menu-ancestor because one of it’s children down the line is the selected item

3. Article 123 – Publications is not the selected item, but will get the classes: current-page-ancestor and current-menu-ancestor because one of it’s children down the line is the selected item

So in short, current-menu-item when selected, [classname part]-parent when direct child is selected and [classname part]-ancestor when child, grand-child or deeper level child is selected