You would need something like the GreaseMonkey addin for Firefox. Then you need to write a script that hides the content of the LI tag with an ID of "today-news-wrapper".
You could also do this (probably a bit easier) using Stylish or even FoxReplace.
Of course, those recommendations assume you are using Firefox as your browser, if using other browsers, you would need to try and find similar addons.
Use the Web Developer tools (usually made visible with F12) to see the structure of the web page so that you can work out what to hide.
Alternatively, click on the "All Updates" drop down at the top of the list, go to settings and unclick all the options. Dont know if that hides everything though and I'm not about to try I'm afraid!