Which activity is NOT part of the expansion of information from DIME?

The correct answer is establishing military bases, as this activity does not directly relate to the expansion of information in the context of DIME (Diplomacy, Information, Military, and Economic). DIME is a framework used to describe the various instruments of national power, particularly how countries can engage in strategic actions to influence other nations or achieve their objectives.

Public diplomacy campaigns, counterintelligence operations, and intercepting communications are all activities that involve the management and dissemination of information. Public diplomacy campaigns are specifically designed to communicate and promote a nation's values and policies overseas, thereby expanding its influence through information. Counterintelligence operations help to gather and protect sensitive information, safeguarding a nation’s strategic initiatives, while intercepting communications pertains to collecting intelligence that can inform policy decisions.

In contrast, establishing military bases is primarily a tactical or strategic military action rather than an information-centric endeavor. While military presence may contribute to a nation's overall strategic goals, it does not directly expand information in the same way that the other activities do. Establishing bases is more about projecting power and ensuring security than about the dissemination or management of information, which is why this choice is identified as the activity that does not fit within the context of DIME.