Abstract: The subject of the research is the grounds of border guards activities at the levels of state and region. The most important objective of national borderline policy should be generalization of international experience and use of this experience in Russia's practice. The authors of the article focus on such issues as the principles of distribution of limited borderline resources among regions and districs as well as development of mechanisms for grounding activities of border guards (concentration of the main and auxiliary efforts). To achieve this task, the authors have applied approaches described in the theory of borderline security, methods of mathematical statistics and borderline statistics. The scientific novelty of the research is caused by the importance of prevention of terrorism, drug smuggling and illegal migration. Taking into account the limited nature of human, material and financial resources, the authors of the article develop their own mathematical model for substantiation of border guards activities and verify it using statistical data about the results of the USA border guards. 

Abstract: The research object is military and frontier activity in the Roman Empire. The research subject is frontier statistics. The Roman Empire left us classic examples of valour and courage in countering threats on the Empire frontiers about 20 000 km long. The article presents qualitative and quantitative analysis of the results of this activity. The author is the first to calculate the density of troops (legions) per a kilometer of a border in frontier provinces of the Roman Empire; substantiates the principles of distribution of legions on the boundaries of the Empire. Using historical and system approaches, with regard to the frontier security theory, the author reconstructs the frontier statistics of the Roman Empire. The scientific novelty of the study consists in the fact that though foreign and Russian scholars are interested in the methods of states borders protection, the issues of frontier statistics and its influence on state defense haven’t been studied in detail yet.