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Scientific research in International Relations has produced a growing corpus of empirically grounded formal theoretical models of phenomena ranging from deterrence to systemic polarity, from conditions of peace to the onset of war. Many of these important theories contain a mix of continuous and discrete dimensions, causal variables, and parameters. Analysis and understanding of this fundamental and intriguing class of theories containing functions with a mix of continuous and discrete variables has puzzled generations of social scientists and applied mathematicians. This challenging and longstanding puzzle now has a solution. Here we demonstrate how the recently created calculus with nabladot operators is beginning to uncover previously unknown properties of hybrid international phenomena. Results include new concepts and precise principles on causal relationships, previously unknown political features, and fundamental properties of probabilistic causality, demonstrated through nabladot analysis of international events, crisis dynamics, and warfare.

"Agent-Based Computational Modeling and International Relations Theory: Quo Vadis?" published on by Oxford University Press.

Agent-based simulation models have a promising future in the social sciences, from political science to anthropology, economics, and sociology. To realize their full scientific potential, however, these models must address a set of key problems, such as the number of interacting agents and their geometry, network topology, time calibration, phenomenological calibration, structural stability, power laws, and other substantive and methodological issues. This paper discusses and highlights these problems and outlines some solutions.

This complex, ambitious, and large book seeks to question,
reformulate, and enhance the scope (and methods) of inter-
national relations theories, particularly those formulated
within a realist framework. The authors question that frame-
work, the Westphalian model of putatively unitary nation-
states, quantitative methods of empirical investigation, and
the levels-of-analysis paradigm. The breadth of their critique
is extensive and, consequently, highly ambitious. Rather than
approach international relations as a system of unitary
nation-states inspired by realist principles, which is arguably
a partial and simplified portrayal of contemporary research,
the authors favor a complex system of "overlapping, layered,
and linked polities" that have both horizontal and vertical
dimensions. The latter dimension is particularly important, as
it concerns patterns of authority, identity (including ethnic-
ity), and institutions that compete for the loyalty of individ-
uals.