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Explore a revised mathematical theory of neural complexity in this conference talk from the Models of Consciousness Conferences. Delve into the challenges faced by the integration and differentiation framework proposed by Tononi, Sporns, and Edelman (TSE) in consciousness research. Discover a new measure called O-information, which quantifies the balance between redundancy and synergy within a system. Learn how this measure improves upon TSE's original approach in describing phenomena where large-scale correlation and short-scale independence coexist. Examine a formalism that decomposes different "modes" of information dynamics, providing a comprehensive taxonomy of redundant and synergistic effects. Gain insights into how these developments allow for the placement of previous measures within a common framework, explaining their similarities and differences. This 24-minute talk by Pedro Mediano from the Department of Computing at Imperial College London offers a fresh perspective on measuring neural dynamics and its implications for consciousness research.