MIT News November 1, 2024 Despite its central role, current methods for causal inference face significant challenges due to nonlinear dependencies, stochastic interactions, self-causation, collider effects, and influences from exogenous factors, among others. While existing methods can effectively address some of these challenges, no single approach has successfully integrated all these aspects. A team of researchers in the US (MIT, Caltech) developed SURD: Synergistic-Unique-Redundant Decomposition of causality which quantified causality as the increments of redundant, unique, and synergistic information gained about future events from past observations. The formulation was non-intrusive and applicable to both computational and experimental investigations, even when […]
Category Archives: Mathematics
Solution to century-old math problem could predict transmission of infectious diseases
Science Daily May 29, 2020 The diffusion equation models random movement and is one of the fundamental equations of physics. The analytic solution of the diffusion equation in finite domains, when time and space is continuous, has been known for a long time. However, the diffusion equation in finite space was not solved until now. Researchers in the UK used Chebyshev polynomials, and the method of images which is used to tackle electrostatic problems to construct the solution to the discrete diffusion equation in higher dimension from the one in lower dimensions. The solution could be used to accurately predict […]
‘Amazing’ Math Bridge Extended Beyond Fermat’s Last Theorem
Quanta Magazine April 6, 2020 An international team of researchers (USA- Princeton, UK) came up with proof of Fermat’s Last Theorem tackling the theorem indirectly by means of an enormous bridge that mathematicians had conjectured should exist between two distant continents in the mathematical world. The proof boiled down to establishing this bridge between just two little plots of land on the two continents. The full bridge would offer mathematicians the hope of illuminating vast swaths of mathematics by passing concepts back and forth across it. Many problems, including Fermat’s Last Theorem, seem difficult on one side of the bridge, […]