Combinatorics and Graph Theory


Cause/effect Correlations Through the Borsuk-Ulam Theorem and Kneser Graphs

Authors: Arturo Tozzi

The assessment of hidden causal relationships, e.g., adverse drug reactions in pharmacovigilance, is currently based on rather qualitative parameters. In order to find more quantifiable parameters able to establish the validity of the alleged correlations between drug intake and onset of symptoms, we introduce the Borsuk-Ulam Theorem (BUT), which states that a single point on a circumference projects to two points on a sphere. The BUT stands for a general principle that describes issues from neuroscience, theoretical physics, nanomaterials, computational topology, chaotic systems, group theory, cosmology. Here we introduce a novel BUT variant, termed operational-BUT, that evaluates causal relationships. Further, we demonstrate that the BUT is correlated with graph theory and in particular with the so-called Kneser graphs: this means that the combinatory features of observables, such as the bodily responses to drug intake, can be described in terms of dynamical mappings and paths taking place on well-established abstract structures. Therefore, physical and biological dynamical systems (including alleged causes and their unknown effects) make predictable moves into peculiar phase spaces, giving rise to constrained trajectories that can be quantified.

Comments: 10 Pages.

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Submission history

[v1] 2018-01-09 13:10:24

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