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Simplicial Complexes Obtained From Qualitative Probability Orders, Paul H. Edelman, Tatiana Gvozdeva, Arkadii Slinko Jan 2013

Simplicial Complexes Obtained From Qualitative Probability Orders, Paul H. Edelman, Tatiana Gvozdeva, Arkadii Slinko

Vanderbilt Law School Faculty Publications

The goal of this paper is to introduce a new class of simplicial complexes that naturally generalize the threshold complexes. These will be derived from qualitative probability orders on subsets of a finite set that generalize subset orders induced by probability measures. We show that this new class strictly contains the threshold complexes and is strictly contained in the shifted complexes. We conjecture that this class of complexes is exactly the set of strongly acyclic complexes, a class that has previously appeared in the context of cooperative games. Beyond the results themselves, this new class of complexes allows us to ...


Book Review: Burden Of Proof: A Review Of Math On Trial, Paul H. Edelman Jan 2013

Book Review: Burden Of Proof: A Review Of Math On Trial, Paul H. Edelman

Vanderbilt Law School Faculty Publications

In Math on Trial, Leila Schneps and Coralie ColĀ­ mez write about the abuse of mathematical arguĀ­ ments in criminal trials and how these flawed arguments "have sent innocent people to prison" (p. ix). Indeed, people "saw their lives ripped apart by simple mathematical errors." The purpose of focusing on these errors, despite mathematics' "relatively rare use in trials" (p. x), is "that many of the common mathematical fallacies that pervade the public sphere are perfectly represented by these trials. Thus they serve as ideal illustrations of these errors and of the drastic consequences that faulty reasoning has on real ...