Geometry of Rank TestsFundamentals for Finding Somitogenesis Clock Genes

Jason Morton, Lior Pachter, Anne Shiu, Bernd Sturmfels, Oliver Wienand

Department of Mathematics, UC Berkeley

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Mary-Lee DequéantOlivier Pourquié

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From Willbrand et al., 2005

Rank Tests

A rank test is a map

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123 132

213

231 321

312

+-

--

++

-+

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123 132

213

231 321

312

+-

--

++

-+

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Graphical Models

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A set of conditional independence triples is a semi-graphoid if the following axiom holds:

Theorem: The map is a bijection between convex rank tests and semi-graphoids. 123 132

213

231 321

312

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--

++

-+

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Graphical Models = Graph Associahedra

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Thanks again to Profs. Strømme, Ranestad, Rudakov and Smaløe.

Thanks again to Profs. Strømme, Ranestad, Rudakov and Smaløe.