Geometry of Rank Tests Fundamentals for Finding Somitogenesis Clock Genes Jason Morton, Lior Pachter, Anne Shiu, Bernd Sturmfels, Oliver Wienand Department.

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



123 132

213

231 321

312

+-

--

++

-+



123 132

213

231 321

312

+-

--

++

-+











Graphical Models



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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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.

Geometry of Rank Tests Fundamentals for Finding Somitogenesis Clock Genes Jason Morton, Lior Pachter, Anne Shiu, Bernd Sturmfels, Oliver Wienand Department.

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