198 citations · 713 across the 38 of their papers we have counts for
9 papers · 1 filter
The Algebraic Degree of Semidefinite Programming
Jiawang Nie, Kristian Ranestad, Bernd Sturmfels
Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minima…
Three Counterexamples on Semigraphoids
Raymond Hemmecke, Jason Morton, Anne Shiu +2
Semigraphoids are combinatorial structures that arise in statistical learning theory. They are equivalent to convex rank tests and to polyhedral fans that coarsen the reflection ar…
On the toric algebra of graphical models
Dan Geiger, Christopher Meek, Bernd Sturmfels
We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or…
Conjunctive Bayesian networks
Niko Beerenwinkel, Nicholas Eriksson, Bernd Sturmfels
Conjunctive Bayesian networks (CBNs) are graphical models that describe the accumulation of events which are constrained in the order of their occurrence. A CBN is given by a parti…
Toric geometry of cuts and splits
Bernd Sturmfels, Seth Sullivant
Associated to any graph is a toric ideal whose generators record relations among the cuts of the graph. We study these ideals and the geometry of the corresponding toric varieties.…
Monomial Dynamical Systems over Finite Fields
O. Colón-Reyes, A. Jarrah, R. Laubenbacher +1
An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear sys…