Data Set Used
The binomial ideal associated with the intersection axiom of conditional probability is shown to be radical and is expressed as an intersection of toric prime ideals. This resolves a conjecture in algebraic statistics due to Cartwright and Engström. Conditional independence contraints are a family of natural constraints on probability distributions,… (More)
— We present a first application of a general approach to learn the behavior of NPCs (and other entities) in a game from observing just the graphical output of the game during game play. This allows some understanding of what a human player might be able to learn during game play. The approach uses object tracking and situation-action pairs with the… (More)
We prove that the ranks of the subsets and the activities of the bases of a matroid define valuations for the subdivisions of a matroid polytope into smaller matroid polytopes.
We present type preserving bijections between noncrossing and nonnesting partitions for all classical reflection groups, answering a question of Athanasiadis and Reiner. The bijections for the abstract Coxeter types B, C and D are new in the literature. To find them we define, for every type, sets of statistics that are in bijection with non-crossing and… (More)
We introduce the notion of a matroid M over a commutative ring R, assigning to every subset of the ground set an R-module according to some axioms. When R is a field, we recover matroids. When R = Z, and when R is a DVR, we get (structures which contain all the data of) quasi-arithmetic matroids, and valuated matroids, respectively. More generally, whenever… (More)