We prove that there is only one imprimitive homogeneous simple unstable 3-graph with finite classes such that all predicates are realised in the union of two classes. 1 Definitions and context. Definition 1.1. An n-graph is a structure (M,R1, . . . , Rn) in which each Ri is binary, irreflexive and symmetric; also, for all distinct x, y ∈ M exactly one of the Ri holds and n ≥ 2. We assume that a...

The investigation of directed acyclic graphs (DAGs) encoding the same Markov property, that is the same conditional independence relations of multivariate observational distributions, has a long tradition; many algorithms exist for model selection and structure learning in Markov equivalence classes. In this paper, we extend the notion of Markov equivalence of DAGs to the case of interventional...

The investigation of directed acyclic graphs (DAGs) encoding the same Markov property, that is the same conditional independence relations of multivariate observational distributions, has a long tradition; many algorithms exist for model selection and structure learning in Markov equivalence classes. In this paper, we extend the notion of Markov equivalence of DAGs to the case of interventional...

Linear time solv-able optimization problems on certain structured graph families, extended abstract. On the xed parameter complexity of graph enumeration problems deenable in monadic second order logic. in preparartion, 1998. 35 the rst case there is no other vertex z of L such that w and z occur in the same equivalence class of R red , or else z and w are adjacent to both u and v, a contradict...

Two edges el and e2 of an undirected graph are cycle-equivalent iff all cycles that contain el also contain e2, i.e., iff el and e2 are a cut-edge pair. The cycle-equivalence classes of the control-flow graph are used in optimizing compilers to speed up ezasting control-flow and data-flow algorithms. While the cycle-equivalence classes can be computed in linear time, we present the first fully ...

An understanding of bacterial diversity and evolution in any environment requires knowledge of phenotypic diversity. In this study, the underlying factors leading to phenotypic clustering were analyzed and interpreted using a novel approach based on a four-tiered graph. Bacterial isolates were organized into equivalence classes based on their phenotypic profile. Likewise, phenotypes were organi...

Recall that last time we have introduced the set of weights Wt(n) ⊂ C and an equivalence relation ∼ on Wt(n). Our goal is to describe this set and this equivalence relation – the equivalence classes are in a natural bijection with Irr(Sn). The first step here is as follows. Pick a path P = V 1 → V 2 → . . . → V n in the branching graph and an integer k with 1 < k < n. We fix all vertices but V ...

Introduction. In a paired comparison experiment n judges give a preference in some or all of the (~) pairs of t items. Frequently the purpose of the experiment is to test the null hypothesis that every preference is equally likely against a vaguely defined alternative of consistency. Our purpose is to study several of the tests used, from the point of view of a natural equivalence relation whic...