It follows that G is acyclic; i.e., it is a dag.
Conditional Plausibility Measures and Bayesian Networks
The kernel of β is C∗ (∆i \ {xi}; E )/C∗(δi ; E ), which is acyclic as δi ֒→ ∆i \ {xi} admits an evident homotopy retract.
Homology for irregular connections
As in the previous lemma, C∗ (W \ {0}) is acyclic.
Homology for irregular connections
In these terms they are fairly ﬂexible: Corollary 1.5, for instance, generalizes the theorem of Huck [H] that any two acyclic 2-complexes can be (up to 2-deformation) dually embedded in S 4 .
Dual 2-complexes in 4-manifolds
Causal sets Causal set (see short review ) V , that is a partially-ordered set with relation ≤, satisfying transitivity, reﬂexivity and acyclicity (if x ≤ y and y ≤ x then x = y ).
Gibbs and Quantum Discrete Spaces
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