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
Figure 8: It is not hard to verify that, no matter what probability is assigned to the event a, the resulting Markov chain has only transient and acyclic states.
The temporal calculus of conditional objects and conditional events
However, the automaton is not acyclic, since it has two states, reachable by a path labelled aa∁ from each other.
The temporal calculus of conditional objects and conditional events
Meyn, Stability of acyclic multiclass queueing networks, IEEE Trans.
Computing stationary probability distributions and large deviation rates for constrained random walks. The undecidability results
Let E be a ϕ-acyclic hermitian vector bundle on M , that is, E is a hermitian vector bundle on M such that the higher direct image Riϕ∗E is trivial if i > 0.
Higher arithmetic K-theory
Let E be a ϕ-acyclic hermitian vector bundle on M .
Higher arithmetic K-theory
Let E be a ϕ-acyclic hermitian vector bund le on M .
Higher arithmetic K-theory
We assume that any exact metrized n-cube on M we deal with is made of ϕ-acyclic hermitian vector bundles.
Higher arithmetic K-theory
Let bS (ϕ-ac) denote the S-construction of the category of ϕ-acyclic hermitian vector bundles on X .
Higher arithmetic K-theory
Then the direct image of a ϕ-acyclic hermitian vector bundle with the L2 -metric gives a morphism of simplicial sets ϕ∗ : bS (ϕ-ac) → bS (Y ).
Higher arithmetic K-theory
E , ω ) = (ϕ∗E , ϕ!(ω ) − T (E )) for a ϕ-acyclic hermitian vector bundle E on X and ω ∈ eA1(X ).
Higher arithmetic K-theory
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