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We call D M ⊂ L the space of all phylogenetic mixtures (on any number of classes) under the algebraic evolutionary model.
A phylogenetic tree T together with the parameters Πand A = (A e ) e ∈ E (T )is said to evolve under the algebraic evolutionary model if Π ∈ W0, and all matrices A e lie in Mod.
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Given a set of taxa [ n] and an algebraic evolutionary model, the set of all phylogenetic mixtures D M is a vector subspace of.
Therefore, equivariant models provide a wide family of examples of algebraic evolutionary models in the sense of Definition 1.
Definition 8. Fix a set of taxa [ n] and an algebraic evolutionary model.
An (algebraic) evolutionary model is specified by giving a vector subspace W 0 ⊂ W such that 1 t Π ≠ 0 for some Π in W0, together with a multiplicatively closed vector subspace Mod(for model) of M k (C ) containing the identity matrix.
Second, based on the algebraic form, the dynamical behavior of evolutionary networked games is discussed, and some interesting results are presented.
The prototypical examples of algebraic semantics for propositional logics are the class BA of Boolean algebras, which is the algebraic semantics for classical logic, and the class HA of Heyting algebras, which is the algebraic semantics for intuitionistic logic.
Using the semi-tensor product method, this paper investigates the algebraic formulation and strategy optimization for a class of evolutionary networked games with "myopic best response adjustment" rule, and presents a number of new results.
This paper studies the algebraic formulation and optimization control for a class of networked evolutionary games with switched topologies via the semi-tensor product method.
Algebras transform via homomorphisms, leaving the algebraic structure invariant.
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