We review and investigate the current status of intransitivity as a potential obstacle in coevolution. Pareto-Coevolution avoids intransitivity by translating any standard superiority relation into a transitive Pareto-dominance relation. Even for transitive problems though, cycling is possible. Recently however, algorithms that provide monotonic progress for Pareto-Coevolution have become avail...

Stuart Rachels and Larry Temkin have put forward a number of alleged counterexamples to the transitivity of the relation " all things considered better than ". 1 Several of these cases share a common structure. 2 A representative example by Rachels is as follows: Each outcome in [this] counterexample involves a single person's experience: A: 1 year of excruciating agony. B: 100 years of pain sl...

Intransitivity is a property of connected, oriented graphs representing species interactions that may drive their coexistence even in the presence of competition, the standard example being the three species Rock-Paper-Scissors game. We consider here a generalization with four species, the minimum number of species allowing other interactions beyond the single loop (one predator, one prey). We ...

Competitive tournaments appear in sports, politics, population ecology, and animal behavior. All of these fields have developed methods for rating competitors ranking them accordingly. A tournament is intransitive if it not consistent with any ranking. Intransitive contain rock-paper-scissors type cycles. The discrete Helmholtz--Hodge decomposition (HHD) well adapted to describing tournaments. ...

the holy koran is the eternal miracle of literature and eloquence. in the field of eloquence, ellipsis is an important issue. grammaticaltadmeen as a type of ellipsis has a special manifestation in the holy koran. tazmeen literally meaning insertion is applied when a verb in the text adds the meaning of another verb to itself and is used as the other word should be used in terms of transitivity...