859 research outputs found
A Universal Construction for (Co)Relations
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic interpretation for diagrams is given in terms of relations or corelations (generalised equivalence relations) of some kind. In this paper we show how semantic categories of both relations and corelations can be characterised as colimits of simpler categories. This modular perspective is important as it simplifies the task of giving a complete axiomatisation for semantic equivalence of string diagrams. Moreover, our general result unifies various theorems that are independently found in literature and are relevant for program semantics, quantum computation and control theory
Asymmetric evolutionary games
Evolutionary game theory is a powerful framework for studying evolution in
populations of interacting individuals. A common assumption in evolutionary
game theory is that interactions are symmetric, which means that the players
are distinguished by only their strategies. In nature, however, the microscopic
interactions between players are nearly always asymmetric due to environmental
effects, differing baseline characteristics, and other possible sources of
heterogeneity. To model these phenomena, we introduce into evolutionary game
theory two broad classes of asymmetric interactions: ecological and genotypic.
Ecological asymmetry results from variation in the environments of the players,
while genotypic asymmetry is a consequence of the players having differing
baseline genotypes. We develop a theory of these forms of asymmetry for games
in structured populations and use the classical social dilemmas, the Prisoner's
Dilemma and the Snowdrift Game, for illustrations. Interestingly, asymmetric
games reveal essential differences between models of genetic evolution based on
reproduction and models of cultural evolution based on imitation that are not
apparent in symmetric games.Comment: accepted for publication in PLOS Comp. Bio
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