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This paper presents a unified treatment of linear time‐variable networks displaying arbitrary geometrical symmetries by incorporating group theory into an analysis scheme. Symmetric networks have their elements arranged so that certain permutations of the network edges result in a configuration which is identical with the original. These permutations lead to a group of monomial matrices which are shown to commute with the network A‐matrix and the state transition matrix of the normal form equation. The representation theory of groups facilitates the study of those network properties which are determined solely by symmetry. By using group theory, a simple arithmetic condition is derived which, when satisfied, implies that the network is noncontrollable or nonobservable because of symmetry alone. The results allow the determination by inspection of linear combinations of the original state variables which result in noncontrollable variables. It is shown that networks displaying axial point group symmetry are generally only weakly controllable.

In this paper we use an experimental approach to investigate how linguistic conventions can emerge in a society without explicit agreement. As a starting point we consider the signaling game introduced by Lewis (Convention 1969). We find that in experimental settings, small groups can quickly develop conventions of signal meaning in these games. We also investigate versions of the game where the theoretical literature indicates that meaning will be less likely to arise-when there are more than two states for actors to transfer meaning about and when some states are more likely than others. In these cases, we find that actors are less likely to arrive at strategies where signals have clear conventional meaning. We conclude with a proposal for extending the use of the methodology of experimental economics in experimental philosophy.

The 'phenotypic gambit,' the assumption that we can ignore genetics and look at the fitness of phenotypes to determine the expected evolutionary dynamics of a population, is often used in evolutionary game theory. However, as this paper will show, an overlooked genotype to phenotype map can qualitatively affect evolution in ways the phenotypic approach cannot predict or explain. This gives us reason to believe that, even in the long-term, correspondences between phenotypic predictions and dynamical outcomes are not robust for all plausible assumptions regarding the underlying genetics of traits. This paper shows important ways in which the phenotypic gambit can fail and how to proceed with evolutionary game theoretic modeling when it does.

The social identity of a researcher can affect their position in a community, as well as the uptake of their ideas. In many fields, members of underrepresented or minority groups are less likely to be cited, leading to citation gaps. Though this empirical phenomenon has been well-studied, empirical work generally does not provide insight into the causes of citation gaps. I will argue, using mathematical models, that citation gaps are likely due in part to the structure of academic communities. The existence of these 'structural causes' has implications for attempts to lessen citation gaps, and for proposals to make academic communities more efficient (e.g. by eliminating pre-publication peer review). These proposals have the potential to create feedback loops, amplifying current structural inequities.