Ramanujan sums as supercharacters

The theory of supercharacters, recently developed by Diaconis-Isaacs and Andre, can be used to derive the fundamental algebraic properties of Ramanujan sums. This machinery frequently yields one-line proofs of difficult identities and provides many novel formulas. In addition to exhibiting a new application of supercharacter theory, this article also serves as a blueprint for future work since some of the abstract results we develop are applicable in much greater generality.Comment: 32 pages. Comments welcom

The Role of Oxytocin on Social Behavior Associated with the Formation of a Social Pair-Bond in the Socially Monogamous Convict Cichlid (Amatitlania nigrofasciata)

The mechanisms for monogamy have evolved several times throughout history across various taxa in accordance with selective pressures. In vertebrates, monogamy is facilitated by the formation and the maintenance of social pair-bonds between mates. Social pair-bonds are a form of selective attachment that require complex neurobiological pathways in order to develop and continue. These neurobiological pathways are often regulated by neuroendocrine mechanisms, such as the release of the two neuroendocrine nonapeptides, oxytocin and arginine vasopressin, in specific parts of the brain or body. These neuroendocrine peptides play a big role in social and sexual behaviors. In prairie voles (Microtus ochrogaster) they influence affiliation toward mates and aggression toward conspecifics. Although, oxytocin can affect such physiological processes in the body as parturition and heart rate, as well as social behaviors such as affiliation, matedefense, and social recognition, these effects are largely species-specific. In prairie voles, oxytocin primarily affects female social behaviors but not those of males’. In other species, however, that is not necessarily the case. For example, in zebra finches (Taeniopygia guttata) and convict cichlids (Amatitlania nigrofasciata) exogenous oxytocin agonists or antagonists appear to influence social pair-bond formations in both males and females. Agonists tend to promote social pair-bonds while antagonist delay or prevent social pair-bonds. I, therefore, hypothesized that endogenous oxytocin levels in monogamous convict cichlids would increase as a social pair-bond develops and would decrease after the paired mates are separated