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Despite evidence from several bird, fish and mammal species that listeners can discriminate between the vocalizations of familiar and unfamiliar adult conspecifics, direct links between discriminatory abilities and fitness benefits have been difficult to identify. In free-ranging populations of African lions (Panthera leo), females with cubs face a substantial threat from one particular category of unfamiliar individuals: infanticidal males. Here we use playback experiments to demonstrate that females with cubs can distinguish immediately between roars from their own resident males (the fathers of the cubs) and those from unfamiliar, potentially infanticidal males. Although they remain relaxed when played roars from resident males, they immediately become agitated on hearing unfamiliar males and retreat rapidly with their cubs if the latter have reached about 4.5 months of age. These responses are not simply a function of the roarers being unfamiliar, for when played the roars of unfamiliar females, females with cubs consistently approach the loudspeaker. Furthermore, females often move towards the cubs in response to playbacks of unfamiliar males but not in response to playbacks of unfamiliar females or resident males. Our results suggest how females with cubs might, by quickly detecting and categorizing unfamiliar intruders within their territory, protect their cubs from infanticidal males and expel intruding females. Distinguishing between individuals on the basis of their vocal characteristics could therefore confer direct fitness benefits on discriminating lionesses.

Cooperation during territorial defense allows social groups of African lions to defend access to resources necessary for individual reproductive success. Some forms of cooperation will be dependent upon cognition: reciprocity places greater cognitive demands on participants than does kinship or mutualism. Lions have well-developed cognitive abilities that enable individuals to recognize and interact with others in ways that seem to enhance their inclusive fitness. Male lions appear to cooperate unconditionally, consistently responding to roaring intruders regardless of their male companions' kinship or behavior. Female lions, however, do keep track of the past behavior of their female companions, apparently using the reliability of a companion as one means of assessing the risks posed by approaching intruders. Some \"laggard\" females may exploit the cooperative tendencies of \"leaders\" during territorial encounters. Although leader females clearly recognize laggards as such, the costs of tolerating laggards may be less than the benefits leaders gain through territorial defense behavior. Thus, although lions clearly have the cognitive ability to base cooperation on reciprocity, territorial defense cooperation appears instead to be based primarily on mutual benefits to participants for both male and female lions.

A new lacunary set for compact abelian groups is introduced; this is called a Λ(p,q)\\Lambda (p,q) set. This set is defined in terms of the Lorentz spaces and is shown to be a generalization of Λ(p)\\Lambda (p) sets and Sidon sets. A number of functional-analytic statements about Λ(p,q)\\Lambda (p,q) sets are established by making use of the structural similarities between LpL^{p} spaces and Lorentz spaces. These statements are analogous to several well-known properties of a set which are equivalent to the definition of a Λ(p)\\Lambda (p) set. Some general set-theoretic and arithmetic properties of Λ(p,q)\\Lambda (p,q) sets are also developed; these properties extend known results on the structure of Λ(p)\\Lambda (p) sets. Open problems and directions for further research are outlined.

After the Black Death in 1348, land values collapsed; the celibate monk became an object of ridicule while the 'productive and reproductive' third estate rose to power. The Catholic Church attempted to re-establish its authority at the Council of Trent (1545-1563) by rallying behind the theology of Saint Thomas Aquinas, but Humanist scientists and artists like Copernicus, Galileo, Raphael and Titian undermined the authority of Saint Thomas by creating a new vision of a united heaven and earth--a vision that still inspires Western civilization.