We present analytical results for long-term growth rates of structured populations in randomly fluctuating environments, which we apply to predict how cellular response networks evolve. We show that networks which respond rapidly to a stimulus will evolve phenotypic memory exclusively under random (i.e. non-periodic) environments. We identify the evolutionary phase diagram for simple response networks, which we show can exhibit both continuous and discontinuous transitions. Our approach enables exact analysis of diverse evolutionary systems, from viral epidemics to emergence of drug resistance.
We construct a family of vector fields that generate local symmetries in the solution space of low frequency massless field perturbations in the general Kerr geometry. This yields a one-parameter family of SL(2, R) × SL(2, R) algebras. We identify limits in which the SL(2, R) × SL(2, R) algebra contracts to an SL(2, R) symmetry of the Schwarzschild background. We note that for a particular value of the free parameter, the symmetry algebra generates the quasinormal mode spectrum of a Kerr black hole in the large damping limit, suggesting a connection between the hidden conformal symmetry and a fundamental CFT underlying the quantum Kerr black hole.
Biological organisms experience constantly changing environments, from sudden changes in physiology brought about by feeding, to the regular rising and setting of the Sun, to ecological changes over evolutionary timescales. Living organisms have evolved to thrive in this changing world but the general principles by which organisms shape and are shaped by time varying environments remain elusive. Our understanding is particularly poor in the intermediate regime with no separation of timescales, where the environment changes on the same timescale as the physiological or evolutionary response. Experiments to systematically characterize the response to dynamic environments are challenging since such environments are inherently high dimensional. This roadmap deals with the unique role played by time varying environments in biological phenomena across scales, from physiology to evolution, seeking to emphasize the commonalities and the challenges faced in this emerging area of research.
Massless fields propagating in a generic Kerr black hole background enjoy a hidden SL(2, R) × SL(2, R) symmetry. We determine how the exact mode functions decompose into representations of this symmetry group. This extends earlier results on the low frequency limit of the massless scalar case to finite frequencies and general spin. As an application, we numerically determine the parameters of the representations that appear in quasinormal modes. These results represent a first step to formulating a more precise mapping to a holographic dual conformal field theory for generic black holes.
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