Backreaction during inflation: a physical gauge invariant formulation.

Within a genuinely gauge invariant approach recently developed for the computation of the cosmological backreaction, we study, in a cosmological inflationary context and with respect to various observers, the impact of scalar fluctuations on the space-time dynamics in the long wavelength limit. We stress that such a quantum backreaction effect is evaluated in a truly gauge independent way using a set of effective equations which describe the dynamics of the averaged geometry. In particular we show under what conditions the free falling (geodetic) observers do not experience any scalar-induced backreaction in the effective Hubble rate and fluid equation of state.

Asymptotic safety in Einstein gravity and scalar-fermion matter.

Within the functional renormalization group approach we study the effective quantum field theory of Einstein gravity and one self-interacting scalar coupled to N(f) Dirac fermions. We include in our analysis the matter anomalous dimensions induced by all the interactions and analyze the highly nonlinear beta functions determining the renormalization flow. We find the existence of a nontrivial fixed point structure both for the gravity and the matter sector, besides the usual Gaussian matter one. This suggests that asymptotic safety could be realized in the gravitational sector and in the standard model. Nontriviality in the Higgs sector might involve gravitational interactions.

An analytical short- and long-term memory model of presynaptic plasticity.

A mathematical model, called the Learning Gate Model (LGM), that describes phenomena responsible for biological synaptic plasticity, is presented. The functionality of the model are mainly based on the work of Kandel and colleagues on the most elementary forms of learning observed in the Aplysia Californica marine mollusc. In particular, emphasis is placed on the double temporal dynamics of synaptic plasticity and the temporal specificity of classical conditioning. By properly modeling the effect of the binding of Ca++ ions to the serotonin-sensitive adenylate cyclase enzyme, it is shown how a positively accelerated learning curve can be obtained for sensitization and classical conditioning. Phenomena of spontaneous recovery and second-order conditioning are reproduced through simulations. Mathematical analyses of the temporal trace of conditioned stimulus and of the Short-Term Memory steady state are also given.