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The free energy of TAP-solutions for the SK-model of mean field spin glasses can be expressed as a nonlinear functional of local terms: we exploit this feature in order to contrive abstract REM-like models which we then solve by a classical large deviations treatment. This allows to identify the origin of the physically unsettling quadratic (in the inverse of temperature) correction to the Parisi free energy for the SK-model, and formalizes the true cavity dynamics which acts on TAP-space, i.e. on the space of TAP-solutions. From a non-spin glass point of view, this work is the first in a series of refinements which addresses the stability of hierarchical structures in models of evolving populations.
Measurements of the production of electrons from heavy-flavour hadron decays in pp collisions at s√=13 TeV at midrapidity with the ALICE detector are presented down to a transverse momentum (pT) of 0.2 GeV/c and up to pT=35 GeV/c, which is the largest momentum range probed for inclusive electron measurements in ALICE. In p−Pb collisions, the production cross section and the nuclear modification factor of electrons from heavy-flavour hadron decays are measured in the pT range 0.5<pT<26 GeV/c at sNN−−−√=8.16 TeV. The nuclear modification factor is found to be consistent with unity within the statistical and systematic uncertainties. In both collision systems, first measurements of the yields of electrons from heavy-flavour hadron decays in different multiplicity intervals normalised to the multiplicity-integrated yield (self-normalised yield) at midrapidity are reported as a function of the self-normalised charged-particle multiplicity estimated at midrapidity. The self-normalised yields in pp and p−Pb collisions grow faster than linear with the self-normalised multiplicity. A strong pT dependence is observed in pp collisions, where the yield of high-pT electrons increases faster as a function of multiplicity than the one of low-pT electrons. The measurement in p−Pb collisions shows no pT dependence within uncertainties. The self-normalised yields in pp and p−Pb collisions are compared with measurements of other heavy-flavour, light-flavour, and strange particles, and with Monte Carlo simulations.