We consider the Curie-Weiss model at initial temperature 0 < β −1 ≤ ∞ in vanishing external field evolving under a Glauber spin-flip dynamics with temperature 0 < β −1 ≤ ∞. We study the limiting conditional probabilities and their continuity properties and discuss their set of points of discontinuity (bad points). We provide a complete analysis of the transition between Gibbsian and non-Gibbsian behavior as a function of time, extending earlier work for the case of independent spin-flip dynamics.For initial temperature β −1 > 1 we prove that the time-evolved measure stays Gibbs forever, for any (possibly low) temperature of the dynamics.In the regime of heating to low-temperatures from even lower temperatures, 0 < β −1 < min{β −1 , 1} we prove that the time-evolved measure is Gibbs initially and becomes nonGibbs after a sharp transition time. We find this regime is further divided into a region where only symmetric bad configurations exist, and a region where this symmetry is broken. In the regime of further cooling from low-temperatures, β −1 < β −1 < 1 there is always symmetry-breaking in the set of bad configurations. These bad configurations are created by a new mechanism which is related to the occurrence of periodic orbits for the vector field which describes the dynamics of Euler-Lagrange equations for the path large deviation functional for the order parameter.To our knowledge this is the first example of the rigorous study of non-Gibbsian phenomena related to cooling, albeit in a mean-field setup.

In this paper we study homogeneous Gibbs measures on a Cayley tree, subjected to an infinite-temperature Glauber evolution, and consider their (non-)Gibbsian properties. We show that the intermediate Gibbs state (which in zero field is the free-boundary-condition Gibbs state) behaves different from the plus and the minus state. E.g. at large times, all configurations are bad for the intermediate state, whereas the plus configuration never is bad for the plus state. Moreover, we show that for each state there are two transitions. For the intermediate state there is a transition from a Gibbsian regime to a non-Gibbsian regime where some, but not all configurations are bad, and a second one to a regime where all configurations are bad.For the plus and minus state, the two transitions are from a Gibbsian regime to a non-Gibbsian one and then back to a Gibbsian regime again.

Role-based access control (RBAC) is a popular framework for modelling access control rules. In this paper we identify a fragment of RBAC called bi-sorted role based access control (RBÄC). We start from the observation that "classic" RBAC blends together subject management aspects and permission management aspects into a single object of indirection: a role. We posit there is merit in distinguishing these administrative perspectives and consequently introducing two distinct objects of indirection: the proper role (which applies solely to subjects) and the demarcation (which applies solely to permissions). We then identify a third administrative perspective called access management where the two are linked up. In this way we enhance organisational scalability by decoupling the tasks of maintaining abstractions over the set of subjects (assignment of subjects into proper roles), maintaining abstractions over the set of permissions (assignment of permissions into demarcations), and maintaining abstract access control policy (granting proper roles access to demarcations). Moreover, the latter conceptual refinement naturally leads us to the introduction of negative roles (and, dually, negative demarcations). The relevance of the four-sorted extension called polarized, bi-sorted role based access control (R ± BÄC), in a semantic sense, is further supported by the existence of Galois connections between sets of subjects and permissions and between positive and negative roles.

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