Why some clusters succeed whereas others decline ? Modelling the ambivalent stability properties of clusters

The aim of this paper is to study the ambivalent properties of stabilities of clusters. We propose to enter the black box of the local knowledge externalities by focusing on the location decision externalities. In particular, we show that the nature of mimetic strategies in the convergence process of locational choices influence the dynamic stability of clusters. Thus, when uncertainty and search for legitimacy prevail on the need for coordination and the associated necessities of compatibility and technological convergence, the clusters are unstable, due to an excess of cognitive proximity and a risk of unintended spillovers. Nevertheless, this search for legitimacy, through the strategy which consists in following the locational choice of companies leader of a sector, can lead to the fast emergence of a cluster. But without relational proximity, its stability is not insured. These results are obtained following the formulation of some theoretical proposals on the links between location decision externalities and the resulting forms of socioeconomic proximities. This set of proposals is validated firstly by a model of simulation which makes it possible to test the properties of stability of aggregate outcomes of locational choices. Secondly, they are illustrated by a comparative empirical analysis of two main French clusters (Silicon Sentier and Sophia-Antipolis)..clusters, proximities, stability, location under decision externalities, Silicon Sentier, Sophia-Antipolis

Hyper Hoare Logic: (Dis-)Proving Program Hyperproperties (extended version)

Hoare logics are proof systems that allow one to formally establish properties of computer programs. Traditional Hoare logics prove properties of individual program executions (so-called trace properties, such as functional correctness). Hoare logic has been generalized to prove also properties of multiple executions of a program (so-called hyperproperties, such as determinism or non-interference). These program logics prove the absence of (bad combinations of) executions. On the other hand, program logics similar to Hoare logic have been proposed to disprove program properties (e.g., Incorrectness Logic), by proving the existence of (bad combinations of) executions. All of these logics have in common that they specify program properties using assertions over a fixed number of states, for instance, a single pre- and post-state for functional properties or pairs of pre- and post-states for non-interference. In this paper, we present Hyper Hoare Logic, a generalization of Hoare logic that lifts assertions to properties of arbitrary sets of states. The resulting logic is simple yet expressive: its judgments can express arbitrary trace- and hyperproperties over the terminating executions of a program. By allowing assertions to reason about sets of states, Hyper Hoare Logic can reason about both the absence and the existence of (combinations of) executions, and, thereby, supports both proving and disproving program (hyper-)properties within the same logic. In fact, we prove that Hyper Hoare Logic subsumes the properties handled by numerous existing correctness and incorrectness logics, and can express hyperproperties that no existing Hoare logic can. We also prove that Hyper Hoare Logic is sound and complete, and admits powerful compositionality rules. All our technical results have been proved in Isabelle/HOL