What qualifies as a cluster theory?

This paper investigates the theoretical backgrounds of the “cluster” and proposes a framework aiming at drawing the contour of cluster theory. The profundity of the notion of ‘clusters’ is arguably conditional on the coherence of three fundamental issues associated with the concept: 1) the economic and social benefits that may accrue to firms when clustering or co-locating (the existence argument); 2) the diseconomies encountered when clustering exceeds certain geographical and sectoral thresholds (the extension argument); and, finally, 3) the possible erosion of economies and onset of diseconomies over the lifecycle of the cluster (the exhaustion argument). Each of these three issues is examined in terms of three relevant major theoretical frameworks that can be brought to bear on the cluster concept. The paper considers approaches based on the idea of externalities (illustrated by the Marshall's work on ‘Industrial district’); on competitiveness issue (illustrated by Michael Porter’s theory of cluster growth); on a territorial perspective (illustrated by the GREMI approach). The paper acknowledges the general shift in explanatory emphasis from considerations of static cost efficiency towards more dynamic interpretations that highlight the creation and use of knowledge as their pivotal theoretical element. By placing these changes within a common conceptual framework the paper shows how different theoretical solutions provide distinct points of departure for subsequent policy recommendations. Three distinctive groups of solutions are identified focusing respectively on local spillovers, on competitiveness and on the region and its development. The paper concludes by identifying areas of particular ambiguity where further theoretical work is most urgently needed.Cluster, cluster theory, industrial district, innovative milieu, regional policy

μ-Dependent model reduction for uncertain discrete-time switched linear systems with average dwell time

In this article, the model reduction problem for a class of discrete-time polytopic uncertain switched linear systems with average dwell time switching is investigated. The stability criterion for general discrete-time switched systems is first explored, and a μ-dependent approach is then introduced for the considered systems to the model reduction solution. A reduced-order model is constructed and its corresponding existence conditions are derived via LMI formulation. The admissible switching signals and the desired reduced model matrices are accordingly obtained from such conditions such that the resulting model error system is robustly exponentially stable and has an exponential H∞ performance. A numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results

Parsimonious Migration History Problem: Complexity and Algorithms

In many evolutionary processes we observe extant taxa in different geographical or anatomical locations. To reconstruct the migration history from a given phylogenetic tree T, one can model locations using an additional character and apply parsimony criteria to assign a location to each internal vertex of T. The migration criterion assumes that migrations are independent events. This assumption does not hold for evolutionary processes where distinct taxa from different lineages comigrate from one location to another in a single event, as is the case in metastasis and in certain infectious diseases. To account for such cases, the comigration criterion was recently introduced, and used as an optimization criterion in the Parsimonious Migration History (PMH) problem. In this work, we show that PMH is NP-hard. In addition, we show that a variant of PMH is fixed parameter tractable (FPT) in the number of locations. On simulated instances of practical size, we demonstrate that our FPT algorithm outperforms a previous integer linear program in terms of running time