The diffusion of knowledge in industrial districts and clusters

ABSTRACT The dissemination of knowledge in industrial districts (ID) and clusters has often been linked to the existence of a specific tacit knowledge. Thus, the companies belonging to ID specialization sector might sustain a distinctive competitive advantage against isolated firms. However, the observation of technological changes in recent decades and the presence of ID whose technological intensity has dramatically increased in the same period suggest the existence and need for codified knowledge in these agglomerations. As result of tacit knowledge decline, the economic performance of ID could move backwards, given the greater ease to imitate and reproduce their contextual knowledge by competitor firms located in not district areas. The paper discusses the above assumptions, suggesting the existence of combinations/hybridizations of both types of knowledge in ID, which we have named locational-translational knowledge. This third type of knowledge could explain the maintenance of ID contextual advantages even in presence of higher doses of codified knowledge. This would require the presence of agents acting as interfaces able to absorb new pieces of codified knowledge in order to combine them with local knowledge for adjusting the specific needs of ID. However, we argue the existence of several constraints, such as the size of 'creative market district’, in ID which may require the opening of ID to knowledge imported from academic institutions and other formal research organizations, in contrast with autarky or isolation suggested by tacit knowledge. Finally, an analysis of the ID evolution enables us to appreciate that the process of absorption, combination and dissemination of external knowledge may have existed throughout the life cycle of ID but supported, at each stage, for different institutional agents: the 'impannatore', the 'cappofiliera' firm and, lastly, for formal knowledge-oriented institutions such as the above referred.

Magnetism and topological phases in an interacting decorated honeycomb lattice with spin-orbit coupling

We study the interplay between spin-orbit coupling (SOC) and Coulomb repulsion in a Hubbard model on a decorated honeycomb lattice which leads to a plethora of phases. While a quantum spin hall insulator is stable at weak Coulomb repulsion and moderate SOC, a semimetallic phase emerges at large SOC in a broad range of Coulomb repulsion. This semimetallic phase has topological properties not observed in conventional metals such as a finite, non-quantized spin Hall conductivity. At large Coulomb repulsion and negligible spin-orbit coupling, electronic correlations stabilize a resonance valence bond (RVB) spin liquid state in contrast to the classical antiferromagnetic state predicted by mean-field theory. Under sufficiently strong SOC, such RVB state is transformed into a magnetic insulator consisting on S~3/2 localized moments on a honeycomb lattice with antiferromagnetic order and topological features.Comment: 13 pages, 10 figure

Lax orthogonal factorisation systems

This paper introduces lax orthogonal algebraic weak factorisation systems on 2-categories and describes a method of constructing them. This method rests in the notion of simple 2-monad, that is a generalisation of the simple reflections studied by Cassidy, H\'ebert and Kelly. Each simple 2-monad on a finitely complete 2-category gives rise to a lax orthogonal algebraic weak factorisation system, and an example of a simple 2-monad is given by completion under a class of colimits. The notions of KZ lifting operation, lax natural lifting operation and lax orthogonality between morphisms are studied.Comment: 59 page

Tensor renormalization group in bosonic field theory

We compute the partition function of a massive free boson in a square lattice using a tensor network algorithm. We introduce a singular value decomposition (SVD) of continuous matrices that leads to very accurate numerical results. It is shown the emergence of a CDL fixed point structure. In the massless limit, we reproduce the results of conformal field theory including a precise value of the central charge.Comment: 5+8 pages, 4+2 figure