Regional artificial intelligence and the geography of environmental technologies: does local AI knowledge help regional green-tech specialization?

We investigate the extent to which artificial intelligence (AI) is harnessed by regions for specializing in green technologies. By considering the transformative role that AI is playing in the invention process and connecting it to the regional development of environmental technologies, we examine the relationship between green-revealed technological advantages and local AI for EU-28 (NUTS-3) regions over the period 1982–2017. Results show that AI knowledge favours the green-tech specializati...

One-dimensionality of the minimizers for a diffuse interface generalized antiferromagnetic model in general dimension

In this paper we study a diffuse interface generalized antiferromagnetic model. The functional describing the model contains a Modica-Mortola type local term and a nonlocal generalized antiferromagnetic term in competition. The competition between the two terms results in a frustrated system which is believed to lead to the emergence of a wide variety of patterns. The sharp interface limit of our model is considered in [23] and in [10]. In the discrete setting it has been previously studied i...

On the optimality of stripes in a variational model with non-local interactions

We study pattern formation for a variational model displaying competition between a local term penalizing interfaces and a non-local term favoring oscillations. By means of a Γ-convergence analysis, we show that as the parameter J converges to a critical value Jc, the minimizers converge to periodic one-dimensional stripes. A similar analysis has been previously performed by other authors for related discrete systems. In that context, a central point is that each “angle” comes with a strictly...

On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces