On Realism and Quantum Mechanics

A discussion of the quantum mechanical use of superposition or entangled states shows that descriptions containing only statements about state vectors and experiments outputs are the most suitable for Quantum Mechanics. In particular, it is shown that statements about the undefined values of physical quantities before measurement can be dropped without changing the predictions of the theory. If we apply these ideas to EPR issues, we find that the concept of non-locality with its 'instantaneous action at a distance' evaporates. Finally, it is argued that usual treatments of philosophical realist positions end up in the construction of theories whose major role is that of being disproved by experiment. This confutation proves simply that the theories are wrong; no conclusion about realism (or any other philosophical position) can be drawn, since experiments deal always with theories and these are never logical consequences of philosophical positions.Comment: 13 pages. Accepted for publication in Il Nuovo Cimento

Weighting Ripley’s K-function to account for the firm dimension in the analysis of spatial concentration

The spatial concentration of firms has long been a central issue in economics both under the theoretical and the applied point of view due mainly to the important policy implications. A popular approach to its measurement, which does not suffer from the problem of the arbitrariness of the regional boundaries, makes use of micro data and looks at the firms as if they were dimensionless points distributed in the economic space. However in practical circumstances the points (firms) observed in the economic space are far from being dimensionless and are conversely characterized by different dimension in terms of the number of employees, the product, the capital and so on. In the literature, the works that originally introduce such an approach (e.g. Arbia and Espa, 1996; Marcon and Puech, 2003) disregard the aspect of the different firm dimension and ignore the fact that a high degree of spatial concentration may result from both the case of many small points clustering in definite portions of space and from only few large points clustering together (e.g. few large firms). We refer to this phenomena as to clustering of firms and clustering of economic activities. The present paper aims at tackling this problem by adapting the popular Kfunction (Ripley, 1977) to account for the point dimension using the framework of marked point process theory (Penttinen, 2006)Agglomeration, Marked point processes, Spatial clusters, Spatial econometrics

Measuring industrial agglomeration with inhomogeneous K-function: the case of ICT firms in Milan (Italy)

Why do industrial clusters occur in space? Is it because industries need to stay close together to interact or, conversely, because they concentrate in certain portions of space to exploit favourable conditions like public incentives, proximity to communication networks, to big population concentrations or to reduce transport costs? This is a fundamental question and the attempt to answer to it using empirical data is a challenging statistical task. In economic geography scientists refer to this dichotomy using the two categories of spatial interaction and spatial reaction to common factors. In economics we can refer to a distinction between exogenous causes and endogenous effects. In spatial econometrics and statistics we use the terms of spatial dependence and spatial heterogeneity. A series of recent papers introduced explorative methods to analyses the spatial patterns of firms using micro data and characterizing each firm by its spatial coordinates. In such a setting a spatial distribution of firms is seen as a point pattern and an industrial cluster as the phenomenon of extra-concentration of one industry with respect to the concentration of a benchmarking spatial distribution. Often the benchmarking distribution is that of the whole economy on the ground that exogenous factors affect in the same way all branches. Using such an approach a positive (or negative) spatial dependence between firms is detected when the pattern of a specific sector is more aggregated (or more dispersed) than the one of the whole economy. In this paper we suggest a parametric approach to the analysis of spatial heterogeneity, based on the socalled inhomogeneous K-function (Baddeley et al., 2000). We present an empirical application of the method to the spatial distribution of high-tech industries in Milan (Italy) in 2001. We consider the economic space to be non homogenous, we estimate the pattern of inhomogeneity and we use it to separate spatial heterogeneity from spatial dependence.

Low temperature analysis of two dimensional Fermi systems with symmetric Fermi surface

We prove the convergence of the perturbative expansion, based on Renormalization Group, of the two point Schwinger function of a system of weakly interacting fermions in d=2, with symmetric Fermi surface and up to exponentially small temperatures, close to the expected onset of superconductivityComment: 60 pages, 3 figure