Proofs Versus Experiments: Wittgensteinian Themes Surrounding the Four-Color Theorem

The Four-Colour Theorem (4CT) proof, presented to the mathematical community in a pair of papers by Appel and Haken in the late 1970's, provoked a series of philosophical debates. Many conceptual points of these disputes still require some elucidation. After a brief presentation of the main ideas of Appel and Haken’s procedure for the proof and a reconstruction of Thomas Tymoczko’s argument for the novelty of 4CT’s proof, we shall formulate some questions regarding the connections between the points raised by Tymoczko and some Wittgensteinian topics in the philosophy of mathematics such as the importance of the surveyability as a criterion for distinguishing mathematical proofs from empirical experiments. Our aim is to show that the “characteristic Wittgensteinian invention” (Mühlhölzer 2006) – the strong distinction between proofs and experiments – can shed some light in the conceptual confusions surrounding the Four-Colour Theorem

Orchestrating Forest Policy in Italy: Mission Impossible?

In the Italian political and economic agenda the forest sector occupies a marginal role. The forest sector in Italy is characterized by a high institutional fragmentation and centralized decision-making processes dominated by Public Forest Administrations. Public participation in forest policy processes has been implemented since the 1990s at national, regional and local levels in several cases. However, today no significant changes have been observed in the overall governance of the forest sector and stakeholders' involvement in Italian forest policy decision-making is still rather limited. The aims of this paper are to describe the state of forest-related participatory processes in Italy at various levels (national, regional and local) and identify which factors and actors hinder or support the establishment and implementation of participatory forest-related processes in the country. The forest-related participatory processes are analyzed adopting a qualitative-based approach and interpreting interactive, complex and non-linear participatory processes through the lens of panarchy theory

Co-constructing a new framework for evaluating social innovation in marginalized rural areas

The EU funded H2020 project \u2018Social Innovation in Marginalised Rural Areas\u2019 (SIMRA; www.simra-h2020.eu) has the overall objective of advancing the state-of-the-art in social innovation. This paper outlines the process for co- developing an evaluation framework with stakeholders, drawn from across Europe and the Mediterranean area, in the fields of agriculture, forestry and rural development. Preliminary results show the importance of integrating process and outcome-oriented evaluations, and implementing participatory approaches in evaluation practice. They also raise critical issues related to the comparability of primary data in diverse regional contexts and highlight the need for mixed methods approaches in evaluation

The role of dark matter in the galaxy mass-size relationship

The observed relationship between stellar mass and effective radius for early type galaxies, pointed out by many authors, is interpreted in the context of Clausius' virial maximum theory. In this view, it is strongly underlined that the key of the above mentioned correlation is owing to the presence of a deep link between cosmology and the existence of the galaxy Fundamental Plane. Then the ultimate meaning is: understanding visible mass - size correlation and/or Fundamental Plane means understanding how galaxies form. The mass - size relationship involves baryon (mainly stellar) mass and its typical dimension related to the light, but it gets memory of the cosmological mass variance at the equivalence epoch. The reason is that the baryonic component virializes by sharing virial energy in about equal amount between baryons and dark matter, this sharing depending, in turn, on the steepness of the dark matter distribution. The general strategy consists in using the two-component tensor virial theorem for determining the virialized baryonic configurations. A King and a Zhao density profile are assumed for the inner baryonic and the outer dark matter component, respectively, at the end of the relaxation phase. All the considerations are restricted to spherical symmetry for simplicity. The effect of changing the dark-to-baryon mass ratio, m, is investigated inside a LambdaCDM scenario. A theoretical mass - size relation is expressed for the baryonic component, which fits fairly well to the data from a recently studied galaxy sample. Finally, the play of intrinsic dispersion on the mass ratio, m, is discussed in the light of the cusp/core problem and some consequences are speculated about the existence of a limit, m_l, expected by the theory.Comment: 36 pages, 8 figures (Accepted for publication in New Astronomy

On the tilt of Fundamental Plane by Clausius' virial maximum theory

The theory of the Clausius' virial maximum to explain the Fundamental Plane (FP) proposed by Secco (2000, 2001,2005) is based on the existence of a maximum in the Clausius' Virial (CV) potential energy of a early type galaxy (ETG) stellar component when it is completely embedded inside a dark matter (DM) halo. At the first order approximation the theory was developed by modeling the two-components with two cored power-law density profiles. An higher level of approximation is now taken into account by developing the same theory when the stellar component is modeled by a King-model with a cut-off. Even if the DM halo density remains a cored power law the inner component is now more realistic for the ETGs. The new formulation allows us to understand more deeply what is the dynamical reason of the FP tilt and in general how the CV theory may really be the engine to produce the FP main features. The degeneracy of FP in respect to the initial density perturbation spectrum may be now full understood in a CDM cosmological scenario. A possible way to compare the FPs predicted by the theory with those obtained by observations is also exemplified.Comment: 35 pages, 8 figure

High-pressure synthesis, crystal and electronic structures of a new scandium tungstate, Sc0.67WO4

Negative thermal expansion (NTE) materials possess a low-density, open structure which can respond to high pressure conditions, leading to new compounds and/or different physical properties. Here we report that one such NTE material -- white, insulating, orthorhombic Sc2W3O12 -- transforms into a black compound when treated at 4 GPa and 1400 oC. The high pressure phase, Sc0.67WO4, crystallizes in a defect-rich wolframite-type structure, a dense, monoclinic structure (space group P2/c) containing 1-D chains of edge-sharing WO6 octahedra. The chemical bonding of Sc0.67WO4 vis-a-vis the ambient pressure Sc2W3O12 phase can be understood on the basis of the Sc defect structure. Magnetic susceptibility, resistivity, thermoelectric power and IR spectroscopic measurements reveal that Sc0.67WO4 is a paramagnet whose conductivity is that of a metal in the presence of weak localization and electron-electron interactions. Oxygen vacancies are suggested as a potential mechanism for generating the carriers in this defective wolframite material.Comment: 29 pages total, 1 table, 7 figure

Structure and Dynamics of Liquid Iron under Earth's Core Conditions

First-principles molecular dynamics simulations based on density-functional theory and the projector augmented wave (PAW) technique have been used to study the structural and dynamical properties of liquid iron under Earth's core conditions. As evidence for the accuracy of the techniques, we present PAW results for a range of solid-state properties of low- and high-pressure iron, and compare them with experimental values and the results of other first-principles calculations. In the liquid-state simulations, we address particular effort to the study of finite-size effects, Brillouin-zone sampling and other sources of technical error. Results for the radial distribution function, the diffusion coefficient and the shear viscosity are presented for a wide range of thermodynamic states relevant to the Earth's core. Throughout this range, liquid iron is a close-packed simple liquid with a diffusion coefficient and viscosity similar to those of typical simple liquids under ambient conditions.Comment: 13 pages, 8 figure

Toward Understanding the origin of the Fundamental Plane for Early-Type Galaxies

We present a panoramic review of several observational and theoretical aspects of the modern astrophysical research about the origin of the Fundamental Plane (FP) relation for Early-Type Galaxies (ETGs). The discussion is focused on the problem of the tilt and the tightness of the FP, and on the attempts to derive the luminosity evolution of ETGs with redshift. Finally, a number of observed features in the FP are interpreted from the standpoint of a new theoretical approach based on the two-component tensor virial theorem.Comment: 30 pages, 3 figure