Saturation Assumption and Finite Element Method for a One-Dimensional Model

In this paper we refer to the hierarchical finite element method and stabilization techniques for convection–diffusion equations. In particular, the aim is to outline an application of saturation assumption to a posteriori error estimates for such problems. We consider here a simple one–dimensional model; the inequality is proved from an analitical point of view for the stabilized finite element solutions in two cases: artificial diffusion and SUPG stabilization techniques

Hybrid spherical approximation

In this paper a local approximation method on the sphere is presented. As interpolation scheme we consider a partition of unity method, such as the modified spherical Shepard's method, which uses zonal basis functions (ZBFs) plus spherical harmonics as local approximants. Moreover, a spherical zone algorithm is efficiently implemented, which works well also when the amount of data is very large, since it is based on an optimized searching procedure. Numerical results show good accuracy of the method, also on real geomagnetic data

Decoding the "Free/Open Source(F/OSS) Software Puzzle" a survey of theoretical and empirical contributions

F/OSS software has been described by many as a puzzle. In the past five years, it has stimulated the curiosity of scholars in a variety of fields, including economics, law, psychology, anthropology and computer science, so that the number of contributions on the subject has increased exponentially. The purpose of this paper is to provide a sufficiently comprehensive account of these contributions in order to draw some general conclusions on the state of our understanding of the phenomenon and identify directions for future research. The exercise suggests that what is puzzling about F/OSS is not so much the fact that people freely contribute to a good they make available to all, but rather the complexity of its institutional structure and its ability to organizationally evolve over time.F/OSS software, Innovation, Incentives, Governance, Intellectual Property Rights

A trivariate interpolation algorithm using a cube-partition searching procedure

In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported weight functions. The partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cube-partition searching procedure. More precisely, we construct a cube structure, which partitions the domain and strictly depends on the size of its subdomains, so that the new searching procedure and, accordingly, the resulting algorithm enable us to efficiently deal with a large number of nodes. Complexity analysis and numerical experiments show high efficiency and accuracy of the proposed interpolation algorithm

Copyright vs. Copyleft Licencing and Software Development

This article aims at clarifying the role played by licenses within the increasingly relevant Open Source Software (OSS) phenomenon. In particular, the article explores from a theoretical point of view the comparative properties of the two main categories of OSS license--copyleft and non-copyleft licenses--in terms of their ability to stimulate innovation and coordination of development efforts. In order to do so, the paper relies on an incomplete contracting model. The model shows that, in spite of the fact that copyleft licenses entail the enjoyment of a narrower set of rights by both licensors and licensees, they may be preferred to non-copyleft licenses when coordination of complementary investments in development is important. It thus provides a non-ideologically-based explanation for the puzzling evidence showing the dominance, in terms of diffusion, of copyleft licenses.intellectual property rights, open source, copyright, copyleft, GPL license, incentives to innovation.

Access to Audio-visual Contents, Exclusivity and Anticommons in New Media Markets

Media markets are characterized by strong peculiarities that often call for longterm exclusivity contracts between content providers and distributors or for vertical or horizontal integration. This paper analyzes and compares the economic effects of existing alternative systems of access to valuable content for new media platforms, under the lens of technological convergence and 'network neutrality'. The analysis suggests the increasing need for a coordinated regulatory framework aimed at balancing costs and benefits of the different models in order to ensure that the development of new markets and new technologies in the age of media convergence is not hindered by "anticommons" tragedies.contents, new media, anticommons, antitrust.

Property rights in the knowledge economy: an explanation of the crisis

Some of the roots underlying the recent crisis may be found in the global convergence towards a model characterized by strong property rights and an extremely limited role attributed to "open science". The modern economy has increasingly moved from an open science - open markets model toward a closed science - closed markets model. Paradoxically, while a non-rival resource like knowledge becomes the most relevant input, small firms and new entrants find it increasingly difficult to be competitive with large and well established organizations. Such a model is progressively increasing the costs of investment in new knowledge, with important negative consequences in terms of overall performance of the economy. We argue that in the knowledge economy, overcoming inequality and the economic crisis can be part of a single coherent policy. If some essential knowledge is moved from the private to the public sphere, this is has not only desirable inequality-decreasing consequences but can also contribute to re-launching the economy, creating the conditions for a sustained development. In a knowledge economy, a super-multiplier could couple the traditional effects of Keynesian spending in time of crisis with the multiplying virtues human knowledge, moved from the private to the public sphere.

Local interpolation schemes for landmark-based image registration: a comparison

In this paper we focus, from a mathematical point of view, on properties and performances of some local interpolation schemes for landmark-based image registration. Precisely, we consider modified Shepard's interpolants, Wendland's functions, and Lobachevsky splines. They are quite unlike each other, but all of them are compactly supported and enjoy interesting theoretical and computational properties. In particular, we point out some unusual forms of the considered functions. Finally, detailed numerical comparisons are given, considering also Gaussians and thin plate splines, which are really globally supported but widely used in applications

Hermite-Birkhoff Interpolation on Arbitrarily Distributed Data on the Sphere and Other Manifolds

We consider the problem of interpolating a function given on scattered points using Hermite-Birkhoff formulas on the sphere and other manifolds. We express each proposed interpolant as a linear combination of basis functions, the combination coefficients being incomplete Taylor expansions of the interpolated function at the interpolation points. The basis functions have the following features: (i) depend on the geodesic distance; (ii) are orthonormal with respect to the point-evaluation functionals; and (iii) have all derivatives equal zero up to a certain order at the interpolation points. Moreover, the construction of such interpolants, which belong to the class of partition of unity methods, takes advantage of not requiring any solution of linear systems