Critical weak-LpL^{p} differentiability of singular integrals

We establish that for every function $u \in L^1_\mathrm{loc}(\Omega)$ whose distributional Laplacian $\Delta u$ is a signed Borel measure in an open set $\Omega$ in $\mathbb{R}^{N}$, the distributional gradient $\nabla u$ is differentiable almost everywhere in $\Omega$ with respect to the weak-$L^{\frac{N}{N-1}}$ Marcinkiewicz norm. We show in addition that the absolutely continuous part of $\Delta u$ with respect to the Lebesgue measure equals zero almost everywhere on the level sets $\{u = \alpha\}$ and $\{\nabla u = e\}$, for every $\alpha \in \mathbb{R}$ and $e \in \mathbb{R}^N$. Our proofs rely on an adaptation of Calder\'on and Zygmund's singular-integral estimates inspired by subsequent work by Hajlasz.Comment: Accepted for publication in Revista Matem\'atica Iberoamerican

Cubism and the Fourth Dimension

This article revisits the historiography of Cubism and mathematics, with a particular focus on Pablo Picasso's uses of geometry at the end of the first decade of the twentieth century. In particular, I consider the artistic appropriation of the concept of the fourth dimension, and its pictorial uses as a conduit for a conceptual reformulation of pictorial space. I investigate Picasso's distinctive adoption of this geometric framework in relation to one of his 1909 experiments across painting and photography, and advocate the possibility of drawing novel historiographical lessons from Picasso's work — lessons that bring the historiography of Cubism in a closer dialogue with recent debates in the historiography of science. I conclude with an appeal to consider the continued relevance of this past experiment in art and science when assessing the contemporary drive toward art-science collaborations, and use the case of Cubism and the fourth dimension as a springboard for a critical reflection on the future directions of art-science collaborations

Objectivity and representative practices across artistic and scientific visualization

This chapter highlights the story of how artists participated in the practices of observation that Lorraine Daston and Peter Galison compellingly define as collective empiricism. It shows the history of scientific objectivity has constantly crossed paths with the history of artistic visualization, from which it has received some powerful challenges. Historicizing the category of representation also has the advantage of reinforcing its vital connection with visualizational connection that is rarely addressed in current philosophical discussions. Distinctive of twentieth-century image- making, trained judgment was a reaction to the constraints imposed by mechanical reproducibility. In the age of computerization, visualization challenges the boundaries between the artifactual and the natural: The new scientific images fulfill the purpose of manipulating the realand they do so in an aesthetically pleasing way. Callanan's artwork is a physical visualization of real-time raw scientific data

Sensitivity and pointing accuracy of the NEMO km3^3 telescope

n this paper we present the results of Monte Carlo simulation studies on the capability of the proposed NEMO km3 telescope to detect high energy neutrinos. We calculated the detector sensitivity to muon neutrinos coming from a generic point-like source. We also simulated the lack of atmospheric muons in correspondence to the Moon disk in order to determine the detector angular resolution and to check the absolute pointing capability.Comment: To be published on VLVNT2 proceedings (Catania, Italy, November 8-11, 2005

Feyerabend on art and science

Paul Feyerabend’s philosophy is replete with artistic metaphors. From theatre to literature, music and painting, the arts were used by Feyerabend not merely as decorative examples to showcase a form of contrived erudition, but as a coherent conceptual framework to articulate key methodological and epistemological questions. With a few isolated exceptions (Couvalis, 1987; Brown, 2009; Kidd, unpublished manuscript), philosophers of science have paid little attention to this intriguing and extremely fruitful aspect of Feyerabend’s work

Mean field limit for Bosons with compact kernels interactions by Wigner measures transportation

We consider a class of many-body Hamiltonians composed of a free (kinetic) part and a multi-particle (potential) interaction with a compactness assumption on the latter part. We investigate the mean field limit of such quantum systems following the Wigner measures approach. We prove the propagation of these measures along the flow of a nonlinear (Hartree) field equation. This enhances and complements some previous results in the subject.Comment: 27 pages. arXiv admin note: text overlap with arXiv:1111.5918 by other author

Comparison between methods for the determination of the primary cosmic ray mass composition from the longitudinal profile of atmospheric cascades

The determination of the primary cosmic ray mass composition from the longitudinal development of atmospheric cascades is still a debated issue. In this work we discuss several data analysis methods and show that if the entire information contained in the longitudinal profile is exploited, reliable results may be obtained. Among the proposed methods FCC ('Fit of the Cascade Curve'), MTA ('Multiparametric Topological Analysis') and NNA ('Neural Net Analysis') with conjugate gradient optimization algorithm give the best accuracy.Comment: 22 pages, 11 figures, accepted by Astroparticle Physics, minor misprints and an extra figure remove