Universality of citation distributions: towards an objective measure of scientific impact

We study the distributions of citations received by a single publication within several disciplines, spanning broad areas of science. We show that the probability that an article is cited $c$ times has large variations between different disciplines, but all distributions are rescaled on a universal curve when the relative indicator $c_f=c/c_0$ is considered, where $c_0$ is the average number of citations per article for the discipline. In addition we show that the same universal behavior occurs when citation distributions of articles published in the same field, but in different years, are compared. These findings provide a strong validation of $c_f$ as an unbiased indicator for citation performance across disciplines and years. Based on this indicator, we introduce a generalization of the h-index suitable for comparing scientists working in different fields.Comment: 7 pages, 5 figures. accepted for publication in Proc. Natl Acad. Sci. US

Cluster Percolation and Thermal Critical Behaviour

Continuous phase transitions in spin systems can be formulated as percolation of suitably defined clusters. We review this equivalence and then discuss how in a similar way, the color deconfinement transition in SU(2) gauge theory can be treated as a percolation phenomenon. In the presence of an external field, spin systems cease to show thermal critical behavior, but the geometric percolation transition persists (Kert\'esz line). For $H\not=0$, we study the relation between percolation and pseudocritical behavior, both for continuous and first order transitions, and show that it leads to the necessity of an $H$-dependent cluster definition. A viable formulation of this kind could serve as definition of deconfinement in QCD with dynamical quarks.Comment: 8 pages, 4 figure

Break-up and electromagnetic response of light weakly-bound dicluster systems

This study is focused on the break-up and electromagnetic response of light weakly-bound dicluster nuclei. The cluster picture in the case of $^7$Li is shown to be a very good approximation and in this framework we calculate nuclear structure observables. We solve the Schr\"odinger equation for the relative motion both for discrete and continuum states and this automatically takes into a proper account the role of resonances. A concentration of strength in the low energy continuum, solely due to the weakly-bound nature of the bound states is seen and explained as a favourable matching between the wavelengths of the initial and final states. Finally preliminary results on form factors are briefly outlined and their microscopic derivation as well as utilization in reaction studies is discussed.Comment: Contribution to the "Symposium on Nuclear Clusters:from Light Exotic to Superheavy Nuclei" 284. WE-Heraeus-Seminar, help in Rauischholzhausen (near Marburg) Germany, 5--9 August 2002. 2 pages, 1 combined figure, rauisch.sty use

All coordinates transformations that separate the center of mass kinetic energy, their group structure and geometry

The most general coordinates transformations that allow for the exact separation of the kinetic energy operator of a quantum many-body system into total center of mass kinetic energy and internal kinetic energy are found and discussed. We find i) that the suitable transformations, depending on the number of particles, have a certain number of free parameters and this allows for the generalization of the Jacobi coordinates to a much larger class of coordinates with the same properties and ii) that there is a new, uncommon, additive group structure hidden in the transformation matrices that is connected to certain geometric properties of the set of coordinates

Quality functions in community detection

Community structure represents the local organization of complex networks and the single most important feature to extract functional relationships between nodes. In the last years, the problem of community detection has been reformulated in terms of the optimization of a function, the Newman-Girvan modularity, that is supposed to express the quality of the partitions of a network into communities. Starting from a recent critical survey on modularity optimization, pointing out the existence of a resolution limit that poses severe limits to its applicability, we discuss the general issue of the use of quality functions in community detection. Our main conclusion is that quality functions are useful to compare partitions with the same number of modules, whereas the comparison of partitions with different numbers of modules is not straightforward and may lead to ambiguities.Comment: 10 pages, 4 figures, invited paper to appear in the Proceedings of SPIE International Conference "Fluctuations and Noise 2007", Florence, Italy, 20-24 May, 200