Spectra of "real-world" graphs: beyond the semicircle law.

Many natural and social systems develop complex networks that are usually modeled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semicircle law is known to describe the spectral densities of uncorrelated random graphs, much less is known about the spectra of real-world graphs, describing such complex systems as the Internet, metabolic pathways, networks of power stations, scientific collaborations, or movie actors, which are inherently correlated and usually very sparse. An important limitation in addressing the spectra of these systems is that the numerical determination of the spectra for systems with more than a few thousand nodes is prohibitively time and memory consuming. Making use of recent advances in algorithms for spectral characterization, here we develop methods to determine the eigenvalues of networks comparable in size to real systems, obtaining several surprising results on the spectra of adjacency matrices corresponding to models of real-world graphs. We find that when the number of links grows as the number of nodes, the spectral density of uncorrelated random matrices does not converge to the semicircle law. Furthermore, the spectra of real-world graphs have specific features, depending on the details of the corresponding models. In particular, scale-free graphs develop a trianglelike spectral density with a power-law tail, while small-world graphs have a complex spectral density consisting of several sharp peaks. These and further results indicate that the spectra of correlated graphs represent a practical tool for graph classification and can provide useful insight into the relevant structural properties of real networks.

Feedback research in postgraduates on efficacy of education in school of medicine.

At the Medical School, Tirgu-Mures/Romania, in the Alumni Office of the Department of Social Medicine, two feed-back researches were performed in 1962 and 1973 on 100 graduates working in basic medical care, in order to evaluate the efficacy of practical medical training. Between 1962 and 1973 efforts have been made to bring the medical teaching nearer to the ambulatory practical training. The compulsory externship (4 to 6 years), the young students' work as nurses at the patients' beds (1 to 2 years), their distribution in rural factory surgeries (5 to 6 years), the night duties at medical emergency services (6 years), as well as their training in prophylactic medico-hygiene activities brought a lot of improvements to the practical training of the students, future general practitioners. However, there are problems in this field of hygiene and epidemiology, as well as in emergency assistance. The improvement of practical education goes on. The next feed-back research is planned for 1976.