The Tenth Article of Ettore Majorana

This year is the centenary of the birth of Ettore Majorana, one of the major Italian physicists of all times. In this note we briefly sketch a few biographical details about Ettore Majorana and introduce and discuss the main points of Majorana's 10th article. In his article Majorana explicitly considers quantum mechanics as an irreducible statistical theory because the theory is not able to describe the time evolution of a single particle or atom in a precise environment at a deterministic level. This lack of determinism at the level of an elementary physical system motivated him to suggest a formal analogy between statistical laws observed in physics and in the social sciences. We hope the occasion of the centenary of the birth of Ettore Majorana will be useful to remember and to reconsider not only his exceptional achievements in theoretical physics but also his fresh and original views on the role of statistical laws in physics and in other disciplines such as the social sciences.Comment: 3 pages, to appear in Europhysics News 37/4 July/August 200

Spectral density of the correlation matrix of factor models: A random matrix theory approach

We studied the eigenvalue spectral density of the correlation matrix of factor models of multivariate time series. By making use of the random matrix theory, we analytically quantified the effect of statistical uncertainty on the spectral density due to the finiteness of the sample. We considered a broad range of models, ranging from one-factor models to hierarchical multifactor models

Kullback-Leibler distance as a measure of information filtered from multivariate data

We show that the Kullback-Leibler distance is a good measure of the statistical uncertainty of correlation matrices estimated by using a finite set of data. For correlation matrices of multivariate Gaussian variables we analytically determine the expected values of the Kullback-Leibler distance of a sample correlation matrix from a reference model and we show that the expected values are known also when the specific model is unknown. We propose to make use of the Kullback-Leibler distance to estimate the information extracted from a correlation matrix by correlation filtering procedures. We also show how to use this distance to measure the stability of filtering procedures with respect to statistical uncertainty. We explain the effectiveness of our method by comparing four filtering procedures, two of them being based on spectral analysis and the other two on hierarchical clustering. We compare these techniques as applied both to simulations of factor models and empirical data. We investigate the ability of these filtering procedures in recovering the correlation matrix of models from simulations. We discuss such ability in terms of both the heterogeneity of model parameters and the length of data series. We also show that the two spectral techniques are typically more informative about the sample correlation matrix than techniques based on hierarchical clustering, whereas the latter are more stable with respect to statistical uncertaint

On the dependence of magnetic stochastic resonance features on the features of magnetic hysteresis

Numerical study of magnetic stochastic resonance (SR) in several magnetic systems having different hysteresis loops was performed. The various hysteresis loops were modeled by using Preisach model in which several identification functions were used. The results showed the dependence of SR on the parameters of Preisach function. The results also showed how the field H/sub 0/ shifted the onset of SR and how a large dispersion of the distribution of hysterons degraded the SR

Multi-scale analysis of the European airspace using network community detection

We show that the European airspace can be represented as a multi-scale traffic network whose nodes are airports, sectors, or navigation points and links are defined and weighted according to the traffic of flights between the nodes. By using a unique database of the air traffic in the European airspace, we investigate the architecture of these networks with a special emphasis on their community structure. We propose that unsupervised network community detection algorithms can be used to monitor the current use of the airspaces and improve it by guiding the design of new ones. Specifically, we compare the performance of three community detection algorithms, also by using a null model which takes into account the spatial distance between nodes, and we discuss their ability to find communities that could be used to define new control units of the airspace.Comment: 22 pages, 14 figure

Statistical Regularities in ATM: network properties, trajectory deviations and delays

One of the key enabler to the productivity and efficiency shift foreseen by SESAR will be the business-trajectory concept. The path to a deep understanding of how this new concept impacts on the future SESAR Air Traffic Management scenario goes through a better understanding of the actual air traffic network, and this will be done in the present paper by analyzing traffic data within the framework of complex network analysis. In this paper we will consider flights trajectory data from the Data Demand Repository database. In a first investigation, we perform a network study of the air traffic infrastructure starting from the airports and then refining our analysis at the level of navigation points in order to understand what are the main features that may help explaining why some nodes of the network happen to be found in the same community, i.e. cluster. In a second investigation we perform a study at the level of flight trajectories with the aim of identify statistical regularities in the spatio-temporal deviations of flights between their planned and actual 4D trajectories

An Agent Based Model of Air Traffic Management

The WP-E ELSA project aims at developing an empirically grounded agent based model that describes some of the stylized facts observed in the Air Traffic Management of the European airspace. The model itself has two main parts: (i) The strategic layer, focused on the interaction between the Network Manager and the Airline Operators and (ii) the tactical layer, focused on aircraft and controllers behaviour in Air Traffic Control (ATC) sectors. The preliminary results for the strategic layer show that when we have a mixing of re-routing and shifting companies, the overall satisfaction can even increase together with the number of flights, which is an effect not observed when only one type of companies is present. The preliminary results for the tactical layer indicate that when shocks in the system are confined in small areas, the interplay between the re-routing and change of flight level strategies may even lead to trajectory modifications that give smaller average delays as long as the number of shocks increases

Applying complexity science to air traffic management

Complexity science is the multidisciplinary study of complex systems. Its marked network orientation lends itself well to transport contexts. Key features of complexity science are introduced and defined, with a specific focus on the application to air traffic management. An overview of complex network theory is presented, with examples of its corresponding metrics and multiple scales. Complexity science is starting to make important contributions to performance assessment and system design: selected, applied air traffic management case studies are explored. The important contexts of uncertainty, resilience and emergent behaviour are discussed, with future research priorities summarised