The role of conditional probability in multi-scale stationary Markovian processes

The aim of the paper is to understand how the inclusion of more and more time-scales into a stochastic stationary Markovian process affects its conditional probability. To this end, we consider two Gaussian processes: (i) a short-range correlated process with an infinite set of time-scales bounded from below, and (ii) a power-law correlated process with an infinite and unbounded set of time-scales. For these processes we investigate the equal position conditional probability P(x,t|x,0) and the mean First Passage Time T(L). The function P(x,t|x,0) can be considered as a proxy of the persistence, i.e. the fact that when a process reaches a position x then it spends some time around that position value. The mean First Passage Time can be considered as a proxy of how fast is the process in reaching a position at distance L starting from position x. In the first investigation we show that the more time-scales the process includes, the larger the persistence. Specifically, we show that the power-law correlated process shows a slow power-law decay of P(x,t|x,0) to the stationary pdf. By contrast, the short range correlated process shows a decay dominated by an exponential cut-off. Moreover, we also show that the existence of an infinite and unbouded set of time-scales is a necessary and not sufficient condition for observing a slow power-law decay of P(x,t|x,0). In the second investigation, we show that for large values of L the more time-scales the process includes, the larger the mean First Passage Time, i.e. the slowest the process. On the other hand, for small values of L, the more time-scales the process includes, the smaller the mean First Passage Time, i.e. when a process statistically spends more time in a given position the likelihood that it reached nearby positions by chance is also enhanced.Comment: 11 pages, 7 figur

Effective strategies for targeted attacks to the network of Cosa Nostra affiliates

Network dismantling has recently gained interest in the fields of intelligence agencies, anti-corruption analysts and criminal investigators due to its efficiency in disrupting the activity of malicious agents. Here, we apply this approach to detect effective strategies for targeted attacks to Cosa Nostra by analysing the collaboration network of affiliates that participate to the same crimes. We preliminarily detect statistically significant homophily patterns induced by being member of the same mafia syndicate. We also find that links between members belonging to different mafia syndicates play a crucial role in connecting the network into a unique component, confirming the relevance of weak ties. Inspired by this result we investigate the resilience properties of the network under random and targeted attacks with a percolation based toy model. Random removal of nodes results to be quite inefficient in dismantling the network. Conversely, targeted attacks where nodes are removed according to ranked network centralities are significantly more effective. A strategy based on a removal of nodes that takes into account how much a member collaborates with different mafia syndicates has an efficiency similar to the one where nodes are removed according to their degree. The advantage of such a strategy is that it does not require a complete knowledge of the underlying network to be operationally effective

Patterns of trading profiles at the Nordic Stock Exchange. A correlation-based approach

We investigate the trading behavior of Finnish individual investors trading the stocks selected to compute the OMXH25 index in 2003 by tracking the individual daily investment decisions. We verify that the set of investors is a highly heterogeneous system under many aspects. We introduce a correlation based method that is able to detect a hierarchical structure of the trading profiles of heterogeneous individual investors. We verify that the detected hierarchical structure is highly overlapping with the cluster structure obtained with the approach of statistically validated networks when an appropriate threshold of the hierarchical trees is used. We also show that the combination of the correlation based method and of the statistically validated method provides a way to expand the information about the clusters of investors with similar trading profiles in a robust and reliable way.Comment: 25 pages, 8 figure

Scale-free relaxation of a wave packet in a quantum well with power-law tails

We propose a setup for which a power-law decay is predicted to be observable for generic and realistic conditions. The system we study is very simple: A quantum wave packet initially prepared in a potential well with (i) tails asymptotically decaying like ~ x^{-2} and (ii) an eigenvalues spectrum that shows a continuous part attached to the ground or equilibrium state. We analytically derive the asymptotic decay law from the spectral properties for generic, confined initial states. Our findings are supported by realistic numerical simulations for state-of-the-art expansion experiments with cold atoms.Comment: improved and extended versio

Two-step estimators of high dimensional correlation matrices

We investigate block diagonal and hierarchical nested stochastic multivariate Gaussian models by studying their sample cross-correlation matrix on high dimensions. By performing numerical simulations, we compare a filtered sample cross-correlation with the population cross-correlation matrices by using several rotationally invariant estimators (RIE) and hierarchical clustering estimators (HCE) under several loss functions. We show that at large but finite sample size, sample cross-correlation filtered by RIE estimators are often outperformed by HCE estimators for several of the loss functions. We also show that for block models and for hierarchically nested block models the best determination of the filtered sample cross-correlation is achieved by introducing two-step estimators combining state-of-the-art non-linear shrinkage models with hierarchical clustering estimators.Comment: 14 pages, 6 figures, 6 table

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

Backbone of credit relationships in the Japanese credit market

We detect the backbone of the weighted bipartite network of the Japanese credit market relationships. The backbone is detected by adapting a general method used in the investigation of weighted networks. With this approach we detect a backbone that is statistically validated against a null hypothesis of uniform diversification of loans for banks and firms. Our investigation is done year by year and it covers more than thirty years during the period from 1980 to 2011. We relate some of our findings with economic events that have characterized the Japanese credit market during the last years. The study of the time evolution of the backbone allows us to detect changes occurred in network size, fraction of credit explained, and attributes characterizing the banks and the firms present in the backbone.Comment: 14 pages, 8 figure