arXiv subjects

T. Di Matteo

Publications and source records attributed to T. Di Matteo.

At least 55 records · Page 3Linked to original sources

arXiv2007

Correlation based networks of equity returns sampled at different time horizons

We investigate the planar maximally filtered graphs of the portfolio of the 300 most capitalized stocks traded at the New York Stock Exchange during the time period 2001-2003. Topological properties such as the average length of shortest paths, the betweenness and the degree are computed on different planar maximally filtered graphs generated by sampling the returns at different time horizons ranging from 5 min up to one trading day. This analysis confirms that the selected stocks compose a hierarchical system progressively structuring as the sampling time horizon increases. Finally, a cluster formation, associated to economic sectors, is quantitatively investigated.

physics.soc-ph↗

arXiv2007

Interplay between topology and dynamics in the World Trade Web

We present an empirical analysis of the network formed by the trade relationships between all world countries, or World Trade Web (WTW). Each (directed) link is weighted by the amount of wealth flowing between two countries, and each country is characterized by the value of its Gross Domestic Product (GDP). By analysing a set of year-by-year data covering the time interval 1950-2000, we show that the dynamics of all GDP values and the evolution of the WTW (trade flow and topology) are tightly coupled. The probability that two countries are connected depends on their GDP values, supporting recent theoretical models relating network topology to the presence of a `hidden' variable (or fitness). On the other hand, the topology is shown to determine the GDP values due to the exchange between countries. This leads us to a new framework where the fitness value is a dynamical variable determining, and at the same time depending on, network topology in a continuous feedback.

physics.soc-ph↗

arXiv2006

An invariant distribution in static granular media

We have discovered an invariant distribution for local packing configurations in static granular media. This distribution holds in experiments for packing fractions covering most of the range from random loose packed to random close packed, for beads packed both in air and in water. Assuming only that there exist elementary cells in which the system volume is subdivided, we derive from statistical mechanics a distribution that is in accord with the observations. This universal distribution function for granular media is analogous to the Maxwell-Boltzmann distribution for molecular gasses.

cond-mat.dis-nn↗

arXiv2006

The Power-law Tail Exponent of Income Distributions

In this paper we tackle the problem of estimating the power-law tail exponent of income distributions by using the Hill's estimator. A subsample semi-parametric bootstrap procedure minimising the mean squared error is used to choose the power-law cutoff value optimally. This technique is applied to personal income data for Australia and Italy.

physics.soc-ph↗

arXiv2006

The parallel lives of supermassive black holes and their host galaxies

We compare all the available observational data on the redshift evolution of the total stellar mass and star formation rate density in the Universe with the mass and accretion rate density evolution of supermassive black holes, estimated from the hard X-ray selected luminosity function of quasars and active galactic nuclei. We find that on average black hole mass must have been higher at higher redshift for given spheroid stellar mass. Moreover, we find negative redshift evolution of the disk/irregulars to spheroid mass ratio. The total accretion efficiency is constrained to be between 0.06 and 0.12, depending on the exact value of the local SMBH mass density, and on the critical accretion rate below which radiatively inefficient accretion may take place.

astro-ph↗

arXiv2006

A study of the personal income distribution in Australia

We analyze the data on personal income distribution from the Australian Bureau of Statistics. We compare fits of the data to the exponential, log-normal, and gamma distributions. The exponential function gives a good (albeit not perfect) description of 98% of the population in the lower part of the distribution. The log-normal and gamma functions do not improve the fit significantly, despite having more parameters, and mimic the exponential function. We find that the probability density at zero income is not zero, which contradicts the log-normal and gamma distributions, but is consistent with the exponential one. The high-resolution histogram of the probability density shows a very sharp and narrow peak at low incomes, which we interpret as the result of a government policy on income redistribution.

physics.soc-ph↗

arXiv2006

Why the fundamental plane of black hole activity is not simply a distance driven artifact

The fundamental plane of black hole activity is a non-linear correlation among radio core luminosity, X-ray luminosity and mass of all accreting black holes, both of stellar mass and supermassive, found by Merloni, Heinz and Di Matteo (2003) and, independently, by Falcke, Koerding and Markoff (2004). Here we further examine a number of statistical issues related to this correlation. In particular, we discuss the issue of sample selection and quantify the bias introduced by the effect of distance in two of the correlated quantities. We demonstrate that the fundamental plane relation cannot be a distance artifact, and that its non-linearity must represent an intrinsic characteristic of accreting black holes. We also discuss possible future observational strategies to improve our understanding of this correlation.

astro-ph↗

arXiv2005

Galactic Centre stellar winds and Sgr A* accretion

(ABRIDGED) We present in detail our new 3D numerical models for the accretion of stellar winds on to Sgr A*. In our most sophisticated models, we put stars on realistic orbits around Sgr A*, include `slow' winds (300 km/s), and account for radiative cooling. We first model only one phase `fast' stellar winds (1000 km/s). For wind sources fixed in space, the accretion rate is Mdot ~ 1e-5 Msun/yr, fluctuates by < 10%, and is in a good agreement with previous models. In contrast, Mdot decreases by an order of magnitude for stars following circular orbits, and fluctuates by ~ 50%. Then we allow a fraction of stars to produce slow winds. Much of these winds cool radiatively, forming cold clumps immersed into the X-ray emitting gas. We test two orbital configurations for the stars in this scenario, an isotropic distribution and two rotating discs with perpendicular orientation. The morphology of cold gas is quite sensitive to the orbits. In both cases, however, most of the accreted gas is hot, with an almost constant Mdot ~ 3e-6 Msun/yr, consistent with Chandra observations. The cold gas accretes in intermittent, short but powerful episodes which may give rise to large amplitude variability in the luminosity of Sgr A* on time scales of 10s to 100s of years. The circularisation radii for the flows are ~ 1e3 and 1e4 Rsch, for the one and two-phase wind simulations, respectively, never forming the quasi-spherical accretion flows suggested in some previous work. Our work suggests that, averaged over time scales of 100s to 1000s of years, the radiative and mechanical luminosity of Sgr A* may be substantially higher than it is in its current state. Further improvements of the wind accretion modelling of Sgr A* will rely on improved observational constraints for the wind properties and stellar orbits.

astro-ph↗

arXiv2005

Correlation filtering in financial time series

We apply a method to filter relevant information from the correlation coefficient matrix by extracting a network of relevant interactions. This method succeeds to generate networks with the same hierarchical structure of the Minimum Spanning Tree but containing a larger amount of links resulting in a richer network topology allowing loops and cliques. In Tumminello et al. \cite{TumminielloPNAS05}, we have shown that this method, applied to a financial portfolio of 100 stocks in the USA equity markets, is pretty efficient in filtering relevant information about the clustering of the system and its hierarchical structure both on the whole system and within each cluster. In particular, we have found that triangular loops and 4 element cliques have important and significant relations with the market structure and properties. Here we apply this filtering procedure to the analysis of correlation in two different kind of interest rate time series (16 Eurodollars and 34 US interest rates).

physics.soc-ph↗

arXiv2005

A tool for filtering information in complex systems

We introduce a technique to filter out complex data-sets by extracting a subgraph of representative links. Such a filtering can be tuned up to any desired level by controlling the genus of the resulting graph. We show that this technique is especially suitable for correlation based graphs giving filtered graphs which preserve the hierarchical organization of the minimum spanning tree but containing a larger amount of information in their internal structure. In particular in the case of planar filtered graphs (genus equal to 0) triangular loops and 4 element cliques are formed. The application of this filtering procedure to 100 stocks in the USA equity markets shows that such loops and cliques have important and significant relations with the market structure and properties.

cond-mat.dis-nn↗

arXiv2005

Accretion of cool stellar winds on Sgr A*: another puzzle of the Galactic Centre?

Sgr A* is currently being fed by winds from a cluster of gravitationally bound young mass-loosing stars. Using observational constraints on the orbits, mass loss rates and wind velocities of these stars, we numerically model the distribution of gas in the ~ 0.1--10'' region around Sgr A*. We find that radiative cooling of recently discovered slow winds leads to the formation of many cool filaments and blobs, and to a thin and rather light accretion disc of about an arcsecond scale. The disc however does not extend all the way to our inner boundary. Instead, hot X-ray emitting gas dominates the inner arcsecond. In our simulations, cool streams of gas frequently enter this region on low angular momentum orbits, and are then disrupted and heated up to the ambient hot gas temperature. The accreting gas around Sgr A* is thus two-phase, with a hot component, observable at X-ray wavelengths, and a cool component, which may be responsible for the majority of time variability of Sgr A* emission on hundred and thousand years time-scales. We obtain an accretion rate of a few times 10^-6 msun/year, consistent with Chandra estimates, but variable on time-scales even shorter than hundred years. These results strongly depend on the chosen stellar orbits and wind parameters. Further observational input is thus key to a better modelling of Sgr A* wind accretion.

astro-ph↗

arXiv2004

Complex Networks on Hyperbolic Surfaces

We explore a novel method to generate and characterize complex networks by means of their embedding on hyperbolic surfaces. Evolution through local elementary moves allows the exploration of the ensemble of networks which share common embeddings and consequently share similar hierarchical properties. This method provides a new perspective to classify network-complexity both on local and global scale. We demonstrate by means of several examples that there is a strong relation between the network properties and the embedding surface.

cond-mat.stat-mech↗

arXiv2004

Innovation flow through social networks: Productivity distribution

A detailed empirical analysis of the productivity of non financial firms across several countries and years shows that productivity follows a non-Gaussian distribution with power law tails. We demonstrate that these empirical findings can be interpreted as consequence of a mechanism of exchanges in a social network where firms improve their productivity by direct innovation or/and by imitation of other firm's technological and organizational solutions. The type of network-connectivity determines how fast and how efficiently information can diffuse and how quickly innovation will permeate or behaviors will be imitated. From a model for innovation flow through a complex network we obtain that the expectation values of the productivity level are proportional to the connectivity of the network of links between firms. The comparison with the empirical distributions reveals that such a network must be of a scale-free type with a power-law degree distribution in the large connectivity range.

physics.soc-ph↗

arXiv2004

Long term memories of developed and emerging markets: using the scaling analysis to characterize their stage of development

The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of daily Foreign Exchange rates, Stock Market indices and fixed income instruments by using the generalized Hurst approach. We show that the scaling exponents are associated with characteristics of the specific markets and can be used to differentiate markets in their stage of development. The robustness of the results is tested by both Monte-Carlo studies and a computation of the scaling in the frequency-domain.

cond-mat.stat-mech↗

arXiv2004

Iron Kalpha emission from the low-luminosity Active Galaxies M81 and NGC 4579

We report on XMM-Newton spectroscopy of the low-luminosity active galaxies (LLAGN) M81 and NGC4579 both of which have known black hole masses and well-sampled spectral energy distributions (SED). The iron Kalpha line profiles from both the LLAGN can be described in terms of two components - a narrow line at 6.4 keV and a moderately broad line (FWHM = 20000 km/s) arising from highly ionized, He-like or H-like species (E \sim 6.8 keV). We interpret the broad lines arising from an accretion disk the inner edge of which is restricted to large radii (r_{in} \sim 100 r_g). However, the Eddington ratio, {L}/{L_{Edd}}, of these sources, is 3 - 4 orders of magnitude lower than that required to photo-ionize a cold disk to He-like iron. We suggest that the lines can be explained as collisionally ionized X-ray lines arising from the transition region between a hot (radiatively inefficient) flow in the inner regions and a cold disk outside r \sim 100r_g. The accretion flow geometry probed by our XMM-Newton observations is consistent with the truncated disk models proposed to explain the SED of LLAGNs.

astro-ph↗

arXiv2004

An interest rates cluster analysis

An empirical analysis of interest rates in money and capital markets is performed. We investigate a set of 34 different weekly interest rate time series during a time period of 16 years between 1982 and 1997. Our study is focused on the collective behavior of the stochastic fluctuations of these time-series which is investigated by using a clustering linkage procedure. Without any a priori assumption, we individuate a meaningful separation in 6 main clusters organized in a hierarchical structure.

cond-mat.stat-mech↗

arXiv2004

On pricing of interest rate derivatives

At present, there is an explosion of practical interest in the pricing of interest rate (IR) derivatives. Textbook pricing methods do not take into account the leptokurticity of the underlying IR process. In this paper, such a leptokurtic behaviour is illustrated using LIBOR data, and a possible martingale pricing scheme is discussed.

cond-mat.stat-mech↗

arXiv2003

Exchanges in complex networks: income and wealth distributions

We investigate the wealth evolution in a system of agents that exchange wealth through a disordered network in presence of an additive stochastic Gaussian noise. We show that the resulting wealth distribution is shaped by the degree distribution of the underlying network and in particular we verify that scale free networks generate distributions with power-law tails in the high-income region. Numerical simulations of wealth exchanges performed on two different kind of networks show the inner relation between the wealth distribution and the network properties and confirm the agreement with a self-consistent solution. We show that empirical data for the income distribution in Australia are qualitatively well described by our theoretical predictions.

cond-mat.stat-mech↗