Michele Catanzaro - Academia.edu (original) (raw)
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Papers by Michele Catanzaro
Physical Review E, 2008
Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networ... more Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networks, such as transport processes or epidemic outbreaks. In most cases, however, they have been studied from a fermionic perspective, in which each vertex can be occupied by at most one particle. While still useful, this approach suffers from some drawbacks, the most important probably being the difficulty to implement reactions involving more than two particles simultaneously. Here we introduce a general framework for the study of bosonic reaction-diffusion processes on complex networks, in which there is no restriction on the number of interacting particles that a vertex can host. We describe these processes theoretically by means of continuous time heterogeneous mean-field theory and divide them into two main classes: steady state and monotonously decaying processes. We analyze specific examples of both behaviors within the class of one-species process, comparing the results (whenever possible) with the corresponding fermionic counterparts. We find that the time evolution and critical properties of the particle density are independent of the fermionic or bosonic nature of the process, while differences exist in the functional form of the density of occupied vertices in a given degree class k. We implement a continuous time Monte Carlo algorithm, well suited for general bosonic simulations, which allow us to confirm the analytical predictions formulated within mean-field theory. Our results, both at the theoretical and numerical level, can be easily generalized to tackle more complex, multi-species, reaction-diffusion processes, and open a promising path for a general study and classification of this kind of dynamical systems on complex networks.
Lecture Notes in Physics, 2004
We present here a brief summary of the various possible applications of network theory in the fie... more We present here a brief summary of the various possible applications of network theory in the field of finance. Since we want to characterize different systems by means of simple and universal features, graph theory could represent a rather powerful methodology. In the following we report our activity in three different subfields, namely the board and director networks, the networks formed by prices correlations and the stock ownership networks. In most of the cases these three kind of networks display scale-free properties making them interesting in their own. Nevertheless, we want to stress here that the main utility of this methodology is to provide new measures of the real data sets in order to validate the different models.
Physica A: Statistical Mechanics and its Applications, 2004
ABSTRACT
Bolyai Society Mathematical Studies, 2008
In this chapter we provide a review of the main results recently obtained in the modeling of bina... more In this chapter we provide a review of the main results recently obtained in the modeling of binary fermionic reaction-diffusion processes on scale-free networks. We show how to derive rate equations within the heterogeneous mean-field formalism, and how information can be obtained from them both for finite networks in the diffusion-limited regime and in the infinite network size lime. By means of extensive numerical simulations, we check the mean field predictions and explore other aspects of the reaction-diffusion dynamics, such as density correlations and the effects of the minimum degree or a tree-like topology.
A Very Short Introduction, 2012
A Very Short Introduction, 2012
A Very Short Introduction, 2012
A Very Short Introduction, 2012
A Very Short Introduction, 2012
A Very Short Introduction, 2012
A Very Short Introduction, 2012
Physical review. E, Statistical, nonlinear, and soft matter physics, 2005
We present a detailed analytical study of the A+A --> 0 diffusion-annihilation process in comp... more We present a detailed analytical study of the A+A --> 0 diffusion-annihilation process in complex networks. By means of microscopic arguments, we derive a set of rate equations for the density of A particles in vertices of a given degree, valid for any generic degree distribution, and which we solve for uncorrelated networks. For homogeneous networks (with bounded fluctuations), we recover the standard mean-field solution, i.e., a particle density decreasing as the inverse of time. For heterogeneous (scale-free networks) in the infinite network size limit, we obtain instead a density decreasing as a power law, with an exponent depending on the degree distribution. We also analyze the role of finite size effects, showing that any finite scale-free network leads to the mean-field behavior, with a prefactor depending on the network size. We check our analytical predictions with extensive numerical simulations on homogeneous networks with Poisson degree distribution and scale-free ne...
Networks representing social systems display speciÿc features that put them apart from biological... more Networks representing social systems display speciÿc features that put them apart from biological and technological ones. In particular, the number of links attached to a node is positively correlated to that of its nearest neighbours. We develop a model that reproduces this feature, starting from microscopical mechanisms of growth. The statistical properties arising from the simulations are in good agreement with those of the real-world social networks of scientists co-authoring papers in condensed matter physics. Moreover, the model highlights the determinant role of correlations in shaping the network's topology.
A Very Short Introduction, 2012
A Very Short Introduction, 2012
The European Physical Journal B - Condensed Matter, 2004
The boards of directors of the largest corporations of a country together with the directors form... more The boards of directors of the largest corporations of a country together with the directors form a dense bipartite network. The board network consist of boards connected through common directors. The director network is obtained taking the directors as nodes, and a membership in the same board as a link. These networks are involved in the decision making processes relevant for the macro-economy of a country. We present an extensive and comparative analysis of the statistical properties of the board network and the director network for the US Fortune 1000 corporations and the Italian Stock Market corporations. Some statistical properties are found to be specific to the director networks and the same in all the different cases of study. Some other statistical properties are instead found to be specific to the board networks but again the same in all the different cases of study. In particular the connectivity degree distribution of the director network has always a power law tail with similar exponent. On the contrary, the connectivity degree distribution of the board network is always rapidly decreasing. All the considered networks are Small World networks, assortative, highly clustered and dominated by a giant component. The presence of lobbies in boards turns out to be a macroscopic phenomenon in all cases of study. These results suggest a common underlying mechanism shaping the corporate control network over time and over different countries and should be taken into account in models of macroeconomic dynamics.
Physical Review E, 2004
In this paper we present a new version of a network growth model, generalized in order to describ... more In this paper we present a new version of a network growth model, generalized in order to describe the behavior of social networks. The case of study considered is the preprint archive at cul.arxiv.org. Each node corresponds to a scientist, and a link is present whenever two authors wrote a paper together. This graph is a nice example of degree-assortative network, that is to say a network where sites with similar degree are connected each other. The model presented is one of the few able to reproduce such behavior, giving some insight on the microscopic dynamics at the basis of the graph structure. PACS numbers: 05.40.-a, 64.60.-1, 87.10.+e Networks [1, 2] are present in different phenomena. The Internet [3, 4] is a graph composed by different computers, connected by cables; the WWW [5, 6] is a graph composed by HTML documents connected by hyperlinks, even social structures [7, 8] can be described as graphs.
Physical Review E, 2008
Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networ... more Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networks, such as transport processes or epidemic outbreaks. In most cases, however, they have been studied from a fermionic perspective, in which each vertex can be occupied by at most one particle. While still useful, this approach suffers from some drawbacks, the most important probably being the difficulty to implement reactions involving more than two particles simultaneously. Here we introduce a general framework for the study of bosonic reaction-diffusion processes on complex networks, in which there is no restriction on the number of interacting particles that a vertex can host. We describe these processes theoretically by means of continuous time heterogeneous mean-field theory and divide them into two main classes: steady state and monotonously decaying processes. We analyze specific examples of both behaviors within the class of one-species process, comparing the results (whenever possible) with the corresponding fermionic counterparts. We find that the time evolution and critical properties of the particle density are independent of the fermionic or bosonic nature of the process, while differences exist in the functional form of the density of occupied vertices in a given degree class k. We implement a continuous time Monte Carlo algorithm, well suited for general bosonic simulations, which allow us to confirm the analytical predictions formulated within mean-field theory. Our results, both at the theoretical and numerical level, can be easily generalized to tackle more complex, multi-species, reaction-diffusion processes, and open a promising path for a general study and classification of this kind of dynamical systems on complex networks.
Lecture Notes in Physics, 2004
We present here a brief summary of the various possible applications of network theory in the fie... more We present here a brief summary of the various possible applications of network theory in the field of finance. Since we want to characterize different systems by means of simple and universal features, graph theory could represent a rather powerful methodology. In the following we report our activity in three different subfields, namely the board and director networks, the networks formed by prices correlations and the stock ownership networks. In most of the cases these three kind of networks display scale-free properties making them interesting in their own. Nevertheless, we want to stress here that the main utility of this methodology is to provide new measures of the real data sets in order to validate the different models.
Physica A: Statistical Mechanics and its Applications, 2004
ABSTRACT
Bolyai Society Mathematical Studies, 2008
In this chapter we provide a review of the main results recently obtained in the modeling of bina... more In this chapter we provide a review of the main results recently obtained in the modeling of binary fermionic reaction-diffusion processes on scale-free networks. We show how to derive rate equations within the heterogeneous mean-field formalism, and how information can be obtained from them both for finite networks in the diffusion-limited regime and in the infinite network size lime. By means of extensive numerical simulations, we check the mean field predictions and explore other aspects of the reaction-diffusion dynamics, such as density correlations and the effects of the minimum degree or a tree-like topology.
A Very Short Introduction, 2012
A Very Short Introduction, 2012
A Very Short Introduction, 2012
A Very Short Introduction, 2012
A Very Short Introduction, 2012
A Very Short Introduction, 2012
A Very Short Introduction, 2012
Physical review. E, Statistical, nonlinear, and soft matter physics, 2005
We present a detailed analytical study of the A+A --> 0 diffusion-annihilation process in comp... more We present a detailed analytical study of the A+A --> 0 diffusion-annihilation process in complex networks. By means of microscopic arguments, we derive a set of rate equations for the density of A particles in vertices of a given degree, valid for any generic degree distribution, and which we solve for uncorrelated networks. For homogeneous networks (with bounded fluctuations), we recover the standard mean-field solution, i.e., a particle density decreasing as the inverse of time. For heterogeneous (scale-free networks) in the infinite network size limit, we obtain instead a density decreasing as a power law, with an exponent depending on the degree distribution. We also analyze the role of finite size effects, showing that any finite scale-free network leads to the mean-field behavior, with a prefactor depending on the network size. We check our analytical predictions with extensive numerical simulations on homogeneous networks with Poisson degree distribution and scale-free ne...
Networks representing social systems display speciÿc features that put them apart from biological... more Networks representing social systems display speciÿc features that put them apart from biological and technological ones. In particular, the number of links attached to a node is positively correlated to that of its nearest neighbours. We develop a model that reproduces this feature, starting from microscopical mechanisms of growth. The statistical properties arising from the simulations are in good agreement with those of the real-world social networks of scientists co-authoring papers in condensed matter physics. Moreover, the model highlights the determinant role of correlations in shaping the network's topology.
A Very Short Introduction, 2012
A Very Short Introduction, 2012
The European Physical Journal B - Condensed Matter, 2004
The boards of directors of the largest corporations of a country together with the directors form... more The boards of directors of the largest corporations of a country together with the directors form a dense bipartite network. The board network consist of boards connected through common directors. The director network is obtained taking the directors as nodes, and a membership in the same board as a link. These networks are involved in the decision making processes relevant for the macro-economy of a country. We present an extensive and comparative analysis of the statistical properties of the board network and the director network for the US Fortune 1000 corporations and the Italian Stock Market corporations. Some statistical properties are found to be specific to the director networks and the same in all the different cases of study. Some other statistical properties are instead found to be specific to the board networks but again the same in all the different cases of study. In particular the connectivity degree distribution of the director network has always a power law tail with similar exponent. On the contrary, the connectivity degree distribution of the board network is always rapidly decreasing. All the considered networks are Small World networks, assortative, highly clustered and dominated by a giant component. The presence of lobbies in boards turns out to be a macroscopic phenomenon in all cases of study. These results suggest a common underlying mechanism shaping the corporate control network over time and over different countries and should be taken into account in models of macroeconomic dynamics.
Physical Review E, 2004
In this paper we present a new version of a network growth model, generalized in order to describ... more In this paper we present a new version of a network growth model, generalized in order to describe the behavior of social networks. The case of study considered is the preprint archive at cul.arxiv.org. Each node corresponds to a scientist, and a link is present whenever two authors wrote a paper together. This graph is a nice example of degree-assortative network, that is to say a network where sites with similar degree are connected each other. The model presented is one of the few able to reproduce such behavior, giving some insight on the microscopic dynamics at the basis of the graph structure. PACS numbers: 05.40.-a, 64.60.-1, 87.10.+e Networks [1, 2] are present in different phenomena. The Internet [3, 4] is a graph composed by different computers, connected by cables; the WWW [5, 6] is a graph composed by HTML documents connected by hyperlinks, even social structures [7, 8] can be described as graphs.