228 research outputs found
Harmony in the Small-World
The Small-World phenomenon, popularly known as six degrees of separation, has
been mathematically formalized by Watts and Strogatz in a study of the
topological properties of a network. Small-worlds networks are defined in terms
of two quantities: they have a high clustering coefficient C like regular
lattices and a short characteristic path length L typical of random networks.
Physical distances are of fundamental importance in the applications to real
cases, nevertheless this basic ingredient is missing in the original
formulation. Here we introduce a new concept, the connectivity length D, that
gives harmony to the whole theory. D can be evaluated on a global and on a
local scale and plays in turn the role of L and 1/C. Moreover it can be
computed for any metrical network and not only for the topological cases. D has
a precise meaning in term of information propagation and describes in an
unified way both the structural and the dynamical aspects of a network:
small-worlds are defined by a small global and local D, i.e. by a high
efficiency in propagating information both on a local and on a global scale.
The neural system of the nematode C. elegans, the collaboration graph of film
actors, and the oldest U.S. subway system, can now be studied also as metrical
networks and are shown to be small-worlds.Comment: 16 pages, 3 figures, accepted for publication in Physica
The Architecture of Complex Systems
A short review of the recent results and models of complex networks.Comment: 8 pages, 1 figure. To appear on "Interdisciplinary Applications of
Ideas from Nonextensive Statistical Mechanics and Thermodynamics", Santa Fe
Institute for Studies of Complexity. Oxford University Pres
Dynamics and Thermodynamics of a model with long-range interactions
The dynamics and the thermodynamics of particles/spins interacting via
long-range forces display several unusual features with respect to systems with
short-range interactions. The Hamiltonian Mean Field (HMF) model, a Hamiltonian
system of N classical inertial spins with infinite-range interactions
represents a paradigmatic example of this class of systems. The equilibrium
properties of the model can be derived analytically in the canonical ensemble:
in particular the model shows a second order phase transition from a
ferromagnetic to a paramagnetic phase. Strong anomalies are observed in the
process of relaxation towards equilibrium for a particular class of
out-of-equilibrium initial conditions. In fact the numerical simulations show
the presence of quasi-stationary state (QSS), i.e. metastable states which
become stable if the thermodynamic limit is taken before the infinite time
limit. The QSS differ strongly from
Boltzmann-Gibbs equilibrium states: they exhibit negative specific heat,
vanishing Lyapunov exponents and weak mixing, non-Gaussian velocity
distributions and anomalous diffusion, slowly-decaying correlations and aging.
Such a scenario provides strong hints for the possible application of Tsallis
generalized thermostatistics. The QSS have been recently interpreted as a
spin-glass phase of the model. This link indicates another promising line of
research, which is not alternative to the previous one.Comment: 12 pages, 5 figures. Recent review paper for Continuum Mechanics and
Thermodynamic
Compromise and Synchronization in Opinion Dynamics
We discuss two models of opinion dynamics. First wepresent a brief review of
the Hegselmann and Krause (HK) compromise model in two dimensions, showing that
it is possible to simulate the dynamics in the limit of an infinite number of
agents by solving numerically a rate equation for a continuum distribution of
opinions. Then, we discuss the Opinion Changing Rate (OCR) model, which allows
to study under which conditions a group of agents with a different natural
tendency (rate) to change opinion can find the agreement. In the context of the
this model, consensus is viewed as a synchronization process.Comment: Talk presented at the international conference Next05 Sigma Phi,
13-18 august 2005, Kolymbari, Crete. EPJ B (2006) in press. Typos corrected,
refs adde
Multiple centrality assessment in Parma : a network analysis of paths and open spaces
One of the largest of Europe, the recently realized university campus 'Area of the Sciences' in Parma, northern Italy, has been planned for a comprehensive programme of renovation and revitalization with a special focus on vehicular accessibility and the quality of open spaces. As part of the problem setting phase, the authors, with Rivi Engineering, applied Multiple Centrality Assessment (MCA) - a process of network analysis based on primal graphs, a set of different centrality indices and the metric computation of distances - in order to understand why the existent system of open spaces and pedestrian paths is so scarcely experienced by students as well as faculty and staff members and why it appears so poorly supportive of social life and human exchange. In the problem-solving phase MCA was also applied, turning out to offer a relevant contribution to the comparative evaluation of two alternative proposed scenarios, leading to the identification of one final solution of urban design. In the present paper, the first professional application of MCA, an innovative approach to the network analysis of geographic complex systems, is presented and its relevance in the context of a problem of urban design illustrated
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