Fluctuation analysis in complex networks modeled by hidden-variable models: necessity of a large cutoff in hidden-variable models.
- M. Ostilli
- PhysicsPhysical review. E, Statistical, nonlinear, and…
- 18 February 2014
This paper reconsider hidden-variable models which turn out to be more analytically treatable and for which recent evidence of non-self-averaging is shown, and shows that large fluctuations are only due to the node-hidden variables variability while, in ensembles where these are frozen, fluctuations are negligible in the thermodynamic limit and equal the fluctuations of classical random graphs.
Duality between equilibrium and growing networks.
- D. Krioukov, M. Ostilli
- EconomicsPhysical review. E, Statistical, nonlinear, and…
- 14 February 2013
It is shown that under certain conditions there exists an equilibrium formulation for any growing network model, and vice versa, and the equivalence between the equilibrium and nonequilibrium formulations is exact not only asymptotically, but even for any finite system size.
Cayley Trees and Bethe Lattices: A concise analysis for mathematicians and physicists
- M. Ostilli
- Physics
- 30 September 2011
Statistical mechanics of rumour spreading in network communities
- M. Ostilli, Eiko Yoneki, I. Leung, J. Mendes, P. Lio’, J. Crowcroft
- Computer ScienceInternational Conference on Conceptual Structures
- 1 May 2010
Spectrum of the tight-binding model on Cayley trees and comparison with Bethe lattices.
- M. Ostilli, C. Bezerra, G. Viswanathan
- PhysicsPhysical Review E
- 12 June 2021
There are few exactly solvable lattice models and even fewer solvable quantum lattice models. Here we address the problem of finding the spectrum of the tight-binding model (equivalently, the…
Phase diagram of an Ising model with competitive interactions on a Husimi tree and its disordered counterpart
- M. Ostilli, F. Mukhamedov, J. Mendes
- Physics
- 26 November 2006
Statistical mechanics of random geometric graphs: Geometry-induced first-order phase transition.
- M. Ostilli, G. Bianconi
- MathematicsPhysical review. E, Statistical, nonlinear, and…
- 2 December 2014
The result shows that, in general, ad hoc optimized networks can hardly be designed, unless to rely to specific heterogeneous constructions, not necessarily scale free.
Effective field theory for models defined over small-world networks: first- and second-order phase transitions.
- M. Ostilli, J. Mendes
- PhysicsPhysical review. E, Statistical, nonlinear, and…
- 2 September 2008
An effective field theory is presented to analyze, in a very general way, models defined over small-world networks, yielding a clear and immediate physical insight, the exact critical behavior and the exactcritical surfaces and percolation thresholds.
Continuous- and discrete-time Glauber dynamics. First- and second-order phase transitions in mean-field Potts models
- M. Ostilli, F. Mukhamedov
- Physics
- 1 March 2013
As is known, at the Gibbs-Boltzmann equilibrium, the mean-field q-state Potts model with a ferromagnetic coupling has only a first-order phase transition when q ⩾ 3, while there is no phase…
Critical behavior and correlations on scale-free small-world networks. Application to network design
- M. Ostilli, A. Ferreira, J. Mendes
- Computer SciencePhysical review. E, Statistical, nonlinear, and…
- 1 January 2011
It is shown that, in large but finite networks, correlations of two given spins may be strong, i.e., approximately power-law-like, at any temperature, contradicting the common opinion that,in mean-field models, correlations always disappear in this limit.
...
...