Biomedical subjects

Filippo Radicchi

Publications and source records attributed to Filippo Radicchi.

4 recordsLinked to original sources

PubMed2006

Reentrant synchronization and pattern formation in pacemaker-entrained Kuramoto oscillators.

We study phase entrainment of Kuramoto oscillators under different conditions on the interaction range and the natural frequencies. In the first part the oscillators are entrained by a pacemaker acting like an impurity or a defect. We analytically derive the entrainment frequency for arbitrary interaction range and the entrainment threshold for all-to-all couplings. For intermediate couplings our numerical results show a reentrance of the synchronization transition as a function of the coupling range. The origin of this reentrance can be traced back to the normalization of the coupling strength. In the second part we consider a system of oscillators with an initial gradient in their natural frequencies, extended over a one-dimensional chain or a two-dimensional lattice. Here it is the oscillator with the highest natural frequency that becomes the pacemaker of the ensemble, sending out circular waves in oscillator-phase space. No asymmetric coupling between the oscillators is needed for this dynamical induction of the pacemaker property nor need it be distinguished by a gap in the natural frequency.

Journal Article↗

PubMed2006

Entrainment of coupled oscillators on regular networks by pacemakers.

We study Kuramoto oscillators, driven by one pacemaker, on d-dimensional regular topologies with nearest neighbor interactions. We derive the analytical expressions for the common frequency in the case of phase-locked motion and for the critical frequency of the pacemaker, placed at an arbitrary position in the lattice, so that above the critical frequency no phase-locked motion is possible. We show that the mere change in topology from an open chain to a ring induces synchronization for a certain range of pacemaker frequencies and couplings, while keeping the other parameters fixed. Moreover, we demonstrate numerically that the critical frequency of the pacemaker decreases as a power of the linear size of the lattice with an exponent equal to the dimension of the system. This leads in particular to the conclusion that for infinite-dimensional topologies the critical frequency for having entrainment decreases exponentially with increasing size of the system, or, more generally, with increasing depth of the network, that is, the average distance of the oscillators from the pacemaker.

Journal Article↗

PubMed2005

Self-similar scale-free networks and disassortativity.

Self-similar networks with scale-free degree distribution have recently attracted much attention, since these apparently incompatible properties were reconciled in [C. Song, S. Havlin, and H. A. Makse, Nature 433, 392 (2005)] by an appropriate box-counting method that enters the measurement of the fractal dimension. We study two genetic regulatory networks (Saccharomyces cerevisiae [N. M. Luscombe, M. M. Babu, H. Yu, M. Snyder, S. Teichmann, and M. Gerstein, Nature 431, 308 (2004)] and Escherichia coli [http://www.ccg.unam.mx/Computational_Genomics/regulondb/DataSets/RegulonNetDataSets.html and http://www.gbf.de/SystemsBiology]) and show their self-similar and scale-free features, in extension to the datasets studied by [C. Song, S. Havlin, and H. A. Makse, Nature 433, 392 (2005)]. Moreover, by a number of numerical results we support the conjecture that self-similar scale-free networks are not assortative. From our simulations so far these networks seem to be disassortative instead. We also find that the qualitative feature of disassortativity is scale-invariant under renormalization, but it appears as an intrinsic feature of the renormalization prescription, as even assortative networks become disassortative after a sufficient number of renormalization steps.

Journal Article↗

PubMed2004

Defining and identifying communities in networks.

The investigation of community structures in networks is an important issue in many domains and disciplines. This problem is relevant for social tasks (objective analysis of relationships on the web), biological inquiries (functional studies in metabolic and protein networks), or technological problems (optimization of large infrastructures). Several types of algorithms exist for revealing the community structure in networks, but a general and quantitative definition of community is not implemented in the algorithms, leading to an intrinsic difficulty in the interpretation of the results without any additional nontopological information. In this article we deal with this problem by showing how quantitative definitions of community are implemented in practice in the existing algorithms. In this way the algorithms for the identification of the community structure become fully self-contained. Furthermore, we propose a local algorithm to detect communities which outperforms the existing algorithms with respect to computational cost, keeping the same level of reliability. The algorithm is tested on artificial and real-world graphs. In particular, we show how the algorithm applies to a network of scientific collaborations, which, for its size, cannot be attacked with the usual methods. This type of local algorithm could open the way to applications to large-scale technological and biological systems.

Algorithms↗