Articles written in Pramana – Journal of Physics
Volume 64 Issue 4 April 2005 pp 553-562
Formation of feedback loops of excitation waves (reentrant circuit) around non-conducting ventricular scar tissue is a common cause of cardiac arrhythmias, such as ventricular tachycardia, often leading to death. This is typically treated by rapid stimulation from an implantable device (ICD). However, the mechanisms of reentry termination success and, more importantly, failure, are poorly understood. To study such mechanisms, we simulated pacing termination of reentry in a model of cardiac tissue having significant restitution and dispersion properties. Our results show that rapid pacing dynamically generates conduction inhomogeneities in the reentrant circuit, leading to successful pacing termination of tachycardia. The study suggests that more effective pacing algorithms can be designed by taking into account the role of such dynamical inhomogeneities.
Volume 71 Issue 2 August 2008 pp 331-340
Several networks occurring in real life have modular structures that are arranged in a hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that, the scaling relation between the clustering and degree of the nodes is not a necessary property of hierarchical modular networks, as had previously been suggested on the basis of a deterministically constructed model. We also look at dynamics on such networks, in particular, the stability of equilibria of network dynamics and of synchronized activity in the network. For both of these, we find that, increasing modularity or the number of hierarchical levels tends to increase the probability of instability. As both hierarchy and modularity are seen in natural systems, which necessarily have to be robust against environmental fluctuations, we conclude that additional constraints are necessary for the emergence of hierarchical structure, similar to the occurrence of modularity through multi-constraint optimization as shown by us previously.
Volume 77 Issue 5 November 2011 pp 833-842 Biological Systems
Many natural and engineered complex networks have intricate mesoscopic organization, e.g., the clustering of the constituent nodes into several communities or modules. Often, such modularity is manifested at several different hierarchical levels, where the clusters deﬁned at one level appear as elementary entities at the next higher level. Using a simple model of a hierarchical modular network, we show that such a topological structure gives rise to characteristic time-scale separation between dynamics occurring at different levels of the hierarchy. This generalizes our earlier result for simple modular networks, where fast intramodular and slow intermodular processes were clearly distinguished. Investigating the process of synchronization of oscillators in a hierarchical modular network, we show the existence of as many distinct time-scales as there are hierarchical levels in the system. This suggests a possible functional role of such mesoscopic organization principle in natural systems, viz., in the dynamical separation of events occurring at different spatial scales.
Volume 96, 2022
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