Abstract

The synchronization and control of dynamical systems on a regular lattice has been extensively studied. However, it has been observed that the underlying topology of a real-system need not always be regular, e.g., the brain has been observed to have a connection structure with small-world properties. Thus, non-standard topologies with long-range connections (i.e., non-local diffusion) are not uncommon in real-life systems and may provide different kinds of spatiotemporal dynamics depending on the extent of non-local diffusion. This led us to investigate the spatiotemporal dynamics of coupled logistic map on four different topological networks, viz., regular, small-world, random and scale-free. In particular, we are interested in the synchronization and control of the spatiotemporal dynamics. It has been shown earlier that the transmission delays between constituent units are capable of sustaining complex dynamical behavior, a phenomenon not observed in the undelayed systems. In fact, the synchronization of the dynamics is observed for a much larger parameter space when the underlying topology is scale-free or random. In our earlier work on the control of spatiotemporal dynamics, we have shown the effect of externally applied perturbation or 'pinning' on regular network. By varying the strength and sign of the pinning strength we were able to target the system to any desired dynamical state. Here we investigate the effect of pinning the dynamics on various topologies. Using graph centrality measures, viz., degree, betweenness and closeness for pinning the nodes, our preliminary results suggest that high betweenness nodes perform better in controlling the spatiotemporal dynamics with as few as 10% of nodes required for pinning in case of system exhibiting weak chaotic dynamics. This study has important practical applications in the control of dynamical diseases such as epileptic seizures and bursts on a small-world brain topology.

Abstract

In most real world networks the connectivity topology between individual entities is not governed by regular, nearest neighbour interactions but also includes long range interactions, e.g., small-world topology of interacting neurons, scale-free behaviour of gene regulatory networks, etc. In this study we have analyzed the synchronization and control of the dynamics in such networks having non-regular topology, viz., small-world, random and scale-free topologies, compared to that in regular networks modeled on coupled map lattices. For the analysis, logistic map, which exhibits rich dynamical behaviour, is modeled on each node and connectivity between the nodes is defined based on the Watt-Strogatz model for small-world and random networks and Albert-Barabasi model for the scale-free network. The synchronization and control of the complex dynamics is analyzed for varying coupling strengths and connectivity delays in the four network topologies. We observe that the synchronization of the network depends on the connection topology and also on connection delays, with poor synchronization observed in regular and small-world networks compared to random and scale-free topology. The connection delays between constituent units are capable of sustaining complex dynamical behaviour not seen in the undelayed system.

Abstract

Abstract. Here we present a simple method based on graph spectral properties to automatically partition multi-domain proteins into individual domains. The identification of structural domains in proteins is based on the assumption that the interactions between the amino acids are higher within a domain than across the domains. These interactions and the topological details of protein structures can be effectively captured by the protein contact graph, constructed by considering each amino acid as a node with an edge drawn between two nodes if the C alpha atoms of the amino acids are within 7. Here we show that Newmans community detection approach in social networks can be used to identify domains in protein structures. We have implemented this approach on protein contact networks and analyze the eigenvectors of the largest eigenvalue of modularity matrix, which is a modified form of the Adjacency matrix, using a quality function called modularity to identify optimal divisions of the network into domains. The proposed approach works even when the domains are formed with amino acids not occurring sequentially along the polypeptide chain and no a priori information regarding the number of nodes is required.

Abstract

This paper examines the Lombard effect on the excitation fea-tures in speech production. These features correspond mostly to the acoustic features at sub segmental (