List of Invited Talks:

• Ravindra Amritkar (PRL, Ahmedabad): Scale free networks and coupled dynamics

  Abstract: Recently, scale free networks have been observed in several growing systems. We study dynamics of coupled maps on scale free networks. For small coupling strengths nodes show turbulent behavior but form phase synchronized clusters as coupling increases. We identify two different ways of cluster formation. For small coupling strengths we get {\it self-organized clusters} which have mostly intra-cluster couplings and for large coupling strengths there is a crossover and reorganization to {\it driven clusters} which have mostly inter-cluster couplings. In the driven synchronization the nodes of one cluster are driven by those of the others.

 

• Kamalesh Bhaumik (SINP, Kolkata): Dynamics of Biochemical Networks: Metabolic Control Analysis

• Indrani Bose (Bose Institute, Kolkata): Gene Regulatory Networks: Nonlinear Dynamics and Stochasticity

  Abstract: Gene expression and regulation are the central activities in a living cell. A gene regulatory network is broadly described in terms of the genes and their protein products. The proteins act as functional and signalling molecules or as constituents of body matter. There is an interdependence in the concentrations of the various protein products. A protein can act as a regulatory molecule and switch on/off the expression of its own gene (autoregulation) or the genes of other proteins. The network dynamics describe the changes in the concentrations of proteins (or other biomolecules) as a function of time. In a deterministic description, the governing equations are a set of coupled, nonlinear partial differential equations. The nonlinear dynamics can give rise to multistability including stable oscillations in biological systems. If the biomolecules are small in number, there are considerable stochastic fluctuations and a deterministic description becomes inadequate. In this talk, some interesting consequences of nonlineraity and stochasticity in the dynamics of gene regulatory networks will be highlighted. Despite the complexity of real life networks, simple mathematical models often capture the essential features of how a network functions. Using the predictive power of such models, it is also possible to construct synthetic gene networks with important applications. A specific example of such a network will be given. The Gillespie algorithm which provides a rigorous description of stochastic kinetics will be described alongwith applications. Lastly, a cooperative stochastic model of gene expression will be discussed. The model has been proposed to explain the experimentally observed "all or none" phenomenon in protein production.

 

• Bikas K. Chakrabarti (SINP, Kolkata): A Self-organising Dynamical Model of Market with Single Commodity

• Debasish Chowdhury (IIT, Kanpur): Self-organisation of Self-driven Interacting Particles

  Abstract: Living objects like, for example, bacteria, ants, locust, bees, fish, birds, etc. are "self-driven" in the sense that they generate the energy required for their movement from the food they consume. These self-driven objects are interesting from the perspective of complex systems because of the interesting collective dynamics that emerges from the self-organisation where the dynamics of each individual is governed by its immediate neighbourhood only. How do ants form the trail? How do bacteria form ordered patterns in bacterial colonies? How does a school of fish move in an ordered pattern? How do flocks of birds migrate over long distances maintaining an ordered pattern? How do the colonies of bees and locust drift in spite of an apparent random movement of individual members? Many of these questions can be addressed using the language of cellular automata which has been used successfully in recent years in describing another class of self-driven interacting particles, namely, vehicular traffic; vehicles are also "self-driven" as they generate the energy for their forward movement from the fuel. After introducing the principles of modeling through cellular-automata, some examples drawn mainly from vehicular traffic will be discussed. Some preliminary results for models of insect trails, which have been formulated in terms of cellular-automata, will also be presented.

 

• David J. Christini (Cornell U., New York): Preventing Sudden Cardiac Death by Terminating Arrhythmia Precursors

  Abstract: Sudden cardiac death, primarily caused by abnormal electrical rhythms (arrhythmias) in the heart's lower chambers (ventricles), kills thousands daily. Yet, its dominant therapy, a device known as the implantable cardioverter defibrillator (ICD), relies on an approach (electrical stimulation) that is fundamentally flawed. ICDs wait to act until after an arrhythmia has started, at which point electrophysiological dynamics are relatively difficult to alter and arrhythmia termination failure can be fatal. We are attempting to interweave dynamical systems theories and physiology to develop a fundamentally new paradigm in arrhythmia treatment that will prevent the onset of arrhythmias through termination of their mechanistic precursors. By preventing arrhythmias rather than waiting to terminate them after they have started (the current ICD approach), we hope that our strategy will keep the heart's rhythm from entering into its lethal dynamical spiral.

 

• Chandan Dasgupta (IISc, Bangalore): Neural Network Modeling of the Dependence of Kindling Rate on Network Properties

  Abstract: Kindling, the process of generation of focal epilepsy by repeated applications of electrical, chemical or hyperthermic stimulation to a specific region of the brain, has been experimentally observed in a wide variety of species ranging from amphibians to subhuman primates. However, the occurrence of kindling in the human brain has not been established. Also, it is known that kindling develops and evolves into spontaneous seizures more slowly in phylogenetically advanced species such as primates. These observations suggest that the rate of kindling may depend crucially on the size, complexity and the degree of organization of the underlying neuronal network. We have developed a biologically plausible neural network model of kindling in which the formation of an epileptic focus is attributed to the generation of new excitatory synapses through a Hebbian learning process. We have used this model to study by simulations the dependence of the rate of kindling on network properties such as the number of neurons and the pattern of synaptic connections among them. These simulations show a clear trend: the rate of kindling decreases as the size of the network is increased. An approximate analytic treatment of the process of generation of new synapses through Hebbian learning provides a semi-quantitative understanding of the simulation data and suggests that the observed dependence of the kindling rate on the size of the network is a fairly general result, independent of the details of the structure of the network.
  [Based on work done in collaboration with B. Biswal, G.R. Ullal and B.R. Niranjan.]

 

• Eytan Domany (Weizmann, Rehevoth): Cancer and the Breakdown of Gene Regulatory Networks

• Neelima Gupte (IIT, Chennai): Connectivity strategies to enhance network capacities

  Abstract: We discuss connectivity strategies to enhance the load-bearing properties of networks, a problem of practical interest. We demonstrate our strategies in the context of the Coppersmith model of granular media. Our strategies lead to significant enhancements of the load-bearing capacity of the networks and to a significant decrease in the failure rates. Our strategies are general and could be exploited to enhance the capacities of other kinds of networks as well. We also discuss other contexts where these strategies could be useful.
  [Work done in collaboration with T.M. Janaki]

 

• Sanjay Jain (IISc, Bangalore): Robustness and Fragility in Dynamical Networks

  Abstract: A complex adaptive system that is robust on a certain time scale can collapse on longer time scales. Often, its very persistence and `success' on short time scales sets in motion processes that change the system or its environment on long time scales and makes it fragile and susceptible to collapse. This talk will discuss a mathematical model of an evolving chemical network that displays this feature. In the model the short term robustness is due to the spontaneous appearance of a cooperative structure, an `autocatalytic set'. Its success leads to the formation of new aggregates within the system whose effective dynamics is competitive. This competition that arises at a `higher level' makes the system fragile, resulting in repeated crashes followed by recoveries. This provides an example of how new aggregates with effectively new degrees of freedom can dynamically arise in a complex system, and influence its future evolution.
  Reference: S. Jain and S. Krishna, "Crashes, recoveries and `core-shifts' in a model of evolving networks", nlin.AO/0107037, to appear in Phys. Rev. E.

 

• Rahul Pandit (IISc, Bangalore): Spatiotemporal Chaos: Characterisation and Control in Models for Ventricular Fibrillation

  Abstract: We give an overview of partial differential equation models for ventricular fibrillation (a lethal form of cardiac arrhythmia) that show spatiotemporal chaos and the associated breakup of spiral waves. We then discuss how such breakup can be controlled by using low-amplitude electrical stimulation on a coarse control mesh of line electrodes in the Panfilov, Beeler-Reuter and Luo-Rudy I models for ventricular fibrillation.

 

• Alexandre V. Panfilov (U. Utrecht): Reentrant mechanisms of cardiac arrhythmias and possibilities of their control using small external interventions

  Abstract: Cardiac arrhythmias are the leading cause of the death in the industrialized countries accounting for about 1 death in 10. In most of the cases cardiac arrhythmias occur due to abnormalities of propagation of electrical waves of excitation in the heart.
  My talk will review basic regimes of abnormal wave propagation in cardiac tissue such as reentrant sources or spiral waves and discuss the relation between their dynamics and types of cardiac arrhythmias.
  I will focus on one of the most important types of arrhythmias: fibrillation, which occurs when a spiral wave decays into a turbulent chaotic behavior. I will discuss the possible mechanisms of ventricular and atrial fibrillation such as Moe's multiple wavelet hypothesis, idea of induced fibrillation and restitution hypothesis. I will show how spiral wave instabilities occur if the slope of the restitution curve has a sufficiently high positive or high negative value.
  I will discuss the problem of quantification of ventricular fibrillation and possible implications of the restitution hypothesis for pharmacological management of ventricular fibrillation.
  Finally I will discuss two possible ways of removing spiral waves from cardiac tissue: using overdrive pacing and using resonance drift of spiral waves and discuss their possible applications for controlling cardiac arrhythmias.

 

• Alain Pumir (INLN, CNRS, Sophia-Antipolis): Electric Fields in Cardiology : From Clinics to Theory, and Back (Possibly)

  Abstract: Electric fields are widely used in clinics to treat potentially life-threatening cardiac arrhythmias. In the case of defibrillation, a brief and intense electric shock suppresses the anomalous and disordered electric activity in cardiac muscle. Anti-Tachycardia-Pacing (ATP) consists of a train of low intensity electric impulses. Under favorable conditions, these methods permit a return to normal electric activity in the heart.
  The interaction of the electric field with cardiac muscle leads to intriguing physical questions, and the important challenge is to improve already existing methods.
  I will first discuss the mechanisms permitting a large electric shock to defibrillate the heart, and I will argue that heterogeneities play a very important in this phenomena.
  I will present recent theoretical results on the drift induced by a periodic wave train on a rotating wave (vortex) of electrical activity. Importantly, when the rotating wave is pinned by an anatomical obstacle (such as an ischemized region), the applied train of waves may fail to induce a drift of the vortex. I will explain how a properly time excitation may solve this difficulty.

 

• Ramakrishna Ramaswamy (JNU, New Delhi): Completely Synchronized Networks under Quasiperiodic Forcing

• Sudeshna Sinha (IMSc, Chennai): Computing with Chaotic Networks

  Abstract: We describe mechanisms that can effectively control networks of chaotic elements onto stable spatiotemporal cycles of all orders. Further we indicate how this wealth of controllable spatiotemporal patterns may be exploited to constitute an effective computing medium.

 

• Angelo Valleriani (MPI, Berlin): Processes in Ecological Networks

  Abstract: Food webs are networks whose structure can be understood in terms of trophic niches or classes, in which the relative abundances are not a passive effect of the availability of species. This fact implies that the processes responsible to provide new species and to mantain diversity also shape the topology of the ecosystem. By means of two simple models, we show how the assumptions about the effects of processes like immigration and adaptation can be related to the shape of the ecosystem and to the complexity of the interaction inside each trophic level.

 

• Christopher Wilmers (UC, Berkeley): Assembling Stable Ecological Communities: Relating Species Richness to Communtiy Resilience and Resistance

  Abstract: The stability-diversity debate in ecology has been polarized by the often contradictory results of empirical and theoretical studies. Here we briefly review the history of this debate. We then present a novel way to model community assembly based on eigenvalue analysis and consider the stability of assembled communities. In concordance with previous work, we find that communities with weaker mean interaction strength support a larger number of species (May 1972). However, as communities increase in average size, resistance, measured as the coefficient of variation of community size and resilience, measured as the average return time to mean community size, both increase. Our results suggest that further study of the temporal variation in community properties may be an important tool in resolving the stability-diversity debate.

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