N. Gupte - Academia.edu (original) (raw)

Papers by N. Gupte

Neural Networks, 2012

We present a neural network model of basal ganglia that departs from the classical Go/NoGo pictur... more We present a neural network model of basal ganglia that departs from the classical Go/NoGo picture of the function of its key pathways-the direct pathway (DP) and the indirect pathway (IP). In classical descriptions of basal ganglia function, the DP is known as the Go pathway since it facilitates movement and the IP is called the NoGo pathway since it inhibits movement. Between these two regimes, in the present model, we posit that there is a third Explore regime, which denotes random exploration of the space of actions. The proposed model is instantiated in a simple action selection task. Striatal dopamine is assumed to switch between DP and IP activation. The IP is modeled as a loop of the subthalamic nucleus (STN) and the globus pallidus externa (GPe), capable of producing chaotic activity. Simulations reveal that, while the system displays Go and NoGo regimes for extreme values of dopamine, at intermediate values of dopamine, it exhibits a new Explore regime denoting a random exploration of the space of action alternatives. The exploratory dynamics originates from the chaotic activity of the STN-GPe loop. When applied to the standard card choice experiment used in the imaging studies of Daw, O&amp;amp;amp;amp;amp;amp;amp;amp;amp;#39;Doherty, Dayan, Seymour, and Dolan (2006), the model favorably describes the exploratory behavior of human subjects.

The European Physical Journal Special Topics, 2014

ABSTRACT The dynamical behavior of spatially extended dynamical systems can have interesting cons... more ABSTRACT The dynamical behavior of spatially extended dynamical systems can have interesting consequences for their statistics. We demonstrate this in a specific context, a system of coupled sine cir- cle maps, and discuss the interconnection between the statistical and dynamical behaviors of the system. The system has an interesting phase diagram in parameter space wherein a spreading transition is seen across an infection line, with spatio-temporal and spatial intermittency of distinct universality classes (directed percolation and non-directed percolation) seen in the spreading/non-spreading regimes. The dynam- ical origins of the spreading transition, lie in a crisis arising from a tangent bifurcation in the system. In addition to changing the statis- tics, and therefore the universality class of the system, the crisis also has dynamical consequences. Unstable dimension variability is seen in the neighbourhood of this crisis, and multiple routes to crisis are seen due to the presence of multi-attractor solutions. We examine the system using a variety of characterizers such as finite time Lyapunov exponents and their distributions. We discuss the signatures of the phenomena seen in the quantifiers, and also whether similar techniques can be extended to other situations. Finally, we demonstrate the success of the quantifiers in another regime, spatio-temporal intermittency with travelling wave laminar solutions, and a solitonic regime.

AIP Conference Proceedings, 2005

Physical Review E, 2000

We study the stability of spatiotemporally periodic orbits in 1-d lattices of piecewise monotonic... more We study the stability of spatiotemporally periodic orbits in 1-d lattices of piecewise monotonic maps coupled via translationally invariant coupling and periodic boundary conditions. States of such systems have independent spatial and temporal periodicities and their stability can be studied through the analysis of a single, uniquely identified reduced matrix of size kxk when the system size is MxM, for M=kN, a multiple of k. This result applies for arbitrary temporal periods and is valid for all coupled map lattice systems coupled in a translationally invariant manner with stability matrices which are irreducible and non-negative, as in the present case. Our analysis could be useful in the analysis of stability regions and bifurcation behavior in a variety of spatially extended systems.

Pramana

which was held in Chennai from 12 to 15 July 2004. This conference, a satellite to Statphys 22, t... more which was held in Chennai from 12 to 15 July 2004. This conference, a satellite to Statphys 22, the international conference on Statistical Physics which took place in the preceding week in Bangalore, attracted over 120 participants, 35 of these from outside India. A detailed report of the meeting can be found in Current Science [87, 1167 (2004)], and a list of the funding agencies as well as the members of the organising committee can be found in this issue. PNLD 2004 brought together leading researchers from across the world and the energetic and active nonlinear dynamics community of India. The success of this conference was due to the enthusiastic participation and support of this collective, which has organised itself into a research community in the past twenty years. The meeting served a dual purpose: to showcase the volume and level of work done in this subject in India to the international community, and to expose the community to the cutting edge of forefront research done by leaders in the field from as many as 14 different countries who attended the meeting. These proceedings which are being brought out in two consecutive issues of Pramana are intended to be a record of this conference, and to serve as a reference for the research which the conference hopes to have nucleated.

Physical review. E, Statistical, nonlinear, and soft matter physics, 2014

We study the dynamics of inertial particles in three-dimensional incompressible maps, as represen... more We study the dynamics of inertial particles in three-dimensional incompressible maps, as representations of volume-preserving flows. The impurity dynamics has been modeled, in the Lagrangian framework, by a six-dimensional dissipative bailout embedding map. The fluid-parcel dynamics of the base map is embedded in the particle dynamics governed by the map. The base map considered for the present study is the Arnold-Beltrami-Childress (ABC) map. We consider the behavior of the system both in the aerosol regime, where the density of the particle is larger than that of the base flow, as well as the bubble regime, where the particle density is less than that of the base flow. The phase spaces in both the regimes show rich and complex dynamics with three types of dynamical behaviors--chaotic structures, regular orbits, and hyperchaotic regions. In the one-action case, the aerosol regime is found to have periodic attractors for certain values of the dissipation and inertia parameters. For ...

New Journal of Physics, 2010

ABSTRACT It was recently found that the heterogeneity of complex networks can enhance transport p... more ABSTRACT It was recently found that the heterogeneity of complex networks can enhance transport properties such as epidemic spreading, electric energy transfer, etc. A trivial deduction would be that the presence of hubs in complex networks can also accelerate the heat transfer although no concrete research has been done so far. In the present study, we have studied this problem and have found a surprising answer: the heterogeneity does not favor but prevents the heat transfer. We present a model to study heat conduction in complex networks and find that the network topology greatly affects the heat flux. The heat conduction decreases with the increase of heterogeneity of the network caused by both degree distribution and the clustering coefficient. Its underlying mechanism can be understood by using random matrix theory. Moreover, we also study the rectification effect and find that it is related to the degree difference of the network, and the distance between the source and the sink. These findings may have potential applications in real networks, such as nanotube/nanowire networks and biological networks.

Physical Review E, 2012

We analyze an idealized model for the transmission or flow of particles, or discrete packets of i... more We analyze an idealized model for the transmission or flow of particles, or discrete packets of information, in a weight bearing branching hierarchical 2 − D networks, and its variants. The capacities add hierarchically down the clusters. Each node can accommodate a limited number of packets, depending on its capacity and the packets hop from node to node, following the links between the nodes. The statistical properties of this system are given by the Maxwell-Boltzmann distribution. We obtain analytical expressions for the mean occupation numbers as functions of capacity, for different network topologies. The analytical results are shown to be in agreement with the numerical simulations. The traffic flow in these models can be represented by the site percolation problem. It is seen that the percolation transitions in the 2−D model and in its variant lattices are continuous transitions, whereas the transition is found to be explosive (discontinuous) for the V − lattice, the critical case of the 2 − D lattice. The scaling behavior of the second order percolation case is studied in detail. We discuss the implications of our analysis.

We study the dynamics of inertial particles in two dimensional incompressible flows. The Maxey-Ri... more We study the dynamics of inertial particles in two dimensional incompressible flows. The Maxey-Riley equation describing the motion of inertial particles is used to construct a four dimensional dissipative bailout embedding map. This map models the dynamics of the inertial particles while the base flow is represented by a 2-d area preserving map. The dynamics of particles heavier than the fluid, the aerosols, as well as that of bubbles, particles lighter than the fluid, can be classified into 3 main dynamical regimes - periodic orbits, chaotic structures and mixed regions. A phase diagram in the parameter space is constructed with the Lyapunov characteristic exponents of the 4-d map in which these dynamical regimes are distinctly identified. The embedding map can target periodic orbits, as well as chaotic structures, in both the aerosol and bubble regimes, at suitable values of the dissipation parameter.

Physica A: Statistical Mechanics and its Applications, 2005

Recent studies have shown that the structure and connectivity properties of networks have importa... more Recent studies have shown that the structure and connectivity properties of networks have important consequences for their function and efficiency. It is therefore useful to ask whether these properties can be exploited to enhance the performance and efficiency of networks. We examine this question in two specific contexts, the load-bearing properties of a branching hierarchical network, and jamming and congestion in a two-dimensional communication network. We show that the capacity and performance of these networks can be enormously enhanced by judicious manipulation of connectivity properties. We discuss the relevance of these results to the general context of information spread processes on networks.

International Journal of Neural Systems, 2008

Synchronization of chaotic low-dimensional systems has been a topic of much recent research. Such... more Synchronization of chaotic low-dimensional systems has been a topic of much recent research. Such systems have found applications for secure communications. In this work we show how synchronization can be achieved in a high-dimensional chaotic neural network. The network used in our studies is an extension of the Hopfield Network, known as the Complex Hopfield Network (CHN). The CHN, also an associative memory, has both fixed point and limit cycle or oscillatory behavior. In the oscillatory mode, the network wanders chaotically from one stored pattern to another. We show how a pair of identical high-dimensional CHNs can be synchronized by communicating only a subset of state vector components. The synchronizability of such a system is characterized through simulations.

Physical Review E, 2001

We set up adaptive control algorithms which can be used to achieve control to desired attractors ... more We set up adaptive control algorithms which can be used to achieve control to desired attractors in spatially extended systems. Traditional adaptive control methods often fail in such systems due to the presence of multiple coexisting attractors that lead to a high probability of the system getting trapped in an undesired attractor despite the application of control. We use quenching techniques to achieve control in such difficult scenarios. When the control parameter evolves through parameter regions that lead to undesired attractors, the control parameter is changed sufficiently fast so that the system does not get time to get trapped in these attractors, but gets quenched instead to the desirable attractor. The rate of change of the parameter is guided by using variable stiffness of control. We demonstrate the efficacy of our technique in a system of coupled sine-circle maps. Further, such variable stiffness schemes can also be used to step up the efficiency of adaptive control algorithms by making frequent suitable changes in the stiffness of control during the control dynamics. This strategy is very successful in reducing the time required to achieve control, while maintaining the stability of the control dynamics.

Pramana, 2008

The phase diagram of the coupled sine circle map lattice exhibits a variety of interesting phenom... more The phase diagram of the coupled sine circle map lattice exhibits a variety of interesting phenomena including spreading regions with spatiotemporal intermittency, non-spreading regions with spatial intermittency, and coherent structures termed solitons. A cellular automaton mapping of the coupled map lattice maps the spreading to non-spreading transition to a transition from a probabilistic to a deterministic cellular automaton. The solitonic sector of the map shows spatiotemporal intermittency with soliton creation, propagation and annihilation. A probabilistic cellular automaton mapping is set up for this sector which can identify each one of these phenomena.

Pramana, 2005

We present a brief report on the conference, a summary of the proceedings, and a discussion on th... more We present a brief report on the conference, a summary of the proceedings, and a discussion on the field of nonlinear science studies and its current frontiers.

Physics Letters A, 2010

Studies of the phase diagram of the coupled sine circle map lattice have identified the presence ... more Studies of the phase diagram of the coupled sine circle map lattice have identified the presence of two distinct universality classes of spatiotemporal intermittency viz. spatiotemporal intermittency of the directed percolation class with a complete set of directed percolation exponents, and spatial intermittency which does not belong to this class. We show that these two types of behavior are special cases of a spreading regime where each site can infect its neighbors permitting an initial disturbance to spread, and a non-spreading regime where no infection is possible , with the two regimes being separated by a line, the infection line. The coupled map lattice can be mapped on to an equivalent cellular automaton which shows a transition from a probabilistic cellular automaton to a deterministic cellular automaton at the infection line. The origins of the spreading-non-spreading transition in the coupled map lattice, as well as the probabilistic to deterministic transition in the cellular automaton lie in a dynamical phenomenon, an attractorwidening crisis at the infection line. Indications of unstable dimension variability are seen in the neighborhood of the infection line. This may provide useful pointers to the spreading behavior seen in other extended systems.

Physical Review E, 2005

We study spatiotemporal intermittency in a system of coupled sine circle maps. The phase diagram ... more We study spatiotemporal intermittency in a system of coupled sine circle maps. The phase diagram of the system shows parameter regimes where the STI lies in the directed percolation class, as well as regimes which show pure spatial intermittency (where the temporal behaviour is regular) which do not belong to the DP class. Thus, both DP and non-DP behaviour can be seen in the same system. The signature of DP and non-DP behaviour can be seen in the dynamic characterisers, viz. the spectrum of eigenvalues of the linear stability matrix of the evolution equation, as well as in the multifractal spectrum of the eigenvalue distribution. The eigenvalue spectrum of the system in the DP regimes is continuous, whereas it shows evidence of level repulsion in the form of gaps in the spectrum in the non-DP regime. The multifractal spectrum of the eigenvalue distribution also shows the signature of DP and non-DP behaviour. These results have implications for the manner in which correlations build up in extended systems.

Physical Review E, 2006

We study spatio-temporal intermittency (STI) in a system of coupled sine circle maps. The phase d... more We study spatio-temporal intermittency (STI) in a system of coupled sine circle maps. The phase diagram of the system shows parameter regimes with STI of both the directed percolation (DP) and non-DP class. STI with synchronized laminar behaviour belongs to the DP class. The regimes of non-DP behaviour show spatial intermittency (SI), where the temporal behaviour of both the laminar and burst regions is regular, and the distribution of laminar lengths scales as a power law. The regular temporal behaviour for the bursts seen in these regimes of spatial intermittency can be periodic or quasi-periodic, but the laminar length distributions scale with the same power-law, which is distinct from the DP case. STI with traveling wave (TW) laminar states also appears in the phase diagram. Soliton-like structures appear in this regime. These are responsible for cross-overs with accompanying non-universal exponents. The soliton lifetime distributions show power law scaling in regimes of long average soliton lifetimes , but peak at characteristic scales with a power-law tail in regimes of short average soliton lifetimes. The signatures of each type of intermittent behaviour can be found in the dynamical characterisers of the system viz. the eigenvalues of the stability matrix. We discuss the implications of our results for behaviour seen in other systems which exhibit spatio-temporal intermittency.

Journal of Physics A: Mathematical and General, 1985

ABSTRACT

Arxiv preprint nlin/0205020, 2002

We investigate the spatiotemporal dynamics of coupled circle map lattices, evolving under synchro... more We investigate the spatiotemporal dynamics of coupled circle map lattices, evolving under synchronous (parallel) updating on one hand and asynchronous (random) updating rules on the other. Synchronous evolution of extended spatiotemporal systems, such as coupled circle map lattices, commonly yields multiple co-existing attractors, giving rise to phenomena strongly dependent on the initial lattice. By marked contrast numerical evidence here strongly indicates that asynchronous evolution eliminates most of the attractor states arising from special sets of initial conditions in synchronous systems, and tends to yield more global attractors. Thus the phenomenology arising from asynchronous evolution is more generic and robust in that it is obtained from many different classes of initial states. Further we show that in parameter regions where both asynchronous and synchronous evolution yield spatio-temporal intermittency, asynchronicity leads to better scaling behaviour.