arXiv subjects

Sitabhra Sinha

Publications and source records attributed to Sitabhra Sinha.

106 records · Page 6Linked to original sources

arXiv2005

Blockbusters, Bombs and Sleepers: The income distribution of movies

The distribution of gross earnings of movies released each year show a distribution having a power-law tail with Pareto exponent $α\simeq 2$. While this offers interesting parallels with income distributions of individuals, it is also clear that it cannot be explained by simple asset exchange models, as movies do not interact with each other directly. In fact, movies (because of the large quantity of data available on their earnings) provide the best entry-point for studying the dynamics of how ``a hit is born'' and the resulting distribution of popularity (of products or ideas). In this paper, we show evidence of Pareto law for movie income, as well as, an analysis of the time-evolution of income.

physics.soc-ph↗

arXiv2005

Evidence for Power-law tail of the Wealth Distribution in India

The higher-end tail of the wealth distribution in India is studied using recently published lists of the wealth of richest Indians between the years 2002-4. The resulting rank distribution seems to imply a power-law tail for the wealth distribution, with a Pareto exponent between 0.81 and 0.92 (depending on the year under analysis). This provides a comparison with previous studies of wealth distribution, which have all been confined to Western advanced capitalist economies. We conclude with a discussion on the appropriateness of multiplicative stochastic process as a model for asset accumulation, the relation between the wealth and income distributions (we estimate the Pareto exponent for the latter to be around 1.5 for India), as well as possible sources of error in measuring the Pareto exponent for wealth.

cond-mat.other↗

arXiv2004

Complexity vs stability in small-world networks

According to the May-Wigner stability theorem, increasing the complexity of a network inevitably leads to its destabilization, such that a small perturbation will be able to disrupt the entire system. One of the principal arguments against this observation is that it is valid only for random networks, and therefore does not apply to real-world networks, which presumably are structured. Here we examine how the introduction of small-world topological structure into networks affect their stability. Our results indicate that, in structured networks, the parameter values at which the stability-instability transition occurs with increasing complexity is identical to that predicted by the May-Wigner criteria. However, the nature of the transition, as measured by the finite-size scaling exponent, appears to change as the network topology transforms from regular to random, with the small-world regime as the cross-over region. This behavior is related to the localization of the largest eigenvalues along the real axis in the eigenvalue plain with increasing regularity in the network.

nlin.AO↗

arXiv2004

Hollywood blockbusters and long-tailed distributions: An empirical study of the popularity of movies

Numerical data for all movies released in theaters in the USA during the period 1997-2003 are examined for the distribution of their popularity in terms of (i) the number of weeks they spent in the Top 60 according to the weekend earnings, and (ii) the box-office gross during the opening week, as well as, the total duration for which they were shown in theaters. These distributions show long tails where the most popular movies are located. Like the study of Redner [S. Redner, Eur. Phys. J. B 4, 131 (1998)] on the distribution of citations to individual papers, our results are consistent with a power-law dependence of the rank distribution of gross revenues for the most popular movies with a exponent close to -1/2.

cond-mat.other↗

arXiv2004

Terminating ventricular tachycardia by pacing induced dynamical inhomogeneities in the reentry circuit

Formation of feedback loops of excitation waves (reentrant circuit) around non-conducting ventricular scar tissue is a common cause of lethal cardiac arrhythmias, such as ventricular tachycardia. 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 of anatomical reentry in an ionic model of cardiac tissue, having significant restitution and dispersion properties. Our results show that rapid pacing causes inhomogeneous conduction 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.

nlin.CD↗

arXiv2004

Controlling spatiotemporal chaos in excitable media by local biphasic stimulation

Controlling spatiotemporal chaos in excitable media by applying low-amplitude perturbations {\em locally} is of immediate applicability, e.g., in treating ventricular fibrillation, a fatal disturbance in the normal rhythmic functioning of the heart. We look at a mechanism of control by the local application of a series of biphasic pulses, i.e., involving both positive and negative stimulation. This results in faster recovery of the medium, making it possible to overdrive the chaos by generating waves with frequency higher than that possible with only positive pulses. This provides the simplest and most general understanding of the effectiveness of biphasic stimulation in controlling fibrillation and allows designing optimal waveshapes for controlling spatiotemporal chaos.

nlin.CD↗

arXiv2003

Termination of Reentry in an Inhomogeneous Ring of Model Cardiac Cells

Reentrant waves propagating in a ring or annulus of excitable media model is the basic mechanism underlying a major class of irregular cardiac rhythms known as anatomical reentry. Such reentrant waves are terminated by rapid electrical stimulation (pacing) from an implantable device. Because the mechanisms of such termination are poorly understood, we study pacing of anatomical reentry in a one-dimensional ring of model cardiac cells. For realistic off-circuit pacing, our model-independent results suggest that circuit inhomogeneities, and the electrophysiological dynamical changes they introduce, may be essential for terminating reentry in some cases.

nlin.CD↗

arXiv2003

Stochastic Maps, Wealth Distribution in Random Asset Exchange Models and the Marginal Utility of Relative Wealth

We look at how asset exchange models can be mapped to random iterated function systems (IFS) giving new insights into the dynamics of wealth accumulation in such models. In particular, we focus on the "yard-sale" (winner gets a random fraction of the poorer players wealth) and the "theft-and-fraud" (winner gets a random fraction of the loser's wealth) asset exchange models. Several special cases including 2-player and 3-player versions of these `games' allow us to connect the results with observed features in real economies, e.g., lock-in (positive feedback), etc. We then implement the realistic notion that a richer agent is less likely to be aggressive when bargaining over a small amount with a poorer player. When this simple feature is added to the yard-sale model, in addition to the accumulation of the total wealth by a single agent ("condensation"), we can see exponential and power-law distributions of wealth. Simulation results suggest that the power-law distribution occurs at the cross-over of the system from exponential phase to the condensate phase.

cond-mat.stat-mech↗

arXiv2001

Spatiotemporal dynamics of pacing in models of anatomical reentry

Reentry around non-conducting ventricular scar tissue, which often causes lethal arrhythmias, is typically treated by rapid stimulation from an implantable defibrillator. However, the mechanisms of termination (success and failure) are poorly understood. To elucidate such mechanisms, we studied pacing of anatomical reentry in 1-D and 2-D excitable cardiac media models. Our results suggest that the existence of inhomogeneity in the reentry circuit is essential for pacing termination of tachycardia to be successful. Considering the role of such inhomogeneities may lead to more effective pacing algorithms.

nlin.CD↗

arXiv2001

Defibrillation via the Elimination of Spiral Turbulence in a Model for Ventricular Fibrillation

Ventricular fibrillation, the major reason behind sudden cardiac death, is turbulent cardiac electrical activity in which rapid, irregular disturbances in the spatiotemporal electrical activation of the heart makes it incapable of any concerted pumping action. Methods of controlling ventricular fibrillation include electrical defibrillation as well as injected medication. Electrical defibrillation, though widely used, involves subjecting the whole heart to massive, and often counterproductive, electrical shocks. We propose a defibrillation method that uses a very-low-amplitude shock (of order mV) applied for a brief duration (of order 100 ms) and over a coarse mesh of lines on our model ventricle.

nlin.CD↗

arXiv2000

Spiral Turbulence: From the Oxidation of CO on Pt(110) to Ventricular Fibrillation

We give a brief overview of systems that show spiral patterns and spatiotemporally chaotic states. We concentrate on two physical systems: (1) the oxidation of CO on Pt(110) and (2) ventricular fibrillation in hearts. The equations that have been suggested as simple models for these two different systems are closely related for they are both {\it excitable media}. We present these equations and give a short summary of the phenomena they yield.}

nlin.CD↗

arXiv1999

Noise-free Stochastic Resonance in Simple Chaotic Systems

The phenomenon of Stochastic Resonance (SR) is reported in a completely noise-free situation, with the role of thermal noise being taken by low-dimensional chaos. A one-dimensional, piecewise linear map and a pair of coupled excitatory-inhibitory neurons are the systems used for the investigation. Both systems show a transition from symmetry-broken to symmetric chaos on varying a system parameter. In the latter state, the systems switch between the formerly disjoint attractors due to the inherent chaotic dynamics. This switching rate is found to ``resonate'' with the frequency of an externally applied periodic perturbation (either parametric or additive). The existence of a resonance in the response of the system is characterized in terms of the residence-time distributions. The results are an unambiguous indicator of the presence of SR-like behavior in these systems. Analytical investigations supporting the observations are also presented. The results have implications in the area of information processing in biological systems.

chao-dyn↗

arXiv1999

Chaotic Dynamics in Iterated Map Neural Networks with Piecewise Linear Activation Function

The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the other inhibitory) connected with each other, is studied in detail. Even such a simple system shows a rich variety of behavior, including high-period oscillations and chaos. Border-collision bifurcations and multifractal fragmentation of the phase space is also observed for a range of parameter values. Extension of the model to a larger number of neurons is suggested under certain restrictive assumptions, which makes the resultant network dynamics effectively one-dimensional. Possible applications of the network for information processing are outlined. These include using the network for auto-association, pattern classification, nonlinear function approximation and periodic sequence generation.

chao-dyn↗

arXiv1998

Response of an Excitatory-Inhibitory Neural Network to External Stimulation: An Application to Image Segmentation

Neural network models comprising elements which have exclusively excitatory or inhibitory synapses are capable of a wide range of dynamic behavior, including chaos. In this paper, a simple excitatory-inhibitory neural pair, which forms the building block of larger networks, is subjected to external stimulation. The response shows transition between various types of dynamics, depending upon the magnitude of the stimulus. Coupling such pairs over a local neighborhood in a two-dimensional plane, the resultant network can achieve a satisfactory segmentation of an image into ``object'' and ``background''. Results for synthetic and and ``real-life'' images are given.

cond-mat.dis-nn↗

arXiv1998

Frustrated synchronization in competing drive-response coupled chaotic systems

Chaotic systems can be synchronized by linking them to a common signal, subject to certain conditions. However, the presence of multiple driving signals coming from different systems, give rise to novel behavior. The particular case of Lorenz systems, with two independent systems driving another system through drive-response coupling has been studied in this paper. This is the simplest arrangement which shows the effect of ``frustrated synchronization'' due to competition between the two driver systems. The resulting response system attractor deviates significantly from the conventional Lorenz attractor. A new measure of desynchronization is proposed, which shows a power-law scaling with the competition parameter.

chao-dyn↗

arXiv1998

Deterministic SR in a Piecewise Linear Chaotic Map

The phenomenon of Stochastic Resonance (SR) is observed in a completely deterministic setting - with thermal noise being replaced by one-dimensional chaos. The piecewise linear map investigated in the paper shows a transition from symmetry-broken to symmetric chaos on increasing a system parameter. In the latter state, the chaotic trajectory switches between the two formerly disjoint attractors, driven by the map's inherent dynamics. This chaotic switching rate is found to `resonate' with the frequency of an externally applied periodic perturbation (multiplicative or additive). By periodically modulating the parameter at a specific frequency $ω$, we observe the existence of resonance where the response of the system (in terms of the residence-time distribution) is maximum. This is a clear indication of SR-like behavior in a chaotic system.

chao-dyn↗