arXiv subjects

Sitabhra Sinha

Publications and source records attributed to Sitabhra Sinha.

At least 55 records · Page 3Linked to original sources

arXiv2016

Emergence of coupling-induced oscillations and broken symmetries in heterogeneously driven nonlinear reaction networks

Many natural systems including the brain comprise coupled non-uniformly stimulated elements. In this paper we show that heterogeneously driven networks of excitatory-inhibitory units exhibit striking collective phenomena, including spontaneous oscillations upon coupling. On varying the coupling strength a novel transition is seen wherein the pattern symmetries of stimulated and unstimulated groups undergo mutual exchange. The system exhibits coexisting chaotic and non-chaotic attractors - an intriguing result in view of earlier reports of varying degrees of chaoticity in the brain.

nlin.AO↗

arXiv2016

Using skewness and the first-digit phenomenon to identify dynamical transitions in cardiac models

Disruptions in the normal rhythmic functioning of the heart, termed as arrhythmia, often result from qualitative changes in the excitation dynamics of the organ. The transitions between different types of arrhythmia are accompanied by alterations in the spatiotemporal pattern of electrical activity that can be measured by observing the time-intervals between successive excitations of different regions of the cardiac tissue. Using biophysically detailed models of cardiac activity we show that the distribution of these time-intervals exhibit a systematic change in their skewness during such dynamical transitions. Further, the leading digits of the normalized intervals appear to fit Benford's law better at these transition points. This raises the possibility of using these observations to design a clinical indicator for identifying changes in the nature of arrhythmia. More importantly, our results reveal an intriguing relation between the changing skewness of a distribution and its agreement with Benford's law, both of which have been independently proposed earlier as indicators of regime shift in dynamical systems.

q-bio.TO↗

arXiv2015

Designer dynamics through chaotic traps: Controlling complex behavior in driven nonlinear systems

Control schemes for dynamical systems typically involve stabilizing unstable periodic orbits. In this paper we introduce a new paradigm of control that involves `trapping' the dynamics arbitrarily close to any desired trajectory. This is achieved by a state-dependent dynamical selection of the input signal applied to the driven nonlinear system. An emergent property of the trapping process is that the signal changes in a chaotic sequence: a manifestation of chaos-induced order. The simplicity of the control scheme makes it easily implementable in experimental systems.

nlin.CD↗

arXiv2015

Complex ordering in spin networks: Critical role of adaptation rate for dynamically evolving interactions

Many complex systems can be represented as networks of dynamical elements whose states evolve in response to interactions with neighboring elements, noise and external stimuli. The collective behavior of such systems can exhibit remarkable ordering phenomena such as chimera order corresponding to coexistence of ordered and disordered regions. Often, the interactions in such systems can also evolve over time responding to changes in the dynamical states of the elements. Link adaptation inspired by Hebbian learning, the dominant paradigm for neuronal plasticity, has been earlier shown to result in structural balance by removing any initial frustration in a system that arises through conflicting interactions. Here we show that the rate of the adaptive dynamics for the interactions is crucial in deciding the emergence of different ordering behavior (including chimera) and frustration in networks of Ising spins. In particular, we observe that small changes in the link adaptation rate about a critical value result in the system exhibiting radically different energy landscapes, viz., smooth landscape corresponding to balanced systems seen for fast learning, and rugged landscapes corresponding to frustrated systems seen for slow learning.

cond-mat.stat-mech↗

arXiv2015

Symmetry warrants rational cooperation by co-action in Social Dilemmas

Is it rational for selfish individuals to cooperate? The conventional answer based on analysis of games such as the Prisoners Dilemma (PD) is that it is not, even though mutual cooperation results in a better outcome for all. This incompatibility between individual rationality and collective benefit lies at the heart of questions about the evolution of cooperation, as illustrated by PD and similar games. Here, we argue that this apparent incompatibility is due to an inconsistency in the standard Nash framework for analyzing non-cooperative games and propose a new paradigm, that of the co-action equilibrium. As in the Nash solution, agents know that others are just as rational as them and taking this into account leads them to realize that others will independently adopt the same strategy, in contrast to the idea of unilateral deviation central to Nash equilibrium thinking. Co-action equilibrium results in better collective outcomes for games representing social dilemmas, with relatively "nicer" strategies being chosen by rational selfish individuals. In particular, the dilemma of PD gets resolved within this framework, suggesting that cooperation can evolve in nature as the rational outcome even for selfish agents, without having to take recourse to additional mechanisms for promoting it.

physics.soc-ph↗

arXiv2015

A dynamical view of different solution paradigms in two-person symmetric games: Nash vs co-action equilibria

The study of games and their equilibria is central to developing insights for understanding many socio-economic phenomena. Here we present a dynamical systems view of the equilibria of two-person, payoff-symmetric games. In particular, using this perspective, we discuss the differences between two solution concepts for such games - namely, those of Nash equilibrium and co-action equilibrium. For the Nash equilibrium, we show that the dynamical view can provide an equilibrium refinement, selecting one equilibrium among several possibilities, thereby solving the issue of multiple equilibria that appear in some games. We illustrate in detail this dynamical perspective by considering three well known 2-person games namely the Prisoner's Dilemma, game of Chicken and the Stag-Hunt. We find that in all of these cases, co-action equilibria tends to correspond to `nicer' strategies than those corresponding to Nash equilibria.

physics.soc-ph↗

arXiv2014

The role of cellular coupling in the spontaneous generation of electrical activity in uterine tissue

The spontaneous emergence of contraction-inducing electrical activity in the uterus at the beginning of labor remains poorly understood, partly due to the seemingly contradictory observation that isolated uterine cells are not spontaneously active. It is known, however, that the expression of gap junctions increases dramatically in the approach to parturition, which results in a significant increase in inter-cellular electrical coupling. In this paper, we build upon previous studies of the activity of electrically excitable smooth muscle cells (myocytes) and investigate the mechanism through which the coupling of these cells to electrically passive cells results in the generation of spontaneous activity in the uterus. Using a recently developed, realistic model of uterine muscle cell dynamics, we investigate a system consisting of a myocyte coupled to passive cells. We then extend our analysis to a simple two-dimensional lattice model of the tissue, with each myocyte being coupled to its neighbors, as well as to a random number of passive cells. We observe that different dynamical regimes can be observed over a range of gap junction conductances: at low coupling strength, the activity is confined to cell clusters, while the activity for high coupling may spread across the entire tissue. Additionally, we find that the system supports the spontaneous generation of spiral wave activity. Our results are both qualitatively and quantitatively consistent with observations from in vitro experiments. In particular, we demonstrate that an increase in inter-cellular electrical coupling, for realistic parameter values, strongly facilitates the appearance of spontaneous action potentials that may eventually lead to parturition.

q-bio.TO↗

arXiv2014

"Defective" Logic: Using spatiotemporal patterns in coupled relaxation oscillator arrays for computation

An intriguing interpretation of the time-evolution of dynamical systems is to view it as a computation that transforms an initial state to a final one. This paradigm has been explored in discrete systems such as cellular automata models, where the relation between dynamics and computation has been examined in detail. Here, motivated by microfluidic experiments on arrays of chemical oscillators, we show that computation can be achieved in continuous-state, continuous-time systems by using complex spatiotemporal patterns generated through a reaction-diffusion mechanism in coupled relaxation oscillators. We present two paradigms that illustrate this computational capability, namely, using perturbations to (i) generate propagating configurations in a system of initially exactly synchronized oscillators, and (ii) transform one time-invariant pattern to another. In particular, we have demonstrated a possible implementation of NAND logic. This raises the possibility of universal computation in such systems as all logic gates can be constructed from NAND gates. Our work suggests that more complex schemes can potentially implement arbitrarily complicated computation using reaction-diffusion processes, bridging pattern formation with universal computability.

nlin.PS↗

arXiv2013

Extreme variability in convergence to structural balance in frustrated dynamical systems

In many complex systems, the dynamical evolution of the different components can result in adaptation of the connections between them. We consider the problem of how a fully connected network of discrete-state dynamical elements which can interact via positive or negative links, approaches structural balance by evolving its links to be consistent with the states of its components. The adaptation process, inspired by Hebb's principle, involves the interaction strengths evolving in accordance with the dynamical states of the elements. We observe that in the presence of stochastic fluctuations in the dynamics of the components, the system can exhibit large dispersion in the time required for converging to the balanced state. This variability is characterized by a bimodal distribution, which points to an intriguing non-trivial problem in the study of evolving energy landscapes.

cond-mat.dis-nn↗

arXiv2013

Complex patterns arise through spontaneous symmetry breaking in dense homogeneous networks of neural oscillators

Recent experiments have highlighted how collective dynamics in networks of brain regions affect behavior and cognitive function. In this paper we show that a simple, homogeneous system of densely connected oscillators representing the aggregate activity of local brain regions can exhibit a rich variety of dynamical patterns emerging via spontaneous breaking of permutation or translational symmetry. Our results connect recent experimental findings and suggest that a range of complicated activity patterns seen in the brain could be explained even without a full knowledge of its wiring diagram.

nlin.PS↗

arXiv2013

Uncovering the network structure of the world currency market: Cross-correlations in the fluctuations of daily exchange rates

The cross-correlations between the exchange rate fluctuations of 74 currencies over the period 1995-2012 are analyzed in this paper. The eigenvalue distribution of the cross-correlation matrix exhibits a bulk which approximately matches the bounds predicted from random matrices constructed using mutually uncorrelated time-series. However, a few large eigenvalues deviating from the bulk contain important information about the global market mode as well as important clusters of strongly interacting currencies.We reconstruct the network structure of the world currency market by using two different graph representation techniques, after filtering out the effects of global or market-wide signals on the one hand and random effects on the other. The two networks reveal complementary insights about the major motive forces of the global economy, including the identification of a group of potentially fast growing economies whose development trajectory may affect the global economy in the future as profoundly as the rise of India and China has affected it in the past decades.

q-fin.ST↗

arXiv2012

Large variability in dynamical transitions in biological systems with quenched disorder

Coherent oscillatory activity can arise spontaneously as a result of increased coupling in a system of excitable and passive cells, each being quiescent in isolation. This can potentially explain the appearance of spontaneous rhythmic contractions in the pregnant uterus close to term. We investigate the transition to periodic activity using a model system comprising a lattice of excitable cells, each being coupled to a variable number of passive cells whose distribution defines a quenched realization (replica) of spatial disorder. Close to the transition between quiescent state and sustained oscillations in the system we observe large fluctuations between different replicas induced by variations in the local density of passive cells around an excitable cell. We demonstrate that the disorder-induced fluctuations can be described in terms of a simple scaling relation which involves the strength of coupling between excitable cells, the mean passive cell density, as well as the logarithm of the system size. Our results can be interpreted as suggesting that larger organs will have greater variability in the onset of persistent activity.

cond-mat.dis-nn↗

arXiv2012

The evolution of interdisciplinarity in physics research

Science, being a social enterprise, is subject to fragmentation into groups that focus on specialized areas or topics. Often new advances occur through cross-fertilization of ideas between sub-fields that otherwise have little overlap as they study dissimilar phenomena using different techniques. Thus to explore the nature and dynamics of scientific progress one needs to consider the large-scale organization and interactions between different subject areas. Here, we study the relationships between the sub-fields of Physics using the Physics and Astronomy Classification Scheme (PACS) codes employed for self-categorization of articles published over the past 25 years (1985-2009). We observe a clear trend towards increasing interactions between the different sub-fields. The network of sub-fields also exhibits core-periphery organization, the nucleus being dominated by Condensed Matter and General Physics. However, over time Interdisciplinary Physics is steadily increasing its share in the network core, reflecting a shift in the overall trend of Physics research.

physics.soc-ph↗

arXiv2012

Dynamical order, disorder and propagating defects in homogeneous system of relaxation oscillators

Reaction-diffusion (RD) mechanisms in chemical and biological systems can yield a variety of patterns that may be functionally important. We show that diffusive coupling through the inactivating component in a generic model of coupled relaxation oscillators give rise to a wide range of spatio-temporal phenomena. Apart from analytically explaining the genesis of anti-phase synchronization and spatially patterned oscillatory death regimes in the model system, we report the existence of a chimera state, characterized by spatial co-occurrence of patches with distinct dynamics. We also observe propagating phase defects in both one- and two-dimensional media resembling persistent structures in cellular automata, whose interactions may be used for computation in RD systems.

nlin.PS↗

arXiv2012

Self-organized transition to coherent activity in disordered media

Synchronized oscillations are of critical functional importance in many biological systems. We show that such oscillations can arise without centralized coordination in a disordered system of electrically coupled excitable and passive cells. Increasing the coupling strength results in waves that lead to coherent periodic activity, exhibiting cluster, local and global synchronization under different conditions. Our results may explain the self-organized transition in a pregnant uterus from transient, localized activity initially to system-wide coherent excitations just before delivery.

nlin.AO↗

arXiv2011

In Square Circle: Geometric Knowledge of the Indus Civilization

The earliest origins of mathematics in the Indian subcontinent is generally dated around 800-500 BCE when the {\em Sulbasutras} are thought to have been written. In this article we suggest that mathematical thinking in South Asia, in particular, geometry, may have had an even earlier beginning - in the third millenium BCE. We base our hypothesis on the analysis of design patterns, such as complex space-filling tiling, seen on artifacts of the Indus Valley Civilization (also referred to as the Mature Harappan Civilization, 2500-1900 BCE) which speaks of a deep understanding of sophisticated geometric principles.

math.HO↗

arXiv2011

Multiple dynamical time-scales in networks with hierarchically nested modular organization

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 intra-modular and slow inter-modular 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.

physics.soc-ph↗

arXiv2011

Critical role of pinning defects in scroll-wave breakup in active media

The breakup of rotating scroll waves in three-dimensional excitable media has been linked to important biological processes. The known mechanisms for this transition almost exclusively involve the dynamics of the scroll filament, i.e., the line connecting the phase singularities. In this paper, we describe a novel defect-induced route to breakup of a scroll wave pinned by an inexcitable obstacle partially extending through the bulk of the medium. The wave is helically wound around the defect inducing sudden changes in velocity components of the wavefront at the obstacle boundary. This results in breakup far from the filament, eventually giving rise to spatiotemporal chaos. Our results suggest a potentially critical role of pinning obstacles in the onset of life-threatening disturbances of cardiac activity.

nlin.PS↗