arXiv subjects

Sitabhra Sinha

Publications and source records attributed to Sitabhra Sinha.

At least 73 records · Page 4Linked to original sources

arXiv2011

Modular organization enhances the robustness of attractor network dynamics

Modular organization characterizes many complex networks occurring in nature, including the brain. In this paper we show that modular structure may be responsible for increasing the robustness of certain dynamical states of such systems. In a neural network model with threshold-activated binary elements, we observe that the basins of attractors, corresponding to patterns that have been embedded using a learning rule, occupy maximum volume in phase space at an optimal modularity. Simultaneously, the convergence time to these attractors decreases as a result of cooperative dynamics between the modules. The role of modularity in increasing global stability of certain desirable attractors of a system may provide a clue to its evolution and ubiquity in natural systems.

cond-mat.dis-nn↗

arXiv2010

Chimera order in spin systems

Homogeneous populations of oscillators have recently been shown to exhibit stable coexistence of coherent and incoherent regions. Generalizing the concept of chimera states to the context of order-disorder transition in systems at thermal equilibrium, we show analytically that such complex ordering can appear in a system of Ising spins, possibly the simplest physical system exhibiting this phenomenon. We also show numerically the existence of chimera ordering in 3-dimensional spin systems that model layered magnetic materials, suggesting possible means of experimentally observing such states.

cond-mat.stat-mech↗

arXiv2010

The statistical laws of popularity: Universal properties of the box office dynamics of motion pictures

Are there general principles governing the process by which certain products or ideas become popular relative to other (often qualitatively similar) competitors? To investigate this question in detail, we have focused on the popularity of movies as measured by their box-office income. We observe that the log-normal distribution describes well the tail (corresponding to the most successful movies) of the empirical distributions for the total income, the income on the opening week, as well as, the weekly income per theater. This observation suggests that popularity may be the outcome of a linear multiplicative stochastic process. In addition, the distributions of the total income and the opening income show a bimodal form, with the majority of movies either performing very well or very poorly in theaters. We also observe that the gross income per theater for a movie at any point during its lifetime is, on average, inversely proportional to the period that has elapsed after its release. We argue that (i) the log-normal nature of the tail, (ii) the bimodal form of the overall gross income distribution, and (iii) the decay of gross income per theater with time as a power law, constitute the fundamental set of {\em stylized facts} (i.e., empirical "laws") that can be used to explain other observations about movie popularity. We show that, in conjunction with an assumption of a fixed lower cut-off for income per theater below which a movie is withdrawn from a cinema, these laws can be used to derive a Weibull distribution for the survival probability of movies which agrees with empirical data. The connection to extreme-value distributions suggests that popularity can be viewed as a process where a product becomes popular by avoiding failure (i.e., being pulled out from circulation) for many successive time periods. We suggest that these results may apply to popularity in general.

physics.soc-ph↗

arXiv2010

Are large complex economic systems unstable ?

Although classical economic theory is based on the concept of stable equilibrium, real economic systems appear to be always out of equilibrium. Indeed, they share many of the dynamical features of other complex systems, e.g., ecological food-webs. We focus on the relation between increasing complexity of the economic network and its stability with respect to small perturbations in the dynamical variables associated with the constituent nodes. Inherent delays and multiple time-scales suggest that economic systems will be more likely to exhibit instabilities as their complexity is increased even though the speed at which transactions are conducted has increased many-fold through technological developments. Analogous to the birth of nonlinear dynamics from Poincare's work on the question of whether the solar system is stable, we suggest that similar theoretical developments may arise from efforts by econophysicists to understand the mechanisms by which instabilities arise in the economy.

physics.soc-ph↗

arXiv2010

Wave-train induced unpinning of weakly anchored vortices in excitable media

A free vortex in excitable media can be displaced and removed by a wave-train. However, simple physical arguments suggest that vortices anchored to large inexcitable obstacles cannot be removed similarly. We show that unpinning of vortices attached to obstacles smaller than the core radius of the free vortex is possible through pacing. The wave-train frequency necessary for unpinning increases with the obstacle size and we present a geometric explanation of this dependence. Our model-independent results suggest that decreasing excitability of the medium can facilitate pacing-induced removal of vortices in cardiac tissue.

physics.bio-ph↗

arXiv2010

Epidemiological dynamics of the 2009 Influenza A(H1N1)v outbreak in India

We analyze the time-series data for the onset of A(H1N1)v influenza pandemic in India during the period June 1- September 30, 2009. Using a variety of statistical fitting procedures, we obtain a robust estimate of the exponential growth rate $\langle λ\rangle \simeq 0.15$. This corresponds to a basic reproductive number $R_0 \simeq 1.45$ for influenza A(H1N1)v in India, a value which lies towards the lower end of the range of values reported for different countries affected by the pandemic.

q-bio.PE↗

arXiv2010

Emergence of universal scaling in financial markets from mean-field dynamics

Collective phenomena with universal properties have been observed in many complex systems with a large number of components. Here we present a microscopic model of the emergence of scaling behavior in such systems, where the interaction dynamics between individual components is mediated by a global variable making the mean-field description exact. Using the example of financial markets, we show that asset price can be such a global variable with the critical role of coordinating the actions of agents who are otherwise independent. The resulting model accurately reproduces empirical properties such as the universal scaling of the price fluctuation and volume distributions, long-range correlations in volatility and multiscaling.

q-fin.ST↗

arXiv2010

Network analysis of a corpus of undeciphered Indus civilization inscriptions indicates syntactic organization

Archaeological excavations in the sites of the Indus Valley civilization (2500-1900 BCE) in Pakistan and northwestern India have unearthed a large number of artifacts with inscriptions made up of hundreds of distinct signs. To date there is no generally accepted decipherment of these sign sequences and there have been suggestions that the signs could be non-linguistic. Here we apply complex network analysis techniques to a database of available Indus inscriptions, with the aim of detecting patterns indicative of syntactic organization. Our results show the presence of patterns, e.g., recursive structures in the segmentation trees of the sequences, that suggest the existence of a grammar underlying these inscriptions.

cs.CL↗

arXiv2010

Response to sub-threshold stimulus is enhanced by spatially heterogeneous activity

Sub-threshold stimuli cannot initiate excitations in active media, but surprisingly as we show in this paper, they can alter the time-evolution of spatially heterogeneous activity by modifying the recovery dynamics. This results in significant reduction of waveback velocity which may lead to spatial coherence, terminating all activity in the medium including spatiotemporal chaos. We analytically derive model-independent conditions for which such behavior can be observed.

nlin.CD↗

arXiv2010

Mesoscopic organization reveals the constraints governing C. elegans nervous system

One of the biggest challenges in biology is to understand how activity at the cellular level of neurons, as a result of their mutual interactions, leads to the observed behavior of an organism responding to a variety of environmental stimuli. Investigating the intermediate or mesoscopic level of organization in the nervous system is a vital step towards understanding how the integration of micro-level dynamics results in macro-level functioning. In this paper, we have considered the somatic nervous system of the nematode Caenorhabditis elegans, for which the entire neuronal connectivity diagram is known. We focus on the organization of the system into modules, i.e., neuronal groups having relatively higher connection density compared to that of the overall network. We show that this mesoscopic feature cannot be explained exclusively in terms of considerations, such as optimizing for resource constraints (viz., total wiring cost) and communication efficiency (i.e., network path length). Comparison with other complex networks designed for efficient transport (of signals or resources) implies that neuronal networks form a distinct class. This suggests that the principal function of the network, viz., processing of sensory information resulting in appropriate motor response, may be playing a vital role in determining the connection topology. Using modular spectral analysis, we make explicit the intimate relation between function and structure in the nervous system. This is further brought out by identifying functionally critical neurons purely on the basis of patterns of intra- and inter-modular connections. Our study reveals how the design of the nervous system reflects several constraints, including its key functional role as a processor of information.

q-bio.NC↗

arXiv2010

Systems biology: From the cell to the brain

With the completion of human genome mapping, the focus of scientists seeking to explain the biological complexity of living systems is shifting from analyzing the individual components (such as a particular gene or biochemical reaction) to understanding the set of interactions amongst the large number of components that results in the different functions of the organism. To this end, the area of systems biology attempts to achieve a "systems-level" description of biology by focusing on the network of interactions instead of the characteristics of its isolated parts. In this article, we briefly describe some of the emerging themes of research in "network" biology, looking at dynamical processes occurring at the two different length scales of within the cell and between cells, viz., the intra-cellular signaling network and the nervous system. We show that focusing on the systems-level aspects of these problems allows one to observe surprising and illuminating common themes amongst them.

q-bio.MN↗

arXiv2009

Anomalous drift of spiral waves in heterogeneous excitable media

We study the drift of spiral waves in a simple model of heterogeneous excitable medium, having gradients in local excitability or cellular coupling. For the first time, we report the anomalous drift of spiral waves towards regions having higher excitability, in contrast to all earlier observations in reaction-diffusion models of excitable media. Such anomalous drift can promote the onset of complex spatio-temporal patterns, e.g., those responsible for life-threatening arrhythmias in the heart.

nlin.PS↗

arXiv2009

Phase of Ising spins on modular networks analogous to social polarization

Coordination processes in complex systems can be related to the problem of collective ordering in networks, many of which have modular organization. Investigating the order-disorder transition for Ising spins on modular random networks, corresponding to consensus formation in society, we observe two distinct phases: (i) ordering within each module at a critical temperature, followed by (ii) global ordering at a lower temperature. This indicates polarization of society into groups having contrary opinions can persist indefinitely even when mutual interactions between agents favor consensus.

cond-mat.stat-mech↗

arXiv2009

Modularity produces small-world networks with dynamical time-scale separation

The functional consequences of local and global dynamics can be very different in natural systems. Many such systems have a network description that exhibits strong local clustering as well as high communication efficiency, often termed as small-world networks (SWN). We show that modular organization in otherwise random networks generically give rise to SWN, with a characteristic time-scale separation between fast intra-modular and slow inter-modular processes. The universality of this dynamical signature, that distinguishes modular networks from earlier models of SWN, is demonstrated by processes as different as spin-ordering, synchronization and diffusion.

physics.bio-ph↗

arXiv2009

Modular networks with hierarchical organization: The dynamical implications of complex structure

Several networks occurring in real life have modular structures that are arranged in an hierarchical fashion. In this paper, we have proposed a model for such networks, using a stochastic generation method. Using this model we show that, the scaling relation between the clustering and degree of the nodes is not a necessary property of hierarchical modular networks, as had previously been suggested on the basis of a deterministically constructed model. We also look at dynamics on such networks, in particular, the stability of equilibria of network dynamics and of synchronized activity in the network. For both of these, we find that, increasing modularity or the number of hierarchical levels tends to increase the probability of instability. As both hierarchy and modularity are seen in natural systems, which necessarily have to be robust against environmental fluctuations, we conclude that additional constraints are necessary for the emergence of hierarchical structure, similar to the occurrence of modularity through multi-constraint optimization as shown by us previously.

physics.soc-ph↗

arXiv2008

From Network Structure to Dynamics and Back Again: Relating dynamical stability and connection topology in biological complex systems

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from statistical physics and non-linear dynamics. In this paper, we look at a few examples of biological networks to see how similar questions can come up in very different contexts. We review some of our recent work that looks at how network structure (e.g., its connection topology) can dictate the nature of its dynamics, and conversely, how dynamical considerations constrain the network structure. We also see how networks occurring in nature can evolve to modular configurations as a result of simultaneously trying to satisfy multiple structural and dynamical constraints. The resulting optimal networks possess hubs and have heterogeneous degree distribution similar to those seen in biological systems.

physics.bio-ph↗

arXiv2007

Inverse cubic law of index fluctuation distribution in Indian markets

One of the principal statistical features characterizing the activity in financial markets is the distribution of fluctuations in market indicators such as the index. While the developed stock markets, e.g., the New York Stock Exchange (NYSE) have been found to show heavy-tailed return distribution with a characteristic power-law exponent, the universality of such behavior has been debated, particularly in regard to emerging markets. Here we investigate the distribution of several indices from the Indian financial market, one of the largest emerging markets in the world. We have used tick-by-tick data from the National Stock Exchange (NSE), as well as, daily closing data from both NSE and Bombay Stock Exchange (BSE). We find that the cumulative distributions of index returns have long tails consistent with a power-law having exponent α\approx 3, at time-scales of both 1 min and 1 day. This ``inverse cubic law'' is quantitatively similar to what has been observed in developed markets, thereby providing strong evidence of universality in the behavior of market fluctuations.

physics.soc-ph↗

arXiv2007

Controlling spatiotemporal chaos in excitable media using an array of control points

The dynamics of activation waves in excitable media can give rise to spiral turbulence, the resulting spatiotemporal chaos being associated with empirical biological phenomena such as life-threatening disturbances in the natural rhythm of the heart. In this paper, we propose a spatially extended but non-global scheme using an array of control points for terminating such spatiotemporally chaotic excitations. A low-amplitude control signal is applied sequentially at each point on the array, resulting in a traveling wave of excitation in the underlying medium which drives away the turbulent activity. Our method is robust even in the presence of significant heterogeneities in the medium, which have often been an impediment to the success of other control schemes.

nlin.CD↗