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M. S. Santhanam

Bio: M. S. Santhanam is an academic researcher from Indian Institute of Science. The author has contributed to research in topics: Quantum chaos & Physics. The author has an hindex of 14, co-authored 68 publications receiving 818 citations. Previous affiliations of M. S. Santhanam include Indian Institute of Science Education and Research, Pune & Physical Research Laboratory.


Papers
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TL;DR: An analytical expression is obtained for the distribution of return intervals in long-range correlated time series which holds good when the average return intervals are large and it is shown that the distribution is actually a product of power law and a stretched exponential form.
Abstract: The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is well known that many physical processes in nature and society display long-range correlations. Hence, in the last few years, considerable research effort has been directed towards studying the distribution of return intervals for long-range correlated time series. Based on numerical simulations, it was shown that the return interval distributions are of stretched exponential type. In this paper, we obtain an analytical expression for the distribution of return intervals in long-range correlated time series which holds good when the average return intervals are large. We show that the distribution is actually a product of power law and a stretched exponential form. We also discuss the regimes of validity and perform detailed studies on how the return interval distribution depends on the threshold used to define extreme events.

99 citations

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TL;DR: This work shows that the random matrix approach can be beneficially applied to a completely different classical domain, namely, to the empirical correlation matrices obtained from the analysis of the basic atmospheric parameters that characterize the state of atmosphere.
Abstract: The study of random matrix ensembles has brought in a great deal of insight in several fields of physics ranging from nuclear, atomic and molecular physics, quantum chaos and mesoscopic systems @1#. The interest in random matrices arose from the need to understand the spectral properties of the many-body quantum systems with complex interactions. With general assumptions about the symmetry properties of the system dictated by quantum physics, random matrix theory ~RMT! provides remarkably successful predictions for the statistical properties of the spectrum, which have been numerically and experimentally verified in the last few decades @2#. In recent times, it has been realized that the fluctuation properties of low-dimensional systems, e.g., chaotic quantum systems, are universal and can be modeled by an appropriate ensemble of random matrices @3#. From its origins in quantum physics of high-dimensional systems, the scope of RMT is further widening with the new approaches based on supersymmetry methods @4# and applications in seemingly disparate fields like quantum chromodynamics @5#, two-dimensional quantum gravity @6#, conformal field theory @1# and even financial markets@7#. Thus, random matrix techniques have potential applications and utility in disciplines far outside of quantum physics. In this paper, we show that the empirical correlation matrices that arise in atmospheric sciences can also be modeled as a random matrix chosen from an appropriate ensemble. The correlation studies are elegantly carried out in the matrix framework. The empirical correlation matrices arise in a multivariate setting in various disciplines, for instance, in the analysis of space-time data in general problems of image processing and pattern recognition, in particular, for image compression and denoising @8#—the weather and climate data are frequently subjected to principal component analysis to identify the independent modes of atmospheric variability @9#—and in the study of financial assets and portfolios through the Markowitz’s theory of optimal portfolios @10#. Most often, the analysis performed on the correlation matrices is aimed at separating the signal from ‘‘noise,’’ i.e., to cull the physically meaningful modes of the correlation matrix from the underlying noise. Several methods based on Monte Carlo simulations have been used for this purpose @11#. The general premise of such methods is to simulate ‘‘noise’’ by constructing an ensemble of matrices with random entries drawn from specified distributions, and the statistical properties of its eigenvalues like the level density, etc., are compared with that of the correlation matrices. Even as the Monte Carlo techniques become computationally expensive beyond a point, asymptotic formulations take over. The deviations from ‘‘pure noise’’ assumptions are interpreted as signals or symptoms of physical significance. In the context of the atmospheric sciences, empirical correlation matrices are widely used, for example, to study the large scale patterns of atmospheric variability. If the random matrix techniques are valid for a correlation matrix, it might be useful as a tool to separate the signal from the noise, with lesser computational expense than with methods based on Monte Carlo techniques. We show that RMT prediction for eigenvector distribution has potential application in this direction for atmospheric correlation matrices.

93 citations

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TL;DR: The independent component analysis technique is applied to mine for patterns in weather data using the North Atlantic Oscillation as a specific example and finds that the strongest independent components match the observed synoptic weather patterns corresponding to the NAO.
Abstract: In this article, we apply the independent component analysis technique for mining spatio-temporal data. The technique has been applied to mine for patterns in weather data using the North Atlantic Oscillation (NAO) as a specific example. We find that the strongest independent components match the observed synoptic weather patterns corresponding to the NAO. We also validate our results by matching the independent component activities with the NAO index.

67 citations

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TL;DR: A random walk model for transport is employed and it reveals an unforeseen, and yet a robust, feature: small degree nodes of a network are more likely to encounter extreme events than the hubs.
Abstract: A wide spectrum of extreme events ranging from traffic jams to floods take place on networks. Motivated by these, we employ a random walk model for transport and obtain analytical and numerical results for the extreme events on networks. They reveal an unforeseen, and yet a robust, feature: small degree nodes of a network are more likely to encounter extreme events than the hubs. Further, we also study the recurrence time distribution and scaling of the probabilities for extreme events. These results suggest a revision of design principles and can be used as an input for designing the nodes of a network so as to smoothly handle extreme events.

63 citations

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TL;DR: It is shown that the spectrum of the system undergoing order to chaos transition displays a characteristic f(-gamma) noise and gamma is correlated with the classical chaos in the system.
Abstract: Level fluctuations in a quantum system have been used to characterize quantum chaos using random matrix models. Recently time series methods were used to relate the level fluctuations to the classical dynamics in the regular and chaotic limit. In this, we show that the spectrum of the system undergoing order to chaos transition displays a characteristic f(-gamma) noise and gamma is correlated with the classical chaos in the system. We demonstrate this using a smooth potential and a time-dependent system modeled by Gaussian and circular ensembles, respectively, of random matrix theory. We show the effect of short periodic orbits on these fluctuation measures.

46 citations


Cited by
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08 Dec 2001-BMJ
TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.
Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

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TL;DR: In this article, the authors studied a random Groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process and showed that shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.
Abstract: We study a certain random groeth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process. The results show that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble.

1,031 citations