Analyzing multiple spike trains with nonparametric granger causality (2009)
Nedungadi, Aatira G, Rangarajan, Govindan, Jain, Neeraj, Ding, Mingzhou
Simultaneous recordings of spike trains from multiple single neurons are becoming commonplace. Understanding the interaction patterns among these spike trains remains a key research area. A question...
Denoising neural data with state-space smoothing: Method and application (2009)
Nalatore, Hariharan, Ding, Mingzhou, Rangarajan, Govindan
Neural data are inevitably contaminated by noise. When such noisy data are subjected to statistical analysis, misleading conclusions can be reached. Here we attempt to address this problem by...
Vivek S. Borkar, Govindan Rangarajan
Abstract. Many complex adaptive systems contain a large diversity of specialized components. The specialization at the level of the microscopic degrees of freedom, and diversity at the level of the...
Biol. Cybern. 90, 318--326 (2004) (2008)
Zimbul Albo, Gonzalo Viana, Di Prisco, Yonghong Chen, Govindan Rangarajan, ...
Partial coherence measures the linear relationship between two signals after the influence of a third signal has been removed. Gersch proposed in 1970 that partial coherence could be used to identify...
Estimating granger causality from fourier and wavelet transforms of time series data (2008)
Dhamala, Mukeshwar, Rangarajan, Govindan, Ding, Mingzhou
Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral...
Estimating granger causality from fourier and wavelet transforms of time series data (2008)
Dhamala, Mukeshwar, Rangarajan, Govindan, Ding, Mingzhou
Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral...
Granger Causality and Cross Recurrence Plots in Rheochaos (2007)
Ganapathy, Rajesh, Rangarajan, Govindan, Sood, A. K.
Our stress relaxation measurements on wormlike micelles using a Rheo-SALS (rheology + small angle light scattering) apparatus allow simultaneous measurements of the stress and the scattered...
Palaniyandi, P., Rangarajan, Govindan
We consider diffusively coupled map lattices with $P$ neighbors (where $P$ is arbitrary) and study the stability of synchronized state. We show that there exists a critical lattice size beyond which...
Mitigating the effects of measurement noise on Granger causality (2007)
Nalatore, Hariharan, Rangarajan, Govindan, Ding, Mingzhou
Computing Granger causal relations among bivariate experimentally observed time series has received increasing attention over the past few years. Such causal relations, if correctly estimated, can...
Estimating Granger causality from Fourier and wavelet transforms of time series data (2007)
Dhamala, Mukeshwar, Rangarajan, Govindan, Ding, Mingzhou
Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral...
Mitigating the effects of measurement noise on Granger causality (2007)
Nalatore, Hariharan, Ding, Mingzhou, Rangarajan, Govindan
Computing Granger causal relations among bivariate experimentally observed time series has received increasing attention over the past few years. Such causal relations, if correctly estimated, can...
Granger causality and cross recurrence plots in rheochaos (2007)
Ganapathy, Rajesh, Rangarajan, Govindan, Sood, AK
Our stress relaxation measurements on wormlike micelles using a Rheo-SALS (rheology + small angle light scattering) apparatus allow simultaneous measurements of the stress and the scattered...
Granger causality and cross recurrence plots in rheochaos (2007)
Ganapathy, Rajesh, Rangarajan, Govindan, Sood, AK
Our stress relaxation measurements on wormlike micelles using a Rheo-SALS (rheology + small angle light scattering) apparatus allow simultaneous measurements of the stress and the scattered...
Mitigating the effects of measurement noise on Granger causality (2007)
Nalatore, Hariharan, Ding, Mingzhou, Rangarajan, Govindan
Computing Granger causal relations among bivariate experimentally observed time series has received increasing attention over the past few years. Such causal relations, if correctly estimated, can...
Chen, Yonghong, Rangarajan, Govindan, Ding, Mingzhou
In arbitrarily coupled dynamical systems (maps or ordinary differential equations), the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) and the...
Spatially Synchronous Extinction of Species under External Forcing (2006)
Amritkar, RE, Rangarajan, Govindan
More than 99% of the species that ever existed on the surface of the Earth are now extinct and their extinction on a global scale has been a puzzle. One may think that a species under an external...
Spatial synchronization and extinction of species under external forcing (2006)
Amritkar, R. E., Rangarajan, Govindan
We study the interplay between synchronization and extinction of a species. Using a general model we show that under a common external forcing, the species with a quadratic saturation term in the...
Chen, Yonghong, Rangarajan, Govindan, Ding, Mingzhou
In arbitrarily coupled dynamical systems (maps or ordinary differential equations), the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) and the...
Analyzing Stability of Equilibrium Points in Neural Networks: A General Approach (2004)
Truccolo, Wilson A., Rangarajan, Govindan, Chen, Yonghong, Ding, Mingzhou
Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable...
Analyzing Multiple Nonlinear Time Series with Extended Granger Causality (2004)
Chen, Yonghong, Rangarajan, Govindan, Feng, Jianfeng, Ding, Mingzhou
Identifying causal relations among simultaneously acquired signals is an important problem in multivariate time series analysis. For linear stochastic systems Granger proposed a simple procedure...
Analyzing multiple nonlinear time series with extended Granger causality (2004)
Chen, Yonghong, Rangarajan, Govindan, Feng, Jianfeng, Ding, Mingzhou
Identifying causal relations among simultaneously acquired signals is an important problem in multivariate time series analysis. For linear stochastic systems Granger proposed a simple procedure...
Fractal dimensional analysis of Indian climatic dynamics (2004)
Rangarajan, Govindan, Sant, Dhananjay A
In this paper, we use fractal dimensional analysis to investigate the Indian climatic dynamics. We analyze time series data of three major dynamic components of the climate––temperature, pressure...
Analyzing multiple nonlinear time series with extended Granger causality (2004)
Chen, Yonghong, Rangarajan, Govindan, Feng, Jianfeng, Ding, Mingzhou
Identifying causal relations among simultaneously acquired signals is an important problem in multivariate time series analysis. For linear stochastic systems Granger proposed a simple procedure...
Fractal dimensional analysis of Indian climatic dynamics (2004)
Rangarajan, Govindan, Sant, Dhananjay A
In this paper, we use fractal dimensional analysis to investigate the Indian climatic dynamics. We analyze time series data of three major dynamic components of the climate––temperature, pressure...
First passage time problem: a Fokker-Planck approach (2004)
Ding, Mingzhou, Rangarajan, Govindan
This chapter reviews the first passage time problem for one dimensional stochastic processes and presents closed form solutions for the underlying distribution function. Using the Fokker-Planck...
First passage time problem: a Fokker-Planck approach (2004)
Ding, Mingzhou, Rangarajan, Govindan
This chapter reviews the first passage time problem for one dimensional stochastic processes and presents closed form solutions for the underlying distribution function. Using the Fokker-Planck...
Analyzing multiple nonlinear time series with extended Granger causality (2004)
Yonghong Chen, Govindan Rangarajan, Jianfeng Feng, Mingzhou Ding
Identifying causal relations among simultaneously acquired signals is an important problem in multivariate time series analysis. For linear stochastic systems Granger proposed a simple procedure...
Analyzing stability of equilibrium points in neural networks: a general approach (2003)
Truccolo, Wilson A, Rangarajan, Govindan, Chen, Yonghong, Ding, Mingzhou
Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable...
Polynomial map factorization of symplectic maps (2003)
Long-term stability studies of nonlinear Hamiltonian systems require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method...
Generalized Turing patterns and their selective realization in spatiotemporal systems (2003)
Rangarajan, Govindan, Chen, Yonghong, Ding, Mingzhou
We consider the pattern formation problem in coupled identical systems after the global synchronized state becomes unstable. Based on analytical results relating the coupling strengths and the...
Generalized Turing Patterns and Their Selective Realization in Spatiotemporal Systems (2003)
Rangarajan, Govindan, Chen, Yonghong, Ding, Mingzhou
We consider the pattern formation problem in coupled identical systems after the global synchronized state becomes unstable. Based on analytical results relating the coupling strengths and the...
General stability analysis of synchronized dynamics in coupled systems (2003)
Chen, Yonghong, Rangarajan, Govindan, Ding, Mingzhou
We consider the stability of synchronized states (including equilibrium point, periodic orbit, or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential...
General stability analysis of synchronized dynamics in coupled systems (2003)
Chen, Yonghong, Rangarajan, Govindan, Ding, Mingzhou
We consider the stability of synchronized states (including equilibrium point, periodic orbit, or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential...
Generalized Turing patterns and their selective realization in spatiotemporal systems (2003)
Rangarajan, Govindan, Chen, Yonghong, Ding, Mingzhou
We consider the pattern formation problem in coupled identical systems after the global synchronized state becomes unstable. Based on analytical results relating the coupling strengths and the...
Expression for a General Element of an SO(n) Matrix (2003)
Janaki, TM, Rangarajan, Govindan
We derive the expression for a general element of an SO(n) matrix. All elements are obtained from a single element of the matrix. This has applications in recently developed methods for computing...
Expression for a General Element of an SO(n) Matrix (2003)
Janaki, TM, Rangarajan, Govindan
We derive the expression for a general element of an SO(n) matrix. All elements are obtained from a single element of the matrix. This has applications in recently developed methods for computing...
Expression for a general element of an SO(n) matrix (2003)
T. M. Janaki, Govindan Rangarajan
We derive the expression for a general element of an SO(n) matrix. All elements are obtained from a single element of the matrix. This has applications in recently developed methods for computing...
Generalized Turing patterns and their selective realization in spatiotemporal systems (2003)
Govindan Rangarajan, Yonghong Chen, Mingzhou Ding
We consider the pattern formation problem in coupled identical systems after the global synchronized state becomes unstable. Based on analytical results relating the coupling strengths and the...
Expression for a general element of an SO(n) matrix (2003)
T. M. Janaki, Govindan Rangarajan
We derive the expression for a general element of an SO(n) matrix. All elements are obtained from a single element of the matrix. This has applications in recently developed methods for computing...
General Stability Analysis of Synchronized Dynamics in Coupled Systems (2002)
Chen, Yonghong, Rangarajan, Govindan, Ding, Mingzhou
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations)....
Polynomial map symplectic algorithm (2002)
Long-term stability studies of nonlinear Hamiltonian systems require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method...
Onset of climate change at Last Glacial-Holocene transition: Role of the tropical Pacific (2002)
Sant, Dhananjay A, Rangarajan, Govindan
We study palaeoclimatic records from various sites spread around the earth, focusing on the start of the last glacial-interglacial transition. The warming, as recorded in the $\delta^{18}O$ record...
Stability of synchronized chaos in coupled dynamical systems (2002)
Rangarajan, Govindan, Ding, Mingzhou
We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove...
Invariant metric for nonlinear symplectic maps (2002)
Rangarajan, Govindan, Sachidanand, Minita
In this paper, we construct an invariant metric in the space of homogeneous polynomials of a given degree ( greater than or equal to 3). The homogeneous polynomials specify a nonlinear symplectic map...
Stability of Synchronized Chaos in Coupled Dynamical Systems (2002)
Rangarajan, Govindan, Ding, Mingzhou
We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove...
Invariant metric for nonlinear symplectic maps (2002)
Rangarajan, Govindan, Sachidanand, Minita
In this paper, we construct an invariant metric in the space of homogeneous polynomials of a given degree ( greater than or equal to 3). The homogeneous polynomials specify a nonlinear symplectic map...
Stability of synchronized chaos in coupled dynamical systems (2002)
Rangarajan, Govindan, Ding, Mingzhou
We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove...
Onset of climate change at Last Glacial-Holocene transition: Role of the tropical Pacific (2002)
Sant, Dhananjay A, Rangarajan, Govindan
We study palaeoclimatic records from various sites spread around the earth, focusing on the start of the last glacial-interglacial transition. The warming, as recorded in the $\delta^{18}O$ record...
Symplectic integration of Hamiltonian systems using polynomial maps (2001)
In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast...
Symplectic Integration of Hamiltonian Systems using Polynomial Maps (2001)
In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast...
First Passage Time Distribution for Anomalous Diffusion (2001)
Rangarajan, Govindan, Ding, Mingzhou
We study the first passage time (FPT) problem in Levy type of anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation, we obtain an analytic expression for the FPT...
Anomalous diffusion and the first passage time problem (2001)
Rangarajan, Govindan, Ding, Mingzhou
We study the distribution of first passage time (FPT) in Levy type of anomalous diffusion. Using recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an...
First passage time problem for biased continuous-time random walks (2001)
Rangarajan, Govindan, Ding, Mingzhou
We study the first passage time (FPT) problem for biased continuous time random walks. Using the recently formulated framework of fractional Fokker-Planck equations, we obtain the Laplace transform...
An integrated approach to the assessment of long range correlation in time series data (2001)
Rangarajan, Govindan, Ding, Mingzhou
To assess whether a given time series can be modeled by a stochastic process possessing long range correlation one usually applies one of two types of analysis methods: the spectral method and the...
Symplectic integration of Hamiltonian systems using polynomial maps (2001)
In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast...
Anomalous diffusion and the first passage time problem (2000)
Rangarajan, Govindan, Ding, Mingzhou
We study the distribution of the first passage time (FPT) in Levy type anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an...
Paleoclimatic data from 74KL and Guliya cores:New insights (2000)
Rangarajan, Govindan, Sant, Dhanajay A
We analyze multi-proxy climatic records from the 74KL marine core and compare it with the delta(18)O record from: the Guliya ice core. These records have important implications for the evolution of...
Symplectic integration using solvable maps (2000)
Rangarajan, Govindan, Sachidanand, Minita
In this paper, a symplectic integration algorithm using solvable maps is investigated. Examples are studied in two and four dimensions. The method is shown to give good results.
Paleoclimatic data from 74KL and Guliya cores:New insights (2000)
Rangarajan, Govindan, Sant, Dhanajay A
We analyze multi-proxy climatic records from the 74KL marine core and compare it with the delta(18)O record from: the Guliya ice core. These records have important implications for the evolution of...
Anomalous diffusion and the first passage time problem (2000)
Rangarajan, Govindan, Ding, Mingzhou
We study the distribution of the first passage time (FPT) in Levy type anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an...
Symplectic integration using solvable maps (2000)
Rangarajan, Govindan, Sachidanand, Minita
In this paper, a symplectic integration algorithm using solvable maps is investigated. Examples are studied in two and four dimensions. The method is shown to give good results.
Integrated approach to the assessment of long range correlation in time series data (2000)
Rangarajan, Govindan, Ding, Mingzhou
To assess whether a given time series can be modeled by a stochastic process possessing long range correlation, one usually applies one of two types of analysis methods: the spectral method and the...
Integrated approach to the assessment of long range correlation in time series data (2000)
Rangarajan, Govindan, Ding, Mingzhou
To assess whether a given time series can be modeled by a stochastic process possessing long range correlation, one usually applies one of two types of analysis methods: the spectral method and the...
First Passage Time Problem For Biased Continuous-Time Random Walks (2000)
Govindan Rangarajan, Mingzhou Ding
We study the first passage time (FPT) problem for biased continuous time random walks.
Computation of the Lyapunov spectrum for continuous-time dynamical systems and discrete maps (1999)
Janaki, TM, Rangarajan, Govindan, Habib, Salman, Ryne, Robert D
In this paper, we describe in detail a method of computing Lyapunov exponents for a continuous-time dynamical system and extend the method to discrete maps. Using this method, a partial Lyapunov...
Dynamic moment invariants for nonlinear Hamiltonian systems (1999)
Janaki, TM, Rangarajan, Govindan
Distributions of particles being transported through a nonlinear Hamiltonian system are studied. Using normal form techniques, a procedure to obtain invariant functions of moments of the distribution...
Evolutionary games with two timescales (1999)
Borkar, Vivek S, Jain, Sanjay, Rangarajan, Govindan
We consider a two timescale model of learning by economic agents wherein active or 'ontogenetic' learning by individuals takes place on a fast scale and passive or 'phylogenetic' learning by society...
Borkar, Vivek S., Jain, Sanjay, Rangarajan, Govindan
Many complex adaptive systems contain a large diversity of specialized components. The specialization at the level of the microscopic degrees of freedom, and diversity at the level of the system as a...
Dynamics of Individual Specialization and Global Diversification in Communities (1998)
Borkar, Vivek S., Jain, Sanjay, Rangarajan, Govindan
We discuss a model of an economic community consisting of $N$ interacting agents. The state of each agent at any time is characterized, in general, by a mixed strategy profile drawn from a space of...
Jolt factorization of pendulum map (1998)
In this paper, we apply the symplectic integration method using jolt factorization described in an earlier paper to the symplectic map describing the nonlinear pendulum Hamiltonian. We compare...
Lyapunov Exponents without Rescaling and Reorthogonalization (1998)
Rangarajan, Govindan, Habib, Salman, Ryne, Robert D
We present a new method for the computation of Lyapunov exponents utilizing representations of orthogonal matrices applied to decompositions of M or $M \~{M}$ where M is the tangent map. This method...
Lyapunov Exponents without Rescaling and Reorthogonalization (1998)
Rangarajan, Govindan, Habib, Salman, Ryne, Robert D.
We present a new method for the computation of Lyapunov exponents utilizing representations of orthogonal matrices applied to decompositions of M or MM_trans where M is the tangent map. This method...
Dynamics of individual specialization and global diversification in communities (1998)
Borkar, Vivek S, Jain, Sanjay, Rangarajan, Govindan
We discuss a model of an economic community consisting of N interacting agents. The state of each agent at any time is characterized, in general, by a mixed strategy profile drawn from a space of s...
Lyapunov Exponents without Rescaling and Reorthogonalization (1998)
Rangarajan, Govindan, Habib, Salman, Ryne, Robert D
We present a new method for the computation of Lyapunov exponents utilizing representations of orthogonal matrices applied to decompositions of M or $M \~{M}$ where M is the tangent map. This method...
Jolt factorization of pendulum map (1998)
In this paper, we apply the symplectic integration method using jolt factorization described in an earlier paper to the symplectic map describing the nonlinear pendulum Hamiltonian. We compare...
Dynamics of individual specialization and global diversification in communities (1998)
Borkar, Vivek S, Jain, Sanjay, Rangarajan, Govindan
We discuss a model of an economic community consisting of N interacting agents. The state of each agent at any time is characterized, in general, by a mixed strategy profile drawn from a space of s...
Representations of Sp(6,R) and SU(3) carried by homogeneous polynomials (1997)
In this paper, we study representations of Sp(6,R) and SU(3) carried by homogeneous polynomials of phase-space variables in six dimensions. These representations are very important for the study of...
Representations of Sp(6,R) and SU(3) carried by homogeneous polynomials (1997)
In this paper, we study representations of Sp(6,R) and SU(3) carried by homogeneous polynomials of phase-space variables in six dimensions. These representations are very important for the study of...
Symplectic completion of symplectic jets (1996)
In this paper, we outline a method for symplectic integration of three degree-of-freedom Hamiltonian systems. We start by representing the Hamiltonian system as a symplectic map. This map (in...
Symplectic completion of symplectic jets (1996)
In this paper, we outline a method for symplectic integration of three degree-of-freedom Hamiltonian systems. We start by representing the Hamiltonian system as a symplectic map. This map (in...
Thesis (Ph. D.)--University of Maryland at College Park, 1990.