{"id":50,"date":"2020-07-31T00:28:06","date_gmt":"2020-07-31T00:28:06","guid":{"rendered":"http:\/\/math.iisc.ac.in\/~rangaraj\/wp\/?page_id=50"},"modified":"2026-02-06T16:39:13","modified_gmt":"2026-02-06T16:39:13","slug":"publications","status":"publish","type":"page","link":"https:\/\/math.iisc.ac.in\/~rangaraj\/publications\/","title":{"rendered":"Publications"},"content":{"rendered":"<style id=\"kt-blocks_afa819-50\" type=\"text\/css\">.kt-accordion-id_afa819-50 .kt-blocks-accordion-header {color:#555555;background:#f2f2f2;border-color:#555555 #555555 #555555 #555555;font-size:18px;line-height:24px;border-radius:0px 0px 0px 0px;border-width:0px 0px 0px 0px;padding:10px 14px 10px 14px;margin-top:15px;}.kt-accordion-id_afa819-50 .kt-blocks-accordion-header .kt-btn-svg-icon svg {width:18px;height:18px;}.kt-accordion-id_afa819-50:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) 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):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header:hover .kt-blocks-accordion-icon-trigger:before {background:#eeeeee;}.kt-accordion-id_afa819-50 .kt-blocks-accordion-header.kt-accordion-panel-active {color:#ffffff;background:#444444;border-color:#444444 #444444 #444444 #444444;}.kt-accordion-id_afa819-50:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id_afa819-50:not( .kt-accodion-icon-style-basiccircle ):not( .kt-accodion-icon-style-xclosecircle ):not( .kt-accodion-icon-style-arrowcircle ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before {background:#ffffff;}.kt-accordion-id_afa819-50:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger {background:#ffffff;}.kt-accordion-id_afa819-50:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:after, .kt-accordion-id_afa819-50:not( .kt-accodion-icon-style-basic ):not( .kt-accodion-icon-style-xclose ):not( .kt-accodion-icon-style-arrow ) .kt-blocks-accordion-header.kt-accordion-panel-active .kt-blocks-accordion-icon-trigger:before {background:#444444;}<\/style>\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-wrap kt-accordion-id_afa819-50 kt-accordion-has-11-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"0\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane_f0f08b-10\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><div class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">Books<\/span><\/div><div class=\"kt-blocks-accordion-icon-trigger\"><\/div><\/button><\/div><div class=\"kt-accordion-panel\"><div class=\"kt-accordion-panel-inner\">\n<ul>\n<li>G. Rangarajan and M. Ding (editors), <em>Processes with Long Range Correlations: Theory and Applications<\/em> (Springer-Verlag, Berlin, 2003). <\/li>\n\n\n\n<li>R. L. Bhatia, A. Pal, G. Rangarajan, V. Srinivas and M. Vanninathan (editors),         <em> Proceedings of the International Congress of Mathematicians<\/em> (Hindustan Book           Agency, New Delhi, 2010). <\/li>\n\n\n\n<li>R. Salgia, M. K. Jolly, P. Kulkarni and G. Rangarajan (editors) <em>Cancer Systems Biology and Translational Mathematical Oncology<\/em> (Oxford University Press, Oxford, 2025).<br><a href=\"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2025\/11\/Book.jpg\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View Cover<\/a><\/li>\n<\/ul>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-8 kt-pane_41292e-dd\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><div class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">In Journals<\/span><\/div><div class=\"kt-blocks-accordion-icon-trigger\"><\/div><\/button><\/div><div class=\"kt-accordion-panel\"><div class=\"kt-accordion-panel-inner\">\n<ul>\n<li>A. J. Dragt, F. Neri, G. Rangarajan, D. R. Douglas, L. M. Healy and \nR. D. Ryne, Lie algebraic treatment of linear and nonlinear beam \ndynamics, <em>Annual Review of Nuclear and Particle Science<\/em> <strong>38<\/strong>, 455 (1988).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/annu_rev_lie_algebra.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>G. Rangarajan and K. C. D. Chan, Transverse resistive wall effects on the dynamics of a bunched electron beam, <em>Physical Review A<\/em> <strong>39<\/strong>, 4749 (1989).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pra_wiggler1.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>G. Rangarajan and K. C. D. Chan, Transient state of a bunched electron beam subject to resistive-wall instability, <em>Physical Review A<\/em> <strong>41<\/strong>, 333 (1990).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pra_wiggler2.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>F. Neri and G. Rangarajan, Kinematic moment invariants for linear Hamiltonian systems, <em>Physical Review Letters<\/em> <strong>64<\/strong>, 1073 (1990).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/prl_moments.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>V. S. Ramamurthy, A. K. Mohanty, S. K. Kataria and G. Rangarajan, \nSub-barrier fusion in a macroscopic model of nuclear shape evolutions, <em> Physical Review C<\/em> <strong>41<\/strong>, 2702 (1990).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/prc_nuclear.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>G. Rangarajan, A. J. Dragt and F. Neri, Solvable map representation of a nonlinear symplectic map, <em>Particle Accelerators<\/em> <strong>28<\/strong>, 119 (1990).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/part_accel_solvable_maps.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan and K. C. D. Chan, Transient resistive-wall effects of a bunched electron beam in a wiggler, <em>Particle Accelerators<\/em> <strong>33<\/strong>, 135 (1990).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/part_accel_wiggler.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>A. J. Dragt, F. Neri and G. Rangarajan, General moment invariants for linear Hamiltonian systems, <em>Physical Review A<\/em> <strong>45<\/strong>, 2572 (1992).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pra_moments.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>G. Rangarajan, A. M. Sessler and W. M. Sharp, Discrete cavity model of a standing-wave free-electron laser, <em>Nuclear Instruments and Methods in Physics Research<\/em> <strong>A318<\/strong>, 745 (1992).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/nimpra_discrete_cavity_fel.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>G. Rangarajan and F. Neri, Canonical representations of sp(2n,R), <em>Journal of Mathematical Physics<\/em> <strong>33<\/strong>, 1247 (1992).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jmp_canonical_rep.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>S. Krishnagopal, G. Rangarajan and A. M. Sessler, Numerical studies of the multi-cavity free-electron laser, <em>Nuclear Instruments and Methods in Physics Research A<\/em> <strong>331<\/strong>, A22 (1993).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/nimpra_multi_cavity_fel.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>S. Krishnagopal, G. Rangarajan and A. M. Sessler, The multi-cavity free-electron laser, <em>Optics Communications<\/em> <strong>100<\/strong>, 518 (1993).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/optics_comm_multi_cavity_fel.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>G. Rangarajan, Symplectic completion of symplectic jets, <em>Journal of Mathematical Physics<\/em> <strong>37<\/strong>, 4514 (1996).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jmp_symplectic.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>G. Rangarajan, Symplectic integration of Hamiltonian systems, <em>Pramana \u2013 Journal of Physics<\/em> <strong>48<\/strong>, 129 (1997).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pramana_symplectic.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>G. Rangarajan, Representations of Sp(6,R) and SU(3) carried by homogeneous polynomials, <em>Journal of Mathematical Physics<\/em> <strong>38<\/strong>, 2710 (1997).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jmp_rep_sp6.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>G. Rangarajan and D. A. Sant, A climate predictability index and its applications, <em>Geophysical Research Letters<\/em> <strong>24<\/strong>, 1239 (1997).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/grl_cpi.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>G. Rangarajan and M. Sachidanand, Spherical aberration and its correction using Lie algebraic techniques, <em>Pramana \u2013 Journal of Physics<\/em> <strong>49<\/strong>, 635 (1997).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pramana_spherical_aberration.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>V. S. Borkar, S. Jain and G. Rangarajan, Dynamics of individual specialization and global diversification in communities, <em>Complexity<\/em> <strong> 3<\/strong>, 50 (1998). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/complexity_grd.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan, S. Habib and R. D. Ryne, Lyapunov exponents without rescaling and reorthogonalization, <em>Physical Review Letters<\/em> <strong>80<\/strong>, 3747 (1998). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/prl_lyap.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan, Jolt factorization of the pendulum map, <em>Journal of Physics A: Mathematical and General<\/em> <strong>31<\/strong>, 3649 (1998). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jolt_jpa.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>V. S. Borkar, S. Jain and G. Rangarajan, Generalized replicator \ndynamics as a model of specialization and diversity in societies, <em>Advances in Complex Systems<\/em> <strong>1<\/strong>, 325 (1998).<a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/acs_grd.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>T. M. Janaki and G. Rangarajan, Lyapunov exponents for continuous-time dynamical systems, <em>Journal of the Indian Institute of Science<\/em> <strong>78<\/strong>, 267 (1998). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jiisc_lyap.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>V. S. Borkar, S. Jain and G. Rangarajan, Evolutionary games with two time scales, <em>Physica D<\/em> <strong>125<\/strong>, 155 (1999).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/physicad_two_timescales.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>T. M. Janaki and G. Rangarajan, Dynamic moment invariants for nonlinear Hamiltonian systems, <em>Physical Review E<\/em> <strong>59<\/strong>, 4577 (1999). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pre_moments.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>T. M. Janaki, G. Rangarajan, S. Habib and R. D. Ryne, Computation of\n Lyapunov spectrum for continuous time dynamical systems and discrete \nmaps, <em>Physical Review E<\/em> <strong>60<\/strong>, 6614 (1999).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pre_lyap.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>G. Rangarajan and M. Ding, First passage time distribution for anomalous diffusion, <em> Physics Letters A <\/em> <strong> 273 <\/strong>, 322 (2000). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pla_fpt.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan and M. Sachidanand, Symplectic integration using solvable maps, <em>Journal of Physics A: Mathematical and General<\/em> <strong>33<\/strong>, 131 (2000). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jpa_solvable.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan and M. Ding, Anomalous diffusion and the first passage time problem, <em>Physical Review E<\/em> <strong>62<\/strong>, 120 (2000). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pre_fpt.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan and D. A. Sant, Paleoclimatic data from 74KL and Guliya cores: New insights, <em>Geophysical Research Letters<\/em> <strong>27<\/strong>, 787 (2000). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/grl_paleo.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan and M. Ding, Integrated approach to the assessment of long range correlation in time series data, <em>Physical Review E<\/em> <strong>61<\/strong> 4991 (2000). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pre_long_range.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan and M. Ding, First passage time problem for biased continuous-time random walks, <em>Fractals<\/em> <strong>8<\/strong>, 139 (2000). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/fractals_fpt.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan, Symplectic integration of Hamiltonian systems using polynomial maps, <em>Physics Letters A<\/em> <strong>286<\/strong>, 141 (2001). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pla_polymaps.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan and M. Ding, Stability of synchronized chaos in coupled dynamical systems, <em> Physics Letters A<\/em> <strong>296<\/strong>, 204 (2002). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pla_synchronized.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan and M. Sachidanand, Invariant metric for nonlinear symplectic maps, <em> Pramana \u2014 Journal of Physics<\/em> <strong>58<\/strong>, 477 (2002).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pramana_metric.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>D. A. Sant and G. Rangarajan, Onset of climate change at last Glacial-Holocene transition: Role of the tropical Pacific, <em> Current Science<\/em> <strong>83<\/strong>, 101 (2002). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/currsci_paleo.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>Y. Chen, G. Rangarajan and M. Ding, General stability analysis of synchronized dynamics in coupled systems, <em> Physical Review E<\/em> <strong>67<\/strong>, 026209 (2003). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pre_synchronized.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan, Y. Chen and M. Ding, Generalized Turing patterns and their selective realization in spatiotemporal systems, <em> Physics Letters A<\/em> <strong>310<\/strong>, 415 (2003). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pla_Turing_patterns.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan and M. Ding, First passage distributions for long memory processes, <em> Lecture Notes in Physics<\/em> <strong>621<\/strong>, 167 (2003).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/lnp_fpt.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>T. M. Janaki and G. Rangarajan, Expression for a general element of an SO(n) matrix, <em> International Journal of Mathematics and Mathematical Sciences<\/em> <strong>2003<\/strong>, 3091 (2003). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/ijmms_so_n.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>W. A. Truccolo, G. Rangarajan, Y. Chen and M. Ding, Analyzing \nstability of equilibrium points in neural networks: A general approach, <em> Neural Networks<\/em> <strong>16<\/strong>, 1453 (2003). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/nn_stability.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan, Polynomial map factorization of symplectic maps, <em> International Journal of Modern Physics C<\/em> <strong>14<\/strong>, 847 (2003). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/ijmpc_polynomial_maps.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>B. S. Daya Sagar, G. Rangarajan and D. Veneziano, Fractals in Geophysics, <em> Chaos, Solitons and Fractals<\/em> <strong>19<\/strong>, 237 (2004). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/fractals_geophysics_preface.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan and D. A. Sant, Fractal dimensional analysis of Indian climatic dynamics, <em> Chaos, Solitons and Fractals<\/em> <strong>19<\/strong>, 285 (2004). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/fractals_geophysics.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>D. A. Sant, K. Krishnan, G. Rangarajan, N. Basavaiah, C. Pandya, M. \nSharma and Y. Trivedi, Characterization of flood plain and climate \nchange using multi-proxy records, <em> Journal of Indian Geophysical Union<\/em> <strong> 8<\/strong>, 39 (2004).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jigu_mahi.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>Y. Chen, G. Rangarajan, J. Feng and M. Ding, Analyzing multiple nonlinear time series with extended Granger causality, <em> Physics Letters A<\/em> <strong> 324<\/strong>, 26 (2004). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pla_nonlinear_causality.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>Z. Albo, G. V. Di Prisco, Y. Chen, G. Rangarajan, W. Truccolo, J. \nFeng, R. P. Vertes and M. Ding, Is partial coherence a viable technique \nfor identifying generators of neural oscillations? <em> Biological Cybernetics<\/em> <strong> 90<\/strong>, 318 (2004). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/biol_cyber_causality.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>Y. Chen, G. Rangarajan and M. Ding, Stability of synchronized \ndynamics and pattern formation in coupled systems: Review of some recent\n results, <em>Communications in Nonlinear Science and Numerical Simulation<\/em> <strong>11<\/strong>, 934 (2006).&nbsp;&nbsp;&nbsp; <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/cnsns_synchronized.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>R. E. Amritkar and G. Rangarajan, Spatially synchronous extinction of species under external forcing, <em>Physical Review Letters<\/em> <strong>96<\/strong>, 258102 (2006). (featured in <a href=\"http:\/\/www.aip.org\/pnu\/2006\/split\/781-1.html\" target=\"_blank\" rel=\"noreferrer noopener\">Physics News Update No. 781<\/a>, 2006) <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/prl_sync_extinction.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>D. A. Sant, G. Rangarajan, K. Krishnan, N. Basavaiah, C. Pandya, M. \nSharma and Y. Trivedi, Flood plain record of southwest Indian monsoon \nduring the last glacial, <em>Man and Environment <\/em> <strong>31<\/strong>, 9 (2006). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/man_environment_flood_plains.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>R. Ganapathy, G. Rangarajan and A. K. Sood, Granger causality and cross recurrence plots in rheochaos, <em>Physical Review E<\/em> <strong>75<\/strong>, 016211 (2007). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pre_rheochaos.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>H. Nalatore, M. Ding and G. Rangarajan, Mitigating the effects of measurement noise on Granger causality, <em>Physical Review E<\/em> <strong>75<\/strong>, 031123 (2007). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pre_denoising.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>P. Palaniyandi and G. Rangarajan, Critical lattice size limit for \nsynchronized chaotic state in one- and two-dimensional diffusively \ncoupled map lattices, <em>Physical Review E<\/em> <strong>76<\/strong>, 027202 (2007). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pre_lattice_size.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>H. Nalatore, W. Truccolo and G. Rangarajan, Fast robust pattern \nclassification algorithms for real time neuro-motor prosthetic \napplications, <em>Journal of the Indian Institute of Science<\/em> <strong>87<\/strong>, 497 (2007). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jiisc_bmi.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>M. Dhamala, G. Rangarajan and M. Ding, Estimating Granger causality from Fourier and wavelet transforms of time series data, <em>Physical Review Letters <\/em> <strong>100<\/strong>, 018701 (2008). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/prl_granger_causality.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>M. Dhamala, G. Rangarajan and M. Ding, Analyzing information flow in brain networks with nonparametric Granger causality, <em> NeuroImage <\/em> <strong>41<\/strong>, 354 (2008). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/neuroimage_granger_causality.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>A. Nedungadi, G. Rangarajan, N. Jain and M. Ding, Analyzing multiple spike trains with nonparametric Granger causality, <em> Journal of Computational Neuroscience <\/em> <strong>27<\/strong>, 55 (2009). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jcn_spike_train.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>H. Nalatore, M. Ding and G. Rangarajan, Denoising neural data with state-space smoothing: Method and application, <em> Journal of Neuroscience Methods<\/em> <strong>179<\/strong>, 131 (2009). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jnm_denoise.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>H. Nalatore and G. Rangarajan, Short-window spectral analysis using AMVAR and multitaper methods: A comparison, <em> Biological Cybernetics<\/em> <strong>101<\/strong>, 71 (2009). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/biol_cyber_AMVAR.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>R. E. Amritkar and G. Rangarajan, Stability of multi-cluster synchronization, <em> International Journal of Bifurcation and Chaos<\/em> <strong>19<\/strong>, 4263 (2009). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/ijbc_multi_cluster.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan and S. Sridharan, Invariant norm quantifying nonlinear content of Hamiltonian systems, <em> Applied Mathematics and Computation<\/em> <strong>217<\/strong>, 2495 (2010). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/amc_invariant_norm.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>V. S. Borkar, M. K. Ghosh and G. Rangarajan, Application of nonlinear filtering to credit risk, <em> Operations Research Letters<\/em> <strong>38<\/strong>, 527 (2010). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/orl_credit_risk.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>S. Ghosh, G. Rangarajan and S. Sinha, Stability of synchronization in a multi-cellular system, <em> Europhysics Letters (EPL)<\/em> <strong>92<\/strong>, 40012 (2010). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/epl_sync_multicellular.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>A. Nedungadi, M. Ding and G. Rangarajan, Block coherence: A method \nfor measuring the interdependence between two blocks of neurobiological \ntime series, <em> Biological Cybernetics<\/em> <strong>104<\/strong>, 197 (2011). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/biol_cyber_block_coherence.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>P. Sukumaran, I. A. Parvez, D. A. Sant, G. Rangarajan and K. \nKrishnan, Profiling of Late Tertiary \u2013 Early Quaternary surface in the \nlower reaches of Narmada Valley using microtremors, <em> Journal of Asian Earth Sciences<\/em> <strong>41<\/strong>, 325 (2011). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jaes_narmada_valley_microtremors.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>P. Sukumaran, D. A. Sant, K. Krishnan and G. Rangarajan, High \nresolution facies record on Late Holocene flood plain sediments from \nlower reaches of Narmada Valley, Western India, <em> Journal of the Geological Society of India <\/em> <strong>79<\/strong>, 41 (2012). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jgsi_high_resolution_facies.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>V. Resmi, G. Ambika, R. E. Amritkar and G. Rangarajan, Amplitude death in complex networks induced by environment, <em> Physical Review E <\/em> <strong>85<\/strong>, 046211 (2012). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pre_amplitude_death.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Mahmoudabadi, K. Rajagopalan, R. H. Getzenberg, S. Hannenhalli, \nG. Rangarajan and P. Kulkarni, Intrinsically disordered proteins and \nconformational noise: Implications in cancer, <em> Cell Cycle<\/em> <strong> 12<\/strong>, 26 (2013). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/cell_cycle_IDP_cancer.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>X. Wen, G. Rangarajan and M. Ding, Multivariate Granger causality: \nAn estimation framework based on factorization of spectral density \nmatrix, <em> Philosophical Transactions of the Royal Society A<\/em> <strong> 371<\/strong>, 20110610 (2013). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/ptrsa_multivariate_granger.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>X. Wen, G. Rangarajan and M. Ding, Is Granger causality a viable technique for analyzing fMRI data? <em> PLOS ONE<\/em> <strong> 8<\/strong>, e67428 (2013). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pone_granger_downsampling.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>P. Gade and G. Rangarajan, Frustration induced oscillator death on networks, <em> Chaos<\/em> <strong> 23<\/strong>, 033104 (2013). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/chaos_frustration.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>A. Ghosh, D. Paria, G. Rangarajan, and A. Ghosh, Velocity fluctuations in helical propulsion: How small can a propeller be, <em> Journal of Physical Chemistry Letters<\/em> <strong> 5<\/strong>, 62 (2014). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jpcl_velocity_fluctuations.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>D. Sampath, K.R. Sabitha, P. Hegde, H. R Jayakrishnan, B. M. Kutty, \nS. Chattarji, G. Rangarajan, T.R. Laxmi, A study on fear memory \nretrieval and REM sleep in maternal separation and isolation stressed \nrats, <em> Behavioural Brain Research<\/em> <strong> 273<\/strong>, 144 (2014). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/bbr_maternal_separation.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>H. Nalatore, N. Sasikumar and G. Rangarajan, Effect of measurement noise on Granger causality, <em> Physical Review E<\/em> <strong> 90<\/strong>, 062127 (2014). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pre_granger_noise.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>A. Ray, N. Sehgal, S. Karunakaran, G. Rangarajan and V. \nRavindranath, MPTP activates ASK1-p38 MAPK signaling pathway through \nTNF-dependent Trx1 oxidation in Parkinsonism mouse model, <em> Free Radical Biology &amp; Medicine <\/em> <strong> 87<\/strong>, 312 (2015). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/frbm_parkinson.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>N. Rangarajan, Z. Fox, A. Singh, P. Kulkarni, G. Rangarajan, \nDisorder, oscillatory dynamics and state switching: The role of c-Myc, <em> Journal of Theoretical Biology <\/em> <strong> 386<\/strong>, 105 (2015). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jtb_myc.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>S. M. Mooney. K. Rajagopalan, G. Rangarajan, P. Kulkarni, \nCancer\/testis antigens and obligate participation in multiple hallmarks \nof cancer: An update, <em> Asian Journal of Andrology<\/em> <strong> 18<\/strong>, 711 (2016). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/aja_cancer_Kulkarni.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>A. U. Joshi, D. A. Sant, I. A. Parvez, G. Rangarajan, M. A. Limaye, \nS. Mukherjee, M. J. Charola, M. N. Bhatt, S. P. Mistry, Sub-surface \nprofiling of granite pluton using microtremor method: Southern Aravalli,\n Gujarat, India, <em> International Journal of Earth Sciences<\/em> (2017) (accepted for publication). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/ijes_narukot_microtremor.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>D. A. Sant, I. A. Parvez, G. Rangarajan, , Satish J. Patel, M. N. \nBhatt and T. A. S. Salam, Subsurface profiling along Banni Plains and \nbounding faults, Kachchh, Western India using microtremors method, <em> Journal of Asian Earth Sciences <\/em> <strong> 146<\/strong>, 326 (2017). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jaes_Banni_microtremors.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>P. Palaniyandi and G. Rangarajan, A mathematical model for storage \nand recall of images using targeted synchronization of coupled maps, <em> Scientific Reports<\/em> <strong> 7<\/strong>, 8921 (2017). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/sci_rep_image_encoding.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>R. Chopra, C. R. Murthy and G. Rangarajan, Statistical tests for detecting Granger causality, <em> IEEE Transactions on Signal Processing<\/em> <strong>66<\/strong>, 5803 (2018). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/tsp_causality.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>X. Lin, S. Roy, M. K. Jolly, F. Bocci, N. P. Schafer, M.-Y. Tsai, Y.  Chen, Y. He, A. Grishaev, K. Weninger, J. Orban, P. Kulkarni, G.  Rangarajan, H. Levine and J. N. Onuchic, PAGE4 and conformational  switching: Insights from molecular dynamics simulations and implications  for prostate cancer, <em> Journal of Molecular Biology<\/em> <strong>430<\/strong>, 2422 (2018). <a href=\"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2026\/02\/jmb_idp.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>D. A. Sant, I. A. Parvez, G. Rangarajan, S. J. Patel, T. A. S. Salam\n and M. N. Bhatt, Subsurface imaging of brown coal bearing Tertiary \nsedimentaries \u2013 Deccan Trap interface using microtremor method, <em> Journal of Applied Geophysics<\/em> <strong>159<\/strong>, 362 (2018). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/jap_subsurface_imaging.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>N. Vishnu Priya, M. Senthilvelan, G. Rangarajan and M. Lakshmanan, \nOn symmetry preserving and symmetry broken bright, dark and antidark \nsoliton solutions of nonlocal nonlinear Schrodinger equation, <em> Physics Letters A<\/em> <strong>383<\/strong>, 15 (2019). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pla_solitons.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>X. Lin, P. Kulkarni, F. Bocci, N. Schafer, S. Roy, M-Y. Tsai, Y. He,\n Y. Chen, K. Rajagopalan, S. Mooney, Y. Zeng, K. Weninger, A. Grishaev, \nJ. Onuchic, H. Levine, P. Wolynes, R. Salgia, G. Rangarajan, V. Uversky,\n J. Orban, M. K. Jolly, Structural and Dynamical Order of a Disordered \nProtein: Molecular Insights into Conformational Switching of PAGE4 at \nthe Systems Level, <em> Biomolecules<\/em> <strong>9<\/strong>, 77 (2019). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/biomolecules_IDP_review.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. A. R. S. R. K. Kashyap, D. Bapat, D. Das, R. D. Gowaikar, R. E. \nAmritkar, G. Rangarajan, V. Ravindranath, G. Ambika, Synapse loss and \nprogress of Alzheimer\u2019s disease \u2013 A network model, <em> Scientific Reports<\/em> <strong> 9<\/strong>, 6555 (2019). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/sci_rep_alzheimers.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>N. Vishnu Priya, M. Senthilvelan, and G. Rangarajan, On the role of  four-wave mixing effect in the interactions between nonlinear modes of  coupled generalized nonlinear Schrodinger equation, <em> Chaos<\/em> <strong>29<\/strong>, 123135 (2019). <a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/chaos_solitons.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><br>\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>P. Sukumaran, D. A. Sant, K. Krishnan, G. Rangarajan, N. Basavaiah, and J-L. Schwenninger, Multi-proxy records of late Holocene flood events from the lower reaches of the Narmada River, Western India, <em>Frontiers in Earth Science<\/em> <strong>9<\/strong>, 634354 (2021).<br><a href=\"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2025\/11\/frontiers_earth_sci_multi_proxy_records.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>P. Kulkarni, S. Achuthan, S. Bhattacharya, M. K. Jolly, S. Kotnala, V. B. P. Leite, A. Mohanty, J. Orban, S. Roy, G. Rangarajan and R. Salgia, Protein conformational dynamics and phenotypic switching, <em>Biophysical Reviews<\/em> <strong>13<\/strong>, 1127 (2021).<br><a href=\"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2025\/11\/biophys_rev__protein_conformational_dynamics.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>A. Nam, A. Mohanty, S. Bhattacharya, S. Kotnala, S. Achutan, K. Hari, S. Srivstava, L. Guo, A. Nathan, R. Chatterjee, M. Jain, M. W. Nasser, S. Batra, G. Rangarajan, E. Massarelli, H. Levine, M. K. Jolly, P. Kulkarni and R.Salgia, Dynamic phenotypic switching and group behavior help non-small cell lung cancer cells evade chemotherapy, <em>Biomolecules<\/em> <strong>12<\/strong>, 8 (2021).<br><a href=\"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2025\/11\/biomolecules_phenotypic_switching_cancer.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>P. Kulkarni, S. Bhattacharya, S. Achuthan, A. Behal, M. K. Jolly, S. Kotnala, A. Mohanty, G. Rangarajan, R. Salgia, and V. Uversky, Intrinsically disordered proteins: critical components of the wetware, <em>Chemical Reviews<\/em> <strong>122<\/strong>, 6614 (2022).<br><a href=\"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2025\/11\/chemical_rev_IDP.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>S. K. Mody and G. Rangarajan, Sparse representation of high dimensional neural data, <em>Scientific Reports<\/em> <strong>12<\/strong>, 7295 (2022).<br><a href=\"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2025\/11\/sci_rep_sparse_representations.pdf\" data-type=\"link\" data-id=\"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2025\/11\/sci_rep_sparse_representations.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>N. Vishnu Priya, S. Monisha, M. Senthilvelan and G. Rangarajan, Nth order smooth positon and breather-positon solutions of a generalized nonlinear Schrodinger equation, <em>The European Physical Journal Plus<\/em> <strong>137<\/strong>, 646 (2022).<br><a href=\"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2025\/11\/epjplus_positon.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>P. Kulkarni, V. B. P. Leite, S. Roy, S. Bhattacharyya, A. Mohanty, S. Achuthan, D. Singh, R. Appadurai, G. Rangarajan, K. Weninger, J. Orban. A. Srivastava, M. K. Jolly, J. N. Onuchic, V. N. Uversky and R. Salgia, Intrinsically Disordered Proteins: Ensembles at the Limits of Anfinsen\u2019s Dogma, <em>Biophysics Rev.<\/em> <strong>3<\/strong>, 011306 (2022).<br><a href=\"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2025\/11\/biophysics_rev_IDP.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>T. R. Sharma, G. Rangarajan and P.M. Gade, The interpolation between random walk and self-avoiding walk by avoiding marked sites, <em>J. Stat. Mech.<\/em> 113203 (2022).<br><a href=\"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2025\/11\/jstat_2022_11_113203.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>P. Kulkarni, R. Salgia and G. Rangarajan, Intrinsically disordered proteins and conformational noise: The hypothesis a decade later, <em>iScience<\/em> <strong>26<\/strong>, 107109 (2023).<br><a href=\"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2025\/11\/iscience_idp.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>D. A. Sant, G. K. Makwana, P. Sukumaran, I. Parvez, G. Rangarajan and K. Krishnan, Modeling near-surface velocity inversion in a sediment sequence using microtremor HVSR, <em>Soil Dynamics and Earthquake Engineering<\/em> <strong>190<\/strong>, 109235 (2025).<br><a href=\"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2025\/11\/soil_dynamics_earthquake_engineering_microtremors.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>S. Bhattacharya, A. Mohanty, G. Rangarajan and R. Salgia, Group behaviour and drug resistance in cancer, in Cancer Systems Biology: Translational Mathematical Oncology, 379 (2025). <br><a href=\"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2025\/11\/book_group_behavior_cancer.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>P. D. Bhoyar, G. Rangarajan, P. M. Gade, Emergence of Continuously varying critical exponents in coupled map lattice as an effect of quenched disorder, <em>Chaos, Solitons and Fractals<\/em> <strong>201<\/strong>, 117253 (2025).<br><a href=\"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2025\/11\/chaos_continuously_varying_critical_exponents.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n<\/ul>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-9 kt-pane_322eb9-62\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><div class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\"> In Refereed Conference Proceedings<\/span><\/div><div class=\"kt-blocks-accordion-icon-trigger\"><\/div><\/button><\/div><div class=\"kt-accordion-panel\"><div class=\"kt-accordion-panel-inner\">\n<ul>\n<li>G. Rangarajan and V. S. Ramamurthy, The effect of the neck degree of freedom in sub-barrier fusion, <em>Proceedings of the Nuclear Physics and Solid State Physics Symposium<\/em>, <strong>26B<\/strong>, 19 (1983).<\/li>\n\n\n\n<li>G. Rangarajan and K. C. D. Chan, Transverse resistive wall instability of a bunched electron beam in a wiggler, <em>Proceedings of the 1988 Linear Accelerator Conference<\/em>, 370 (1989).<\/li>\n\n\n\n<li>G. Rangarajan, F. Neri and A. J. Dragt, Generalized emittance invariants, <em>Proceedings of the 1989 IEEE Particle Accelerator Conference<\/em>, 1280 (1989).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pac_1989_emittance.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>A. J. Dragt, F. Neri, J. v. Zeijts and G. Rangarajan, Release of Marylie 3.0, <em>Proceedings of the 1989 IEEE Particle Accelerator Conference<\/em>, 1283 (1989).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pac_1989_marylie.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>W. M. Sharp, G. Rangarajan, A. M. Sessler and J. S. Wurtele, Phase stability of a standing-wave free-electron laser, <em>Proceedings of the SPIE Conference 1407<\/em>, 535 (1991).<\/li>\n\n\n\n<li>G. Rangarajan, A. J. Dragt and F. Neri, Invariant metrics for Hamiltonian systems, <em>Proceedings of the 1991 IEEE Particle Accelerator Conference<\/em>, 1630 (1991).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pac_1991_metric.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>A. J. Dragt, I. M. Gjaja and G. Rangarajan, Kick factorization of symplectic maps, <em>Proceedings of the 1991 IEEE Particle Accelerator Conference<\/em>, 1621 (1991).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/pac_1991_kick.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a>&nbsp;<\/li>\n\n\n\n<li>G. Rangarajan and Minita Sachidanand, Solvable map method for integrating nonlinear Hamiltonian systems, in <em>Lecture Notes in Computer Science (Proceedings of the International Conference on Computational Science)<\/em>, eds. V. N. Alexandrov, J. J. Dongarra and C. J. K. Tan (Springer-Verlag, Berlin, 2001) 894.<\/li>\n\n\n\n<li>G. Rangarajan, Y. Chen and M. Ding, Synchronized chaotic state: Stability and pattern formation, in <em>Proceedings of the National Conference on Nonlinear Systems &amp; Dynamics<\/em>, 93 (2003).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/ncnds_synchronized.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n\n\n\n<li>G. Rangarajan, Long term stability studies of particle storage rings using polynomial maps, in <em> Proceedings of the International Conference on Industrial Mathematics<\/em>, eds. M. C. Joshi, A. K. Pani and S. V. Sabnis, 357 (2006).<br><a href=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/07\/icim_poly.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">\u203a\u203a View PDF<\/a><\/li>\n<\/ul>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-10 kt-pane_bad780-b1\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><div class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">Chapters in Books<\/span><\/div><div class=\"kt-blocks-accordion-icon-trigger\"><\/div><\/button><\/div><div class=\"kt-accordion-panel\"><div class=\"kt-accordion-panel-inner\">\n<ul>\n<li>A. J. Dragt, R. L. Gluckstern, F. Neri and G. Rangarajan, Theory of emittance invariants, <em>Lecture Notes in Physics<\/em> 343, 94 (1989). <\/li>\n\n\n\n<li>G. Rangarajan and A. M. Sessler, Sensitivity studies of a standing-wave free-electron laser, in <em>Advanced Accelerator Concepts<\/em>, ed. J. S. Wurtele (American Institute of Physics, New York, 1993) p.156. <\/li>\n\n\n\n<li>G. Rangarajan, S. Habib, and R. D. Ryne, A new method for computing Lyapunov exponents, in <em> Nonlinear Dynamics and Brain Functioning<\/em>, eds. N. Pradhan, P. E. Rapp and R. Sreenivasan (Nova Science Publishers, New York, 1999).<\/li>\n\n\n\n<li>G. Rangarajan, Fractals in geophysics, in <em> Application of Fractals in Earth Sciences,<\/em> ed. V. P. Dimri (A. A. Balkema Rotterdam, 2000).<\/li>\n\n\n\n<li>G. Rangarajan, Applications of Lie algebraic techniques to nonlinear Hamiltonian systems, in <em>Nonlinear Phenomena<\/em>, eds. S. K. Malik, M. K. Chandrasekhar and N. Pradhan (Indian National Science Academy, New Delhi, 2000) p. 1015.<\/li>\n\n\n\n<li>G. Rangarajan and M. Sachidanand, An invariant norm for nonlinear Hamiltonian systems, in <em>Nonlinear Systems<\/em>, eds. M. Lakshmanan and R. Sahadevan (Narosa Publishers, New Delhi, 2002). <\/li>\n\n\n\n<li>V. S. Borkar, S. Jain and G. Rangarajan, Collective behaviour and \ndiversity in economic communities: Some insights from an evolutionary \ngame, in <em> The Application of Econophysics<\/em>, ed. H. Takayasu (Springer-Verlag, Tokyo, 2003) p. 330.<\/li>\n\n\n\n<li>M. Ding and G. Rangarajan, First passage time problem: A Fokker-Planck approach, in <em>New Directions in Statistical Physics \u2014 Econophysics, Bioinformatics, and Pattern Recognition<\/em>, ed. L. T. Wille (Springer-Verlag, Berlin, 2004) p. 31. <\/li>\n\n\n\n<li>D. A. Sant and G. Rangarajan, Study of Indian climate variability using predictability indices, in <em> Modern Applied Mathematics<\/em>, ed. J. C. Misra (Narosa, New Delhi, 2005) p. 145.<\/li>\n\n\n\n<li>M. Ding and G. Rangarajan, Parametric spectral analysis, in <em> Encyclopedia of Computational Neuroscience: SpringerReference<\/em>, eds. D. Jaeger and R. Jung (Springer-Verlag, Berlin Heidelberg, 2015).<\/li>\n<\/ul>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-11 kt-pane_b60cee-04\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><div class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">Popular Articles<\/span><\/div><div class=\"kt-blocks-accordion-icon-trigger\"><\/div><\/button><\/div><div class=\"kt-accordion-panel\"><div class=\"kt-accordion-panel-inner\">\n<ul>\n<li>G. Rangarajan, A brief introduction to chaotic behaviour in dissipative systems, <em>Mathematics Newsletter<\/em> <strong>4<\/strong>, 43 (1994) (invited contribution).<\/li>\n\n\n\n<li>G. Rangarajan, Kolmogorov-Arnold-Moser Theorem, <em>Resonance (Journal of Science Education)<\/em> <strong>3<\/strong>, no. 4, 43 (1998) (invited contribution). <\/li>\n<\/ul>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-7 kt-pane_1f3f7a-f5\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><div class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">Book Reviews<\/span><\/div><div class=\"kt-blocks-accordion-icon-trigger\"><\/div><\/button><\/div><div class=\"kt-accordion-panel\"><div class=\"kt-accordion-panel-inner\">\n<ul>\n<li>G. Rangarajan, Review of \u201cA Brief Introduction to Numerical Analysis\u201d by E. E. Tyrtyshnikov, <em>Current Science<\/em> <strong>74<\/strong>, 918 (1998).<\/li>\n\n\n\n<li>G. Rangarajan, Review of \u201cFractal Geometry in Architecture and Design\u201d by C. Bovill, <em>Journal of the Indian Institute of Science<\/em> <strong> 78<\/strong>, 158 (1998).<\/li>\n\n\n\n<li>G. Rangarajan, Review of \u201cThe Computational Beauty of Nature\u201d by Gary William Flake, <em>Journal of the Indian Institute of Science<\/em> <strong> 78<\/strong>, 416 (1998).<\/li>\n\n\n\n<li>G. Rangarajan, Review of \u201cFractals in Biology and Medicine (Volume \nII)\u201d by G. A. Losa, D. Merlini, T. F. Nonnenmacher and E. R. Weibel, <em>Current Science<\/em> <strong>76<\/strong>, 1588 (1999).<\/li>\n\n\n\n<li>G. Rangarajan, Review of \u201cMathematics and its History\u201d by J. F. Stillwell, <em>Current Science<\/em> <strong>83<\/strong> 1593 (2002).<\/li>\n\n\n\n<li>G. Rangarajan, Review of \u201cSymmetry in Mechanics\u201d by S. F. Singer, <em> Journal of the Indian Institute of Science<\/em> <strong>81<\/strong>, 611 (2003).<\/li>\n\n\n\n<li>G. Rangarajan, Review of \u201cStatistical analysis of fMRI data\u201d by F. G. Ashby, <em> Current Science<\/em> (in press) (2013).\nMost recent revision December 1, 2019\n<\/li>\n<\/ul>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"https:\/\/scholar.google.co.in\/citations?user=nFZYuaAAAAAJ&amp;hl=en\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"180\" height=\"40\" src=\"http:\/\/math.iisc.ac.in\/~rangaraj\/wp-content\/uploads\/2020\/08\/logo-googlescholar.png\" alt=\"\" class=\"wp-image-204\"\/><\/a><\/figure>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":5,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"kt_blocks_editor_width":"","footnotes":""},"categories":[],"tags":[],"_links":{"self":[{"href":"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-json\/wp\/v2\/pages\/50"}],"collection":[{"href":"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-json\/wp\/v2\/comments?post=50"}],"version-history":[{"count":23,"href":"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-json\/wp\/v2\/pages\/50\/revisions"}],"predecessor-version":[{"id":253,"href":"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-json\/wp\/v2\/pages\/50\/revisions\/253"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-json\/wp\/v2\/media\/5"}],"wp:attachment":[{"href":"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-json\/wp\/v2\/media?parent=50"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-json\/wp\/v2\/categories?post=50"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.iisc.ac.in\/~rangaraj\/wp-json\/wp\/v2\/tags?post=50"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}