# Faculty Information

## Gemunu Gunaratne

Professor and Chairman

**Department of Physics**

**Office:** SR1-629B

**Contact:** gemunu@uh.edu - (713) 743-3534

**Education:** Ph.D., Cornell University

## Spatio-Temporal Dynamics

Research in the group is focused on how to implement modal decomposition on experimental data and how symmetries and other general characteristics of the modes can be used to gain theoretical understanding of turbulent flame flows.

## Genetic Networks

By now it is apparent that biological processes are affected by large collections of genes/proteins/metabolites. In general, neither the full membership of the gene network associated with a biological process nor the precise form of interactions between nodes is known. What is available, through microarrays or sequencing, are gene expression profiles of an organism or its viable mutants. Our group is developing a methodology whereby expression profiles of a selected group of mutants can be used to make predictions on how the network can be moved to a pre-specified state. We are collaborating with experimentalists to determine how Drosophila can be genetically altered to a sleep-deprived like state.

## Quantitative Finance

Physicists are motivated to study financial markets in the expectation that stochastic analysis developed in the context of statistical mechanics and nonlinear physics may find applications there. The relevant issues are the characteristics of the stochastic processes underlying financial markets. Recent analyses of financial markets have shown that the process is highly complex and that the intensity of fluctuations depends on the time of day and on variations in price during the day. Our research involves modeling and stochastic analyses of such processes.

## Models of Animal Behavior:

Behavior of animals introduced into a novel arena is highly complex and includes a preference for boundaries and decay in activity as the novelty of the area is abrogated. We quantify the behavior by analyzing a large number of trajectories of Drosophila introduced into both (geometrically) simple and complex arenas. The results are used to gain a quantitative understanding of exploration.

## Book Reviews

J. A. Glazier and G. H. Gunaratne, Book Review for James Gleick, Chaos: Making a New Science, Viking Press, New York, 1987. Physics Today, February 1988.

## Patents

- Methods For Performing DAF Data Filtering And Padding (2005).
- Fabrication of Self-Assembling Nano-Structures (Pending).
- New Methods for Gene Expression Pro%uFB01ling (provisional Patent).

- S. Roy, J.-C. Hua, W. Barnhill, G. H. Gunaratne, and J. R. Gord, Deconvolution of reacting flow dynamics using proper orthogonal and dynamic mode decompositions, Phys. Rev. E., 91, 013001 (2015).
- J. Shulman, F. Malatino, M. Widjaja, and G. H. Gunaratne, Experimental Deter- mination of Circuit Equations, American Journal of Physics, 83 64 (2015).
- J.-C. Hua, L. Chen, L. Falcon, J. L. McCauley, and G. H. Gunaratne, Variable Diffusion in Stock Market Fluctuations, Physica A 419, 221-233 (2015).
- B. Soibam, L. Chen, G. W. Roman, and G. H. Gunaratne, Exploratory Activity and Habituation of Drosophila in Confined Domain, European Journal of Physics 223, 1787-1803 (2014).
- J. Shulman, F. Malatino, A. Mo, K. Ryan, and G. H. Gunaratne, Controlling Net- works of Nonlinearly-Coupled Nodes using Response Surfaces, Scientific Reports 4, 7574 (2014).
- B. Soibam, S. Shah, G. H. Gunaratne, and G. W. Roman, Modeling novelty ha- bituation during exploratory activity in Drosophila, Behavioral Processes, 97, 63-75 (2013).
- J.-C. Hua, G. H. Gunaratne, S. Kostka, N. Jiang, B. V. Kiel, J. R. Gord, and S. Roy, Dynamical-systems analysis and unstable periodic orbits in reacting flows behind symmetric bluff bodies, Phys. Rev. E, 88, 033011 (2013).
- S. Narayan, G. H. Gunaratne, and F. Hussain, Dynamical systems approach to the control of chaotic dynamics in a spatiotemporal jet flow, Chaos, 23, 033133 (2013).
- B. Soibam, R. L. Goldfeder, C. Manson-Bishop, R. Gramblin, S. Pletcher, S. Shah, G. H. Gunaratne, G. Roman, Modeling Drosophila Positional Preferences in Open Field Arenas with Directional Persistence and Wall Attraction, PLoS one 7, e476570 (2012).
- L. Seemann, J. Shulman, and G. H. Gunaratne, A Robust Topology-Based Algorithm for Gene Expression Profiling, ISNR Bioinformatics, 2012, 381023 (2012).
- L. Seemann, J.-C. Hua, J. L. McCauley, G. H. Gunaratne, Ensemble vs. Time Averages in Financial Time-Series Analysis, Physics A 391, 6024-32 (2012).
- B. Soibam, M. Mann, L. Liu, J.Tran, M. Lobaina, Y. Y. Kang, G. H. Gunaratne, S. Pletcher, and G. Roman, Open-field arena boundary is a primary object of explo- ration for Drosophila, Brain and Behavior, 1-12 (2012).
- J. Shulman, L. Seemann, G. Roman, and G. H. Gunaratne, Effective Models for Gene Networks and their Applications, Biophysical Reviews and Letters 7, 41-70 (2012).
- J. D. Kelly, A. Palacios, J. Shulman, and G. H. Gunaratne, Modal Decomposition and Normal Form for Hydrodynamic Flows: Examples from Cellular Flame Patterns, European Physical Journal-Special Topics, 204, 119-131 (2012).
- J. Shulman, L. Seemann, and G. H. Gunaratne, Effective Models of Periodically Driven Networks, Biophysical Journal, 101, 2563-2571 (2011).
- L. Seeman, J. L. McCauley, and G. H. Gunaratne, Intraday Volatility and Scaling in High Frequency Foreign Exchange Markets, Int. Rev. Fin. Anal., 2011.
- F. Shi, A. Bhalla, C. L. Chen, G. H. Gunaratne, J. Jiang, and E. I. Meletis, Atomistically- Informed Continuum Model of Hydrogen Storage on Graphene, Interface, Spring (2011) 57-61.
- G. H. Gunaratne, P. H. Gunaratne, L. Seeman, and A. Torok, Using Effective Subnet- works to Predict Selected Properties of Gene Networks, PLoS one, 5 e13080 (2010).
- H. Zhu, P. H. Gunaratne, G. W. Roman, and G. H. Gunaratne, A theory for the arrangement of sensory organs in Drosophila, Chaos 20, 013132 (2010).
- F. Shi, P. Sharma, and G. H. Gunaratne, Creating perfectly ordered quantum-dot arrays via self-assembly, Chaos 19, 033141 (2009).
- G. H. Gunaratne, M. Nicol, L. Seeman, and A. Torok, Clustering of Volatility in Variable Diffusion Processes, Physica A 388, 4424-4430 (2009).
- J. S. E. Ortiz and G. H. Gunaratne, Critical indices of random planar electrical networks, brazilian Journal of Physics 39, 306-311(2009).
- G. H. Gunaratne, M. Nicol. L. Seeman, and A. Torok, Clustering of volatility in variable diffusion processes, Physics A 338, 4424-4430 (2009).
- J. L. McCauley, K. E. Bassler, and G. H. Gunaratne,Is integration I(d) applicable to observed economics and finance time series? Int. Rev. Fin. Anal. 18, 101-108 (2009).
- S. L. Chen, W. Liu, D. Zhang, and G. H. Gunaratne, Magnetic Properties and Magnetic Domains of Nd-Fe-B Thin Films, J. Appl. Phys., 103, 023922 (2008).
- J. L. MacCauley, G. H. Gunaratne, K. E. Bassler, The Unusual Fluctuations of Finance Markets, in Anomalous Fluctuation Phenomena in Complex Systems: Plas- mas, Fluids and Financial Markets, eds. C. Riccardi and E Eduardo Roman, pp.245- 260 (2008).
- J. G. Reid, A. K. Nagaraja, F. C. Lynn, R. B. Drabek, D. M. Munzy, C. A. Shaw, M. K. Weiss, A. O. Naghavi, M. Khan, H. F. Zhu, J. Tennekoon, G. H. Gunaratne, D. B. Corrt, J. Miller, M. T. McManus, M. S. German, R. A. Gibbs, M. M. Matzuk, and P. H. Gunaratne, Mouse let-7 miRNA populations exhibit RNA editing that is constrained in the 5-seed/cleavage/anchor regions and stabilize predicted mmu-let-7a: mRNA duplexes, Genome Research 18, 1571-1581 (2008).
- F. Shi, P. Sharma, D. J. Kouri, F. Hussain, and G. H. Gunaratne, Nanostructures with Long-Range Order in Monolayer Self-Assembly, Phys. Rev. E 78, 025203 (2008) (Rapid Communication).
- K. E. Bassler, G. H. Gunaratne, and J. L. McCauley, Empirically Based Modeling in Finance and Physics and Spurious Stylized Facts, International Review of Financial Analysis 17, 767-783 (2008).
- K. E. Bassler, G. H. Gunaratne, and J. L. McCauley, The Dynamics of Real Financial Markets: A Reply to Franks Comment, Physics A, 387, 3239-3241 (2008).
- J. L. McCauley, K. E. Bassler, and G. H. Gunaratne, Martingales, Nonstationary Increments and the Efficient Market Hypothesis, Physica A, 387, 3916-3920 (2008).
- J. L. McCauley, K. E. Bassler, and G. H. Gunaratne, Martingales, Detrending Data and the Efficient Market Hypothesis, Physica A, 387, 202-216 (2008).
- K. E. Bassler, J. L. McCauley, and G. H. Gunaratne, Nonstationary Increments, Scaling Distributions, and Variable Diffusion Processes in Financial Markets, PNAS 104, 17287-17290 (2007).
- S. Hu. G. Nathan, F. Hussain, D. J. Kouri, P. Sharma, and G. H. Gunaratne, On Stability of Self-Assembled Nanoscale Patterns, Journal of Mechanics and Physics of Solids 55, 1357-1384 (2007).
- J. L. McCauley, G. H. Gunaratne, and K. E. Bassler, Martingale Option Pricing, Physica A, 380, 351-356 (2007).
- J. L. McCauley, G. H. Gunaratne, and K. E. Bassler, Hurst Exponents, Markov Processes, and Fractional Brownian Motion, Physica A, 379, 1-9 (2007).
- Y. Song and G. H. Gunaratne, A Method for Vibrational Assessment of Solid Bone, Chaos 16, 033102 (2006).
- J. L. McCauley, G. H. Gunaratne, and K. E. Bassler, What Economists Should Learn from Econophysics, in Dynamics of Complex Interconnected Systems: Networks and Bioprocesses, Eds. A. T. Skjeltorp and A. Belyushkin, Springer (2006), pp 191-202.
- K. E. Bassler, G. H. Gunaratne, and J. L. McCauley, Markov Processes, Hurst Ex- ponents, and Nonlinear Diffusion Equations: With Applications to Finance, Physica A 369, 343-353 (2006).
- A. A. Alehandro-Quinones, K. E. Bassler, M. Field, J. L. McCauley, M. Nicol, I. Timofeyev, A. Torok, and G. H. Gunaratne, A Theory of Fluctuations in Stock Prices, Physica A, 363, 383-392 (2006).
- G. H. Gunaratne, J. L. McCauley, M. Nicol, and A. T or ok. Variable Step Random Walks and Self-Similar Distributions, J. Stat. Phys., 121, 887-899 (2005).
- M. A. K. Liebschner, R. Mu ller, C. S. Rajapakse, S. J. Wimalawansa, and G. H. Gunaratne. Testing Two Predictions for Fracture Load Using Computer Models of Trabecular Bone, Biophysical Journal, 89, 759-767 (2005).
- A. A. Alehandro-Quinones, K. E. Bassler, J. L. McCauley, and G. H. Gunaratne, A Theory of Fluctuations in Stock Prices: Effects of Discreteness, Proceedings of the SPIE, 5848, 27 (2005).
- G. H. Gunaratne and J. L. McCauley. Theory of Fluctuations in Stock Prices and Valuation of their Options, Proceedings of the SPIE, 5848, 131 (2005).
- G. Nathan and G. H. Gunaratne. New Set of Measures to Analyze Dynamics of Non-Equilibrium Structures, Phys. Rev. E, 71, 035101 (Rapid Communications) (2005).
- Y. Song, M. A. K. Liebschner, and G. H. Gunaratne, A Study of Age-Related Ar- chitectural Changes that are Most Damaging to Bones, Biophysical Journal, 87, 3642-47 (2004).
- G. Nathan and G. H. Gunaratne. Characterizations of Far From Equilibrium Struc- tures Using Their Contours, in Dynamics and Bifurcation of Patterns in Dissipative Systems, G. Dangelmayr and I. Opera (eds.), World Scientific Series on Nonlinear Science, Vol. 12, World Scientific, Singapore, 2004.
- C. S. Rajapaksa, J. S. Thomsen, J. S. Espinoza-Ortiz, S. J. Wimalawansa, E. N. Ebbesen, L. Mosekilde, and G. H. Gunaratne, An Expression Relating Breaking Stress and Density of Trabecular Bone, J. Biomechanics, 37, 1241-1249 (2004).
- S. Hu, D. I. Goldman, D. J. Kouri, D. K. Hoffman, H. L. Swinney, and G. H. Gu- naratne, Stages of Relaxation of Patterns and the Role of Stochasticity on the Final Stage, Nonlinearity, 17 (4), 1535-1546 (2004).
- C. Zhang, H. Zhang, Q.. Ouyang, B. Hu, and G. H. Gunaratne, Transition from Spi- ral Waves to Defect-Medated Turbulence induced by Gradient Effects in a Reaction- Diffusion System, Phys. Rev. E, 68, 036202 (2003).
- J. L. McCauley and G. H. Gunaratne, An Empirical Model of Volatility Returns and Option Pricing, Physica A, 329, 178-198 (2003).
- J. L. McCauley and G. H. Gunaratne, On CAPM and Black-Scholes Differing Risk- Return Strategies, Physica A, 329, 170-177 (2003).
- J. S. Espinoza Ortiz and G. H. Gunaratne, Current Distributions in Fused Electrical Networks, Brazilian Journal of Physics, 33, 368-375 (2003).
- J. S. Espinoza Ortiz, C. S. Rajapakse, and G. H. Gunaratne, Strength reduction in Electrical and Elastic networks, Phys. Rev. B, 66, 144203 (2002).
- G. H. Gunaratne, Estimating the Strength of Bone Using Linear Response, Phys. Rev. E, 67, 061904 (2002).
- G. H. Gunaratne, K. K. Mohanty, and S. W. Wimwlawansa. A Model of Trabecular Bone and an Application to Osteoporosis, Physica A, 315, 98-104 (2002).
- D. I. Goldman, M. Shattuck, H. L. Swinney, and G. H. Gunaratne. Characterization of the Emergence of Order in an Oscillated Granular Layer, Physica A 306 180-188 (2002).
- G. H. Gunaratne, C. S. Rajapaksa, K. E. Bassler, K. K. Mohanty, and S. J. Wimalawansa. A Model for Bone Strength and Osteoporotic Fracture, Phys. Rev. Lett., 88, 068101 (2002).
- D. K. Hoffman, G. H. Gunaratne, D. S. Zhang, and D. J. Kouri. A Method to Fourier Filter Textured Images, Chaos, 10, 240-247 (2000).
- Z. Shi, H. Wang, D. J. Kouri, G. H. Gunaratne, J. U. Quevedi, I. Kakadiaris, and D. K. Hoffmann. A Perceptual Mammogram Solution Using a Class of Smooth Wavelets, IEEE First Joint Meeting of BMES and EMBS, 982, 1160 (1999).
- D. S. Zhang, G. W. Wei, D. J. Kouri, D. K. Hoffman, M. E. Gorman, A. Palacios, and G. H. Gunaratne. Integrating the Kuramoto-Sivashinsky Equation in Polar Coordinates: Application of the Distributed Approximating Functional Approach, Phys. Rev. E, 60, 3353-3360 (1999).
- A. Palacios, M. E. Gorman, and G. H. Gunaratne. Modal Decomposition of Hopping States in Cellular Flames, Chaos, 9, 755-767 (1999).
- D. S. Zhang, D. J. Kouri, D. K. Hoffman, and G. H. Gunaratne. Distributed Approx- imating Functional Treatment of Noisy Signals, Computer Physics Communications, 120, 1-12 (1999).
- G. H. Gunaratne, A. Ratnaweera, and K. Tennekone. Emergence of Order in Tex- tured Patterns, Phys. Rev. E, 59, 5058-5064 (1999).
- G. H. Gunaratne. A Quantitative Description of the Relaxation of Patterns, in Pattern Formation in Continuous and Coupled Systems, eds. M. Golubitsky, D. Luss, and S. Strogatz, pp 111-120 (1999).
- R. E. Jones and G. H. Gunaratne. Characterization of Labyrinthine Patterns and their Evolution, J. Stat. Phys., 93, 427 (1998).
- G. H. Gunaratne, D. K. Hoffman, and D. J. Kouri. Characterizations of Natural Patterns, Phys. Rev. E, 57, 5146-5149 (1998).
- A. Palacios, G. H. Gunaratne, M. E. Gorman, and K. Robbins. A Karhunen-L eove Analysis of Flame Patterns, Phys. Rev. E, 57, 5958-5971 (1998).
- A. Palacios, G. H. Gunaratne, M. Gorman, and K. A. Robbins. Cellular Pattern Formation in Circular Domain, CHAOS, 7, 463-475 (1997).
- G. H. Gunaratne, M. el-Hamdi, M. Gorman, and K. A. Robbins. Asymmetric cells and rotating rings in cellular flames, Mod. Phys. Lett. B, 10, 1379-1387 (1996).
- G. H. Gunaratne, R. E. Jones, Q. Ouyang, and H. L. Swinney. An invariant measure of disorder in patterns, Phys. Rev. Lett., 75, 3281 (1995).
- G. H. Gunaratne. A Theory of Patterns, Chaos, Solitons and Fractals, 5, 1447 (1995).
- G. H. Gunaratne, Q. Ouyang, and H. L. Swinney. Pattern Formation in the Presence of Symmetries, Phys. Rev. E, 50, 2802 (1994).
- J. H. Miller, G. H. Gunaratne, Z. Zou, M. F. Davis, H. R. Rampersad, and J. C. Wolfe. Self-organized Phase Coherence in Hysteretic Magnetic Behavior of Parallel Josephson Junction Arrays, Phys. Rev. B, 49, 15317 (1994).
- G. H. Gunaratne. Reply to a Comment on Complex Spatial Patterns on Planar Continua. Phys. Rev. Lett., 72, 945 (1994).
- Q. Ouyang, G. H. Gunaratne, and H. Swinney. Rhombic Patterns: Broken Hexago- nal Symmetry, Chaos, 3, 707 (1993).
- G. H. Gunaratne. Complex Spatial Patterns on Planar Continua, Phys. Rev. Lett., 71, 1367 (1993).
- J. H. Miller, G. H. Gunaratne, and Z. Zou. Detection of Magnetic Flux with Super- conducting Quantum Interference Gratings, IEEE Trans. on Applied Superconduc- tivity, 3, 1804 (1993).
- J. Huang, J. H. Miller, T. D. Golding, and G. H. Gunaratne. Enhanced Quan- tum Interference Effects in Normal and Superconducting Arrays, Superlattices and Microstructures, 11, 159 (1992).
- J. H. Miller, G. H. Gunaratne, Z. Zou, J. Huang and T. D. Golding. Applications of Parallel Josephson Junction Arrays for the Detection of Magnetic Flux, Materials Research Symposium, vol. 275, p. 759, 1992.
- R. E. Goldstein, G. H. Gunaratne, L. Gil, and P. Coullet. Hydrodynamic and Inter- facial Patterns with Broken Spacetime Symmetry, Phys. Rev. A, 43, 6700 (1991).
- J. H. Miller, G. H. Gunaratne, J. Huang, and T. D. Golding. Enhanced Quantum Interference Effects in Parallel Josephson Junction Arrays, App. Phys. Lett., 59, 3330 (1991).
- P. Cvitanovi c, G. H. Gunaratne, and M. J. Vinson. On the Global Universality in Critical Circle Maps, Nonlinearity, 3, 873 (1990).
- G. H. Gunaratne. Universality Beyond the Onset of Chaos, Chaos: Soviet-American Perspectives on Nonlinear Science, ed. D. K. Campbell, American Institute of Physics, New York (1990), pp 37-70.
- G. H. Gunaratne. Characterization of Strange Attractors, New Directions in Chaos, Vol.3, ed. Hao Bai-lin, World Scientific Publishing Co. Pte. Ltd. (1990), pp 213-226.
- R. E. Goldstein, G. H. Gunaratne, and L. Gil. Defects and Traveling-Wave States in Hydrodynamic Systems, Phys. Rev. A, 41, 5731 (1990).
- M. C. Vieira and G. H. Gunaratne. Universality in Chaotic Differentiable Flows, Phys. Rev. A, 41, 1823 (1990).
- M. C. Vieira and G. H. Gunaratne. Trajectory Scaling Function for Period Doubling in Differentiable Flows, J. Stat. Phys., 58, 1245 (1990).
- P. Coullet, R. E. Goldstein, and G. H. Gunaratne. Parity-breaking Transitions in Modulated Hydrodynamic Structures, Phys. Rev. Lett., 63, 1954 (1989).
- G. H. Gunaratne, P. S. Linsay, and M. J. Vinson. Chaos Beyond Onset: A Compar- ison of Experiment and Theory, Phys. Rev. Lett., 63, 1 (1989).
- B. Castaing, G. H. Gunaratne, F. Heslot, A. Libchaber, L. P. Kadanoff, S. Thomae, X. Wu, S. Zaleski, and G. Zanetti. Scaling Theory for Hard Thermal Turbulence in Rayleigh-B enard convection, J. Fluid. Mech, 204, 1 (1989).
- A. Belmonte, M. J. Vinson, J. Glazier, G. H. Gunaratne, and B. Kenny. Trajectory Scaling Functions at the Onset of Chaos: Experimental Results, Phys. Rev. Lett., 61, 539 (1988).
- P. Cvitanovi c, G. H. Gunaratne, and I. Procaccia. Topological and Metric Properties of H enon Type Strange Attractors, Phys. Rev. A, 38, 1503 (1988).
- G. H. Gunaratne, M. H. Jensen, and I. Procaccia. Universal Strange Attractors on Wrinkled Tori, Nonlinearity, 1, 157 (1988).
- J. Glazier, G. H. Gunaratne, and A. Libchaber. f() Curves: Experimental Results, Phys. Rev. A, 37, 523 (1988).
- G. H. Gunaratne and I. Procaccia. Organization of Chaos, Phys. Rev. Lett., 59, 1377 (1987).
- M. J. Vinson and G. H. Gunaratne. Trajectory Scaling Function for Symplectic Maps in Four Dimensions, Phys. Rev. A, 36, 2418 (1987).
- G. H. Gunaratne. Trajectory Scaling Function for Period Tripling in Near Conformal Maps, Phys. Rev. A, 36, 1834 (1987).
- D. Auerbach, P. Cvitanovi c, J. P. Eckmann, G. H. Gunaratne, and I. Procaccia. Exploring Chaotic Motion Through Periodic Orbits, Phys. Rev. Lett., 58, 2387 (1987).
- T. Bohr and G. H. Gunaratne. Scaling in Super-critical Circle Maps: Numerical Investigation of the Onset of Bistability, Phys. Lett. A, 113, 55 (1985).
- G. H. Gunaratne and M. J. Feigenbaum. Trajectory Scaling Function for Bifurcations in Area Preserving Maps, Physica D, 17, 295 (1985).