Professor Erik M Bollt
I am the W. Jon Harrington Professor of Mathematics at Clarkson
Director of C3S2, the Clarkson Center for Complex Systems Science
General Description of My Interests:
My office is: CAMP 322.
Addresses: Electrical and Computer Engineering ECE Department, Potsdam, NY 13699-5815
VOICE: (315)-268-2307, FAX: (315)-268-2395
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Endowed W. Jon Harrington Professor of Mathematics, Clarkson University, Potsdam, NY. Awarded 2010- . (Associate Professor 2002-2006, Professor 2006-present)
and dual appointment to Electrical and Computer Engineering ECE Department, and adjunct appointment to Physics Department.
Ph.D. Applied Mathematics, University of Colorado at Boulder , Boulder, CO, May 1995.
Dissertation: Controlling Chaos, Targeting, and Transport
PhD Advisor: Professor James D. Meiss.
M.S. Applied Mathematics, University of Colorado at Boulder, Boulder, CO, 1992.
B.A. Applied Mathematics, University of California at Berkeley, Berkeley, CA, 1990.
Grants and Funding
Army Research Office: PI, W911NF2310393, Mechanical Sciences, Complex Dynamics and Systems: Reduced Models, Control and Fragility in Complex Systems by An Informatics Perspective, $479K, 2023-2026.
Army Research Office: PI, STTR, W911NF2310395, Analysis and Observables of Scale Coherence, Onset of Mixing, Transport and Turbulence, $60K, 2023-2024.
NSF-NIH CRCNS: (with Wake Forest U. Med. School), 'Functional Brain Networks with Tensioned Stability for Optimal Processing,' $1.29M, Clarkson, $601k, 2021-2025.
Office of Naval Research: PI, 'Transformations for Geometric Analysis Reveal the Simplicity of Complex Dynamical Systems,' $192K, 2022-2025.
DARPA: PI, with Jeremie Fish and Mahesh Banavar as co-PI, subcontract through Raytheon BBN 'RSDN,' $420K, 2023-2027.
Army Research Office: N68164-EG, PI, 'Criticality and Information Fragility in Complex Systems,' $879K, 2016-2023.
Air Force Research Office: Clarkson, PI, STTR subcontract from ResCon, $50k, 2022-2023.
DARPA: PI, with Mahesh Banavar as co-PI, subcontract through Raytheon BBN 'LogX,' $233K, 2020-2022.
Army Research Office: Clarkson, PI, SBIR subcontract with OMBRA, BioBML, $42K, 2021-2022.
DARPA: PI, with Jie Sun and Daqing Hou as co-PI, subcontract through Raytheon BBN 'CauseEx,' $656K, 2017-2021.
Army Research Office: N68164-EG, PI 'Foundations of Probability for Data Analytics of Decision Making in Complex Systems,' $25K, 2018-2019.
Office of Naval Research: PI, N00014-15-1-2093 'Coherence, Transport, and Inference in Turbulent Dynamical Systems,' $271k, 2015-2018.
Army Research Office: W911NF-12-1- 0276, PI, with Jie Sun as co-PI 'On Hierarchical Scales, Information Reduction Efficiency and Inference in Complex Systems,' $478K, 2012-2016.
National Geospatial Intelligence Agency - NGA: PI, (Jie Sun and Nicholas Tufillaro as coPIs), ' Remote Multi-Attribute Spatiotemporal Dynamical Systems Analysis,' $384k, 2013-2016.
Office of Naval Research: PI, with Joe Skufca as co-PI, 'Reduced-Order Representations for Design A Manifold Learning Approach to Reduced-Order Basis', $320K, 2011-2016.
Office of Naval Research: with William Jemison as PI, 'Lidar Systems', $280K, 2014-2016.
Army Research Office: PI, with Jie Sun as co-PI ' Workshop: Information in Dynamical Systems and Complex Systems July 18-19, 2013,' $25K, 2013.
Office of Naval Research: PI, 'Transport Analysis and Ecological Modeling of Remotely Observed Hyperspectral Oceanographic Spatiotemporal Systems,' $130K, 2012-2014.
National Science Foundation : CMMI 1129859, PI, coupled to parallel grant with Maurizio Porfiri at Polytechnic Institute of New York University, 'DynSyst_Special_Topics: Collaborative Research: Geometry of group behaviors with application to fish schooling', Clarkson Share: $143K, 2011-2013.
Office of Naval Research: PI, with Aaron Luttman and Takashi Nishikawa as co-PIs, #GRANT00539561, 'A Variational Approach to Data Mining from Hyperspectral Image Sequences and Transport Analysis with Model Filtering of Spatiotemporal Dynamical Systems', $324K, 2009-2012.
National Science Foundation: PI, with Joe Skufca as co-PI, Applied Mathematics Division, DMS-0708083, 'Almost Conjugacy.' $380K, 2007-2010.
AFSOR : (Co-PI with several others), Goodarz Ahmadi is PI, ; Advancement of Intelligent Aerospace Systems, Joint with Syracuse, U, $876K to Clarkson U, 2009-2010.
Metropolitan Development Foundation : with Vento Tek and ARI, co-PI, with P. Marzocca (PI), G. Ahmadi, R. Jha, "Fabrication and Marketing of Smart Wind Turbine Blade," $50k, 2008.
Syracuse Center of Excellence in Environmental and Energy Systems - COE - CAP IV : co-PI, (PI is Pier Marzocca) 'Development and Commercialization of Novel Wind Turbines.' $117,312, 2007-2008.
National Science Foundation: PI, Applied Mathematics Division, DMS-0404778-extension, A Transfer Operator Approach to Modeling Deterministic and Stochastic Transport, with Applications in the Physical Sciences. $22,698, 2007-2008.
National Institutes of Health : co-PI, (PI is C. Robinson), R01 AG026553-01A2, 'Phase-Locked Postural Pertubation Psychophysical Models.' $1,590,000, 2007-2010.
Army Research Office : PI, Mathematical Science Division, 51950-MA, "Modeling Spatiotemporal Systems on Arbitrary Networks by Uncovering Spatial Scales and Component Interactions: Uncovering Hierarchical Scale Interactions for Problems of Mathematical Epidemiology," $258,608, 2007-2010
National Science Foundation: PI, Applied Mathematics Division, DMS-0404778, 'A Transfer Operator Approach to Modeling Deterministic and Stochastic Transport, with Applications in the Physical Sciences.' $147K, 2004-2008.
Grants for Growth (GRG), New York State : co-PI, (PI is P. Marzocca), 'Fabrication and Marketing of Smart Wind Turbine.' $50K, 2006-2007.
Los Alamos National Laboratory, DOE: PI, (co-Pi is Peter Schultz), 'Advanced Methods for Analysis of Image Like Data.' $475K, 2003-2006.
Naval Research Laboratory BAA : PI, 'Experimental Network Modeling in Local Area Network Data.' $25K, 2003-2004.
United States Army Research Office, ARO, STAS, Research in Symbolic Dynamics, $30K 2005-2006.
United States Army Research Office, ARO, STAS, Research in Symbolic Dynamics, $30K 2005-2006.
Naval Research Laboratory BAA : PI, 'Virus Spread on Complex Network Topologies-Detection, Analysis and Control.' $40K, 2002-2003.
Naval Research Laboratory/Office of Naval Research : PI, 'Information Flow Dynamics.' Contract Grant No. N0001401wx20362, $25,000, (Contractor) grant period May 15, 2001 through May 14, 2002.
Efecta Technologies, Steamboat Springs, CO, Consulting in Dynamical Systems Methods for Image Compression Algorithms, $30K, 2001.
National Science Foundation, (PI) Applied Mathematics Division, DMS-0071314, RUI: Combinatorial Control of Chaos, Symbolic Dynamics, Optimal Control and Inverse Frobenius-Perron Problem; $68,925, grant period Sept, 1, 2000 through Aug 31, 2003.
National Science Foundation, (PI) Applied Mathematics Division, DMS-9704639, Applications and Theory of Controlling Symbol Dynamics: Communicating with Chaos; $49,230, grant period Sept, 15, 1997 through Aug 31, 2000.
USNA, "Chaos and Complexity Center"
and "Chaos Lab" internal grant, Faculty Development Award, (PI), $10K,
Army Research Laboratory, Information Sciences Directorate, Davies Fellowship, summers of 1996 and 1997.
Honors, Awards, And Fellowships
Regents' Scholar for undergraduate studies at U.C. Berkeley, 1985-1990.
National Science Foundation Graduate Traineeship, 1993-1995.
Project Next Fellow, AMS-MAA, 1996-1997.
Davies Research and Teaching Fellow, 1995-1998.
Member of Pi Mu Epsilon
Young Author (<35) runner-up, presented by the Russian Academy of Sciences at the IEEE Circuits and Systems Society First International Conference on Controlling Chaotic Oscillations, St. Petersburg, Russia, August, 1997.
Department of Defense, Superior Civilian Service Medal, 1997.
US Naval Academy APGAR Teaching Award Nominee, 2000.
1. Visiting Scientist, Los Alamos National Laboratories, Computational Science Methods Group (X-8), 2001-continuing.
2. Associate Member, Centre Chaos Control & Syncronization, Department of Electrical Engineering, City University of Hong Kong. 2002-continuing.
Anil Kumar, 2022 - Present, NIH-CRCNS, Dynamics in Functional Brain Networks.
Neranjaka Jayarathna, 2022 - Present, ONR, Transformations for Geometric Analysis Reveal Simplicity of Complex Dynamical Systems.
Jeremie Fish, 2017 - present, DARPA-CauseEx, DARPA-LogX.
A. AlMomani, 2019-2021, ARO, inverse problems and entropic system identification.
Ranil Basnayake, 2013 - 2017, Remote Multieln-Attribute Spatiotemporal Dynamical Systems Analysis.
Carlo Cafaro, 2013 - 2015, Information aspects of networks and dynamical systems.
Rana Parshad, 2009-2011, Mostly Conjugacy, and Modelling.
Fernando J. Quevedo, PhD Student, Clarkson University , 2016-.
Former Graduate Students:
Sudam Surasinghe, PhD student, Clarkson University, 2016-2022. post doc, Yale University. webpage PhD Thesis
Tyler Diggins, PhD student, Clarkson University, 2018-2022, Hierarchy, Graph Conductance, and the Essential Synchronization Backbone. senior scientist, Air Force Research Labs.
Alex DeWitt, PhD student, Clarkson University, 2017-2020. MS.
A. AlMomani, PhD student, Clarkson University, 2015-2019, Prediction Analysis and System Identification of Complex Systems. PhD Thesis, Assistant Profesor, Embry Riddle University. webpage
Amila N. Sudu Ambegedara, PhD student, Clarkson University, 2015-2019, Methods of Identification of Structural Damage. PhD Thesis Faculty, University of Peradeniya, Sri Lanka.
Kanaththa G. Priyankara, PhD student, Clarkson University, 2015-2019. Assistant Professor, University of Alabama.
Warren Lord, PhD student, Clarkson University, 2014-2018, Inference of networks of causal relationships using Causation Entropy. PhD Thesis post doc, Dartmouth College.
Kelum Hewa Gajamannage, PhD student, Clarkson University, 2011-2016, Manifold Learning and Cooperative Group Behavior. PhD Thesis Texas A&M Corpus Christi.
Ranil Basnayake, PhD student, Clarkson University, 2009-2014, Inverse Problems for Image Processing of Spatiotemporal Dynamical Systems. PhD Thesis
Matt Fowler, MS student, Clarkson University, 2013-2015. Brasher Falls Mathematics High School Teacher
Tian Ma, PhD student, Clarkson University, 2010-2015, Transfer Operator Methods for Transport Study Informed by Remote Sensing and Spatiotemporal Satellite Imagry.
Ling Chen, MS student, Clarkson University, 2012-214, Compressive Sensing and Observables.
Sean Kramer, PhD student, Clarkson University, 2009-2013, Ecological Oceanographic as Informed by Spatiotemporal Satellite Imagry. Faculty at Norwich University. PhD Thesis
Jiongxuan Zheng (Chris), PhD student, Clarkson University, 2008-2013, Analysis of Mostly Conjugacy and Defect Measure. Decision technology analyst at Jp Morgan Chase PhD Thesis
Bruce Alstrom, PhD student, Mechanical Engineering, Clarkson U, 2008 - 2013, Aeroelastic Control.PhD Thesis University of Western Ontario
Kevin Matthews, Masters student, Clarkson University, 2010 , GE Fellowship Program, Smart Grid
Jie Sun (Rio), PhD student, Clarkson University, 2006-2009, Networked Networks: Uncovering Hierarchical Scales of Spatial-Temporal Dynamics, PhD Thesis Faculty at Clarkson University
Scott LaLonde, MS student, Clarkson University, 2008-2009, Modelling and Defect Measure. Masters Thesis,
Naratip Santitissadeekorn, Transport Analysis and Motion Estimation of Dynamical Systems of Time-Series Data, PhD student, Clarkson University, 2004-2008. PhD Thesis, Faculty at University of Surrey.
Jim Bagrow, PhD student, Clarkson University, Analysis and Applications of Complex Networks, co-direct with Dani ben-Avraham, 2004-2008. PhD Thesis, Faculty at University of Vermont.
Chen Yao, PhD student, Clarkson University, 2002-2007, Model reduction techniques. PhD Thesis, went to Fleet Financial Group, NYC. Operation Research Analyst.
Undergraduate Trident, Honors, and Projects Students:
Benjamin Walleshauser, Research Project Reservoir Computing, Clarkson University, 2021-continuing.
Adam Allanad, Honors Thesis, Clarkson University 2003-2005. Went to U. Chicago grad school.
Michael, Allard, Clarkson University. 2003.
KadianStephenson, McNair Scholar, Clarkson University, Summer 2003, Realtime video experimental time-series capturing.
Noah Reddell, USNA, Trident Scholar, "Development of Digital Signal Processor (DSP) Based Chaotic Commincation System With Emphasis on Military Applications," (.pdf) USNA graduate 2002, Next to Stanford Electrical Engineering grad school. See also MILOCM 02' Proceedings publication. (.pdf)
Joshua Wood, USNA, Trident Scholar, "Statistics of Chaotic Time-Series Prediction," USNA graduate 1999. Next to Penn State Math grad school.
Monjure, USNA, Mathematics Honors Project, "Communication With Chaos," USNA graduate 2000.
Jamie Lusk, USNA, Mathematics Project Student, "Small Worlds," USNA graduate 2001.
Associate Editor of Mathematical Biosciences and Engineering (MBE). (2003- ).
Associate Editor of Dynamics of Continuous, Discrete and Impulsive Systems, Series B: Series B: Applications & Algorithms. (2003- ).
Senior Editor: DSWeb. About the Dynamical Systems Profession, (2004- ) http://www.dynamicalsystems.org/ap/eb/
Associate Editor of International Journal of Bifurcations and Chaos - IJBC. (2010- ).
Associate Editor of Focus Edition Editor, Chaos: An Interdisciplinary Journal of Nonlin. (2018).
Associate Editor of Special Edition Editor, Entropy. (2014), (2020).
Associate Editor of Editorial Board of Complexity. (2020-).
1. Erik M. Bollt and Naratip Santitissadeekorn, Applied and Computational Measurable Dynamics, Book Publisher: Society for Industrial and Applied Mathematics, (2013).
1. Ranil Basnayake and Erik M Bollt, A Multi-Time Step Method to Compute Optical Flow with Scientific Priors for Observations of a Fluidic System, BIRS Book Chapter, in Ergodic Theory, Open Dynamics, and Coherent Structures, Editors, Froyland, Gary; Bahsoun, Wael; BOSE, CHRIS, Springer Proceedings in Mathematics & Statistics, Vol 70, pp 59-79, April, (2014). Book .pdf
2. E. Bollt, Targeting Control
of Chaotic Systems, in Chaos and Bifurcations Control: Theory and Applications,
invited chapter, Editors G. Chen, X. Yu, D.J. Hill, p1-25
(Springer-Verlag) ISBN: 3540404058 (2003). pdf
3. E. Bollt, J. Skufca, Markov Partitions, Encyclopedia of Nonlinear Science, invited short, Editor, Alwyn Scott, Routledge, New York, (2005). pdf.
4. E. Bollt, Order From Chaos, Encyclopedia of Nonlinear Science, invited short, Editor, Alwyn Scott, Routledge, New York, (2005). .ps
- Inventors: Stephen J. McGregor, Erik Bollt, Frank J. Fedel, Method of monitoring human body movement US 20130110011 A1, September 2, 2014. pdf.
Sanjeeva Balasuriya, Erik Bollt, " Globally Optimal Stretching Foliations of Dynamical Systems," submitted (2023). pdf,
Erik Bollt, Jeremie Fish, Anil Kumar, Edmilson Roque dos Santos and Paul J. Laurienti, " Fractal Basins as a Mechanism for the Nimble Brain," Scientific Reports 13:20860 (2023). pdf, SI pdf
Erik Bollt, "How Neural Networks Work: Unraveling the Mystery of Randomized Neural Networks For Functions and Chaotic Dynamical Systems," submitted (2023). pdf
Christopher W. Curtis, D. Jay Alford-Lago, Erik Bollt, and Andrew Tuma, "Machine Learning Enhanced Hankel Dynamic-Mode Decomposition," Chaos: An International Journal of Nonlinear Science 33.8 (2023). pdf , arXiv:2303.06289.
Y. Park, K. Gajamannage, D.I. Jayathilake, and E. Bollt, "Recurrent Neural Networks for Dynamical Systems: Applications to Ordinary Differential Equations, Collective Motion, and Hydrological Modeling," submitted (2023). pdf , arXiv:2202.07022.
D. G. Neranjaka Jayarathne and E. Bollt, "Autoencoding for the 'Good Dictionary' of eigen pairs of the Koopman Operator," to appear AIMS Mathematics and Computation (2023). pdf , arXiv:2306.05224.
Jie Sun, Abd AlRahman R AlMomani, and Erik Bollt, "Data-Driven Learning of Boolean Networks and Functions by Optimal Causation Entropy Principle (BoCSE)," Patterns 3, 100631 (2022). pdf , preview
Shane Ross, Jeremie Fish; Klaus Moeltner; Erik M. Bollt; Landon Bilyeu; Tracy Fanara, " Beach-level 24-hour forecasts of Florida red tide-induced respiratory irritation," Harmful Algae 111 (2022) 102149. pdf
Benjamin Walleshauser and Erik Bollt, "Predicting Sea Surface Temperatures with Coupled Reservoir Computers," Nonlinear Proc. in Geophysics Discussions: 1-19, (2022). pdf
C. Tyler Diggans, Erik M. Bollt, Daniel ben-Avraham, "Spanning Trees of Recursive Scale-Free Graphs," Phys. Rev. E 105.2 024312 (2022). pdf , arXiv:2112.07325.
Md Sayeed Anwar, Sarbendu Rakshit, Dibakar Ghosh, Erik Bollt, "Stability of intralayer synchronization in dynamic multilaye hypernetwork with generic coupling functions," Phys. Rev. E, 105 024303 (2022). pdf
Naratip Santitissadeekorn, Christof Meile, Erik Bollt, and George Waldbusser, " Parametric approach to promote a divergence-free flow in the image-based motion estimation with application to bioirrigation," European J of Applied Mathematics, 1-21 (2022). pdf
Jie Sun, Fernando J. Quevedo, Erik Bollt, "Data Fusion Reconstruction of Spatially Embedded Complex Networks," 10.4 J. Complex Networks (2022). arXiv:1707.00731, pdf
K.G.D. Sulalitha Priyankara, Sanjeeva Balasuriya, and Erik Bollt, "Melnikov theory for two-dimensional manifolds in three-dimensional flows," SIAM Journal on Applied Dynamical Systems 21.4 (2022): 2642-2696. pdf
Jeremie Fish, Daqing Hou, Jie Sun, and Erik Bollt, "Interaction Networks for Discrete Event Data From Poisson Multivariate Mutual Information and Information Flow with Applications from Gene Expression Data," Applied Network Science 7.1 1-22 (2022). pdf
Jeremie Fish, Mahesh Banavar, Erik Bollt, "How fragile is your network? More than you think," submitted (2022). pdf , arXiv:2203.13943.
Sudam Surasinghe, Jeremie Fish, Erik Bollt, "Learning Transfer Operators by Kernel Density Estimation," submitted (2022). pdf
Jeremie Fish and Erik Bollt, " Non-Normality, Optimality and Synchronization," submitted (2022). pdf
C. Tyler Diggans, Jeremie Fish, Abd AlRahman R. AlMomani, Erik M. Bollt, " The Essential Synchronization Backbone Problem," Chaos 31, 113142 (2021). pdf
Daniel J. Gauthier, Erik Bollt, Aaron Griffith, Wendson A.S. Barbosa, "Next Generation Reservoir Computing," Nature Communications, 12:5564 (2021). pdf and chosen as Nature Comm. Featured Articles in AI and machine learning.
Erik Bollt, "On Explaining the Surprising Success of Reservoir Computing Forecaster of Chaos? The Universal Machine Learning Dynamical System with Contrasts to VAR and DMD," Chaos 31, 013108 (2021). pdf erratum
Erik Bollt, "Geometric Considerations of a Good Dictionary for Koopman Analysis of Dynamical Systems: Cardinality, 'Primary Eigenfunction,' and Efficient Representation," Communications in Nonlinear Science and Numerical Simulation (2021): 105833. pdf
Abd AlMomani, Erik Bollt, "An Early Warning Sign of Critical Transition in The Antarctic Ice Sheet - A Data Driven Tool for Spatiotemporal Tipping Point," Nonlin. Processes Geophys., 28, 1-14, (2021). pdf
CT Diggans, J Fish, E Bollt, "Emergent hierarchy through conductance-based node constraints," Northeast Journal of Complex Systems (NEJCS) 3 (1), 4 (2021). pdf
Amila Sudu Ambegedara , U. G. I. G. K. Udagedara and Erik M. Bollt, "Spatial Mesh Refinement using Cubic Smoothing Spline Interpolation in Simulation of 2-D Elastic Wave Equation: Forward Modeling of Full-waveform Inversion," J. of Advances in Math. and Comp. Sci. 36(5): 66-83, (2021). pdf
Mack, K. V., Athavale, P., Jemison, W. D., Illig, D. W., Rumbaugh, L. K., Banavar, M. K., & Bollt, E. M., "Restoration of time-of-flight (ToF) underwater images using TV regularization," Ocean Sensing and Monitoring XIII (Vol. 11752, p. 117520N). International Society for Optics and Photonics. (2021).
Carmela Calabrese, Maria Lombardi, Erik Bollt, Pietro De Lellis, Benoit G. Bardy, and Mario di Bernardo, "Spontaneous emergence of leadership patterns drives synchronization in complex human networks," Scientific reports 11 (1), 1-12 (2021). pdf
Jeremie Fish, Alexander DeWitt, Abd AlRahman R. AlMomani, Paul J. Laurienti, and Erik Bollt, "Entropic Causal Inference for Neurological Applications," Chaos 31, 113105 (2021). pdf
Erik Bollt, Shane Ross, "Is the Finite-Time Lyapunov Exponent Field a Koopman Eigenfunction?" Mathematics 2021, 9(21), 2731. pdf
Sudam Surasinghe, Erik Bollt, "On Geometry of Information Flow for Causal Inference," Entropy (2020), 22, 396; doi:10.3390/e22040396. pdf arXiv:2002.02078,
Sudam Surasinghe, Erik Bollt, "Koopman Operator, Dynamic Mode Decomposition(DMD), Johnson-Lindenstrauss Lemma, Random Projection, Data-driven method," Mathematics 9, 2803 (2021). pdf arXiv:2110.01718.
Nitu Kumari, Erik M Bollt, Nishith Mohan, Sandeep Sharma, "Hopf-bifurcation and Pattern Formation in a host-parasitoid-hyperparasitoid system with Beddington-DeAngelis response, " submitted (2021). pdf
Abd AlMomani, Erik Bollt, "Informative Ranking of Stand Out Collections of Symptoms: A New Data-Driven Approach to Identify the Strong Warning Signs of COVID 19," submitted (2020). pdf , medrxiv:2020.04.25.20079905v2. , arXiv:2004.08897.
Sudam Surasinghe, Erik Bollt, "On Geometry of Information Flow for Causal Inference," Entropy (2020), 22, 396; doi:10.3390/e22040396 arXiv:2002.02078. (Journal cover). pdf
C. Tyler Diggans, Erik M. Bollt, Daniel ben-Avraham, "Stochastic and mixed flower graphs: takane no hana," arXiv:2001.05041, Physical Review E 101, 052315 (2020). pdf arXiv:2001.05041,
Abd AlMomani, E Bollt, "ERFit: Entropic Regression Fit Matlab Package, for Data-Driven System Identification of Underlying Dynamic Equations," arXiv:2001.05041, submmitted (2020). pdf arXiv:2010.02411, code at github,
Abd AlRahman R. AlMomani, Jie Sun, and Erik Bollt, "How Entropic Regression Beats the Outliers Problem in Nonlinear System Identification," Chaos 30, 013107 (2020). pdf
Pilkiewicz, K; Rowland, M; Hein, A; Sun, Jie; Berdahl, A; Mayo, M; Moehlis, J; Porfiri, M; Fernandez-Juricic, E; Bollt, E; Tarampi, M; Macuga, K; Rossi, L; Shen, Chien-Chung, "Decoding collective communications from the individual's perspective using Information Theory tools," Journal of the Royal Society Interface 17 (164), 20190563 (2020) pdf,
Felix Dietrich and Mahdi Kooshkbaghi and Erik M. Bollt and Ioannis G. Kevrekidis, "Manifold Learning for Bifurcation Diagram Observations," Chaos 30, 043108 (2020). pdf arXiv:1810.12952,
S. Rakshit , B. K. Bera , E. Bollt and Dibakar Ghosh, "Intralayer synchronization in evolving multiplex hypernetworks: Analytical approach," SIAM Journal on Applied Dynamical Systems 19.2 (2020): 918-963. pdf
Naratip Santitissadeekorn and Erik M. Bollt, "Ensemble-based method for Inverse Frobenius-Perron Operator Problem: Data Driven Global Analysis from Spatiotemporal, Movie data" Physica D: Nonlinear Phenomena (2020): 132603. pdf
Erik Bollt, "Regularized Kernel Machine Learning for Data Driven Forecasting of Chaos," Annual Review of Chaos Theory, Bifurcations and Dynamical Systems, 9, 1-26 (2020). pdf
J. Runge, S. Bathiany, E. Bollt, G. Camps-Valls, D. Coumou, E. Deyle, C. Glymour, M. Kretschmer, M.D. Mahecha, E.H. van Nes, J. Peters, R. Quax, M. Reichstein, M. Scheffer, B. Scholkopf, P. Spirtes, G. Sugihara, J. Sun, K. Zhang, & J. Zscheischler, "Perspective article: Inferring causation from time series with perspectives in Earth system sciences," Nature Communications, volume 10, Article number: 2553 (2019). link
Kelum Gajamannage, Randy Paffenroth, and Erik Bollt, "A Nonlinear Dimensionality Reduction Framework Using Smooth Geodesics," Pattern Recognition 87 226-236 (2019). pdf
Jim Bagrow, Erik Bollt, "An information-theoretic, all-scales approach to comparing networks," Applied Network Science (2019) 4:45, pdf
Erik Bollt, Qianxiao Li, Felix Dietrich, Ioannis Kevrekidis, "On Matching, and Even Rectifying, Dynamical Systems through Koopman Operator Eigenfunctions," SIAM Journal on Applied Dynamical Systems 17.2 (2018): 1925-1960. pdf arXiv:1712.07144,
Erik Bollt, "Open or Closed? Information Flow Decided by Transfer Operators and Forecastability Quality Metric," Chaos: An Interdisciplinary Journal of Nonlin, 28, 075309 (2018). pdf
Erik Bollt, Jie Sun, Jakob Runge, "Introduction to Focus Issue: Causation inference and information flow in dynamical systems: Theory and applications" Chaos: An Interdisciplinary Journal of Nonlin 28, 075201 (2018).
Joshua Garland, Andrew M. Berdahl, Jie Sun, and Erik Bollt, "The Anatomy of Leadership in Collective Behaviour" Chaos: An Interdisciplinary Journal of Nonlin, 28, 075308 (2018). arXiv:1802.01194, pdf
Warren M. Lord, Jie Sun, Erik Bollt, "Geometric k-nearest neighbor estimation of entropy and mutual information," Chaos: An Interdisciplinary Journal of Nonlin, 28, 033114 (2018). arXiv:1711.00748, pdf
Robert Bruce Alstrom, Stephane Moreau, Pier Marzocca, Erik Bollt, "Nonlinear characterization of a Rossler system under periodic closed-loop control via time-frequency and bispectral analysis," Mechanical Systems and Signal Processing (MSSP), 99 (2018) 567-585, pdf
A. AlMomani and E. M. Bollt, "Go With the Flow, on Jupiter and Snow. Coherence From Model-Free Video Data without Trajectories," J Nonlinear Sci (2018). https://doi.org/10.1007/s00332-018-9470-1. pdf link arXiv:1610.01857,
Jie Sun, Fernando Quevedo, Erik Bollt, "Statistical Inverse Formulation of Optical Flow with Uncertainty Quantification," Inverse Problems 34 105008 (2018), pdf
Felix P. Kemetha, Sindre W. Haugland, Felix Dietrich, Tom Bertaland, Kevin, Hohlein, Qianxiao Lie, Erik M. Bollt, Ronen Talmon, Katharina Krischera, and Ioannis G. Kevrekidis, "An Emergent Space for Distributed Data with Hidden Internal Order through Manifold Learning," IEEE Access, Special Section: Big Data Learning and Discovery, 10.1109/ACCESS.2018.2882777 (2018). pdf
Qianxiao Li, Felix Dietrich, Erik Bollt, Ioannis G. Kevrekidis, "Extended dynamic mode decomposition with dictionary learning: a data-driven adaptive spectral decomposition of the Koopman operator," Chaos: An Interdisciplinary Journal of Nonlin (Vol.27, Issue 10), 103111 (2017). arxiv , pdf
K.G.D. Sulalitha Priyankara, Sanjeeva Balasuriya, and Erik Bollt, "Quantifying the Role of Folding in Nonautonomous Flows: the Unsteady Double-Gyre," International Journal of Bifurcation and Chaos, Vol. 27, No. 10 (2017) 1750156. pdf
Kelum Gajamannage, Erik Bollt, "Detecting Phase Transitions in Collective Motion Using Manifold's Curvature , " Mathematical Biosciences and Engineering (MBE), vol. 14, no. 2, pp. 437-453, (2017), pdf
Erik Bollt, "Regularized Forecasting of Chaotic Dynamical Systems," Chaos Solitons and Fractals, 94 8-15 (2017). pdf
Sean Kramer, Erik Bollt, "An Observer for an Occluded Reaction-Diffusion System With Spatially Varying Parameters," Chaos: An Interdisciplinary Journal of Nonlinear Science, 27, 035810 (2017) (2017), pdf
Bruce Alstrom, Stephane Moreau, Noureddine Atalla Erik Bollt, Pier Marzocca, "Nonlinear Systems Identification of a NACA 0015 High Lift System Under Dual Location Open Loop Control," 52nd 3AF International Conference on Applied Aerodynamics 27 – 29 March 2017, Lyon - France, FP58-AERO2017-alstrom (2017), pdf
Kelum Gajamannage, Erik Bollt, Mason A. Porter, and Marian S. Dawkins, "Modeling the lowest-cost splitting of a herd of cows by optimizing a cost function," Chaos 27, 063114 (2017), pdf
Amila Sudu Ambegedara, Jie Sun, Kerop Janoyan and Erik Bollt, "Information Theoretical Noninvasive Damage Detection In Bridge Structures," CHAOS 26, 116312 (2016), pdf
Warren M. Lord, Jie Sun, Nicholas T. Ouellette, and Erik M. Bollt, "Inference of Causal Information Flow in Collective Animal Behavior," IEEE Transactions on Molecular, Biological, and Multi-Scale Communications as a Shannon Centennial Special Issue, VOL. 2, NO. 1, 2016, pdf
Pileun Kim and Jonathan Rogers, Jie Sun, and Erik Bollt, "Causation Entropy Identifies Sparsity Structure for Parameter Estimation of Dynamic Systems," Journal of Computational and Nonlinear Dynamics, 12(1), 011008 (2016) link
Luke K. Rumbaugh ; Kaitlin J. Dunn ; Erik M. Bollt ; Brandon Cochenour ;William D. Jemison, "An underwater chaotic lidar sensor based on synchronized blue laser diodes," (Conference Proceedings), Ocean Sensing and Monitoring VIII, Weilin W. Hou; Robert A. Arnone, Baltimore, Maryland, United States | April 17, 2016.
Ranil Basnayake, Erik Bollt, Nicholas Tufillaro, Jie Sun, Michelle Gierach "Regularization Destriping of Remote Sensing Imagery with Missing Data Preprocessing, " Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016-74, 2016, pdf
Kelum Gajamannage, Sachit Butail, Maurizio Porfiri, and Erik Bollt, "Identifying manifolds underlying group motion in Vicsek agents, " The European Physical Journal Special Topics 224.17-18 (2015): 3245-3256, pdf
Tian Ma, Nicholas Ouellette, Erik M Bollt, "Stretching and Folding in Finite Time , " Chaos 26, 023112 (2016), pdf
Jie Sun, Dane Taylor, Erik M Bollt, "Causal Network Inference by Optimal Causation Entropy," SIAM J. of Dynamical Systems, Vol. 14, No. 1, pp. 73-106 (SIADS), 2015, pdf
Erik Bollt, Joseph D. Skufca, "A Low-Dimensional Principal Manifold as the "Attractor Backbone" of a Chaotic Beam System, " International Journal of Bifurcation and Chaos, 25, 3 1550037 (2015), pdf
Tian Ma and Erik Bollt, "Shape Coherence and Finite-Time Curvature Evolution, " International Journal of Bifurcations and Chaos, 25 5 1550076 2015, pdf
Carlo Cafaro, Warren M. Lord, Jie Sun, and Erik Bollt, "Causation Entropy from Symbolic Representations of Dynamical Systems, " CHAOS 25, 043106 (2015), pdf
Tian Ma and Erik Bollt, " Comparison of Differential Geometry of Shape Coherence by Nonhyberbolic Splitting to Coherent Pairs and Geodesics, " Journal of Applied Mathematics and Physics, 2015, 3, 781-791. pdf
Jie Sun, Carlo Cafaro and Erik Bollt, "Identifying Coupling Structure in Complex Systems through the Optimal Causation Entropy Principle , " Entropy, 16(6), 3416-3433; (2014) pdf
Erik Bollt and Jie Sun "Editorial Comment on the Special Issue of Information in Dynamical Systems and Complex Systems , " Entropy 2014, 16(9), 5068-5077; doi:10.3390/e16095068, pdf
Tian Ma and Erik Bollt, "Differential Geometry Perspective of Shape Coherence and Curvature Evolution by Finite-Time Nonhyperbolic Splitting, " SIAM Journal on Applied Dynamical Systems (SIADS), Vol. 13 No. 3 Pg. 1106-1136 2014, pdf
Pietro DeLelllis, Giovanni Polverino, Gozde Ustuner, Nicole Abaid, Simone Macri, Erik Bollt and Maurizio Porfiri "Collective behaviour across animal species, " Scientific Reports 4, 3723, (2014), pdf
Sachit Butail, Philip Salerno, Erik M. Bollt, and Maurizio Porfiri, " Classification of collective behavior: a comparison of tracking and machine learning methods to study the effect of ambient light on fish shoaling, " Behavior Research Methods, 8 Oct, pp 1-12, 2014,
Kelum Gajamannage; Sachit Butail; Maurizio Porfiri; Erik M Bollt, "Dimensionality Reduction of Collective Motion by Principle Manifolds , " Physica D, 291 62-73 2014, pdf
Jie Sun, Erik. M. Bollt, "Causation Entropy Identifies Indirect Influences, Dominance of Neighbors and Anticipatory Couplings , " Physica D Special Issue: Evolving Dynamical Systems, Volume 267, 15 January 2014, Pages 49 - 57. pdf
Erik M. Bollt and Tian Ma, "Finite Time Curvature and a Differential Geometry Perspective of Shape Coherence by Nonhyperbolic Splitting, " Extended Abstract for Coherent Sets Workshop at Oberwolfach, Germany, Feb. 2014. pdf
Sachit Butail, Erik. M. Bollt, Maurizio Porfiri, "Analysis and Classification of Collective Behavior Using Generative Modeling and Nonlinear Manifold Learning, " Journal of Theoretical Biology 336(7), 185-199, (2013), pdf
Luke K. Rumbaugh, Erik M. Bollt, William D. Jemison, and Yifei Li, "A 532 nm Chaotic Lidar Transmitter for High Resolution Underwater Ranging and Imaging, " MTS/IEEE Oceans 2013, pdf
Robert Bruce Alstrom, Pier Marzocca, Goodarz Ahmadi, Erik. M. Bollt, "Flow Induced Noise Considerations for the Wind Tunnel Testing of a NACA 0015 Airfoil with Slots , " submitted to the Journal of Vibration and Acoustics, 2013, pdf
DeLellis, P., Polverino, G., Ustuner, G., Abaid, N., Bollt, E. M., Porfiri, M., " Analysis of collective behavior among species by the presence of low-dimensional embedding manifolds , " ASME DSCC - Dynamic Systems and Control Conference, (2013).
Jiongxuan Zheng, Joseph D. Skufca, Erik. M. Bollt, "The Bundle plot: Evolution of symbolic space under the system parameter changes, " International Journal of Bifurcation and Chaos 1330028 Volume 23, Issue 08, August 2013, pdf
Jiongxuan Zheng, Joseph D. Skufca, Erik. M. Bollt, " Comparing Dynamical Systems By Graph Matching Method, " Physica D, Volume 255, 15 July (2013), Pages 12–21, pdf
Pietro DeLellis, and Maurizio Porfiri, and Erik M. Bollt, "Topological analysis of group fragmentation in multi-agent systems, " Physical Review E 87(2), 022818 (2013), pdf
Ranil Basnayake, Aaron Luttman, and Erik Bollt, "A Lagged Diffusivity Method for Computing Total Variation Regularized Fluid Flow, " Eighth Intl Conf. Sci. Computing and Appl., Las Vegas 57-64 586 (2013), pdf or direct to link
Robert Bruce Alstrom, Goodarz Ahmadi, Erik Bollt, Pier Marzocca, " Synchronization for the Flow Control of a High Lift System , " SDMAIAA (2013), pdf
Tian Ma, Erik Bollt, "Relatively Coherent Sets as a Hierarchical Partition Method , " International Journal of Bifurcations and Chaos, 23 7 1330026 (2013), pdf
Sean Kramer, Erik Bollt, "Spatially Dependent Parameter Estimation and Nonlinear Data Assimilation by Autosynchronization of a System of Partial Differential Equations, " Chaos 23, 033101 (2013), pdf
Jiongxuan Zheng, Joe Skufka, Erik Bollt, " Heart Rate Variability as Determinism with Jump Stochastic Parameters," 1253 - 1264, Volume 10, Issue 4, August 2013, pdf
Aaron Luttman, Erik M. Bollt, Ranil Basnayake, Sean Kramer, Nicholas B. Tullaro, "A Stream Function Framework for Estimating Fluid Flow from Digital Imagery," CHAOS 23, 033134 (2013), pdf
Robert Bruce Alstrom, Erik Bollt, Pier Marzocca, Goodarz Ahmadi, "The Application of Nonlinear Pre-Filters to Prevent Aeroservoelastic Interactions due to Actuator Rate Limiting," 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference (2012), pdf
Nicole Abaid, Erik Bollt, and Maurizio Porfiri, "Topological analysis of complexity in multi-agent systems," Phys. Rev. E 85, 041907 (2012), pdf
Aaron Luttman, Erik Bollt, Ranil Basnayake, and Sean Kramer, "A Stream Function Approach to Optical Flow with Applications to Fluid Transport Dynamics," Proceedings in Applied Mathematics and Mechanics 11 1 855 - 856 (2012), pdf and the vector field movie movie and FTLE movie movie at group link
McGregor SJ, and Bollt E., "Control entropy: What is it and what does it tell us? " Clinical Kinesiology 66(1) 7-12; Spring, (2012). pdf
Erik Bollt, "Synchronization as a Process of Sharing and Transferring Information," International Journal of Bifurcations and Chaos, 22 1250261 (2012) pdf
Rana D. Parshad, Stephen J. McGregor, Michael A. Busa, Joseph D. Skufca, Erik Bollt "A statistical approach to the use of Control Entropy identifies differences in constraints of gait in highly trained versus untrained runners," Mathematical Sciences and Engineering (MBE) Volume 9,Number 1, 123 - 145 January (2012). pdf
Erik M. Bollt, Aaron Luttman, Sean Kramer, Ranil Basnayake, "Measurable Dynamics Analysis of Transport in the Gulf of Mexico During the Oil Spill," International Journal of Bifurcation and Chaos 22(3):1230012 (2012). pdf and the movie movie
Rana D. Parshad, Jiongxuan Zheng, Erik M. Bollt, Joseph D. Skufca, " Mostly Conjugacy of Stochastically Perturbed Dynamical Systems," Int. J. Contemp. Math. Sciences, Vol. 7, no. 9, 395 - 412 (2012). pdf
Rana D. Parshad, Stephen J. McGregor, Michael A. Busa, Joseph D. Skufca, Erik Bollt, "A novel statistical approach to the use of Control Entropy identifies differences in constraints of gait in highly trained versus untrained runners," Mathematical Biosciences and Engineering (MBE) 9 1 123-145 (2012).
Aaron Luttman, Erik Bollt, and Jason Holloway, "An Optical Flow Approach to Analyzing Species Density Dynamics and Transport," Journal of Computational Mathematics 30 249-261 (2012). pdf
R. B. Pilkar, E. M. Bollt, and C. J. Robinson "EMPIRICAL MODE DECOMPOSITION/ HILBERT TRANSFORM ANALYSIS OF POSTURAL RESPONSES TO SMALL AMPLITUDE ANTERIOR-POSTERIOR SINUSOIDAL TRANSLATIONS OF VARYING FREQUENCIES," Mathematical Sciences and Engineering (MBE) 8, 4, October (2011). pdf
Douglas Bohl, Naratip Santitissadeekorn, Akshey Mehta, and Erik Bollt, "Characterization of mixing using experimentally derived velocity fields and lagrangian coherent structures in a simple paddle mixer," 133 6 061202 Journal of Fluids Engineering (2011). pdf
Jie Sun, Erik M. Bollt, and Takashi Nishikawa, "Judging Model Reduction of Complex Systems ," Physical Review E, 83(4), 046125 (2011). pdf
Stephen J. McGregor, Michael A. Busa, Rana Parshad, James A. Yaggie, Erik Bollt "Control Entropy of Gait: Does Running Fitness Affect Complexity Of Walking?," Clinical Kinesiology 65(1); 9-17, Spring, 2011 pdf
Jiongxuan Zheng, Erik M Bollt, Joseph D Skufca, "Regularity of commuter functions for homeomorphic defect measure in dynamical systems model comparison ," DCDS-A Discrete and Continuous Dynamical Systems 18 363-382 (2011). pdf
Jie Sun, Erik M Bollt, Mason A, Porter, Marian S. Dawkins, "A Mathematical Model for the Dynamics and Synchronization of Cows," Physica D 240 1497 - 1509 (2011). pdf
Stephen J McGregor, William J Armstrong, James A Yaggie, Erik M Bollt, Rana Parshad, Jerry J Bailey, Sean M Johnson, Aleta M Goin and Samuel R Kelly, " Lower extremity fatigue increases complexity of postural control during a single-legged stance ," J Neuroeng Rehabil 8: 43, 2011.
Robert Bruce Alstrom, Goodarz Ahmadi, Erik Bollt, Pier Marzocca, " The Effect of Electro-Hydraulic and Electro-Hydrostatic Actuators Dynamics on the Adaptive Control of Chaotic Motions of a Nonlinear Aeroservoelastic (ASE) System ," AIAA GNC/AFM/MST/ASC/ASE 2010 Conference(2010). pdf
Robert Bruce Alstrom, Pier Marzocca , Erik Bollt , Goodarz Ahmadi, "Controlling Chaotic Motions of a Nonlinear Aeroelastic System Using Adaptive Control Augmented with Time Delay," AIAA GNC/AFM/MST/ASC/ASE 2010 Conference(2010). pdf
MA Busa, T Muth, C Herman, J Hornyak, E Bollt, S McGregor, " High Resolution Accelerometry Can Identify Changes in Running Dynamics Across an Inter-collegiate Cross Country Season, " Medicine & Science in Sports & Exercise, 42 (5), 91 (2010).
Joseph D. Skufca, Erik M. Bollt, Rakesh Pilkar, Charles J. Robinson, "Eigenposes: Using Principal Components to Describe Body Configuration for Analysis of Postural Control Dynamics.," WCCI 2010 - IEEE World Congress on Compuational Intelligence Barcelona, Spain (2010). pdf
Erik M. Bollt, Chen Yao, Ira B. Schwartz, "Dimensional Implications of Dynamical Data on Manifolds to Empirical KL Analysis ," 239, 23-24, 2039-2049 Physica D, (2010). pdf
Erik M. Bollt, Joseph D. Skufca, "On comparing dynamical systems by defective conjugacy: A symbolic dynamics interpretation of commuter functions," Physica D Volume 239, Issue 10, 15 May, Pages 579-590 (2010). pdf
Erik M. Bollt, Joseph D. Skufca, Stephen J McGregor, "Control Entropy: A Complexity Measure for Nonstationary Signals," Mathematical Biosciences and Engineering, 6 1 1-25 (2009). pdf
Jie Sun, Erik M. Bollt, Takashi Nishikawa, "Synchronization Stability of Coupled Near-Identical Oscillator Network ," Book chapter in Complex Sciences (published by Springer). Part 1, Volume 4, pp. 900~911 (2009). http://www.complex-sys.org/ pdf
Jie Sun, Erik M. Bollt, Takashi Nishikawa, "Constructing Generalized Synchronization Manifolds by A Manifold Equation ," SIAM J. Appl. Dyn. Syst. Volume 8, Issue 1, pp. 202-221 (2009). pdf
WJ Armstrong, EM Bollt, ME Gebraad, NA Stegenga, SJ McGregor, "Linear And Control Entropy Analysis of Electromyography And Mechanomyography Signals During The Wingate Anaerobic Test, " Medicine & Science in Sports & Exercise, 41 (5), 196 (2009).
Stephen J. McGregor, Michael A. Busa, Joseph Skufca, James A. Yaggie, Erik M. Bollt "Control Entropy identifies differential changes in complexity of walking and running gait patterns with increasing speed in highly trained runners," CHAOS 19, 026109 (2009). pdf
Stephen McGregor, Michael Busa, James Yaggie, and Erik Bollt, "Using High Resolution MEMS Accelerometers (HRA) for the Estimation of VO2 in Highly Trained Inter-collegiate Distance Runners," PloS one (10):e7355 (2009). pdf
Jie Sun, Erik M. Bollt, and Takashi Nishikawa, "Master Stability Functions for Coupled Near-Identical Dynamical System," arXiv:0811.0649, EPL 85 (2009) 60011. pdf
R. J. Schilling, E. M. Bollt, G. D. Fulk, J. D. Skufca, A. F. Al-Ajlouni, R. Robinson, and C. J. Robinson, "A Quiet Standing Index for Testing the Postural Sway of Healthy and Diabetic Adults Across a Range of Ages," IEEE Trans. on BME 56 2 292-302 (2009). pdf
Jie Sun, James P. Bagrow, Erik M. Bollt, and Joesph D. Skufca, "Dynamic Computation of Network Statistics via Updating Schema ," Phys. Rev. E 79, 036116(2009). pdf
Naratip Santitissadeekorn, Erik M Bollt, "Image Edge Respecting Denoising with Edge Denoising by A Designer Nonisotropic Structure Tensor Method," Image and Vision Computing, 9 3 309Ð318 (2009). pdf
R. Chartrand, K. Vixie, B. Wohlberg, E. Bollt, "A gradient descent solution to the Monge-Kantorovich problem ," Applied Mathematical Sciences, Vol. 3, no. 22, 1071 - 1080 (2009). pdf
Erik M. Bollt, Rick Chartrand, Selim Esedoglu, Pete Schultz, Kevin R. Vixie, "Graduated adaptive image denoising: local compromise between total variation and isotropic diffusion ," The Journal of Advances in Computational Mathematics, (A Springer journal) in the special issue on "Mathematical Methods for Image Processing." Adv Comput Math DOI 10.1007/s10444-008-9082-7 (2008). pdf
Maurizio Porfiri, Daniel J. Stilwell and Erik M. Bollt, "Synchronization in random weighted directed networks ," IEEE Transactions on Circuits and Systems I, 55(10), 3170-3177 (2008). pdf
Joseph D. Skufca, Erik M. Bollt, "A Concept of Homeomorphic Defect for Defining Mostly Conjugate Dynamical Systems," Chaos: An Interdisciplinary Journal of Nonlinear Science, 18 013118 (2008). pdf
SJ Mcgregor, J Armstrong, EM Bollt, "Control entropy of mechanomyogram (MMG) and electromyogram (EMG) during fatiguing isometric muscle actions, " The FASEB Journal, 22 1220.2-1220.2 (2008).
Jie Sun, Erik M. Bollt and Daniel ben-Avraham, "Graph Compression -- Save Information by Exploiting Redundancy," arXiv:0712.3312, J. Stat. Mech. (2008) P06001. pdf
Erik Bollt, Pawel Gora, Andrzej Ostruszka, and Karol Zyczkowski, "Basis Markov Partitions and Transition Matrices for Stochastic Systems," SIAM Journal on Applied Dynamical Systems, 7 2 341-360 (2008). pdf
Joseph D Skufca, Erik M Bollt, "Relaxing Conjugacy To Fit Modelling in Dynamical Systems," Physical Review E, 76 026220 (2007). pdf
Joseph D Skufca, Erik M Bollt, "Relaxing Conjugacy To Fit Modelling in Dynamical Systems," Virtual J. of Biological Physics, 14 5 (2007). link
James P. Bagrow, Erik M. Bollt, Joseph D. Skufca, and Daniel ben-Avraham, "Portraits of Complex Networks," cond-mat/0703470, Euro Physics Letters, EPL 81 68004 (2007). pdf
Chen Yao, Erik Bollt, "Modeling and Nonlinear Parameter Estimation with Kronecker product Representation for Coupled Oscillators and Spatiotemporal Systems," Physica D 227 1, 78-99 (2007). pdf
K. O'Donnell, A. Milanese, C. Hoover, M. Stolk, L. Miller, P. Marzocca, R. Jha, G. Armadi, E. Bollt, "Active Flow and Aeroelastic Control of Lifting Surfaces ," 2007 SAE AeroTech Congress & Exhibition, September 17-20, 2007 Los Angeles, (2007). pdf
Jim Bagrow, Erik Bollt, Luciano da Fontoura Costa "On Short Cycles and Their Role in Network Structure," http://arxiv.org/abs/cond-mat/0612502, submitted Physical Review E, (2007). pdf
Erik Bollt, "Attractor Modeling and Empirical Nonlinear Model Reduction of Dissipative Dynamical Systems," International Journal of Bifurcation and Chaos (IJBC) in Applied Sciences and Engineering, Vol. 17, No. 4 (2007) 1199-1219. pdf
Keegan Keegan S. O'Donnell, Charles McNall, Piergiovanni Marzocca, Ratneshwar Jha, Erik M. Bollt, "Design of a Wind Tunnel Apparatus to assist Flow and Aeroelastic Control via Zero Net Mass Flow Actuators," 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2007). pdf
Naratip Santitissadeekorn and Erik M. Bollt, "The infinitestimal operator for the semigroup of the Frobenius-Perron operator from image sequence data: Vector fields and computational measurable dynamics from movies," Chaos 17, 023126 (2007). pdf
Shawn D. Pethel, Ned J. Corron, and Erik M. Bollt, "Deconstructing High-Dimensional Spatiotemporal Chaos Using Simpler Local Symbolic Dynamics," Phys. Rev. Lett. 214101 (2007). pdf
Maurizio M. Porfiri, Daniel J. Stilwell, Erik M. Bollt, Joseph D. Skufca, "Stochastic synchronization over a moving neighborhood network," Proceedings of the IEEE 2007 American Control Conference, July (2007). pdf
Maurizio M. Porfiri, Dan Stilwell, Erik M. Bollt, Joseph D. Skufca, "Random Talk: Random Walk and Synchronizability in a Moving Neighborhood Network," Physica D Special Issue on Dynamics on Complex Networks, 224 102-113 (2006). pdf
Maurizio M. Porfiri, Dan Stilwell, Erik M. Bollt, "Decline of minorities in stubborn societies," Europhysics Letter B 57(4) 481-486 (2007). pdf
Luciano da Fontoura Costa, Erik M. Bollt, "A Fast and Accurate Nonlinear Spectral Method for Image Recognition and Registration," http://xxx.lanl.gov/pdf/cs.DC/0604094 Applied Physics Letters, v. 89(17), p. 174102, 2006. pdf
N. Santitissadeekorn and E. M. Bollt, "Identifying Stochastic Basin Hopping and Mechanism by Partitioning with Graph Modularity ,” Physica D, 231 95-107 (2007). pdf
Tom Asaki, Erik M. Bollt, Kevin R. Vixie, "Sparse Radiographic Tomography and System Identification Imaging from Single View, Multiple Time Sample Density Plots," International Mathematical Journal Computational Methods in Applied Mathematics 6(4):354-366, (2006). pdf
Christina Rubilloa, Erik Bollt, Piergiovanni Marzocca, "Active Aeroelastic Control of Lifting Surfaces via Jet Reaction Limiter Control," International Journal of Bifurcation and Chaos (IJBC) in Applied Sciences and Engineering, 16 9 2559-2574 (2006). pdf
Thomas Rendall, Christopher Chang, Pier Marzocca, Erik Bollt, and Parsa Zamankha, "Aeroelastic Behavior of a Non-rigidizable Inflatable UAV Wing," 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 1 - 4 May 2006, Newport, Rhode Island, (2006).
Shawn D. Pethel, Erik Bollt, and Ned J. Corron, "Symbolic Dynamics of Coupled Map Lattices ," PRL 96, 034105 (2006)..pdf
Noah F. Reddell, Erik M. Bollt, Thad B. Welch, "A Dual-Synchrony Chaotic Communication Scheme ," Circuits, Systems and Signal Processing Special Issue on Applications of Chaos in Communications, 24 5 557-570 (2005). pdf
Daniel J. Stilwell, Erik M. Bollt, D. Gray Roberson,"Sufficient Conditions for Fast Switching Synchronization in Time Varying Network Topologies ," nlin.CD/0502055, SIAM J. Dynamical Systems, 5:1 140:156 (2006). pdf
J.P. Bagrow, E. M. Bollt, "A Local Method for Detecting Communities," cond-mat/0412482, Phys. Rev. E, 72 046108 (2005). pdf
Daniel J. Stilwell, Erik M. Bollt, D. Gray Roberson, "Synchronization of Time-Varying Networks Under Fast Switching," Proceedings of the American Control Conference, Minneapolis, MN, (2006). pdf
E.M. Bollt, "The Path Towards a Longer Life: On Invariant Sets and The Escape Time Landscape," International Journal of Bifurcations and Chaos (IJBC) in Applied Sciences and Engineering, 15 (5) 1615-1624 (2005). pdf
E.M. Bollt, D. ben-Avraham, “What is Special about Diffusion on Scale-Free Nets?” New J. Phys. 7 26 1-21 (2005). pdf
Christina Rubilloa, Erik Bollt, Pier Marzocca, " Active Aeroelastic Control of Lifting Surfaces via Jet Reaction Limiter Control ," AIAA-2005-2076, 46th AIAA/ASME/ASCE/ASC Structures, Structural Dynamics, and Materials Conference, Austin, Texas, 18-21 April 2005. pdf
H. D. Rozenfeld, J. E. Kirk, E. M. Bollt, and D. ben-Avraham "Statistics of Cycles: How Loopy is your Network?," cond-mat/0403536, J. Phys. A: Math. Gen. 38 (2005) 4589-4595. pdf
James Bagrow, Hernan Rozenfeld, Erik Bollt, and Daniel ben-Avraham, "How Famous is a Scientist? --- Famous to Those Who Know Us," cond-mat/0404515, Europhys. Lett., 67 (4) 511-516 (2004). pdf
J.D. Skufca, E. Bollt, "Communication and Synchronization in Disconnected Networks with Dynamic Topology: Moving Neighborhood Networks," nlin.CD/0307010, Mathematical Biosciences and Engineering (MBE), 1 (2) 347 (2004). pdf
D. ben-Avraham, E. Bollt, C. Tamon "One-dimensional continuous-time quantum walks," Quantum Information Processing 3 (2004), 295-308. pdf
I.B. Schwartz, L. Billings, E. Bollt, "Dynamical epidemic suppression using stochastic prediction and control," Physical Review E 70, 046220 (2004). pdf.
L. Billings,I. B. Schwartz, D. S. Morgan, E.M. Bollt,R. Meucci, and E. Allaria, "Stochastic Bifurcation in a Driven Laser System-Experiment and Theory," Physical Review E 70 026220 (2004). pdf
E. Bollt, "Review of Chaos Communication by Feedback Control of Symbolic Dynamics," IJBC, 13 2 269-285 (2003)..pdf
Skufca, E. Bollt, "Feedback Control with Finite Accuracy, More Knowlege
and Better Control for Free," Physica D 179 18-32 (2003). pdf
Triandaf, E. Bollt, I. Schwartz, "Approximating Stable and Unstable Manifolds in Experiments," Phys. Rev. E, 67, 037201-1-4 (2003) .pdf
Morgan, E. Bollt, I. Schwartz, "Constructing constrained invariant sets in multiscale continuum systems," Phys. Rev. E 68, 56210 (2003). .pdf
Zhu, Y.C. Lai, F.C. Hoppensteadt, "Numerical and Experimental
Investigation of the Effect of Filtering on Chaotic Symbolic Dynamics,"
Chaos 13 1 410-419 (2003). .pdf
Y-C Lai, E. Bollt, Z. Liu, "Low-dimensional chaos in high-dimensional phase space: how does it occur?" Chaos, Solitons, and Fractals 15, 219-232 (2003).
E. Bollt, L. Billings, I. Schwartz, "A manifold independent approach to understanding transport in stochastic dynamical systems," Physica D, 173 3-4 153-177 (2002). pdf
Bollt, A. Klebanoff, "A new and simple chaos toy," International
Journal of Bifurcation and Chaos(IJBC) in Applied Sciences and Engineering. 12 (8) 1843-1857 (2002) .pdf Cover Article:
Billings, E. M. Bollt, and I. B. Schwartz, "Phase-Space
Transport of Stochastic Chaos in Population Dynamics of Virus Spread," Physical Review Letters 88 (2002), art. no. 234101.
N. Reddell, E. Bollt, T.
Welch, "Development of a digital signal processor (DSP) based chaotic communication system with emphasis on military applications ," appeared MILCOM (2002). pdf
Qingxian Xie, Guanrong Chen, and E. Bollt, "Hybrid Chaos Synchronization and Its Application in Information Processing," Math Comput Modeling 35 145-163 (2002).pdf
Klebanoff, E. Bollt,
"Convergence of the Davidchack-Lai algorithm for finding periodic orbits," Chaos,
Solitons, and Fractals. 12 1305-1322 (2001). pdf.
E. Bollt, "Combinatorial Control of Global Dynamics in a Chaotic Differential Equation," International Journal of Bifurcation and Chaos (IJBC) in Applied Sciences and Engineering. Vol. 11, No. 8 2145-2162 (2001).pdf
R.L.Davidchack, Y-C. Lai, A. Klebanoff, E. Bollt, "Towards complete detection of unstable periodic orbits in chaotic systems," Physics Letters A 287 (2001) 99-104. .pdf
E. Bollt, T.Stanford, Y-C. Lai, K. Zyczkowski, "What Symbolic Dynamics Do We Get With A Misplaced Partition? On the Validity of Threshold Crossings Analysis of Chaotic Time-Series," Physica D. 154 3-4 259-286 (2001). pdf
L. Billings and E. Bollt, "Probability density functions of some skew tent maps," Chaos Solitons and Fractals 12 365-376 (2001)..pdf
E. Bollt, T.Stanford, Y-C. Lai, K. Zyczkowski, "Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series," Physical Review Letters, 85 16 3524-3527 (2000) pdf
E. Bollt, "Model Selection, Confidence, and Scaling in Predicting Chaotic Time-Series," International Journal of Bifurcation and Chaos (IJBC) in Applied Sciences and Engineering, Vol. 10, No. 6, 1407-1422 (2000)..pdf
E. Bollt, "Controlling Chaos and the Inverse Frobenius-Perron Problem: Global Stabilization of Arbitrary Invariant Measures," International Journal of Bifurcation and Chaos (IJBC) in Applied Sciences and Engineering, Vol. 10, No. 5, 1033-1050 (2000). pdf
E. Bollt, "Controlling Invariant Density: An $l^\infty$ Solution to the Inverse Frobenius-Perron Problem," IEEE Circuits and Systems Society ISCAS'2000, Conference Proceedings, Geneva, Switzerland, May (2000) Paper ID: #749..pdf
Bollt, M.A. Jones, "The Complexity of Artificial Grammars,"Nonlinear Dynamics,
Psychology, and Life Sciences, 4 2 153-168, (2000). zipped
R. Davidchack, Y-C Lai, E. Bollt, M. Dhamala, " Estimating generating partitions of chaotic systems by unstable periodic orbits," Physical Review E, 61 2 1353-1356, (2000). .pdf
E. Bollt, "Stability of Order: An Example of Horseshoes "Near" a Linear Map," International Journal of Bifurcation and Chaos (IJBC) in Applied Sciences and Engineering, Vol. 9, No. 10, Oct (1999). pdf
K.Zyczkowski, E.Bollt, "On the entropy devil's staircase in a family of gap-tent maps," Physica D 132 3 392-410 (1999). pdf
Y-C Lai, E. Bollt, C. Grebogi, "Communicating with chaos using high-dimensional symbolic dynamics," Physics Letters A 255 (1-2) (1999) 75. .pdf
M. Dolnik, E. Bollt, "Communication with Chemical Chaos in the Presence of Noise," Chaos 8 3, 702-710, (1998). .pdf
E. Bollt, Y.C. Lai, "Dynamics of coding in communicating with chaos,"Physical Review E, 58 2 1724-1736, (1998). ps.
E. Bollt, E. Kostelich, "Optimal targeting of chaos," Physics Letters A 245(5) 399-406 (1998). pdf
E. Bollt, Y.C. Lai, C. Grebogi, "Coding, Channel Capacity, and Noise Resistance with Chaos," Physical Review Letters, 79 19 3787-3790, (1997). .pdf
E. Bollt, M. Dolnik, "Encoding Information in Chemical Chaos by Controlling Symbolic Dynamics," Physical Review E, June, (1997). .pdf
Bollt, "Controlling the Chaotic Logistic Map," PRIMUS (Problems
Resources, and Issues in Mathematics Undergraduate Studies), Vol VII, No 1,
1-18, March (1997).
Bollt, M. Dolnik, "Learning the Grammar of a Chaotic Dynamical System in a
Format Suitable for Controlling Symbol Dynamics and Communications,"
refereed conference proc, IEEE Circuits and Systems Society Proc. First International Conference on
Controlling Chaotic Oscillations, St. Petersburg, Russia, pp 573,
August, (1997). ps
Bollt, "Channel Capacity of A Noise Resistant Chaotic Communication
Device," Proc. 5th Annual US Army Research Lab Technical Symposium,
Bollt, "Communicating with a High Power Digital Transmitter Using Only
Small Power Variations through Control of Chaos," Proc. 4th Annual US
Army Research Lab Technical Symposium, October, (1996).
Bollt, J.D. Meiss, "Targeting Chaotic Orbits to the Moon through
Recurrence," Physics Letters A 204 373-378 (1995). pdf.
E. Bollt, J.D. Meiss, "Controlling Chaos through Recurrence," Physica
D 81 280-294 (1995). pdf.
E. Bollt, J.D. Meiss, "Breakup of Invariant Tori for the Four-Dimensional
Semi-Standard Map," Physica D 66 282-297 (1993).
Articles in The Popular Press
Refereed many papers for the
Journal of Bifurications and Chaos, CNSNS, SRE, SIADS, Physica D, Physics Letters A, American
Journal of Physics, Physical Review Letters, Physical
Physica D, Physics Letters A, American
Journal of Physics, Physical Review Letters, Physical
Physics Letters A, American
Journal of Physics, Physical Review Letters, Physical
American Journal of Physics, Physical Review Letters, Physical Review
Clarkson University, Potsdam, NY. 2002 to present. Full Professor since 2006. Associate Professor 2002-2006, Mathematics and Computer Science Department, and Physics Department.
Los Alamos National Laboratories, Consultant Visiting Scientist, Computational Science Methods Group (X-8), 2001-2011.
Efecta Technologies, Colorado Springs, CO. 2002. Consultant on Image Compression Algorithms.
United States Naval Academy, Annapolis, MD. 2000 to 2002. Associate Professor, Mathematics Department
United States Naval Academy, Annapolis, MD. 1997 to 2000. Assistant Professor, Mathematics Department
United States Military Academy, West Point, NY. 1995 to 1997. Assistant Professor, Department of Mathematical Sciences
Army Research Labs, Directorate of Signals and Information Technology, Adelphi, MD. 1996. Research consultant on low energy communications through controlling chaos.
University of Colorado at Boulder, Boulder, CO. 1993 to 1995. Research Assistant as a National Science Foundation graduate trainee fellow under Dr. James Meiss. We studied chaotic Hamiltonian dynamics, K.A.M. theory, controlling chaos and time-series embedding.
U.S. West Advanced Technologies, Boulder, CO. Summer 1993. Mathematical Modeling group member. I designed a large queuing network model of the phone company for the purpose of their systems optimization. This was implemented in the discrete simulation language SIMSCRIPT.
University of Colorado at Boulder, Boulder, CO. 1990 to 1993. Recitation Instructor for seven semesters.
Lawrence Berkeley Laboratory, X-Ray Optics Group, Berkeley, CA. 1987 to 1990. Research Assistant for Dr. Kwang-Je Kim. We modeled the resonant modes of a free electron laser cavity.
Institute for Defense Analysis, Arlington, VA. Summer 1986. Computer Programmer and Systems Operator.
National Institutes of Health, Bethesda, MD, 1985. Nuclear Medicine group member, responsible for managing and processing of nuclear magnetic resonance (NMR) imaging data.
University of Maryland, Plasma Energy Fusion Research Laboratory, College Park, MD. Summers of 1984 and 1985. Research Assistant, computer programmer, and machine shop technician for Dr. William Destler.
Avante-Garde Creations, Eugene, OR. 1984. Independent computer programmer. I created "Trompers," a 6502 machine language arcade game published for the Apple II+ and Atari 800.
Scientific Computing Experience
I have substantial computer experience, including
extensive experience in the languages: C, Fortran, Pascal, ADA, SIMSCRIPT, 6502
machine language, Mathematica, Maple, MatLab and MathCad. I have also spent time working on the
following platforms and operating systems:
VMS, UNIX, DOS, Windows 3.1, Windows 95/98/NT, and Silicon Graphics
including the forms graphics library.
FAMILY, then flying small airplanes, science fairs, cycling including velodrome (including in the past track) racing, cross country skiing, rowing, sea kayaking, choir. In 1991, I was a collegiate national cycling champion.
When I first got to USNA
Here I am in 1973 at USNA. Above left is just after I joined the sailing team. Above right is me in front of Chauvenet Hall, right after I joined the faculty, not too long after I graduated from grad school, and just before my first Nobel prize.
Here I am in 1971. In this picture, I am conferring with current faculty member at USNA, and a former colleague of mine who gave me a horse ride long before we were on the same faculty together.