Tyrus Berry Assistant Professor, Mathematics Department of Mathematical Sciences George Mason University Exploratory Hall
Email: tberry (at) gmu.edu
Google Scholar Page Research Gate Page
Teaching Fall 2017, Math 315, Advanced Calculus I (Blackboard) Fall 2016, Math 685 / OR 682, Numerical Methods Fall 2015, Nonlinear Data Analysis Seminar
Background Curriculum Vitae Research Statement
Research Interests My research is motivated by the rapid expansion of model complexity and data availability in the applied sciences. Traditional parametric modeling is subject to model error and I believe that modern complex systems call for model-free and semi-parametric approaches. In order to avoid the curse-of-dimensionality, these approaches must effectively incorporate available prior knowledge and existing models. My goal is to develop these techniques with careful consideration of the goals and constraints of real world case studies. Geometry of data: diffusion maps/local kernels, nonlinear dimensionality reduction and decomposition Statistics: kernel density/operator estimation, semi-parametric modeling of dynamical systems Dynamical systems: data assimilation, prediction/control, and uncertainty quantification Harmonic analysis: Sampling theory on manifolds, connections to kernel based statistical estimates
Publications and Preprints Geometry of Data T. Berry, T. Sauer, Consistent Manifold Representation for Topological Data Analysis. Submitted to Foundations of Computational Mathematics, 2016. (arXiv) T. Berry, J. Harlim, Iterated Diffusion Maps for Feature Identification. Journal of Applied and Computational Harmonic Analysis, 2016. (pdf,arXiv) T. Berry, T. Sauer, Density Estimation on Manifolds with Boundary. Computational Statistics and Data Analysis, 2016. (pdf,arXiv) T. Berry, T. Sauer, Local Kernels and the Geometric Structure of Data. Journal of Applied and Computational Harmonic Analysis, 2015. (pdf,arXiv) T. Berry, J. Harlim, Variable Bandwidth Diffusion Kernels. Journal of Applied and Computational Harmonic Analysis, 2015. (pdf,arXiv) Dynamics and Forecasting T. Berry, J. Harlim, Semiparametric forecasting and filtering: correcting low-dimensional model error in parametric models. JCP, 2016. (pdf,arXiv) T. Berry, D. Giannakis, J. Harlim, Nonparametric forecasting of low-dimensional dynamical systems. Physical Review E, 2015. (video files,pdf,arXiv) F. Hamilton, T. Berry, T. Sauer, Predicting chaotic time series with a partial model. Phys. Rev. E (2015). (pdf) J. Harlim, T. Berry, Forecasting Turbulent Modes with Nonparametric Diffusion Models. Physica D, 2016. (pdf,arXiv) T. Berry, J. Harlim, Nonparametric Uncertainty Quantification for Stochastic Gradient Flows. SIAM JUQ, 2014. (pdf,video files,arXiv) T. Berry, R. Cressman, Z. Greguric-Ferencek, T. Sauer, Time-scale separation from diffusion-mapped delay coordinates. SIAM J. Appl. Dyn. Sys. (2013). (pdf) Filtering J. Harlim, T. Berry, Correcting biased observation model error in data assimilation. Submitted to Monthly Weather Review (2016). (arXiv) F. Hamilton, T. Berry, T. Sauer, Kalman-Takens filtering in the presence of dynamical noise. Submitted to EPJ (2016). (arXiv) F. Hamilton, T. Berry, T. Sauer, Ensemble Kalman filtering without a model. Phys. Rev. X (2016). (pdf) T. Berry, J. Harlim, Linear theory for filtering nonlinear multi scale systems with model error. Proc. R. Soc. A (2014). (pdf,arXiv) T. Berry, T. Sauer, Adaptive ensemble Kalman filtering of nonlinear systems. Tellus A (2013). (pdf) F. Hamilton, T. Berry, N. Peixoto, T. Sauer, Real-time tracking of neuronal network structure using data assimilation. Phys. Rev. E (2013). (pdf) Other Topics T. Berry, Model free techniques for reduction of high-dimensional dynamics. Thesis, published on MARS database. T. Berry, T. Sauer, Convergence of periodically-forced rank-type equations. Journal of Difference Equations and Applications 17 (2011). T. Berry, F. Hamilton, T. Sauer, N. Peixoto, Detecting Connectivity Changes in Neuronal Networks. J. Neuroscience Methods 209, 388-397 (2012). T. Berry An Overview of Optimal Stopping Times for Various Discrete Time Games. Masters Thesis, Ohio State University (2008). T. Berry, S. Heilman, R. Strichartz Outer Approximation of the Spectrum of a Fractal Laplacian. Experiment. Math. 18 (2009), no.4, 449-480. Unpublished Technical Reports T. Berry, T. Sauer, Spectral Clustering from a Geometrical Viewpoint. Technical Report, 2015. T. Berry, Diffusion Wavelets for Natural Image Analysis Technical Report, 2011. T. Berry, Global Principal Geodesic Analysis for Latent Variable Identification Technical Report, 2011.
Presentations Nov. 29, 2017. (slides) JHU - Nov. 15, 2017. (slides) PSU-UMD Data Assimilation Workshop - June 27, 2017. (slides) Extreems - June 26, 2017. (slides) SIAM Dynamical Systems - Snowbird, UT, May 24, 2017. (slides) Idea Testing Session - George Mason University, April 7, 2017. (slides) Topology, Arithmetic and Dynamics Seminar - George Mason University, March 10, 2017. (slides) Mathematical Biology Seminar - NJIT, Feb. 28, 2017. (slides) Mathematical Sciences Colloquium - George Mason University, Feb. 24, 2017. (slides) Statistics Seminar - George Mason University, Feb. 10, 2017. (slides) Applied Dynamics Seminar Series - University of Maryland, Sept. 29, 2016. (slides) 2016 AIMS Conference - Orlando, FL, July 2, 2016. (slides) Introduction to Nonlinear Data Analysis, Dec. 11, 2015. (vid1,vid2,vid3,vid4) 2015 AMMCS-CAIMS Congress - Wilfrid Laurier University, June 11, 2015. (slides) Courant Institute Applied Math Seminar, March 13, 2015. (slides) George Mason University Applied Math Seminar, February 27, 2015. (slides) 2014 SIAM Conference on Uncertainty Quantification, Savannah, GA, April 1, 2014. (program) ONR-MURI Workshop, Courant Institute, January 20-22, 2014. (slides) 4th Annual Joint PSU-UMD Data Assimilation Workshop, Pennsylvania State University, Dec. 18, 2013. (slides) WMO Sixth Symposium on Data Assimilation, University of Maryland, College Park, October 7-11, 2013. (poster) 2013 Interdisciplinary Summer School: Data Assimilation in Geosciences, University of Maryland, College Park, June 3-14, 2013. (slides (revised), original) Snowbird SIAM Conference on Applications of Dynamical Systems, May 19-23, 2013. (Presentation) IMA Annual Program Year Workshop: Stochastic Modeling of the Oceans and Atmosphere, University of Minnesota, Twin Cities Campus, March 11-15, 2013. (poster) Building Engineered Complex Systems Workshop, Jan. 24-25, 2013 (poster) Joint Mathematics Meeting at Boston, January 4, 2012 at 9:30, Special Session for Difference Equations and Applications, I. (abstract) Snowbird SIAM Conference on Applications of Dynamical Systems, May 22-26, 2011 (poster) Building Engineered Complex Systems Workshop, Mar. 28-29, 2011 (poster) February Fourier Talks, University of Maryland, Feb. 17 - 18, 2011 (poster) AMS Meeting at Syracuse University, October 2, 2010, Special Session on Difference Equations and Applications. (schedule, abstract)