Tyrus Berry Assistant Professor, Mathematics Google Scholar Page Research Gate Page Department of Mathematical Sciences Exploratory Hall, 4452 Email: tberry (at) gmu.edu

Publications and Preprints

Geometry of Data

• T. Berry, D. Giannakis, Spectral Exterior Calculus. Communications on Pure and Applied Mathematics, 2020. (pdf,arXiv,code)
• T. Berry, D. Giannakis, J. Harlim, Bridging data science and dynamical systems theory. Notices of the AMS, 2020. (pdf,arXiv)
• R. Vaughn, T. Berry, H. Antil, Diffusion Maps for Embedded Manifolds with Boundary with Applications to PDEs, Preprint, 2019.
• H. Antil, T. Berry, J. Harlim, Fractional Diffusion Maps. ACHA, 2021. (pdf,arXiv)
• T. Berry, T. Sauer, Consistent Manifold Representation for Topological Data Analysis. Foundations of Data Science. (pdf, arXiv,code)
• T. Berry, S. Schluchter, Applications of topological graph theory to 2-manifold learning. Preprint, 2018.
• 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,code)
• 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

• D. Easley, T. Berry, A Higher Order Unscented Transform. To Appear in SIAM JUQ, 2021. (pdf,arXiv,code)
• 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,code)
• 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

• D. Ebeigbe, T. Berry, S. Schiff, T. Sauer, Poisson Kalman filter for disease surveillance. Physical Review Research, 2020. (pdf,code)
• D. Ebeigbe, T. Berry, M. Norton, A. Whalen, D. Simon, T. Sauer, S. Schiff, A Generalized Unscented Transformation for Probability Distributions. Preprint, 2021. (arxiv)
• T. Sauer, T. Berry, D. Ebeigbe, M. Norton, A. Whalen, S. Schiff, Identifiability of infection model parameters early in an epidemic. Preprint, 2020. (pdf,medRxiv)
• F. Hamilton, T. Berry, T. Sauer, Correcting Observation Model Error in Data Assimilation. (2019). (pdf)
• J. Guan, T. Berry, T. Sauer, Limits on reconstruction of dynamics in networks. PRE (2018). (pdf, supplement)
• T. Berry, T. Sauer, Correlation between System and Observation Errors in Data Assimilation. MWR (2018). (pdf)
• F. Hamilton, T. Berry, T. Sauer, Tracking intracellular dynamics through extracellular measurements. PLOS ONE (2018). (pdf)
• F. Hamilton, T. Berry, T. Sauer, Kalman-Takens filtering in the presence of dynamical noise. EPJ (2017). (pdf,code)
• J. Harlim, T. Berry, Correcting biased observation model error in data assimilation. Monthly Weather Review (2017). (arXiv, pdf)
• 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

• M. Panagoda, T. Berry, H. Antil Convergence Analysis of the Rank-Restricted Soft SVD Algorithm. Submitted to SIMAX, 2021. (arxiv)
• 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.
  
• Link to my REU website from Summer 2005 at Cornell with Dr. Strichartz.

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.