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Research from the Department of Mathematics at Illinois

AI/ML

• Gauge invariant autoregressive neural networks for quantum lattice models | 2021 | D. Luo, Z. Chen, K. Hu, Z. Zhao, V.M. Hur, B.K. Clark

• Spacetime neural network for high dimensioinal quantum dynamics | 2021 | J. Wang, Z. Chen, D. Luo, Z. Zhao, V.M. Hur, B.K. Clark | Video

Data Science

• Congestion barcodes: Exploring the topology of urban congestion using persisent homology | 2017 | Y. Wu, G. Shindnes, V. Karve, D. Yager, D.B. Work, A. Chakraborty, R.B. Sowers

• Algorithmic geolocation of harvest in hand-picked agriculture | 2018 | N. Srivastava, P. Maneykowski, R.B. Sowers

• Exploring characteristic features in gait patterns for predicting multiple sclerosis | 2019 | R. Kaur, S. Menon, X. Zhang, R. Sowers, M.E. Hernandez

• Tradeoffs between safety and time: A routing view | 2019 | D.R. Carmody, R.B. Sowers

• Automatic identification of brain independent components in electroencephalography data collected while standing in a virtually immersive environment: A deep learning-based approach | 2020 | R. Kaur, M. Korolkov, M.E. Hernandez, R. Sowers

• Seasonal disorder in urban traffic patterns: A low rank analysis | 2021 | V. Karve, D. Yager, M. Abolhelm, D.B Work, R. B. Sowers

• Topological analysis of traffic pace via persistent homology | 2021 | D.R. Carmody, R.B. Sowers

• The thresholding greedy algorithm, greedy bases, and duality | 2003 | S.J. Dilworth, N J. Kalton, D. Kutzarova, V.N. Temlyakov

• On the existence of almost greedy bases in Banach spaces | 2003 |  S.J. Dilworth, N.J. Kalton, D. Kutzarova

• Weak convergence of greedy algorithms in Banach spaces  | 2008 | S.J. Dilworth, D. Kutzarova, K.L. Shuman, V.N. Temlyakov, P. Wojtaszczyk

• Explicit constructions of RIP matrices and related problems  | 2011 | J. Bourgain, S.J. Dilworth, K. Ford, D. Kutzarova, S. Konyagin

• Breaking the k² barrier for explicit RIP matrices | 2011 | J. Bourgain, S.J. Dilworth, K. Ford, D. Kutzarova, S. Konyagin

• Weak thresholding greedy algorithms in Banach spaces | 2012 | S.J. Dilworth, D. Kutzarova, T. Schlumprecht, P. Wojtaszczyk

• On the convergence of a weak greedy algorithm for the multidimensional Haar basis | 2014 | S.J. Dilworth, S. Gogyan, D. Kutzarova

• Stability of low-rank matrix recovery and its connections to Banach space geometry | 2015 | A. Chavez-Dominguez, D. Kutzarova

• Existence and uniqueness of greedy bases in Banach spaces | 2016 | F. Albiac, J.L. Ansorena, S.J. Dilworth, D. Kutzarova  

• On the boundedness of the threshold operators in L₁[0,1] with respect to the Haar basis | 2017 | S.J. Dilworth, S. Gogyan, D. Kutzarova, T. Schlumprecht

• Building highly conditional almost greedy and quasi-greedy bases in Banach spaces | 2019 | F. Albiac, J.L. Ansorena, S.J. Dilworth, D. Kutzarova

• Lebesgue-type inequalities in greedy approximation | 2021 | S. Dilworth, G. Garrigos, E. Hernandez, D. Kutzarova, V. Temlyakov