Papers

Preprints

  • PHATE: A Dimensionality Reduction Method for Visualizing Trajectory Structures in High-Dimensional Biological Data. With Kevin R. Moon, David van Dijk, Zheng Wang, William Chen, Ronald R. Coifman, Natalia B. Ivanova, Guy Wolf and Smita Krishnaswamy. 2017. pdf, bioRxiv.
  • Time Coupled Diffusion Maps. With Nicholas Marshall. Submitted, 2016. pdf, arXiv.

Journal

  • Wavelet Scattering Regression of Quantum Chemical Energies. With Stéphane Mallat and Nicolas Poilvert. Multiscale Modeling and Simulation, volume 15, issue 2, 827-863, 2017. pdfarXiv, MMSSoftware.
  • Computing minimal interpolants in  C^{1,1}(\mathbb{R}^d). With Ariel Herbert-Voss and Frederick McCollum. Revista Matemática Iberoamericana, volume 33, issue 1, pages 29-66, 2017. pdfarXiv, RMISoftware.
  • A general theorem of existence of quasi absolutely minimal Lipschitz extensionsWith Erwan Le Gruyer. Mathematische Annalen, volume 359, issue 3-4, pages 595-628, August 2014. pdfarXivHALSpringer.
    N.B. The published version of the paper in Mathematische Annalen has an error in Example 2.4.3. Namely, alpha-Hölder functions, for alpha stricly less than one, do not satisfy (P3). Thus one cannot conclude that quasi-AMLEs exist in this case. The error has been corrected in the online version of the paper on this website, as well as on arXiv.
  • Diffusion maps for changing data. With Ronald R. Coifman. Applied and Computational Harmonic Analysis, volume 36, issue 1, pages 79-107, January 2014. pdfarXivScienceDirectSoftware.
  • Bi-stochastic kernels via asymmetric affinity functions. With Ronald R. Coifman. Applied and Computational Harmonic Analysis, volume 35, issue 1, pages 177-180, July 2013. pdfarXivScienceDirect.
  • The number of harmonic frames of prime orderLinear Algebra and Its Applications, volume 432, issue 5, pages 1105-1125, February 2010. pdfarXivScienceDirect.
  • The refinability of step functionsProceedings of the American Mathematical Society, volume 136, issue 3, pages 899-908, 2008. pdfAMS.

Conference and Workshop

  • A Diffusion-based Condensation Process for Multiscale Analysis of Single Cell Data. With Tobias Welp, Guy Wolf and Smita Krishnaswamy. In ICML Workshop Computational Biology, New York, June 24, 2016. 5 pages. pdfICML WCB.
  • Sparse endmember extraction and demixing. With Martin Ehler. In Proceedings of the IEEE 2012 International Geoscience and Remote Sensing Symposium, pages 1385-1388, Munich, Germany, July 22-27, 2012. pdfIEEE Xplore.
  • Wavelet packets for multi- and hyper-spectral imagery. With John J. Benedetto, Wojciech Czaja, Martin Ehler and Justin C. Flake. In Proceedings of IS&T/SPIE Electronic Imaging 2010, Wavelet Applications and Industrial Processing VII, volume 7535, San Jose, California, January 2010. pdfSPIE.
  • Frame based kernel methods for automatic classification in hyperspectral data. With John J. Benedetto, Wojciech Czaja and Justin C. Flake. In Proceedings of the IEEE 2009 International Geoscience and Remote Sensing Symposium, volume 4, pages 697-700, Cape Town, South Africa, July 12-17, 2009. pdfIEEE Xplore.

Expository

  • Distinguished lecture series: Assaf Naor on the Lipschitz extension problemFields Notes, volume 12, issue 3, page 14, winter 2013. pdfFields.

Unpublished

  • Quantum Energy Regression using Scattering Transforms. With Nicolas Poilvert and Stéphane Mallat. 2015. pdfarXiv.
    N.B. This paper has been replaced by “Wavelet Scattering Regression of Quantum Chemical Energies.”
  • Algorithms for computing the optimal Lipschitz constant of interpolants with Lipschitz derivative. 2013. pdfarXiv.
    N.B. All material in this paper is contained in “Computing minimal interpolants in C^{1,1}(\mathbb{R}^d).”
  • Frames for subspaces of \mathbb{C}^N. With David Widemann. 2007. pdfarXiv.

Dissertation

  • Enumeration of harmonic frames and frame based dimension reduction. Department of Mathematics, University of Maryland. 2009. pdf.