In June 2009 I moved to the Department of Biostatistics at University of Rochester.

Nikolay Balov's home page at


Education

    Ph.D. in Statistics, 2009, Florida State University
    Dissertation Slides
    M.S. in Mathematics, 1998, Sofia Univesity
    B.S. in Mathematics, 1994, Sofia University

Research

    I am interested in studying distributions on non-Euclidean spaces. Specifically, I develop non-parametric methods for representation, comparison and interpolation of random variables on Riemannian manifolds by extending the concept of covariance into a new much richer structure called covariance field.

    Covariance field concept can be used for comparing distributions on any Riemannian manifold. For illustration purposes, I implement this approach on Euclidean spaces and show how the proposed method performs against some standard tests for different distributions.
    The real advantage of the covariance based comparison methods is clear when one goes to non-Euclidean spaces like the unit 2-sphere. There the classical tests do not have obvious extensions and my framework is well motivated.

    Covariance field analysis opens a number of new opportunities to study distributions. Distribution interpolation is one of them. Here I implement and demonstrate a procedure for interpolation on the circle and interpolation on the 2-sphere that is expandable to spheres of all dimensions.

    I am also interested in applying statistical methods for solving problems of medical imaging. For the recently developed MRI technique for in vivo brain scanning called Diffusion-Tensor Imaging (DTI), we research new algorithms for building connectivity maps. There is a strong evidence that some of the covariance based techniques for interpolation and comparison of spherical data can be successfully applied to analysis of DTI, as well as for its next iteration, HARDI(High Angular Resolution Diffusion Imaging). These modern neuro-imaging modalities challenge the classical statistical methodology and clearly show the need for non-Euclidean techniques.

    Another area of research I find exciting is the analysis of genomic data in form of microarrays. The high-dimensionality and non-linearity of microarray data makes it suitable for processing with the techniques I develop and this is an area I would be happy to work in in future.

    The last bit here is analysis vector fields on the sphere.

Technical reports

  • Covariance of centered distributions on manifold, arxiv:0805.0732v1
  • Comparing and interpolating distributions on manifold, arxiv:0807.0782v2
  • Covariance fields, arxiv:0807.4690v2
  • On the Stochastic Rank of Metric Functions, arxiv:0810.5549v2

    • Conference proceedings

  • Comparing Random Variables on Manifolds, Nikolay Balov. JSM 2008, Denver

  • Shape Analysis of Open Curves in R3 with Applications to Study of Fiber Tracts in DT-MRI Data, Nikolay Balov, Anuj Srivastava, Chunming Li, Zhaohua Ding . EMMCVPR 2007

  • Mapping genetic influences on brain fiber architecture with high angular resolution diffusion imaging (HARDI), Ming-Chang Chiang,; Barysheva, Marina; Lee, Agatha D.; Madsen, Sarah; Klunder, Andrea D.; Toga, Arthur W.; McMahon, Katie L.; de Zubicaray, Greig I.; Meredith, Matthew; Wright, Margaret J.; Srivastava, Anuj; Balov, Nikolay; Thompson, Paul M., ISBI 2008: 871-874.


    • Some not so serious stuff

  • A bit from my country's history.
  • You may also play with my tone synthesizer - see and hear different sound waves and even compose a tune.

    • Links and Acknowledgments

  • Several people are responsible for my dissertation: my adviser, Anuj Srivastava, who gave me support when I was really needed it; Vic Patrangenary, from whom I received great encouragements during my thesis writing; Dan McGee another member of my committee and currently chair of our department.
  • Special thanks to my friend Svetla Slaveva-Griffin and congratulations for her new book , for which I happened to draw some illustrations.