Scientific Research of Steven B Damelin

Any files attached below are my own. Work where copyright has been transfered are acknowledged to the respective places where they will appear or have appeared.

  • My work on Google Scholar, by typing Google Scholar and then Steven Damelin.
  • My work on Microsoft Academic Research
  • My work on ResearchGate
  • My work on DBLP(uni-trier.de)

    My research interests are varied and I have worked in the following areas: computer vision(for example dimension estimation and reduction, diffusion methods, data matching, compressive sensing, metrics, clustering, compression), imaging, signal processing, bioinformatics, mathematics education , coding theory and finite fields, computational and pure harmonic analysis, econometrics, graph theory, potential theory, approximation theory, numerical analysis, geometric analysis

    Books, Book Chapters and Editorial Volumes

  • S. B. Damelin and W. Miller, Mathematics and Signal Processing, Cambridge Texts in Applied Mathematics (No. 48) February 2012
  • J. H. Ann, S. B. Damelin and P. Bigeleisen, Medical Image segmentation using modified Mumford segmentation methods, Ultrasound-Guided Regional Anesthesia and Pain Medicine, eds P. Bigeleisen, Chapter 40, Birkhauser, 2009.
  • Topics in Integrable Systems, Special Functions, Orthogonal Polynomials and Random Matrices, Journal of Computational and Applied Mathematics, Special Volume, 202, (1), May 2007, pp 1-154 (with W. Xu-Ma (University of South Florida)).

    Papers (Submitted and Accepted)

    2013

  • S. Wang, S. B. Damelin, and A. Hero, "Shortest path through random points", being revised for Annals of Probability .
  • Kerry Cawse, Steven B. Damelin, Amandine Robin, Michael Sears, A parameter free approach for determining the intrinsic dimension of a hyperspectral image using Random Matrix Theory, Transactions on Image Processing, to appear
  • Charles Fefferman, Steven. B. Damelin and William Glover, BMO Theorems for $\varepsilon$ distorted diffeomorphisms on $\mathbb R^D$ and an application to comparing manifolds of speech and sound, Involve, a Journal of Mathematics 5-2 (2012), 159--172. DOI 10.2140/involve.2012.5.159
  • S. B. Damelin, J. Levesley and D. Ragozin, Hyperinterpolation on projective spaces, being revised for Journal of Approximation Theory.

    2012-1993.

  • Louis du Plessis, Rui Xu, Steven Damelin, Michael Sears and Donald Wunsch, Reducing dimensionality of hyperspectral data with diffusion maps and clustering with K-means and fuzzy art, Int. J. Systems Control and Communications, (3) (2011), pp 232-251.
  • Cawse K, Sears M, Robin A, Damelin S, Wessels K, van den Bergh F, Mathieu R, Using random matrix theory to determine the number of endmembers in a hyperspectral image, WHISPERS 2010, June 14-16 2010, Reykjavik, Iceland.
  • Michael Mitchley, Michael Sears and Steven Damelin, Target detection I Hyperpectral mineral data using wavelet analysis, Proceedings of the 2009 IEEE Geosciences and Remote Sensing Symposium, Cape Town, pp 23-45.
  • Louis du Plessis, Steven Damelin and Michael Sears, Reducing the dimensionality of hyperpectral data using diffusion maps, Proceedings of the 2009 IEEE Geosciences and Remote Sensing Symposium, Cape Town, pp 105-132.
  • Louis du Plessis, Rui Xu, Steven Damelin, Michael Sears and Donald Wunsch, Reducing dimensionality of hyperspectral data with diffusion maps and clustering with K-means and fuzzy art, Proceedings of International Conference of Neural Networks, Atlanta, 2009, pp 32-36.
  • D. Benko, S. B. Damelin and P. Dragnev, On supports of equilibrium measures with concave signed equilibria and the Iterated Balayage Algorithm, to appear, Journal of Computational Analysis and Applications.
  • S. B. Damelin, J. Levesley, D. L. Ragozin and X. Sun, Energies, Group Invariant Kernels and Numerical Integration on Compact Manifolds, Journal of Complexity, 25(2009), pp 152-162.
  • S. B. Damelin, F. Hickernell, D. Ragozin and X. Zeng, On energy, discrepancy and G invariant measures on measurable subsets of Euclidean space, Journal of Fourier Analysis and its Applications (2010) (16), pp 813-839.
  • S. B. Damelin, A Walk through Energy, Discrepancy, Numerical Integration and Group Invariant Measures on Measurable Subsets of Euclidean Space, Numerical Algorithms, Volume 48 Number 1-3, 2008, pp 213-235.
  • Kerry-Anne Cawse, Steven Damelin, Richard McIntyre, Michael Mitchley, Louis du Plessis and Michael Sears, An Investigation of data compression for Hyperspectral core image data, Proceedings of the Mathematics in Industry Study Group 2008, South Africa, 2008, pp. 1-25
  • R. Xu, S. B. Damelin and D. Wunsch, Clustering of High-Dimensional Gene Expression Data with Feature Filtering Methods and Diffusion Maps, Proceedings of the 2008 International Conference on BioMedical Engineering and Informatics, 2008, pp. 245-249.
  • Rui Xu, Steven Damelin, B. Nadler, and Donald C. Wunsch II, Clustering of High-Dimensional Gene Expression Data with Feature Filtering Methods and Diffusion Maps, 2008 AIIM Special Issue: AI in BioMedical Engineering and Informatics.
  • Rui Xu, Steven Damelin, and Donald C. Wunsch II, "Applications of diffusion maps in gene expression data-based cancer diagnosis analysis," In Proceedings of the 29th Annual International Conference of IEEE Engineering in Medicine and Biology Society, Lyon, France, pp. 4613-4616, August, 2007.
  • S. B. Damelin, G. Michalski and G. Mullen, The cardinality of sets of k independent vectors over finite fields, Monatsh.Math, 150(2008), pp 289-295.
  • S. B. Damelin and V. Maymeskul, Minimal Discrete Energy Problems and Numerical Integration on Compact Sets in Euclidean Spaces, Algorithms for Approximation, (2007) pp 369-378.
  • S. B. Damelin and A. J Devaney, Local Paley Wiener theorems, Proceedings of Inverse Problems Symposium, East Lansing, Michigan, pp 1-12, June 2007.
  • S. B. Damelin, On Bounds for Diffusion, Discrepancy and Fill Distance Metrics, Springer Lecture Notes in Computational Science and Engineering, (2008) Vol. 58, pp 32-42.
  • S. B. Damelin and A. J. Devaney, Local Paley Wiener theorems for analytic functions on the unit sphere, Inverse Problems, (23)(2007), pp 1-12.
  • Y. Ma, S. B. Damelin, O. Masoud and N. Papanikolopoulos, Activity Recognition via Classification Constrained Diffusion Maps, ISCV (International Symposium of Computer Vision), 2006, pp 1-8.
  • D. Benko, S. B. Damelin and P. Dragnev, On the support of the equilibrium measure for arcs of the unit circle and real intervals, Electronic Transactions on Numerical Analysis, (25)(2006), pp 27-40.
  • S. B. Damelin and V. Maymeskul, On Point Energies, Separation Radius and Mesh Norm for s-Extremal Configurations on Compact Sets in R^n, Journal of Complexity, Volume 21(6)(2006), pp 845-863.
  • S.B. Damelin, J. Levesley and X. Sun, Energy estimates and the Weyl criterion on compact homogeneous manifolds, Algorithms for Approximation, (2007), pp 359-368.
  • S.B. Damelin, Pointwise bounds of orthogonal expansions on the real line via weighted Hilbert Transforms, Advances in Computational Mathematics (2006), pp 1-21.
  • S.B. Damelin and H.S. Jung, Pointwise convergence of derivatives of weighted Lagrange interpolation polynomials, Journal of Computational and Applied Mathematics, Volume 173, (2)(2005), pp 303-319.
  • S.B. Damelin and K. Diethelm, Weighted polynomial approximation and Hilbert Transforms: Their connections to the numerical solution of singular integral equations, Proceedings of Dynamic Systems and Applications, Volume 4 (2004), pp 20-26 Ed. G. S. Ladde, N.G. Medhin. M. Sambandham.
  • S.B. Damelin, Asymptotics of recurrence coefficients for orthonormal polynomials on the line-Magnus's method revisited, Mathematics of Computation, 73(2004), pp 191-209.
  • S.B. Damelin and K. Diethelm, Numerical solution of Fredholm integral equations on the line, Journal of Integral equations and Applications, Volume 13(3), 2004, pp 273-292.
  • S.B. Damelin and P. Grabner, Numerical integration, energy and asymptotic equidistribution on the sphere, Journal of Complexity, 19(2003), pp 231-246. (Postscript) Corrigendum, Journal of Complexity, (20)(2004), pp 883-884.
  • S.B. Damelin, H.S. Jung and K.H. Kwon, Mean convergence of extended Lagrange interpolation for exponential weights, Acta Applicandae Mathematicae, 76(2003), pp 17-36.
  • S.B. Damelin, G. Michalski, G. Mullen and D.Stone, On the number of linearly independent binary vectors of fixed length with applications to the existence of completely orthogonal structures, Monatsh Math, (1)(2003), pp 1-12.
  • S.B. Damelin, Marcinkiewicz-Zygmund inequalities and the Numerical approximation of singular integrals for exponential weights: Methods, Results and Open Problems, some new, some old; Journal of Complexity, 19(2003), pp 406-415.
  • S.B. Damelin, On the maximum modulus of weighted polynomials in the plane, a theorem of Rakhmanov, Mhaskar and Saff revisited, Journal of Computational and Applied Mathematics, vol. 155 (2003), pp 455-459.
  • S.B. Damelin, Weighted polynomial approximation on discrete sets, Monatshefte fur Mathematik, (138)(2)(2003), pp 111-131.
  • S.B. Damelin, The distribution of general interpolation arrays for exponential weights, Electronic Transactions of Numerical Analysis, Volume 12, 2002, pp 12-20.
  • . Bajnok, S.B. Damelin, J. Li and G. Mullen, A constructive method of scattering points on d dimensional spheres using finite fields, Computing (Springer), 68 (2002), pp 97-109.
  • S.B. Damelin, The Hilbert transform and orthonormal expansions for exponential weights, Approximation Theory X: Abstract and Classical Analysis, Chui, Schumaker and Stoekler (eds), Vanderbilt Univ. Press (2002), pp 117-135.
  • S.B. Damelin, H.S. Jung and K.H. Kwon, Converse quadrature sum estimates for weights on the real line, Analysis, 22(2002), pp 33-55.
  • S.B. Damelin, P. Dragnev and A. Kuijlaars, The support of the equilibrium measure for a class of external fields on a finite interval, Pacific Journal of Mathematics, Volume 199 (2)(2001), pp 303-321.
  • S.B. Damelin, H.S. Jung and K.H. Kwon, Mean convergence of Hermite-Fej'er and Hermite interpolation of higher order for Freud weights, Journal of Approximation Theory, 113 (2001), pp 21-58.
  • S.B. Damelin, H.S. Jung and K.H. Kwon, A note on mean convergence of Lagrange interpolation in Lp, Journal of Computational and Applied mathematics, 133 (1-2) (2001), pp 277-282.
  • S.B. Damelin, H.S. Jung and K.H. Kwon, On mean convergence of Hermite-Fej'er and Hermite interpolation for Erdos weights on the real line, Journal of Computational and Applied Math, Volume 137 (2001), pp 71-76.
  • S.B. Damelin and K. Diethelm, Boundedness and uniform approximation of the weighted Hilbert transform on the real line, Numer. Funct. Anal. and Optimiz., 22(1 and 2) (2001), pp 13-54.
  • S.B. Damelin, H.S Jung and K.H Kwon, Necessary conditions for mean convergence of Lagrange interpolation for exponential weights, Journal of Computational and Applied Mathematics, Volume 132(2)(2001), pp 357-369.
  • L. H. Damelin, S. Volles, J. M. Whitcutt, S. B. Damelin, J. J. Alexander, Hormesis: A stress response in cells exposed to low levels of heavy metals, Human and Experimental Toxicology, Volume 19 (2000), pp 420-430.
  • S.B. Damelin, Smoothness theorems for generalized symmetric Pollakzek weights on [- 1,1], Journal of Computational and Applied Mathematics., 101 (1999), pp 87-103.
  • S.B. Damelin and K. Diethelm, Interpolatory Product quadratures for Cauchy principal value integrals with Freud weights, Numer. Math. 83 (1999), pp. 87-105.
  • S.B. Damelin, Smoothness theorems for Erdos Weights II, J. Approx. Theory., Volume 97, (1999), pp 220-239.
  • S.B. Damelin and A. Kuijlaars, The support of the extremal measure for monomial external fields on [ -1,1]., Trans.Amer.Math. Soc. 351 (1999), 4561-4584.
  • S.B. Damelin, Lagrange interpolation for non Szego weights on [-1,1], in the Proceedings of the International Workshop on Approximation Theory and Numerical Analysis., Dedicated to Prof. M. R. Occorsio, 1998, pp 10-20.
  • S.B. Damelin, A characterisation of smoothness for Freud weights, Journal of Computational and Applied Mathematics., 99(1998), pp 463-473.
  • S.B. Damelin, The weighted Lebesgue constant of Lagrange interpolation for exponential weights on [-1,1], Acta-Mathematica (Hungarica)., 81(3) (1998), pp 211-228.
  • S.B. Damelin, The Lebesgue constant of Lagrange interpolation for Erdos weights, J. Approx. Theory., Volume 94, 2, (1998), pp 235-262.
  • S.B. Damelin and D.S. Lubinsky, Jackson theorems for Erdos weights in L_p, J. Approx. Theory., Volume 94, (3) (1998), pp 333-382.
  • S.B. Damelin, Converse and smoothness theorems for Erdos weights in L_p, J. Approx. Theory., Volume 93, (3)(1998), pp 349-398.
  • S.B. Damelin and D.S. Lubinsky, Necessary and sufficient conditions for mean convergence of Lagrange interpolation for Erdos weights II, Canad. Math. J., (40) (1996), pp 737--757.
  • S.B. Damelin and D.S. Lubinsky, Necessary and sufficient conditions for mean convergence of Lagrange interpolation for Erdos weights, Canad. Math. J., (40)(1996), pp 710-736.
  • S.B. Damelin, Weighted approximation for Erdos weights, Diss. Math., Vol 1 (1996), pp 163--171.
  • S.B. Damelin, Marchaud inequalities for a class of Erdos weights, Approximation Theory VIII-Vol I (1995)., Approximation and Interpolation, Chui et al, pp 169--175.
  • D. Greenblatt and S.B. Damelin, Laminar boundary layers subject to high frequency travelling--wave fluctuations, AJAA Journal., Vol. 31, 5 (1993), pp 957--959.

    Completed manuscripts in process.

  • S. B. Damelin, D. L. Ragozin and M. Werman, Computable Metrics between Motion Group and Similarity Group Equivalence Classes of Images, manuscript.
  • S. B. Damelin, J. Levesley and R. Randall, A new algorthim to distribute points well on the sphere, manuscript..
  • Charlie Fefferman and S. B. Damelin On the Approximate and Exact Alignment of $\delta$ distorted Data in Euclidean Space II, manuscript.
  • Charlie Fefferman and S. B. Damelin, On the Approximate and Exact Alignment of $\delta$ distorted Data in Euclidean Space I, manuscript.
  • R. Raich, J. Costa, S. B. Damelin and A. Hero, Classification Constrained Dimensionality Reduction, manuscript.