Doug Hardin

Publications

Books

  • A. Statnikov, C. F. Aliferis, D. P Hardin, and I. Guyon, A Gentle Introduction to Support Vector Machines in Biomedicine, Volume 2: Case Studies, World Scientific, 2013.

Articles

2013

  • A. V. Bondarenko, D. P. Hardin, and E. B. Saff , Minimal N-Point Diameters and f-Best-
    Packing Constants in Rd, Proc. Amer. Math. Soc (2011), accepted for publication.  PDF
  • L. Baratchart, D.P. Hardin, E.A. Lima, E.B. Saff, and B.P. Weiss, Characterizing Kernels of Operators Related to Thin Plate Magnetizations via Generalizations of Hodge Decompositions, Inverse Problems 29 (2013), 015004. PDF

2012

  • D. P. Hardin, E. B. Sa ff, and J. T. Whitehouse, Quasi-uniformity of Minimal Weighted Energy
    Points, Journal of Complexity 28 (2012), 177-191. PDF
  • L. Brown, I. Tsamardinos, and D. P. Hardin, To Feature Space and Back: Identifying Top
    Weighted Features in Polynomial Support Vector Machines Models, Intelligent Data Analysis
    16 (2012), 551–579.  PDF
  • J. S. Brauchart, D. P. Hardin, and E. B. Saff, The Next-Order Term for Minimal Riesz and Logarithmic Energy Asymptotics on the Sphere, Contemp. Math. 578 (2012), 31–61.
  • J. S. Brauchart, D. P. Hardin, and E. B. Saff, Discrete Energy Asymptotics on a Riemannian Circle, Uniform Distribution Theory 7 (2012), 77–108.

 

2009

  • J. S. Brauchart, D. P. Hardin, and E. B. Saff , The Riesz energy of the N-th roots of unity: an
    asymptotic expansion for large N, Bull. Lond. Math. Soc. 41 (2009), 621-633.
  • M. T. Calef and D. P. Hardin, Riesz s-equilibrium measures on d-recti able sets as s approaches d, Potential Analysis 30 (2009), 385-401.
  • S. Borodachov, D. P. Hardin, and E. B. Saff , Asymptotics of Weighted Best-Packing on Rec-
    ti able Sets, Matematicheskii Sbornik 199 (2009), 1579-1595.
  • J. Brauchart, D. P. Hardin, and E. B. Saff, Riesz Energy and Sets of Revolution in R3, Con- temporary Mathematics 481 (2009), 47–57.

2008

  • S. Borodachov, D. P. Hardin, and E. B. Saff , On asymptotics of the weighted Riesz energy for recti fiable sets, Trans. Amer. Math. Soc. 360 (2008), 1559-1580.

2007

  • A. Aldroubi, C. Cabrelli, D. P. Hardin, and U. Molter, Optimal Shift invariant spaces and their Parseval frame generators, Appl. Comp. Harm. Anal. 23 (2007), 273-283.
  • J. Brauchart, D. P. Hardin, and E. B. Saff , The support of the limit distribution of optimal
    Riesz energy points on sets of revolution in R3, J. Math. Phys. 48 (2007), no. 12, 122901.
  • S. Borodachov, D. P. Hardin, and E. B. Saff, Asymptotics of Best-Packing on Rectifiable Sets, Proc. Amer. Math. Soc. 135 (2007), 2369–2380.
  • D. P. Hardin, E. B. Saff, and H. Stahl, The support of the logarithmic equilibrium measure on sets of revolution in R3, J. Math. Phys. 48 (2007), 022901–022914.

2006

 

2005

    • Y. Aphinyanaphongs, C. Aliferis, I. Tsamardinos, A. Statnikov, and D. P. Hardin, Text Cat- egorization Models For Retrieval of High Quality Articles in Internal Medicine, J. Am. Med. Inform. Assoc. 12 (2005), 207–216.
    • D. P. Hardin and E. B. Saff, Minimal Riesz energy point configurations for rectifiable d- dimensional manifolds, Adv. Math. 193 (2005), 174–204.
    • A. Statnikov, C. F. Aliferis, I. Tsamardinos, D. P. Hardin, and S. Levy, A Comprehensive Evaluation of Multicategory Classification Methods for Microarray Gene Expression Cancer Diagnosis, Bioinformatics 21 (2005), 631–643.

    • 2004

  • D. P. Hardin and E. B. Saff, Discretizing manifolds via minimum energy points, Notices of the Amer. Math. Soc. (2004), to appear. (Warning: this is a 19.6MB file.) PDF
  • D. P. Hardin and E. B. Saff, Minimal Riesz energy point configurations for rectifiable d-dimensional manifolds, Advances in Math. (2004), to appear. PDF
  • A. Statnikov, C. F. Aliferis, I. Tsamardinos, D. P. Hardin, and S. Levy, Bioinformatics (2004), to appear. PDF
  • D. P. Hardin, C. Aliferis, and I. Tsamardinos, A Theoretical Characterization of SVM-Based Feature Selection, 2004 International Conference on Machine Learning (ICML) (St. Augustine, FL, 2004), Proceedings of the ICML-2004, 2004, to appear. PDF
  • D. P. Hardin, T. A. Hogan, and Q. Sun, The matrix-valued Riesz lemma and local orthonormal bases in shift-invariant spaces, Adv. Comput. Math. 20 (2004), no. 4, 367-384. PDF

    2003

  • D. P. Hardin and D. Hong, Construction of wavelets and prewavelets over triangulations, J. Comput. Appl. Math. 155 (2003), no. 1, 91-109. PDF
  • D. P. Hardin and B. Kessler, Orthogonal macroelement scaling vectors and wavelets in 1-D, Arab. J. Sci. Eng. Sect. C Theme Issues 28 (2003), no. 1, 73-88. Invited paper for special issue: Wavelet and fractal methods in science and engineering, Part I.
  • D. P. Hardin, Orthogonal piecewise polynomial wavelets, International Conference on Wavelets and its Applications (Chennai, India, anuary 4), Wavelets and Their Applications (M. Krishna, R. Radha, and S. Thangavelu, eds.), Allied Publishers Pvt. Ltd, 2003, pp. 171-182.
  • A. Aldroubi, C. Cabrelli, D. P. Hardin, U. Molter, and A. Rodado, Determining sets of shift invariant spaces, International Conference on Wavelets and its Applications (Chennai, India, anuary 4), Wavelets and Their Applications (M. Krishna, R. Radha, and S. Thangavelu, eds.), Allied Publishers Pvt. Ltd, 2003, pp. 171-182.
  • C. F. Aliferis, I. Tsamardinos, P. Massion, A. Statnikov, N. Fananapazir, and D. P. Hardin, Machine Learning Models For Classification Of Lung Cancer and Selection of Genomic Markers Using Array Gene Expression Data, 16th International Florida Artificial Intelligence Research Society (FLAIRS) Conference (St. Augustine, FL, 2003), Proceedings of the 16th International Florida Artificial Intelligence Research Society (FLAIRS) Conference, 2003, pp. 67-71. 4
  • C. F. Aliferis, I. Tsamardinos, P. Massion, A. Statnikov, and D. P. Hardin, Why Classification Models Using Array Gene Expression Data Perform So Well: A Preliminary Investigation Of Explanatory Factors, 2003 International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences (METMBS) (Las Vegas, Nev., 2003), Proceedings of the 2003 International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, 2003, pp. 47-53.

    2002

  • G. C. Donovan, J. S. Geronimo, and D. P. Hardin, Squeezable orthogonal bases: accuracy and smoothness, SIAM J. Numer. Anal. 40 (2002), no. 3, 1077-1099. PDF
  • K. Attakitmongcol, D. P Hardin, and D. M. Wilkes, Multiwavelet Prefilters II: Optimal orthogonal prefilters, IEEE Trans. Image Proc. 10 (2002), 1476-1487.
  • C. F. Aliferis, D. P. Hardin, and P. Massion, Machine Learning Models For Lung Cancer Classification Using Array Comparative Genomic Hybridization, American Medical Informatics Association (AMIA) Annual Symposium (San Antonio, TX, 2002), Proceedings of the 2002 American Medical Informatics Association (AMIA) Annual Symposium, 2002, pp. 7-11.
  • D. P. Hardin, Wavelets are piecewise fractal interpolation functions, Fractals in multimedia (Minneapolis, MN, 2001), 2002, pp. 121-135.
  • D. Bruff and D. P. Hardin, Squeezable bases and semi-regular multiresolutions, Wavelet analysis (Hong Kong, 2001), 2002, pp. 9-22.
  • D. P. Hardin and T. A. Hogan, Constructing orthogonal refinable function vectors with prescribed approximation order and smoothness, Wavelet analysis and applications (Guangzhou, 1999), 2002, pp. 139-148.

    2001

  • K. Attakitmongcol, D. P. Hardin, and D. M. Wilkes, Optimal prefilters for the multiwavelet filter banks, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) , Salt Lake City, 2001, 2001.
  • J. S. Geronimo and D. P. Hardin, Squeezable bases and orthogonal wavelets on irregular grids, Wavelet applications in signal and image processing IX, (San Diego, CA 2001), 2001, pp. 263� 270.

    2000

  • D. P. Hardin and T. A. Hogan, Refinable subspaces of a refinable space, Proc. Amer. Math. Soc. 128 (2000), no. 7, 1941-1950. PDF
  • G. C. Donovan, J. S. Geronimo, and D. P. Hardin, Compactly supported, piecewise affine scaling functions on triangulations, Constr. Approx. 16 (2000), no. 2, 201-219. PDF
  • ] T. Dinsenbacher, G. Rhode, D. P. Hardin, A. Aldroubi, and B. Dawant, Multiscale nonrigid data registration with automatic point selection, Wavelet applications in signal and image processing VIII, (San Diego, CA 2000, 2000, pp. 1076�1083.

    1999

  • T. B. Dinsenbacher and D. P. Hardin, Multivariate nonhomogeneous refinement equations, J. Fourier Anal. Appl. 5 (1999), no. 6, 589-597.
  • G. C. Donovan, J. S. Geronimo, and D. P. Hardin, Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets, SIAM J. Math. Anal. 30 (1999), no. 5, 1029-1056. PDF
  • D. P. Hardin and J. A. Marasovich, Biorthogonal multiwavelets on [?1, 1], Appl. Comput. Harmon. Anal. 7 (1999), no. 1, 34-53. PDF
  • G. Donovan, J. S. Geronimo, and D. P. Hardin, Construction of orthogonal multiwavelets using fractal interpolation functions, Self-similar systems (Dubna, 1998), 1999, pp. 71-78.
  • G. C. Donovan, J. S. Geronimo, and D. P. Hardin, Orthogonal multiwavelet constructions: 101 things to do with a hat function, Advances in wavelets (Hong Kong, 1997), 1999, pp. 187-197.

    1998

  • D. P. Hardin and D. Roach, Multiwavelet prefilters I: Orthogonal prefilters preserving approximation order p � 2, IEEE Trans. Circ. and Sys. II: Anal. and Dig. Sign. Proc. 45 (1998), no. 8, 1106-1112.
  • T. B. Dinsenbacher and D. P. Hardin, Nonhomogeneous refinement equations, Wavelets, multiwavelets, and their applications (San Diego, CA, 1997), 1998, pp. 117-127.
  • D. P. Hardin and D. Roach, Semi-orthogonal wavelets for elliptic variational problems, Proc. Tangier 98 International Wavelet Conference on Multiscale Methods, INRIA, 1998, pp. 6.

    1997

  • G. C. Donovan, J. S. Geronimo, and D. P. Hardin, Squeezable orthogonal bases and adaptive least squares, Wavelet applications in signal and image processing V, (San Diego, CA 1997), 1997, pp. 48�54.

    1996

  • G. C. Donovan, J. S. Geronimo, and D. P. Hardin, Intertwining multiresolution analyses and the construction of piecewise-polynomial wavelets, SIAM J. Math. Anal. 27 (1996), no. 6, 1791- 1815.
  • X.-G. Xia, J. S. Geronimo, D. P. Hardin, and B. Suter, Design of prefilters for discrete multiwavelet transforms, IEEE Trans. Sig. Proc. 44 (1996), 251-35.
  • G. C. Donovan, J. S. Geronimo, D. P. Hardin, and P. R. Massopust, Construction of orthogonal wavelets using fractal interpolation functions, SIAM J. Math. Anal. 27 (1996), no. 4, 1158- 1192.
  • G. C. Donovan, J. S. Geronimo, D. P. Hardin, and B. Kessler, Construction of two-dimensional multiwavelets on a triangulation, Wavelet applications in signal and image processing IV, (Denver, CO, 1996), 1996, pp. 98�108.
  • G. C. Donovan, J. S. Geronimo, and D. P. Hardin, Constructing orthogonal spline wavelets, Proceedings of Advances in Scientific Computing & Modeling, 1996, pp. 134�138.

    1995

  • G. C. Donovan, J. S. Geronimo, and D. P. Hardin, A class of orthogonal multiresolution analyses in 2D, Mathematical methods for curves and surfaces (Ulvik, 1994), 1995, pp. 99- 110.
  • G. C. Donovan, J. S. Geronimo, and D. P. Hardin, C 0 spline wavelets with arbitrary approximation order, Wavelet applications in signal and image processing, III (San Diego, CA, 1995), 1995, pp. 376�380.

    1994

  • J. S. Geronimo, D. P. Hardin, and P. R. Massopust, Fractal functions and wavelet expansions based on several scaling functions, J. Approx. Theory 78 (1994), no. 3, 373-401. PDF
  • J. S. Geronimo, D. P. Hardin, and P. R. Massopust, Fractal Surfaces, Multiresolution Analyses and Wavelet Transforms, NATO ASI Series F 126 (1994), 275-294.
  • J. S. Geronimo, D. P. Hardin, and P. R. Massopust, An application of Coxeter groups to the construction of wavelet bases in R n, Fourier analysis (Orono, ME, 1992), 1994, pp. 187-196.
  • G. C. Donovan, J. S. Geronimo, and D. P. Hardin, Fractal Functions, Splines, Intertwining Multiresolution Analysis, and Wavelets, Wavelet applications in signal and image processing, III (San Diego, CA, 1994), 1994, pp. 238�243.

    prior to 1994

  • D. P. Hardin and P. R. Massopust, Fractal interpolation functions from R n into Rm and their projections, Z. Anal. Anwendungen 12 (1993), no. 3, 535-548.
  • J. S. Geronimo and D. P. Hardin, Fractal interpolation surfaces and a related 2-D multiresolution analysis, J. Math. Anal. Appl. 176 (1993), no. 2, 561-586. PDF
  • D. P. Hardin, B. Kessler, and P. R. Massopust, Multiresolution analyses based on fractal functions, J. Approx. Theory 71 (1992), no. 1, 104-120.
  • A. Deliu, J. S. Geronimo, R. Shonkwiler, and D. P. Hardin, Dimensions associated with recurrent self-similar sets, Math. Proc. Cambridge Philos. Soc. 110 (1991), no. 2, 327-336.
  • G. S. Strang and D. P. Hardin, A thousand points of light, College Mathematics Journal 21 (1991), no. 2, 327-336.
  • G. S. Strang and D. P. Hardin, A thousand points of light, Proceedings of the 1990 Conference on Technology in Collegiate Mathematics Contributed Papers, 1991, pp. 4.
  • D. P. Hardin, P. Takac, and G. Webb, Dispersion population models discrete in time and continuous in space, J. Math. Biol. 28 (1990), no. 1, 406 -409.
  • M. F. Barnsley and D. P. Hardin, A Mandelbrot set whose boundary is piecewise smooth, Trans. Amer. Math. Soc. 315 (1989), no. 2, 641-659. PDF
  • M. F. Barnsley, J. Elton, D. P. Hardin, and P. Massopust, Hidden variable fractal interpolation functions, SIAM J. Math. Anal. 20 (1989), no. 5, 1218-1242.
  • J. S. Geronimo and D. P. Hardin, An exact formula for the measure dimensions associated with a class of piecewise linear maps, Constr. Approx. 5 (1989), no. 1, 89-98. Fractal approximation.
  • M. F. Barnsley, J. Elton, and D. P. Hardin, Recurrent iterated function systems, Constr. Approx. 5 (1989), no. 1, 3-31.
  • D. P. Hardin, P. Takac, and G. Webb, A comparison of dispersal strategies for survival of spatially heterogeneous populations, SIAM J. Appl. Math. 48 (1988), no. 6, 1396-1423. PDF
  • D. P. Hardin, P. Takac, and G. F. Webb, Asymptotic properties of a continuous-space discretetime population model in a random environment, J. Math. Biol. 26 (1988), no. 4, 361-374.
  • D. P. Hardin and P. R. Massopust, The capacity for a class of fractal functions, Comm. Math. Phys. 105 (1986), no. 3, 455-460.
  • M. F. Barnsley, V. Ervin, D. P. Hardin, and J. Lancaster, Solution of an inverse problem for fractals and other sets, Proc. Nat. Acad. Sci. U.S.A. 83 (1986), no. 7, 1975-1977.
  • D. P. Hardin and J. V. Herod, Solutions for model Boltzmann equations proposed by Ziff, Differential equations (Birmingham, Ala., 1983), 1984, pp. 285�291.
  • J. R. Jones and D. P. Hardin, A dual-ported, dual-polarized Spherical Near-Field probe, Proc. Ant. App. Symp., 1983, pp. 15.
  • J. R. Jones and D. P. Hardin, A dual-ported, dual-polarized Spherical Near-Field probe, Proc. AMTA, 1983, pp. 14.

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