Publications of Doug Hardin

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Refereed Publications

Journal Publications

  1. 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

  2. D. P. Hardin and E. B. Saff, Minimal Riesz energy point configurations for rectifiable d-dimensional manifolds, Advances in Math. (2004), to appear. PDF

  3. A. Statnikov, C. F. Aliferis, I. Tsamardinos, D. P. Hardin, and S. Levy, Bioinformatics (2004), to appear. PDF

  4. 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

  5. D. P. Hardin and D. Hong, Construction of wavelets and prewavelets over triangulations, J. Comput. Appl. Math. 155 (2003), no. 1, 91-109. PDF

  6. 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.

  7. 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

  8. K. Attakitmongcol, D. P Hardin, and D. M. Wilkes, Multiwavelet Prefilters II: Optimal orthogonal prefilters, IEEE Trans. Image Proc. 10 (2002), 1476-1487.

  9. D. P. Hardin and T. A. Hogan, Refinable subspaces of a refinable space, Proc. Amer. Math. Soc. 128 (2000), no. 7, 1941-1950. PDF

  10. 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

  11. T. B. Dinsenbacher and D. P. Hardin, Multivariate nonhomogeneous refinement equations, J. Fourier Anal. Appl. 5 (1999), no. 6, 589-597.

  12. 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

  13. D. P. Hardin and J. A. Marasovich, Biorthogonal multiwavelets on [?1, 1], Appl. Comput. Harmon. Anal. 7 (1999), no. 1, 34-53. PDF

  14. D. P. Hardin and D. Roach, Multiwavelet prefilters I: Orthogonal prefilters preserving approximation order p ² 2, IEEE Trans. Circ. and Sys. II: Anal. and Dig. Sign. Proc. 45 (1998), no. 8, 1106-1112.

  15. 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.

  16. 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.

  17. 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.

  18. 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

  19. 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.

  20. 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.

  21. 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

  22. D. P. Hardin, B. Kessler, and P. R. Massopust, Multiresolution analyses based on fractal functions, J. Approx. Theory 71 (1992), no. 1, 104-120.

  23. 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.

  24. G. S. Strang and D. P. Hardin, A thousand points of light, College Mathematics Journal 21 (1991), no. 2, 327-336.

  25. 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.

  26. 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

  27. 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.

  28. 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.

  29. M. F. Barnsley, J. Elton, and D. P. Hardin, Recurrent iterated function systems, Constr. Approx. 5 (1989), no. 1, 3-31.

  30. 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

  31. 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.

  32. D. P. Hardin and P. R. Massopust, The capacity for a class of fractal functions, Comm. Math. Phys. 105 (1986), no. 3, 455-460.

  33. 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.

    Submitted or in manuscript



  34. Y. Aphinyanaphongs, C. Aliferis, I. Tsamardinos, A. Statnikov, and D. P. Hardin, Text Categorization Models For Retrieval of High Quality Articles in Internal Medicine, J. Amer. Med. Inf. Assoc. (2004), submitted, conditionally accepted. MS-WORD DOC

  35. T. N. T. Goodman and D. P. Hardin, Refinable shift-invariant spaces of spline functions (expected submission, Oct., 2004).

  36. D. P. Hardin and T. A. Hogan, Shift-invariant spaces in terms of kernels of difference operators: minimal support and refinability (expected submission, Oct., 2004). (2001) manuscript, currently in revision.

    Publications in Refereed Conference Proceedings and Edited Volumes



  37. 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

  38. 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.

  39. 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.

  40. 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.

  41. 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

  42. 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.

  43. D. P. Hardin, Wavelets are piecewise fractal interpolation functions, Fractals in multimedia (Minneapolis, MN, 2001), 2002, pp. 121-135.

  44. D. Bruff and D. P. Hardin, Squeezable bases and semi-regular multiresolutions, Wavelet analysis (Hong Kong, 2001), 2002, pp. 9-22.

  45. 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.

  46. 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.

  47. 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.

  48. 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.

  49. T. B. Dinsenbacher and D. P. Hardin, Nonhomogeneous refinement equations, Wavelets, multiwavelets, and their applications (San Diego, CA, 1997), 1998, pp. 117-127.

  50. 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.

  51. 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.

    PUBLICATIONS-unrefereed Conference Proceedings



  52. 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.

  53. 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.

  54. 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.

  55. 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.

  56. 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.

  57. 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.

  58. 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.

  59. 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.

  60. 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.

  61. D. P. Hardin and J. V. Herod, Solutions for model Boltzmann equations proposed by Ziff, Differential equations (Birmingham, Ala., 1983), 1984, pp. 285-291.

  62. J. R. Jones and D. P. Hardin, A dual-ported, dual-polarized Spherical Near-Field probe, Proc. Ant. App. Symp., 1983, pp. 15.

  63. J. R. Jones and D. P. Hardin, A dual-ported, dual-polarized Spherical Near-Field probe, Proc. AMTA, 1983, pp. 14.

    IN PREPARATION



  64. S. Borodachov, D. P. Hardin, and E. B. Saff, On asymptotics of the weighted Riesz energy for rectifiable sets (2004), in preparation.

  65. D. Bruff, J. S. Geronimo, and D. P. Hardin, Orthogonal wavelets on irregular 1 ?d grids: the golden mean multiresolution (2004), in preparation.

  66. G. C. Donovan, J. S. Geronimo, D. P. Hardin, and B. Kessler, A wavelet construction on 2-D triangulations (2004), in preparation.

  67. T. N. T. Goodman and D. P. Hardin, Symmetric shift-invariant spaces (2004), in preparation.

  68. D. P. Hardin, E. B. Saff, and H. Stahl, The support of the s-Riesz energy equilibrium measure for sets of rotation (2004), in preparation.