Publications

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Books:

Stalking the Riemann Hypothesis, Random House/Pantheon, April, 2005.

Stalking the Riemann Hypothesis, (paperback) Pantheon Press, 2006, 304 pages, ISBN: 037542136X

Modern Signal Processing (w./ D. Healy - editors), Cambridge University Press, 2004.

Music and Computers: A Theoretical and Historical Approach (w/P. Burk, L. Polansky, d. repetto, and

M. Roberts), Key College Publishing, 2004.

Cyclic Renormalization and Automorphism Groups of Rooted Trees (w/H. Bass, M. V. Espinar, and C.

Tresser), Lecture Notes in Mathematics, Volume 1621, Springer-Verlag, NY 1996.

Film Projects:

From Mind to Machine - The Discovery of Artificial Intelligence (with W. Conquest and B. Drake), 2007.

The Math Life (with W. Conquest and B. Drake), a 51 minute documentary about the people, process, and problems of modern mathematics. Distributed by Films for the Humanities and Sciences (www.films.com) and (as of 3/10/03) to appear on at least 55% (and at most 90%) of the Public Television marketplace.

Mathematics Illuminated (host, lead content advisor, a 13 part series on mathematics, funded by the Annenberg Foundation, produced by Oregon Public Broadcasting)

Journal/Conference Publications:

· Using Hierarchical Change Mining to Manage Network Security Policy Evolution (w/G. Weaver, N. Foti, S. Bratus, and S. Smith), The Workshop on Hot Topics in Management of Internet, Cloud, and Enterprise Networks and Services (Hot-ICE '11), (2011), in press.

· Nonparametric sparsification of complex multiscale networks (w./N. Foti and James M. Hughes), PLoS ONE, 6(2): e16431. doi:10.1371/journal.pone.0016431 (2011)

· Intelligent data analysis of intelligent systems, (w./D. C. Krakauer, J. C. Flack, S. Dedeo, and D. Farmer, Advances in Intelligent Data Analysis IX 6065:8-17(2010).

· Improved IBD detection using incomplete haplotype information (w./G. Genovese, G. Leibon, and M.Pollak), BMC Genetics, 11:58 (2010).

· The packet-switching brain (w./D. Graham), J. of Cognitive Neuroscience, Early Access Posted Online March 29, 2010. (doi:10.1162/jocn.2010.21477).

· Preference for artwork: Similarity, statistics, and selling price (w. D. Graham, J. Friedenberg, and C. McCandless), in Proc. SPIE: Human Vision and Electronic Imaging 7527 (2010).

· Stylometrics of artwork: Uses and limitations (w./D. Graham and J. M. Hughes), Proc. SPIE: Computer Vision and Image Analysis of Art 7531 (2010).

· Deblurring of motionally averaged images with applications to single-particle cryo-electron microscopy, (w./G. Chirikjian, W. Park, and D. Madden), arXiv: 0710.0690, Inverse Problems, 26, Number 3, March 2010 doi: 10.1088/0266-5611/26/3/035002.

· Quantification of artistic style through sparse coding analysis in the drawings of Pieter Bruegel the Elder (w./J. Hughes and D. Graham), Proceedings of the National Academy of Sciences USA, vol. 107, no. 4, pp. 1279–1283, 2010.

· Fast Fourier transforms for the rook monoid, (w./M. Malandro) Transactions of the AMS, 362(2) pp. 1009 – 1045, (2010).

· Accurate image rotation using Hermite expansions (w./G. Chirikjian, W. Park, and G. Leibon), IEEE Transactions on Image Processing, 18(9) pp. 1988–2003, (2009).

· Mapping the similarity space of paintings: Is there a role for image statistics? (w./D. J. Graham, J. N., Friedenberg, and D. J. Field,), Visual Cognition, July 15, 2009, DOI: 10.1080/13506280902934454.

· A mathematical model for optimal tuning systems (w./L. Polansky, M.K. Johnson, D. Repetto and W. Pan), Perspectives in New Music, 47(1), p. 69–110, 2009.

· Spectral analysis for phylogenetic trees (w./P. Rinker), NIPS (2009), Workshop on Ranked Data.

· Intensity statistics of artwork: connections to human visual perception (w./ D. J. Graham, J. N. Friedenberg, and D. J. Field), SPIE, 2009. Proc. SPIE. 7240.

· Topological structures in the equities market, (w./G. Leibon, S. Pauls, R. Savell), PNAS, 105(52):20589-94, 2008.

· A fast Hermite transform, (w./G. Leibon, R. Taintor, G. Chirikjian, and W. Park), Theoretical Computer Science, 409(2): 211-228 (2008).

· Evolution of community structure in the world trade web, (w./I. Tzekina and K. Danthi), European J. Phys. B, 63, 541-545 (2008) DOI: 10.1140/epjb/e2008-00181-2

· A SNP Streak Model for the Identification of Genetic Regions Identical-by-descent, (w./G. Leibon and M.Pollak), Statistical Applications in Genetics and Molecular Biology, 7(1), Article 16 (2008). (Available at: http://www.bepress.com/sagmb/vol7/iss1/art16)

· FFTs on the Rotation Group (w./P. Kostelec), Journal of Fourier Analysis and Applications, 14(2) 145– 179, (2008).

· Multifractal analysis for Jackson Pollock (w./J. Coddington, J. Elton, and Y. Wang), SPIE 2008, Paper 6810-13.

· The Power of Strong Fourier Sampling: Quantum Algorithms for Affine Groups and Hidden Shifts (w./C. Moore, A. Russell, and L. Schulman), SIAM J. Computing, 37, 938–958 (2007)

· Steps toward Digital Authentication (w./G. Leibon), in Matematica e cultura, 2007, MIchele Emmer (ed.), Springer-Verlag.

· A Fast Hermite Transform with Applications to Protein Structure Determination (w./G. Leibon and G. Chirikjian), Proceedings of 2007 International Workshop on Symbolic-Numeric Computation, ACM, 117–124 (2007).

· Generic Quantum Fourier Transforms (w./C. Moore and A. Russell), ACM Transactions on Algorithms, 2(4), pp. 707–723, 2006.

· Stochastic Analysis of Geometric Image Processing Using B-Splines, (w./ G. Rohde, D. Healy, C. Bernstein, A. Aldroubi), Proceedings of 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 1017-1020, 2006.

· A Digital Technique for Authentication in the Digital Arts (w./S. Lyu and H. Farid), International Foundation for Art Research Journal, spring, 2006.

· Wavelet Analysis for Authentication,” (w./S. Lyu and H. Farid), Art+Math = X, Conference on the interface of Art and Mathematics, CU, Boulder, June 2005

· A Digital Technique for Art Authentication (w./S. Lyu and H. Farid), PNAS, vol. 101 (49), pp. 17006-17010 (2004).

· Rooted trees and iterated wreath products of cyclic groups (with R. Orellana and D. Rockmore), Adv. in Appl. Math., 33(3) (2004), 531-547.

· Sharing Neuroimaging Studies of Human Cognition, (w./ J. D. Van Horn, S. T. Grafton, and M. S. Gazzaniga), Nature Neuroscience, 7, (2004), 473–481.

· Computing isotypic projections with the Lanczos iteration (w./ D. Maslen and M. Orrison) SIAM J. Matrix Analysis and Appplications PDF version 25 (3), 784--803, (2004).

• R. Foote, G. Mirchandani, and D. Rockmore, "Two-dimensional wreath product transforms" PDF version J. Symbolic Computation 37 (2) pp. 187--207, (2004).

• Towards Safe and Effective High-Order Legendre Transforms with Applications to FFTs for the 2-sphere (w/ D. M. Healy, Jr. and P. Kostelec) PDF version Advances in Computational Mathematics 21 (1-2): 59-105, July 2004
• Generic Quantum FFTs" PDF version (w/ C. Moore and A. Russell) Proceedings of ACM-SIAM Symposium On Discrete

Algorithms. 2004, pp. 771-780.

• The Hidden Subgroup Problem in Affine Groups: Basis Selection in Fourier Sampling (w/ C. Moore, A. Russell, and L. Schulman), PDF version Proceedings of ACM-SIAM Symposium On Discrete Algorithms. 2004, pp. 1106--1115.

• Recent Progress and Applications in Group FFTs, PDF version In Advanced Study Institute on Computational Noncommutative Algebra and Applications, J. Byrnes, ed., Kluwer Acad. Pub., Netherlands, (2004) pp. 227--254.

• FFTs for the 2-Sphere-Improvements and Variations (w/ D. M. Healy, Jr., P. Kostelec, and S. Moore) PDF version Journal of Fourier Analysis and Applications 9 4: 341--385, July 2003

• Eigenvalues spacings for quantized cat maps (w/A. Gamburd and J. Lafferty), J. Phys A, 36 (2003), no. 12, 3487–3499.

• Recent Progress and Applications of Group FFTs, 36th Asilomar Conference on Signals and Systems, IEEE Publications, January, 2003.

• Landscapes on spaces of trees (w/ O. Bastert, P. Stadler, and G. Tinhofer,) Appl. Math. Comput., 131 (2002), no. 2-3, 439--459.

• Fast Fourier transforms for fitness landscapes (w/ W. Hordijk, P. Kostelec, and P. Stadler), Applied and Computational Harmonic Analysis, 12 No. 1, Jan 2002, pp. 57-76.

• Description of an interactive, sound making online computer music tutorial web book, International Conference Music and Computers 2002 Short Paper/Demo, Voices of Nature Conference, Goeborg (w./P. Burk, L. Polansky, d. repetto, M. Roberts)

• The Cooley-Tukey FFT and group theory (with D. Maslen) Notices Amer. Math. Soc. 48 (10), 2001, pp. 1151 –1160.

• Nonlinear approximation theory on finite groups (w/ K.-L. Kueh, T. Olson, and K.-S. Tan,) PDF version Postscript version J. Fourier Analysis and Appl., 7 No. 3, 2001, pp. 257–281

• Lesion Size Estimation Using Warped Registration of Interval Images, (w./J.B. Weaver, S. Periaswamy, H. Farid, D.N. Rockmore, C.J. Kasales, W. Black, D.M. Healy, Jr.), Proceedings of the Society of Magnetic Resonance, Glasgow, UK, April, 2001, p. 795

• The Functional Magnetic Resonance Imaging Data Center (fMRIDC): The Challenges and rewards of large-scale databasing of neuroimaging studies (w/ J. Van Horn, J. Grethe, P. Kostelec, J. Woodward, J.B., J. Aslam, D. Rus, and M. S. Gazzaniga), Philosophical Transactions of the Royal Society, 356 No. 1412 (2001).

• The FFT - An algorithm the whole family can use PDF version Postscript version Computing in Science & Engineering, January/February 2000, 2, Number 1, pp. 60--64.

• A wreath product group approach to signal and image processing: Part II – convolutions, correlations, and applications (w/ R. Foote, G. Mirchandani, D. Healy and T. Olson ),, IEEE Trans. in Signal Processing, 48(3), 2000, pp. 749--767.

• "A wreath product group approach to signal and image processing: Part I -- multiresolution analysis " (w/ R. Foote, G. Mirchandani, D. Healy and T. Olson ), IEEE Trans. in Signal Processing, 48(1), 2000, pp. 102--132

• "Double coset decompositions and computational harmonic analysis on groups," (w/D. Maslen), J. Fourier Analysis and Applications, 6(4), 2000, pp. 349—388

· FFTs for tensor and vector harmonics on the 2-sphere (with D. Healy, D. Maslen and P. Kostelec), J. Computational Physics, 162, 2000, pp. 514–535.

• A National Data Center for the Storage and Retrieval of Neuroimaging Data (w./J. Aslam, D. Rus, P. Kostelec, J. Grethe, R. Fendrich, S. Grafton, and M. Gazzaniga. Society for Neuroscience Abstracts, 26(2):2235, 2000

• Codes and iterative decoding on algebraic expander graphs (w./J. Lafferty) ISITA 2000.

• Differential Affine Motion Estimation for Medical Image Registration (w./S. Periaswamy, J. Weaver, D. Healy, P. Kostelec and H. Farid), presented at SPIE 2000, August 2000.

• A rhomboidal local cosine transform (w/D. Healy and D. Warner), presented at SPIE 2000, August 2000.

• Wreath Product Cyclic Group-Based Convolution: A New Class of Noncommutative Filters (w/G. Mir- chandani, R. Foote, D. Healy and T. Olson) ICASSP 2000, Istanbul, Turkey

· A Combinatorial Description of the Spectrum of the Tsetlin Library and its Generalization to Hyperplane Arrangements (w/P. Bidigare, P. Hanlon), Duke J. Math., 99(1), 1999, pp. 135–174.

• "Deciding Finiteness for Matrix Groups over Function Fields" (w/K.-S. Tan, R. Beals), Israel J. Math. 109, 1999, pp. 93–116.

· Level spacings for Cayley graphs (with J. Lafferty), in Emerging Applications of Number Theory, D. Hejhal (ed.), Institute for Mathematics and its Applications, Volume 109, 1999, pp. 373–386.

• "Some applications of generalized FFTs" in Proceedings of the DIMACS Workshop on Groups and Computation, June 7-10, 1995 eds. L. Finkelstein and W. Kantor, (1997) 329--369.

• "Generalized FFTs -- A survey of some recent results" (w/D. Maslen) Proceedings of the DIMACS Workshop on Groups and Computation, June 7-10, 1995 eds. L. Finkelstein and W. Kantor, (1997) 183--237.

• "Separation of Variables and the Computation of Fourier Transforms on Finite Groups, I" (w/D. Maslen) Journal of the American Math Society, 1 (10) (1997) 169--214.

• "Fast Polynomial Transforms with Applications to Data Analysis for Distance Transitive Graphs" (w/ J. Driscoll and D. Healy) SIAM J. Comp. 26, (1997), pp. 1066--1099.

• The *-product in kneading theory (w/ K. Brucks, R. Galeeva, P. Mumbre, and C. Tresser), Fundamenta Math. 152, 1997, pp. 189–209.

• J. Lafferty and D. Rockmore, "Spectral Techniques for Expander Codes" , 1997 STOC, pp. 160—167.

• A Smooth Non-Rectangular Time-Frequency Segmentation of L²(R²) (w/D. Warner and D. Healy), ICIP ’97

• Spectral Techniques for Expander Codes and Generalized Cyclic Codes (with J. Lafferty) in ISIT 97

· An FFT for the 2-sphere and applications (w/ D. Healy and S. Moore), in ICASSP 96

• Wreath Products for Image Processing (w/D. Healy and T. Olson) in ICASSP 96

• An FFT for the 2-sphere and imaging applications (with D. Healy and S. Moore) in IMDSP96

• "Fast Fourier Transforms for Wreath Products", J. Applied and Computational Harmonic Analysis, 2, (1995) 279--292.

• "Numerical Investigation of the Spectrum for Certain Families of Cayley Graphs" (w/ J. Lafferty) DIMACS Series in Disc. Math. and Theor. Comp. Sci., Volume 10, J. Friedman, ed., (1993), 63-73. (Note: the postscript is WITHOUT the figures. We are happy to provide reprints which contain them.)

• "A Note on the Order of Finite Subgroups of GL(n,Z)" (w/ K.-S. Tan), Arch. der Math., Vol 64, 283-288 (1995)

• Adapted diameters and the efficient computation of Fourier transforms on finite groups (w/D. Maslen), Proceedings of 1995 ACM-SIAM Symposium on Discrete Algorithms, pp. 253--262.

• Fast Fourier inversion for finite groups. J. of Assoc. of Comp. Mach., 41(1) (1994) 31-66.

• "Efficient Computation of Isotypic Projections for the Symmetric Group" (w/P. Diaconis), DIMACS Series in Disc. Math. and Theor. Comp. Sci., Volume 11, L. Finkelstein and W. Kantor (eds.), (1993), 87-104.

• Deciding finiteness of matrix groups in deterministic polynomial time (w/L. Babai and R. Beals). Proc. of 1993 ISSAC, 117-126.

• Symmetry stabilization for fast discrete monomial transforms and polynomial evaluation. (w/S. Moore and D. Healy). Lin. Alg. and Appl., 192 (1993) 249-299.

• Renormalization for the n-torus. (w/V. Baladi, N. Tongring, and C. Tresser). Nonlinearity, 5 (1992), 1111-1136.

• Computation of L-series for elliptic curves over function fields, (w/ K.-S. Tan), Crelle’s Jour., 424 (1992), 107-135.

• Even n-colorings of the integers, flows on the n-torus, continued fractions and renormalization. (w/R. Siegel, N. Tongring, and C. Tresser) Chaos, 1 (1991), 25-30.

• Efficient computation of Fourier transforms on finite groups, (w/P. Diaconis), Journal of the American Mathematical Society, 3 (1990), 297-332

• "Fast Fourier Analysis for Abelian Group Extensions" , Adv. in Appl. Math., Vol 11, 164-204 (1990)

• Computation of Fourier transforms on the symmetric group, Proceedings of 1989 Conference on Computers and Mathematics, Springer-Verlag, NY, 1989, 156-165.

Preprints/Papers in Revision

· Stability of the world trade network over time: an extinction analysis (w/ N. Foti, and S. Pauls), in revision.

· Partition decoupling for multi-gene analysis of gene expression profiling data (w/R. Braun, G. Leibon, and Scott Pauls), in revision.

· Partition decomposition for roll call data (w/M. Herron, G. Leibon, S. Pauls, and R. Savell), in revision.

· Robustness and contagion in the international financial network (w/T. Dette and S. Pauls), in revision

· A simple computational method for the identification of disease- associated loci in complex pedigrees” (w./M. Pollak and G. Leibon),, arXiv:0710.5625.

· Data Mining and Network Analysis in the Life and Social Sciences: Potential Opportunities for the DoD and National Security, in IDA Paper P-3704, Defense Science Study Group 2000-2001 Papers 1-11,

· December 2002.

· Ruffles and the turning point algebra (with P. Doyle), number to be assigned.

· Computation of Fourier transforms on the symmetric group, Proceedings of 1989 Conference on Computers and Mathematics, Springer-Verlag, NY, 1989, 156-165.

Expository Work

• D. Rockmore, "Are you my Mother...Tongue?" PDF version SFI Bulletin, to appear
• D. Rockmore, "Network Research: Thinking about the web requires a web of thinking" PDF version For SFI End of year report, Spring 2003

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