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* ''Optimal detection.'' In the field of [[detection theory]], Marks and his colleagues developed the first closed form solution for the [[Neyman&ndash;Pearson lemma|Neyman–Pearson]] optimal detection of signals in non-[[Gaussian noise]]<ref>S. A. Kassam, Signal Detection in Non-Gaussian Noise. Springer Verlag, 1988.</ref><ref>[http://marksmannet.com/RobertMarks/REPRINTS/1978_DetectionInLaplaceNoise.pdf Detection in Laplace noise] R.J. Marks II, G.L. Wise, D.G. Haldeman and J.L. Whited, IEEE Transactions on Aerospace and Electronic Systems, vol. AES-14, pp. 866&ndash;872 (1978).</ref>
* ''Optimal detection.'' In the field of [[detection theory]], Marks and his colleagues developed the first closed form solution for the [[Neyman&ndash;Pearson lemma|Neyman–Pearson]] optimal detection of signals in non-[[Gaussian noise]]<ref>S. A. Kassam, Signal Detection in Non-Gaussian Noise. Springer Verlag, 1988.</ref><ref>[http://marksmannet.com/RobertMarks/REPRINTS/1978_DetectionInLaplaceNoise.pdf Detection in Laplace noise] R.J. Marks II, G.L. Wise, D.G. Haldeman and J.L. Whited, IEEE Transactions on Aerospace and Electronic Systems, vol. AES-14, pp. 866&ndash;872 (1978).</ref>
{{quotation| Marks, Wise, Haldeman and Whited have derived exact expressions for the test statistic distribution functions, and thus were able to analyze the performance of the optimal detector for given values of signal strength and sample size.<ref>M. W. Thompson, D. R. Halverson and G. L. Wise. "Robust Detection in Nominally Laplace Noise." IEEE Transactions on Communications, Volume 42 Issue 2-4, pp. 1651&ndash;1660, Feb&ndash;Apr. 1994 </ref>}}
{{quotation| Marks, Wise, Haldeman and Whited have derived exact expressions for the test statistic distribution functions, and thus were able to analyze the performance of the optimal detector for given values of signal strength and sample size.<ref>M. W. Thompson, D. R. Halverson and G. L. Wise. "Robust Detection in Nominally Laplace Noise." IEEE Transactions on Communications, Volume 42 Issue 2-4, pp. 1651&ndash;1660, Feb&ndash;Apr. 1994 </ref>}}
* ''Power load forecasting using neural networks.'' With his colleagues at the [[University of Washington]], Marks was the first<ref name=ANNSTLF> A. Khotanzad, R. Afkhami-Rohani, Lu Tsun-Liang, A. Abaye, M. Davis, D.J. Maratukulam, "ANNSTLF-a neural-network-based electric load forecasting system," IEEE Transactions on Neural Networks, Volume 8, Issue 4, Jul 1997 pp. 835&ndash;846.</ref> to apply an [[artificial neural network]] to forecast power demands for utilities in 1991.<ref>D.C. Park, M.A. El-Sharkawi, R.J. Marks II, L.E. Atlas & M.J. Damborg, "Electric load forecasting using an artificial neural network", IEEE Transactions on Power Engineering, vol.6, pp. 442&ndash;449 (1991).</ref> Six years later neural networks were being used by 32 major North American utilities <ref name=ANNSTLF/> and remains in common use today. Concerning the success of the technology introduced in his paper, Marks said "My wife’s grandfather was fond of saying if he had known how long he would have lived, he would have taken better care of himself. If I had known how successful the load forecasting paper would become, I would have spent more time polishing it."<ref>Bing Sheu, "Neural Networks and Beyond-An Interview with Robert J. Marks," IEEE Circuits and Devices Magazine, Volume 12, Issue 5, 1996 [DOI 10.1109/MCD.1996.537355]</ref>
* ''Power load forecasting using neural networks.'' With his colleagues at the [[University of Washington]], Marks was the first<ref name=ANNSTLF> A. Khotanzad, R. Afkhami-Rohani, Lu Tsun-Liang, A. Abaye, M. Davis, D.J. Maratukulam, "ANNSTLF-a neural-network-based electric load forecasting system," IEEE Transactions on Neural Networks, Volume 8, Issue 4, Jul 1997 pp. 835&ndash;846.</ref> to apply an [[artificial neural network]] to forecast power demands for utilities in 1991.<ref>D.C. Park, M.A. El-Sharkawi, R.J. Marks II, L.E. Atlas & M.J. Damborg, "Electric load forecasting using an artificial neural network", IEEE Transactions on Power Engineering, vol.6, pp. 442&ndash;449 (1991).</ref> Six years later neural networks were being used by 32 major North American utilities <ref name=ANNSTLF/> and remains in common use today. [[IEEE]] sponsors a [[MATLAB]] based webinar on use of neural networks in load forecasting.<ref>[http://spectrum.ieee.org/webinar/1705522] IEEE Spectrum Webinar, "Electricity Demand and Price Forecasting with MATLAB," </ref> Concerning the success of the technology introduced in his paper, Marks said "My wife’s grandfather was fond of saying if he had known how long he would have lived, he would have taken better care of himself. If I had known how successful the load forecasting paper would become, I would have spent more time polishing it."<ref>Bing Sheu, "Neural Networks and Beyond-An Interview with Robert J. Marks," IEEE Circuits and Devices Magazine, Volume 12, Issue 5, 1996 [DOI 10.1109/MCD.1996.537355]</ref>
* ''Signal display in time and frequency.'' The Zhao-Atlas-Marks time-frequency distribution,<ref>Leon Cohen, Time Frequency Analysis: Theory and Applications, Prentice Hall, (1994)</ref> (a.k.a. the ZAM distribution or ZAMD), was originally called the cone shaped time-frequency distribution.<ref>[http://marksmannet.com/RobertMarks/REPRINTS/1990-07_TheUseOfCone.pdf] Y. Zhao, L. E. Atlas, and R. J. Marks, “The use of cone-shape kernels for generalized time-frequency representations of nonstationary signals,” IEEE Trans. Acoustics, Speech, Signal Processing, vol. 38, no. 7, pp. 1084–1091, July 1990</ref>
* ''Signal display in time and frequency.'' The Zhao-Atlas-Marks time-frequency distribution,<ref>Leon Cohen, Time Frequency Analysis: Theory and Applications, Prentice Hall, (1994)</ref> (a.k.a. the ZAM distribution or ZAMD), was originally called the cone shaped time-frequency distribution.<ref>[http://marksmannet.com/RobertMarks/REPRINTS/1990-07_TheUseOfCone.pdf] Y. Zhao, L. E. Atlas, and R. J. Marks, “The use of cone-shape kernels for generalized time-frequency representations of nonstationary signals,” IEEE Trans. Acoustics, Speech, Signal Processing, vol. 38, no. 7, pp. 1084–1091, July 1990</ref>
** The ZAMD is a special case of [[Cohen's class distribution function|Cohen's class]] of [[time–frequency representation|time-frequency distributions]].
** The ZAMD is a special case of [[Cohen's class distribution function|Cohen's class]] of [[time–frequency representation|time-frequency distributions]].

Revision as of 19:31, 12 October 2010

Robert J. Marks II
Born (1950-08-25) August 25, 1950 (age 74)
West Virginia, United States
Main interests
Intelligent Design · Electrical Engineering · Evolutionary Computation · Computational Intelligence

Robert Jackson Marks II is a Distinguished Professor of Electrical and Computer Engineering at Baylor University and proponent of intelligent design. From 1977 to 2003, he was on the faculty of the University of Washington in Seattle. He was the first president of the Institute of Electrical and Electronics Engineers (IEEE) Neural Networks Council (now the IEEE Computational Intelligence Society) and the editor-in-chief of the IEEE Transactions on Neural Networks.[1] Marks has over 300 peer-reviewed technical publications, and is a fellow of the IEEE and the Optical Society of America.[2] An old earth creationist,[3] he is a subject of the 2008 pro-intelligent design motion picture, Expelled: No Intelligence Allowed.[4][5] In 2010, he was named as one of the twenty most brilliant living Christian professors.[6][7]

The Evolutionary Informatics Lab website controversy

Main article: Evolutionary Informatics Lab

In 2007, Marks created on a Baylor University server a website for the Evolutionary Informatics Lab, a site promoting intelligent design.[8] The website, initially hosted on Baylor servers, was deleted when Baylor's administration determined that it violated university policy forbidding professors from creating the impression that their personal views represent Baylor as an institution. Baylor said they would permit Marks to repost his website on their server, provided a 108 word disclaimer accompany any intelligent design-advancing research to make clear that the work does not represent the university's position.[9][10][11] The site now resides on a third-party server [12] and still contains the material advancing intelligent design.

Additional controversy arose when it was discovered that William Dembski, a notable intelligent design proponent and former Baylor staff member at the heart of a previous intelligent design controversy at Baylor over the Michael Polanyi Center's promotion of intelligent design who was removed as the center's director, had returned to Baylor as a member of the Evolutionary Informatics Lab.[13] Dembski's participation was funded by a $30,000 grant from the Lifeworks Foundation, which was funded and administrated by researcher Brendan Dixon of the Biologic Institute, another lab promoting intelligent design affiliated with the Discovery Institute.[14][15]

Marks agrees that "associating with [intelligent design] proponents can be harmful to your career" and expressed sympathy for Guillermo Gonzalez and William Dembski, who feature with Marks in the pro-intelligent design film Expelled: No Intelligence Allowed.[16] Interview footage with Marks was shot for Expelled following the deletion of the website.[4] The motion picture alleges persecution of intelligent design advocates by academic institutions and the scientific establishment.[5]

Describing the work of Marks and Dembski, Stephen C. Meyer, Senior Fellow of the pro intelligent design think tank the Discovery Institute, writes:[17]

Marks shows that despite claims to the contrary by their sometimes overly enthusiastic creators, [evolutionary] algorithms ... do not produce large amounts of information "from scratch." //

Marks ... quantified the amount of active information that a computer program imparts into a system with each iteration as the result of the knowledge provided to it by the programmer. //

Marks's analysis of evolutionary algorithms shows that, in order to produce or find the ... information present in the target, a programmer must design a search algorithm that reduced the information requirements of the search to a manageable level.

A Dembski and Marks paper introducing endogenous information and AI, published in a peer reviewed cybernetics journal,[18] was #1 in Access Research Network's "2009 Top Ten Darwin and Design Science News Stories."[19]

Technical contributions

Marks is a researcher in the area of electrical engineering.[20]

  • Treatment of prostate cancer. Marks and his colleagues developed algorithms for real time identification of placement of radioactive seeds in cancerous prostates.[21][22] For this work, he was a co-recipient of the Judith Stitt Best Abstract Award from the American Brachytherapy Society.[23] The algorithm is used clinically .[24]
  • Optimal detection. In the field of detection theory, Marks and his colleagues developed the first closed form solution for the Neyman–Pearson optimal detection of signals in non-Gaussian noise[25][26]

Marks, Wise, Haldeman and Whited have derived exact expressions for the test statistic distribution functions, and thus were able to analyze the performance of the optimal detector for given values of signal strength and sample size.[27]

  • Power load forecasting using neural networks. With his colleagues at the University of Washington, Marks was the first[28] to apply an artificial neural network to forecast power demands for utilities in 1991.[29] Six years later neural networks were being used by 32 major North American utilities [28] and remains in common use today. IEEE sponsors a MATLAB based webinar on use of neural networks in load forecasting.[30] Concerning the success of the technology introduced in his paper, Marks said "My wife’s grandfather was fond of saying if he had known how long he would have lived, he would have taken better care of himself. If I had known how successful the load forecasting paper would become, I would have spent more time polishing it."[31]
  • Signal display in time and frequency. The Zhao-Atlas-Marks time-frequency distribution,[32] (a.k.a. the ZAM distribution or ZAMD), was originally called the cone shaped time-frequency distribution.[33]

The Zhao–Atlas–Marks distribution produces a good resolution in time and frequency domains. The ZAMD method reduces the interference resulting from the cross-terms present in multi-component signals. It is useful in resolving close spectral peaks and capturing non-stationary and multi-component signals. [36]

[T]he Zhao-Atlas-Marks time-frequency distribution ... significantly enhances the time and frequency resolution and eliminates all undesirable cross terms. // The ZAM distribution has been applied to speech with remarkable results.[37]

  • Remote sensing. Marks and his colleagues [38][39] were the first to use neural network inversion in remote sensing. They measured snow parameters from microwave measurements made by satellites. Their general approach is widely used today.[40][41]
  • Wireless arrays. Marks is a co-recipient of a NASA Tech Brief for pioneering power efficient communication in wireless arrays.[42][43]
  • Power generation. Working with Southern California Edison, Marks and his colleagues pioneered computational intelligence based methods for early detection of intermittent shorted windings in multi ton electric generators while the rotors were still turning.[44][45]

[Their diagnostic test performs] detection and localization of shorted turns in the DC field winding of turbine-generator rotors using novelty detection and fuzzified neural networks. Use of neural networks with fuzzy logic outputs and traveling wave techniques ... is an accurate locator of shorted turns in turbo-generator rotors.[46]

  • Marks has made a number of contributions to the sampling theorem including authoring the first book exclusively dedicated to the subject.[47]
  • Restoration of lost samples. Using "sophisticated estimation of the missing samples using previous and future samples,"[48] Marks[49] first showed that, when a signal sampled above its Nyquist rate, lost samples are "are redundant, in the sense that any finite number of them can be obtained from the remaining ones by solving a system of linear equations."[50]
  • Ill-posed sampling. The sampling theorem's Cheung–Marks theorem[51] shows that samples taken from a signal at or above the Nyquist rate may prove incapable of restoring the signal in the presence of small amounts of noise.[52]
  • Optimal image sampling. Cheung and Marks [53] also first showed that images could be sampled below their Nyquist rate and still be recovered without aliasing.

Their "very interesting multidimensional construction ... exploit[s] the [required] spectral gaps that occur when sampling multidimensional signals. Their approach is to slice the spectrum into narrow bands, and handle separately those bands which contain signal energy and those which do not." [54]

  • System representation using samples. Marks and his colleagues showed continuous dynamic systems can be characterized using the sampling theorem.[55] [56]

Techniques have been developed by Walkup, Marks, and their co-workers whereby a shift-variant transformation can be separated into a number of discrete operations. // Marks et al. have derived a generalized sampling theorem that gives the ... rates necessary for dealing with shift-variant operations. // Marks has [also] proposed a number of processors based on temporally multiplexing the impulse response. [57]

  • Optical computers. Marks invented [58] and implemented [59] an all optical computer that – using lenses, mirrors, and light from a laser – performs iterative calculations literally at the speed of light.

While many problems in optics can be solved by projections, it is difficult to solve such problems using all-optical methods. A notable exception is Marks' all-optical implementations of the convex projection algorithm for implementing super-resolution.[60]

Religious activities

Marks served as the faculty adviser to the University of Washington's chapter of Campus Crusade for Christ for seventeen years. He has presented his talk "What Does Calculus Have to Do with Christianity?" [61] in Poland, Japan, Canada, Russia, and the United States.[2]

Marks has made science-oriented Christian apologetics presentations.[62] Venues include Poland, Japan, Moscow, Canada, and Siberia.[23] His creationist view is highlighted in "Genesis and Science: Compatibility Extraordinaire."[3] There he says the God of Genesis is the creator of the universe, and indicates that, from an observers perspective on the surface of the earth (granting an opaque to translucent to transparent atmosphere), the "sequence of events in Genesis is consistent with the sequence of events in science."

Marks refers to himself as "A servant of Jesus Christ."[2]

Other activities

Books by Robert J. Marks II

  • R.J. Marks II, "Handbook of Fourier Analysis and Its Applications," Oxford University Press, (2009).[25]
  • R. D. Reed and R.J. Marks II, Neural Smithing: Supervised Learning in Feedforward Artificial Neural Networks, MIT Press, Cambridge, MA, (1999).
  • M. Palaniswami, Y. Attikiouzel, R.J. Marks II, David Fogel and Toshio Fukuda; Editors, Computational Intelligence: A Dynamic System Perspective, IEEE Press, (1995).
  • R.J. Marks II, Editor, Fuzzy Logic Technology and Applications, IEEE Technical Activities Board, Piscataway, (1994).
  • J.Zurada, R.J. Marks II and C.J. Robinson; Editors, Computational Intelligence: Imitating Life, (IEEE Press, 1994).
  • R.J. Marks II, Introduction to Shannon Sampling and Interpolation Theory, Springer-Verlag, (1991).[26]
  • M.A. El-Sharkawi and R. J. Marks II, Editors, Applications of Neural Networks to Power Systems, IEEE Press, Piscataway, (1991).

See also

Wikiquote has quotations related to Robert J. Marks II.

References

  1. ^ [1] IEEE Transactions on Neural Networks
  2. ^ a b c d Marks' 'expanded biography' Cite error: The named reference "BaylorBio" was defined multiple times with different content (see the help page).
  3. ^ a b Genesis and Science: Compatibility Extraordinaire (slide presentation)
  4. ^ a b Jerry Pierce, "Baptist professors featured in new film," Southern Baptist Texan (January 28, 2008)
  5. ^ a b Lesley Burbridge-Bates (2007-08-22). "Expelled [[Press Release]]" (PDF). Premise Media. Retrieved 2008-04-07. {{cite web}}: External link in |publisher= (help); URL–wikilink conflict (help)
  6. ^ [2] Tim Woods, "Baylor faculty member named one of '20 Most Brilliant Christian Professors,'" Waco Tribune-Herald,(April 15, 2010)
  7. ^ The 20 Most Brilliant Christian Professors, CollegeCrunch.com, (April 4, 2010)
  8. ^ Follow the money: more Dembski/Baylor-related mischief? Andrea Bottaro. Panda's Thumb, September 7, 2007.
  9. ^ William Dembski Addresses Forthcoming Intelligent Design Research that Advances ID and Answers Critics, Evolution News & Views, Discovery Institute
  10. ^ Crisis averted, Mark Bergin, World Magazine
  11. ^ Baylor U. Removes a Web Page Associated With Intelligent Design From Its Site by Elizabeth F. Farrell. Chronicle of Higher Education, Sept. 4, 2007. onlinesubscription access
  12. ^ EvoInfo.org
  13. ^ Grace Maalouf, Brad Briggs "BU had role in Dembski return," Baylor Lariat, Nov. 16, 2007[3]
  14. ^ Follow the money: more Dembski/Baylor-related mischief?, Andrea Bottaro, Panda's Thumb
  15. ^ Lifeworks Foundation 990 form for the year 2006
  16. ^ Well-Informed: Dr. Robert Marks and the Evolutionary Informatics Lab, Casey Luskin interviewer, "Intelligent Design the Future" podcast series of The Center for Science and Culture of the Discovery Institute.
  17. ^ Stephen C. Meyer, Signature in the Cell: DNA and the Evidence for Intelligent Design, HarperOne (2009)
  18. ^ [4], William A. Dembski and Robert J. Marks II, "Conservation of Information in Search: Measuring the Cost of Success," IEEE Transactions on Systems, Man and Cybernetics A, Systems and Humans, vol.39, #5, September 2009, pp. 1051–1061
  19. ^ [5], Access Research Network, "2009 Top Ten Darwin and Design Science News Stories."
  20. ^ [6] Marks's CV.
  21. ^ [7] S. Narayanan, P.S. Cho and R.J. Marks II, "Fast Cross-Projection Algorithm for Reconstruction of Seeds in Prostate Brachytherapy", Med. Phys. 29 (7), July 2002, pp. 1572–1579.
  22. ^ [8] S. Narayanan, P.S. Cho and R.J. Marks II, "Three-dimensional seed reconstruction from an incomplete data set for prostate brachytherapy", Phys. Med. Biol., vol.49, pp. 3483–3494 (2004).
  23. ^ a b Marks' curriculum vitae Cite error: The named reference "MarksCV" was defined multiple times with different content (see the help page).
  24. ^ D.R. Reed, K.E. Wallner, S.Narayanan, S.G. Sutlief, E.C. Ford, P.S. Cho, "Intraoperative fluoroscopic dose assessment in prostate brachytherapy patients," International Journal of Radiation Oncology Biology Physics, Vol 63, Issue 1, September, 2005, pp. 301–307
  25. ^ S. A. Kassam, Signal Detection in Non-Gaussian Noise. Springer Verlag, 1988.
  26. ^ Detection in Laplace noise R.J. Marks II, G.L. Wise, D.G. Haldeman and J.L. Whited, IEEE Transactions on Aerospace and Electronic Systems, vol. AES-14, pp. 866–872 (1978).
  27. ^ M. W. Thompson, D. R. Halverson and G. L. Wise. "Robust Detection in Nominally Laplace Noise." IEEE Transactions on Communications, Volume 42 Issue 2-4, pp. 1651–1660, Feb–Apr. 1994
  28. ^ a b A. Khotanzad, R. Afkhami-Rohani, Lu Tsun-Liang, A. Abaye, M. Davis, D.J. Maratukulam, "ANNSTLF-a neural-network-based electric load forecasting system," IEEE Transactions on Neural Networks, Volume 8, Issue 4, Jul 1997 pp. 835–846.
  29. ^ D.C. Park, M.A. El-Sharkawi, R.J. Marks II, L.E. Atlas & M.J. Damborg, "Electric load forecasting using an artificial neural network", IEEE Transactions on Power Engineering, vol.6, pp. 442–449 (1991).
  30. ^ [9] IEEE Spectrum Webinar, "Electricity Demand and Price Forecasting with MATLAB,"
  31. ^ Bing Sheu, "Neural Networks and Beyond-An Interview with Robert J. Marks," IEEE Circuits and Devices Magazine, Volume 12, Issue 5, 1996 [DOI 10.1109/MCD.1996.537355]
  32. ^ Leon Cohen, Time Frequency Analysis: Theory and Applications, Prentice Hall, (1994)
  33. ^ [10] Y. Zhao, L. E. Atlas, and R. J. Marks, “The use of cone-shape kernels for generalized time-frequency representations of nonstationary signals,” IEEE Trans. Acoustics, Speech, Signal Processing, vol. 38, no. 7, pp. 1084–1091, July 1990
  34. ^ [11] Time-Frequency Toolbox For Use with MATLAB
  35. ^ [12] National Instruments. LabVIEW Tools for Time-Frequency, Time-Series, and Wavelet Analysis. [13] TFA Cone-Shaped Distribution VI
  36. ^ G.X. Chena and Z.R. Zhou, "Time–frequency analysis of friction-induced vibration under reciprocating sliding conditions," Wear, Volume 262, Issues 1–2, 4 January 2007, Pages 1–10
  37. ^ Lokenath Debnath, Wavelet transforms and their applications, Birkhäuser Boston, (2001) p.355
  38. ^ [14] L. Tsang, Z. Chen, S. Oh, R.J. Marks II and A.T.C. Chang, "Inversion of snow parameters from passive microwave remote sensing measurements by a neural network trained with a multiple scattering model" IEEE Transactions on Goescience and Remote Sensing, vol. 30, no.5, pp. 1015–1024 (1992).
  39. ^ A. Ishimaru, R.J. Marks II, L. Tsang, C.M. Lam, D.C. Park and S. Kitamaru, "Particle size distribution using optical sensing and neural networks", Optics Letters, vol.15, pp. 1221–1223 (1990).
  40. ^ Vladimir M. Krasnopolsky and Helmut Schillerb, "Some neural network applications in environmental sciences. Part I: forward and inverse problems in geophysical remote measurements," Neural Networks, Volume 16, Issues 3–4, April–May 2003, pp. 321–334
  41. ^ F. Van der Meer, "Geophysical inversion of imaging spectrometer data for geologic modelling," International Journal of Remote Sensing, Volume 21, Issue 2, pp. 387–393 (2000)
  42. ^ NASA Recognizes Baylor Engineer For Innovative Technology
  43. ^ A.K. Das, R.J. Marks II, M.A. El-Sharkawi, Payman Arabshahi and Andrew Gray, "Minimum Power Broadcast Trees for Wireless Networks: Optimization Using the Viability Lemma", Proceedings of the NASA Earth Science Technology Conference, June 11–13, 2002, Pasadena, CA
  44. ^ [15] M.A. El-Sharkawi, R.J. Marks II, S.Oh, S.J. Huang, I. Kerszenbaum and A. Rodriguez, "Localization of Winding Shorts Using Fuzzified Neural Networks", IEEE Transactions on Energy Conversion, vol. 10, no.1, March 1995, pp. 147–155.)
  45. ^ S. Guttormsson, R.J. Marks II, M.A. El-Sharkawi and I. Kerszenbaum, "Elliptical novelty grouping for on-line short-turn detection of excited running rotors", IEEE Transactions on Energy Conversion, IEEE Transactions on Volume: 14 1 , March 1999 , pp. 16–22
  46. ^ M.E. El-Hawary, Fuzzy System Theory in Electrical Power Engineering, (IEEE Press, 1998), p.xxiv
  47. ^ R.J. Marks II, Introduction to Shannon Sampling and Interpolation Theory, Springer-Verlag, (1991).[16]
  48. ^ Farokh A. Marvasti, Peter M. Clarkson, Miroslav V. Dokic, Ut Goenchanart, and Chuande Liu, "Reconstruction of Speech Signals with Lost Samples," IEEE Transactions on Signal Processing, Volume 40, Issue 12, pp. 2897–2903, December 1992.
  49. ^ R.J. Marks II, "Restoring lost samples from an oversampled bandlimited signal", IEEE Transactions on Acoustics, Speech and Signal Processing, vol. ASSP-31, pp. 752–755 (1983).
  50. ^ P.J.S.G. Ferreira, Incomplete sampling series and the recovery of missing samples from oversampled bandlimited signals," IEEE Transactions on Signal Processing, (40) 1 pp. 225 227 (1992).
  51. ^ J.L. Brown and S.D.Cabrera, "On well-posedness of the Papoulis generalized sampling expansion," IEEE Transactions on Circuits and Systems, May 1991 Volume: 38 , Issue 5, pp. 554–556
  52. ^ [17] K.F. Cheung and R.J. Marks II, "Ill-posed sampling theorems", IEEE Transactions on Circuits and Systems, vol. CAS-32, pp. 829–835 (1985).
  53. ^ [18] K.F. Cheung and R.J. Marks II, "Image sampling below the Nyquist density without aliasing", Journal of the Optical Society of America A, vol.7, pp. 92–105 (1990)
  54. ^ Cormac Herley and Ping Wah Wong, "Minimum Rate Sampling and Reconstruction of Signals with Arbitrary Frequency Support," IEEE Transactions on Information Theory, Vol 45, No. 5, July 1999, pp. 1555–1564.
  55. ^ R.J. Marks II, J.F. Walkup and M.O. Hagler, "Sampling theorems for linear shift-variant systems", IEEE Transactions on Circuits and Systems, vol. CAS-25, pp. 228–233 (1978).
  56. ^ R.J. Marks II, "Two-dimensional coherent space-variant processing using temporal holography", Applied Optics, vol. 18, pp. 3670 3674 (1979).
  57. ^ Joseph L. Horner, Optical Signal Processing, Academic Press, (1987) pp.315,317
  58. ^ [19] R.J. Marks II, "Coherent optical extrapolation of two-dimensional signals: processor theory", Applied Optics, vol. 19, pp. 1670–1672 (1980)
  59. ^ R.J. Marks II and D.K. Smith "Gerchberg – type linear deconvolution and extrapolation algorithms", in Transformations in Optical Signal Processing, edited by W.T. Rhodes, J.R. Fienup and B.E.A. Saleh, SPIE vol. 373, pp. 161–178 (1984).
  60. ^ Henry Stark and Yongyi Yang,Vector Space Projections: A Numerical Approach to Signal and Image Processing, Neural Nets, and Optics, Wiley-Interscience,(1998), p.281.
  61. ^ "What Does Calculus Have to Do with Christianity" Presentation
  62. ^ Marks' apologetics page
  63. ^ [20] Benjamin Hawkins, "Southwestern professors make no bones about Christ’s resurrection," Mar 26, 2008
  64. ^ [21] W.A. Dembski and R.J. Marks II, ``The Jesus Tomb Math," in Buried Hope Or Risen Savior?: The Search for the Jesus Tomb, edited by Charles Quarles.
  65. ^ [22] Sketch Marks (from Marks's web page.)
  66. ^ [23] WPFR TeleTalk (from Marks's web page.)
  67. ^ [24] "Robert J. Marks II has an Erdos-Bacon number of five." Retrieved 2010-05-05.
Wikiquote has quotations related to Robert J. Marks II.
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