Biography:Robert J. Marks II

From HandWiki
Revision as of 04:42, 9 February 2024 by Rtexter1 (talk | contribs) (correction)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Short description: American engineer and intelligent design advocate (born 1950)
Robert J. Marks II
Robert J. Marks II (2016).png
Marks in 2016
Born (1950-08-25) August 25, 1950 (age 74)
West Virginia, United States
Alma mater
Known for
Scientific career
Fields
Institutions
ThesisSpace-variant coherent optical processing (1977)
Doctoral advisorJ.F. Walkup

Robert Jackson Marks II (born August 25, 1950) is an American electrical engineer, computer scientist and Distinguished Professor at Baylor University. His contributions include the Zhao-Atlas-Marks (ZAM) time-frequency distribution in the field of signal processing,[1] the Cheung–Marks theorem[2] in Shannon sampling theory and the Papoulis-Marks-Cheung (PMC) approach in multidimensional sampling.[3] He was instrumental in the defining of the field of computational intelligence and co-edited the first book using computational intelligence in the title.[4][5] A Christian[6] and an old earth creationist,[7] he is a subject of the 2008 pro-intelligent design motion picture, Expelled.

Professional career

Marks has received his bachelor's and master's degrees from Rose–Hulman Institute of Technology in 1972 and 1973, respectively.[8] During his doctoral studies at Texas Tech University, he was supervised by J.F. Walkup; his dissertation focused on optical signal processing.[9] He obtained his Ph.D. degree in 1977.[8]

Marks is a Distinguished Professor of Electrical and Computer Engineering at Baylor University and serves as the Director of the Walter Bradley Center for Natural and Artificial Intelligence.[10] 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).[11] He is a Fellow of the IEEE[12][8] and the Optical Society of America.[8][13]

Technical contributions

Marks is a researcher in the area of electrical engineering.[14]

  • Treatment of prostate cancer. Marks and his colleagues developed algorithms for real time identification of placement of radioactive seeds in cancerous prostates.[15][16] For this work, he was a co-recipient of the Judith Stitt Best Abstract Award from the American Brachytherapy Society.[17] The algorithm is used clinically.[18]
  • 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[19][20]

"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."[21]

  • Power load forecasting using neural networks. With his colleagues at the University of Washington, Marks was the first[22] to apply an artificial neural network to forecast power demands for utilities in 1991.[23] Six years later neural networks were being used by 32 major North American utilities [22] and remains in common use today. IEEE sponsors a MATLAB based webinar on use of neural networks in load forecasting.[24] A technique "similar to one already used to successfully forecast electrical load needs" has been used to forecast Dow Jones closing values using data from millions of Twitter messages.[25]
  • The Smith Tube. Marks was a member of the Baylor research team that introduced the Smith Tube, a visualization tool useful in advanced microwave systems design.[26] A generalization of the Smith Chart, the Smith Tube is currently in Keysight's Advanced Design System (ADS) software package.[27]
  • Convolutional neural networks. With Homma and Atlas, Marks developed a temporal convolutional neural network[28] used widely in Deep learning.
  • Signal display in time and frequency. The Zhao-Atlas-Marks time-frequency distribution,[1] (a.k.a. the ZAM distribution or ZAMD), was originally called the cone shaped time-frequency distribution.[29]
    • The ZAMD is a special case of Cohen's class of time-frequency distributions.
    • The ZAMD is currently in the MATLAB Time-Frequency Toolbox[30] and National Instruments' LabVIEW Tools for Time-Frequency, Time-Series, and Wavelet Analysis [31]
    • The ZAMD has been applied in numerous areas:

      "[The ZAMGTFR [ZAMD] has advantage over most of the other TFRs under conditions of low SNR and some characteristic features are easy to be extracted from the 2-D time-frequency plane."[32]

"The ZAM-TFD [ZAMD] has been shown to be effective in tracking frequency hopping signals and representing signals in the presence of white noise."[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."[34]

"[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."[35]

  • Remote sensing. Marks and his colleagues [36][37] 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.[38][39]
  • Wireless arrays. Marks is a co-recipient of a NASA Tech Brief for pioneering power efficient communication in wireless arrays.[40][41]
  • 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.[42][43]

    "[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."[44]

  • Marks has made contributions to the sampling theorem including authoring the first book exclusively dedicated to the subject.[45]
    • Restoration of lost samples. Using "sophisticated estimation of the missing samples using previous and future samples,"[46] Marks[47] first showed that, when a signal is sampled above its Nyquist rate, lost samples "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."[48]
    • Ill-posed sampling (The Cheung-Marks Theorem). The sampling theorem's Cheung–Marks theorem[49] 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.[50]
    • Optimal image sampling. An image is said to be optimally sampled when the samples per unit area are minimized subject to no degradation of the interpolated image. Marks's contributions to optimal image sampling include:
    • The Papoulis-Marks-Cheung Approach.[3] Marks and Cheung[51] extended the generalized sampling expansion of Athanasios Papoulis[52] to higher dimensions.

      "Marks and Cheung focused on images with a given spectral support region and an initial base sampling lattice such that the induced spectral replicas of this support region do not overlap. They then showed that cosets of some sublattice could be removed from the base lattice until the sampling density was minimal (in the Landau sense) or approached minimal ... [This] allows the sampling rate to be reduced until it equals or approaches the Landau minimum."[3]

    • Sub-Nyquist Sampling. Cheung and Marks [53] 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]

  • Optical computers. Marks invented [55] and implemented [56] 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."[57]

Evolutionary Informatics Lab website

In 2006 Marks hired William Dembski as a part-time post-doctoral researcher; Dembski is an 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, which had been resolved when Baylor disbanded that center in 2000. Dembski's position in Marks' lab was funded by a $30,000 gift from the Lifeworks Foundation; the gift went through the university's development department and not its academic grant administration. Dembski's role was stated in the gift documents. Marks said that he kept Dembksi's presence quiet. By December 2006 Dembski's university position had been brought to the university administration's attention, and the university returned the unspent funds and terminated Dembski's position.[58]

Marks created a website to describe the work that he and Dembski were doing, which the website described as happening at the "Evolutionary Informatics Lab" at Baylor. In the summer of 2007 that website was called to the attention of the Baylor administration after Marks discussed that work on a podcast hosted by Casey Luskin of the Discovery Institute, and the university administration shut the website down.[58] Marks challenged the removal.[58][59][60] The site was reposted to a server outside of Baylor.[59]

The dispute over the website was covered in the 2008 pro-intelligent design film Expelled.[61]

Christianity

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?" [62] in Poland, Japan, Canada, Russia, and the United States.[8]

Marks has made science-oriented Christian apologetics presentations.[63] Venues include Poland, Japan, Moscow, Canada, and Siberia.[8]

Other activities

Books by Robert J. Marks II

  • R.J. Marks II, Non-Computable You: What You Do Artificial Intelligence Never Will, Discovery Press, (2022). [24]
  • R.J. Marks II and William A. Dembski with J. P. Moreland, For a Greater Purpose: The Life and Legacy of Walter Bradley, Erasmus Press, (2020). [25]
  • R.J. Marks II, The Case for Killer Robots: Why America's Military Needs to Continue Development of Lethal AI, Discovery Institute Press, (2020). [26]
  • R.J. Marks II, William A. Dembski and Winston Ewert, Introduction to Evolutionary Informatics, World Scientific, Singapore, (2017).[27]
  • R.J. Marks II, Michael Behe, William A. Dembski, Bruce L. Gordon, John C. Sanford, Editors, Biological Information - New Perspectives, World Scientific, Singapore, (2013).[28]
  • R.J. Marks II, Handbook of Fourier Analysis and Its Applications, Oxford University Press, (2009).[29]
  • 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 B. 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).
  • Jacek M. Zurada, R.J. Marks II and C.J. Robinson; Editors, Computational Intelligence: Imitating Life, (IEEE Press, 1994).
  • R.J. Marks II, Editor, Advanced Topics in Shannon Sampling and Interpolation Theory, (Springer-Verlag, 1993).
  • R.J. Marks II, Introduction to Shannon Sampling and Interpolation Theory, Springer-Verlag, (1991).[30]
  • M.A. El-Sharkawi and R. J. Marks II, Editors, Applications of Neural Networks to Power Systems, IEEE Press, Piscataway, (1991).

References

  1. ↑ 1.0 1.1 Leon Cohen, Time Frequency Analysis: Theory and Applications, Prentice Hall, (1994)
  2. ↑ 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
  3. ↑ 3.0 3.1 3.2 Matthew A. Prelee and David L. Neuhoff. "Multidimensional Manhattan Sampling and Reconstruction." IEEE Transactions on Information Theory 62, no. 5 (2016): 2772-2787.
  4. ↑ "Donald C. Wunsch Interviews Robert J. Marks II for the IEEE Computational Intelligence Society's History Committee". http://missinganybal.com/2012_WunschInterviewsMarks.html. 
  5. ↑ Computational Intelligence: Imitating Life. IEEE Press (1994). 1994. ISBN 978-0780311046. 
  6. ↑ Robert J. Marks II. "The Impact of Christian Faith on Mathematics & Science: Yesterday & Today". http://missinganybal.com/2014/2014%20The%20Impact%20of%20Christian%20Faith%20on%20Mathematics.html. [yes|permanent dead link|dead link}}]
  7. ↑ Casey Luskin. "ID the Future: Dr. Robert Marks - Active Information in Metabiology". http://missinganybal.com/2014/Dr%20Robert%20Marks%20-%20Active%20Information%20in%20Metabiology.html. [yes|permanent dead link|dead link}}]
  8. ↑ 8.0 8.1 8.2 8.3 8.4 8.5 8.6 Robert J. Marks II. "Curriculum Vitae". http://robertmarks.org/CV/CV.pdf. 
  9. ↑ Marks II, Robert Jackson (1977). Space-variant coherent optical processing (PhD). Texas Tech University.
  10. ↑ Bradley Center home page
  11. ↑ [1] IEEE Transactions on Neural Networks
  12. ↑ "For leadership and contributions to the field of neural networks."(1994)[2]
  13. ↑ "For contributions to image recovery and synthesis, optical processing, and electro-optical neural networks." (1989)
  14. ↑ [3] Marks's CV.
  15. ↑ [4] 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.
  16. ↑ [5] 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).
  17. ↑ American Brachytherapy Society homepage
  18. ↑ 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
  19. ↑ S. A. Kassam, Signal Detection in Non-Gaussian Noise. Springer Verlag, 1988.
  20. ↑ 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).
  21. ↑ 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
  22. ↑ 22.0 22.1 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.
  23. ↑ 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).
  24. ↑ [6] IEEE Spectrum Webinar, "Electricity Demand and Price Forecasting with MATLAB,"
  25. ↑ [7] "Analyzing almost 10 million tweets, research finds public mood can predict Dow days in advance," Indiana University Press Release.
  26. ↑ Fellows, Matthew, Matthew Flachsbart, Jennifer Barlow, Charles Baylis, and Robert J. Marks. "The Smith Tube: Selection of radar chirp waveform bandwidth and power amplifier load impedance using multiple-bandwidth load-pull measurements." WAMICON 2014, pp. 1-5. IEEE, 2014.[8]
  27. ↑ Agilent's "3D Smith Chart for Broadband PA Design" announcement
  28. ↑ Homma, Toshiteru; Les Atlas; Robert Marks II (1988). "An Artificial Neural Network for Spatio-Temporal Bipolar Patters: Application to Phoneme Classification". Advances in Neural Information Processing Systems 1: 31–40. http://papers.nips.cc/paper/20-an-artificial-neural-network-for-spatio-temporal-bipolar-patterns-application-to-phoneme-classification.pdf. 
  29. ↑ [9] 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
  30. ↑ [10] Time-Frequency Toolbox For Use with MATLAB
  31. ↑ [11] National Instruments. LabVIEW Tools for Time-Frequency, Time-Series, and Wavelet Analysis. [12] TFA Cone-Shaped Distribution VI
  32. ↑ D. Zeng, X. Zeng, G. Lu, and B. Tang. "Automatic modulation classification of radar signals using the generalised time-frequency representation of Zhao, Atlas and Marks." IET radar, sonar & navigation 5, no. 4 (2011): 507–516.
  33. ↑ James R. Bulgrin, Bernard J. Rubal, Theodore E. Posch, and Joe M. Moody. "Comparison of binomial, ZAM and minimum cross-entropy time-frequency distributions of intracardiac heart sounds." In Signals, Systems and Computers, 1994. 1994 Conference Record of the Twenty-Eighth Asilomar Conference on, vol. 1, pp. 383–387. IEEE, 1994.
  34. ↑ 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
  35. ↑ Lokenath Debnath, Wavelet transforms and their applications, Birkhäuser Boston, (2001) p.355
  36. ↑ [13] 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).
  37. ↑ 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).
  38. ↑ 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
  39. ↑ 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)
  40. ↑ NASA Recognizes Baylor Engineer For Innovative Technology
  41. ↑ 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
  42. ↑ [14] 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.)
  43. ↑ 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
  44. ↑ M.E. El-Hawary, Fuzzy System Theory in Electrical Power Engineering, (IEEE Press, 1998), p.xxiv
  45. ↑ R.J. Marks II, Introduction to Shannon Sampling and Interpolation Theory, Springer-Verlag, (1991).[15]
  46. ↑ 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.
  47. ↑ 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).
  48. ↑ 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).
  49. ↑ John L. Brown, Jr. and Sergio D. Cabrera, "On Well-Posedness of the Papoulis Generalized Sampling Expansion," IEEE Transactions on Circuits and Systems, pp.554-556, 1991.
  50. ↑ [16] 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).
  51. ↑ R. J. Marks, II, "Multidimensional-signal sample dependency at Nyquist densities," J. Opt. Soc. Amer. A, vol. 3, pp. 268–273, Feb. 1986. K. F. Cheung and R. J. Marks, II, "Imaging sampling below the Nyquist density without aliasing," J. Opt. Soc. Amer. A, vol. 7, no. 1, pp. 92–105, Jan. 1990. K. F. Cheung, "A multidimensional extension of Papoulis' generalized sampling expansion with the application in minimum density sampling," in Advanced Topics in Shannon Sampling and Interpolation Theory, Robert J. Marks II, Editor. New York, NY, USA: Springer-Verlag, 1993, pp. 85–119.
  52. ↑ Athanasios Papoulis, "Generalized sampling expansion," IEEE Trans. Circuits Syst., vol. 24, no. 11, pp. 652–654, Nov. 1977.
  53. ↑ [17] 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. ↑ [18] R.J. Marks II, "Coherent optical extrapolation of two-dimensional signals: processor theory", Applied Optics, vol. 19, pp. 1670–1672 (1980)
  56. ↑ 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).
  57. ↑ 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.
  58. ↑ 58.0 58.1 58.2 Briggs, Brad; Maalou, Grace (November 27, 2007). "BU had role in Dembski return". Baylor Lariat. https://www.baylor.edu/content/services/document.php?id=55567. 
  59. ↑ 59.0 59.1 Loring, Nicole (September 8, 2007). "Baylor forces professor to shut down site". The Daily Orange. http://dailyorange.com/2007/09/baylor-forces-professor-to-shut-down-site/. 
  60. ↑ Farrell, Elizabeth F. (4 September 2007). "Baylor U. Removes a Web Page Associated With Intelligent Design From Its Site". The Chronicle of Higher Education. https://www.chronicle.com/article/Baylor-U-Removes-a-Web-Page/121996.  (Subscription content?)
  61. ↑ Jablonski, Stephen (April 22, 2008). "Obviously not objective, 'Expelled' explores academic freedom" (in en). The Baylor Lariat. https://www.baylor.edu/lariatarchives/news.php?action=story&story=50601. 
  62. ↑ "What Does Calculus Have to Do with Christianity" Presentation
  63. ↑ Marks' apologetics page
  64. ↑ [19] Benjamin Hawkins, "Southwestern professors make no bones about Christ's resurrection," Mar 26, 2008
  65. ↑ [20] 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.
  66. ↑ [21] Sketch Marks (from Marks's web page.)
  67. ↑ [22] WPFR TeleTalk (from Marks's web page.)
  68. ↑ [23] "Robert J. Marks II has an Erdős-Bacon number of five." Retrieved 2010-05-05.

External links



Retrieved from "https://handwiki.org/wiki/index.php?title=Biography:Robert_J._Marks_II&oldid=3440860"