Anant P. Godbole

Curriculum Vitæ

September 2006

  

 

Department of Mathematics,

East Tennessee State University,

Box 70663,

Johnson City, TN 37614-0663.

Telephones: (423)-439-5359/4349 (Work), (423)-282-2086 (Home)

E-mail: godbolea@etsu.edu; FAX: (423)-439-8361;

Website: http://www.etsu.edu/math/godbole/anant.htm

REU Homepage: http://www.etsu.edu/math/godbole/nsf.htm

  

Education:

  

Ph.D.,1984, Michigan State University, East Lansing.

M.S., 1980, Michigan State University, East Lansing.

B.Sc. (Honors), 1975, University of Bombay.

    

Professional Experience:

  

June 2000 to present: 

 

            Professor and Chair, Department of Mathematics,

            East Tennessee State University.

 

September 1997 to May 2000:

 

            Associate Dean, College of Sciences and Arts,

Michigan Technological University.

 

September 1996 to November 1996:

 

            Visiting Scholar, Department of Statistics,

University of California, Berkeley.

 

September 1994 to May 2000:

 

            Professor of Mathematical Sciences,

            Michigan Technological University.

 

September 1990 to August 1994:

 

            Associate Professor of Mathematical Sciences,

            Michigan Technological University.

 

September 1990 to August 1991:

 

Visiting Associate Professor of Statistics and Applied Probability,

University of California, Santa Barbara.

 

September 1984 to August 1990:

 

            Assistant Professor of Mathematical Sciences,

Michigan Technological University.

 

September 1982 to August 1984:

 

Lecturer of Mathematics,

Texas A &M University.

  

Teaching and Research Recognition:

  

·        Finalist, Distinguished Teacher Award, Michigan Tech University, 1987, 1988, 1989 and 1990.

·        Nominated for MTU Research Award, 1995 and 1998.

·        Distinguished Visiting Professor, Bucknell Universiy, Spring 1998.

·        Finalist, State of Michigan Distinguished Teaching Award, 1989 and 1990.

·        Awarded the inaugural Department of Mathematical Sciences Teaching Award in 1990. 

·        Awarded the Distinguished Researcher Award by the Department of Mathematical Sciences at Michigan Technological University in 1992, 1993, and 1999.

·        ETSU Mathematics Department Distinguished Research Award, 2004.

·        ETSU College of Arts and Sciences Distinguished Research Award, 2006.

  

Research Interests:

 

Applied Probability, Mathematical Statistics, Probability, and Combinatorics, with a special emphasis on:   Classical probability in Banach spaces and on the real line; Poisson approximation; DNA Sequence Analysis; Random combinatorial, number-theoretic, geometric, and algebraic structures; Statistical tests for randomness; Mathematical Population Genetics; and Reliability Theory.

  

Publications:

(undergraduate authors indicated by a * and graduate students by a **)

  

1. “On Klass’ series criterion for the minimal growth rate of partial maxima, Statistics and Probability Letters 5, 235-238, 1987.

2. “On the strong law of large numbers in Banach spaces,” Proceedings of the American Mathematical Society 100, 543-550, 1987. 

3. “Some remarks on Kolmogorov's strong law in Hilbert spaces,” Calcutta Statistical Association Bulletin 37, 91-94, 1988.

4. “Specific formulæ  for some success run distributions,” Statistics and Probability Letters 10, 119-124, 1990.

5. “Degenerate and Poisson convergence criteria for success runs,” Statistics and Probability Letters 10, 247-255, 1990.

6. “On hypergeometric and related distributions of order k,” Communications in Statistics A 19, 1291-1301, 1990.

7. “On the Markov-binomial distribution and its Poisson limit,” Technical Report No. 139, Department of Statistics and Applied Probability, University of California, Santa Barbara, 12 pp., 1990 (with Candace N. McLean*).

8. “Poisson approximations for runs and patterns of rare events,” Advances in Applied Probability 23, 851-865, 1991.

9. “A new exact runs test for randomness,” in Computing Science and Statistics, C.

Page and R. LePage, eds., pp. 281-285, Springer Verlag, New York, 1992 (with Marilyn A. Agin**).

10. “The exact and asymptotic distribution of overlapping success runs,” Communications in Statistics A 21, 953-967, 1992.

11. “Exact and approximate runs distributions,” Communications in Statistics A 21, 2151-2167, 1992 (with Michelle Gornowicz*).

12. “Self-normalized bounded laws of the iterated logarithm in Banach spaces,”

in Probability in Banach Spaces 8, Progress in Probability 30, Richard Dudley, Marjorie Hahn and James Kuelbs, eds., pp. 292-303, Birkhäuser, Boston, 1992.

13. “Contributions to the coupon collector problem,” in Proceedings of the

6th NCUR Conference 2, Robert Yearout, ed., pp. 1009-1013, University of North Carolina, Asheville, 1992 (with Robert Weishaar* and Mark Geske*).

14. “Poisson approximations in reliability,” in Proceedings of the 6th NCUR Conference 2, Robert Yearout, ed., pp. 1032-1035, University of North Carolina, Asheville, 1992 (with Laurel Deegan*).

15. “Improved Poisson approximations for word patterns,” Advances in Applied Probability 25, 334-347, 1993 (with Andrew Schaffner*).

16. “Approximate reliabilities of  m-consecutive-k-out-of-n: failure systems,” Statistica Sinica 3, 321-327, 1993.

17. “Applications of the Stein-Chen method to the theory of patterns and runs,” in Runs and Patterns in Probability, A. Godbole and S. Papastavridis, eds., pp. 253-262, Mathematics and its Applications 283,  Kluwer, Boston, 1994.

18. “Runs of superimposed Poisson processes,” in Runs and Patterns in Probability, A. Godbole and S. Papastavridis, eds., pp. 263-286, Mathematics and its Applications 283, Kluwer, Boston, 1994 (with Hao Zhang**).

19. “Exact and approximate hypercube reliabilities,” in Runs and Patterns in Probability, A. Godbole and S. Papastavridis, eds., pp. 163-172, Mathematics and its Applications 283,  Kluwer, Boston, 1994 (with Sanjay Khunger** and Esther Ososanya).

20. “The asymptotic lower bound on the diagonal Ramsey numbers: A closer look,” in Discrete Probability and Algorithms, D. Aldous, P. Diaconis, J. Spencer and J. M. Steele, eds., pp. 81-94, IMA Volumes in Mathematics and its Applications 72, Springer Verlag, New York, 1995 (with Daphne Skipper* and Rachel Sunley*).

21. “A Poisson approximation for the number of k-matches,” Statistics and

Probability Letters 21, 1-8, 1994 (with Patrick Burghardt* and Amy Prengaman*).

22. “General upper bounds for covering numbers,” Ars Combinatoria 42, 211--221, 1996 (with Sandra Thompson* and Eric Vigoda*).

23. “Discriminating between sequences of Bernoulli and Markov-Bernoulli trials,”

Communications in Statistics A 23, 2787-2814, 1994  (with Sharyn Campbell* and Stephanie Schaller*).

24. “Formulæ  and recursions for the joint distribution of success runs of several different lengths,” The Annals of the Institute of Statistical Mathematics 49, 141--153, 1997  (with Robert Weishaar* and Stavros Papastavridis).

25. Runs and Patterns in Probability: Selected Papers, Anant P. Godbole and Stavros Papastavridis eds., Mathematics and its Applications 283, Kluwer Academic Publishers, Boston, 1994. xvii + 340 pp.

26. “Compound Poisson approximations for word patterns under Markovian hypotheses,”Journal of Applied Probability 32, 877-892, 1995 (with Mark Geske*, Andrew Schaffner*, Allison Skolnick* and Garrick Wallstrom*).

27. “Probability theory: a program of undergraduate research,” CUR Quarterly 15, 96-102, 1994.

28. “t-covering arrays: upper bounds and Poisson approximations,” Combinatorics, Probability and Computing 5, 105-118,  1996 (with Daphne Skipper* and Rachel Sunley*). 

29. “Random covering designs,” Journal of Combinatorial Theory, Series A 75, 85--98, 1996 (with Svante Janson).

30. “Reliability analysis of a software redundancy system,” Interstat 1, June 1995 (with Nicholas Locantore* and Gomathi Sadhasivan**).

31. “Imperfections in random tournaments,” Combinatorics, Probability and Computing 6, 1--16, 1997 (with Andrew Barbour and Jinghua Qian**). 

32.  “Palindromes in random letter generation:  Poisson approximations, rates of growth, and Erdös-Rényi laws,” Athens Conference on Applied Probability and Time Series, Volume 1: Applied Probability, C. Heyde, Yu V. Prohorov, R. Pyke, and S.T. Rachev, eds., pp. 99--115, Lecture Notes in Statistics 114, Springer Verlag, New York, 1996 (with Debashis Ghosh*).

33. 3 articles on “Acceptance sampling,” in Encyclopedia of Mathematics,

Supplemental Volume I, pp. 19--20, M. Hazewinkel, ed., Kluwer Academic Publishers, Dordrecht, 1997.

34.  “If rooks could kill: vertex degrees in random bipartite graphs,” in

Proceedings of the 8th Quadrennial International Conference on Graph Theory 2, 445--450, New Issues Press 1998 (With Ben Lamorte* and Jessica Sklar*).

35. “Random Sidon sequences,  Journal of Number Theory 75, 7--22, 1999,  (with  Svante Janson, Nick Locantore*, and Rebecca Rapoport*). 

36. “On the size of a random sphere of influence graph,” Advances in Applied Probability 31, 596—609, 1999, (with Tae Chalker*, Pawel  Hitczenko, Josh Radcliff* and Otto Ruehr).

37. “Threshold functions for the bipartite Turán property,” Electronic Journal of Combinatorics 4, Paper R-18, 15 pages, 1997 (with Ben Lamorte* and Erik Sandquist*).

38.  “Improved upper bounds for the reliability of d-dimensional consecutive k-out-of-n:F systems,” Naval Research Logistics  45, 219--230, 1998  (with Laura Potter* and Jessica Sklar*).

39. “Generalized k-matches,” Statistics and Probability Letters 38, 167--175, 1998 (with Chris McLaren* and Jonathan Herzog*). 

40.  “Beyond the method of bounded differences,” in Microsurveys in Discrete Probability, David Aldous and Jim Propp, eds., pp. 43--58, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 41, American Mathematical Society, Providence, 1998, (with Pawel  Hitczenko). 

41.   “Sign-balanced covering matrices,” Discrete Mathematics 190, 79--93, 1998 (with  Laura Potter* and Erik Sandquist*). 

42. “Contributions to the problem of Zarankiewicz,” Journal of Statistical Planning and Inference 95, 197—208, 2001 (with Heidi Graziano*). 

43. “Computational aspects of a new test for multinomial probabilities,” in Dimension Reduction, Computational Complexity, and Information, Sanford Weisberg, ed., pp. 169—173, Computing science and Statistics 30, Interface Foundation of North America, Fairfax Station, 1998, (with Matt  Gregas*).

44. “Near-matches and successions in random permutations,” Congressus Numerantium 135, 159--170, 1999 (with Papa Sissokho**).

45. “Random sphere of influence graphs in the Lp metrics,” Congressus Numerantium 134, 175--188, 1999 (with Spencer Slade**).

46. “Turán Number,” Encyclopedia of Mathematics,  Supplemental Volume II, p. 471, M. Hazewinkel, ed., Kluwer Academic Press, Dordrecht, 2000.

47. “The Michigan Tech REU Program in Probability,” Proceedings of the Conference on Summer Undergraduate Mathematics Programs, Joe Gallian, ed., American Mathematical Society, pp. 93--104, 2000.

48. “A statistical perspective on inquiry,” Of Significance 1, 41--46, 1999 (with Peg Balachowski**).

49. “On the domination number of a random graph,” Electronic Journal of Combinatorics 8, Paper R37, 13 pages, 2001 (with Ben Wieland*).

50. “Euler’s formula and random geometric graphs,” The Mathematical Scientist 27, 8—15, 2002 (with Jacob Benfield*).

51. “Cliques and independent neighbor sets in random graphs,” Congressus Numerantium 153, 113-128, 2001 (with Dan Ramras* and Sam Greenberg*).

52. “Cooperative learning through undergraduate research,” in Cooperative Learning in Undergraduate Mathematics Education (CLUME), N. Erfan and V. Perera, eds., Karunaratne and Sons, Ltd., pp. 89—101.

53. “An improved upper bound for the pebbling threshold of the n-path,” Discrete Mathematics 275, 367—373, 2004 (with Adam Wierman*, Julia Salzman*, and Michael Jablonski*).

54. “Improved Pebbling Bounds,” submitted to Discrete Mathematics, (with Melody Chan*).

55. “Even 2 X 2 Submatrices of a Random Zero-One Matrix,” Graphs and Combinatorics 20, 457 – 466, 2004 (with Joseph Johnson*).

56. “Some properties of alphabet overlap graphs,” (with Debra Knisley and Rick Norwood).

57. “Probabilistic extensions of the Erdös-Ko-Rado theorem, to appear in Methodology and Computing in Applied Probability, (with Anna Celaya* and Mandy Schleifer*).

58. “Products imply sums,” submitted to College Mathematics Journal, (with Patricia Carey*).

59. “Sierpinski gasket graphs and some of their properties,” Australasian Journal of Combinatorics, 35, 181--192, 2006.  (with Alberto Teguia**).

60. “The fair and random maximal division of “pizza”,” submitted to The Mathematical Scientist, (with Floyd Brown).

61. “Domination cover pebbling:  graph families,” submitted to Journal of Combinatorial Mathematics and Combinatorial Computing, (with James Gardner*, Alberto Teguia**, Annalies Vuong*, Nathaniel Watson*, and Carl Yerger*).

62. “Threshold and complexity results for the cover pebbling game,” submitted to Discrete Mathematics, (with Nathaniel Watson* and Carl Yerger*).

63. “Partial covering arrays and a generalized Erdös-Ko-Rado property,” submitted to J. Combinatorial Designs, (with Patricia Carey*).

64. “Cover pebbling thresholds for the complete graph,” Electronic Notes in Discrete Mathematics, 22, 301—304, 2005. (With Nathaniel Watson* and Carl Yerger*).

65. “Maximal number of regions obtained by a straight line drawing of the complete bipartite graph K_{n,n},” Encyclopedia of Integer Sequences, A117717, 2006 (with Patricia Carey*).

66.  “2 X 2 determinants in the C. L. Dodgson Method,” Encyclopedia of Integer Sequences, A049652, 2006.

 

Professional Service and Editorships:

 

·        Editor of the Council on Undergraduate Research Quarterly (1998-2001).

·        Editor of the Mathematical and Computer Science Division of the Council on Undergraduate Research Quarterly (1995--1998).

·        Councilor in the Mathematics/Computer Science Division of the Council on Undergraduate Research (1992-2000).

·        Member of the Mathematical Association of America's National Committee on the Curriculum for the Undergraduate Program in Mathematics (1996-2002).

·        Reviewer of research proposals for the National Security Agency and the National Science Foundation.  Member of six NSF panel reviews (REU and GK-12 twice, and STEP and Discrete Math and Combinatorics once).

·        Associate Editor of the electronic journal Interstat (1995-2004).

·         Facilitator at the CUR Institute on Grantwriting, 2000, 2004.

·         External reviewer for the Eastern Illinois University Mathematics Department.

·         External reviewer of the Central Michigan University REU Site.

·         Associate Editor of the Kluwer journal Methodology and Computing in Applied Probability (1997-).

·        Reviewer for Mathematical Reviews since 1990.

·        Review panel member of the Bioinformatics program at the University of Texas, San Antonio.

·        Referee for the ~50 professional journals and volumes:  

 

Conferences and Special Sessions Organized:

  

1. Organizer of the Special Session entitled The Probability Theory of

Patterns and Runs held at the American Mathematical Society Meeting in Denton, Texas, November 1990.

2. Co-organizer (with Svetlozar T. Rachev) of the Special Session entitled

Applied Probability held at the American Mathematical Society Meeting in Santa Barbara, California, November 1991.

3. Co-organizer (with Gary Sherman) of two Special Sessions entitled Undergraduate Research in Pure Mathematics and Undergraduate Research in Applied Mathematics, held at the American Mathematical Society Meeting in Washington, D. C., April 1993.

4.  Organizer of the NSF-CBMS Regional Research Conference Probability, Algorithms and Combinatorial Optimization, held in Houghton, Michigan, July 1995.  J. Michael Steele of the University of Pennsylvania was the Principal Lecturer.

5.  Co-organizer (with Prasad Tetali) of the Session on Random Structures and Algorithms, held at the ORSA/TIMS Meeting in Atlanta, June 1995.

6. Organizer of the workshop Undergraduate Research in Mathematics and

Computer Science: Special Problems and Solutions, Council on Undergraduate

Research April Dialogs, National Science Foundation, Arlington, April 1999.

7. Co-Organizer of the NSF-CBMS Regional Research Conference Statistical Inference from Genetic Data on Pedigrees, MTU, July 1999 (with Jianping Dong).  Elizabeth Thompson of the University of Washington was the Principal Lecturer.

8. Co-Organizer of the NSF-CBMS Regional Research Conference Structure and decomposition of Graphs, ETSU, May 2002 (with Debra Knisley).  Robin Thomas of Georgia Tech was the Principal Lecturer.

9. Local Organizer of the Council on Undergraduate Research Proposal Writing Institute, Johnson City, July 2004.

10. Co-Organizer of the Workshop on Mathematical Tools and Statistical Techniques for Quantitative Medical Data Analysis, ETSU, October 2005 (with Don Hong and Robert Gardner).

11. Co-Organizer of the Future Teachers Conference, Johnson City, TN, April 2006 (with Michele Banner).

   

Sponsored Research Grants:

  

1. 1990-91: Pilot Grant for Undergraduate Research awarded by the College of Sciences and Arts, Michigan Technological University.

2. 1991-1992: PI: The Probability Theory of Patterns and Runs, National Science Foundation Grant No. DMS-9100829,  $30,000.

3. 1992-1994: PI: Discrete Probability and Associated Limit Theorems, National Science Foundation Grant No. DMS-9200409,  $60,000.

4. 1994-1997: PI: Probabilistic Methods in Graph Theory, Combinatorics and Number Theory, National Science Foundation Grant No. DMS-9322460,  $90,000.

5. 1995: PI: NSF-CBMS Regional Research Conference in the Mathematical Sciences: Probability, Algorithms, and Combinatorial Optimization, National Science Foundation Grant No. DMS-9415060,  $25,000.

6. 1996: MTU Research and Graduate School Grant to support visit to UC Berkeley, Fall 1996,  $4,500.  

7. 1997-2002: PI: Discrete Random Structures, National Science Foundation Grant No. DMS-9619889,  $200,000.

8. 1997: Genetic Data Analysis, and 1998: Ethics Across the Curriculum; MTU Faculty Development Grants.

9. 1998-1999: co-PI: NSF-CBMS Regional Research Conference in the Mathematical Sciences: Statistical Inference from Genetic Data on Pedigrees, National Science Foundation Grant No. DMS-9813767,  $27,000 (with Jianping Dong).

10. 1998-1999: State of Michigan Research Excellence Fund Grant: Statistical, Mathematical and Computational Problems in Molecular Biology (with Jianping Dong, Renfang Jiang, Huann-Sheng Chen, and Xiaoqiu Huang).

11. 1998-1999:  Girls in Astronomy, Michigan Space Grant Consortium,  $2,500 (with Brenda DeBlois).

12. 1998-1999: PI: Research Experiences for Teachers: Discrete Random Structures,

National Science Foundation Grant DMS 9619889-AMD 002,  $7,500.

13. 1998-1999: Visiting Women and Minority Scholar Grant, MTU Presidential

Commission for Women,  $1,600.

14. 2001-02: Improving the Preparation of Elementary  Education Majors at ETSU, NSF/American Association of State Colleges and Universities, $4,000 (with Janice Huang, Debra Knisley, Bert Bach, and Rhona Cummings).

15. 2001-02:  PI: Research Experiences for Teachers: Discrete Random Structures, National Science Foundation, $25,433.

16. 2002-03: co-PI: NSF-CBMS Regional Research Conference in the Mathematical Sciences: Structure and Decomposition of Graphs, National Science Foundation Grant No. DMS-0122278,  $27,500 (with Debra Knisley).

17. 2002-05: PI: Discrete Random Structures, National Science Foundation Grant No. DMS-0139286,  $144,000.

18. 2002-03: PI: The Unicoi County K-8 Mathematics Initiative, W.K. Kellogg Foundation, $39,000, (with Edith Seier and Debra Knisley).  (Additional Funding in 2003-04: $5850.)

19. 2003-04: PI: Discrete Random Structures – RET Supplement, National Science Foundation Grant No. DMS-0139291, $15,250.

20. 2005: co-PI: Workshop on Mathematical Tools and Statistical Techniques for Quantitative Medical Data Analysis, National Security Agency, $15,000 (with Don Hong and Robert Gardner).

21. 2005—08: co-PI: Tennessee Board of Regents Teacher Preparation Collaborative, National Science Foundation, $1,200,000 (with Jim Kelley, Judy Hector and Maggie Phelps), Grant No. NSF 0501440.

22.  2005—2010, PI:  Talent Expansion in Quantitative Biology, National Science Foundation, $1,000,000 (with Jay Boland, Jack Rhoton, Lev Yampolsky and Hugh Miller), Grant No. NSF 0525447,

23. 2006—09, Probability and Discrete Mathematics, PI.  $181,000, National Science Foundation Grant 0552730.

24. 2006-2010, Planner and Senior Advisor on the Symbiosis grant, $1.7M, Howard Hughes Medical Institute.

 

Administrative and Advising Experience:

 

  

·        Chair, Department of Mathematics, East Tennessee State University, June 2000-present.  Undergraduate Advisor; Member of the University Assessment Committee; Member of the ETSU Quality Enhancement Committee; Member of the Kellogg III Grant-writing Team (joint with Northeastern University, University of Texas (El Paso) and West Virginia University); Chair of History Chair Search Committee; Member of Political Science Department Review Team; member of Dean Search Committee; member of the Master of Arts in Liberal Studies Advisory Board; Chair Biological Sciences Chair Search Committee; Institute for Quantitative Biology Steering Committee; P-16 Committee; State P-16 Math Committee; University School Revisioning Committee;

·        Supervised over 130 undergraduate student projects as part of my involvement with undergraduate research since 1990 – both at ETSU and at MTU.  Several of these projects have culminated in published research.

·        Authored ETSU Mathematics Ph.D. proposal currently under strategic revision.  This program will feature a modeling based doctoral program with internships within the ETSU College of Medicine and Life Sciences Community.

·        Mentored the writing of several NSF and other proposals at ETSU.  These include NSF-CCLI (funded); ITQ (funded); and NSF-MSP/IPSE/STEP (unfunded) proposals.  Was co-PI on several of the latter proposals, with budgets as high as $12.5M.  See http://www.etsu.edu/math/welcome2003.htm and http://www.etsu.edu/math/welcome2006.htm for a list of recent and exciting departmental initiatives.

·        Associate Dean of the MTU College of Sciences and Arts, 1997-2000. Duties include overseeing matters related to curriculum reform, semester conversion, and general education reform within the College; proposal writing for support of interdisciplinary research, integration of research and education, and outreach activity; formation of interdisciplinary research groups; representing the College at various campus forums; development of internships and coop opportunities; formation of a cross-campus group on undergraduate research; development of an Honors program in the Sciences  & Arts; coordinating external departmental reviews, etc.

·        Associate Chair of the Department of Mathematical Sciences at Michigan Tech, 1991-1994. 

·        Director of Graduate Studies from 1990 to 1993.

·        Chief author of the proposal for the Ph.D. program in the Mathematical Sciences. 

·        Member of the Departmental Coordinating; Advisory; Recruitment; Tenure and Reappointment; Curriculum; Ph.D. Proposal; and Statistics Committees. 

·        Advisor to Freshman and Sophomore Mathematics majors.

·        Member of the College of Sciences and Arts Recruitment Committee; member of the College Council; Chair of College Curriculum Committee member of the Academic Forum, member of the Deans/Directors Forum, member of the Academic Deans' Forum.

·        Chair of the University Sabbatical Leave Committee; member of General Education Taskforce; Assessment Council; Diversity Forum; Retention Taskforce; Graduate Council; Continuous Improvement of Academic Advising Committee.

·        Directed several Master's theses in Mathematics and Electrical Engineering; served on several Master’s and Doctoral committees. Major advisees include:  Marilyn Agin (’91), Sanjay Khunger (’92), Hao Zhang (’93), Jinghua Qian (’94), Gomathi Sadhasivan (’95), Matt Gregas (’98), Spencer Slade (’99), Papa Sissokho (’99), Peg Balachowski (’99), Kevin Lynch (2005); and Janeane Young (2006), Crystal Hall (2006), Travis Buck (2006), and James Ray (2006).