Curriculum Vitae

ALEXANDER Y. GORDON

Contact information:

Department of Mathematics and Statistics, University of North Carolina at Charlotte,

9201 University City Blvd, Charlotte, NC 28223, U.S.A.

Phone: 704-687-4576; Fax: 704-687-6415

E-mail: aygordon@uncc.edu

 

EDUCATION AND DEGREES

1988 – Ph.D. in Mathematics: Moscow Institute of Electronic Machine Building
(since 1993 – Moscow State Institute of Electronics and Mathematics).

Thesis: “Spectral Properties of Operators Approximable by Periodic Ones and Decay of Gaps for a Bounded Potential” (Prof. S. A. Molchanov supervised the thesis).
1970 – M.S. with High Honors in Mathematics: Moscow State University.

Thesis: “On Linear Conjugation of Homeomorphisms of Compact Spaces”.

Advisors: Prof. E. A. Gorin, Prof. V. Ya. Lin.

 

POSITIONS HELD OVER THE LAST 15 YEARS

  • University of North Carolina at Charlotte, Department of Mathematics and Statistics (Charlotte, NC)
    Associate Professor (August, 2012 – present)
  • University of North Carolina at Charlotte, Department of Mathematics and Statistics (Charlotte, NC)
    Assistant Professor (August, 2006 – July 2012)
  • University of Rochester, Department of Biostatistics and Computational Biology (Rochester, NY)
    Assistant Professor (July, 2004 – August, 2006)
  • University of Rochester, Department of Biostatistics and Computational Biology (Rochester, NY)
    Analyst/Programmer lead (December, 2002 – June, 2004)
  • PDH International, Inc. (Hallandale, FL)
    Senior Software Engineer/Research Mathematician (January, 1999 – November, 2002)
  • UNC-Charlotte, Department of Mathematics (Charlotte, NC)
    Visiting Assistant Professor/Lecturer/Visiting Research Assistant Professor
    (January, 1995 – December, 1998)

REFEREED ARTICLES

  1. Gordon, A.Y.  (2014)   Absence of $l^1$ eigenfunctions for lattice
    operators with fast local periodic approximation. – To be published in
    Journal of Spectral Theory.
  2. Gordon, A.Y.  (2014)   New operator inequalities in finite-dimensional
    vector spaces. –  To be published in Proceedings of the American Mathematical Society.
  3. Gordon, A.Y.  (2014)   Imperfectly grown periodic medium:
    absence of localized states. – To be published in Journal of Spectral Theory.
  4. Gordon, A.Y., Ray, E. (2014)   Extendability of eigenvalues for continuous families of self-adjoint operators. – To be published in Applicable Analysis.
    Published online: 08 May 2013;  DOI:10.1080/00036811.2013.770476
  5. Gordon, A.Y.  Smoothing of stepwise multiple testing procedures. –
    Statistics and Probability Letters 87 (2014) pp. 149-157.
    DOI: 10.1016/j.spl.2013.12.018
  6. Gordon, A.Y.   A spectral alternative for continuous families of self-adjoint opera-
    tors. – Journal of Spectral Theory 3 (2013) pp. 129-145.    DOI: 10.4171/JST/40
  7. Gordon, A.Y.   A sharp upper bound for the expected number of false rejections. – Statistics and Probability Letters 82 (2012) pp. 1507-1514.
  8. Gordon, A.Y.   A new optimality property of the Holm step-down procedure. – Statistical Methodology 8 (2011) pp. 129-135.
  9. Gordon, A.Y. and Quinn, J.E. Iterated conditional expectations. – Journal of Mathematical Analysis and Applications 367 (2010) pp. 699-704. doi:10.1016/j.jmaa.2010.02.001.
  10. Gordon, A.Y. Inequalities between generalized familywise error rates of a multiple testing procedure. – Statistics and Probability Letters 79 (2009), pp. 1996-2004. doi: 10.1016/j.spl.2009.06.009
  11. Gordon, A., Chen, L., Glazko, L. and Yakovlev, A. Balancing type one and two errors in multiple testing for differential expression of genes. – Computational statistics and data analysis 53(2009), pp. 1622-1629.
  12. Gordon, A.Y. On a problem of Borsuk and Ulam. – Proceedings of the American Mathematical Society 137 (2009), pp. 2135-2137.
  13. Gordon, A.Y. and Salzman, P. Optimality of the Holm procedure among general step-down multiple testing procedures. – Statistics and Probability Letters 78 (2008), pp. 1878-1884.
  14. Gordon, A., Glazko, G., Qiu, X. and Yakovlev, A. Control of the mean number of false discoveries, Bonferroni, and stability of multiple testing. – The Annals of Applied Statistics 1 (2007), pp. 179-190. DOI: 10.1214/07-AOAS102.
  15. Xiao, Y., Gordon, A. and Yakovlev, A. A C++ program for the Cramér-von Mises two-sample test. – Journal of Statistical Software 17, issue 8 (2007), 15 p.
  16. Gordon, A.Y. Explicit formulas for generalized family-wise error rates and unimprovable step-down multiple testing procedures. – Journal of Statistical Planning and Inference 137 (2007), pp. 3497?-3512 (S.N.Roy Centennial Volume); available online at http://dx.doi.org/10.1016/j.jspi.2007.03.027
  17. Gordon, A.Y. Family-wise error rate of a step-down procedure. – Random Operators and Stochastic Equations 15 (2007), pp. 397-406.
  18. Gordon, A.Y. Unimprovability of the Bonferroni procedure in the class of general step-up multiple testing procedures. – Statistics and Probability Letters 77 (2007), pp. 117-122; available online at www.sciencedirect.com.
  19. Gordon, A., Holt, J., Laptev, A. and Molchanov, S. On the Simon-Spencer theorem. – Journal of Mathematical Physics, Analysis, Geometry 4 (2007) pp. 1-14.
  20. Klebanov, L., Gordon, A., Xiao, Y., Land, H., and Yakovlev, A. A permutation test motivated by microarray data analysis. – Computational Statistics and Data Analysis 50 (2006), pp. 3619-3628.
  21. Qiu, X., Xiao, Y., Gordon, A., and Yakovlev, A. Assessing stability of gene selection in microarray data analysis. – BMC Bioinformatics 2006 7:50.
  22. Xiao, Y., Gordon, A. and Yakovlev, A. The -version of the Cramér-von Mises test for two-sample comparisons in microarray data analysis. – EURASIP Journal on Bioinformatics and Systems Biology Volume 2006, Article ID 85769, pp. 1-9. doi:10.1155/BSB/2006/85769.
  23. Glazko, G., Gordon, A., and Mushegian, A. The choice of optimal distance measure in genome-wide data sets. – Bioinformatics 2005 21: iii3-iii11.
  24. Dow, A., Ganguli, S., Gordon, A.Y., and Molchanov, S. A problem by E. Landis and generic behavior of non-generic sets. – Applicable Analysis 84 (2005), pp. 927-952.
  25. Xiao, Y., Frisina, R., Gordon, A.Y., Klebanov, L., and Yakovlev, A. Multivariate search for differentially expressed gene combinations. – BMC Bioinformatics 2004, 5:134.
  26. Derfel, G., Gordon, A.Y., and Molchanov, S.A. Random matrices over  and testing random number generators. – Random Operators and Stochastic Equations 12 (2004), pp. 1-10.
  27. Figotin, A., Gordon, A.Y., Molchanov, S.A., Quinn, J.E., and Stavrakas, N. Occupancy numbers in testing random number generators. – SIAM Journal of Applied Mathematics 62 (2002), no. 6, pp. 1980-2011.
  28. Figotin, A., Gordon, A.Y., Molchanov, S.A., Quinn, J.E., and Stavrakas, N. Generalized quantum statistics and testing of randomizers with and without asymptotic assumptions. – Monte Carlo Methods and Applications 7 (2001), pp. 167-176.
  29. Gordon, A.Y. and Kechris, A.S. Measurable enumeration of eigenelements, – Applicable Analysis, 71 (1999), pp. 41-62.
  30. Gordon, A.Y. Purely continuous spectrum for generic almost-periodic potential. – Contemporary Mathematics, 217 (1998), pp. 183-189.
  31. Gordon, A.Y., Jitomirskaya, S., Last, Y., and Simon, B. Duality and singular continuous spectrum in the almost Mathieu equation, Acta Mathematica 178 (1997), pp. 169-183.
  32. Gordon, A.Y. Instability of dense point spectrum under finite rank perturbations, Communications in Mathematical Physics 187 (1997), pp. 583-595.
  33. Gordon, A.Y. A fast algorithm for the solution of the inviscid Burgers equation, Vychislitel’naja Seismologija (Computational Seismology) 29, Moscow, 1997, pp. 179-189 (in Russian).
  34. Gordon, A.Y. Eigenvalues of the one-dimensional Schrédinger operator that are located on its essential spectrum, Algebra i Analiz (Algebra and Analysis) 8, no. 1 (1996), pp. 113-121 (in Russian).
  35. Gordon, A.Y. Strong unboundedness of unbounded analytic functions, Proceedings of the American Mathematical Society 122 (1994), pp. 525-529.
  36. Gordon, A.Y. Pure point spectrum under one-parameter perturbations and instability of Anderson localization, Communications in Mathematical Physics 164 (1994), pp. 489-505.
  37. Gordon, A.Y., Jaksic, V., Molchanov, S.A., and Simon, B. Spectral properties of random Schrédinger operators with unbounded potentials, Communications in Mathematical Physics 157(1993), pp. 23-50.
  38. Maslov, V.P., Molchanov, S.A., and Gordon, A.Y. Behaviour of generalized eigenfunctions at infinity and the Schrédinger conjecture. Russian Journal of Mathematical Physics 1, no. 1 (1993), pp. 71-104.
  39. Gordon, A.Y. On exceptional values of boundary phase for Schrédinger equation on the half-axis, Russian Mathematical Surveys 47, no. 1 (1992), pp. 260-261.
  40. Gordon, A.Y., Molchanov, S. A., and Tzagani, B. Spectral theory of one-dimensional Schrédinger operators with strongly fluctuating potentials, Functional Analysis and its Applications 25, no. 3 (1991), pp. 236-238.
  41. Gordon, A.Y. A deterministic potential with pure point spectrum, Mathematical Notes 48, no. 5 – 6 (1990), pp. 1197-1203.
  42. Gordon, A.Y. A sufficient condition for the continuity of the spectrum of a discrete Schrédinger operator, Functional Analysis and its Applications 20, no. 4 (1986), pp. 313-315.
  43. Gordon, A.Y. An example of an analytic flow on a torus with a mixed spectrum, Theory of Functions, Functional Analysis and their Applications, No. 33, Kharkov Univ. Press, Kharkov, 1980, pp. 40-45 (in Russian). English translation: Selecta Mathematica Sovetica 8, no. 4, pp. 292-298, Birkhéuser Verlag, Basel, 1989.
  44. Gordon, A.Y. Continuous spectrum of a one-dimensional Schrédinger operator, Functional Analysis and its Applications 13, no. 3 (1979), pp. 218-219.
  45. Gordon, A.Y. On the point spectrum of one-dimensional Schrédinger operator, Uspehi Matematicheskih Nauk (Russian Mathematical Surveys) 31, no. 4 (1976), pp. 257-258 (in Russian).
  46. Gordon, A.Y. Sufficient condition for unsolvability of the additive functional homological equation connected with the ergodic rotation of a circle, Functional Analysis and its Applications 9, no. 4 (1975), pp. 334-336.
  47. Gordon, A.Y. and Levin, B.Y. On the division of quasi-polynomials, Functional Analysis and its Applications 5, no. 1 (1971).
  48. Gordon, A.Y. The linear conjugation of homeomorphisms of compact spaces, Uspehi Matematicheskih Nauk (Russian Mathematical Surveys) 25, no. 6 (1970) pp. 257-258 (in Russian).

 

REFEREED BOOK CHAPTERS

  1. Gordon, A.Y. Multiple testing procedures: monotonicity and some of its implications. – Accepted for publication in the Collections series of the Institute of Mathematical Statistics.
  2. Gordon, A. and Sonin, I. The expected number of intersections of a four valued bounded martingale with any level may be infinite. – In: Optimality and Risk – Modern Trends in Mathematical Finance (Editors: F. Delbaen et al), Springer-Verlag, Berlin (2009), pp. 87-98. DOI: 10.1007/978-3-642-02608-9_1.
  3. Gordon, A., Holt, J. and Molchanov, S. Spectral theory of 1-D Schrédinger operators with unbounded potentials. – In: CRM Proceedings and Lecture Notes 42 (2007), pp. 181-198.
  4. Gordon, A., Molchanov, S. and Quinn, J. Fermi – Dirac generators and tests for randomness. – In: CRM Proceedings and Lecture Notes 42 (2007), pp. 199-224.
  5. Gordon, A.Y. On the inverse problem of the best approximation by the entire functions of exponential type. – In: “Studies in the theory of functions of several real variables”. – Yaroslavl University Press, Yaroslavl, 1990 (in Russian). – English version in: Lecture Notes in Mathematics 1043 (Linear and Complex Analysis Problem Book), Springer-Verlag, 1984, pp. 592-594.
  6. Gordon, A.Y., Gorin, E.A., Lin, V.Ya., and Tonev, T.V. On topological conjugation of semi-linear homeomorphisms. – In: “Studies in the theory of functions of several real variables”, Yaroslavl University Press, Yaroslavl, 1980, pp. 63-83 (in Russian; review 84j:54028 in Mathematical Reviews).
  7. Gordon, A.Y. An algorithm for the solution of the minimax scheduling problem. – In: “Studies in Discrete Optimization”, Moscow, “Nauka”, 1976, pp. 327-333 (in Russian).

 

PATENT

US Patent No. US 6,745,217 B2 (awarded June 1, 2004)

“Random number generator based on the spontaneous alpha-decay”

(A. Figotin, I. Vitebskiy, V. Popovich, G. Stetsenko, S. Molchanov, A. Gordon, J. Quinn, N. Stavrakas)

 

RECENT CONFERENCE TALKS

  1. 35th Conference of SIAM-SEAS (Society for Industrial and Applied Mathematics, Southeastern Atlantic Section), Charlotte, NC, March 26-27, 2011. “A class of random operators with continuous spectra” (contributed talk).
  2. Central Section Meeting of AMS (American Mathematical Society), Iowa City, IA, March 18-20, 2011. “On the Simon-Spencer Theorem” (contributed talk). This was a joint research with J.Holt, A.Laptev and S.Molchanov.
  3. Annual meeting of WNAR (Western North American Region of the International Biometric Society), Seattle, WA, June 20-23, 2010. “Expected number of false discoveries for stepwise procedures” (contributed talk).
  4. Joint Statistical Meeting, Washington, DC, August 2-6, 2009. “A new optimality property of the Holm procedure” (contributed talk in Biometrics section).
  5. Statistical Modeling for Biological Systems, Rochester, NY, June 8-9, 2009. “Monotone multiple testing procedures” (invited talk).
  6. Joint Statistical Meeting, Denver, TX, August 2-7, 2008. “Monotone multiple testing procedures and implications of monotonicity” (contributed talk in Biometrics section).
  7. Joint Statistical Meeting, Salt Lake City, UT, July 29 – August 2, 2007. “Exonerating Bonferroni’s multiple testing procedure” (contributed talk in Biometrics section). This was a joint research with G. Glazko, X. Qiu and A. Yakovlev.
  8. Annual meeting of WNAR (Western North American Region of the International Biometric Society), Irvine, CA, June 24-27, 2007. “Multiple testing procedures and their generalized family-wise error rates” (contributed talk).
  9. Joint Statistical Meeting, Minneapolis, MN, August 6-11, 2005. “Generalized family-wise error rates for threshold step-down multiple testing procedures” (contributed talk in Biometrics section).
  10. Conference “Probability and Mathematical Physics”, CRM, Université de Montréal, Montréal, June 27 – July 1, 2005. “Cantor spectrum for a generic almost periodic operator with given frequencies” (invited talk).
  11. Annual meeting of ENAR (Eastern North American Region of the International Biometric Society), Austin, TX, March 20-23, 2005. “-value-only-based stepwise procedures for multiple testing and their optimality properties” (contributed talk).

 

RECENT COLLOQUIUM TALKS

  1. Seminar in Mathematical Physics, University of California at Irvine, June 28, 2007. “Iterated conditional expectations”.
  2. Seminar in Mathematical Physics, Rice University, Houston, TX, February 23, 2007. “A spectral alternative for continuous families of self-adjoint operators”.
  3. Seminar in Mathematical Physics, University of California at Irvine, June 19, 2006. “Genericity of Cantor spectrum for almost periodic operators”.

 

MEMBERSHIP IN A HONORARY SCIENTIFIC ASSOCIATION

– International Association of Mathematical Physics
MEMBERSHIP IN OTHER PROFESSIONAL ASSOCIATIONS

– Institute of Mathematical Statistics

– American Mathematical Society

– Mathematical Association of America

 

EDITORIAL BOARD MEMBERSHIP

– “Biology Direct”

 

TEACHING

  • Spring 2011

MATH2241-003 (Calculus III)

MATH2241-090 (Calculus III)

  • Fall 2010

MATH2241-005 (Calculus III)

MATH2241-006 (Calculus III)

  • Spring 2010

MATH2241-004 (Calculus III)

MATH2241-090 (Calculus III)

  • Fall 2009

MATH2241-005 (Calculus III)

MATH3122/STAT3122-090 (Probability and Statistics I)

  • Spring 2009

MATH2241-004 (Calculus III)

MATH7141/MATH8141-090 (Complex Analysis – graduate course)

  • Fall 2008

MATH2241-005 (Calculus III)

MATH3122/STAT3122-090 (Probability and Statistics I)

  • Spring 2008

MATH2241-004 (Calculus III)

MATH2242-090 (Calculus IV)

  • Fall 2007

MATH2241-004 (Calculus III)

MATH2241-090 (Calculus III)

  • Spring 2007

MATH2242-001 (Calculus IV)

MATH2242-090 (Calculus IV)

  • Fall 2006

STAT5126-001 (Theory of statistics I – graduate course)

 

WORK IN PROGRESS

  • Gordon, A.Y., Molchanov, S., Sonin, I. The shift and index inequalities and their properties. – Under review.

 

  • Gordon, A.Y. A sharp upper bound for the expected number of false discoveries in microarray data analysis. – In preparation.

 

  • Gordon, A.Y., Holt, J., Laptev, A., Molchanov, S. Generalized Simon – Spencer theorem. – In preparation.

 

  • Gordon, A.Y., Molchanov, S. The limit behavior on the real line of Hilbert transforms of discrete approximations to a measure. – In preparation.

 

Listed below are some of those projects on which I worked over the last few years and which are most likely to become papers in the near future.

 

  • Gordon, A.Y. Multiple testing procedures: some general notions and their applications.

 

  • Gordon, A.Y. Smoothing of stepwise multiple testing procedures.

 

  • Gordon, A.Y. Familywise error rate of a step-up-down procedure.

 

  • Gordon, A.Y. Unsolvable homological equations on the circle.

 

  • Gordon, A.Y. The Borsuk – Ulam problem on a general compact manifold.