J. Maurice Rojas' Mathematical Papers (Including Supplemental Software)

All downloadable papers listed below are in gzip'd Postscript format. If you're on a Windows system then you may need to install PKunzip and Adobe Acrobat (or Ghostview), or some similar pair of file decompression and Postscript viewing software. If you have trouble finding a non-downloadable paper below then please e-mail me at rojas@math.tamu.edu .

You can also find abstracts (in HTML format) for the papers listed below by clicking HERE.

58. ``A Sparse Effective Real Nullstellensatz for Complex Dimension Zero,'' in preparation.
57 ``A Complex Analytic Approach to Real Solving,'' in preparation.
56. ``Tropical Mixed Volumes and non-Archimedean Amoebae,'' in preparation.
55. ``Algorithmic Arithmetic Fewnomial Theory I: One Variable,'' with Ashraf Ibrahim and Korben Rusek, submitted for publication.
54. Book Review: Basu, Pollack, and Roy's Algorithms in Real Algebraic Geometry,, Foundations of Computational Mathematics, to appear.
53. ``New Complexity Bounds for Certain Real Fewnomial Zero Sets (Extended Abstract),'' with Joel Gomez and Andrew Niles, accepted for presentation at MEGA 2007, RICAM (Johann Radon Institute for Compuational and Applied Mathematics), Strobl, Austria, June 24-30, 2007.
52. ``Sharpness of Fewnomial Bound and the Number of Components of a Fewnomial Hypersurface,'' (with Frederic Bihan and Frank Sottile), Algorithms in Algebraic Geometry (Alicia Dickenstein, Frank-Olaf Schreyer, and Andrew J. Sommese, eds.), IMA Volumes in Mathematics and its Applications, Vol. 146, pp. 15-20, Springer-Verlag, 2007.
51. ``On Interpolating Between Quantum and Classical Complexity Classes,'' Proceedings of Mathematics of Quantum Computation and Quantum Technology (November 13-16, 2005, Texas A&M University), pp. 67-88, Taylor & Francis, 2007.
50. ``Efficiently Detecting Subtori and Torsion Points,'' proceedings of MAGIC 2005 (Midwest Algebra, Geometry, and their Interactions Conference, Oct. 7-11, 2005, Notre Dame University, Indiana), edited by A. Corso, J. Migliore, and C. Polini), pp. 213-233, Contemporary Mathematics, vol. 448, AMS Press, 2007.
49. ``Extremal Real Algebraic Geometry and A-Discriminants,'' (with Alicia Dickenstein, Korben Rusek, and Justin Shih), Moscow Mathematical Journal, vol. 7, no. 3, July-September 2007, pp. 425-452.
48. ``A New Method of Motion Coordination of a Group of Mobile Robots,'' (with S. Sethuraman, M. Lal, and S. Jayasuriya), Proceedings of IMECE 2006 (ASME International Mechanical Engineering Congress and Exposition, Nov. 5-10, 2006, Chicago, Illinois), to appear.
47. ``Open Questions on Extensions of Hilbert's Tenth Problem,'' expository paper for Workshop on Extensions of Hilbert's Tenth Problem, American Institute of Mathematics (March 21-25, 2005), Palo Alto, California
46. ``Practical Conversion from Torsion Space to Cartesian Space for in silico Protein Synthesis,'' (with Jerod Parsons, Brad Holmes, Jerry Tsai, and Charlie E. Strauss), Journal of Computational Chemistry, vol. 26 (July 2005), Issue 10, pp. 1063-1068.
45. ``First Steps in Algorithmic Real Fewnomial Theory,'' with Frederic Bihan and Casey E. Stella, submitted for publication.
44. ``Open Questions on Amoeba Theory and Tropical Geometry,'' expository paper for Workshop on Amoebas and Tropical Geometry, October 23-26, 2003, American Institute of Mathematics, Palo Alto, California.
43. ``A Direct Ultrametric Approach to Additive Complexity and the Shub-Smale Tau Conjecture, submitted for publication.
42. ``Dedekind Zeta Functions and the Complexity of Hilbert's Nullstellensatz,'' paper corresponding to semi-plenary talk at FoCM 2002 (August 5-14, 2002, University of Minnesota, Minneapolis), submitted for publication.
41. ``An Improved Bound on the VC-Dimension of Neural Networks with Polynomial Activation Functions'' (with M. Vidyasagar), submitted for publication.
40. ``On Solving Univariate Sparse Polynomials in Logarithmic Time,'' (with Yinyu Ye), Journal of Complexity, Volume 21, Issue 1 (Foundations of Computational Mathematics Conference 2002 special issue), February 2005, pp. 87-110.
39. ``The Exact Rational Univariate Representation for Detecting Degeneracies,'' (with John Keyser and Koji Ouchi), Geometric and Algorithmic Aspects of Computer-Aided Design and Manufacturing (AMS/DIMACS Series in Discrete Mathematics and Theoretical Computer Science), edited by Ravi Janardan, Michiel Smid, and Debasis Dutta, pp. 299-328, AMS Press (2005).
38. ``High Probability Analysis of the Condition Number of Sparse Polynomial Systems'' (with Gregorio Malajovich), Theoretical Computer Science, special issue on algebraic and numerical algorithms, Vol. 315, no. 2-3, pp. 525-555 (May 6, 2004).
37. ``Attitude and Position Estimation from Vector Observations,'' (with Daniele Mortari and John L. Junkins), Proceedings of the AAS/AIAA Space Flight Mechanics Meeting (February 9-13, 2004, Maui, Hawaii), paper AAS 04-140.
36. ``Arithmetic Multivariate Descartes' Rule,'' American Journal of Mathematics, vol. 126, no. 1, February 2004, pp. 1-30. A bit of supplemental Maple code can be found HERE.
35. ``On the Determination of the Degree of an Equation Obtained by Elimination,'' (with David A. Cox), (translation of, and commentary on, a famous 1841 paper of Ferdinand Minding), Contemporary Mathematics, vol. 334, pp. 351-361, American Mathematical Society, 2003.
34. ``Why Polyhedra Matter in Non-Linear Equation Solving,'' paper corresponding to an invited talk delivered at a conference on Algebraic Geometry and Geometric Modelling (Vilnius, Lithuania, July 29-August 2, 2002), Contemporary Mathematics, vol. 334, pp. 293-320, American Mathematical Society, 2003.
33. ``Counting Real Connected Components of Trinomials Curve Intersections and m-nomial Hypersurfaces,'' (with Tien-Yien LI and Xiaoshen WANG), Discrete and Computational Geometry, 30 (2003), no. 3, pp. 379-414.
32. ``1+1=0 and Information Security'', (invited 2 page expository article for non-scientists), Advance, Texas A&M University, Office of the Vice President for Research, 2003.
31. ``Random Polynomial Systems,'' (with Gregorio Malajovich), Math ArXiV preprint math.NA/0012104.
30. ``Computing Complex Dimension Faster and Deterministically,'' Math ArXiV preprint math.AG/0005028.
29. ``Descartes' Rule for Trinomials in the Plane and Beyond,'' Math ArXiV preprint math.CO/0008069v2.
28. Geometry and Topology: Seven Lectures by Raoul Bott, (notes edited by J. Maurice Rojas), Lecture Notes in Mathematics, Liu Bie Ju Centre for the Mathematical Sciences, City University of Hong Kong, to appear.
27. ``Additive Complexity and the Roots of Polynomials Over Number Fields and p-adic Fields,'' Proceedings of ANTS-V (5th Annual Algorithmic Number Theory Symposium, University of Sydney, July 7-12, 2002), Lecture Notes in Computer Science #2369, Springer-Verlag (2002), pp. 506-515. A bit of supplemental Maple code can be found HERE.
26. Proceedings of Smalefest 2000: Papers From an International Conference in Honor of Steve Smale's 70th Birthday (July 2000, City University of Hong Kong), edited with Felipe Cucker, World Scientific, 2002. You can view the cover, title page, foreword, and table of contents now.
25. ``Extending Triangulations and Semistable Reduction,'' (with Dan Abramovich), Proceedings of FoCM 2000, special meeting in honor of Steve Smale's 70th birthday (July 2000, City University of Hong Kong, Hong Kong), pp. 1-13, World Scientific, 2002.
24. ``Polynomial Systems and the Momentum Map,'' (with Gregorio Malajovich), Proceedings of FoCM 2000, special meeting in honor of Steve Smale's 70th birthday (July 2000, City University of Hong Kong, Hong Kong), pp. 251-266, World Scientific, 2002.
23. ``Finiteness for Arithmetic Fewnomial Systems,'' invited paper, Contemporary Mathematics, vol. 286, AMS-IMS-SIAM Joint Summer Research Conference Proceedings of ``Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering (June 11-15, 2000, Mount Holyoke College),'' edited by E. Green, S. Hosten, R. Laubenbacher and V. Powers, pp. 107-114, AMS Press, 2001.
22. ``Computational Arithmetic Geometry I: Sentences Nearly in the Polynomial Hierarchy,'' Journal of Computer and Systems Science, vol. 62, no. 2, march 2001, pp. 216-235.
21. ``Algebraic Geometry Over Four Rings and the Frontier to Tractability,'' invited paper, Contemporary Mathematics, vol. 270, Proceedings of a Conference on Hilbert's Tenth Problem and Related Subjects (University of Gent, November 1-5, 1999), edited by Jan Denef, Leonard Lipshitz, Thanases Pheidas, and Jan Van Geel, pp. 275-321, AMS Press (2000).
20. ``Some Speed-Ups and Speed Limits for Real Algebraic Geometry,'' Journal of Complexity, FoCM 1999 special issue, vol. 16, no. 3 (sept. 2000), pp. 552-571.
[Winner of the Journal of Complexity 2000 Best Paper Award!]
19. ``Uncomputably Large Integral Points on Algebraic Plane Curves?,'' Theoretical Computer Science, special issue in honor of Manuel Blum's 60th birthday, vol. 235, no. 1, March 2000, pp. 145-162.
18. ``On the Complexity of Diophantine Geometry in Low Dimensions,'' Proceedings of the 31st Annual ACM Symposium on Theory of Computing (STOC '99, May 1-4, 1999, Atlanta, Georgia), pp. 527-536, ACM Press, 1999.
17. ``Solving Degenerate Sparse Polynomial Systems Faster,'' Journal of Symbolic Computation, vol. 28 (special issue on elimination theory), no. 1/2, July and August 1999, pp. 155-186.
16. ``Toric Intersection Theory for Affine Root Counting,'' Journal of Pure and Applied Algebra, vol. 136, no.1, March, 1999, pp. 67-100.
15. ``Intrinsic Near Quadratic Complexity Bounds for Real Multivariate Root Counting,'' Proceedings of the Sixth Annual European Symposium on Algorithms, Lecture Notes on Computer Science, vol. 1461, pp. 127-138, Springer-Verlag (1998).
14. ``Affine Elimination Theory (Extended Abstract),'' Proceedings of a conference in honor of the 60th birthday of David A. Buchsbaum, Northeastern University, October, 1997.
13. ``Toric Generalized Characteristic Polynomials,'' MSRI Preprint #1997-017.
12. ``Some New Applications of Toric Geometry,'' MSRI Preprint.
11. ``A New Approach to Counting Nash Equilibria,'' Proceedings of the IEEE/IAFE Conference on Computational Intelligence for Financial Engineering, Manhattan, New York, March 23--25, 1997, pp. 130-136.
10. ``Toric Laminations, Sparse Generalized Characteristic Polynomials, and a Refinement of Hilbert's Tenth Problem,'' Foundations of Computational Mathematics, selected papers of a conference, held at IMPA in Rio de Janeiro, January 1997, Felipe Cucker and Mike Shub (eds.), pp. 369-381, Springer-Verlag (1997).
9. ``Commutative Algebra Without Commutativity,'' sole solution to Problem 10437, American Mathematical Monthly, vol. 104, no. 7, Aug.-Sep. 1997.
8. ``Counting Affine Roots Via Pointed Newton Polytopes,'' (with Xiaoshen Wang), Journal of Complexity, vol. 12 (June 1996), pp. 116-133.
7. ``On the Average Number of Real Roots of Certain Sparse Polynomial Systems,'' Lectures in Applied Mathematics, Vol. 32 (1996), pp. 689-699, American Mathematical Society.
6. ``Extensions and Corrections for `A Convex Geometric...','' MSRI preprint.
5. Cohomology, Combinatorics, and Complexity Arising from Solving Polynomial Systems, Ph.D. thesis, UC Berkeley, 1995.
4. Problem 10437, American Mathematical Monthly, Vol. 102, #2, February 1995, page 170.
3. ``A Convex Geometric Approach to Counting the Roots of a Polynomial System,'' Theoretical Computer Science, vol. 133 (1), pp. 105-140, October, 1994.
2. ``A New Upper Bound on the Number of Roots of a Multilinear System,'' technical report, SCAMP 1992, Center for Communications Research, Princeton, New Jersey.
1. ``An Optimal Condition for Determining the Exact Number of Roots of a Polynomial System,'' (with John Canny), Proceedings of ISSAC '91 (Bonn, Germany), pp. 96-102, ACM Press, 1991.

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