Anthony Macula

Professor of Mathematics
South 325D

Anthony Macula has been a member of the Geneseo faculty since 1993.

Anthony Macula Profile

Office Hours

  • Tu/Th: 2:30 - 4:00
  • or by appointment

Curriculum Vitae


  • B.S., State University of New York at Plattsburgh, 1983

  • Ph.D., Wesleyan University, 1989


  • PCR Nonadaptive Group Testing of DNA Libraries for Biomolecular Computing and Taggant Applications, Discrete Mathematics, Algorithms and Applications, Volume: 1, Issue 1(March 2009), 59 - 69 (with former student Morgan Bishop et al.)

  • Successful preparation and analysis of a 5-site 2-variable DNA library, Natural Computing, 8 (2009), no. 2, 333?347

  • Erdos-Renyi like uniform vaccination bound for a small-world network 2-D lattice. Bull. Inst. Combin. Appl. 56 (2009) (with students Daniel Marcus and Jordan Rogers)

  • Random Coding Bounds for DNA Codes Based on Fibonacci Ensembles of DNA Sequences, 2008 IEEE Proceedings of International Symposium on Information Theory, pp. 2292 - 2296

  • Hypothesis group testing for disjoint pairs, Journal Combinatorial Optimization, 15, 2008, 7-16 (with student Vladmir Ufimstev)

  • Nonadaptive and trivial two-stage group testing with error-correcting (d,e)-disjunct inclusion matrices. Entropy, search, complexity, 71?83, Bolyai Soc. Math. Stud., 16, Springer, Berlin, 2007.

  • New, improved, and practical k-stem sequence similarity measures for probe design, Journal of Computational Biology, 2008 Jun;15(5):525-34 (with former student Morgan Bishop)

  • Free energy gap and statistical thermodynamic fidelity of DNA codes. J. Comput. Biol. 14 (2007), no. 8, 1088?1104 (with former student Morgan Bishop)

  • DNA Codes Based on Stem Similarities Between DNA Sequences, DNA 13, Memphis, TN. Springer Lecture Notes in Computer Science, Volume 4848 (2008) 146-151.

  • Component averages in subgraphs of circulant-like graphs. Bull. Inst. Combin. Appl. 51 (2007), 55?68 (with students Jacqueline Dresch and Niels Hansen)

  • Group testing to annihilate pairs applied to DNA cross-hybridization elimination using SYBR Green I. J. Comput. Biol. 14 (2007), no. 1, 84?96 (with students Kayla Nimmo, Lauren Wood, Morgan Bishop)

  • Network structure, and vaccination strategy and effort interact to affect the dynamics of influenza epidemics, J. Theor. Biol. 2007 May 21;246(2):205-13 (with students Jacqueline Dresch, Amy Zielski)

  • New t-gap insertion-deletion-like metrics for DNA hybridization thermodynamic modeling. J. Comput. Biol. 13 (2006), no. 4, 866?881

  • Experimental validation of DNA sequences for DNA computing: Use of a SYBR green I assay, Proceedings DNA 11, London, Ont. Springer Lecture Notes in Computer Science, Volume 3892 (2006) 248-256

  • A Weighted Insertion-Deletion Stacked Pair Thermodynamic Metric for DNA Codes, Lecture Notes in Computer Science, Springer-Verlag , Volume 3384, 90-103 (2005)

  • A group testing method for finding patterns in data, Discrete Appl. Math. 144, 149-157, 2004

  • Exordium for DNA codes, J. Comb. Optim. 7, no. 4, 369-379, 2004

  • Trivial two-stage group testing with high error rates, J. Comb. Optim. 7, no. 4, 361--369. 2004

  • Trivial two-stage group testing for complexes using almost disjunct matrices, Discrete Applied Mathematics, Volume 137, Issue 1, 27 February 2004, Pages 97-107

  • One-stage balance scale searching with errors, Bulletin of the Institute of Combinatorics and its Applications 38, 76-83, 2004 (with student Charles Engelhart)

  • Trivial two-stage group testing for complexes using almost disjunct matrices. 1st International Workshop on Combinatorics of Searching, Sorting, and Coding (COSSAC '01) (Ischia). Discrete Appl. Math. 137 (2004), no. 1, 97?107.

  • Families of finite sets in which no intersection of l sets is covered by the union of s others. J. Combin. Theory Ser. A 99 (2002), no. 2, 195?218.

  • Probabilistic nonadaptive group testing in the presence of errors and inhibitors. Recent advances in experimental designs and related topics (Philadelphia, PA, 1999), 73?85, Nova Sci. Publ., Huntington, NY, 2001

  • Two models of nonadaptive group testing for designing screening experiments. mODa 6?advances in model-oriented design and analysis (Puchberg/Schneeberg, 2001), 63?75, Contrib. Statist., Physica, Heidelberg, 2001

  • Two-stage group testing for complexes in the presence of errors. Discrete mathematical problems with medical applications (New Brunswick, NJ, 1999), 145?157, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 55, Amer. Math. Soc., Providence, RI, 2000

  • A new data mining technique for the analysis of simulated genetic data, Proceedings of Genetic Analysis Workshop 12, Wiley-Liss, 2001; Genetic Epidemiology, 21 Suppl. 1: S390-5

  • New constructions of superimposed codes. IEEE Trans. Inform. Theory 46 (2000), no. 1, 284?290

  • Probabilistic nonadaptive group testing in the presence of errors and DNA library screening. Combinatorics and biology (Los Alamos, NM, 1998). Ann. Comb. 3 (1999), no. 1, 61?69

  • A Combinatorial Profiling Model for Intrusion Detection and Analysis, IEEE Conference on Information Assurance and Security, West Point, NY, 2000, 47-52.

  • On the probability that subset sequences are minimal. Discrete Math. 207 (1999), no. 1-3, 285?289. (with student Dung Le)

  • New applications and results of superimposed code theory arising from the potentialities of molecular biology. Numbers, information and complexity (Bielefeld, 1998), 265?282, Kluwer Acad. Publ., Boston, MA, 2000

  • Nonadaptive and Two-Stage Group Testing with Relatively Small Pools and DNA Library Screening, Journal of Combinatorial Optimization, 2, 385-397 (1999)

  • An analysis of the lines in the three dimensional affine space over F3, Ars Combinatoria, 53, 1999, 161-171

  • Simplified searching for two defects. J. Statist. Plann. Inference 66 (1998), no. 1, 77?82 (with student George Reuter)

  • Error-correcting nonadaptive group testing with (d,e)-disjunct matrices. Discrete Appl. Math. 80 (1997), no. 2-3, 217?222

  • Using generating functions to compute allowable plane separations by nearly simple arrangements. Bull. Inst. Combin. Appl. 21 (1997), 104?107 (with student Lisa Orloff)

  • A non-adaptive search algorithm that identifies up to three defects. J. Statist. Plann. Inference 60 (1997), no. 2, 269?272.

  • A nonadaptive version of Ulam's problem with one lie. J. Statist. Plann. Inference 61 (1997), no. 1, 175?180

  • Two applications of separating systems to nonadaptive procedures. Discrete Math. 169 (1997), no. 1-3, 257?262,

  • Using separating systems to extract subfamilies of set systems with minimum Hamming distance three and four. Bull. Inst. Combin. Appl. 19 (1997), 118?120

  • A simple construction of d-disjunct matrices with certain constant weights. Discrete Math. 162 (1996), no. 1-3, 311?312

  • Lewis Carroll and the enumeration of minimal covers. Math. Mag. 68 (1995), no. 4, 269?274.

  • The point-slope formula leads to the Fundamental Theorem of Calculus, College Mathematics Journal, 26, No. 2, 135-139 (1995)

  • Covers of a finite set, Mathematics Magazine 67 no. 2, 141-144 (1994).

  • Quantifying order in plane separation problems, Journal of Recreational Mathematics, 26, no. 4, 267-273 (1994) (with student Cindy Musante)

  • On k-bounded and q-weakly regular separating systems. Proceedings of the Twenty-fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1994). Congr. Numer. 104 (1994)

  • Average search lengths of predetermined algorithms with very small question set intersections. Proceedings of the Twenty-fourth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1993). Congr. Numer. 97 (1993), 91?98

  • Heads or tails? A dual approach to a counterfeit coin problem. Proceedings of the Twenty-fourth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1993). Congr. Numer. 96 (1993), 3?9.

  • ?-Dedekind complete Archimedean vector lattices versus quasi-F spaces. Proceedings of the Symposium on General Topology and Applications (Oxford, 1989). Topology Appl. 44 (1992), no. 1-3, 217?234.

  • Free ?-extensions of an Archimedean vector lattice and their topological duals. Trans. Amer. Math. Soc. 332 (1992), no. 1, 437?448.

  • Monic sometimes means ?-irreducible. General topology and applications (Staten Island, NY, 1989), 239?260, Lecture Notes in Pure and Appl. Math., 134, Dekker, New York, 1991.

  • An ?-disconnected space has no proper monic preimage. Topology Appl. 37 (1990), no. 2, 141?151.

  • Archimedean vector lattices versus topological spaces with filters. Thesis (Ph.D.)?Wesleyan University. 1989. 158 pp

Research Interests

I have published papers with significant content in the following areas: Anti-Counterfeiting, Biomolecular Computing, Genomics, Disease Transmission, Group Testing, Search Theory, Information Theory, Combinatorics, Coding Theory, Computer Security, Statistics, Probability, Finite Geometry, Topology, Category Theory and Math Education. Most of the papers below have co-authors (over 40 in total, including 14 undergrads). My Erdos number is 3. I have been the Project Director for 13 externally funded research grants totaling 2.5 million dollars. I've been a reviewer for several journals, the National Science Foundation and I am an associate editor for the journal Discrete Mathematics Algorithms and Applications. In 2007, I received the SUNY Research Foundation Excellence in Research Award.


  • MATH 221: R/Calculus I

    Topics studied are limits and continuity; derivatives and antiderivatives of the algebraic and trigonometric functions; the definite integral; and the fundamental theorem of the calculus. Prerequisites: MATH 112 or Precalculus with trigonometry or the equivalent. Offered every semester

  • MATH 315: Combinatorics

    As calculus seeks to develop proficiency in analysis problem solving, the aim of this course is to develop proficiency in basic combinatorial problem solving and reasoning. Topics include: Enumeration, generating functions, sieve formulas, recurrence relations, graph theory, network analysis, trees, search theory, and block designs. Prerequisites: MATH 222, MATH 233 and either MATH 237 or MATH 239. Offered fall, even years