Research


Current Research Interests

I love to collaborate, explore interesting new ideas, expand my breadth, and learn new things. If you're interested in talking about my work, your work that I might be interested in, or anything inbetween, don't hestitate to contact me!

Publications

I post most of my papers to the arXiv. Though they are scattered across math, q-bio, and cs subject-classes, the complete list can be found here. In spirit with the Stone Vertical Epic Ales, I sometimes wait until an interesting date to post a paper. Thus far, I have papers time-stamped with the following dates: 2/29/08, 8/8/08, 9/9/09, 10/10/10, and 11/11/11, and 2/29/12. I also have several papers that contain a "hidden message" in the abstract of the pdf version, relating to the posting date. Can you find them? One is in my arXiv paper from 10/21/15, and another in 11/8/16.

Journal articles

• A. Jenkins and M. Macauley. Bistability and asynchrony in a Boolean model of the L-arabinose operon in Escherichia coli, Bull. Math. Biol. (2017), to appear. q-bio.MN/1611.02656

• D. Einstein, M. Farber, E. Gunawan, M. Joseph, M. Macauley, J. Propp, S. Rubinstein-Salzedo. Noncrossing partitions, toggles, and homomesies. Electron. J. Combin., (2016), 23(3) #P3.52, 26pp. math.CO/1510.06362

• M. Macauley. Morphisms and order ideals of toric posets. Mathematics. 4(2), (2016), 31 pages. math.CO/1501.02239

• Q. He and M. Macauley. Stratification and enumeration of Boolean functions by canalizing depth. Physica D. 314 (2016), 1--8. cs.DM/1504/07591

• M. Develin, M. Macauley, and V. Reiner. Toric partial orders. Trans. Amer. Math. Soc. 368 (2016), 2263--2287. math.CO/1211.4247

• B. Rabern, L. Rabern, and M. Macauley. Dangerous reference graphs and semantic paradoxes. J. Philos. Logic, 42 (2013), 727--765.

• T. Boothby, J. Burkert, M. Eichwald, D.C. Ernst, R.M. Green, and M. Macauley. On the Cyclically Fully Commutative Elements of Coxeter Groups. J. Algebraic Combin. 36(1) (2012), 123-148. math.CO/1202.6657

• L. Layne, E. Dimitrova, and M. Macauley. Nested Canalyzing Depth and Network Stability. Bull. Math. Biol. 74(2) (2012), 422-433. q-bio.MN/1111.2759

• M. Macauley and H.S. Mortveit. Posets from Admissible Coxeter Sequences. Electron. J. Combin. 18(1) (2011) #P197, 18 pp. math.CO/0910.4376

• M. Macauley, J. McCammond, and H.S. Mortveit. Dynamics Groups of Asynchronous Cellular Automata. J. Algebraic Combin. 33 (2011), 31-55. math.DS/0808.1238

• M. Macauley and H.S. Mortveit. Update Sequence Stability in Graph Dynamical Systems. Discrete Cont. Dyn. Sys. Ser. S 4 (2011), 1533-1542. [math.DS/0909.1723]

• E. Goldstein, A. Apolloni, B. Lewis, J. Miller, M. Macauley, S. Eubank, M. Lipsitch, and J. Wallinga. Distribution of vaccine / antivirals and the "least spread line" in a stratified population. J. Royal Soc. Interface 7 (2010), 755-764. PubMed #19828505

• M. Macauley and H.S. Mortveit. Cycle Equivalence of Graph Dynamical Systems. Nonlinearity 22 (2009) 421-436. math.DS/0802.4412

• K. Atkins, J. Chen, A. Kumar, M. Macauley, and A. Marathe. Locational Market Power in Network Constrained Markets. J. Econ. Behav. Organ. 70(1-2) 416-430, 2009. DOI 10.1016/j.jebo.2008.11.001

• J. Chen, M. Macauley, and A. Marathe. Network Topology and Locational Market Power. Comput. Econ. 34(1) 21-35, 2009

• M. Macauley and H.S. Mortveit. On Enumeration of Conjugacy Classes of Coxeter Elements. Proc. Amer. Math. Soc. 136 (2008), 4157-4165. math.CO/0711.1140

• M. Macauley, J. McCammond, and H.S. Mortveit. Order Independence in Asynchronous Cellular Automata. J. Cell. Autom. 3 (2008) 37-56. math.DS/0707.2360

• M. Banister, M. Macauley, and M. Smukler. Thinking Outside the Box and Over the Elephant. UMAP 24 (3), 2003.

Refereed Conference Proceedings

• D. Einstein, M. Farber, E. Gunawan, M. Joseph, M. Macauley, J. Propp, S. Rubinstein-Salzedo. Noncrossing partitions, toggles, and homomesies. Formal Power Series and Algebraic Combinatorics (2016), Discrete Math. Theor. Comput. Sci. Proc., BC, 419-430.

• M. Macauley and H.S. Mortveit. Coxeter Groups and Asynchronous Cellular Automata. Lect. Notes Comput. Sci. 6350 (2010), 409-418. [ SpringerLink ]

• V.S.A. Kumar, M. Macauley, and H.S. Mortveit. Limit Set Reachability in Asynchronous Graph Dynamical Systems. Lect. Notes Comput. Sci. 5796 (2009), 217-232. [ SpringerLink ]

• J. Chen, M. Macauley, and A. Marathe. Role of Network and Production Capacity in Allocating Market Power. Proceedings of the Trans-Atlantic INFRADAY Conference on Applied Infrastructure Modeling and Policy Analysis. College Park, MD. November, 2007. [online version]

• K. Atkins, J. Chen, A. Kumar, M. Macauley, and A. Marathe. Locational Market Power in Network Constrained Markets. Proceedings of the 29th IAEE International Conference. Potsdam, Germany. June 2006.

Other writings

• M. Macauley and H.S. Mortveit. Equivalences on Acyclic Orientations. math.CO/0709.0291

• M. Macauley. Protesters Lack Key Facts on Nukes, UC. Daily Nexus, Issue 121 / Volume 87. Thursday, May 10, 2007. [online version]

• M. Macauley. Juggling By The Numbers. (Book review). Math Horizons, Feb. 2004.

• M. Macauley. Coxeter Theory and Discrete Dynamical Systems. Ph.D. Thesis. University of California, Santa Barbara, 2008. [pdf]

• M. Macauley. Braids and Juggling Patterns. Senior Thesis. Harvey Mudd College, 2003. [pdf]

• E. Blew, Y. Grabovsky, M. Jacobs, M. Macauley, J. Quah, and E. Ruppin. Computing Special Jordan Pencils.

• M. Macauley and M. Orrison. Braids and Juggling Patterns [pdf]


Erdős, Bacon, and Bigfoot numbers

My Erdős Number is 3:

me <--> Jiangzhuo Chen <--> László Lovász <--> Paul Erdős
me <--> Achla Marathe <--> Vance Faber <--> Paul Erdős

The database probably isn't aware, though, because the path goes through an economics paper.

Speaking of small-world network measures, I appeared as a unicyclist in the movie "Slackers". Technically, I was a "special ability extra", which despite not paying much more than a regular extra, does have the perk that the actors actually thought we were cool. It took over 12 hours to film what ended up being a 25-second scene. But Margaret Easley had a small role in the film (and it wasn't even on a unicycle), and she has a Kevin Bacon number of 1 (From "We Married Margo"). So, if this counts, my Erdős-Bacon number is 3+2=5. In contrast, Stephen Hawking has an Erdős-Bacon number of 7, and Carl Sagan and Richard Feynman have Erdős-Bacon numbers of 6.

I am also the undisputed world-record holder in having the lowest Erdős-Bacon-Bigfoot number. As everybody knows, Bigfoot was a regular in the Monster Truck Show for years, and in the late 1990s, I performed (juggled) in the opening of several shows in the now-demolished Kingdome. This gives me a Bigfoot number of 1, and an Erdős-Bacon-Bigfoot number of 2+3+1=6.