Robert K. Moniot

• Accelerator-based mass spectrometry measurement of long-lived radioisotopes, applied to archeology, geophysics and meteoritics.
• Scale-space and equation-error minimization approaches to problems in image reconstruction and solution of partial differential equations.
• Least-squares fitting data with experimental uncertainties in all coordinates.
  1. Fit to a hyperplane having only one dependent coordinate and any number of independent coordinates. This work was done when I was a graduate student many years ago. It was never published except as a tech report. Here is that tech report in PDF format, HTML format, or the original LaTeX document.

     Download source code of an implementation of this method.

  2. Fit to a hyperplane having any number of dependent coordinates and any number of independent coordinates. Applied Numerical Mathematics, 59, (2009), pp. 135-150. doi:10.1016/j.apnum.2008.01.001. An expanded version of that paper is available in PDF format here.
• I am the developer of the ftnchek program for debugging FORTRAN programs.

• The Red-and-Blue-Balls Puzzle. The National Museum of Mathematics Varsity Math puzzle number 117 "Fifty-Fifty" asks how to fill a bag with red and blue balls such that if one draws out two balls at random, the odds that they are different colors will be exactly 50-50. But what about other odds? Can one fill the bag to achieve any desired odds from nil to certainty? This problem turns out to have many interesting features, and can be solved completely. I wrote a paper on this problem, titled "Solution of an Odds Inversion Problem," which has been published as an open-access article in the American Mathematical Monthly, available here.
  • Here is a PDF digest of the analysis (generated from a Mathematica notebook).
  • For those who have Mathematica and would like to explore the problem themselves, here is the notebook itself, including also an appendix defining a function that solves the problem for any odds.
  • And for those who really want to dive into it, here is a Mathematica notebook with a complete analysis of the problem, including the proofs, and a great deal more. Here is a PDF printout of the notebook.
• The Taxman Game is a mathematical amusement, often used as an assignment for classes in computer programming. I wrote an article about it aimed at math students, which appeared in Math Horizons, February 2007. This paper was awarded the 2008 Trevor Evans Prize of the Mathematical Association of America.
  • Here is a somewhat expanded version of my paper, in PDF format.
  • You can play the Taxman Game here.
  • Another name for the game is "Number Shark."
  • Norman Perlmutter, then a student at Grinnell College and now at City University of New York, has answered one of the open questions in the paper: a winning strategy for the game does exist, at least asymptotically (i.e., for pot sizes larger than some as-yet undetermined value). He has published a paper on this topic in the Pi Mu Epsilon Journal 14:3, pp. 199-204 (2015).
  • After the Math Horizons paper appeared, I learned that the game was invented by Diane Resek of San Francisco State University. She writes: I came up with the game when I was working at the Lawrence Hall of Science in Berkeley from about 1969 to 1972. I was coordinating a grant Leon Henkin (UC Berkeley) and Robert Davis (I think he was at U of Illinois at that time) had from NSF to work with K-6 teachers in the Berkeley Unified School District. One of the things I tried to do was to come up with interesting ways for kids to practice their skills or their facts which would involve them in some thinking and not be so boring. The Taxman was one game I came up with for multiplication facts. It was named for the Beatle's song -"Taxman". At the same time other people were working with kids on teletype machines. They taught them Basic and had games on it for them to play. When I came up with a game or an activity, they would turn it into a program. (slightly edited).
  • John A. Trono published a short analysis of the Taxman game, comparing various strategies, in "Taxman Revisited," SIGCSE Bulletin 26:4, pp. 56-58 (Dec. 1994).
  • The "Taxman sequence" is the sequence of optimal scores as a function of pot size. It is posted at The On-Line Encyclopedia of Integer Sequences. That site includes references to other studies. Using an approach by Dan Hoey (cited there) in which the pot is represented by a directed acyclic graph, one can dramatically reduce the search space for optimal sequences. The Taxman sequence has been determined out to a pot size of 701 by Brian Chess.
• I am also an amateur Galileo scholar. Here is a talk about Galileo that I presented as part of Fordham's College At 60 lecture series.

My Erdős Number is at most 5, via the following chain:

1. Erdős, Paul; Taylor, S. James. Some problems concerning the structure of random walk paths. (Russian summary) Acta Mathematica. Academiae Scientiarum Hungaricae 11, 137–162. (unbound insert) (1960).
2. Taylor, S. James; Tricot, Claude. Packing measure, and its evaluation for a Brownian path. Transactions of the American Mathematical Society 288, no. 2, 679–699 (1985).
3. Dubuc, Benoit; Zucker, Steven W.; Tricot, Claude, Jr.; Quiniou, J. F.; Wehbi, D. Evaluating the fractal dimension of surfaces. Proceedings of the Royal Society of London Series A 425 no. 1868, 113–127 (1989).
4. Rosenfeld, Azriel; Hummel, Robert A.; Zucker, Steven W. Scene labeling by relaxation operations. IEEE Transactions on Systems, Man, and Cybernetics SMC-6, no. 6, 420–433 (1976).
5. Hummel Robert A.; Moniot, Robert K. Reconstructions from zero-crossings in scale-space. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37, 2111–2130 (1989).

My publications