Robert K. Moniot
I have also dabbled in some other areas:
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
- 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
HTML format, or the original
Download source code of an implementation of this method.
- Fit to a hyperplane having any number of dependent coordinates and any number of independent coordinates.
Numerical Mathematics, 59, (2009), pp. 135-150.
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
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,
- 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. Here is
a PDF printout of the notebook,
and a PDF table of contents.
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,
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
- 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
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
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.
- 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:
- 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).
- 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).
- 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).
- 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).
- 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).