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 Tony Phillips' Take on Math in the MediaA monthly survey of math news |
October 2000
Online Math Quiz October 17. "Sharpen your pencils,
set your alarm clocks and clean your mouses!" is the start of
a report in the September 15 2000 Science on an online math quiz organized
by the Centre de Recerca Matemática in Barcelona. It starts
at midnight Universal Time on October 17. Questions "will challenge even
experts but are suitable for computer grading." Top five teams
win Sun workstations. Check it out at Maths Quiz 2000. (Should that have been "mice"?)
Computation with 2-dimensional DNA. The latest news in
DNA computation is the use of double-width (and triple-width)
DNA molecules.
 Triple-crossover DNA molecule TAO35. |
 Triple-crossover DNA molecule TAE22. |
 Assembly of TAO35 molecules. |
These molecules can be considered as 2-dimensional tiles, and can
self-organize into 2-dimensional patterns, as shown on the left.
Since tiling patterns form a very general class of mathematical problems,
the extension of DNA structures to 2 dimensions bodes well for the
applications of DNA computing. Recent progress is reported in "Logical computation using algorithmic self-assembly of DNA triple-crossover molecules" by a team of two NYU chemists (Chengde Mao, Nadrian C. Seeman) and two Duke Computer Scientists ( Thomas LaBean, John Reif), in the 28 September 2000 Nature. They report "a successful one-dimensional algorithmic self-assembly of DNA triple-crossover molecules that performs four steps of a cumulative Exclusive-OR operation on a string of 1's and 0's." Background information is available in an "HTML lecture" Biomolecular Computation Using Self Assembly of DNA by LaBean, E. Winfree, and Reif to go along with an article by the same authors. |
More math into biology! That's the aim of a new
National Science Foundation initiative, "Quantitative Environmental and
Integrative Biology," recently announced, and reported in an article by
Rex Dalton in the 28 September 2000 Nature. Starting budget
$ 3 million and scheduled to increase. One goal is to
provide tools for analyzing the large data sets produced by
research in ecology. Another goal
is to improve statistical techniques for studying species spread
over large geographical areas. Targeted sciences: population genetics,
ecological system restoration, and animal physiology and behavior.
"Principal investigators are being encouraged to train undergraduates and graduates in the new
techniques, with a view to them becoming involved in the research. NSF officials see this as a
way to create a much-needed generation of scientists skilled in both biology and mathematics."
Math genes? The point is that there are many of them, and
that everyone has enough: "the capacity to do mathematics, at least through
high-school algebra and geometry." This is brought out in a charming and
on-target piece "Finding your Inner Mathematician" by Keith Devlin in the
29 September 2000 Chronicle of
Higher Education. Devlin reminds us that math only requires "nine
basic mental abilities, which our ancestors developed thousands of years
ago ..." which he enumerates and describes. For example, # 4 is
"A sense of cause and effect," and # 7 is "The ability to
understand abstraction," which he describes "the key." There is a lovely
riff on "math as soap opera," but here are two nuggets from this
excellent article. "Mathematicians don't have a different kind of brain.
They have learned to use a standard-issue brain in a slightly different
way." "The real value of learning basic math skills ... is to make the
abstract objects of mathematics become so familiar -and seem so real-
that you can reason about them using the same mental capacities you use
to reason about everyday things." (See Multiple Mathematical Intelligences in the What's
New Archive for another take on the same phenomena.)
Slime-mould topology. "... this simple organism has the
ability to find the minimum-length solution between two points in a
labyrinth."
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| Initially the plasmodium forms a net covering the entire maze. Images from Nature 407:470 (2000) @2000 Macmillan Magazines Ltd., used with permission. | Four hours after the (yellow) food blocks have been introduced in the maze, pruning of non-essential branches is well under way. | Eight hours after introduction of food blocks, the organism has formed into a single thick, minimum-length strand from one food source to the other. |
Retinal Calculus.
It has been known that the retina contains
direction-selective ganglion cells (DSGCs) each of which has
a "preferred direction," and fires to report a
dark-light or light-dark separator moving by it in that direction.
Motion in non-preferred directions gives much lower output.
The cells are performing a kind of directional derivative.
An explanation of the synaptic mechanisms involved is given
by Rowland Taylor of Australian
National University and co-authors
("Dendritic Computation of
Direction Selectivity
by Retinal Ganglion Cells, " in the September 29 2000 Science.)
The authors show by a series of experiments with rabbit retinal cells
that
"the key mechanism underlying direction selectivity in
DSGCs is spatially asymmetric inhibition, which counteracts
excitation for motion in the null
direction but not in the preferred direction."
This paper was reviewed in a news piece (same issue) "A New Look at How
Neurons Compute" by Marcia Barinaga, who reports some dissent from the
turtle people.
The idea that image processing
takes place to some extent in the retina, rather than in the brain,
dates back to the oft (but not here) cited 1959 article "What the Frog's
Eye Tells the Frog's Mind" by
Lettvin, Maturana, McCullogh and Pitts,
Proceedings of the IRE, Vol. 47, No. 11, pp. 1940-51.
-Tony Phillips
SUNY at Stony Brook
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