Comments for Nanoexplanations

Comment on In memoriam: Yitzchak Dumiel by Alan

Alan — Mon, 11 Mar 2013 23:50:10 +0000

Aaron, very nicely put together in Isaac’s memory. I enjoyed reading it and the memories evoked in the process. I’m glad I got to know your brother during the last few years of his life, it’s made my life much richer. Alan.

Comment on Minimum edge length partitioning of rectilinear polygons by Peter

Peter — Fri, 20 Jul 2012 21:32:20 +0000

Very helpful article, and thanks for the link to the MEL-RP paper!

You seem to start your argument with
“The argument reduces the minimum-length rectangular partition problem to Planar 3-SAT.”
Shouldn’t this be
reduces Planar 3-SAT to the minimum-length rectangular partition problem?

Comment on Ian Stewart’s Mathematics of Life by John Power

John Power — Mon, 09 Jul 2012 15:19:56 +0000

All life is programmed, software, in their genes. Certain genes control the development of cells into complex “body” parts which function to keep the body living and to enable it to survive. An example is the “master eye gene”
which is programmed to construct a complete eye anywhere on the body of a living organism that has eyes. I am sure that mathematics has a part in the program that constructs a complete eye that can see.

Reference the discovery of Dr. Walter Gehring of Switzerland.

Comment on Minimum edge length partitioning of rectilinear polygons by Mohammed

Mohammed — Mon, 23 Apr 2012 19:40:35 +0000

Dear Aaron,

Thank you for your reply. Well, I mean a 2D array (a matrix) or a 2d rectangle. A very simple polygon.

Thanks again for your reply

Comment on Minimum edge length partitioning of rectilinear polygons by Aaron Sterling

Aaron Sterling — Mon, 23 Apr 2012 14:59:59 +0000

Hi Mohammed,

Sorry for the delay in responding to you; I’ve been away from the blog for a bit. I’m not yet sure what you mean by a matrix (grid)? Do you mean a geometric object like a grid graph?

Comment on Minimum edge length partitioning of rectilinear polygons by Mohammed

Mohammed — Sat, 21 Apr 2012 21:17:25 +0000

Great Post,

I was also looking for this paper. But I am still not quite sure if this might help me in my current problem, I am looking for a way to partition a matrix (grid) into rectangles .. such that they all have minimum edge length. Does this O(n^4) solve this problem?

Thanks again.

Comment on Polygon rectangulation wrap up by amit erez

amit erez — Sun, 12 Feb 2012 06:13:39 +0000

Interesting variant of rectilinear polygon coverage which was not mentioned is the one where a coverage made of maximal rectangles is looked for. this is usefull for some interesting VLSI CAD problems. for example – placement and design rule checking

Comment on Watermarking molecules by Aaron Sterling

Aaron Sterling — Mon, 30 Jan 2012 01:34:05 +0000

Yes, I agree. Thanks for the comment; you say it much more clearly than I did. I don’t know a way around this problem.

Comment on Watermarking molecules by Aaron Sterling

Aaron Sterling — Mon, 30 Jan 2012 01:33:00 +0000

Thanks for the question. One goal would be for a company to share chemical information with a partner or subcontractor, without leaving itself open to vulnerability. So encryption where you can’t see any molecular feature isn’t what we want. Rather, we want a “molecule in a locked box” somehow, so other entities can use the molecule for certain tests or whatever, but their privileges are limited.

Comment on Watermarking molecules by Peter Gerdes

Peter Gerdes — Mon, 30 Jan 2012 01:23:06 +0000

Taking a brief look at the paper and your description I get the feeling any such scheme would be susceptible to the following attack:

Take the given database of structures and run a standard energy minimization algorithm starting with the structures in the database. Unlike attempts to solve for molecular structure by brute force this can be done fairly cheaply since we only look for the nearest local minimum and don’t bother trying to tunnel across higher energy solutions to find a lower absolute minimum.

Since the molecular structure database, in order to provide correct results to it’s users, must provide structures very similar to those taken by the molecules in the real world and such real world structures always occupy a local energy minimum the results of our computations surely compute the structures at least as well as the original dataset.

Moreover, since local energy minimization algorithms should be independent of initial state as long as that state is close to the computed energy minimum our output data would necessarily be indistinguishable from a run of the same program starting on any other nearly correct database of molecular structures.