11,263 research outputs found
The Knowlton-Graham partition problem
A set partition technique that is useful for identifying wires in cables can
be recast in the language of 0--1 matrices, thereby resolving an open problem
stated by R.~L. Graham in Volume 1 of this journal. The proof involves a
construction of 0--1 matrices having row and column sums without gaps
Measuring questions: relevance and its relation to entropy
The Boolean lattice of logical statements induces the free distributive
lattice of questions. Inclusion on this lattice is based on whether one
question answers another. Generalizing the zeta function of the question
lattice leads to a valuation called relevance or bearing, which is a measure of
the degree to which one question answers another. Richard Cox conjectured that
this degree can be expressed as a generalized entropy. With the assistance of
yet another important result from Janos Aczel, I show that this is indeed the
case, and that the resulting inquiry calculus is a natural generalization of
information theory. This approach provides a new perspective on the Principle
of Maximum Entropy.Comment: 8 pages, 1 figure. Presented to the MaxEnt 2004 meeting in Garching
Germany. To be published in: R. Fischer, V. Dose (eds.), Bayesian Inference
and Maximum Entropy Methods in Science and Engineering, Garching, Germany
2004, AIP Conference Proceedings, American Institute of Physics, Melville N
A note on digitized angles
We study the configurations of pixels that occur when two digitized straight
lines meet each other
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