The set of codewords for a standard error-correcting code can be viewed
as subset of the vertices of a hypercube. Two vertices are adjacent in a hypercube exactly when their Hamming distance is 1. A code is a perfect-error-correcting code if no two codewords are adjacent and every non-codeword is...
Basic biological information is stored in strings of nucleic acids (DNA, RNA) or amino acids
(proteins). Teasing out the meaning of these strings is a central problem of modern biology. Matching and
aligning strings brings out their shared characteristics. Although string matching is well-understood in the
edit-distance model, biological strings...
"Fifty years after the pioneering work of McCulloch and Pitts, the study of neural nets is alive and active. In this paper, I have discussed some of the work that is of current interest to me and my co-workers. I would, perhaps, be remiss if I failed to mention some...
This note briefly discusses some of the classical results of McCulloch and Pitts. It then deals with some current research in neural nets. Several questions about neural nets are shown to be computationally difficult by showing that they are NP-Complete or worse. The size of neural nets necessary to compute...
Data structures are more easily understood when
they are presented visually rather than textually. We have
developed a system, Calypso, to allow the visual
definition of data structures programs using pictorial
pattern/action pairs in an imperative setting. We present
several examples including rebalancing an AVL tree and
sorting an array...
It is well known that the Fibonacci numbers can be expressed in the
form Round {1/√5 λ₀[superscript n]} where λ₀ = (1 + √5)/2. [Knu75] We look at integer sequences which are solutions to non-negative difference equations and show that if the equation is 1-Bounded then the solution can be...
One dimensional nonlinear difference equations have been used to model population growth. The standard biological models have the interesting characteristic that
they display global stability if they display local stability. Various researchers have sought
a simple explanation for this agreement of local and global stability. Here, we show that
enveloping...