Ternary DNA computing using 3 × 3 multiplication matrices

Ternary DNA computing using 3 × 3 multiplication matrices.

Non-Boolean computations implementing operations on multi-valued variables beyond base 2 allow enhanced computational complexity. We introduce DNA as a functional material for ternary computing, and in particular demonstrate the use of three-valued oligonucleotide inputs to construct a 3 × 3 multiplication table. The system consists of two three-valued inputs of -1; 0; +1 and a fluorophore/quen...

Ternary DNA computing using 3 × 3 multiplication matrices† †Electronic supplementary information (ESI) available: Gel electrophoresis analysis, the stepwise treatment of H1, the individual 3 × 3 multiplication matrices operation of H2 and H3 and examples of fluorescence spectra corresponding to the parallel computation of three multiplication tables. See DOI: 10.1039/c4sc02930e

Automatic formulation of falling multiple flexible-link robotic manipulators using 3×3 rotational matrices

In this paper, the effect of normal impact on the mathematical modeling of flexible multiple links is investigated. The response of such a system can be fully determined by two distinct solution procedures. Highly nonlinear differential equations are exploited to model the falling phase of the system prior to normal impact; and algebraic equations are used to model the normal collision of this ...

The geometry of rank decompositions of matrix multiplication II: 3×3 matrices

This is the first in a series of papers on rank decompositions of the matrix multiplication tensor. In this paper we: establish general facts about rank decompositions of tensors, describe potential ways to search for new matrix multiplication decompositions, give a geometric proof of the theorem of [3] establishing the symmetry group of Strassen’s algorithm, and present two particularly nice s...

The geometry of rank decompositions of matrix multiplication II: $3\times 3$ matrices

This is the second in a series of papers on rank decompositions of the matrix multiplication tensor. We present new rank $23$ decompositions for the $3\times 3$ matrix multiplication tensor $M_{\langle 3\rangle}$. All our decompositions have symmetry groups that include the standard cyclic permutation of factors but otherwise exhibit a range of behavior. One of them has 11 cubes as summands and...