Dave Bernick is working on sequencing random DNA strands. The problem starts in a 136-dimensional space — the canonical k-mer universe for k=4, giving 136 unique k-mers once reverse complements are accounted for. He has reduced this to 10 dimensions. The challenge he describes as a giant jigsaw puzzle: reconstructing original strands from overlapping fragments.
The dimensionality reduction
Getting from 136 to 10 dimensions suggests an embedding space — possibly k-mer frequency vectors or a learned representation. The key question is whether the 10-dimensional space preserves overlap relationships geometrically. If so, assembly becomes a nearest-neighbor traversal in reduced space.
Quaternion connection
A paper — "DNA Sequence Representation and Comparison Based on Quaternion Number System" — proposes quaternion cross-correlation for alignment. The real part identifies the globally best-matching position; imaginary parts reveal local alignment detail. The open question: is quaternion representation the input to Dave's dimensionality reduction, or the reduction mechanism itself? That distinction matters.
Relevant tools
- De Bruijn graphs — workhorse of modern assemblers (Velvet, SPAdes). Turns assembly into an Eulerian path problem.
- Overlap-Layout-Consensus (OLC) — better for long reads; Hamiltonian path through an overlap graph.
- KMAP — k-mer manifold approximation and projection. Uses Hamming distance, projects to 2D. Possible visualization layer on top of Dave's reduction.
Three questions for the 1pm call
- Is quaternion the input to the dimensionality reduction, or the mechanism itself?
- Is the 10-dimensional space biologically interpretable — do the axes mean anything?
- Has he looked at KMAP as a visualization layer on top of whatever he's built?
The hard part of any assembly is repeated sequences — ambiguous fragments that fit multiple places. Worth understanding how Dave's embedding handles those.