30 research outputs found
A comprehensive introduction to the theory of word-representable graphs
Letters x and y alternate in a word w if after deleting in w all letters but the copies of x and y we either obtain a word xyxy⋯ (of even or odd length) or a word yxyx⋯ (of even or odd length). A graph G=(V,E) is word-representable if and only if there exists a word w over the alphabet V such that letters x and y alternate in w if and only if xy ∈ E. Word-representable graphs generalize several important classes of graphs such as circle graphs, 3-colorable graphs and comparability graphs. This paper offers a comprehensive introduction to the theory of word-representable graphs including the most recent developments in the area
Optimization of Enzymatic Biochemical Logic for Noise Reduction and Scalability: How Many Biocomputing Gates Can Be Interconnected in a Circuit?
We report an experimental evaluation of the "input-output surface" for a
biochemical AND gate. The obtained data are modeled within the rate-equation
approach, with the aim to map out the gate function and cast it in the language
of logic variables appropriate for analysis of Boolean logic for scalability.
In order to minimize "analog" noise, we consider a theoretical approach for
determining an optimal set for the process parameters to minimize "analog"
noise amplification for gate concatenation. We establish that under optimized
conditions, presently studied biochemical gates can be concatenated for up to
order 10 processing steps. Beyond that, new paradigms for avoiding noise
build-up will have to be developed. We offer a general discussion of the ideas
and possible future challenges for both experimental and theoretical research
for advancing scalable biochemical computing