Implementation of the Timetable Problem Using Self-assembly of DNA Tiles

DNA self-assembly is a promising paradigm for nanotechnology. Recently, many researches demonstrate that computation by self-assembly of DNA tiles may be scalable. In this paper, we show how the tile self-assembly process can be used for implementing the timetable problem. First the timetable problem can be converted into the graph edge coloring problem with some constraints, then we give the tile self-assembly model by constructing three small systems including nondeterministic assigning system, copy system and detection system to perform the graph edge coloring problem, thus the algorithm is proposed which can be successfully solved the timetable problem with the computation time complexity ofΘ(mn), parallely and at very low cost

3D DNA Self-Assembly Model for Graph Vertex Coloring

DNA self-assembly technology has brought novel inspirations to the development of DNA computing Diversified computational models based on DNA self-assembly have been used to solve various NP problems. In this paper, a 3D DNA self-assembly model is presented to solve the Graph Vertex Coloring problem. With the capacity of DNA molecules in massive parallel computation, the model can simulate a non-deterministic algorithm and solve the problem in linear time Theta(n) The number of distinct tiles used in the model is Theta(k(2)), where k is the size of the color set For the vertex 3-coloring problem, the model requires only 22 types of distinct tiles. Our work makes a significant attempt for exploring the computational power of 3D DNA self-assembl

A combinatorial approach to knot recognition

This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in a compact, accessible manner, and to show how to use it for computational purposes. In particular, we address how to determine colorability of a knot, and propose to use SAT solving to search for colorings. The computational complexity of the problem, both in theory and in our implementation, is discussed. In the last part, we explain how coloring can be utilized in knot recognition

Application of The Method of Elastic Maps In Analysis of Genetic Texts

Abstract - Method of elastic maps ( http://cogprints.ecs.soton.ac.uk/archive/00003088/ and http://cogprints.ecs.soton.ac.uk/archive/00003919/ ) allows us to construct efficiently 1D, 2D and 3D non-linear approximations to the principal manifolds with different topology (piece of plane, sphere, torus etc.) and to project data onto it. We describe the idea of the method and demonstrate its applications in analysis of genetic sequences. The animated 3D-scatters are available on our web-site: http://www.ihes.fr/~zinovyev/7clusters/ We found the universal cluster structure of genetic sequences, and demonstrated the thin structure of these clusters for coding regions. This thin structure is related to different translational efficiency