11,451 research outputs found
Codes for DNA Storage Channels
We consider the problem of assembling a sequence based on a collection of its
substrings observed through a noisy channel. The mathematical basis of the
problem is the construction and design of sequences that may be discriminated
based on a collection of their substrings observed through a noisy channel. We
explain the connection between the sequence reconstruction problem and the
problem of DNA synthesis and sequencing, and introduce the notion of a DNA
storage channel. We analyze the number of sequence equivalence classes under
the channel mapping and propose new asymmetric coding techniques to combat the
effects of synthesis and sequencing noise. In our analysis, we make use of
restricted de Bruijn graphs and Ehrhart theory for rational polytopes.Comment: 32 pages, 5 figure
De Bruijn Structured Illumination Studying Within The Task Of Restoring Hands Relief
In the course of studies on the problem of restoring hands relief, using the de Bruijn structured illumination, methods of solving this problem are proposed. This is a method of simple quantitative detection of Hough segments on the skin of the hand, a method of qualitative visual evaluation of the effectiveness of the color palette using the dominant color, and a method of the weight coefficients of the components of the color palette.The proposed methods make it possible to quantitatively determine the optimal choice of the color scheme for generating the de Bruijn bands when illumination of the hand, to restore its relief.The work describes the stages of this study, led from visual observation to a full quantitative calculation of the quality of calibration illuminations, with the possibility of their optimal choice.In the course of experiments and observations, the requirements for the technical support of research were developed to achieve the best quality of the images of the hands. Also, the paper presents a high-speed de Bruijn sequence generating algorithm using Lyndon's words, which excludes the search for Euler chains or Hamiltonian cycles, for various kinds of de Bruijn graphs. With its help, the generation of structured light patterns with various color schemes was carried out, with the purpose of further analysis of their use in 3D reconstruction systems of hands
Rates of DNA Sequence Profiles for Practical Values of Read Lengths
A recent study by one of the authors has demonstrated the importance of
profile vectors in DNA-based data storage. We provide exact values and lower
bounds on the number of profile vectors for finite values of alphabet size ,
read length , and word length .Consequently, we demonstrate that for
and , the number of profile vectors is at least
with very close to one.In addition to enumeration
results, we provide a set of efficient encoding and decoding algorithms for
each of two particular families of profile vectors
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