3,140 research outputs found
Deterministic Polynomial-Time Algorithms for Designing Short DNA Words
Designing short DNA words is a problem of constructing a set (i.e., code) of
n DNA strings (i.e., words) with the minimum length such that the Hamming
distance between each pair of words is at least k and the n words satisfy a set
of additional constraints. This problem has applications in, e.g., DNA
self-assembly and DNA arrays. Previous works include those that extended
results from coding theory to obtain bounds on code and word sizes for
biologically motivated constraints and those that applied heuristic local
searches, genetic algorithms, and randomized algorithms. In particular, Kao,
Sanghi, and Schweller (2009) developed polynomial-time randomized algorithms to
construct n DNA words of length within a multiplicative constant of the
smallest possible word length (e.g., 9 max{log n, k}) that satisfy various sets
of constraints with high probability. In this paper, we give deterministic
polynomial-time algorithms to construct DNA words based on derandomization
techniques. Our algorithms can construct n DNA words of shorter length (e.g.,
2.1 log n + 6.28 k) and satisfy the same sets of constraints as the words
constructed by the algorithms of Kao et al. Furthermore, we extend these new
algorithms to construct words that satisfy a larger set of constraints for
which the algorithms of Kao et al. do not work.Comment: 27 page
Dagstuhl Reports : Volume 1, Issue 2, February 2011
Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn
Noise-Resilient Group Testing: Limitations and Constructions
We study combinatorial group testing schemes for learning -sparse Boolean
vectors using highly unreliable disjunctive measurements. We consider an
adversarial noise model that only limits the number of false observations, and
show that any noise-resilient scheme in this model can only approximately
reconstruct the sparse vector. On the positive side, we take this barrier to
our advantage and show that approximate reconstruction (within a satisfactory
degree of approximation) allows us to break the information theoretic lower
bound of that is known for exact reconstruction of
-sparse vectors of length via non-adaptive measurements, by a
multiplicative factor .
Specifically, we give simple randomized constructions of non-adaptive
measurement schemes, with measurements, that allow efficient
reconstruction of -sparse vectors up to false positives even in the
presence of false positives and false negatives within the
measurement outcomes, for any constant . We show that, information
theoretically, none of these parameters can be substantially improved without
dramatically affecting the others. Furthermore, we obtain several explicit
constructions, in particular one matching the randomized trade-off but using measurements. We also obtain explicit constructions
that allow fast reconstruction in time \poly(m), which would be sublinear in
for sufficiently sparse vectors. The main tool used in our construction is
the list-decoding view of randomness condensers and extractors.Comment: Full version. A preliminary summary of this work appears (under the
same title) in proceedings of the 17th International Symposium on
Fundamentals of Computation Theory (FCT 2009
Compressive Sensing DNA Microarrays
Compressive sensing microarrays (CSMs) are DNA-based sensors that operate using group testing and compressive sensing (CS) principles. In contrast to conventional DNA microarrays, in which each genetic sensor is designed to respond to a single target, in a CSM, each sensor responds to a set of targets. We study the problem of designing CSMs that simultaneously account for both the constraints from CS theory and the biochemistry of probe-target DNA hybridization. An appropriate cross-hybridization model is proposed for CSMs, and several methods are developed for probe design and CS signal recovery based on the new model. Lab experiments suggest that in order to achieve accurate hybridization profiling, consensus probe sequences are required to have sequence homology of at least 80% with all targets to be detected. Furthermore, out-of-equilibrium datasets are usually as accurate as those obtained from equilibrium conditions. Consequently, one can use CSMs in applications in which only short hybridization times are allowed
Generating Probability Distributions using Multivalued Stochastic Relay Circuits
The problem of random number generation dates back to von Neumann's work in
1951. Since then, many algorithms have been developed for generating unbiased
bits from complex correlated sources as well as for generating arbitrary
distributions from unbiased bits. An equally interesting, but less studied
aspect is the structural component of random number generation as opposed to
the algorithmic aspect. That is, given a network structure imposed by nature or
physical devices, how can we build networks that generate arbitrary probability
distributions in an optimal way? In this paper, we study the generation of
arbitrary probability distributions in multivalued relay circuits, a
generalization in which relays can take on any of N states and the logical
'and' and 'or' are replaced with 'min' and 'max' respectively. Previous work
was done on two-state relays. We generalize these results, describing a duality
property and networks that generate arbitrary rational probability
distributions. We prove that these networks are robust to errors and design a
universal probability generator which takes input bits and outputs arbitrary
binary probability distributions
Alignment-free phylogenetic reconstruction: Sample complexity via a branching process analysis
We present an efficient phylogenetic reconstruction algorithm allowing
insertions and deletions which provably achieves a sequence-length requirement
(or sample complexity) growing polynomially in the number of taxa. Our
algorithm is distance-based, that is, it relies on pairwise sequence
comparisons. More importantly, our approach largely bypasses the difficult
problem of multiple sequence alignment.Comment: Published in at http://dx.doi.org/10.1214/12-AAP852 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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