46,260 research outputs found
A fast algorithm for the constrained multiple sequence alignment problem
Given n strings S1, S2, ..., Sn, and a pattern string P, the constrained multiple sequence alignment (CMSA) problem is to find an optimal multiple alignment of S1, S2, ..., Sn such that the alignment contains P, i.e. in the alignment matrix there exists a sequence of columns each entirely composed of symbol P[k] for every k, where P[k] is the kth symbol in P, 1 ≤ k ≤ |P|, and in the sequence, a column containing P[i] appears before the column containing P[j] for all i,j, i < j. The problem is motivated from the problem of comparing multiple sequences that share a common structure, or sequence pattern. There are O(2ns1s2...snr)-time dynamic programming algorithms for the problem, where s1,s2, ...,sn and r are, respectively, the lengths of the input strings and the pattern string. Feasibility of these algorithms in practice is limited when the number of sequences is large, or the sequences are long because of the impractically long time required by these algorithms. We present a new algorithm with worst-case time complexity also O(2ns1s2...snr), but the algorithm avoids redundant computations in existing dynamic programming solutions. Experiments on both randomly generated strings and real data show that this algorithm is much faster than the existing algorithms. We present an analysis that explains the speed-up obtained in our experiments by our algorithm over the naive dynamic programming algorithm for constrained multiple sequence alignment of protein sequences. The speed-up is more significant when pattern is long, or n is large. For example in the case of constrained pairwise sequence alignment (the CMSA problem with n=2) when the pattern is sufficiently long for strings S1 and S2, the asymptotic time complexity is observed to be O(s1s2) instead of O(s1s2r). Main ideas in our algorithm can also be used in other constrained sequence alignment problems
Inference with Constrained Hidden Markov Models in PRISM
A Hidden Markov Model (HMM) is a common statistical model which is widely
used for analysis of biological sequence data and other sequential phenomena.
In the present paper we show how HMMs can be extended with side-constraints and
present constraint solving techniques for efficient inference. Defining HMMs
with side-constraints in Constraint Logic Programming have advantages in terms
of more compact expression and pruning opportunities during inference.
We present a PRISM-based framework for extending HMMs with side-constraints
and show how well-known constraints such as cardinality and all different are
integrated. We experimentally validate our approach on the biologically
motivated problem of global pairwise alignment
MAVID: Constrained ancestral alignment of multiple sequences
We describe a new global multiple alignment program capable of aligning a
large number of genomic regions. Our progressive alignment approach
incorporates the following ideas: maximum-likelihood inference of ancestral
sequences, automatic guide-tree construction, protein based anchoring of
ab-initio gene predictions, and constraints derived from a global homology map
of the sequences. We have implemented these ideas in the MAVID program, which
is able to accurately align multiple genomic regions up to megabases long.
MAVID is able to effectively align divergent sequences, as well as incomplete
unfinished sequences. We demonstrate the capabilities of the program on the
benchmark CFTR region which consists of 1.8Mb of human sequence and 20
orthologous regions in marsupials, birds, fish, and mammals. Finally, we
describe two large MAVID alignments: an alignment of all the available HIV
genomes and a multiple alignment of the entire human, mouse and rat genomes
Algorithms for the Problems of Length-Constrained Heaviest Segments
We present algorithms for length-constrained maximum sum segment and maximum
density segment problems, in particular, and the problem of finding
length-constrained heaviest segments, in general, for a sequence of real
numbers. Given a sequence of n real numbers and two real parameters L and U (L
<= U), the maximum sum segment problem is to find a consecutive subsequence,
called a segment, of length at least L and at most U such that the sum of the
numbers in the subsequence is maximum. The maximum density segment problem is
to find a segment of length at least L and at most U such that the density of
the numbers in the subsequence is the maximum. For the first problem with
non-uniform width there is an algorithm with time and space complexities in
O(n). We present an algorithm with time complexity in O(n) and space complexity
in O(U). For the second problem with non-uniform width there is a combinatorial
solution with time complexity in O(n) and space complexity in O(U). We present
a simple geometric algorithm with the same time and space complexities.
We extend our algorithms to respectively solve the length-constrained k
maximum sum segments problem in O(n+k) time and O(max{U, k}) space, and the
length-constrained maximum density segments problem in O(n min{k, U-L})
time and O(U+k) space. We present extensions of our algorithms to find all the
length-constrained segments having user specified sum and density in O(n+m) and
O(nlog (U-L)+m) times respectively, where m is the number of output.
Previously, there was no known algorithm with non-trivial result for these
problems. We indicate the extensions of our algorithms to higher dimensions.
All the algorithms can be extended in a straight forward way to solve the
problems with non-uniform width and non-uniform weight.Comment: 21 pages, 12 figure
An Efficient Dynamic Programming Algorithm for the Generalized LCS Problem with Multiple Substring Exclusion Constrains
In this paper, we consider a generalized longest common subsequence problem
with multiple substring exclusion constrains. For the two input sequences
and of lengths and , and a set of constrains
of total length , the problem is to find a common subsequence of and
excluding each of constrain string in as a substring and the length of
is maximized. The problem was declared to be NP-hard\cite{1}, but we
finally found that this is not true. A new dynamic programming solution for
this problem is presented in this paper. The correctness of the new algorithm
is proved. The time complexity of our algorithm is .Comment: arXiv admin note: substantial text overlap with arXiv:1301.718
Stochastic Block Coordinate Frank-Wolfe Algorithm for Large-Scale Biological Network Alignment
With increasingly "big" data available in biomedical research, deriving
accurate and reproducible biology knowledge from such big data imposes enormous
computational challenges. In this paper, motivated by recently developed
stochastic block coordinate algorithms, we propose a highly scalable randomized
block coordinate Frank-Wolfe algorithm for convex optimization with general
compact convex constraints, which has diverse applications in analyzing
biomedical data for better understanding cellular and disease mechanisms. We
focus on implementing the derived stochastic block coordinate algorithm to
align protein-protein interaction networks for identifying conserved functional
pathways based on the IsoRank framework. Our derived stochastic block
coordinate Frank-Wolfe (SBCFW) algorithm has the convergence guarantee and
naturally leads to the decreased computational cost (time and space) for each
iteration. Our experiments for querying conserved functional protein complexes
in yeast networks confirm the effectiveness of this technique for analyzing
large-scale biological networks
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