Efficient Algorithms for Sequence Analysis

Eppstein, David; Galil, Zvi; Giancarlo, Raffaele; Italiano, Giuseppe F.

doi:10.1007/978-1-4613-9323-8_17

Cited by 8 publications

(4 citation statements)

References 59 publications

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“…At first sight, it is surprising that any finite graph of degree can be treated as a graph with a set of single errors which are permutations of vertices in the case of regular . Coding theory, the theory of sequences, and computational molecular biology (see [1], [6], [8], [19]) give numerous examples of types of single errors (one-to-one partial mappings ) for which the property or the weaker parallelogram property is satisfied. An important problem is to describe types of single errors inherent to genes, genomes, and other objects of molecular biology and determine the minimum number of erroneous patterns sufficient for exact reconstruction.…”

Section: B Reducible -Recontructors For Discrete Channelsmentioning

confidence: 99%

Efficient reconstruction of sequences

Levenshtein

2001

IEEE Trans. Inform. Theory

168

126

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In this paper, we introduce and solve some new problems of efficient reconstruction of an unknown sequence from its versions distorted by errors of a certain type. These erroneous versions are considered as outputs of repeated transmissions over a channel, either combinatorial channel defined by the maximum number of permissible errors of a given type, or a discrete memoryless channel. We are interested in the smallest such that erroneous versions always suffice to reconstruct a sequence of length , either exactly or with a preset accuracy and/or with a given probability. We are also interested in simple reconstruction algorithms. Complete solutions for combinatorial channels with some types of errors of interest in coding theory, namely, substitutions, transpositions, deletions, and insertions of symbols are given. For these cases, simple reconstruction algorithms based on majority and threshold principles and their nontrivial combination are found. In general, for combinatorial channels the considered problem is reduced to a new problem of reconstructing a vertex of an arbitrary graph with the help of the minimum number of vertices in its metrical ball of a given radius. A certain sufficient condition for solution of this problem is presented. For a discrete memoryless channel, asymptotic behavior of the minimum number of repeated transmissions which are sufficient to reconstruct any sequence of length within Hamming distance with error probability is found when and tend to 0 as. A similar result for the continuous channel with discrete time and additive Gaussian noise is also obtained.

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Section: B Reducible -Recontructors For Discrete Channelsmentioning

confidence: 99%

Efficient reconstruction of sequences

Levenshtein

2001

IEEE Trans. Inform. Theory

168

126

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“…The set of all components can be given the structure of a directed graph whose nodes correspond to the components, with an arrow from component C 1 to component C 2 if and only if there exist c 1 ∈ C 1 , c 2 ∈ C 2 with an arrow from c 1 to c 2 . This graph is the component graph or condensation of the original network, Eppstein [31].…”

Section: Feedforward Liftsmentioning

confidence: 99%

Stable Synchronous Propagation of Signals by Feedforward Networks

Stewart,

Wood

2024

SIAM J. Appl. Dyn. Syst.

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“…(f) The directed graph induced on the components is the component graph or condensation of the original network, Eppstein [28].…”

Section: Feedforward Liftsmentioning

confidence: 99%

Stable Synchronous Propagation of Signals by Feedforward Networks

Stewart¹,

Wood²

2023

Preprint

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We analyse the dynamics of networks in which a central pattern generator (CPG) transmits signals along one or more feedforward chains in a synchronous or phasesynchronous manner. Such propagating signals are common in biology, especially in locomotion and peristalsis, and are of interest for continuum robots. We construct such networks as feedforward lifts of the CPG. If the CPG dynamics is periodic, so is the lifted dynamics. Synchrony with the CPG manifests as a standing wave, and a regular phase pattern creates a travelling wave. We discuss Liapunov, asymptotic, and Floquet stability of the lifted periodic orbit and introduce transverse versions of these conditions that imply stability for signals propagating along arbitrarily long chains. We compare these notions to a simpler condition, transverse stability of the synchrony subspace, which is equivalent to Floquet stability when nodes are 1-dimensional.

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Efficient Algorithms for Sequence Analysis

Cited by 8 publications

References 59 publications

Efficient reconstruction of sequences

Efficient reconstruction of sequences

Stable Synchronous Propagation of Signals by Feedforward Networks

Stable Synchronous Propagation of Signals by Feedforward Networks

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