Delocalization transitions of semiflexible manifolds

Bundschuh, Ralf; Lässig, Michael

doi:10.1103/physreve.65.061502

Cited by 37 publications

(74 citation statements)

References 36 publications

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“…Note that the directness of this technique allows for it's ready adaptation to more complex sequence comparison algorithms along the lines of Ref. [15]. However, this generally requires a significantly larger number of states thus incurring a greater computational cost.…”

Section: Fig 2: This Picture Shows Our 45mentioning

confidence: 99%

“…We will call this the uncorrelated LCS problem and identify all quantities calculated for this problem by an additional hat; specifically, we will call a c the analog of the Chvátal-Sankoff constant in the uncorrelated LCS problem. This approximation to the real LCS problem has been used in various theoretical approaches to sequence comparison statistics [12,15,22]. For the LCS problem itself, only very careful numerical studies could show that the Chvátal-Sankoff constant for the correlated and uncorrelated problem are actually different [3,4,22,24].…”

Section: Review Of the Lcs Problemmentioning

confidence: 99%

“…There have been numerous numerical and analytical studies that attempt to characterize the behavior of these algorithms on random sequence data [8,9,10,11,12,13,14,15,16]. However, there are difficulties with both kinds of approaches to the problem of characterizing sequence alignment algorithms statistically.…”

Section: Introductionmentioning

confidence: 99%

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Finite width model sequence comparison

Chia

Bundschuh

2004

Phys. Rev. E

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Sequence comparison is a widely used computational technique in modern molecular biology. In spite of the frequent use of sequence comparisons the important problem of assigning statistical significance to a given degree of similarity is still outstanding. Analytical approaches to filling this gap usually make use of an approximation that neglects certain correlations in the disorder underlying the sequence comparison algorithm. Here, we use the longest common subsequence problem, a prototype sequence comparison problem, to analytically establish that this approximation does make a difference to certain sequence comparison statistics. In the course of establishing this difference we develop a method that can systematically deal with these disorder correlations.

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Section: Fig 2: This Picture Shows Our 45mentioning

confidence: 99%

Section: Review Of the Lcs Problemmentioning

confidence: 99%

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Finite width model sequence comparison

Chia

Bundschuh

2004

Phys. Rev. E

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“…The PASEP is regarded as a primitive model for biopolymerization [14], traffic flow [17], and formation of shocks [10]; it also appears in a kind of sequence alignment problem in computation biology [4].…”

Section: Introductionmentioning

confidence: 99%

A Markov Chain on Permutations which Projects to the PASEP

Corteel

Williams

2010

International Mathematics Research Notices

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Abstract. The partially asymmetric exclusion process (PASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of N sites. It is partially asymmetric in the sense that the probability of hopping left is q times the probability of hopping right. Additionally, particles may enter from the left with probability α and exit to the right with probability β.It has been observed that the (unique) stationary distribution of the PASEP has remarkable connections to combinatorics -see for example the papers of Derrida et al [8,9], Duchi and Schaeffer [11], Corteel [5], and Shapiro and Zeilberger [18]. Most recently we proved [7] that in fact the (normalized) probability of being in a particular state of the PASEP can be viewed as a certain weight generating function for permutation tableaux of a fixed shape. (This result implies the previous combinatorial results.) However, our proof relied on the matrix ansatz of Derrida et al [9], and hence did not give an intuitive explanation of why one should expect the steady state distribution of the PASEP to involve such nice combinatorics.In this paper we define a Markov chain -which we call the PT chain -on the set of permutation tableaux which projects to the PASEP, in a sense which we shall make precise. This gives a new proof of the main result of [7] which bypasses the matrix ansatz altogether. Furthermore, via the bijection of [19], the PT chain can also be viewed as a Markov chain on the symmetric group. Another nice feature of the PT chain is that it possesses a certain symmetry which extends the particle-hole symmetry of the PASEP.

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“…It has been shown in [34] that, one can map the kinetics of the annihilation process A + B → 0 with driven diffusion onto the (1+1)-dimensional KPZ equation. Also the KPZ equation is closely related to the dynamics of a sine-Gordon chain [35], the driven-diffusion equation [36][37], high T csuperconductor [38] and directed paths in the random media [39][40][41][42][43][44][45][46][47][48][49][50][51][52] and charge density waves [53], dislocations in disordered solids [3], formation of large-scale structure in the universe [54][55][56][57] , Burgers turbulence 90] and etc.…”

Section: −Dmentioning

confidence: 99%

Statistical theory for the Kardar-Parisi-Zhang equation in(1+1)dimensions

et al. 2002

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The Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimension dynamically develops sharply connected valley structures within which the height derivative is not continuous. There are two different regimes before and after creation of the sharp valleys. We develop a statistical theory for the KPZ equation in 1+1 dimension driven with a random forcing which is white in time and Gaussian correlated in space. A master equation is derived for the joint probability density function of height difference and height gradient P (h −h, ∂ x h, t) when the forcing correlation length is much smaller than the system size and much bigger than the typical sharp valley width. In the time scales before the creation of the sharp valleys we find the exact generating function of h −h and ∂ x h. Then we express the time scale when the sharp valleys develop, in terms of the forcing characteristics. In the stationary state, when the sharp valleys are fully developed, finite size corrections to the scaling laws of the structure functions (h −h) n (∂ x h) m are also obtained. PACS: 05.70.Ln,68.35.Fx.

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Delocalization transitions of semiflexible manifolds

Cited by 37 publications

References 36 publications

Finite width model sequence comparison

Finite width model sequence comparison

A Markov Chain on Permutations which Projects to the PASEP

Statistical theory for the Kardar-Parisi-Zhang equation in(1+1)dimensions

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