Poincaré recurrences of DNA sequences

Frahm, Klaus M.; Shepelyansky, Dima L.

doi:10.1103/physreve.85.016214

Cited by 13 publications

(17 citation statements)

References 25 publications

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“…[69] Onedimensional Hubbard model has been well understood by means of the Bethe ansatz [70][71][72] and conformal field theory. [73][74][75] The solutions established a novel concept of the Tomonaga-Luttinger liquid [76] which is described by the scalar bosons corresponding to charge and spin sectors, respectively. The correlated electrons in twoand three-dimensional space are still far from a complete understanding in spite of the success for the onedimensional Hubbard model.…”

Section: The Hubbard Hamiltonian Ismentioning

confidence: 99%

Correlated-Electron Systems and High-Temperature Superconductivity

Yanagisawa¹,

Miyazaki²,

Yamaji³

2013

JMP

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We present recent theoretical results on superconductivity in correlated-electron systems, especially in the twodimensional Hubbard model and the three-band d-p model. The mechanism of superconductivity in high-temperature superconductors has been extensively studied on the basis of various electronic models and also electron-phonon models. In this study, we investigate the properties of superconductivity in correlated-electron systems by using numerical methods such as the variational Monte Carlo method and the quantum Monte Carlo method. The Hubbard model is one of basic models for strongly correlated electron systems, and is regarded as the model of cuprate high temperature superconductors. The d-p model is more realistic model for cuprates. The superconducting condensation energy obtained by adopting the Gutzwiller ansatz is in reasonable agreement with the condensation energy estimated for YBa 2 Cu 3 O 7 . We show the phase diagram of the ground state using this method. We have further investigated the stability of striped and checkerboard states in the under-doped region. Holes doped in a half-filled square lattice lead to an incommensurate spin and charge density wave. The relationship of the hole density x and incommensurability  ,  period has also been observed by scanning tunneling microscopy experiments in Bi2212 and Na-CCOC compounds. We have performed a variational Monte Carlo simulation on a two-dimensional t -t -t -U Hubbard model with a Bi-2212 type band structure and found that the 4 4  period checkerboard spin modulation, that is characterized by multi Q vectors, is indeed stabilized. We have further performed an investigation by using a quantum Monte Carlo method, which is a numerical method that can be used to simulate the behavior of correlated electron systems. We present a new algorithm of the quantum Monte Carlo diagonalization that is a method for the evaluation of expectation value without the negative sign problem. We compute pair correlation functions and show that pair correlation is indeed enhanced with hole doping.

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Section: The Hubbard Hamiltonian Ismentioning

confidence: 99%

Correlated-Electron Systems and High-Temperature Superconductivity

Yanagisawa¹,

Miyazaki²,

Yamaji³

2013

JMP

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“…3 the distribution Rω(t) of first return-time between two consecutive appearances of the oligonucleotide ω is studied in Refs. [32,33]. Rω(t) can be written as a sum of different P (X).…”

Section: Statistical Properties Of the Model And Predictionsmentioning

confidence: 99%

The common origin of symmetry and structure in genetic sequences

Cristadoro

Esposti

Altmann

2017

Preprint

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When exploring statistical properties of genetic sequences two main features stand out: the existence of non-random structures at various scales (e.g., long-range correlations) and the presence of symmetries (e.g., Chargaff parity rules). In the last decades, numerous studies investigated the origin and significance of each of these features separately. Here we show that both symmetry and structure have to be considered as the outcome of the same biological processes, whose cumulative effect can be quantitatively measured on extant genomes. We present a novel analysis (based on a minimal model) that not only explains and reproduces previous observations but also predicts the existence of a nested hierarchy of symmetries emerging at different structural scales. Our genome-wide analysis of H. Sapiens confirms the theoretical predictions.

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“…It was observed that the RTS is capable of describing the relevant aspects of the dynamics in complex systems. In this context, we mention that the RTS is able to describe universal algebraic decays in Hamiltonian systems [2][3][4], including random walk penetration of the Kolmogorov-Arnold-Moser (KAM) islands [5,6], biased random walk to escape from KAM island [7], DNA sequence [8], synchronization of oscillator [9], generalized bifurcation diagram of conservative systems [10], fine structure of resonance islands [11], transient chaos in systems with leaks [12], among others.…”

Section: Introductionmentioning

confidence: 99%

“…This mixing occurs via a spiralling motion (see [23] for more details). Figure 8 shows the RTS curves for the model (8). In our simulations we use fourth-order Runge-Kutta algorithm with fixed time-step ∆t = 0.01 for 10 6 recurrences.…”

Section: Rts In a Fluid Flow Modelmentioning

confidence: 99%

Recurrence-time statistics in non-Hamiltonian volume-preserving maps and flows

2015

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We analyze the recurrence-time statistics (RTS) in three-dimensional non-Hamiltonian volume preserving systems (VPS): an extended standard map, and a fluid model. The extended map is a standard map weakly coupled to an extra-dimension which contains a deterministic regular, mixed (regular and chaotic) or chaotic motion. The extra-dimension strongly enhances the trapping times inducing plateaus and distinct algebraic and exponential decays in the RTS plots. The combined analysis of the RTS with the classification of ordered and chaotic regimes and scaling properties, allows us to describe the intricate way trajectories penetrate the before impenetrable regular islands from the uncoupled case. Essentially the plateaus found in the RTS are related to trajectories that stay long times inside trapping tubes, not allowing recurrences, and then penetrates diffusively the islands (from the uncoupled case) by a diffusive motion along such tubes in the extra-dimension. All asymptotic exponential decays for the RTS are related to an ordered regime (quasi-regular motion) and a mixing dynamics is conjectured for the model. These results are compared to the RTS of the standard map with dissipation or noise, showing the peculiarities obtained by using three-dimensional VPS. We also analyze the RTS for a fluid model and show remarkable similarities to the RTS in the extended standard map problem.

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Poincaré recurrences of DNA sequences

Cited by 13 publications

References 25 publications

Correlated-Electron Systems and High-Temperature Superconductivity

Correlated-Electron Systems and High-Temperature Superconductivity

The common origin of symmetry and structure in genetic sequences

Recurrence-time statistics in non-Hamiltonian volume-preserving maps and flows

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