Quasi-periodic Sequence Research Articles

Long-range correlations and charge transport properties of DNA sequences

By using Hurst's analysis and transfer approach, the rescaled range functions and Hurst exponents of human chromosome 22 and enterobacteria phage lambda DNA sequences are investigated and the transmission coefficients, Landauer resistances and Lyapunov coefficients of finite segments based on above genomic DNA sequences are calculated. In a comparison with quasiperiodic and random artificial DNA sequences, we find that λ-DNA exhibits anticorrelation behavior characterized by a Hurst exponent 0.5 < H < 1 while, as far as the segments selected in our Letter are concerned, Ch22 sequence displays a transition from correlation behavior to anticorrelation behavior. The resonant peaks of the transmission coefficient in genomic sequences can survive in longer sequence length than in random sequences but in shorter sequence length than in quasiperiodic sequences. It is shown that the genomic sequences have long-range correlation properties to some extent but the correlations are not strong enough to maintain the scale invariance properties.

Electromagnetic scattering by a quasiperiodic generalized multilayer Fibonacci structure with grates of magnetodielectric bars

The scattering coefficients of a finite quasiperiodic Fibonacci sequence for the incident wave of perpendicular and parallel polarization are obtained using the matrix polynomials methods. The structure consists of isotropic layers and thick periodic grates of magnetodielectric bars. The grates are placed either orthogonal or parallel to each other. Each grate is approximated as a layer of anisotropic medium with some efficient permittivity and permeability tensors. Closed-form formulae for the scattering coefficients are obtained. The location of quasi-stop and quasi-pass bands and the conditions of resonant structure transparency are determined.

The Fibonacci quantum walk and its classical trace map

We study the quantum walk in momentum space using a coin arranged in quasi-periodic sequences following a Fibonacci prescription. We build for this system a classical map based on the trace of the evolution operator. The sub-ballistic behavior of this quantum walk is connected with the power-law decay of the time correlations of the trace map.

Photon statistics in the cooperative spontaneous emission

The second-order photon correlation function g((2))(tau) of photons emitted by a continuously pumped ensemble of N two-level systems coupled to a single-mode optical cavity well below the lasing threshold is investigated theoretically. A giant photon bunching is found for N < 10 emitters as the microscopic counterpart of spontaneous emission noise driven quasi-periodic superradiant pulse sequences in macroscopic systems of large numbers of emitters N >> 1. The phenomenon of giant photon bunching is preserved even for N = 2 and can be explained by the cooperative evolution via dark and bright two-atom states resulting into emission of superradiant photon pairs. The sensitivity of g((2)) to microscopic dephasing processes and resonance frequency detuning opens the door for photon bunching spectroscopy.

Optical properties of a quasi-periodic generalized Fibonacci structure of chiral and material layers

The reflection and transmission coefficients of the perpendicular and parallel polarization plane electromagnetic waves of a finite quasi-periodic Fibonacci sequence of chiral and convenient isotropic magnetodielectric layers are obtained using the 2×2-block-representation transfer-matrix formulation. A correlation has been established between geometrical and spectral properties of the structure under consideration. Numerical simulations are carried out for different structures to reveal the dependence of the reflection and transmission coefficients on the frequency, chirality parameter, and the angle of wave incidence.

Electronic transport in double-strand poly(dG)–poly(dC) DNA segments

We study the electronic properties of a double-strand quasiperiodic DNA molecule modeled by a one-dimensional effective Hamiltonian, which includes contributions from the nucleobasis system as well as the sugar-phosphate backbone. Our theoretical approach makes use of Dyson's equation together with a transfer-matrix treatment, considering an electronic tight-binding Hamiltonian model to investigate the electronic density of states (DOS) and the electronic transmissivity of sequences of DNA finite segments. To mimic the DNA segments, we consider the finite quasiperiodic sequences of Fibonacci's type, in a poly(dG)–poly(dC) configuration, whose building blocks are the bases guanine G and cytosine C. We compared the electronic transport found for the quasiperiodic structure to those using a sequence of natural DNA, as part of the human chromosome Ch22.

Recurrent substorm activity during the passage of a corotating interaction region

Recent observations of magnetospheric dynamics driven by interaction with both high-speed solar wind streams (HSSs) and interplanetary coronal mass ejections (ICMEs) have shown periodic substorms to be common under strong driving, but with different periods of ∼ 4 and 2–3 h, respectively. However, it is unclear what causes these substorms and what determines their periodicity. Observations during the passage of a corotating interaction region preceding a high-speed stream are presented here and the observed enhancements in the AE index are shown to be a quasi-periodic sequence of substorms. The occurrence times of these substorms and the variation of the AL index are shown to be consistent with a simple loading–unloading model without the need for external triggers. A possible explanation is given for the lengthening of the inter-substorm period during HSS relative to that of sawtooth events during ICMEs.

A posteriori joint detection of a recurring tuple of reference fragments in a quasi-periodic sequence

The problem of joint detection of a recurring tuple of reference fragments in a noisy numerical quasi-periodic sequence is solved in the framework of the a posteriori (off-line) approach. It is assumed that (i) the total number of fragments in the sequence is known, (ii) the index of the sequence member corresponding to the beginning of a fragment is a deterministic (not random) value, and (iii) a sequence distorted by an additive uncorrelated Gaussian noise is available for observation. It is shown that the problem consists of testing a set of simple hypotheses about the mean of a random Gaussian vector. A specific feature of the problem is that the cardinality of the set grows exponentially as the vector dimension (i.e., the length of the observed sequence) and the number of fragments in the sequence increase. It is established that the search for a maximum-likelihood hypothesis is equivalent to the search for arguments that maximize a special auxiliary objective function with linear inequality constraints. It is shown that this function is maximized by solving the basic extremum problem. It is proved that this problem is solvable in polynomial time. An exact algorithm for its solution is substantiated that underlies an algorithm guaranteeing optimal (maximum-likelihood) detection of a recurring tuple of reference fragments. The results of numerical simulation demonstrate the noise stability of the detection algorithm.

All-optical diode action with quasiperiodic photonic crystals

We theoretically investigate the possibility of realizing a nonlinear all-optical diode by using the unique features of quasiperiodic one-dimensional photonic crystals. The interplay between the intrinsic spatial asymmetry in odd-order Thue–Morse lattices and Kerr nonlinearity, combined with the unconventional field localization properties of this class of quasiperiodic sequences, gives rise to sharp resonances that can be used to give a polarization-insensitive nonreciprocal propagation with a contrast close to unity for low optical intensities.

Decoherence of Bell states by local interactions with a dynamic spin environment

We study the evolution of a system of two qubits, each of which interacts locally with a spin chain with nontrivial internal Hamiltonian. We present an exact solution to this problem and analyze the dependence of decoherence on the distance between the interaction sites. In the strong coupling regime we find that decoherence increases with increasing distance. In the weak coupling regime the dependence of decoherence with distance is not generic (i.e., it varies according to the initial state). Decoherence becomes independent of distance when the latter is over a saturation length $l$. Numerical results for the Ising chain suggest that the saturation scale is related to the correlation length $\ensuremath{\xi}$. For strong coupling we display evidence of the existence of non-Markovian effects (such as environment-induced interactions between the qubits). As a consequence the system can undergo a quasiperiodic sequence of ``sudden deaths and revivals'' of entanglement, with a time scale related to the distance between qubits.

Optimal detection of a recurring tuple of reference fragments in a quasiperiodic sequence

An a posteriori (off-line) approach to the problem of maximum likelihood detection of a repeated tuple of reference fragments in a numerical quasi-per iodic sequence is studied. The problem is considered under the following assumptions

Specific heat spectra of non-interacting fermions in a quasiperiodic ladder sequence

We compute the specific heat spectra of non-interacting fermions whose energy spectrum was obtained from a quasiperiodic ladder sequence (Fibonacci and Rudin–Shapiro type), mimicking a DNA molecule model. The specific heat is calculated from their underlying multi-fractal energy spectrum, considering several values of energy densities. Comparisons are made with a real DNA sequence, namely the human chromosome 22 (Ch22).

A posteriori joint detection of reference fragments in a quasi-periodic sequence

The problem of joint detection of quasi-periodic reference fragments (of given size) in a numerical sequence and its partition into segments containing series of recurring reference fragments is solved in the framework of the a posteriori approach. It is assumed that (i) the number of desired fragments is not known, (ii) an ordered reference tuple of sequences to be detected is given, (iii) the index of the sequence member corresponding to the beginning of a fragment is a deterministic (not random) value, and (iv) a sequence distorted by an additive uncorrelated Gaussian noise is available for observation. It is established that the problem consists of testing a set of hypotheses about the mean of a random Gaussian vector. The cardinality of the set grows exponentially as the vector dimension (i.e., the sequence length) increases. It is shown that the search for a maximum-likelihood hypothesis is equivalent to the search for arguments that minimize an auxiliary objective function. It is proved that the minimization problem for this function can be solved in polynomial time. An exact algorithm for its solution is substantiated. Based on the solution to an auxiliary extremum problem, an efficient a posteriori algorithm producing an optimal (maximum-likelihood) solution to the partition and detection problem is proposed. The results of numerical simulation demonstrate the noise stability of the algorithm.

PROBABILISTIC ASPECTS OF EXTREME EVENTS GENERATED BY PERIODIC AND QUASIPERIODIC DETERMINISTIC DYNAMICS

We consider the distribution of the maximum for finite, deterministic, periodic and quasiperiodic sequences, and contrast the extreme value distributions in these cases with the classical results for iidrv's. A significant feature in the case of deterministic sequences is a multi-step structure for the distribution function. The extreme value distribution for the circle map with an irrational parameter is obtained in closed form with the help of the three-gap theorem for the map Xj+1 = (Xj + a) mod 1 where a ∈ (0,1) is an irrational number.

Entanglement in One-Dimensional Anderson Model with Long-Range Correlated Disorder

By using the measure of concurrence, the entanglement of the ground state in the one-dimensional Anderson model is studied with consideration of the long-range correlations. Three kinds of correlations are discussed. We compare the effects of the long-rang Gaussian and power-law correlations between the site energies on the concurrence, and demonstrate the existence of the band structure of the concurrence in the power-law case. The emergence of the sharp kink on the concurrence curve shown in the intraband or in the interband indicates the position at which the localization extent of the state may have the severe variation. We use the Rudin–Shapiro model to describe the site energy distribution of the nucleotides of the DNA chain: guanine (G), adenine (A), cytosine(C), thymine (T). This model is a tetradic quasiperiodic sequence and is shown to be long-range correlated. Our results show that correlations between the site energies increase the concurrences.

Electronic transport in double-strand DNA segments

We report in this work a numerical study of the electronic density of states in π-stacked arrays of DNA double-strand segments made up from the nucleotides guanine G, adenine A, cytosine C and thymine T. In order to reveal the relevance of the underlying correlations in the nucleotides distribution, we compare the results for a genomic DNA sequence, considering a segment of the first sequenced human chromosome 22 (Ch 22), with those of two artificial sequences forming a Rudin-Shapiro (RS) as well as a Fibonacci (FB) polyGC quasiperiodic sequences. Our theoretical method uses an electronic tight-binding Hamiltonian suitable to describe the DNA segments modeled by the quasiperiodic chains.

Specific heat of magnetic and semiconductor quasiperiodic structures

We have performed a theoretical study of the specific heat C ( T ) , as a function of temperature, of magnetic and semiconductor quasiperiodic structures. The quasiperiodic structures considered here are constructed according to the Fibonacci, double-period and Thue–Morse quasiperiodic sequences. On one hand, we assume the magnetic structures composed of ferromagnetic films, each one described by the Heisenberg model. On the other hand, we consider semiconductor structures composed of slabs of AlN and GaN, which are characterized by the dielectric functions ε A ( ω ) and ε B ( ω ) , and have thicknesses d a and d b , respectively. Our results illustrate the effects of disorder on the oscillatory behavior of the specific heat in the low temperature regime.

Specific heat spectra for quasiperiodic ladder sequences

We performed a theoretical study of the specific heat C(T) as a function of the temperature for double-strand quasiperiodic sequences. To mimic DNA molecules, the sequences are made up from the nucleotides guanine G, adenine A, cytosine C and thymine T, arranged according to the Fibonacci and Rudin-Shapiro quasiperiodic sequences. The energy spectra are calculated using the two-dimensional Schrodinger equation, in a tight-binding approximation, with the on-site energy exhibiting long-range disorder and non-random hopping amplitudes. We compare the specific heat features of these quasiperiodic artificial sequences to the spectra considering a segment of the first sequenced human chromosome 22 (Ch22), a real genomic DNA sequence.

A posteriori concurrent detection and identification of quasiperiodic fragments in a sequence from their pieces

An a posteriori (off-line) approach to solving the problem of concurrent detection and identification of quasiperiodic fragments in a numeric sequence from their pieces is considered. A solution of the problem is given for the case of an unknown number of sought fragments. It is supposed that: (1) each fragment to be found is identical with an element from a given alphabet of reference sequences comprising the same number of terms; (2) only a piece (part) of each sought fragment is potentially available for processing, with their inaccessible parts interpreted as missing data; (3) the ordinal numbers of sequence elements corresponding to the beginning of the sought fragment and to the endpoints of its piece are predetermined (nonrandom) variables, with piece endpoints varying from fragment to fragment and the sought fragments occurring in the sequence quasiperiodically; and (4) a Gaussian uncorrelated noise conceals from observation the input sequence containing quasiperiodic reference sequences. It is shown that the problem under study is, in its nature, equivalent to testing a set of hypothesis about the mean of a random Gaussian vector. The cardinality of this set grows exponentially with the vector dimension, which is the number of sequence elements. An efficient algorithm of a posteriori type, ensuring detection and identification under the maximum likelihood criterion, is developed and mathematically substantiated. Estimates for the time and space complexity of the algorithm as a function of problem parameters are given. Results of numeric simulation are presented.

Ability to detect weak effective seismic signals by utilizing chaotic vibrator system

Taking the advantage of CVS (Chaotic Vibrator System) sensitivity of large-scale periodic phase-state response to quasi-periodic or periodic signals, a series of numerical experiments were made to understand the ability of CVS to detect weak effective seismic signals in the common-shot seismic record distorted by strong stochastic noise. The results demonstrate that the large-scale periodic phase-states of CVS are correlated with the signal composition of the quasi-periodic wavelet sequence constructing from horizontal moveout of seismic events, noise strength and the noise distortion degree to signal. For the same kind of events, the higher the noise distortion degree is, the lower the detectable SNR can be reached by CVS. For seismic data with the same noise distortion degree, the closer the scanning seismic velocity (the trial moveout velocity) approaches to the accurate velocity, the higher the detectable SNR can be reached by CVS. Moreover, the truncating scanning velocities form an asymmetric belt, which indirectly makes CVS achieve a large-scale periodic phase-state and then the ratio of wavelet distortion coefficients in events can be a biggish variable scope.