Chaos game representation walk model for the protein sequences

A new chaos game representation of protein sequences based on the detailed hydrophobic--hydrophilic (HP) model has been proposed by Yu et al (Physica A 337 (2004) 171). A CGR-walk model is proposed based on the new CGR coordinates for the protein sequences from complete genomes in the present paper. The new CGR coordinates based on the detailed HP model are converted into a time series, and a long-memory ARFIMA(p, d, q) model is introduced into the protein sequence analysis. This model is applied to simulating real CGR-walk sequence data of twelve protein sequences. Remarkably long-range correlations are uncovered in the data and the results obtained from these models are reasonably consistent with those available from the ARFIMA(p, d, q) model.     

Wavelet-based multifractal analysis of DNA sequences by using chaos-game representation

Chaos game representation (CGR) is proposed as a scale-independent representation for DNA sequences and provides information about the statistical distribution of oligonucleotides in a DNA sequence. CGR images of DNA sequences represent some kinds of fractal patterns, but the common multifractal analysis based on the box counting method cannot deal with CGR images perfectly. Here, the wavelet transform modulus maxima (WTMM) method is applied to the multifractal analysis of CGR images. The results show that the scale-invariance range of CGR edge images can be extended to three orders of magnitude, and complete singularity spectra can be calculated. Spectrum parameters such as the singularity spectrum span are extracted to describe the statistical character of DNA sequences. Compared with the singularity spectrum span, exon sequences with a minimal spectrum span have the most uniform fractal structure. Also, the singularity spectrum parameters are related to oligonucleotide length, sequence component and species, thereby providing a method of studying the length polymorphism of repeat oligonucleotides.     

Characteristics of alternating current hopping conductivity in DNA sequences

This paper presents a model to describe alternating current (AC) conductivity of DNA sequences, in which DNA is considered as a one-dimensional (1D) disordered system, and electrons transport via hopping between localized states. It finds that AC conductivity in DNA sequences increases as the frequency of the external electric field rises, and it takes the form of σ_ac (ω)～ω ²\ln ²(1/ω). Also AC conductivity of DNA sequences increases with the increase of temperature, this phenomenon presents characteristics of weak temperature-dependence. Meanwhile, the AC conductivity in an off-diagonally correlated case is much larger than that in the uncorrelated case of the Anderson limit in low temperatures, which indicates that the off-diagonal correlations in DNA sequences have a great effect on the AC conductivity, while at high temperature the off-diagonal correlations no longer play a vital role in electric transport. In addition, the proportion of nucleotide pairs p also plays an important role in AC electron transport of DNA sequences. For p < 0.5, the conductivity of DNA sequence decreases with the increase of p, while for p ≥ 0.5, the conductivity increases with the increase of p.     

Quasispecies distribution of Eigen model

We have studied sharp peak landscapes of the Eigen model from a new perspective about how the quasispecies are distributed in the sequence space. To analyse the distribution more carefully, we bring in two tools. One tool is the variance of Hamming distance of the sequences at a given generation. It not only offers us a different avenue for accurately locating the error threshold and illustrates how the configuration of the distribution varies with copying fidelity $q$ in the sequence space, but also divides the copying fidelity into three distinct regimes. The other tool is the similarity network of a certain Hamming distance $d_{0}$, by which we can gain a visual and in-depth result about how the sequences are distributed. We find that there are several local similarity optima around the centre (global similarity optimum) in the distribution of the sequences reproduced near the threshold. Furthermore, it is interesting that the distribution of clustering coefficient $C(k)$ follows lognormal distribution and the curve of clustering coefficient $C$ of the network versus $d_{0}$ appears to be linear near the threshold.     

A new traffic model with the consideration of coupling effect with two lanes

This paper introduces a new two-lane high-order continuum model by embedding the two delay time scales continuum traffic model presented by Xue (2003 Phys. Rev. E 68 066123) into the multi-lane model proposed by Daganzo (1997 Transpn. Res. B 31 83) with the consideration of the coupling effect between the vehicles of two lanes in instantaneous traffic situation and lane-change effect. In the novel model, the coupling effect of two lanes and phenomena of lane change, which were not discussed in Daganzo's model and Xue's model, are taken into account. Numerical simulation shows that it is in accordance with real traffic flow. This obviously indicates that the new phenomenon and behaviour are analogous results as single lane presented by Xue, and the proposed model is more reasonable on two lanes. Furthermore, the generation rate between two lanes is also investigated. The results show that the formation and diffusion of traffic shock wave can be better simulated on two lanes.     

Influence of Breaking Waves and Wake Bubbles on Surface-Ship Wake Scattering at Low Grazing Angles

A surface-ship wake model is proposed for calculating the scattering of ship wake from a nonlinear sea surface at a high sea state. Ship waves are simulated based on the Kelvin wave model by the point-source method.A Creamer Ⅱ sea surface based on the Elfouhaily sea spectrum is generated, and breaking waves and foam layer effects are taken into account for the background sea scattering at slight, moderate and high wind speeds.Turbulent bubbles scattering from the ship, which is different from wind-driven bubble breaking, is taken into account with a different concentration distribution using a polynomial fitting function combined with measured data. The surface-ship wake scattering is presented for different wind speeds. Numerical simulations show that ship wake scattering results will be higher when wake bubbles are taken into account. The ship beam is a key parameter that influences the width of the turbulent wake, and results in different scattering characteristics on the scattering image. The wind-induced surface in the presence of breaking waves and whitecaps results in scattering enhancement. This will cause the ship wake signal to be submerged in the back-ground of sea noise, leading to false alarms.     

Protein structural classification and family identification by multifractal analysis and wavelet spectrum

Family identification is helpful for predicting protein functions. It has been known from the literature that longer sequences of base pairs or amino acids are required to study patterns in biological sequences. Since most protein sequences are relatively short, we randomly concatenate or link the protein sequences from the same family or superfamily together to form longer protein sequences. The 6-letter model, 12-letter model, 20-letter model, the revised Schneider and Wrede scale hydrophobicity, solvent accessibility and stochastic standard state accessibility are used to convert linked protein sequences into numerical sequences. Then multifractal analyses and wavelet analysis are performed on these numerical sequences. The parameters from these analyses can be used to construct parameter spaces where each linked protein is represented by a point. The four classes of proteins, namely the α,β, α+βand α /β classes, are then distinguished in these parameter spaces. The Fisher linear discriminant algorithm is used to assess the discriminant accuracy. Numerical results indicate that the discriminant accuracies are satisfactory in separating these classes. We find that the linked proteins from the same family or superfamily tend to group together and can be separated from other linked proteins. The methods are helpful for identifying the family of an unknown protein.     

Wave dispersion and attenuation in viscoelastic isotropic media containing multiphase flow and its application

In this paper,we introduce the complex modulus to express the viscoelasticity of a medium.According to the correspondence principle,the Biot-Squirt(BISQ)equations in the steady-state case are presented for the space-frequency domain described by solid displacements and fluid pressure in a homogeneous viscoelastic medium.The effective bulk modulus of a multiphase flow is computed by the Voigt formula,and the characteristic squirt-flow length is revised for the gas-included case.We then build a viscoelastic BISQ model containing a multiphase flow.Through using this model,wave dispersion and attenuation are studied in a medium with low porosity and low permeability.Furthermore,this model is applied to observed interwell seismic data.Analysis of these data reveals that the viscoelastic parameter tanδ is not a constant.Thus,we present a linear frequency-dependent function in the interwell seismic frequency range to express tanδ.This improves the fit between the observed data and theoretical results.     

Research on the response model of microbolometer

There are certain limitations in the application of uncooled focal plane array (FPA) detector due to the lack of an effective response model which reliably transforms the target temperature to analog output voltage. This paper establishes the response model of microbolometer through researching the detection theory of microbolometer and the heat balance equation under the condition of the pulsed voltage bias. In the establishing process, we simplified the heat balance equation to acquire a simple answer. The experimental data show that, in the temperature dynamic range of 30 K, the biggest tolerance between the model data and the experiment data is 0.2 K; while in the temperature dynamic range of 100 K, it is 1 K. This model can reflect the real response of the microbolometer with only small differences which are acceptable in engineering applications.     

甲型流感病毒DNA序列的长记忆ARFIMA模型

流感病毒分为三类:甲型(A型),乙型(B型),丙型(C型).在这三种类型中甲型(A型)流感病毒是最致命的流感病毒,对人类引起了严重疾病.本文对甲型流感病毒DNA序列建立了一种新的时间序列模型,即CGR(Chaos Game Representation)弧度序列.利用CGR坐标将甲流病毒DNA序列转换成CGR弧度序列,且引入长记忆ARFIMA模型去拟合此类序列,发现随机找来的10条H1N1序列,10条H3N2序列都具有长相关性且拟合很好,并且还发现这两种序列可以尝试用不同的ARFIMA模型去识别,其中H1 关键词： 甲型流感 时间序列模型 CGR (p')" href="#">ARFIMA(p d 模型')" href="#">q)模型     

Approximating long-memory DNA sequences by short-memory process

This paper analyzes the approximation of a general long-memory ARFIMA (p,d,q) process by a short-memory ARMA(1, 1) process. To validate this approximation, a mean square error forecast criterion is considered, and the calculation of the mean square error between the observation X_t+l of an ARFIMA process and the l-step-ahead forecast of the ARMA(1, 1) process is presented. The performance of the ARMA(1, 1) approximation to an ARFIMA model is illustrated by using an application to a DNA sequence of orf virus. This paper gives some theoretical justification on the mean square error forecast criterion based on a selected ARMA(1, 1) model when compared to the general ARFIMA(p,d,q) process. The paper also provides a DNA sequence of orf virus analysis when the time series is originated from the tangent values of the Chaos Game Representation coordinates for each nucleotide. The conclusions of this paper work well because the estimator value of d is small (). The paper also gives the other parameter estimate of the fitted ARFIMA (0, d, 1) model and one-step predictions using ARMA(1, 1) model.     

Q-Dependent Susceptibilities in Ferromagnetic Quasiperiodic Z-Invariant Ising Models

We study the q-dependent susceptibility χ(q) of a series of quasiperiodic Ising models on the square lattice. Several different kinds of aperiodic sequences of couplings are studied, including the Fibonacci and silver-mean sequences. Some identities and theorems are generalized and simpler derivations are presented. We find that the q-dependent susceptibilities are periodic, with the commensurate peaks of χ(q) located at the same positions as for the regular Ising models. Hence, incommensurate everywhere-dense peaks can only occur in cases with mixed ferromagnetic–antiferromagnetic interactions or if the underlying lattice is aperiodic. For mixed-interaction models the positions of the peaks depend strongly on the aperiodic sequence chosen. Supported in part by NSF Grant No. PHY 01-00.     

可积开边界条件下的q形变玻色子模型

利用代数Bethe Ansatz方法在可积开边界条件下推广了q形变玻色子模型，得到可积开边界条件下此模型的哈密顿量及其本征方程.该工作可为在更小尺度下研究具有相互作用的玻色子系统提供有效的理论基础. 关键词： 代数Bethe Ansatz q形变玻色子模型')" href="#">q形变玻色子模型 开边界 可积系统     

Correlation and anticorrelation of fractal aggregates. A model for «spinodal-type» aggregation

Summary We present a simple phenomenological model, based on mass conservation arguments, in order to describe aggregation in dense solutions. It has been previously shown that fordiffusion-limited processes scattered intensity distributions exhibit a peak atq≠0 which grows in time and moves to smaller and smallerq vectors. According to the model, each aggregate is surrounded by a depletion region whose size depends on the aggregation kinetics. The form factor for such a cluster should satisfy local mass conservation and hence exhibit a pronounced depression atq=0. the initial stages of aggregation, when the clusters are far apart, are accounted on the basis of a form factor alone. The model shows good agreement with the data and also explains the experimental evidence that the peak does not appear inreaction-limited conditions. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Some observations related to intermittency and multifractality in Si and C-nucleus collisions at

An attempt is made to study the existence of dynamical fluctuations of relativistic particles using the methods of modified multifractal moments, G_q, and scaled factorial moments, F_q, in terms of new scaled variable X(η) suggested by Bialas and Gazdzicki. For this purpose analyses of experimental and UrQMD data involving interactions of ²⁸Si and ¹²C nuclei at with nuclear emulsion are used. The variation of lnG_q and lnF_q with lnM in pseudorapidity (η) phase space reveals power law behaviour. The values of slopes, τ_q and _q determined from the analyses of G_q and F_q moments are discussed. The generalized fractal dimensions, D_q, determined from the above methods are found to decrease with the order of the moments, q, indicating multifractality in multiparticle production. It is also observed that the spectral function f(α_q) for heavier projectile is much broader than for lighter beam due to larger number of participating nucleons present in heavier projectile.     

Quantum mechanics with difference operators

A formulation of quantum mechanics with additive and multiplicative (q-) difference operators instead of differential operators is studied from first principles. Borel-quantisation on smooth configuration spaces is used as guiding quantisation method. After a short discussion this method is translated step-by-step to a framework based on difference operators. To restrict the resulting plethora of possible quantisations additional assumptions motivated by simplicity and plausibility are required. Multiplicative difference operators and the corresponding q-Borel kinematics are given on the circle and its N-point discretisation; the connection to q-deformations of the Witt algebra is discussed. For a “natural” choice of the q-kinematics a corresponding q-difference evolution equation is obtained. This study shows general difficulties for a generalisation of a physical theory from a known one to a “new” framework.     

Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas

Many two-dimensional spin models can be transformed into Coulomb-gas systems in which charges interact via logarithmic potentials. For some models, such as the eight-vertex model and the Ashkin-Teller model, the Coulomb-gas representation has added significantly to the insight in the phase transitions. For other models, notably theXY model and the clock models, the equivalence has been instrumental for almost our entire understanding of the critical behavior. Recently it was shown that theq-state Potts model and then-vector model are equivalent to a Coulomb gas with an asymmetry between positive and negative charges. Fieldlike operators in these spin models transform noninteger charges and magnetic monopoles. With the aid of exactly solved models the Coulombgas representation allows analytic calculation of some critical indices.