Error Thresholds in Single-Peak Gaussian Distributed Fitness Landscapes

Based on the Eigen and Crow-Kimura models with a single-peak fitness landscape, we propose the fitness values of all sequence types to be Gausslan distributed random variables to incorporate the effects of the fluctuations of the fitness landscapes （noise of environments） and investigate the concentration distribution and error threshold of quasispecies by performing an ensemble average within this theoretical framework. We find that a small fluctuation of the fitness landscape causes only a slight change in the concentration distribution and error threshold, which implies that the error threshold is stable against small perturbations. However, for a sizable fluctuation, quite different from the previous deterministic models, our statistical results show that the transition from quasi-species to error catastrophe is not so sharp, indicating that the error threshold is located within a certain range and has a shift toward a larger value. Our results are qualitatively in agreement with the experimental data and provide a new implication for antiviral strategies.     

Relaxation Property and Stability Analysis of the Quasispecies Models

The relaxation property of both Eigen model and Crow-Kimura model with a single peak fitness landscape is studied from phase transition point of view. We first analyze the eigenvalue spectra of the replication mutation matrices. For sufficiently long sequences, the almost crossing point between the largest and seeond-largest eigenvalues locates the error threshold at which critical slowing down behavior appears. We calculate the critical exponent in the limit of infinite sequence lengths and compare it with the result from numerical curve fittings at sufficiently long sequences. We find that for both models the relaxation time diverges with exponent 1 at the error （mutation） threshold point. Results obtained from both methods agree quite well. From the unlimited correlation length feature, the first order phase transition is further confirmed. Finally with linear stability theory, we show that the two model systems are stable for all ranges of mutation rate. The Igigen model is asymptotically stable in terms of mutant classes, and the Crow-Kimura model is completely stable.     

Population Growth of Small Harmful Rats in Grassland Subjected to Noise

The population growth of small harmful rats in grassland subjected to environment fluctuation has been modelled in a logistic equation. Two correlated random variables responsible to the fluctuation of the genetic factor and the suppression factor are used. A two-peak structure of the steady probability distribution of rate population is observed in the large fluctuation regime of the genetic factor. With the increase of correlation constant A, the steady probability distribution can change from two peaks to a single peak. The suppression factor μ and its fluctuation also affect the steady probability distribution and can push it toward a small population.     

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 do, by which we can gain a visual and in-depth result about how the sequences axe 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 do appears to be linear near the threshold.     

Effect of structural parameters of Gaussian repaired pit on light intensity distribution inside KH_2PO_4 crystal

KH2PO4 （KDP） crystal with excellent optical properties is a very important element of inertial confinement fusion （ICF） device. However, KDP crystal surface micro-defects severely reduce the crystal laser damage threshold, affecting the crystal service life. In this paper, Gaussian repaired pit is used to replace the crystal surface micro-defects, in order to improve the laser damage resistance of the KDP crystal with surface micro-defects. At first, the physical model of Gaussian repaired pit is built by Fourier model method, and the accuracy of the method is analyzed. It is found that the calculation error can be reduced by increasing the product of the width-period ratio and the truncation constant of the repaired pit. The calculation results about the physical model of Gaussian repaired pit show that the light intensity distribution within the crystal is symmetrical, and there are evidently enhanced light intensity regions in the crystal. Meanwhile, the maximum relative intensity inside the KDP crystal decreases gradually with the increase of the width of the Gaussian repaired pit. Secondly, the Gaussian repaired pits with different widths and the same depth of 20 μm are processed by micro-milling. Their surfaces are very smooth and present the ductile cutting state under the microscope. Finally, the laser damage threshold of the Gaussian repaired pits on the surface of the KDP crystal sample is measured by a 3 ω, 6-ns laser. The results showthat the maximum threshold of the Gaussian repaired pits is 3.12 J/cm2, which is 60% higher than the threshold of initial damage point, and the laser damage threshold increases with the increase of the width of the Gaussian repaired pit.     

Weak Nonlinearity of Ablative Rayleigh--Taylor Instability

The weakly nonlinear regime of single mode ablative Rayleigh-Taylor instability is studied, with consideration of preheat effect and the width of the ablation front. The Rayleigh-Taylor linear growth rate agrees well with the direct numerical simulation. For the density perturbation, the amplitude distribution of the fundamental mode has one peak value whereas those of the second and third harmonics have two and three peak values, respectively. Harmonics generation versus wave number is also given and it is close to the result of direct numerical simulation.     

Steady-State Analysis of a Two-Mode Laser System with Cross-Correlation Between Real and Imaginary Parts of Quantum Noise

An inhomogeneously broadened two-mode laser system with cross-correlations between the real and imag- inary parts of quantum noise is considered. The Fokker-Planek equation of the system is derived by the phase-locking method. The steady-state probability distribution, the mean light intensity, the normalization autocorrelation function, and cross correlation function are calculated. The results indicate that： （i） The cross-correlation between the real and imaginary parts of quantum noise can cause the stationary probability distribution from one peak structure to two extrema structure when the laser system is operated above threshold; （ii） The cross-correlation between the real and imaginary parts of quantum noise enhance the light intensity fluctuation and decrease the laser output when the laser system is operated below or near threshold; （iii） The effect of the cross-correlation between the real and imaginary parts of quantum noise is very weak on the stationary properties when the laser system is operated far above threshold.     

Study on digital holography with single phase-shifting operation

The digital holography with single phase-shifting operation has been studied. Experimental results and computer-simulated work are presented. The phase-shifting error makes the intensity of primary image decrease and the conjugate image appear in reconstruction. The explicit equation for explaining these effects is given. The calculation of the normalized intercorrelation peak between the input and the reconstruction for different algorithms shows that, when the phase-shifting operation is the main error source, the quality of the image reconstructed from the digital holography with single phase-shifting operation is favorable.     

Breakup of Spiral Waves in Coupled Hindmarsh--Rose Neurons

Breakup of spiral wave in the Hindmarsh-Rose neurons with nearest-neighbour couplings is reported. Appropriate initial values and parameter regions are selected to develop a stable spiral wave and then the Gaussian coloured noise with different intensities and correlation times is imposed on all neurons to study the breakup of spiral wave, respectively. Based on the mean field theory, the statistical factor of synchronization is defined to analyse the evolution of spiral wave. It is found that the stable rotating spiral wave encounters breakup with increasing intensity of Gaussian coloured noise or decreasing correlation time to certain threshold.     

The pulsed microwave damage trend of a bipolar transistor as a function of pulse parameters

In the present paper we conduct a theoretical study of the thermal accumulation effect of a typical bipolar transistor caused by high power pulsed microwaves(HPMs),and investigate the thermal accumulation effect as a function of pulse repetition frequency(PRF) and duty cycle.A study of the damage mechanism of the device is carried out from the variation analysis of the distribution of the electric field and the current density.The result shows that the accumulation temperature increases with PRF increasing and the threshold for the transistor is about 2 kHz.The response of the peak temperature induced by the injected single pulses indicates that the falling time is much longer than the rising time.Adopting the fitting method,the relationship between the peak temperature and the time during the rising edge and that between the peak temperature and the time during the falling edge are obtained.Moreover,the accumulation temperature decreases with duty cycle increasing for a certain mean power.     

随机化的Eigen模型研究

为了使Eigen模型能够更真实地描述物种的演化过程,将确定性Eigen模型改造成随机模型.以Eigen模型为理论框架,把基因序列中每一个位点的突变率看作一个高斯随机变量,从而导出随机性Eigen模型.对于此随机性Eigen模型,当突变率的涨落强度较小时,准物种的误差阈位置几乎没有改变,仍是个相变点;而当突变率的涨落强度变大时,误差阈由一个相变点变为一个转变区域.在真实的物种演化过程中,误差阈应是一个转变区域,而且在解决实际问题时应考虑该转变区域的上限.     

Talbot Images of Two-Dimensional Gaussian Beam Arrays with Amplitude Fluctuation

Talbot images constructed in the Fresnel diffraction region due to two-dimensional Gaussian beam arrays with amplitude fluctuation are statistically investigated using a mathematical model based on the propagation law of a Gaussian beam. The average intensity distribution of Talbot images is analyzed theoretically, and the corresponding simulation is conducted by computer. The relative fluctuation of the peak intensity to the mean with respect to Talbot images is found to be less than that of the source by approximately 1/4. Furthermore, the effect of the finite size of source arrays on the formation of Talbot images is revealed throughout the simulation as well as the effect of the amplitude fluctuation.     

Research on FBG sensor signal wavelength demodulation based on improved wavelet transform

A new Fiber Bragg Grating (FBG) wavelength demodulation scheme is studied in the paper, which consists of an improved de-noising method and Gaussian fitting peak searching algorithm. The improved translational invariant wavelet without threshold adjust factor is proposed to get a better de-noising performance for FBG sensor signal and overcome the drawbacks of soft or hard threshold wavelets. In order to get a high wavelength demodulation precision of FBG sensor signal, this de-noising method is designed to combine with Gaussian fitting peak searching algorithm. The simulation results show that the wavelength maximum measurement error is lower than 1 pm, and can get a much higher accuracy.     

隧穿量子点分子模型与光场相互作用系统中光场的相位特性

应用Pegg-Barnett相位理论,研究了隧穿量子点分子模型与光场相互作用系统中光场的相位特性,着重分析了光场的相位概率分布及相位涨落,并讨论了平均光子数和失谐量以及时间对相位概率分布的影响．结果发现：光场相位概率分布在零附近的概率分布最大,且涨落最小,而其它范围内概率分布小且容易振荡,适当调节平均光子数和时间,能使相位概率分布由单峰结构向对称的三峰高斯分布转化,且能调节峰值的大小．     

Simultaneous measurement of vibration amplitude and rotation angle based on a single-channel laser self-mixing interferometer

Based on a single-channel laser self-mixing interferometer,we present a new simultaneous measurement of the vibration amplitude and the rotation angle of objects that both affect the power spectrum containing two peaks of the interferometer signals.The fitted results indicate that the curve of the peak frequency versus the vibration amplitude follows a linear distribution,and the curve of the difference of the two-peak power values versus the angle follows a Gaussian distribution.A vibration amplitude with an error less than 3.0% and a rotation angle with an error less than 11.7% are calculated from the fitted results.     

Error thresholds for quasispecies on dynamic fitness landscapes

In this paper we investigate error thresholds on dynamic fitness landscapes. We show that there exists both a lower and an upper threshold, representing limits to the copying fidelity of simple replicators. The lower bound can be expressed as a correction term to the error threshold present on a static landscape. The upper error threshold is a new limit that only exists on dynamic fitness landscapes. We also show that for long genomes and/or highly dynamic fitness landscapes there exists a lower bound on the selection pressure required for the effective selection of genomes with superior fitness independent of mutation rates, i.e. there are distinct nontrivial limits to evolutionary parameters in dynamic environments.     

星间光通信中局部波前畸变对捕获精度的影响

 提出了一种针对反射式光学天线的简单椭圆高斯模型来描述局部波前畸变,研究了星间光通信中局部波前畸变对捕获精度的影响。理论分析和仿真结果表明:局部畸变半径、畸变深度以及畸变位置是影响捕获精度的主要因素;捕获偏差随着畸变半径以及畸变中心相对于光束中心的距离的增大而增大;随局部畸变深度的增加呈周期性振荡衰减变化,且振荡周期和峰值对应的畸变深度不依赖于其它畸变参数。对口径为240 mm的反射式接收天线系统,当遮挡比为0.15时,局部畸变引起的捕获偏差近似可达0.5 μrad。为了减小捕获偏差,所需的光学元件的加工精度应远高于0.25λ。     

基于高斯拟合的条纹管成像激光雷达目标重构

为得到更为精细的三维重构,提出一种基于信赖域法高斯拟合的峰值探测法,对每帧图像单时间通道的回波进行高斯建模,建模结果可有效减小噪声干扰,具有唯一峰值,该结果作为新的回波波形,再对其进行峰值探测,并基于空中目标实验数据对本文方法进行验证.实验结果表明,基于高斯拟合的峰值探测法可将特征数据的提取误差降至10%以内;利用该方法提取特征数据进行目标三维重构,可实现探测深度方向上最小30cm的空间分辨力,提高了条纹管激光雷达的三维成像精度.     

Design of optical system for flattop beam shaper based on the measurement of laser induced damage threshold of thin films

To solve the problem of large error when measure the laser induced damage threshold of thin films in the case of Gaussian distribution beam induced damage thin films, optical system of flattop beam shaper which is capable of redistributing a beam with a Gaussian profile to a flattop profile was designed with optical design software ZEMAX. The Fermi-Dirac beam model was chosen as the distribution function of the flattop beam in this paper, the mapping formula of the input Gaussian beam and the output flattop beam was establish, the surface coefficient of aspheric was given. The energy conversion efficiency was 95.33% and the flattened degree was 93.66% in this design. The accuracy of measurement has been improved when measure the laser induced damage threshold of thin films by the flattop beam.     

Evaluation of the scattering coefficient for high-frequency sound scattered from the sea surface

The effect of the deviation of the real rough sea surface from the Gaussian isotropic surface on the scattering coefficient of high-frequency sound is analyzed. The analysis relies on the data on the sea surface slopes, obtained from field experiments in the Black Sea with the use of a two-dimensional laser slopemeter. It is shown that the effect of the anisotropy of the surface wave field on the scattering coefficient is small when the angle of incidence is small, but this effect rapidly increases as the angle of incidence grows. The deviation of the real statistical moments of the sea surface slopes from those corresponding to the Gaussian distribution results in a ±20% error in the theoretical values of the scattering coefficient.