Non-perturbative dynamics of flat-band systems with correlated disorder

We develop a numerical method for the time evolution of Gaussian wave packets on flat-band lattices in the presence of correlated disorder.To achieve this,we introduce a method to generate random on-site energies with prescribed correlations.We verify this method with a one-dimensional(1D)cross-stitch model,and find good agreement with analytical results obtained from the disorder-dressed evolution equations.This allows us to reproduce previous findings,that disorder can mobilize 1D flat-band states which would otherwise remain localized.As explained by the corresponding disorder-dressed evolution equations,such mobilization requires an asymmetric disorder-induced coupling to dispersive bands,a condition that is generically not fulfilled when the flat-band is resonant with the dispersive bands at a Dirac point-like crossing.We exemplify this with the 1D Lieb lattice.While analytical expressions are not available for the two-dimensional(2D)system due to its complexity,we extend the numerical method to the 2D a–T3 model,and find that the initial flat-band wave packet preserves its localization when a=0,regardless of disorder and intersections.However,when a̸=0,the wave packet shifts in real space.We interpret this as a Berry phase controlled,disorder-induced wave-packet mobilization.In addition,we present density functional theory calculations of candidate materials,specifically Hg1−xCdxTe.The flat-band emerges near the G point(α=0)in the Brillouin zone.

Quantitative determination of the critical points of Mott metal–insulator transition in strongly correlated systems

Mottness is at the heart of the essential physics in a strongly correlated system as many novel quantum phenomena occur in the metallic phase near the Mott metal–insulator transition. We investigate the Mott transition in a Hubbard model by using the dynamical mean-field theory and introduce the local quantum state fidelity to depict the Mott metal–insulator transition. The local quantum state fidelity provides a convenient approach to determining the critical point of the Mott transition. Additionally, it presents a consistent description of the two distinct forms of the Mott transition points.

A Denoiser for Correlated Noise Channel Decoding: Gated-Neural Network

This letter proposes a sliced-gated-convolutional neural network with belief propagation(SGCNN-BP) architecture for decoding long codes under correlated noise. The basic idea of SGCNNBP is using Neural Networks(NN) to transform the correlated noise into white noise, setting up the optimal condition for a standard BP decoder that takes the output from the NN. A gate-controlled neuron is used to regulate information flow and an optional operation—slicing is adopted to reduce parameters and lower training complexity. Simulation results show that SGCNN-BP has much better performance(with the largest gap being 5dB improvement) than a single BP decoder and achieves a nearly 1dB improvement compared to Fully Convolutional Networks(FCN).

Impact of correlated private signals on continuous-time insider trading

A model of continuous-time insider trading in which a risk-neutral in-sider possesses two imperfect correlated signals of a risky asset is studied.By conditional expectation theory and filtering theory,we first establish three lemmas:normal corre-lation,equivalent pricing and equivalent profit,which can guarantee to turn our model into a model with insider knowing full information.Then we investigate the impact of the two correlated signals on the market equilibrium consisting of optimal insider trading strategy and semi-strong pricing rule.It shows that in the equilibrium,(1)the market depth is constant over time;(2)if the two noisy signals are not linerly correlated,then all private information of the insider is incorporated into prices in the end while the whole information on the asset value can not incorporated into prices in the end;(3)if the two noisy signals are linear correlated such that the insider can infer the whole information of the asset value,then our model turns into a model with insider knowing full information;(4)if the two noisy signals are the same then the total ex ant profit of the insider is increasing with the noise decreasing,while down to O as the noise going up to infinity;(5)if the two noisy signals are not linear correlated then with one noisy signal fixed,the total ex ante profit of the insider is single-peaked with a unique minimum with respect to the other noisy signal value,and furthermore as the noisy value going to O it gets its maximum,the profit in the case that the real value is observed.

CHARACTERISTICS OF FAN STALLING BASED ON CORRELATED DIMENSIONS

Different from the previous qualitative analysis of linear systems in time and frequency domains, the method for describing nonlinear systems quantitatively is proposed based on correlated dimensions. Nonlinear dynamics theory is used to analyze the pressure data of a contrarotating axial flow fan. The delay time is 18 and the embedded dimension varies from 1 to 25 through phase-space reconstruction. In addition, the correlated dimensions are calculated before and after stalling. The results show that the correlated dimensions drop from 1. 428 before stalling to 1. 198 after stalling, so they are sensitive to the stalling signal of the fan and can be used as a characteristic quantity for the judging of the fan stalling.

Effects of Perfectly Correlated and Anti-Correlated Noise in a Logistic Growth Model

The logistic growth model with correlated additive and multiplicative Gaussian white noise is used to anedyze tumor cell population. The effects of perfectly correlated and anti-correlated noise on the stationary properties of tumor cell population are studied. As in both cases the diffusion coefficient has zero point in real number field, some special features of the system are arisen. It is found that in cause tumor cell extinction. In the perfectly anti-correlated tumor cell population exhibit two extrema. both cases, the increase of the multiplicative noise intensity case, the stationary probability distribution as a function of

ON THE RUIN FUNCTIONS FOR A CORRELATED AGGREGATE CLAIMS MODEL WITH POISSON AND ERLANG RISK PROCESSES

This article considers a risk model as in Yuen et al. （2002）. Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is derived for the distribution of the surplus immediately before ruin, for the distribution of the surplus immediately after ruin and the joint distribution of the surplus immediately before and after ruin. The asymptotic property of these ruin functions is also investigated.

Reliability Index of Caisson Breakwaters for Load Variables Correlated

In order to suit the condition that the wave uplift is correlated with the horizontal wave load acting on a vertical breakwater, a generally used method for determining the reliability index β of the breakwater, i.e. the Hasofer-Lind method, is extended in a generalized stochastic space for correlative variables. The computational results for a caisson breakwater indicate that the value of β for the case of correlated variables is obviously smaller than that for the case of independent variables.

A multivariate partial least squares approach to joint association analysis for multiple correlated traits

Many complex traits are highly correlated rather than independent. By taking the correlation structure of multiple traits into account, joint association analyses can achieve both higher statistical power and more accurate estimation. To develop a statistical approach to joint association analysis that includes allele detection and genetic effect estimation, we combined multivariate partial least squares regression with variable selection strategies and selected the optimal model using the Bayesian Information Criterion(BIC). We then performed extensive simulations under varying heritabilities and sample sizes to compare the performance achieved using our method with those obtained by single-trait multilocus methods. Joint association analysis has measurable advantages over single-trait methods, as it exhibits superior gene detection power, especially for pleiotropic genes. Sample size, heritability,polymorphic information content(PIC), and magnitude of gene effects influence the statistical power, accuracy and precision of effect estimation by the joint association analysis.

Joint Analysis Method for Major Genes Controlling Multiple Correlated Quantitative Traits

Based on the major gene and polygene mixed inheritance model for multiple correlated quantitative traits, the authors proposed a new joint segregation analysis method of major gene controlling multiple correlated quantitative traits, which include major gene detection and its effect and variation estimation. The effect and variation of major gene are estimated by the maximum likelihood method implemented via expectation-maximization （EM） algorithm. Major gene is tested with the likelihood ratio （LR） test statistic. Extensive simulation studies showed that joint analysis not only increases the statistical power of major gene detection but also improves the precision and accuracy of major gene effect estimates. An example of the plant height and the number of tiller of F2 population in rice cross Duonieai x Zhonghua 11 was used in the illustration. The results indicated that the genetic difference of these two traits in this cross refers to only one pleiotropic major gene. The additive effect and dominance effect of the major gene are estimated as -21.3 and 40.6 cm on plant height, and 22.7 and -25.3 on number of tiller, respectively. The major gene shows overdominance for plant height and close to complete dominance for number of tillers.

LINEAR FILTERING FOR VASICEK TERM STRUCTURE MODEL WITH SEQUENTIALLY CORRELATED NOISE

When Kalman filter is used in the estimation of Vasicek term structure of interest rates,it is usual to assume that the measurement noise is uncorrelated.Study results are more favorable to the assumption of correlated measurement noise.An augmented state Kalman filter form for Vasicek model is proposed to optimally estimate the unobservable state variable with the assumption of correlated measurement noise.Empirical results indicate that the model with sequentially correlated measurement noise can more accurately describe the dynamics of the term structure of interest rates.

BER Performance of FSO Communication System with Differential Signaling over Correlated Atmospheric Turbulence Fading

Free space optical(FSO) communication system with differential signaling possesses the advantage of requiring no channel state information and avoiding computational load or link throughput reduction compared to the systems with conventional receivers. In this work, we investigate bit error rate(BER) performance of this system over partially and fully correlated atmospheric turbulence fading. In order to conduct the above analysis, we obtain a probability density functions(PDF) of the channel fading on the differential signals and derive our instantaneous BER using differential signaling scheme. Based on these results, we develop two closed-form mathematical expressions for the average BER under fully correlated and partially correlated fading in the convergent infinite series confirmed by Cauchy’s ratio test. The accuracy of the derived BER expressions is demonstrated by the Monte Carlo simulations, and the analyses for the effects of the system parameters on the BER performance are provided.

HARMONIC FUNCTION WITH CORRELATED COEFFICIENTS

In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.

Steady-state analysis subject to a coloured and a white additive of a bistable system multiplicative noise noise with coloured cross-correlated noises

The steady-state properties of a bistable system are investigated when both the multiplicative noise and the coupling between additive and multiplicative noises are coloured with different values of noise correlation times T1 and T2. After introducing a dimensionless parameter R（R = α/D, D is the intensity of the multiplicative noise and a is the intensity of the additive noise）, and performing the numerical computations, we find the following points： （1） For the case of R 〉 1, A （the intensity of correlation between additive and multiplicative noises）, T1 and T2 can induce the stationary probability distribution （SPD） transition from bimodal to unimodal in structure, but for the cases of R _〈 1, the bimodal structure is preserved; （2） a can also induce the SPD transition from bimodal to unimodal in structure; （3） the bimodal structure of the SPD exhibits a symmetrical structure as D increases.

Entropic noise induced stability and double entropic stochastic resonance induced by correlated noises

For the activated dynamics of a Brownian particle moving in a confined system with the presence of entropic barriers, this paper investigates a periodic driving and correlations between two noises. Within the two-state approximation, the explicit expressions of the mean first passage time （MFPT） and the spectral power amplification （SPA） axe obtained, respectively. Based on the numerical computations, it is found that： （i） The MFPT as a function of the noise intensity exhibits a maximum with the positive correlations between two noises （λ〉0）, this maximum for MFPT shows the characteristic of the entropic noise induced stability （ENIS） effect. The intensity A of correlations between two noises can enhance the ENIS effect. （ii） The SPA as a function of the noise intensity exhibits a double-peak by tuning the noise correlation intensity λ, i.e., the existence of a double-peak behaviour is the identifying characteristic of the double entropic stochastic resonance phenomenon.

New sigma point filtering algorithms for nonlinear stochastic systems with correlated noises

New sigma point filtering algorithms, including the unscented Kalman filter （UKF） and the divided difference filter （DDF）, are designed to solve the nonlinear filtering problem under the condition of correlated noises. Based on the minimum mean square error estimation theory, the nonlinear optimal predictive and correction recursive formulas under the hypothesis that the input noise is correlated with the measurement noise are derived and can be described in a unified framework. Then, UKF and DDF with correlated noises are proposed on the basis of approximation of the posterior mean and covariance in the unified framework by using unscented transformation and second order Stirling＇s interpolation. The proposed UKF and DDF with correlated noises break through the limitation that input noise and measurement noise must be assumed to be uneorrelated in standard UKF and DDF. Two simulation examples show the effectiveness and feasibility of new algorithms for dealing with nonlinear filtering issue with correlated noises.

Statistical fluctuations in a saturation laser model with correlated noises

We study the effects of correlations between quantum and pump noises on fluctuations of the laser intensity in a saturation laser model. An approximative Fokker-Planck equation and analytic expressions of the steady-state probability distribution function （SPD） of the laser system are derived. Based on the SPD, the normalized mean, the normalized variance, and the normalized skewness of the steady-state laser intensity are calculated numerically. The results indicate that （i） the correlation strength A of correlated noises always enhances the fluctuation of laser intensity; （ii） the correlation time v of correlated noises strengthens the fluctuation of laser intensity for the below-threshold case but τ weakens it for the above-threshold case.

A novel multi-sensor multiple model particle filter with correlated noises for maneuvering target tracking

Aiming at the effective realization of particle filter for maneuvering target tracking in multi-sensor measurements,a novel multi-sensor multiple model particle filtering algorithm with correlated noises is proposed.Combined with the kinetic evolution equation of target state,a multi-sensor multiple model particle filter is firstly constructed,which is also used as the basic framework of a new algorithm.In the new algorithm,in order to weaken the adverse influence from random measurement noises in the measuring process of particle weight,a weight optimization strategy is introduced to improve the reliability and stability of particle weight.In addition,considering the correlated noise existing in the practical engineering,a decoupling method of correlated noise is given by the rearrangement and transformation of the state transition equation and measurement equation.Since the weight optimization strategy and noise decoupling method adopt respectively the center fusion structure and the off-line way,it improves the adverse effect effectively on computational complexity for increasing state dimension and sensor number.Finally,the theoretical analysis and experimental results show the feasibility and efficiency of the proposed algorithm.

Modified MUSIC estimation for correlated signals with compressive sampling arrays

This paper addresses the issue of the direction of arrival （DOA） estimation under the compressive sampling （CS） framework. A novel approach, modified multiple signal classification （MMUSIC） based on the CS array （CSA-MMUSIC）, is proposed to resolve the DOA estimation of correlated signals and two closely adjacent signals. By using two random CS matrices, a large size array is compressed into a small size array, which effectively reduces the number of the front end circuit. The theoretical analysis demonstrates that the proposed approach has the advantages of low computational complexity and hardware structure compared to other MMUSIC approaches. Simulation results show that CSAMMUSIC can possess similar angular resolution as MMUSIC.

An Iterative Detection/Decoding Algorithm of Correlated Sources for the LDPC-Based Relay Systems

An iterative detection/decoding algorithm of correlated sources for the LDPC-based relay systems is presented. The signal from the source-destination(S-D) link is formulated as a highly correlated counterpart from the relay-destination(R-D) link. A special XOR vector is defined using the correlated hard decision information blocks from two decoders and the extrinsic information exchanged between the two decoders is derived by the log-likelihood ratio(LLR) associated with the XOR vector. Such the decoding scheme is different from the traditional turbo-like detection/decoding algorithm, where the extrinsic information is computed by the side information and the soft decoder outputs. Simulations show that the presented algorithm has a slightly better performance than the traditional turbo-like algorithm(Taking the(255,175) EG-LDPC code as an example, it achieves about 0.1 dB performance gains aroundBLER=10^(-4)). Furthermore, the presented algorithm requires fewer computing operations per iteration and has faster convergence rate. For example, the average iteration of the presented algorithm is 33 at SNR=1.8 dB, which is about twice faster than that of the turbo-like algorithm, when decoding the(961,721) QC-LDPC code. Therefore, the presented decoding algorithm of correlated sources provides an alternative decoding solution for the LDPC-based relay systems.