Simulation study of the effects of time delay on the correlation function of a bistable system with correlated noises

The effects of time delay on the fluctuation properties of a bistable system are investigated by simulating its normalised correlation function C（s）. Three cases including linear delay, cubic delay and global delay in the system are considered respectively. The simulation results indicate that the linear delay enhances the fluctuation of the system （reduces the stability of the system） while the cubic delay and global delay weaken it （enforce the stability of the system）, and the effect of cubic delay is more pronounced than the linear delay and global delay.

Double differential cross sections for ionization of H by 75 keV proton impact:Assessing the role of correlated wave functions

The effect of final-state dynamic correlation is investigated for ionization of atomic hydrogen by 75-keV proton impact by analyzing double differential cross sections.The final state is represented by a continuum correlated wave(CCW-PT)function which accounts for the interaction between the projectile and the target nucleus(PT interaction).The correlated final state is nonseparable solutions of the wave equation combining the dynamics of the electron motion relative to the target and projectile,satisfying the Redmond’s asymptotic conditions corresponding to long range interactions.The transition matrix is evaluated using the CCW-PT function and the undistorted initial state.Both the correlation effects and the PT interaction are analyzed by the present calculations.The convergence of the continuous correlated final state is examined carefully.Our results are compared with the absolute experimental data measured by Laforge et al.[Phys.Rev.Lett.103,053201(2009)]and Schulz et al.[Phys.Rev.A 81,052705(2010)],as well as other theoretical models(especially the results of the latest non perturbation theory).We have shown that the dynamic correlation plays an important role in the ionization of atomic hydrogen by proton impact.While overall agreement between theory and the experimental data is encouraging,detailed agreement is still lacking.However,such an analysis is meaningful because it provides valuable information about the dynamical correlation and PT interaction in the CCW-PT theoretical model.

Weighted Multi-sensor Data Level Fusion Method of Vibration Signal Based on Correlation Function

As the differences of sensor＇s precision and some random factors are difficult to control,the actual measurement signals are far from the target signals that affect the reliability and precision of rotating machinery fault diagnosis.The traditional signal processing methods,such as classical inference and weighted averaging algorithm usually lack dynamic adaptability that is easy for trends to cause the faults to be misjudged or left out.To enhance the measuring veracity and precision of vibration signal in rotary machine multi-sensor vibration signal fault diagnosis,a novel data level fusion approach is presented on the basis of correlation function analysis to fast determine the weighted value of multi-sensor vibration signals.The approach doesn＇t require knowing the prior information about sensors,and the weighted value of sensors can be confirmed depending on the correlation measure of real-time data tested in the data level fusion process.It gives greater weighted value to the greater correlation measure of sensor signals,and vice versa.The approach can effectively suppress large errors and even can still fuse data in the case of sensor failures because it takes full advantage of sensor＇s own-information to determine the weighted value.Moreover,it has good performance of anti-jamming due to the correlation measures between noise and effective signals are usually small.Through the simulation of typical signal collected from multi-sensors,the comparative analysis of dynamic adaptability and fault tolerance between the proposed approach and traditional weighted averaging approach is taken.Finally,the rotor dynamics and integrated fault simulator is taken as an example to verify the feasibility and advantages of the proposed approach,it is shown that the multi-sensor data level fusion based on correlation function weighted approach is better than the traditional weighted average approach with respect to fusion precision and dynamic adaptability.Meantime,the approach is adaptable and easy to use,can be applied to other areas of vibration measurement.

Influence of Noise on Time Evolution of Intensity Correlation Function

Using the linear approximation method, we have studied how the correlation function C（t） of the laser intensity changes with time in the loss-noise model of the single-mode laser driven by the colored pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts. We have found that when the pump noise self-correlation time T changes, （i） in the case of r 〈〈 1, the C（t） vs. t curve experiences a changing process from the monotonous descending to monotonous rise, and finally to the appearance of a maximum; （ii） in the case of r 〉〉 1, the curve only exhibits periodically surging with descending envelope. When r 〈〈 i and T does not change, with the increase of the pump noise intensity P, the curve experiences a repeated changing process, that is, from the monotonous descending to the appearance of a maximum, then to monotonous rise, and finally to the appearance of a maximum again. With the increase of the quantum noise intensity O,, the curve experiences a changing process from the monotonous rise to the appearance of a maximum, and finally to the monotonous descending. The increase of the quantum noise with cross-correlation between the real and imaginary parts will lead to the fall of the whole curve, but not affect the form of the time evolution of C（t）.

Calculation of Scale of Fluctuation and Variance Reduction Function

The scale of fluctuation is one of the vital parameters for the application of random field theory to the reliability analysis of geotechnical engineering. In the present study, the fluctuation function method and weighted curve fitting method were presented to make the calculation more simple and accurate. The vertical scales of fluctuation of typical layers of Tianjin Port were calculated based on a number of engineering geotechnical investigation data, which can be guidance to other projects in this area. Meanwhile, the influences of sample interval and type of soil index on the scale of fluctuation were analyzed, according to which, the principle of determining the scale of fluctuation when the sample interval changes was defined. It can be obtained that the scale of fluctuation is the basic attribute reflecting spatial variability of soil, therefore, the scales of fluctuation calculated according to different soil indexes should be basically the same. The non-correlation distance method was improved, and the principle of determining the variance reduction function was also discussed.

Criterion for Blind Signals Separation Based on Correlation Function

Blind separation of source signals usually relies either on the condition of statistically independence or involving their higher-order cumulants. The model of two channels signal separation is considered. A criterion based on correlation functions is proposed. It is proved that the signals can be separated, using only the condition of noncorrelation. An algorithm is derived, which only involves the solution to quadric nonlinear equations.

Temporal variation of noise correlation function(NCF) in Beijing and surroundings:Its relation with climate events and implications

Noise correlation function （NCF） was calculated using the data of the Beijing Capital-Area Telemetered Digital Seismograph Network from June 12 to September 12, 2005. Signal-to-noise ratio （SNR） is used to characterize the quality of NCF at each station pair. The SNR （in dB） is shown to be dependent on the separation distance R of the station pair via SNR= A -BlogR. ＇Normalized average SNR＇ for all the station pairs can then be calculated, as represented by the value of SNR taking R = 250 km in the empirical SNR-R relation, to measure the overall quality of the NCF result. The ＇normalized average SNR＇ of the NCF shows temporal variation and is apparently dependent on the root-mean-square （RMS） velocity of the microseism. The result obtained by this experiment provides clues to the explanation of the properties of NCF, such as the dominant mechanism underlying （diffuse wave fields or uncorrelated sources）, and the dependence of SNR on the time length of recordings.

Intensity Correlation Function of a Single-Mode Laser Driven by Colored Cross-Correlation Noises in Modulation of a Bias Signal

By using the linear approximation method, the intensity correlation function is calculated for a single-mode laser modulated by a bias signal and driven by colored pump and quantum noises with colored cross-correlation. We found that, when the correlation time between the two noises is very short, the behavior of the intensity correlation function versus the time, in addition to decreasing monotonously, also exhibits several cases, such as one maximum, one minimum, and two extrema. When the correlation time between the two noises is very long, the behavior of the intensity correlation function exhibits oscillation and the envelope is similar to the case of short cross-correlation time.

Spectral Theorem of Many-Body Green's Functions When Complex Eigenvalues Appear

In this paper, an extended spectral theorem is given, which enables one to calculate the correlation functions when complex eigenvalues appear. To do so, a Fourier transformation with a complex argument is utilized. We treat all the Matsbara frequencies, including Fermionic and Bosonic frequencies, on an equal footing. It is pointed out that when complex eigenvalues appear, the dissipation of a system cannot simply be ascribed to the pure imaginary part of the Green function. Therefore, the use of the name fluctuation-dissipation theorem should be careful.

Dynamical correlation functions of the quadratic coupling spin-Boson model

The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method.We focus on the dynamical auto-correlation functions CO（ω）, with the operator taken as σx, σz, and X, respectively. In the weak-coupling regime α 〈 αc, these functions show power law ω-dependence in the small frequency limit, with the powers 1 ＋ 2s, 1 ＋ 2s, and s, respectively. At the critical point α = αc of the boson-unstable quantum phase transition, the critical exponents yO of these correlation functions are obtained as yσx= yσz= 1-2s and yX=-s, respectively. Here s is the bath index and X is the boson displacement operator. Close to the spin flip point, the high frequency peak of Cσx（ω） is broadened significantly and the line shape changes qualitatively, showing enhanced dephasing at the spin flip point.

Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas

The Lieb-Liniger model is a prototypical integrable model and has been turned into the benchmark physics in theoretical and numerical investigations of low-dimensional quantum systems. In this note, we present various methods for calculating local and nonlocal M-particle correlation functions, momentum distribution, and static structure factor. In particular, using the Bethe ansatz wave function of the strong coupling Lieb-Liniger model, we analytically calculate the two-point correlation function, the large moment tail of the momentum distribution, and the static structure factor of the model in terms of the fractional statistical parameter a = 1 - 2/γ, where γ, is the dimensionless interaction strength. We also discuss the Tan＇s adiabatic relation and other universal relations for the strongly repulsive Lieb-Liniger model in terms of the fractional statistical parameter.

Simulation study of the two-time intensity correlation function of a two-mode laser system with both pump and quantum noises

This paper investigates the two-time intensity correlation function of a two-mode ring laser system subjected to both pump and quantum noises by stochastic simulation. It finds that the decay rate of the intensity correlation function of one mode gets faster with decreasing values of relevant parameters, i.e., the coupling constant ξ, the cross-correlation coefficient A, the difference of the pump parameters Aa and the pump parameter al; however, its variations get complex in the other mode when relevant parameters are changed. The investigating results also show that the effects of the mode competition on intensity correlation function are obvious.

Spin-correlation function of the fully frustrated Ising model and ±J Ising spin glass on a square lattice

In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.

Calculation of Energy and Other Properties of Muonic Helium Atom Using Boundary Conditions of Wave Function

The properties of muonic helium atom （^4He＋2μ-e-） in ground state are considered. In this work, the energy and average distance between particles have been obtained using a wave function, which satisfies boundary conditions. It is shown that the obtained energy are very close to the values calculated by others. But the small differences of the expectation values of r^2n are due to the incorporated boundary conditions in proposed wave function and are expected.

Filling dependence of correlation exponents and metal-Mott insulator transition in strongly correlated electron systems

Using a universal relation between electron filling factor and ground state energy, this paper studies the dependence of correlation exponents on the electron filling factor of one-dimensional extended Hubbard model in a strong coupling regime, and demonstrates that in contrast to the usual Hubbard model （gc = 1/2）, the dimensionless coupling strength parameter gc heavily depends on the electron filling, and it has a ＂particle-hole＂ symmetry about electron quarter filling point. As increasing the nearest neighbouring repulsive interaction, the single particle spectral weight is transferred from low energy to high energy regimes. Moreover, at electron quarter filling, there is a metal-Mott insulator transition at the strong coupling point gc = 1/4, and this transition is a continuous phase transition.

How to Extend the Bridge Density Functional Approximation to the Confined Non-hard Sphere Fluid

A theoretical method was proposed to extend a bridge density functional approximation （BDFA） for the non-uniform hard sphere fluid to the non-uniform Lennard-Jones （LJ） fluid. The DFT approach for LJ fluid is simple, quantitatively accurate in a wide range of coexistence phase and external field parameters. Especially, the DFT approach only needs a second order direct correlation function （DCF） of the coexistence bulk fluid as input, and is therefore applicable to the subcritical temperature region. The present theoretical method can be regarded as a non-uniform counterpart of the thermodynamic perturbation theory, in which it is not at the level of the free energy but at the level of the second order DCF.the National Natural Science Foundation of China （No. 20546004） and the Natural Science Foundation of Education Department of Hunan Province （No.04C711）.

SELF-TUNING MEASUREMENT FUSION KALMAN FILTER WITH CORRELATED MEASUREMENT NOISES

For the multisensor system with correlated measurement noises and unknown noise statistics, based on the solution of the matrix equations for correlation function, the on-line estimators of the noise variances and cross-covariances is obtained. Further, a self-tuning weighted measurement fusion Kalman filter is presented, based on the Riccati equation. By the Dynamic Error System Analysis (DESA) method, it rigorously proved that the presented self-tuning weighted measurement fusion Kalman filter converges to the optimal weighted measurement fusion steady-state Kalman filter in a realization or with probability one, so that it has asymptotic global optimality. A simulation example for a target tracking system with 3-sensor shows that the presented self-tuning measurement fusion Kalman fuser converges to the optimal steady-state measurement fusion Kalman fuser.

Boundary Correlation Functions of the gl(1|1) Supersymmetric Vertex Model

The gl（1/1） supersymmetric vertex model with domain wall boundary conditions （DWBC） on an N × N square lattice is considered. We derive the reduction formulae for the one-point boundary correlation functions of the model. The determinant representation for the boundary correlation functions is also obtained.

Weak value amplification via second-order correlated technique

We propose a new framework combining weak measurement and second-order correlated technique. The theoretical analysis shows that weak value amplification （WVA） experiment can also be implemented by a second-order correlated system. We then build two-dimensional second-order correlated function patterns for achieving higher amplification factor and discuss the signal-to-noise ratio influence. Several advantages can be obtained by our proposal. For instance, detectors with high resolution are not necessary. Moreover, detectors with low saturation intensity are available in WVA setup. Finally, type-one technical noise can be effectively suppressed.

Correlation of cognitive function with acetylcholinesterase activity and P300 event-related potential of patients with type 2 diabetes mellitus

BACKGROUND： At present, central cholinergic neuron system is regarded the most major structural basis of cognitive function. Changes in structure of cholinergic neuron system of brain and receptor expression after brain injury can cause cognitive impairment. OBJECTIVE＂ To comparatively observe the intelligence quotient （IQ）, latent period and wave amplitude of P300 event-related potential and the difference of activity of acetylcholinesterase （ACHE） in blood and cerebrospinal fluid between patients with type 2 diabetes mellitus and with non-diabetes mellitus, and analyze the correlation of IQ of cognitive impairment patients with diabetes mellitus with AChE activity, latent period and wave amplitude of P300 event-related potential in cerebrospinal fluid. DESIGN： Correlation analysis of contrast observation SETTING： Department of Endocrinology, Affiliated Hospital of Binzhou Medical College PARTICIPANTS： Totally 32 patients with type 2 diabetes mellitus who received the treatment in the Department of Endocrinology, Affiliated Hospital of Binzhou Medical College between April 2004 and April 2005 were recruited, serving as diabetes mellitus group. They, including 19 male and 13 female, aged 49 to 73 years, with disease course of 4 to 11 years, all met the diagnostic criteria of diabetes mellitus revised by World Health Organization in 1999. Another 30 patients with non-diabetes mellitus who homeochronously underwent lumbar anesthesia in the Department of Surgery and Department of Gynecology were recruited, serving as non-diabetes mellitus group. The 30 patients included 18 male and 12 female, and their age ranged from 46 to 71 years. Informed consents of detected items were obtained from the involved patients. METHODS： ① Evaluation,on IQ： The IQ of involved subjects was evaluated with Chinese Version of the Wechsler Adult Intelligence Scale revised by Gong Yao-xian （WAIS-RC）. WAIS-RC included 6 verbal subscales and 5 performance subscales. The test scores of the 11 subscales integrated into the scores of the whole scale, and the scores on the WAIS-RC included verbal IQ （VlQ）, performance IQ （PIQ） and full scale IQ （FIQ）. FIQ ≤79 scores indicated low IQ and FIQ≤69 indicated intelligence impairment. ② Detection of P300 wave： P300 wave was detected with evoked potential instrument （MYTOPRO, Italian）, and data of latent period and amplitude of P300 event-related potential were automatically shown by computer. ③ Detection of AChE activity in blood and cerebrospinal fluid： Activity of AChE of blood and cerebrospinal fluid was measured with biochemical methods by using CORNING-560 autoanalyzer.④Correlation analysis： Correlation of FIQ with AChE of cerebrospinal fluid and P300 wave of patients with type 2 diabetes mellitus was analyzed, t test was used in intergroup comparison and linear correlation analysis for relevant treatment. MAIN OUTCOME MEASURES： ① Comparison of IQ, latent period and wave amplitude of P300 wave as well as the activity of AChE between two groups. ② Analysis on the correlation of FIQ of patients with type 2 diabetes mellitus with AChE of cerebrospinal fluid and P300 wave. RESULTS： Thirty-two patients with diabetes mellitus and 30 non-diabetes mellitus participated in the result analysis. ①Comparison of IQ, latent period and wave amplitude of P300 wave as well as the activity of AChE between two groups： The scores of VIP, PIQ and FIQ of patients with type 2 diabetes mellitus were （97.4±10.4）. （92.6±8.4） and （95.2±9.7） scores, respectively; and those of patients with non-diabetes mellitus were （104.7±9.6）, （102.5±8.5）and（102.7±8.9） scores, respectively, and P 〈 0.05-0.01 was set in intergroup comparison. The latent period of P300 wave at points Fz , Cz and Pz of patients with type 2 diabetes mellitus was （370.8±41.8）.（371.5±39.1）and （375.1±43.1） ms, respectively, and that of patients with non-diabetes mellitus was （ 332.1 ±28.3 ）, （335.7 ±29.4）and （339.7 ±27.3） ms, respectively, and P 〈 0.01 was set in intergroup comparison; Wave amplitude of P300 of patients with type 2 diabetes mellitus was （8.6±4.1）,（8.6±4.0） and （7.7±4.0） μV, respectively and that of patients with non-diabetes mellitus was （11.9±4.1）,（11.5±4.4） and （10.9±5.0） μV, respectively , and P 〈 0.05-0.01 was set in intergroup comparison; The level of AChE in blood and cerebrospinal fluid of patients with type 2 diabetes mellitus was （235.61 ±50.34）and （17.89±4.46） μkat/L, respectively, which was significantly higher than that of patients with non-diabetes mellitus [（205.03±44.15）and （14.63±0.48） μkat /L, respectively], and P 〈 0.05-0.01 was set in the intergroup comparison. ② Correlation of FIQ value of patients with type 2 diabetes mellitus with AChE of cerebrospinal fluid and P300 wave： The value of FIQ was significantly negatively correlated with the AChE activity of cerebrospinal fluid （r=-0.588 1, P 〈 0.01 ）, significantly negatively correlated with the latent period at points Fz. C and Pz of P300 wave （r= -0.700 5, -0.689 4, -0.688 5, P 〈 0.01 ）, and significantly positively correlated with the amplitude at points Fz . Cz and Pz of P300 wave（r= 0.607 4,0.616 1,0.592 0,P 〈 0.01 ）. CONCLUSION： ① Cognitive impairment of patients with type 2 diabetes mellitus might be related to the increase of activity of AChE in cerebrospinal fluid. ②Combined application of examination of P300 wave and evaluation of IQ is more useful in deciding the state of cognitive function of patients with type 2 diabetes mellitus.