Second-Order Correlation Function for Asymmetric-to-Symmetric Transitions due to Spectrally Indistinguishable Biexciton Cascade Emission

We report the observed photon bunching statistics of biexciton cascade emission at zero time delay in single quantum dots by second-order correlation function g（2） （T） measurements under continuous wave excitation. It is found that the bunching phenomenon is independent of the biexciton binding energy when it varies from 0.59 meV to nearly zero. The photon bunching takes place when the exeiton photon is not spectrally distinguishable from the biexciton photon, and either of them can trigger the %tart＇ in a Hanbury-Brown and Twiss setup. However, if the exciton energy is spectrally distinguishable from the biexciton, the photon statistics will become asymmetric and a cross-bunching lineshape can be obtained. The theoretical calculations based on a model of three-level rate-equation analysis are consistent with the result of g（2）（τ） correlation function measurements.

Application of Serum Apelin and MMP-9 in Evaluation of Silicosis and Their Correlation with Lung Function

[Objectives]This study was conducted to explore the combination of serum Apelin and MMP-9 in the assessment of silicosis and their correlation with lung function. [Methods] From January 2020 to January 2021, eight patients with silicosis(including 3, 2 and 3 patients with silicosis in stages I, II and III respectively) were selected as the observation group, and eight persons frees of silicosis were selected as the control group during the same period. All patients were detected for serum APJ endogenous ligand(Apelin) of G protein-coupled receptor, matrix metalloproteinase-9(MMP-9) and pulmonary function indexes. The levels of serum Apelin and MMP-9 and lung function in the two groups were compared, and the correlation between serum Apelin and MMP-9 indexes and lung function was analyzed. [Results] The serum Apelin and lung function in the observation group were lower than those in the control group, and the level of MMP-9 in the observation group was higher than that in the control group, and the differences were statistically significant(P<0.05). The MMP-9 index in patients with silicosis in stage III was higher than those in patients with silicosis in stage II and stage I, and the MMP-9 index in patients with silicosis in stage II was higher than that in patients with silicosis in stage I, and the differences were statistically significant(P<0.05). The serum Apelin and lung function indexes of patients with silicosis in stage III were lower than those of patients with silicosis in stage II and stage I, and the serum Apelin and lung function indexes of patients with silicosis in stage II were lower than those of patients with silicosis in stage I, and the differences were statistically significant(P<0.05). The correlation analysis showed a positive correlation between serum Apelin and lung function indexes, and a negative correlation between MMP-9 and lung function indexes. [Conclusions] A lower serum Apelin and a higher MMP-9 value in patients with silicosis indicate severer lung function impairment, and the combined detection of serum Apelin and MMP-9 is conducive to effective evaluation of the disease of silicosis. The serum Apelin index was negatively correlated with silicosis, and the level of MMP-9 was positively correlated with silicosis, which could provide a scientific basis for clinical diagnosis and treatment.

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.

Effect of source size and emission time on the p–p momentum correlation function in the two-proton emission process

The effect of source size and emission time on the proton-proton(p-p)momentum correlation function(Cpp(q))has been studied systematically.Assuming a spherical Gaussian source with space and time profile according to the function S(r,t)~exp(-r2/2 r02-t/τ)in the correlation function calculation code(CRAB),the results indicate that one Cpp(q)distribution corresponds to a unique combination of source size r0 and emission timeτ.Considering the possible nuclear deformation from a spherical nucleus,an ellipsoidal Gaussian source characterized by the deformation parameter∈=ΔR/R has been simulated.There is almost no difference of Cpp(q)between the results of spherically and ellipsoidally shaped sources with small deformation.These results indicate that a unique source size r0 and emission time could be extracted from the p-p momentum correlation function,which is especially important for identifying the mechanism of twoproton emission from proton-rich nuclei.Furthermore,considering the possible existence of cluster structures within a nucleus,the double Gaussian source is assumed.The results show that the p-p momentum correlation function for a source with or without cluster structures has large systematical differences with the variance of r0 andτ.This may provide a possible method for experimentally observing the cluster structures in proton-rich nuclei.

Correlation Degree and Correlation Coefficient of Multi-Output Functions

We present definitions of the correlation degree and correlation coefficient of multi-output functions. Two relationships about the correlation degree of multi-output functions are proved. One is between the correlation degree and independency, the other is between the correlation degree and balance. Especially the paper discusses the correlation degree of affine multioutput functions. We demonstrate properties of the correlation coefficient of multi-output functions. One is the value range of the correlation coefficient, one is the relationship between the correlation coefficient and independency, and another is the sufficient and necessary condition that two multi-output functions are equivalent to each other.

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.

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）.

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.

MODAL PARAMETERS EXTRACTION WITH CROSS CORRELATION FUNCTION AND CROSS POWER SPECTRUM UNDER UNKNOWN EXCITATION

In most of real operational conditions only response data are measurable while the actual excitations are unknown, so modal parameter must be extracted only from responses. This paper gives a theoretical formulation for the cross-correlation functions and cross-power spectra between the outputs under the assumption of white-noise excitation. It widens the field of modal analysis under ambient excitation because many classical methods by impulse response functions or frequency response functions can be used easily for modal analysis under unknown excitation. The Polyreference Complex Exponential method and Eigensystem Realization Algorithm using cross-correlation functions in time domain and Orthogonal Polynomial method using cross-power spectra in frequency domain are applied to a steel frame to extract modal parameters under operational conditions. The modal properties of the steel frame from these three methods are compared with those from frequency response functions analysis. The results show that the modal analysis method using cross-correlation functions or cross-power spectra presented in this paper can extract modal parameters efficiently under unknown excitation.

Walsh Spectral Characteristics and the Auto-Correlation Function Characteristics of Forming Orthomorphic Permutations of Multi-Output Functions

Orthomorphic permutations have good characteristics in cryptosystems. In this paper, by using of knowledge about relation between orthomorphic permutations and multi-output functions, and conceptions of the generalized Walsh spectrum of multi-output functions and the auto-correlation function of multi-output functions to investigate the Walsh spectral characteristics and the auto-correlation function characteristics of orthormophic permutations, several results are obtained.

FROM WAVE FUNCTIONS TO TAU-FUNCTIONS FOR THE VOLTERRA LATTICE HIERARCHY

For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave functions.As an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators.

Charge self-consistent dynamical mean field theory calculations incombination with linear combination of numerical atomic orbitalsframework based density functional theory

We present a formalism of charge self-consistent dynamical mean field theory(DMFT)in combination with densityfunctional theory(DFT)within the linear combination of numerical atomic orbitals(LCNAO)framework.We implementedthe charge self-consistent DFT+DMFT formalism by interfacing a full-potential all-electron DFT code with threehybridization expansion-based continuous-time quantum Monte Carlo impurity solvers.The benchmarks on several 3d,4fand 5f strongly correlated electron systems validated our formalism and implementation.Furthermore,within the LCANOframework,our formalism is general and the code architecture is extensible,so it can work as a bridge merging differentLCNAO DFT packages and impurity solvers to do charge self-consistent DFT+DMFT calculations.

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.

Cognitive dysfunction in schizophrenia patients caused by downregulation of γ-aminobutyric acid receptor subunits

BACKGROUND The expression pattern of gamma aminobutyric acid(GABA)receptor subunits are commonly altered in patients with schizophrenia,which may lead to nerve excitation/inhibition problems,affecting cognition,emotion,and behavior.AIM To explore GABA receptor expression and its relationship with schizophrenia and to provide insights into more effective treatments.METHODS This case-control study enrolled 126 patients with schizophrenia treated at our hospital and 126 healthy volunteers who underwent physical examinations at our hospital during the same period.The expression levels of the GABA receptor subunits were detected using 1H-magnetic resonance spectroscopy.The recognized cognitive battery tool,the MATRICS Consensus Cognitive Battery,was used to evaluate the scores for various dimensions of cognitive function.The correlation between GABA receptor subunit downregulation and schizophrenia was also analyzed.RESULTS Significant differences in GABA receptor subunit levels were found between the case and control groups(P<0.05).A significant difference was also found between the case and control groups in terms of cognitive function measures,including attention/alertness and learning ability(P<0.05).Specifically,as the expression levels of GABRA1(α1 subunit gene),GABRB2(β2 subunit gene),GABRD(δsubunit),and GABRE(εsubunit)decreased,the severity of the patients’condition increased gradually,indicating a positive correlation between the downregulation of these 4 receptor subunits and schizophrenia(P<0.05).However,the expression levels of GABRA5(α5 subunit gene)and GABRA6(α6 subunit gene)showed no significant correlation with schizophrenia(P>0.05).CONCLUSION Downregulation of the GABA receptor subunits is positively correlated with schizophrenia.In other words,when GABA receptor subunits are downregulated in patients,cognitive impairment becomes more severe.

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.

Improvement of a new rotation function for molecular replacement by designing new scoring functions and dynamic correlation coefficient

A previously published new rotation function has been improved by using a dynamic correlation coefficient as well as two new scoring functions of relative entropy and mean-square-residues to make the rotation function more robust and independent of a specific set of weights for scoring and ranking. The previously described new rotation function calculates the rotation function of molecular replacement by matching the search model directly with the Patterson vector map. The signal-to-noise ratio for the correct match was increased by averaging all the matching peaks. Several matching scores were employed to evaluate the goodness of matching. These matching scores were then combined into a single total score by optimizing a set of weights using the linear regression method. It was found that there exists an optimal set of weights that can be applied to the global rotation search and the correct solution can be ranked in the top 100 or less. However, this set of optimal weights in general is dependent on the search models and the crystal structures with different space groups and cell parameters. In this work, we try to solve this problem by designing a dynamic correlation coefficient. It is shown that the dynamic correlation coefficient works for a variety of space groups and cell parameters in the global search of rotation function. We also introduce two new matching scores： relative entropy and mean-square-residues. Last but not least, we discussed a valid method for the optimization of the adjustable parameters for matching vectors.

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.

Evaluation of right ventricular volume and systolic function in normal fetuses using intelligent spatiotemporal image correlation

BACKGROUND Heart defects are the most common congenital malformations in fetuses.Fetal cardiac structure and function abnormalities lead to changes in ventricular volume.As ventricular volume is an important index for evaluating fetal cardiovascular development,an effective and reliable method for measuring fetal ventricular volume and cardiac function is necessary for accurate ultrasonic diagnosis and effective clinical treatment.The new intelligent spatiotemporal image correlation(iSTIC)technology acquires high-resolution volumetric images.In this study,the iSTIC technique was used to measure right ventricular volume and to evaluate right ventricular systolic function to provide a more accurate and convenient evaluation of fetal heart function.AIM To investigate the value of iSTIC in evaluating right ventricular volume and systolic function in normal fetuses.METHODS Between October 2014 and September 2015,a total of 123 pregnant women received prenatal ultrasound examinations in our hospital.iSTIC technology was used to acquire the entire fetal cardiac volume with off-line analysis using QLAB software.Cardiac systolic and diastolic phases were defined by opening of the atrioventricular valve and the subsequent closure of the atrioventricular valve.The volumetric data of the two phases were measured by manual tracking and summation of multiple slices and recording of the right ventricular end-systolic volume and the right ventricular end-diastolic volume.The data were used to calculate the right stroke volume,the right cardiac output,and the right ejection fraction.The correlations of changes between the above-mentioned indices and gestational age were analyzed.The right ventricular volumes of 30 randomly selected cases were measured twice by the same sonographer,and the intraobserver agreement measurements were calculated.RESULTS Among the 123 normal fetuses,the mean right ventricular end-diastolic volume increased from 0.99±0.34 mL at 22 wk gestation to 3.69±0.36 mL at 35+6 wk gestation.The mean right ventricular end-systolic volume increased from 0.43±0.18 mL at 22 wk gestation to 1.36±0.22 mL at 35+6 wk gestation.The mean right stroke volume increased from 0.62±0.29 mL at 22 wk gestation to 2.33±0.18 mL at 35+6 wk gestation.The mean right cardiac output increased from 92.23±40.67 mL/min at 22 wk gestation to 335.83±32.75 mL/min at 35+6 wk gestation.Right ventricular end-diastolic volume,right ventricular end-systolic volume,right stroke volume,and right cardiac output all increased with gestational age and the correlations were linear(P<0.01).Right ejection fraction had no apparent correlation with gestational age(P>0.05).CONCLUSION Fetal right ventricular volume can be quantitatively measured using iSTIC technology with relative ease and high repeatability.iSTIC technology is expected to provide a new method for clinical evaluation of fetal cardiac function.

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.

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.