For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The propose...For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The proposed algorithm integrates two-point and multi-point time correlation functions into a unified framework.Further,it is verified by a practical application in complex financial systems,demonstrating its potential in various complex dynamic systems.展开更多
BACKGROUND Studies have shown that locomotive syndrome(LS)is significantly correlated with adverse outcomes,such as decreased self-care abilities,fractures,and increased mortality.Subthreshold depression(StD)is consid...BACKGROUND Studies have shown that locomotive syndrome(LS)is significantly correlated with adverse outcomes,such as decreased self-care abilities,fractures,and increased mortality.Subthreshold depression(StD)is considered an independent predictor of clinical depression,regarded as its prodromal stage,and even linked to increased mortality risk.Limited research has addressed the prevalence and relationship between LS and StD in elderly cancer patients.Understanding the prevalence of LS and StD among elderly cancer patients and elucidating their relationship will provide evidence to support the development of targeted interventions,thereby improving health outcomes in this population.AIM To investigate the relationship between musculoskeletal system function and predepressive states in elderly cancer patients.METHODS A convenience sampling method was employed to recruit 500 elderly cancer patients undergoing follow-up visits at the Department of Oncology,Affiliated Hospital of Jiangnan University,from April 2024 to December 2024.Participants completed the general information questionnaire, the 25-question Geriatric Locomotive Function Scale, and theGeriatric Depression Scale-Short Form-15. Influencing factors were analyzed, and correlation analyses wereperformed.RESULTSA total of 483 elderly cancer patients successfully completed the study. The prevalence of LS and StD amongparticipants was 56.5% and 38.7%, respectively. Logistic regression analysis identified age, tumor metastasis,exercise habits, and the presence of StD as significant risk factors for LS in elderly cancer patients. Additionally,having three or more chronic diseases and LS were significant predictors for developing StD. Spearman’s correlationanalysis revealed a significant positive correlation between LS and StD (r = 0.424, P < 0.001).CONCLUSIONElderly cancer patients exhibit a high prevalence of LS and StD, conditions which are positively correlated andmutually influential. Thus, it is critical to monitor and address pre-depressive states while evaluating and managingmotor function in this population.展开更多
BACKGROUND Psychological comorbidities,such as anxiety and depression,in patients with chronic ankle instability(CAI)may impede ankle function improvement,although the precise nature of this association warrants furth...BACKGROUND Psychological comorbidities,such as anxiety and depression,in patients with chronic ankle instability(CAI)may impede ankle function improvement,although the precise nature of this association warrants further investigation.AIM To analyze the correlation of anxiety and depression with ankle function in patients with CAI and discussing the risk factors.METHODS This study included 116 patients with CAI,who were admitted to our hospital from July 2022 to July 2024.Anxiety and depression states of patients were assessed with the self-rating anxiety scale(SAS)and self-rating depression scale(SDS),respectively,and their ankle joint function was assessed with the anklehindfoot function score of the American Orthopedic Foot and Ankle Society.Further,the ankle function of patients with CAI with different anxiety and depression states was discussed.Furthermore,the Pearson correlation coefficient was used to analyze the correlation of anxiety and depression with ankle joint function in such patients.Univariate and multivariate analyses were conducted to investigate the factors affecting ankle joint function in patients with CAI.RESULTS Among the 116 patients with CAI,97,13,5,and 1 cases demonstrated none,mild,moderate,and severe anxiety,whereas 95,15,6,and 0 cases showed none,mild,moderate,and severe depression,respectively.The average ankle joint function score was 74.82±6.93 points.The ankle joint function in patients with CAI presented a significant downward tendency as the degree of anxiety and depression increased.Correlation analysis revealed that both the SAS and SDS scores of patients with CAI were significantly negatively correlated with the ankle joint function score.Univariate and multivariate analyses indicated that the risk factors affecting patients’ankle joint function included early functional rehabilitation,visual analog scale,and SDS.CONCLUSION A substantial number of patients with CAI suffer from anxiety and depression,and these negative emotions,to a certain extent,harm the smooth rehabilitation of ankle joint function.展开更多
Establishing the structure-property relationship in amorphous materials has been a long-term grand challenge due to the lack of a unified description of the degree of disorder.In this work,we develop SPRamNet,a neural...Establishing the structure-property relationship in amorphous materials has been a long-term grand challenge due to the lack of a unified description of the degree of disorder.In this work,we develop SPRamNet,a neural network based machine-learning pipeline that effectively predicts structure-property relationship of amorphous material via global descriptors.Applying SPRamNet on the recently discovered amorphous monolayer carbon,we successfully predict the thermal and electronic properties.More importantly,we reveal that a short range of pair correlation function can readily encode sufficiently rich information of the structure of amorphous material.Utilizing powerful machine learning architectures,the encoded information can be decoded to reconstruct macroscopic properties involving many-body and long-range interactions.Establishing this hidden relationship offers a unified description of the degree of disorder and eliminates the heavy burden of measuring atomic structure,opening a new avenue in studying amorphous materials.展开更多
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 correlati...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.展开更多
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 generalize...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.展开更多
The sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. In this paper, the relationships among crosscorrelation functions of arbitrary four...The sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. In this paper, the relationships among crosscorrelation functions of arbitrary four binary sequences of period N are presented. Based on them, for a sequences set, the relationships between cross-correlation functions and autocorrelation functions are studied, by which we prove that they cannot keep optimal at the same time.展开更多
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...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.展开更多
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...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.展开更多
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 ...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.展开更多
The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differenc...The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differences be- tween the roles of quadratic time-delayed feedback and cubic time-delayed feedback on the correlations of an autonomous stochastic system. Under quadratic time-delayed feedback, the nonlinear time delay fails to improve the noisy state of the autonomous stochastic system, the auto-correlation decreases monotonously to zero, and the cross-correlation increases monotonously to zero with the decay time. Under cubic time-delayed feedback, the nonlinear time delay can improve the noisy state of the autonomous stochastic system; the auto-correlation and the cross-correlation show periodical oscillation and attenuation, finally tending to zero with the decay time. Comparing the correlations of the system between with nonfinear time-delayed feedback and linear time-delayed feedback, we find that nonlinear time-delayed feedback lowers the correlation strength of the autonomous stochastic system.展开更多
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 ...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.展开更多
A large class of linear structural functions(LSF) satisfying the condition of correlational immunity of order one are constructed by studying the linear structural Boolean functions. With these new founded functions, ...A large class of linear structural functions(LSF) satisfying the condition of correlational immunity of order one are constructed by studying the linear structural Boolean functions. With these new founded functions, the known enumeration bounds of correlation-immune functions of order one are greatly improved. In fact, the best, up to now, lower bound is found.展开更多
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 ...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.展开更多
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...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.展开更多
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 t...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.展开更多
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...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.展开更多
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 wit...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）.展开更多
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 charact...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.展开更多
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 f...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.展开更多
基金Project supported by the Postdoctoral Fellowship Program of China Postdoctoral Science Foundation(Grant No.GZC20231050)the National Natural Science Foundation of China(Grant Nos.12175193 and 11905183)the 13th Five-year plan for Education Science Funding of Guangdong Province(Grant No.2021GXJK349)。
文摘For non-stationary complex dynamic systems,a standardized algorithm is developed to compute time correlation functions,addressing the limitations of traditional methods reliant on the stationary assumption.The proposed algorithm integrates two-point and multi-point time correlation functions into a unified framework.Further,it is verified by a practical application in complex financial systems,demonstrating its potential in various complex dynamic systems.
基金Supported by Wuxi Institute of Translational Medicine Project Program,No.LCYJ202336the Scientific and Technological Achievements Promotion Project of Wuxi Municipal Health Commission Project Program,No.T202336+1 种基金the Hospital Management Innovation Research Project of Jiangsu Hospital Association,No.JSYGY-3-2024-601Jiangsu Provincial Traditional Chinese Medicine Science and Technology Development Plan Project,No.MS2024063.
文摘BACKGROUND Studies have shown that locomotive syndrome(LS)is significantly correlated with adverse outcomes,such as decreased self-care abilities,fractures,and increased mortality.Subthreshold depression(StD)is considered an independent predictor of clinical depression,regarded as its prodromal stage,and even linked to increased mortality risk.Limited research has addressed the prevalence and relationship between LS and StD in elderly cancer patients.Understanding the prevalence of LS and StD among elderly cancer patients and elucidating their relationship will provide evidence to support the development of targeted interventions,thereby improving health outcomes in this population.AIM To investigate the relationship between musculoskeletal system function and predepressive states in elderly cancer patients.METHODS A convenience sampling method was employed to recruit 500 elderly cancer patients undergoing follow-up visits at the Department of Oncology,Affiliated Hospital of Jiangnan University,from April 2024 to December 2024.Participants completed the general information questionnaire, the 25-question Geriatric Locomotive Function Scale, and theGeriatric Depression Scale-Short Form-15. Influencing factors were analyzed, and correlation analyses wereperformed.RESULTSA total of 483 elderly cancer patients successfully completed the study. The prevalence of LS and StD amongparticipants was 56.5% and 38.7%, respectively. Logistic regression analysis identified age, tumor metastasis,exercise habits, and the presence of StD as significant risk factors for LS in elderly cancer patients. Additionally,having three or more chronic diseases and LS were significant predictors for developing StD. Spearman’s correlationanalysis revealed a significant positive correlation between LS and StD (r = 0.424, P < 0.001).CONCLUSIONElderly cancer patients exhibit a high prevalence of LS and StD, conditions which are positively correlated andmutually influential. Thus, it is critical to monitor and address pre-depressive states while evaluating and managingmotor function in this population.
文摘BACKGROUND Psychological comorbidities,such as anxiety and depression,in patients with chronic ankle instability(CAI)may impede ankle function improvement,although the precise nature of this association warrants further investigation.AIM To analyze the correlation of anxiety and depression with ankle function in patients with CAI and discussing the risk factors.METHODS This study included 116 patients with CAI,who were admitted to our hospital from July 2022 to July 2024.Anxiety and depression states of patients were assessed with the self-rating anxiety scale(SAS)and self-rating depression scale(SDS),respectively,and their ankle joint function was assessed with the anklehindfoot function score of the American Orthopedic Foot and Ankle Society.Further,the ankle function of patients with CAI with different anxiety and depression states was discussed.Furthermore,the Pearson correlation coefficient was used to analyze the correlation of anxiety and depression with ankle joint function in such patients.Univariate and multivariate analyses were conducted to investigate the factors affecting ankle joint function in patients with CAI.RESULTS Among the 116 patients with CAI,97,13,5,and 1 cases demonstrated none,mild,moderate,and severe anxiety,whereas 95,15,6,and 0 cases showed none,mild,moderate,and severe depression,respectively.The average ankle joint function score was 74.82±6.93 points.The ankle joint function in patients with CAI presented a significant downward tendency as the degree of anxiety and depression increased.Correlation analysis revealed that both the SAS and SDS scores of patients with CAI were significantly negatively correlated with the ankle joint function score.Univariate and multivariate analyses indicated that the risk factors affecting patients’ankle joint function included early functional rehabilitation,visual analog scale,and SDS.CONCLUSION A substantial number of patients with CAI suffer from anxiety and depression,and these negative emotions,to a certain extent,harm the smooth rehabilitation of ankle joint function.
基金supported by the National Key R&D Program of China under Grant No.2021YFA1400500the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No.XDB33000000+1 种基金the National Natural Science Foundation of China under Grant No.12334003the Beijing Municipal Natural Science Foundation under Grant Nos.JQ22001 and QY23014。
文摘Establishing the structure-property relationship in amorphous materials has been a long-term grand challenge due to the lack of a unified description of the degree of disorder.In this work,we develop SPRamNet,a neural network based machine-learning pipeline that effectively predicts structure-property relationship of amorphous material via global descriptors.Applying SPRamNet on the recently discovered amorphous monolayer carbon,we successfully predict the thermal and electronic properties.More importantly,we reveal that a short range of pair correlation function can readily encode sufficiently rich information of the structure of amorphous material.Utilizing powerful machine learning architectures,the encoded information can be decoded to reconstruct macroscopic properties involving many-body and long-range interactions.Establishing this hidden relationship offers a unified description of the degree of disorder and eliminates the heavy burden of measuring atomic structure,opening a new avenue in studying amorphous materials.
文摘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.
基金Supported by State Key Laboratory of InformationSecurity Opening Foundation(01-02) .
文摘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.
基金Supported by the Natural Science Foundation of Anhui(1608085MF143)the National Natural Science Foundation of China(60573026,10101008)the Natural Science Foundation of Anhui Higher Education Institutions of China(KJ2018A0678)
文摘The sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. In this paper, the relationships among crosscorrelation functions of arbitrary four binary sequences of period N are presented. Based on them, for a sequences set, the relationships between cross-correlation functions and autocorrelation functions are studied, by which we prove that they cannot keep optimal at the same time.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10674172 and 10874229)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11374331 and 11534014)the National Key R&D Program of China(Grant No.2017YFA0304500)partially supported by CAS-TWAS President’s Fellowship for International PhD Students
文摘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.
基金supported by the National Key Basic Research Program of China(Grant No.2012CB921704)the National Natural Science Foundation of China(Grant No.11374362)+1 种基金the Fundamental Research Funds for the Central Universities,Chinathe Research Funds of Renmin University of China(Grant No.15XNLQ03)
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant No.11265012Yunnan Province Open Key Laboratory of Mechanics in Colleges and Universities
文摘The auto-correlation function and the cross-correlation of an autonomous stochastic system with nonlinear time-delayed feedback are investigated by using the stochastic simulation method. There are prominent differences be- tween the roles of quadratic time-delayed feedback and cubic time-delayed feedback on the correlations of an autonomous stochastic system. Under quadratic time-delayed feedback, the nonlinear time delay fails to improve the noisy state of the autonomous stochastic system, the auto-correlation decreases monotonously to zero, and the cross-correlation increases monotonously to zero with the decay time. Under cubic time-delayed feedback, the nonlinear time delay can improve the noisy state of the autonomous stochastic system; the auto-correlation and the cross-correlation show periodical oscillation and attenuation, finally tending to zero with the decay time. Comparing the correlations of the system between with nonfinear time-delayed feedback and linear time-delayed feedback, we find that nonlinear time-delayed feedback lowers the correlation strength of the autonomous stochastic system.
基金National Natural Science Foundation of China under Grant No.90403019
文摘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.
文摘A large class of linear structural functions(LSF) satisfying the condition of correlational immunity of order one are constructed by studying the linear structural Boolean functions. With these new founded functions, the known enumeration bounds of correlation-immune functions of order one are greatly improved. In fact, the best, up to now, lower bound is found.
基金This work was supported in part by the National Natural Science Foundation of China (10071058, 70273029) the Ministry of Education of China.
文摘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.
基金supported by National Hi-tech Research and Development Program of China (863 Program, Grant No. 2007AA04Z433)Hunan Provincial Natural Science Foundation of China (Grant No. 09JJ8005)Scientific Research Foundation of Graduate School of Beijing University of Chemical and Technology,China (Grant No. 10Me002)
文摘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.
基金supported by the National Key R&D Program of China(No.2018YFA0404404)the National Natural Science Foundation of China(Nos.11925502,11935001,11961141003,11421505,11475244,and 11927901)+2 种基金the Shanghai Development Foundation for Science and Technology(No.19ZR1403100)the Strategic Priority Research Program of the CAS(No.XDB34030000)the Key Research Program of Frontier Sciences of the CAS(No.QYZDJ-SSW-SLH002).
文摘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.
文摘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.
文摘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）.
基金supported by the Fundamental Research and Development of Institute of Geophysics,China Earthquake Administration (DQJB07B03)
文摘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.
基金Item of the 9-th F ive Plan of the Aeronautical Industrial Corporation
文摘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.
