We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for m...We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.展开更多
On the basis of high precision requirement for input signals in the power system protection and control system,this paper,only for the influence of power system frequency deviation on extracting fundamental harmonic,s...On the basis of high precision requirement for input signals in the power system protection and control system,this paper,only for the influence of power system frequency deviation on extracting fundamental harmonic,studies the amplitude error of Fourier algorithm,presents a method of correcting frequency deviation,and further derives the formulas of improved Fourier algorithm.The simulation results verified the effectiveness of the algorithm,it not only can greatly weaken the influence of frequency deviation,but also increase the precision of the power system protection and control.As a result the study in this paper has practical application value.展开更多
M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large devi...M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.展开更多
Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove mod...Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.展开更多
We study moderate deviations for estimators of the drift parameter of the fractional Ornstein-Uhlenbeck process. Two moderate deviation principles are obtained.
The authors consider the moderate deviations of hydrodynamic limit for Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg-Landau model is obtained and an explicit fo...The authors consider the moderate deviations of hydrodynamic limit for Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg-Landau model is obtained and an explicit formula of the rate function is derived.展开更多
This paper presents a small perturbation Cramer method for obtaining the large deviation principle of a family of measures (β,ε> 0) on a topological vector space. As an application, we obtain the moderate deviati...This paper presents a small perturbation Cramer method for obtaining the large deviation principle of a family of measures (β,ε> 0) on a topological vector space. As an application, we obtain the moderate deviation estimations for uniformly ergodic Markov processes.展开更多
Typical representation of dimension and geometric accuracy is limited to the self-representation of dimension and geometric deviation based on geometry variation thinking, yet the interactivity affection of geometric ...Typical representation of dimension and geometric accuracy is limited to the self-representation of dimension and geometric deviation based on geometry variation thinking, yet the interactivity affection of geometric variation and gesture variation of multi-rigid body is not included. In this paper, a kinematic matrix model based on Lagrangian coordinate is introduced, with the purpose of unified model for geometric variation and gesture variation and their interactive and integrated analysis. Kinematic model with joint, local base and movable base is built. The ideal feature of functional geometry is treated as the base body; the fitting feature of functional geometry is treated as the adjacent movable body; the local base of the kinematic model is fixed onto the ideal geometry, and the movable base of the kinematic model is fixed onto the fitting geometry. Furthermore, the geometric deviation is treated as relative location or rotation variation between the movable base and the local base, and it＇s expressed by the Lagrangian coordinate. Moreover, kinematic matrix based on Lagrangian coordinate for different types of geometry tolerance zones is constructed, and total freedom for each kinematic model is discussed. Finally, the Lagrangian coordinate library, kinematic matrix library for geometric deviation modeling is illustrated, and an example of block and piston fits is introduced. Dimension and geometric tolerances of the shaft and hole fitting feature are constructed by kinematic matrix and Lagrangian coordinate, and the results indicate that the proposed kinematic matrix is capable and robust in dimension and geometric tolerances modeling.展开更多
In this article, we obtain the large deviations and moderate deviations for negatively dependent （ND） and non-identically distributed random variables defined on （-∞, ＋∞）. The results show that for some non-ide...In this article, we obtain the large deviations and moderate deviations for negatively dependent （ND） and non-identically distributed random variables defined on （-∞, ＋∞）. The results show that for some non-identical random variables, precise large deviations and moderate deviations remain insensitive to negative dependence structure.展开更多
To eliminate rotation deviation of sequential images mosaic when measuring linear dimensions of large scale parts with computer vision, a novel algorithm based on the chain code searching method is proposed. After ima...To eliminate rotation deviation of sequential images mosaic when measuring linear dimensions of large scale parts with computer vision, a novel algorithm based on the chain code searching method is proposed. After image preprocessing, including image filtering, image segmentation, and edge detection, the chain code length of the contour line can be searched out by the proposed method. Then, the angle from the contour line to the coordinate axis is computed with the length of the contour line. After that, the sequence is rotated in the opposite direction and the rotation deviation is eliminated. It is prepared for the next mosaic of sequences in eliminating shifting deviation. Experiments are carried out on parts with a linear profile rotating angle from 0° to 9°. The results show that compared with the commonly used Hough transform, the new method has higher precision and faster speed, which is important in realizing online high precision measurements of large scale parts with a linear profile.展开更多
The differences between two sequences of nonnegative independent and identically distributed random variables with sub-exponential tails and the random index are studied. The random index is a strictly stationary rene...The differences between two sequences of nonnegative independent and identically distributed random variables with sub-exponential tails and the random index are studied. The random index is a strictly stationary renewal counting process generated by some negatively associated random variables. Using a revised large deviation result of partial sums, the elementary renewal theorem and the central limit theorem of negatively associated random variables, a precise large deviation result is derived for the random sums. The result is applied to the customer-arrival-based insurance risk model. Some uniform asymptotics for the ruin probabilities of an insurance company are obtained as the number of customers or the time tends to infinity.展开更多
Advertising English is viewed as an English style with such functional factors as attention value, readability, memorability, selling power. Commercial advertisements are the major concern of this paper. Deviation, na...Advertising English is viewed as an English style with such functional factors as attention value, readability, memorability, selling power. Commercial advertisements are the major concern of this paper. Deviation, namely the violation to the norms of a language, frequently appears in advertisements and can meet requirements of the style of advertising English. Due to limited space, this paper focuses on deviation on the phonological, graphological, lexical, grammatical, and semantic level. Analyzing deviation in advertising English can promote readers' aesthetic and appreciative ability and encourage advertisers to create advertisements with more efficiency, novelty, innovation in more effective language.展开更多
Most edge-detection methods rely on calculating gradient derivatives of the potential field, a process that is easily affected by noise and is therefore of low stability. We propose a new edge-detection method named c...Most edge-detection methods rely on calculating gradient derivatives of the potential field, a process that is easily affected by noise and is therefore of low stability. We propose a new edge-detection method named correlation coefficient of multidirectional standard deviations（CCMS） that is solely based on statistics. First, we prove the reliability of the proposed method using a single model and then a combination of models. The proposed method is evaluated by comparing the results with those obtained by other edge-detection methods. The CCMS method offers outstanding recognition, retains the sharpness of details, and has low sensitivity to noise. We also applied the CCMS method to Bouguer anomaly data of a potash deposit in Laos. The applicability of the CCMS method is shown by comparing the inferred tectonic framework to that inferred from remote sensing（RS） data.展开更多
In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain the stochastic Burgers’ equation and the stochastic...In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain the stochastic Burgers’ equation and the stochastic reaction-diffusion equation. The weak convergence method plays an important role.展开更多
We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be c...We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be calculated explicitly which is a squared function.展开更多
Song is one of Christina Georgina Rossetti's most outstanding death poems,dealing with the main themes that she concerns:death,love and religion.This paper tries to use the technique of deviation that refers to vi...Song is one of Christina Georgina Rossetti's most outstanding death poems,dealing with the main themes that she concerns:death,love and religion.This paper tries to use the technique of deviation that refers to violations to the standard language and readers'expectations to interpret this poem's stylistic features from the aspects of grammar,phonology,image,theme and narrative point of view.Through the stylistic analysis with the method of deviation,its solemn theme is exposed clearly.展开更多
The welding deviation detection is the basis of robotic tracking welding, but the on-line real-time measurement of welding deviation is still not well solved by the existing methods. There is plenty of information in ...The welding deviation detection is the basis of robotic tracking welding, but the on-line real-time measurement of welding deviation is still not well solved by the existing methods. There is plenty of information in the gas metal arc welding（GMAW） molten pool images that is very important for the control of welding seam tracking. The physical meaning for the curvature extremum of molten pool contour is revealed by researching the molten pool images, that is, the deviation information points of welding wire center and the molten tip center are the maxima and the local maxima of the contour curvature, and the horizontal welding deviation is the position difference of these two extremum points. A new method of weld deviation detection is presented, including the process of preprocessing molten pool images, extracting and segmenting the contours, obtaining the contour extremum points, and calculating the welding deviation, etc. Extracting the contours is the premise, segmenting the contour lines is the foundation, and obtaining the contour extremum points is the key. The contour images can be extracted with the method of discrete dyadic wavelet transform, which is divided into two sub contours including welding wire and molten tip separately. The curvature value of each point of the two sub contour lines is calculated based on the approximate curvature formula of multi-points for plane curve, and the two points of the curvature extremum are the characteristics needed for the welding deviation calculation. The results of the tests and analyses show that the maximum error of the obtained on-line welding deviation is 2 pixels（0.16 ram）, and the algorithm is stable enough to meet the requirements of the pipeline in real-time control at a speed of less than 500 mm/min. The method can be applied to the on-line automatic welding deviation detection.展开更多
This paper takes the synthesizing evaluation about industrial economic benefits by examples and proposes a new method named maximizing deviation method for multiindices decision. The new method can automatically deter...This paper takes the synthesizing evaluation about industrial economic benefits by examples and proposes a new method named maximizing deviation method for multiindices decision. The new method can automatically determine the weight coefficients among the multiindices and also can obtain the exact and reliable evaluation results without subjectivity.展开更多
Automatic on-line detection of welding deviation based on machine vision is one of the key technologies of arc welding robot tracking welding,in which obtaining high quality weld pool image and accurate welding deviat...Automatic on-line detection of welding deviation based on machine vision is one of the key technologies of arc welding robot tracking welding,in which obtaining high quality weld pool image and accurate welding deviation detection algorithm are two important steps of tracking welding.Through the research and analysis of the weld pool image of gas metal arc welding(GMAW),it was found that the weld pool contains abundant welding information.First,the average gray value of the weld pool image can reflect the interference degree of arc to weld pool image and the heat input of welding process.Secondly,the tip of the weld pool image contour can reflect the center of the groove gap.Finally,the horizontal distance between the center coordinate of the wire contour and the tip coordinate of the weld pool image contour can reflect the welding deviation.On the basis of analyzing the characteristics of weld pool image,this paper proposes a new method of weld seam deviation detection,which includes the collection of weld pool image,image preprocessing,contour extraction and deviation calculation.The results of the tests and analyses showed that the maximum error of the on-line welding deviation obtained was about 2 pixels(0.17 mm)when the welding speed was≤60 cm/min,and the algorithm was stable enough to meet the requirements of real-time deviation detection for I-groove butt welding.The method can be applied to the on-line automatic welding deviation detection of arc welding robot.展开更多
We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.
基金Project supported by the Natural Science Foundation of Jiangsu Province (Grant No.BK20220917)the National Natural Science Foundation of China (Grant Nos.12001213 and 12302035)。
文摘We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.
文摘On the basis of high precision requirement for input signals in the power system protection and control system,this paper,only for the influence of power system frequency deviation on extracting fundamental harmonic,studies the amplitude error of Fourier algorithm,presents a method of correcting frequency deviation,and further derives the formulas of improved Fourier algorithm.The simulation results verified the effectiveness of the algorithm,it not only can greatly weaken the influence of frequency deviation,but also increase the precision of the power system protection and control.As a result the study in this paper has practical application value.
基金Partly supported by the National Natural Science Foundation of China and the Ministry of Education of ChinaPartly supported by the Science and Technology Research Item of Hubei Provincial Department of Education,Jiaghan University
文摘M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved. Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.
基金Research supported by the National Natural Science Foundation of China (10271091)
文摘Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜.
基金Research supported by the National Natural Science Foundation of China (10571139)
文摘We study moderate deviations for estimators of the drift parameter of the fractional Ornstein-Uhlenbeck process. Two moderate deviation principles are obtained.
基金Supported by the National Natural Science Foundation of China (10271091)
文摘The authors consider the moderate deviations of hydrodynamic limit for Ginzburg-Landau models. The moderate deviation principle of hydrodynamic limit for a specific Ginzburg-Landau model is obtained and an explicit formula of the rate function is derived.
文摘This paper presents a small perturbation Cramer method for obtaining the large deviation principle of a family of measures (β,ε> 0) on a topological vector space. As an application, we obtain the moderate deviation estimations for uniformly ergodic Markov processes.
基金Supported by National Natural Science Foundation of China(Grant Nos.51305140,61203060)Fundamental Research Funds of the Central Universities of China(Grant No.D2132730)Guangdong Provincial Science and Technology Planning Project of China(Grant No.2013B010402011)
文摘Typical representation of dimension and geometric accuracy is limited to the self-representation of dimension and geometric deviation based on geometry variation thinking, yet the interactivity affection of geometric variation and gesture variation of multi-rigid body is not included. In this paper, a kinematic matrix model based on Lagrangian coordinate is introduced, with the purpose of unified model for geometric variation and gesture variation and their interactive and integrated analysis. Kinematic model with joint, local base and movable base is built. The ideal feature of functional geometry is treated as the base body; the fitting feature of functional geometry is treated as the adjacent movable body; the local base of the kinematic model is fixed onto the ideal geometry, and the movable base of the kinematic model is fixed onto the fitting geometry. Furthermore, the geometric deviation is treated as relative location or rotation variation between the movable base and the local base, and it＇s expressed by the Lagrangian coordinate. Moreover, kinematic matrix based on Lagrangian coordinate for different types of geometry tolerance zones is constructed, and total freedom for each kinematic model is discussed. Finally, the Lagrangian coordinate library, kinematic matrix library for geometric deviation modeling is illustrated, and an example of block and piston fits is introduced. Dimension and geometric tolerances of the shaft and hole fitting feature are constructed by kinematic matrix and Lagrangian coordinate, and the results indicate that the proposed kinematic matrix is capable and robust in dimension and geometric tolerances modeling.
基金supported by the Youth Foundation of Hubei Province Department of Education of China (Q200710002)
文摘In this article, we obtain the large deviations and moderate deviations for negatively dependent （ND） and non-identically distributed random variables defined on （-∞, ＋∞）. The results show that for some non-identical random variables, precise large deviations and moderate deviations remain insensitive to negative dependence structure.
基金The National Natural Science Foundation of China(No.50805023)the Program for Special Talent in Six Fields of Jiangsu Province(No.2008144)Jiangsu Provincial Science and Technology Achievement Transformation Project(No.BA2010093)
文摘To eliminate rotation deviation of sequential images mosaic when measuring linear dimensions of large scale parts with computer vision, a novel algorithm based on the chain code searching method is proposed. After image preprocessing, including image filtering, image segmentation, and edge detection, the chain code length of the contour line can be searched out by the proposed method. Then, the angle from the contour line to the coordinate axis is computed with the length of the contour line. After that, the sequence is rotated in the opposite direction and the rotation deviation is eliminated. It is prepared for the next mosaic of sequences in eliminating shifting deviation. Experiments are carried out on parts with a linear profile rotating angle from 0° to 9°. The results show that compared with the commonly used Hough transform, the new method has higher precision and faster speed, which is important in realizing online high precision measurements of large scale parts with a linear profile.
基金The National Natural Science Foundation of China (No.10671139,11001052)the Natural Science Foundation of Jiangsu Province(No. BK2008284 )+2 种基金China Postdoctoral Science Foundation ( No.20100471365)the Natural Science Foundation of Higher Education Institutions of Jiangsu Province (No. 09KJD110003)Postdoctoral Research Program of Jiangsu Province (No.0901029C)
文摘The differences between two sequences of nonnegative independent and identically distributed random variables with sub-exponential tails and the random index are studied. The random index is a strictly stationary renewal counting process generated by some negatively associated random variables. Using a revised large deviation result of partial sums, the elementary renewal theorem and the central limit theorem of negatively associated random variables, a precise large deviation result is derived for the random sums. The result is applied to the customer-arrival-based insurance risk model. Some uniform asymptotics for the ruin probabilities of an insurance company are obtained as the number of customers or the time tends to infinity.
文摘Advertising English is viewed as an English style with such functional factors as attention value, readability, memorability, selling power. Commercial advertisements are the major concern of this paper. Deviation, namely the violation to the norms of a language, frequently appears in advertisements and can meet requirements of the style of advertising English. Due to limited space, this paper focuses on deviation on the phonological, graphological, lexical, grammatical, and semantic level. Analyzing deviation in advertising English can promote readers' aesthetic and appreciative ability and encourage advertisers to create advertisements with more efficiency, novelty, innovation in more effective language.
基金supported by the National Hi-Tech Research and Development Program of China(863 Program)(No.2006AA06Z107)the National Natural Science Foundation of China(No.40930314)
文摘Most edge-detection methods rely on calculating gradient derivatives of the potential field, a process that is easily affected by noise and is therefore of low stability. We propose a new edge-detection method named correlation coefficient of multidirectional standard deviations（CCMS） that is solely based on statistics. First, we prove the reliability of the proposed method using a single model and then a combination of models. The proposed method is evaluated by comparing the results with those obtained by other edge-detection methods. The CCMS method offers outstanding recognition, retains the sharpness of details, and has low sensitivity to noise. We also applied the CCMS method to Bouguer anomaly data of a potash deposit in Laos. The applicability of the CCMS method is shown by comparing the inferred tectonic framework to that inferred from remote sensing（RS） data.
基金supported by NSFF(17BTJ034)The research of WANG was supported by NSFC(11871382,11771161).
文摘In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain the stochastic Burgers’ equation and the stochastic reaction-diffusion equation. The weak convergence method plays an important role.
基金the National Natural Science Foundation of China (10571139)
文摘We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be calculated explicitly which is a squared function.
文摘Song is one of Christina Georgina Rossetti's most outstanding death poems,dealing with the main themes that she concerns:death,love and religion.This paper tries to use the technique of deviation that refers to violations to the standard language and readers'expectations to interpret this poem's stylistic features from the aspects of grammar,phonology,image,theme and narrative point of view.Through the stylistic analysis with the method of deviation,its solemn theme is exposed clearly.
基金Supported by National Natural Science Foundation of China(Grant Nos.51275051,51505035)National Hi-tech Research and Development Program of China(863 Program,Grant No.2009AA04Z208)Beijing Education Commission Innovation Ability Upgrade Program of China(Grant No.TJSHG201510017023)
文摘The welding deviation detection is the basis of robotic tracking welding, but the on-line real-time measurement of welding deviation is still not well solved by the existing methods. There is plenty of information in the gas metal arc welding（GMAW） molten pool images that is very important for the control of welding seam tracking. The physical meaning for the curvature extremum of molten pool contour is revealed by researching the molten pool images, that is, the deviation information points of welding wire center and the molten tip center are the maxima and the local maxima of the contour curvature, and the horizontal welding deviation is the position difference of these two extremum points. A new method of weld deviation detection is presented, including the process of preprocessing molten pool images, extracting and segmenting the contours, obtaining the contour extremum points, and calculating the welding deviation, etc. Extracting the contours is the premise, segmenting the contour lines is the foundation, and obtaining the contour extremum points is the key. The contour images can be extracted with the method of discrete dyadic wavelet transform, which is divided into two sub contours including welding wire and molten tip separately. The curvature value of each point of the two sub contour lines is calculated based on the approximate curvature formula of multi-points for plane curve, and the two points of the curvature extremum are the characteristics needed for the welding deviation calculation. The results of the tests and analyses show that the maximum error of the obtained on-line welding deviation is 2 pixels（0.16 ram）, and the algorithm is stable enough to meet the requirements of the pipeline in real-time control at a speed of less than 500 mm/min. The method can be applied to the on-line automatic welding deviation detection.
文摘This paper takes the synthesizing evaluation about industrial economic benefits by examples and proposes a new method named maximizing deviation method for multiindices decision. The new method can automatically determine the weight coefficients among the multiindices and also can obtain the exact and reliable evaluation results without subjectivity.
基金supported by the National Natural Foundation of China(Grant No.51875384)the Natural Science Foundation of Shanxi Province(Grant No.201601D011036)the Natural Science Foundation of Shanxi Province(Grant No.201801D121082)
文摘Automatic on-line detection of welding deviation based on machine vision is one of the key technologies of arc welding robot tracking welding,in which obtaining high quality weld pool image and accurate welding deviation detection algorithm are two important steps of tracking welding.Through the research and analysis of the weld pool image of gas metal arc welding(GMAW),it was found that the weld pool contains abundant welding information.First,the average gray value of the weld pool image can reflect the interference degree of arc to weld pool image and the heat input of welding process.Secondly,the tip of the weld pool image contour can reflect the center of the groove gap.Finally,the horizontal distance between the center coordinate of the wire contour and the tip coordinate of the weld pool image contour can reflect the welding deviation.On the basis of analyzing the characteristics of weld pool image,this paper proposes a new method of weld seam deviation detection,which includes the collection of weld pool image,image preprocessing,contour extraction and deviation calculation.The results of the tests and analyses showed that the maximum error of the on-line welding deviation obtained was about 2 pixels(0.17 mm)when the welding speed was≤60 cm/min,and the algorithm was stable enough to meet the requirements of real-time deviation detection for I-groove butt welding.The method can be applied to the on-line automatic welding deviation detection of arc welding robot.
基金supported by the National Natural Science Foundation of China(11171262)the Specialized Research Fund for the Doctoral Program of Higher Education (200804860048)
文摘We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.
