Computing large deviation prefactors of stochastic dynamical systems based on machine learning

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.

LARGE DEVIATIONS FOR TOP EIGENVALUES OFβ-JACOBI ENSEMBLES AT SCALING TEMPERATURES

Letλ=(λ_(1),…,λ_(n))beβ-Jacobi ensembles with parameters p_(1),p_(2),n andβ,withβvarying with n.Set■.Suppose that■and 0≤σγ<1.We offer the large deviation for p_(1)+p_(2)/p_(1)■λ_(i)whenγ>0 via the large deviation of the corresponding empirical measure and via a direct estimate,respectively,whenγ=0.

A novel lattice model integrating the cooperative deviation of density and optimal flux under V2X environment

A novel lattice hydrodynamic model is proposed by integrating the cooperative deviation of density and optimal flux under vehicle to X(V2X) environment. According to the theoretical analysis, the stability conditions and the mKdV equations affected by the cooperative deviation of traffic information are explored. And the density wave, hysteresis loop and energy consumption of the traffic flow have been investigated via numerical simulation. The results indicate that the cooperative deviation of density and optimal flux can effectively alleviate the traffic congestion. More importantly, our new consideration can reduce fuel consumption and exhaust emission under the V2X environment.

Assessment of Deviation in Quality of Steel Reinforcing Bars Used in Some Building Sites in Cameroon

The present work evaluated the deviations in the quality of steel reinforcing bars in terms of markings, diameter, yield strength and ductility in order to facilitate the drawing up of a yield strength value for the Cameroon National Annex to Eurocode 2. The methodology of the work started with the collection of steel samples from various active building project sites in four different towns viz: Bamenda, Douala, Maroua and Yaoundé and testing their tensile strength and elongation using a Universal Testing Machine and also carrying out the bending test. Results show that bars without marked manufacturer’s name fell all the tests. Other results show that 52% of all the steel had yield stresses below 400 Mpa and the highest deviation in the yield strengths was 22.50%. The study recommends that properly marked grade 500 steel bars should be adopted in the Cameroon national annex to Eurocode 2.

Application Research of an Intelligent Detection Algorithm for Vehicle Trajectory Route Deviation

In the vehicle trajectory application system, it is often necessary to detect whether the vehicle deviates from the specified route. Trajectory planning in the traditional route deviation detection is defined by the driver through the mobile phone navigation software, which plays a more auxiliary driving role. This paper presents a method of vehicle trajectory deviation detection. Firstly, the manager customizes the trajectory planning and then uses big data technologies to match the deviation between the trajectory planning and the vehicle trajectory. Finally, it achieves the supervisory function of the manager on the vehicle track route in real-time. The results show that this method could detect the vehicle trajectory deviation quickly and accurately, and has practical application value.

A LARGE DEVIATION PRINCIPLE FOR THE STOCHASTIC GENERALIZED GINZBURG-LANDAU EQUATION DRIVEN BY JUMP NOISE

In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).

Effect of Froude similitude deviation on curved channel simulations: A case study in the Middle Yangtze River

Froude similitude and friction similitude are the two crucial similarity conditions that are often used in physical-scale modeling of rivers.However,models often deviate from Froude similitude when dealing with real-world situations.This study developed several fixed-bed river models with various curvatures to determine the effect of Froude similitude deviation on curved channel modeling.Models were constructed according to the characteristics of the Middle Yangtze River.Differences in longitudinal slope,transverse slope,and main stream line location were measured by varying Froude similitude deviation.The deviations of longitudinal slope and velocity were negligible because friction similitude was accounted for.The transverse slope varied significantly with the Froude similitude deviation,and the main stream line varied with the curvature and Froude similitude deviation.Formulae were derived to estimate the slope deviation.These analyses helped to clarify the feasibility of the method of Froude similitude deviation for curved channels.

Modified inferior oblique anterior transposition for dissociated vertical deviation combined with superior oblique palsy:A case report

BACKGROUND Inferior oblique anterior transposition(IOAT)has emerged as an effective surgery in the management of dissociated vertical deviation(DVD)combined with superior oblique palsy(SOP).Traditional IOAT usually provides satisfactory primary position alignment and simultaneously restricts the superior floating phenomenon.However,it also increases the risk of the anti-elevation syndrome and narrowing of the palpebral fissure in straight-ahead gaze,especially after the unilateral operation.CASE SUMMARY We report the outcomes of the modified unilateral IOAT in two patients with unilateral DVD combined with SOP.The anterior-nasal fibers of the inferior oblique muscle were attached at 9 mm posterior to the corneal limbus along the temporal board of the inferior rectus muscle,the other fibers were attached a further 5 mm temporal to the anterior-nasal fibers.Postoperatively,both hypertropia and floating were improved,and no obvious complications occurred.CONCLUSION In these cases,the modified unilateral IOAT was an effective and safe surgical method for treating DVD with SOP.

The Inheritance and Deviation of the Subjective Construction“You Bei X Dao(有被X到)”

Sentence“bei”(“被”字句)and“bei xx”(被xx)provide syntactic and semantic basis for the generation of the construction“You Bei X Dao(有被x到)”.They are in a continuum and have family similarity.The sentence“bei”is a typical member,while“bei xx”is an atypical member.Because the construction“You Bei X Dao”has a single function and less attention,it is at the edge of the continuum and is a marginal member.However,it has certain research value in the inheritance and innovation of“bei”and“bei xx”.

Influence of highway space alignment continuous degradation in 3- dimensional space on autonomous vehicle trajectory deviation based on PreScan simulation

The advent of autonomous vehicles(AVs)is expected to transform the current transportation system into a safe and reliable one.The existing infrastructures,operational criteria,and design method were developed to meet the requirements of human drivers.However,previous studies have shown that in the traditional horizontal and vertical combined design methods,where the two-dimensional alignment elements change,there are varying changes in curvature and torsion,which cause the continuous degradation of the spatial curve and torsion.This continuous degradation will inevitably cause changes in the trajectory of Autonomous Vehicles(AVs),thereby affecting driving safety.Therefore,studying the characteristics of autonomous vehicles trajectory deviation has theoretical significance for optimizing highway alignment safety design.Driving simulation tests were performed by using PreScan and Simulink to calibrate the lateral deviation.A machine learning approach called the Gradient Boosting Decision Tree(GBDT)algorithm was implemented to build a model and express the relationship between space alignment parameters and lane deviation.The results showed that the AV’s driving trajectory is significantly affected by the space alignment factors when the vehicle is driving in the inner lane,the downhill section,and the left-turn section.These findings will provide a novel perspective for road safety research based on autonomous vehicle driving trajectories.

IMPROVED FOURIER ALGORITHM FOR CORRECTING POWER SYSTEM FREQUENCY DEVIATION

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.

A novel method for eliminating rotation deviation in sequential images mosaic

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.

Precise large deviation result for heavy-tailed random sums and applications to risk theory

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.

Deviation in Advertising English from a Stylistic Perspective

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.

Stylistic Analysis of Rossetti's Song with the Technique of Deviation

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.

Edge detection in the potential field using the correlation coefficients of multidirectional standard deviations

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.

Deviation Theories and Applications in Poetry Analysis

Poetry is prominent for its stylistic characteristics since texts themselves are the carrier of meaning,an analysis of the stylistic features of poems is conducive to the understanding and interpretation of them.It is of great significance to learn something about stylistics if we want to explore the meaning of poetry,this kind of method can also be used to analyze other literary works.

LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR m-NEGATIVELY ASSOCIATED RANDOM VARIABLES

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.

MODERATE DEVIATIONS AND LARGEDE VIATIONS FOR A TEST OF SYMMETRY BASED ON KERNEL DENSITY ESTIMATOR

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） ｜.

An Analysis of the Linguistic Deviation in Chapter X of Oliver Twist

Charles Dickens is one of the greatest critical realist writers of the Victorian Age.In language,he is often compared with William Shakespeare for his adeptness with the vernacular and large vocabulary.Charles Dickens achieved a recognizable place among English writers through the use of the stylistic features in his fictional language.Oliver Twist is the best representative of Charles Dickens’style,which makes it the most appropriate choice for the present stylistic study on Charles Dickens.No one who has ever read the dehumanizing workhouse scenes of Oliver Twist and the dark,criminal underworld life can forget them.This thesis attempts to investigate Oliver Twist through the approach of modern stylistics,particularly the theory of linguistic devia tion.This thesis consists of an introduction,the main body and a conclusion.The introduction offers a brief summary of the com ments on Charles Dickens and Chapter X of Oliver Twist,introduces the newly rising linguistic deviation theories,and brings about the theories on which this thesis settles.The main body explores the deviation effects produced from four aspects:lexical deviation,grammatical deviation,graphological deviation,and semantic deviation.It endeavors to show Dickens’manipulating language and the effects achieved through this manipulation.The conclusion mainly sums up the previous analysis,and reveals the theme of the novel,positive effect of linguistic deviation and significance of deviation application.