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.

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.

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).

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.

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.

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.

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”.

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.

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.

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） ｜.

MODERATE DEVIATIONS FOR PARAMETER ESTIMATORS IN FRACTIONAL ORNSTEIN-UHLENBECK PROCESS

We study moderate deviations for estimators of the drift parameter of the fractional Ornstein-Uhlenbeck process. Two moderate deviation principles are obtained.

MODERATE DEVIATIONS FROM HYDRODYNAMIC LIMIT OF A GINZBURG-LANDAU MODEL

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.

SMALL PERTURBATION CRAMER METHODS AND MODERATE DEVIATIONS FOR MARKOV PROCESSES

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.

Geometric Deviation Modeling by Kinematic Matrix Based on Lagrangian Coordinate

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.

LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR SUMS OF NEGATIVELY DEPENDENT RANDOM VARIABLES

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.

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.