Problem Of Large Deviations Research Articles

Weighted Jump in Random Walk graph sampling

Graph sampling is a challenging problem in network analysis due to the complex structures of networks. Currently, a series of graph sampling algorithms based on random walks achieve good results in graph sampling tasks. However, the existing methods often reduce the conductance of graphs, causing the sampler to stay in the same node for a long time. This results in undersampling. In this paper, we propose a novel Weighted Jump Random Walk (WJRW) algorithm to generate representative samples. We design a parameter in the WJRW algorithm that can adjust the proportions of random walk and random jump in every step. According to the issue of repeated sample nodes in the Generalized Maximum Degree (GMD) method and the problem of large deviations in the Simple Random Walk (SRW), WJRW addresses the weaknesses of the GMD method and enhances the diffusion of a random walker on graphs, leading to a more representative sample. Then, WJRW addresses the issue of large deviations in SRW and enhances the efficiency of the unbiased estimator. By generating smoother stationary distributions. Numerical experiments with extensive real-world networks verify that our method achieves higher accuracy than classical and state-of-the-art methods in estimating distribution estimation.

Whitham approach to certain large fluctuation problems in statistical mechanics

We show the relationship between the strongly non-linear limit (also termed the dispersionless or the Whitham limit) of the macroscopic fluctuation theory of certain statistical models and the inverse scattering method. We show that in the strongly non-linear limit the inverse scattering problem can be solved using the steepest descent method of the associated Riemann–Hilbert problem. The importance of establishing this connection, is that the equations in the strongly non-linear limit can often be solved exactly by simple means, the connection then provides a limit in which one can solve the inverse scattering problem, thus aiding potentially the exact solution of a particular large deviation problem.

A small time large deviation principle for stochastic differential delay equations

In this paper, we prove a small time large deviation principle for a type of stochastic differential delay equations. The key point is to translate small time asymptotic behavior problems into Freidlin–Wentzell type large deviation problems. The weak convergence method plays an important role in obtaining the large deviation principle.

A novel health prognosis method for system based on improved degenerated Hidden Markov model

• An improved Degenerated Hidden Markov Model (DGHMM) with a core of the quasi power relation is presented based on prognostics information. • The quasi power relation accelerated degradation can better describe the process that the performance of the system decreases gradually with the increase of service age. • The model adopts the degradation factors described the process of recession for equipment continuous decreasing in performance. • The improved genetic algorithm can replace the conventional EM algorithm for parameters estimation. • An algorithm named greed approximation based on approximation algorithm and Viterbi algorithm can be proposed. Health prognosis for power system is considered as a crucial process of condition-based maintenance. In order to solve the problem of large deviation between Hidden Markov Model and actual system health diagnosis, this paper developed an improved Degenerated Hidden Markov Model (DGHMM) with a core of the quasi power relation. First, the model adopts the degradation factors described the process of recession for equipment continuous decreasing in performance. Compared with the conventional exponential accelerated degradation, the quasi power relation accelerated degradation can better describe the process that the performance of the system decreases gradually with the increase of service age. Then, the improved genetic algorithm can replace the conventional EM algorithm for parameters estimation, which overcomes the limitation that the EM algorithm is easy to fall into local optimization. At the same time, in terms of the limitation of life prognosis problem as a result of the Hidden Markov Model must obey exponential distribution, an algorithm named greed approximation based on approximation algorithm and Viterbi algorithm can be proposed to seek maximum probability remaining observation for the purpose of seeking maximum probability dynamically surplus state path to predict the residual life of system. Finally, the proposed method is validated and evaluated with the data set of caterpillar hydraulic pumps. The results show that the method of system health diagnosis and life prognosis based on the improved degraded hidden Markov model is more effective in describing system degeneration and the accuracy of equipment state diagnosis, and is also feasible in the prediction of residual life.

Research on Adaptive Exponential Droop Control Strategy for VSC-MTDC System

To solve the problem of large DC voltage deviation caused by the power fluctuations and poor power distribution characteristics of converters in a voltage source converter multi-terminal DC (VSC-MTDC) system based on traditional droop control, this paper proposes an adaptive exponential droop control strategy. This strategy introduces the relative power deviation factor of the converter, and replaces the traditional linear droop control curve with a nonlinear exponential curve. Under different working conditions, the converter adaptively adjusts the droop control coefficient of the converter according to the relative power deviation factor to realize stability for the DC voltage and a reasonable power distribution for the MTDC system. A simulation model of a three-terminal VSC-MTDC was established in MATLAB/Simulink, and the feasibility and effectiveness of the proposed strategy were verified.

Study on Interparticle Interaction Force Model to Correct Saturation Density of Real Cryogenic Fluid for LBM Simulation

Cryogenic liquefaction energy storage is an important form of storage for sustainable energy liquid hydrogen and other gases. The weighting parameter A in the parameter-adjusted two-phase LBM model is important for the deviation of simulation results. The aim of this paper is to discover the appropriate parameter to eliminate the deviation, and to solve the problem of large deviation between the theoretical solution and the simulated value that is caused by using different equations of state in LBM simulation. The modified PT equation of state, which is suitable for cryogenic fluids, is combined with the parameter-adjustable two-phase model to simulate the saturation density at different temperatures. Four typical cryogenic fluids—nitrogen, hydrogen, oxygen, and helium—are exploratively simulated to find the suitable parameters to eliminate errors by analyzing the results with theoretical solutions. This is an efficient solution to the deviation between the simulated value and the theoretical solutions, which is caused by the different equation of state in LBM. The optimal A-value of the model based on the PT equation of state was obtained as −0.21, while droplets and bubbles were set into the calculation region, and an inverse relationship between the interface density gradient and temperature was analyzed. The analysis and comparison of the simulation results under the optimal value and the experimental values have laid an important foundation for the phase change simulation of the real cryogenic fluids at the mesoscopic scale.

Adaptive Bright and Dark Channel Combined with Defogging Algorithm Based on Depth of Field

Aiming at the problem that the dark channel prior algorithm is not ideal in removing fog at the distant view and the sudden change of depth, this paper proposes an adaptive bright and dark channel combined with defogging algorithm based on the depth of field. The algorithm divides the image into a distant area and a near area based on the depth of field. The near area uses the dark channel to remove the fog, and the distant area uses the bright channel to remove the fog, combined with the use of adaptive superpixel segmentation to give the content-based local area division and defogging control factor based on depth of field. It better solves the problem of large transmittance deviation and defogging distortion under content changes and sudden depth of field changes. From the subjective and objective indicators, the algorithm in this paper has achieved a good defogging effect, and the main indicators and comprehensive defogging quality are better than common algorithms.

Rare event asymptotics for exploration processes for random graphs

Large deviations for random graph models has been a topic of significant recent research activity. Much work in this area is focused on the class of dense random graph models (number of edges in the graph scale as n2, where n is the number of vertices) where the theory of graphons has emerged as a principal tool in the study of large deviation properties. These tools do not give a good approach to large deviation problems for random graph models in the sparse regime. The aim of this paper is to study an approach for large deviation problems in this regime by establishing large deviation principles (LDP) on suitable path spaces for certain exploration processes of the associated random graph sequence. Exploration processes are an important tool in the study of sparse random graph models and have been used to understand detailed asymptotics of many functionals of sparse random graphs, such as component sizes, surplus, deviations from trees, etc. In the context of rare event asymptotics of interest here, the point of view of exploration process transforms a large deviation analysis of a static random combinatorial structure to the study of a small noise LDP for certain stochastic dynamical systems with jumps. Our work focuses on one particular class of random graph models, namely the configuration model; however, the general approach of using exploration processes for studying large deviation properties of sparse random graph models has broader applicability. The goal is to study asymptotics of probabilities of nontypical behavior in the large network limit. The first key step for this is to establish a LDP for an exploration process associated with the configuration model. A suitable exploration process here turns out to be an infinite-dimensional Markov process with transition probability rates that diminish to zero in certain parts of the state space. Large deviation properties of such Markovian models is challenging due to poor regularity behavior of the associated local rate functions. Our proof of the LDP relies on a representation of the exploration process in terms of a system of stochastic differential equations driven by Poisson random measures and variational formulas for moments of nonnegative functionals of Poisson random measures. Uniqueness results for certain controlled systems of deterministic equations play a key role in the analysis. Next, using the rate function in the LDP for the exploration process we formulate a calculus of variations problem associated with the asymptotics of component degree distributions. The second key ingredient in our study is a careful analysis of the infinite-dimensional Euler–Lagrange equations associated with this calculus of variations problem. Exact solutions of these systems of nonlinear differential equations are identified which then provide explicit formulas for decay rates of probabilities of nontypical component degree distributions and related quantities.

Method for counting labeled neurons in mouse brain regions based on image representation and registration.

An important step in brain image analysis is to divide specific brain regions by matching brain slices to standard brain reference atlases, and perform statistical analysis on the labeled neurons in each brain region. Taking mouse fluorescently labeled brain slices as an example, due to the noise and distortion introduced during the preparation of brain slices, and the modal differences with standard brain atlas, the brain slices cannot directly establish an accurate one-to-one correspondence with the brain atlas, which in turn affects the accuracy of the number of labeled neurons in each brain region. This paper introduces the idea of image representation, uses neural networks to realize the registration of different modal mouse brain slices and brain atlas, completes the regional localization of the brain slices, and uses threshold segmentation to detect and count the labeled neurons in each brain region. The method proposed in this paper can effectively solve the problem of large deviation of neurons count caused by the inaccurate division of brain regions in large deformed brain slices, and can automatically realize accurate count of labeled neurons in each brain region of brain slices. The whole framework of method for counting labeled neurons in mouse brain regions based on image representation and registration.

BIM Engineering Cost Budgeting Method based on Social Network Analysis Method

Engineering cost budgeting is crucial to the healthy development of the engineering and construction industry. To solve the problem of large deviations in budget results from using traditional methods of cost budgeting based on evaluation results or drawing conversions, the BIM engineering cost budgeting method based on social network analysis method is studied in this paper. On the basis of analyzing cost budgeting requirements and determining modeling economic criteria, the social network analysis method is used to analyze the project cost risks. According to the project quantity list, professional BIM software is used to budget the project cost. Case verification proves the feasibility of this budgeting method as the budget deviation is reduced by about 78% compared with the traditional method. The result of the paper has a more ideal practical application effect and positive significance for optimizing the traditional cost budgeting methods

A clock synchronization method in power dispatching based on BeiDou navigation system

This paper introduces the problems of poor signal condition of a single time source in time synchronization or error in time source switching in the power system. It adopts the two-clock mode timing scheme of BeiDou 2 synchronous satellite and GPS synchronous satellite to ensure the stable output of the main clock within a certain accuracy. The system takes full advantage of the field programmable gate array (FPGA) hardware method, aligns the internal clock lock signal with the input second pulse phase, and proposes an improved method for the problem of large clock synchronization deviation based on the network, which proves the effectiveness and superiority of the system to accurately output the pulse and provide reliable time synchronization for the power dispatching system.

Design of intelligent power distribution robot system based on machine vision

With the increasingly serious aging of our society, labor shortage will seriously hinder the development of social economy. Robots gradually integrate into human production and life, and gradually serve more and more people. In order to solve the problem of large path deviation of the transmission system in the food conveying path, an intelligent food conveying system based on machine vision is proposed. The hardware circuit of the whole system is composed of image acquisition module, power module, electric drive module, etc. in the software part, the vertical volume matching method is used to set the optimal path. Through practical investigation, the scheme is feasible, can rely on the actual intelligence of catering distribution, has good application and promotion value.

Intelligent Recognition System for the Curves Trajectory and Track Capture Using Artificial Intelligence Technology

Aiming at the problem of large deviation of the recognition results of the traditional recognition system, this article carried out the design and research of the intelligent recognition system of the football curve ball movement trajectory. The hardware structure design includes the acceleration sensor selection, the angular motion detection device selection and the power supply circuit design, and the software structure design includes the motion trajectory data filtering processing and the football curve ball motion speed displacement recognition. Experiments show that, compared with the traditional system, the design system has a smaller deviation of the recognition results, significantly fewer recognition errors, and higher accuracy.

Hamilton-Jacobi Equations with Semilinear Costs and State Constraints, with Applications to Large Deviations in Games

We characterize solutions of a class of time-homogeneous optimal control problems with semilinear running costs and state constraints as maximal viscosity subsolutions to Hamilton-Jacobi equations and show that optimal solutions to these problems can be constructed explicitly. We present applications to large deviations problems arising in evolutionary game theory.

Large deviations of the entropy production rate for a class of Gaussian processes

We prove a large deviation principle (LDP) and a fluctuation theorem for the entropy production rate (EPR) of the following d dimensional stochastic differential equation dXt=AXtdt+QdBt, where A is a real normal stable matrix, Q is positive definite, and the matrices A and Q commute. The rate function for the EPR takes the following explicit form: I(x)=x1+ℓ0(x)−12+12∑k=1dαk2−βk2ℓ0(x)+αk for x ≥ 0 and I(x)=−x1+ℓ0(x)+12+12∑k=1dαk2−βk2ℓ0(x)+αk for x < 0, where αk ±iβk are the eigenvalues of A and ℓ0(x) is the unique solution of the equation x=1+ℓ×∑k=1dβk2αk2−ℓβk2,−1≤ℓ<mink=1,…,dαk2βk2. Simple closed form formulas for rate functions are rare, and our work identifies an important class of large deviation problems where such formulas are available. The logarithmic moment generating function (the fluctuation function) Λ associated with the LDP is given as Λ(λ)=−12∑k=1dαk2−4λ(1+λ)βk2+αk for λ∈D and Λ(λ) = ∞ for λ∉D, where D is the domain of Λ. The functions Λ(λ) and I(x) satisfy the Cohen–Gallavotti symmetry properties: Λ(x)=Λ(−(1+x)),I(x)=I(−x)−x, for all x∈R. In particular, the functions I and Λ do not depend on the diffusion matrix Q and are determined completely by the real and imaginary parts of the eigenvalues of A. Formally, the deterministic system with Q = 0 has zero EPR, and thus, the model exhibits a phase transition in that the EPR changes discontinuously at Q = 0.

Inertia estimation of diesel generators based on modified loading rejection tests

An inertia identification approach has been proposed for diesel generators by using the modified load rejection procedures. Large frequency deviation problems often occur in the Kinmen island power system where many diesel generators are used. In order to avoid erroneous evaluation of frequency deviation caused by generator tripping, one of the critical issues in system planning is to accurately estimate the maximum frequency deviation during system outage events. The main factors that influence the frequency deviation include the generator inertia (H), damping constant (D), and governor controller parameters. In order to improve the accuracy of the transient stability analysis to obtain more actual frequency deviation, it is critical to have more accurate inertia values of these diesel generators. This paper proposes a useful approach to evaluate reasonable inertia values. With the identified inertia values of diesel generators, the frequency responses of the Kinmen power system obtained from PSS/E simulation are more consistent with the field measurement results.

Pattern recognition-based decoding method for the negative pulsed downlink signal with a narrow pulse width

The negative pulsed downlink communication system is used to send surface control commands to the downhole rotary steering tool at thousands of meters, which is a significant part of the current rotary steering technology. At present, the transmission efficiency of negative pulsed downlink communication is very low, and only simple control commands can be transmitted in a few minutes, which limits the development of rotary steering technology with complex control functions. To improve the transmission rate of the downlink system, the downlink pulse width needs to be shortened. However, due to the influence of signal transmission characteristics, the waveform of a narrow pulse width signal will be severely distorted, which increases the difficulty of decoding the downlink signal. Therefore, a decoding method based on pattern recognition for negative pulsed downlink signal with narrow pulse width is proposed in this paper, which establishes a Euclidean distance matrix model between similar characteristic signal segments on the rising or falling edge of the downlink signal, the pulse coding timing of among the signal segment with each rising or falling edge is analyzed, the decoding and recognition of the downlink instruction are achieved, which solves the problem of large timing deviation in decoding the downlink signal with a current threshold method. The experimental results show that the method proposed in this paper can achieve accurate decoding of the 6 s pulse width downlink signal. Compared with the threshold method, it can be seen that the decoding accuracy of the method proposed in this paper can be greatly improved, and the smaller the signal pulse width, the more significant the advantage.

Випадковi еволюцiї в схемi пуассонової апроксимацiї

The operator approach in the study of random evolutions allows us to obtain the following results in the Poisson approximation scheme: functional limit theorems at increasing time intervals and the solution of the large deviations problem. We will focus on the last task. To solve the problem, asymptotic analysis of nonlinear generators of random evolutions with Markov switching should be conducted in the series scheme. The specifics of asymptotic analysis is conditioned by the fact that the jump values of the stochastic system are split into two parts: a small jump taking values with probabilities close to one and a big jump taken values with probabilities tending to zero together with the series parameter $\varepsilon\to 0$. So, in the Poisson approximation principle the probabilities (or intensities) of jumps are normalized by the series parameter $\varepsilon >0$. Having the limit nonlinear generator, we are able to construct the rate functional to solve the large deviations problem.

Detection method for the impact strength of a nano-piezoelectric resonant microcantilever

In order to solve the problem of large deviation in the impact strength test results of the same nanomaterial, a test method for the impact strength of a nano-piezoelectric resonant microcantilever is proposed. The structure of the nano-piezoelectric resonant microcantilever is designed. The release and surface patterning of the cantilever are completed by using bulk silicon technology. The uncertainty in the impact strength of the cantilever is detected and analyzed. The experimental results show that the standard deviation S is large when the tool speed is low, and the dispersion of impact results is large when the tool speed is high. The impact strength of the sample prepared using a worn milling cutter is 82.7% of that prepared by a new milling cutter, and its standard deviation increases from 0.256 to 2.996.

DC voltage control for MMC‐based railway power supply integrated with renewable generation

The full controllable electronic device based railway feeder station offers better power quality and more flexible configurations than conventional transformer based stations. This study investigates a modular multilevel converter (MMC)-based static frequency converter station with renewable energy access. Wind power generation is coupled into the station via DC link of the back to back converter. The dynamic single-phase traction load and intermittent renewable generation bring double frequency oscillation and large deviation problems to the DC link voltage. Special design considerations and control schemes are proposed for the MMC to stabilise DC link voltage by controlling the total number of total inserted modules. The proposed control scheme resolves the voltage oscillation issue caused by single-phase load and reduces the DC link voltage deviation under 10 MW step change. A series of device-based simulations validate the control scheme which realises a reliable coupling interface for connecting the renewable generation to the DC bus.