Exact scaling for the mean first-passage time of random walks on a generalized Koch network with a trap

In this paper, we study the scaling for the mean first-passage time （MFPT） of the random walks on a generalized Koch network with a trap. Through the network construction, where the initial state is transformed from a triangle to a polygon, we obtain the exact scaling for the MFPT. We show that the MFPT grows linearly with the number of nodes and the dimensions of the polygon in the large limit of the network order. In addition, we determine the exponents of scaling efficiency characterizing the random walks. Our results are the generalizations of those derived for the Koch network, which shed light on the analysis of random walks over various fractal networks.

Transient Properties of a Bistable System with Delay Time Driven by Non-Gaussian and Gaussian Noises:Mean First-Passage Time

The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker-Planck equation is obtained by applying the unified coloured noise approximation, the small time delay approximation and the Novikov Theorem. The functional analysis and simplification are employed to obtain the approximate expressions of MFPT. The effects of non-Gaussian parameter （measures deviation from Gaussian character） r, the delay time τ, the noise correlation time to, the intensities D and a of noise on the MFPT are discussed. It is found that the escape time could be reduced by increasing the delay time τ, the noise correlation time τ0, or by reducing the intensities D and α. As far as we know, this is the first time to consider the effect of delay time on the mean first-passage time in the stochastic dynamical system.

Mean First-Passage Time of an Asymmetric Kinetic Model Driven by Two Different Kinds of Colored Noises

The mean first-passage time （MFPT） of an asymmetric bistable system between multiplicative non-Gaussian noise and additive Gaussian white noise with nonzero cross-correlation time is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker Planck equation is obtained by applying the unified colored noise approximation and the.Novikov Theorem. The steady-state probability distribution （SPD） is also obtained. The basal functional analysis and simplification are employed to obtain the approximate expressions of MFPT T^±. The effects of the asymmetry parameter β, the non-Gaussian parameter （measures deviation from Gaussian character） r, the noise correlation times τ and τ2, the coupling coefficient A, the intensities D and a of noise on the MFPT are discussed. It is found that the asymmetry parameter β, the non-Gaussian parameter r and the coupling coefficient A can induce phase transition. Moreover, the main findings are that the effect of self-existent parameters （D, α, and τ） of noise and cross-correlation parameters （A, 7-2） between noises on MFPT T^± is different.

Mean first-passage time of an asymmetric bistable system driven by colour-correlated noise

In this paper, the effect of every parameter （including p, q, r, λ, τ） on the mean first-passage time （MFPT） is investigated in an asymmetric bistable system driven by colour-correlated noise. The expression of MFPT has been obtained by applying the steepest-descent approximation. Numerical results show that （1） the intensity of multiplicative noise p and the intensity of additive noise q play different roles in the MFPT of the system, （2） suppression appears on the curve of the MFPT with small λ （e.g. λ 〈 0.5） but there is a peak on the curve of the MFPT when λ is big （e.g. λ 〉 0.5）, and （3） with different values of r （e.g. r = 0.1, 0.5, 1.5）, the effort of τ on the MFPT is diverse.

FIRST-PASSAGE TIME OF QUASI-NON-INTEGRABLE-HAMILTONIAN SYSTEM

Studies on first-passage failure are extended to the multi-degree-of-freedom quasi-non-integrable-Hamiltonian systems under parametric excitations of Gaussian white noises in this paper. By the stochastic averaging method of energy envelope, the system's energy can be modeled as a one-dimensional approximate diffusion process by which the classical Pontryagin equation with suitable boundary conditions is applicable to analyzing the statistical moments of the first-passage time of an arbitrary order. An example is studied in detail and some numerical results are given to illustrate the above procedure.

基于改进k-means算法的科研仪器机时智能计算系统

传统的机时统计常使用人工,不仅效率低,而且成本相对较大,因此在传统的机时计算的基础上提出一种基于改进k均值聚类算法的科研仪器机时智能计算系统。通过对仪器机时电流数据的聚类分析,完成对仪器机时的计算和统计,同时将传统k均值聚类算法进行改进,提升其系统机时计算的准确性。结果表明,使用改进k均值聚类算法后的机时系统在仪器的机时计算中表现更为优异,计算的时间与正常运行时间相同,能够在一定程度上达到0误差标准。由此可见,使用改进聚类算法进行仪器的机时统计能够提升机时计算结果的准确性。

基于K-means聚类分析和多元线性回归的相关流量数据处理方法

相关流量计在油井产出剖面测量中得到了成功的应用。但因传感器、调理电路以及流体本身噪声的影响,相关流量计所测量的渡越时间值会出现少量异常数据,使瞬时流速的计算结果与实际值相差很大,进而平均流量计算也出现较大的测量误差。对此提出基于K-means聚类算法对渡越时间样本数据聚类分析,并根据聚类结果建立多元线性回归预测模型,合理预测渡越时间值,以修正渡越时间的异常值。对预测值与实际值进行比较,最终获得准确的相关流量数据。采用多相流装置的实验数据对所建立的方法进行验证,结果表明,该方法可有效消除渡越时间的异常,优化流量测量的数据,对两相流流量测量有一定的实践意义。

融合SOM神经网络与K-means聚类算法的用户信用画像研究

为提高现阶段基于K-Means聚类算法的用户信用画像模型的准确性和实时性,提出一种融合自组织映射(SOM,Self-Organizing Map)神经网络与K-Means聚类算法的改进方法。通过SOM对用户数据进行降维和特征提取,直接获得最优聚类数目后再用K-Means算法进行聚类分析。通过真实在线借贷平台数据对所提方法进行验证,结果表明,该方法可提升用户信用画像分析的质量,更好地满足金融数据分析中对实时管理和风险控制的要求,为金融机构提供精准的决策支持。

基于K-means-LSTM组合算法的地质灾害监测设备故障排查模型设计

为提高地质灾害预警的准确性和效率,提出了一种基于K-means聚类和长短期记忆网络(LSTM)的地质灾害监测设备故障排查模型。通过对地质监测数据的聚类分析,该模型能有效区分正常和异常运行状态的设备,为后续的深度学习分析提供了精准的数据基础。LSTM时序分析部分利用聚类结果,深入挖掘时间序列数据中的潜在模式和趋势,实现对设备故障类型及其发展趋势的准确预测。实验验证表明,该组合模型在地质灾害监测领域具有良好的应用潜力,能够为灾害预防和减灾提供有力的技术支持。未来研究将集中于进一步提升模型的准确性和泛化能力,探索更多算法组合和数据处理方法,以适应更加复杂的监测环境,推进监测系统的自动化和智能化。

Moments and Mean First—Passage Time of Parabolic—Bistable Potential System Driven by Colored Noise

A parabolic-bistable potential system driven by colored noise is studied. The exact analytical expressions of the stationary probability distribution (SPD) and the moments of the system are derived. Furthermore, the mean first-passage time is calculated by the use of two approximate methods, respectively. It is found that (i) the double peaks of SPD are rubbed-down into a flat single peak with the increasing of noise intensity; (ii) a minimum occurs on the curve of the second-order moment of the system vs. noise intensity at the point ; (iii) the results obtained by our approximate approach are in good agreement with the numerical calculations for either small or large correlation time , while the conventional steepest descent approximation leads to poor results.

基于改进粒子群和K-means聚类的优化算法

为了解决粒子群优化(particle swarm optimization, PSO)收敛速度慢和迭代次数多,以及传统K-means聚类算法采取的欧氏距离划分准则会导致聚类效果不理想等问题,构建了基于改进粒子群和K-means聚类的优化算法.根据Sigmoid函数优势,对PSO算法中速度更新公式的惯性权重参数实施改进,得到新的惯性权重公式,有效提高PSO算法的收敛速度;在PSO算法的位置更新公式中引入时间权重,通过调整时间权重大小,控制粒子的空间搜索范围,增强粒子的搜索能力;在传统的欧氏距离中引入属性权值,得到新的欧氏距离计算公式,该公式在计算两个向量相似度时,同时考虑了两个向量间的累积差异以及它们之间的相似性,与改进的PSO算法相结合,设计了基于改进粒子群和K-means聚类的优化算法.在6个基准测试函数和13个UCI数据集上,将所提出的优化算法与其他算法进行对比实验分析.实验结果表明:所提算法在收敛速度和寻优稳定性方面得到了明显提升,有效地提高了聚类准确率并且降低了迭代次数.

Feedback minimization of first-passage failure of quasi integrable Hamiltonian systems

Abstract A nonlinear stochastic optimal control strategy for minimizing the first-passage failure of quasi integrable Hamiltonian systems （multi-degree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations） is proposed. The equations of motion for a controlled quasi integrable Hamiltonian system are reduced to a set of averaged It6 stochastic differential equations by using the stochastic averaging method. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximization of reliability and mean first-passage time are formulated. The optimal control law is derived from the dynamical programming equations and the control constraints. The final dynamical programming equations for these control problems are determined and their relationships to the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the mean first-passage time are separately established. The conditional reliability function and the mean first-passage time of the controlled system are obtained by solving the final dynamical programming equations or their equivalent Kolmogorov and Pontryagin equations. An example is presented to illustrate the application and effectiveness of the proposed control strategy.

Alpha-reliable combined mean traffic equilibrium model with stochastic travel times

Based on the reliability budget and percentile travel time(PTT) concept, a new travel time index named combined mean travel time(CMTT) under stochastic traffic network was proposed. CMTT here was defined as the convex combination of the conditional expectations of PTT-below and PTT-excess travel times. The former was designed as a risk-optimistic travel time index, and the latter was a risk-pessimistic one. Hence, CMTT was able to describe various routing risk-attitudes. The central idea of CMTT was comprehensively illustrated and the difference among the existing travel time indices was analyzed. The Wardropian combined mean traffic equilibrium(CMTE) model was formulated as a variational inequality and solved via an alternating direction algorithm nesting extra-gradient projection process. Some mathematical properties of CMTT and CMTE model were rigorously proved. Finally, a numerical example was performed to characterize the CMTE network. It is founded that that risk-pessimism is of more benefit to a modest(or low) congestion and risk network, however, it changes to be risk-optimism for a high congestion and risk network.

Mean waiting time approximation for a real time polling system

This paper considers a novel polling system with two classes of message which can experience an up-per bounded time before being served. The station serves these two classes with mixed service discipline, one class with exhaustive service discipline, and the other with gated service discipline. Using iterative method, we have developed an approximation method to obtain the mean waiting time for each message class. The performance of approximation has been compared with the simulation results. The expression for the upper bound of waiting time is given too.

A Novel Multiple Dependent State Sampling Plan Based on Time Truncated Life Tests Using Mean Lifetime

The design of a new adaptive version of the multiple dependent state(AMDS)sampling plan is presented based on the time truncated life test under the Weibull distribution.We achieved the proposed sampling plan by applying the concept of the double sampling plan and existing multiple dependent state sampling plans.A warning sign for acceptance number was proposed to increase the probability of current lot acceptance.The optimal plan parameters were determined simultaneously with nonlinear optimization problems under the producer’s risk and consumer’s risk.A simulation study was presented to support the proposed sampling plan.A comparison between the proposed and existing sampling plans,namely multiple dependent state(MDS)sampling plans and a modified multiple dependent state(MMDS)sampling plan,was considered under the average sampling number and operating characteristic curve values.In addition,the use of two real datasets demonstrated the practicality and usefulness of the proposed sampling plan.The results indicated that the proposed plan is more flexible and efficient in terms of the average sample number compared to the existing MDS and MMDS sampling plans.

The mean first passage time of a three-level atomic optical bistable system subjected to noise

The transient properties of a three-level atomic optical bistable system in the presence of multiplicative and additive noises are investigated. The explicit expressions of the mean first-passage time （MFPT） of the transition from the high intracavity intensity state to the low one are obtained by numerical computations. The impacts of the intensities of the multiplicative noise DM and the additive noise DA, the intensity of correlation between two noises λ, and the intensity of the incident light y on the MFPT are discussed, respectively. Our results show： （i） for the case of no correlation between two noises （2, = 0.0）, the increase in DM and DA can lead to an increase in the probability of the transition to the low intracavity intensity state, while the increase in y can lead to a retardation of the transition; and （ii） for the case of correlation between two noises （λ≠ 0.0）, the increase in λ can cause an increase in the probability of the transition, and the increase in DA can cause a retardation of the transition firstly and then an increase in the probability of the transition, i.e., the noise-enhanced stability is observed for the case of correlation between two noises.

Mean First Passage Time for System with Fluctuating Potential Barrier and Coupled Noise

In this paper we study the mean first passage time （MFPT） over a fluctuation potential barrier driven by a coupled noise. It is shown that the MFPT over the fluctuation potential barrier displays resonant activations as the function of the flipping rate of the fluctuation potential barrier, and as the function of the dichotomous noise transition rate.

Fuzzy Time Series Forecasting Based On K-Means Clustering

Many forecasting models based on the concepts of Fuzzy time series have been proposed in the past decades. These models have been widely applied to various problem domains, especially in dealing with forecasting problems in which historical data are linguistic values. In this paper, we present a new fuzzy time series forecasting model, which uses the historical data as the universe of discourse and uses the K-means clustering algorithm to cluster the universe of discourse, then adjust the clusters into intervals. The proposed method is applied for forecasting University enrollment of Alabama. It is shown that the proposed model achieves a significant improvement in forecasting accuracy as compared to other fuzzy time series forecasting models.

Time is Not Money!——It Is a Providence of Opportunities

The essay discusses the interrelations between Time and Money and the right ways for managing them.Additionally it discusses other aspects of life and time,such as:definition of time,smart use of time,use of time as distincting between men and animals,time,age and responsibility,time and the“meaning of life”,quality and quantity of lifetime,social aspects of time and science,technology and time.The author clearly expresses his opinion,that Time is a neutral abstract entity,exists in free democratic regimes and in less-liberatated autocracies.It is the explicit responsibility of every man and woman,anywhere,and everywhere,to prepare and train themselves for a smart use of the time awarded to them.On the other hand,Time is available for everyone and everything.The busy diligent hard-working person always seeks more challenging missions,while the less-energetic idle person,is always busy and tire of doing nothing.The author also claims that Time is an opportunity.It is available and inviting every active person,a thinker,a doer,and an entrepreneur to use and have it to achieve their goals.The author advises:Do not complain I have no time-dare to make the first step and“the other will come,tumbling after”.Active individuals have time for every challenging initiative;passive ones have no time for anything.

Analytical and NumericalMethods to Study the MFPT and SR of a Stochastic Tumor-Immune Model

The Mean First-Passage Time (MFPT) and Stochastic Resonance (SR) of a stochastic tumor-immune model withnoise perturbation are discussed in this paper. Firstly, considering environmental perturbation, Gaussian whitenoise and Gaussian colored noise are introduced into a tumor growth model under immune surveillance. Asfollows, the long-time evolution of the tumor characterized by the Stationary Probability Density (SPD) and MFPTis obtained in theory on the basis of the Approximated Fokker-Planck Equation (AFPE). Herein the recurrenceof the tumor from the extinction state to the tumor-present state is more concerned in this paper. A moreefficient algorithmof Back-Propagation Neural Network (BPNN) is utilized in order to testify the correction of thetheoretical SPDandMFPT.With the existence of aweak signal, the functional relationship between Signal-to-NoiseRatio (SNR), noise intensities and correlation time is also studied. Numerical results show that both multiplicativeGaussian colored noise and additive Gaussian white noise can promote the extinction of the tumors, and themultiplicative Gaussian colored noise can lead to the resonance-like peak on MFPT curves, while the increasingintensity of the additiveGaussian white noise results in theminimum of MFPT. In addition, the correlation timesare negatively correlated with MFPT. As for the SNR, we find the intensities of both the Gaussian white noise andthe Gaussian colored noise, as well as their correlation intensity can induce SR. Especially, SNR is monotonouslyincreased in the case ofGaussian white noisewith the change of the correlation time.At last, the optimal parametersin BPNN structure are analyzed for MFPT from three aspects: the penalty factors, the number of neural networklayers and the number of nodes in each layer.