Exponential Weights Research Articles

Bergman Projection on Lebesgue Space Induced by Doubling Weight

Let ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} and ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document} be radial weights on the unit disc of the complex plane, and denote σ=ωp′ν-p′p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma =\\omega ^{p'} \ u ^{-\\frac{p'}{p}}$$\\end{document} and ωx=∫01sxω(s)ds\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _x =\\int _0^1\\,s^x \\omega (s)\\,ds$$\\end{document} for all 1≤x<∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\le x<\\infty $$\\end{document}. Consider the one-weight inequality ‖Pω(f)‖Lνp≤C‖f‖Lνp,1<p<∞,(†)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\Vert P_\\omega (f)\\Vert _{L^p_\ u }\\le C\\Vert f\\Vert _{L^p_\ u },\\quad 1<p<\\infty , \\qquad \\qquad (\\dagger ) \\end{aligned}$$\\end{document}for the Bergman projection Pω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_\\omega $$\\end{document} induced by ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document}. It is shown that the moment condition Dp(ω,ν)=supn∈N∪{0}νnp+11pσnp′+11p′ω2n+1<∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} D_p(\\omega ,\ u )=\\sup _{n\\in {\\mathbb {N}}\\cup \\{0\\}} \\frac{\\left( \ u _{np+1}\\right) ^\\frac{1}{p}\\left( \\sigma _{np'+1} \\right) ^\\frac{1}{p'}}{\\omega _{2n+1}}<\\infty \\end{aligned}$$\\end{document}is necessary for (†\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\dagger $$\\end{document}) to hold. Further, Dp(ω,ν)<∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_p(\\omega ,\ u )<\\infty $$\\end{document} is also sufficient for (†\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\dagger $$\\end{document}) if ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document} admits the doubling properties sup0≤r<1∫r1ν(s)sds∫1+r21ν(s)sds<∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sup _{0\\le r<1}\\frac{\\int _r^1\ u (s) s\\,ds}{\\int _{\\frac{1+r}{2}}^1\ u (s)s\\,ds}<\\infty $$\\end{document} and sup0≤r<1∫r1ν(s)sds∫r1-1-rKν(s)sds<∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sup _{0\\le r<1}\\frac{\\int _r^1\ u (s)s\\,ds}{\\int _r^{1-\\frac{1-r}{K}} \ u (s)s\\,ds}<\\infty $$\\end{document} for some K>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K>1$$\\end{document}. In addition, an analogous result for the one weight inequality ‖Pω(f)‖Dν,kp≤C‖f‖Lνp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Vert P_\\omega (f)\\Vert _{D^p_{\ u ,k}} \\le C\\Vert f\\Vert _{L^p_\ u }$$\\end{document}, where ‖f‖Dν,kpp=∑j=0k-1|f(j)(0)|p+∫D|f(k)(z)|p(1-|z|)kpν(z)dA(z)<∞,k∈N,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\Vert f \\Vert _{D^p_{\ u , k}}^p =\\sum \\limits _{j=0}^{k-1}\\vert f^{(j)}(0)\\vert ^p +\\int _{{\\mathbb {D}}} \\vert f^{(k)}(z)\\vert ^p (1-\\vert z \\vert )^{kp} \ u (z)\\,dA(z)<\\infty , \\quad k\\in {\\mathbb {N}}, \\end{aligned}$$\\end{document}is established. The inequality (†\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\dagger $$\\end{document}) is further studied by using the necessary condition Dp(ω,ν)<∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_p(\\omega ,\ u )<\\infty $$\\end{document} in the case of the exponential type weights ν(r)=exp-α(1-rl)β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u (r)=\\exp \\left( -\\frac{\\alpha }{(1-r^l)^{\\beta }} \\right) $$\\end{document} and ω(r)=exp-α~(1-rl~)β~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega (r)= \\exp \\left( -\\frac{ \\widetilde{\\alpha }}{(1-r^{\\widetilde{l}})^{\\widetilde{\\beta }}} \\right) $$\\end{document}, where 0<α,α~,l,l~<∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0<\\alpha , \\, \\widetilde{\\alpha }, \\, l, \\, \\widetilde{l}<\\infty $$\\end{document} and 0<β,β~≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0<\\beta , \\, \\widetilde{\\beta }\\le 1$$\\end{document}.

Fredholm and Schatten Class Operators on Bergman Spaces with Exponential Weights

In this paper, we give a characterization of Fredholmness of the Toeplitz operators on the Bergman spaces A φ p with exponential weights in D when 0 &lt; p &lt; ∞ . Also, we obtain the sufficient and necessary conditions which the Toeplitz and Hankel operators on A φ 2 belong to h -Schatten class, where h is a continuous increasing convex function.

Comparison of different auto-detection methods for wave V with a wireless automated auditory brainstem response (AABR) measurement system

The wireless automatic auditory brainstem response measurement system developed in the previous research uses Kalman filter with exponential weight averaging method (Kalman filter with EWA) to filter signal and used the differential method to detect the Wave V of ABR. However, the signals are too noisy to be accurately determined. Therefore, this study compares the Wavelet Kalman filter and Moving average to the Kalman filter with EWA, and the fitted parametric peak (FPP) to the differential method, respectively. The simulation results showed that the signal-to-noise ratio of ABR is the highest after Wavelet Kalman filtering, and the audiologist can mark the waves III and V of ABR the most. The latency of the wave V detected by FPP was used to calculate the Pearson product-moment correlation coefficient with the audiologist’s manual mark. The two latencies are highly correlated, and the correlation coefficient is higher than the differential method. Therefore, the Wavelet-Kalman filter and FPP algorithm were implemented in the AABR measurement system. To evaluate the accuracy of the algorithm in this study, subjective experiments were conducted with four normal hearing subjects. The Mann-Whitney U test was used to test thedifference between the average value of automatic detection and reproducibility.

An active noise control algorithm based on an improved convex combination loop

The conflict between a faster convergence using a Filtered-X Least Mean Square (FXLMS) algorithm and the requirement of a small steady-state error of an adaptive active control (ANC) system which limits its performance in terms of computation efficiency and the control error. The problem can be solved by using two paralleling adaptive filters to form a convex combination loop in the control system. However, the exponential weight function used in the original convex combination loop design can consume a large computer power which has limited its application. As a result, a new weight function is proposed to replace the original exponential function in the original convex combination loop to enhance the convergence rate of the adaptive ANC system. Furthermore, a MRFXLMS algorithm is used to replace the FXLMS algorithm in the ANC system so that it can be used for impulse noise control. The result shows that the proposed algorithm performs well in the control of input impulse noise with different intensity.

WildWood: A New Random Forest Algorithm

We introduce WildWood (WW), a new ensemble algorithm for supervised learning of Random Forest (RF) type. While standard RF algorithms use bootstrap out-of-bag samples to compute out-of-bag scores, WW uses these samples to produce improved predictions given by an aggregation of the predictions of all possible subtrees of each fully grown tree in the forest. This is achieved by aggregation with exponential weights computed over out-of-bag samples, that are computed exactly and very efficiently thanks to an algorithm called context tree weighting. This improvement, combined with a histogram strategy to accelerate split finding, makes WW fast and competitive compared with other well-established ensemble methods, such as standard RF and extreme gradient boosting algorithms.

Non-linear heat equation on the Hyperbolic space: Global existence and finite-time Blow-up

We consider the following Cauchy problem for the semi linear heat equation on the hyperbolic space : \begin{align} \left\{\begin{array}{ll} \partial_{t}u=\Delta_{\mathbb{H}^{n}} u+ f(u, t) & \hbox{ in }~ \mathbb{H}^{n}\times (0, T), \\ \quad u =u_{0} & \hbox{ in }~ \mathbb{H}^{n}\times \{0\}. \end{array}\right. \tag{0.1} \end{align} We study Fujita phenomena for the non-negative initial data $u_0$ belonging to $C(\mathbb{H}^{n}) \cap L^{\infty}(\mathbb{H}^{n})$ and for different choices of $f$ of the form $f(u,t) = h(t)g(u).$ It is well-known that for power nonlinearities in $u,$ the power weight $h(t) = t^q$ is sub-critical in the sense that non-negative global solutions exist for small initial data. On the other hand, (0.1) exhibits Fujita phenomena for the exponential weight $h(t) = e^{\mu t},$ i.e., there exists a critical exponent $ \mu^*$ such that if $\mu > \mu^*$, then all non-negative solutions blow-up in finite time and if $\mu \leq \mu^*$, there exists non-negative global solutions for small initial data. One of the main objectives of this article is to find an appropriate nonlinearity in $u$ so that (0.1) with the power weight $h(t) = t^q$ does exhibit Fujita phenomena. In the remaining part of this article, we study Fujita phenomena for exponential nonlinearity in $u.$ We further generalize some of these results to Cartan-Hadamard manifolds.

On the power of standard information for tractability for L∞ approximation of periodic functions in the worst case setting

We study multivariate approximation of periodic functions in the worst case setting with the error measured in the L∞ norm. We consider algorithms that use standard information Λstd consisting of function values or general linear information Λall consisting of arbitrary continuous linear functionals. We investigate equivalences of various notions of algebraic and exponential tractability for Λstd and Λall under the absolute or normalized error criterion, and show that the power of Λstd is the same as the one of Λall for various notions of algebraic and exponential tractability. Our results can be applied to weighted Korobov spaces and Korobov spaces with exponential weights. This gives a special solution to Open Problem 145 as posed by Novak and Woźniakowski (2012) [40].

Energy Efficiency of Mobile Devices Using Fuzzy Logic Control by Exponential Weight with Priority-Based Rate Control in Multi-Radio Opportunistic Networks

The rapid development of mobile devices and wireless network technologies have made them indispensable. This has created a demand for faster networks and longer battery life. The assurance of a stable network service and the enhancement of network experiences for mobile devices is equally crucial to meeting these demands. To address these challenges, mobile devices employ various techniques to decrease power consumption when they connect to wireless networks. Moreover, enhancing the endurance of mobile devices to maintain stable network services is critical when using wireless networks. In this paper, we propose a dual-radio opportunistic network for energy efficiency (DRONEE)–exponential weight with priority-based on rate control (WPRC) method which can extend and enhance the DRONEE hybrid network. By leveraging fuzzy logic control (FLC) and quality of service (QoS), our proposed method effectively solves the weighting problem in the DRONEE–weight (DRONEE–W) method. Through efficient allocation of network resources within each cluster, we minimize resource wastage and maximize resource utilization. Simulation results demonstrate the superior performance of our DRONEE–WPRC method in terms of throughput, buffer size, delay time, and power consumption compared to other methods. Therefore, our proposed method achieves optimal network resource allocation and energy efficiency.

Priority Based Transmission Rate Control with Neural Network Controller in WMSNs

Wireless Multimedia Sensor Networks (WMSNs) are networks of wirelessly interconnected sensor nodes equipped with multimedia devices, such as cameras and microphones. Thus a WMSN will have the capability to transmit multimedia data, such as video and audio streams, still images, and scalar data from the environment. Most applications of WMSNs require the delivery of multimedia information with a certain level of Quality of Service (QoS). This is a challenging task because multimedia applications typically produce huge volumes of data requiring high transmission rates and extensive processing; the high data transmission rate of WMSNs usually leads to congestion, which in turn reduces the Quality of Service (QoS) of multimedia applications. To address this challenge, This paper proposes the Neural Control Exponential Weight of Priority Based Rate Control (NEWPBRC) algorithm for adjusting the node transmission rate and facilitate the problem of congestion occur in WMSNs. The proposed algorithm combines Neural Network Controller (NC) with the Exponential Weight of Priority Based Rate Control (EWPBRC) algorithms. The NC controller can calculate the appropriate weight parameter λ in the Exponential Weight (EW) algorithm for estimating the output transmission rate of the sink node, and then ,on the basis of the priority of each child node , an appropriate transmission rate is assigned . The proposed algorithm can support four different traffic classes namely, Real Time traffic class (RT class); High priority, Non Real-Time traffic class (NRT1 class); Medium priority, Non Real-Time traffic class (NRT2 class); and Low priority, Non Real-Time traffic class (NRT3 class). Simulation result shows that the proposed algorithm can effectively reduce congestion and enhance the transmission rate. Furthermore, the proposed algorithm can enhance Quality of Service (QoS) by achieve better throughput, and reduced the transmission delay and loss probability.

Multi-armed bandit-based hyper-heuristics for combinatorial optimization problems

There are significant research opportunities in the integration of Machine Learning (ML) methods and Combinatorial Optimization Problems (COPs). In this work, we focus on metaheuristics to solve COPs that have an important learning component. These algorithms must explore a solution space and learn from the information they obtain in order to find high-quality solutions. Among the metaheuristics, we study Hyper-Heuristics (HHs), algorithms that, given a number of low-level heuristics, iteratively select and apply heuristics to a solution. The HH we consider has a Markov model to produce sequences of low-level heuristics, which we combine with a Multi-Armed Bandit Problem (MAB)-based method to learn its parameters. This work proposes several improvements to the HH metaheuristic that yields a better learning for solving problem instances. Specifically, this is the first work in HHs to present Exponential Weights for Exploration and Exploitation (EXP3) as a learning method, an algorithm that is able to deal with adversarial settings. We also present a case study for the Vehicle Routing Problem with Time Windows (VRPTW), for which we include a list of low-level heuristics that have been proposed in the literature. We show that our algorithms can handle a large and diverse list of heuristics, illustrating that they can be easily configured to solve COPs of different nature. The computational results indicate that our algorithms are competitive methods for the VRPTW (2.16% gap on average with respect to the best known solutions), demonstrating the potential of these algorithms to solve COPs. Finally, we show how algorithms can even detect low-level heuristics that do not contribute to finding better solutions to the problem.

Multi-objective reward shaping for global and local trajectory planning of wing-in-ground crafts based on deep reinforcement learning

AbstractThe control of a wing-in-ground craft (WIG) usually allows for many needs, like cruising, speed, survival and stealth. Various degrees of emphasis on these requirements result in different trajectories, but there has not been a way of integrating and quantifying them yet. Moreover, most previous studies on other vehicles’ multi-objective trajectory is planned globally, lacking for local planning. For the multi-objective trajectory planning of WIGs, this paper proposes a multi-objective function in a polynomial form, in which each item represents an independent requirement and is adjusted by a linear or exponential weight. It uses the magnitude of weights to demonstrate how much attention is paid relatively to the corresponding demand. Trajectories of a virtual WIG model above the wave trough terrain are planned using reward shaping based on the introduced multi-objective function and deep reinforcement learning (DRL). Two conditions are considered globally and locally: a single scheme of weights is assigned to the whole environment, and two different schemes of weights are assigned to the two parts of the environment. Effectiveness of the multi-object reward function is analysed from the local and global perspectives. The reward function provides WIGs with a universal framework for adjusting the magnitude of weights, to meet different degrees of requirements on cruising, speed, stealth and survival, and helps WIGs guide an expected trajectory in engineering.

Computing integrals with an exponential weight on the real axis in floating point arithmetic

The aim of this work is to propose a fast and reliable algorithm for computing integrals of the type∫−∞∞f(x)e−x2−1x2dx, where f(x) is a sufficiently smooth function, in floating point arithmetic. The algorithm is based on a product integration rule, whose rate of convergence depends only on the regularity of f, since the coefficients of the rule are “exactly” computed by means of suitable recurrence relations here derived. We prove stability and convergence in the space of locally continuous functions on R equipped with weighted uniform norm. By extensive numerical tests, the accuracy of the proposed product rule is compared with that of the Gauss–Hermite quadrature formula w.r.t. the function f(x)e−1x2. The numerical results confirm the effectiveness of the method, supporting the proven theoretical estimates.

Feature Correlation Transformer for Estimating Ambiguous Optical Flow

Cost volume is widely used to establish correspondences in optical flow estimation. However, when dealing with low-texture and occluded areas, it is difficult to estimate the cost volume correctly. Therefore, we propose a replacement: feature correlation transformer (FCTR), a transformer with self- and cross-attention alternations for obtaining global receptive fields and positional embedding for establishing correspondences. With global context and positional information, FCTR can produce more accurate correspondences for ambiguous areas. Using position-embedded feature allows the removal of the context network; the positional information can be aggregated within ambiguous motion boundaries, and the number of model parameters can be reduced. To speed up network convergence and strengthen robustness, we introduce a smooth L1 loss with exponential weights in the pre-training step. At the time of submission, our method achieves competitive performance with all published optical flow methods on both the KITTI-2015 and MPI-Sintel benchmarks. Moreover, it outperforms all optical flow and scene flow methods in KITTI-2015 foreground-region prediction.

Exponential Weight Portmanteau Tests of Univariate Time Series

Exponential Weight Portmanteau Tests of Univariate Time Series

Positioning failure error identification of industrial robots based on particle swarm optimization and Kriging surrogate modeling

AbstractTo tackle the low identification accuracy of robot positioning, this paper proposes a positioning failure error identification method for industrial robots, combining the Kriging surrogate model and the improved particle swarm optimization algorithm. First, based on the Denavit‐Hartenberg and the small displacement screw methods, the kinematic model of a six‐degree‐of‐freedom industrial robot with joint errors is constructed. Then, the Kriging surrogate model of the kinematic error is constructed, which is trained by generated training samples. Finally, the joint error identification of industrial robots is solved by an improved particle swarm optimization algorithm based on exponential inertia weight and sub‐population cooperation under the multi‐attitude positioning condition. The simulation results show that the proposed optimization algorithm can significantly improve the convergence accuracy and accurately identify the actual errors at each joint of the industrial robot.

Kalman recursions Aggregated Online

In this article, we aim to improve the prediction from experts’ aggregation by using the underlying properties of the models that provide the experts involved in the aggregation procedure. We restrict ourselves to the case where experts perform their predictions by fitting state-space models to the data using Kalman recursions. Using exponential weights, we construct different Kalman recursions Aggregated Online (KAO) algorithms that compete with the best expert or the best convex combination of experts in a more or less adaptive way. When the experts are Kalman recursions, we improve the existing results on experts’ aggregation literature, taking advantage of the second-order properties of the Kalman recursions. We apply our approach to Kalman recursions and extend it to the general adversarial expert setting by state-space modeling the experts’ errors. We apply these new algorithms to a real-data set of electricity consumption and show how they can improve forecast performances compared to other exponentially weighted average procedures.

Evolutionary gate recurrent unit coupling convolutional neural network and improved manta ray foraging optimization algorithm for performance degradation prediction of PEMFC

Performance degradation prediction is an effective method to improve the durability of proton exchange membrane fuel cell (PEMFC). In this study, a hybrid deep learning model based on two-dimensional convolutional neural network (CNN2D), gate recurrent unit (GRU), and improved manta ray foraging optimization (IMRFO) algorithm is proposed for performance degradation prediction of PEMFC. Firstly, the mutual information (MI) and the locally weighted scatterplot smoothing (LOESS) are used to preprocess the data in order to boost the sample quality and reduce the influence of insignificant and noisy data on the model prediction. Secondly, CNN2D is used to deeply explore the nonlinear degradation characteristics in the data. Thirdly, three strategies including half uniform initialization, exponential weight coefficient and fitness-distance balance (FDB) are added to the algorithm to improve the defect that the optimization algorithm is easy to fall into local optimum. Finally, the GRU model optimized by the improved MRFO algorithm is used to predict the degradation data and obtain the final prediction results. The experimental results show that the prediction accuracy of the proposed prediction model in this study is 99.79%, and the RMSE and MAE are 0.0072 and 0.0042, respectively. Therefore, the method can effectively explore the deep features in the data and improve the accuracy, reliability, and robustness of PEMFC performance degradation prediction.

Upper Tail Bounds for Stationary KPZ Models

We present a proof of an upper tail bound of the correct order (up to a constant factor in the exponent) in two classes of stationary models in the KPZ universality class. The proof is based on an exponential identity due to Rains in the case of last passage percolation with exponential weights, and recently re-derived by Emrah–Janjigian–Seppäiläinen (EJS). Our proof follows very similar lines for the two classes of models we consider, using only general monotonocity and convexity properties, and can thus be expected to apply to many other stationary models.

A novel FMEA approach for submarine pipeline risk analysis based on IVIFRN and ExpTODIM-PROMETHEE-II

The failure mode and effects analysis (FMEA) approach based on TODIM has been widely applied in risk analysis in several fields. To fill the gap in relevant research in the field of submarine pipeline risk analysis and to address possible problems in the classical TODIM method, a novel FMEA model is proposed in this paper. Firstly, an improvement to the existing interval-valued intuitionistic fuzzy rough number (IVIFRN) theory is made and used to collect expert opinions better to consider individual and group uncertainty. Secondly, ExpTODIM, which is more in line with prospect theory, is combined with the PROMETHEE-II method. And it also incorporates weight calculation methods such as the maximizing deviation method for ranking failure modes. Thirdly, the exponential entropy weight method based on the improved IVIFRN theory is combined with the analytical hierarchical process (AHP) for application in fuzzy comprehensive evaluation to complete the calculation of risk values. Fourthly, the proposed novel FMEA approach is applied to the risk analysis of the submarine pipeline to obtain its failure mode ranking and risk value results. Comparisons with other methods in concept and example analysis show that the proposed method is relatively reliable and has certain advantages over other current FMEA methods based on MCDM. In particular, the proposed method overcomes the theoretical problems of the classical TODIM and is more consistent with logic. It also improves the accuracy and comprehensiveness of analysis results, which can provide a valid and accurate reference for the practical engineering of submarine pipelines.

Trees with exponential height dependent weight

We consider planar rooted random trees whose distribution is even for fixed height h and size N and whose height dependence is of exponential form $$e^{-\mu h}$$ . Defining the total weight for such trees of fixed size to be $$Z^{(\mu )}_N$$ , we determine its asymptotic behaviour for large N, for arbitrary real values of $$\mu $$ . Based on this we identify the local limit of the corresponding probability measures and find a transition at $$\mu =0$$ from a single spine phase to a multi-spine phase. Correspondingly, there is a transition in the volume growth rate of balls around the root as a function of radius from linear growth for $$\mu <0$$ to the familiar quadratic growth at $$\mu =0$$ and to cubic growth for $$\mu > 0$$ .