Exponential Weights Research Articles

An ultrasonic Lamb wave-based non-linear exponential RAPID method for delamination detection in composites

Accurate detection of defects, particularly delamination, in carbon-fiber reinforced polymer (CFRP) composites is crucial but challenging. This study proposes a baseline-free Lamb wave damage imaging framework that incorporates an adaptive time-reversal technique, and a nonlinear exponential reconstruction algorithm for probabilistic inspection of defects (NE-RAPID) in composites. The framework combines two image fusion strategies: full-summation and full-multiplication. NE-RAPID enhances the traditional RAPID algorithm by replacing linear weights with faster-decaying exponential weights, which improves the localization of delamination and other defect regions with higher resolution. A nonlinear exponential weight is introduced to address uneven probability distributions caused by the non-uniform density of the sensor network, thereby improving the accuracy and reliability of defect detection, including delamination. Experimental validation on CFRP composite plates demonstrates that NE-RAPID significantly outperforms RAPID. NE-RAPID achieves a maximum detection error of only 5.1 mm across different frequencies, while RAPID shows a much higher error of 34.41 mm. Furthermore, NE-RAPID produces sharper damage images with fewer artifacts, significantly reducing the risk of false positives. These findings indicate that NE-RAPID is a highly promising method for precise and reliable delamination detection in composite materials.

Improved sparrow algorithm to optimize kernel extreme learning machines for lithium battery status of health estimation on incremental capacity curve

Abstract The advancement of new energy vehicles and energy storage devices has increasingly demanded a more accurate state of health estimation for lithium batteries. Data-driven models are gradually widely used but still have the problems of long iteration time, low accuracy, and unreliable selection of feature factors. Thus, to promote the application of data-driven models in estimating the health state of lithium batteries, this paper proposes a multi-method improved sparrow algorithm optimized kernel extreme learning machine framework for lithium battery health state estimation. To improve the speed and accuracy issues of the data-driven model, this paper selects the kernel extreme learning machine as the network model and the improved sparrow algorithm using chaotic mapping and self-designed exponential weight factors as the optimization algorithm for automatic parameter search to achieve high accuracy and speed. Secondly, to strengthen the reliability of data feature factor selection, multiple feature factors are selected in the incremental capacity curve to improve the stability of feature factors. Finally, the rapidity and reliability of the proposed model on the SOH prediction of lithium batteries are verified by experiments, which provides an effective way to manage lithium batteries healthily.

Do premorbid weight parameters predict BMI 30 years after adolescent-onset anorexia nervosa?

PurposeTo examine anthropometric predictors of BMI 30 years after the onset of adolescent AN. MethodsA group of 51 individuals with adolescent-onset AN were identified in Sweden in 1985. Anthropometric data have been collected from birth records and school nurse charts. A group matched for gender, school and age constituted a healthy control group. Possible predictors of BMI 30 years after AN onset including ponderal index (a variable that estimates body proportionality and composition during the infancy period) and highest BMI Z score (highest BMI in childhood, adjusted for age and sex) were analyzed with linear regression and multivariate analysis. ResultsNone of the five possible predictors were significantly correlated to BMI outcome 30 years after AN onset. In the control group, BMI at the 18- and 30-year follow-ups were statistically significantly predicted by ponderal index at birth (18-year follow-up: r = 0.36, p = .015; 30-year follow-up: r = 0.32, p = .034). ConclusionsWe found no statistically significant premorbid anthropometric predictors of BMI 30 years after the onset of AN. Ponderal index at birth appears to normally predict BMI outcomes in the general adult population. Having had AN during adolescence may have caused a disruption of the expected long-term BMI trajectory, resulting in a lower weight status than expected. These findings may be implemented in clinical practice to address patients' fear of exponential weight gain after recovery.

A convergence analysis for the approximation to the solution of an age-structured population model with infinite lifespan

Considering the numerical approximation of the density distribution for an age-structured population model with unbounded lifespan on a compact interval [0,T], we prove second order of convergence for a discretization that adaptively selects its truncated age-interval according to the exponential rate of decay with age of the solution of the model. It appears that the adaptive capacity of the length in the truncated age-interval of the discretization to the infinity lifespan is a very convenient approach for a long-time integration of the model to establish the asymptotic behavior of its dynamics numerically. The analysis of convergence uses an appropriate weighted maximum norm with exponential weights to cope with the unbounded age lifespan. We report experiments to exhibit numerically the theoretical results and the asymptotic behaviour of the dynamics for an age-structured squirrel population model introduced by Sulsky.

A Proportional–Integral–Derivative type regulation scheme with non-Lipschitz control actions for mechanical systems with constrained inputs

Motivated by the benefits that recent finite-time continuous control approaches have proven to give rise, this work aims to design a proportional–integral–derivative (PID) type control scheme for the global regulation of constrained-input mechanical systems that incorporates design features characteristic of such finite-time continuous algorithms. This is proven to be achieved through a more general PID type control structure that incorporates exponential weights on the P and D type terms, through which such control actions are permitted to loose Lipschitz-continuity at the desired equilibrium values. This entails an important challenge consisting on the introduction of an appropriate analytical framework and the development of a suitable closed-loop analysis through which the resulting design is properly supported. The study is complemented by experimental tests which show that appropriate (less-than-unity) values on the incorporated exponential weights indeed give rise to closed-loop improvements characteristic of finite-time continuous control approaches, such as reduction of overshoot on the position error responses and of the control effort, alleviating such a performance adjustment task.

Nested replicator dynamics, nested logit choice, and similarity-based learning

We consider a model of learning and evolution in games whose action sets are endowed with a partition-based similarity structure intended to capture exogenous similarities between strategies. In this model, revising agents have a higher probability of comparing their current strategy with other strategies that they deem similar, and they switch to the observed strategy with probability proportional to its payoff excess. Because of this implicit bias toward similar strategies, the resulting dynamics – which we call the nested replicator dynamics – do not satisfy any of the standard monotonicity postulates for imitative game dynamics; nonetheless, we show that they retain the main long-run rationality properties of the replicator dynamics, albeit at quantitatively different rates. We also show that the induced dynamics can be viewed as a stimulus-response model in the spirit of Erev and Roth (1998), with choice probabilities given by the nested logit choice rule of Ben-Akiva (1973) and McFadden (1978). This result generalizes an existing relation between the replicator dynamics and the exponential weights algorithm in online learning, and provides an additional layer of interpretation to our analysis and results.

Toeplitz operators and Hankel operators on a Bergman space with an exponential weight on the unit ball

Toeplitz operators and Hankel operators on a Bergman space with an exponential weight on the unit ball

High‐dimensional sparse classification using exponential weighting with empirical hinge loss

In this study, we address the problem of high‐dimensional binary classification. Our proposed solution involves employing an aggregation technique founded on exponential weights and empirical hinge loss. Through the employment of a suitable sparsity‐inducing prior distribution, we demonstrate that our method yields favorable theoretical results on prediction error. The efficiency of our procedure is achieved through the utilization of Langevin Monte Carlo, a gradient‐based sampling approach. To illustrate the effectiveness of our approach, we conduct comparisons with the logistic Lasso on simulated data and a real dataset. Our method frequently demonstrates superior performance compared to the logistic Lasso.

The distance decay effect and spatial reach of spillovers

This paper quantifies and graphically illustrates the distance decay effect and spatial reach of spillover effects derived from a spatial Durbin (SD) model with parameterized spatial weight matrices. Building on attributes of the concept of spatial autocorrelation developed by Arthur Getis, we adopt a distance-based negative exponential spatial weight matrix and parameterize it by a decay parameter that is different for each spatial lag in this model, both of the regressand and of all regressors. The quantification and illustration are applied to the spatially augmented neoclassical growth framework, which we estimate using data for 266 NUTS-2 regions in the EU over the period 2000–2018. We find distance decay parameters ranging from 0.233 to 2.224 and spatial reaches ranging from 700 to more than 1500 km for the different growth determinants in this model. These wide ranges highlight the restrictiveness of the conventional SD model based on one common spatial weight matrix for all spatial lags.

Solving Maxmin Optimization Problems via Population Games

Population games are games with a finite set of available strategies and an infinite number of players, in which the reward for choosing a given strategy is a function of the distribution of players over strategies. The paper shows that, in a certain class of maxmin optimization problems, it is possible to associate a population game to a given maxmin problem in such a way that solutions to the optimization problem are found from Nash equilibria of the associated game. Iterative solution methods for maxmin optimization problems can then be derived from systems of differential equations whose trajectories are known to converge to Nash equilibria. In particular, we use a discrete-time version of the celebrated replicator equation of evolutionary game theory, also known in machine learning as the exponential multiplicative weights algorithm. The resulting algorithm can be viewed as a generalization of the Iteratively Reweighted Least Squares (IRLS) method, which is well known in numerical analysis as a useful technique for solving Chebyshev function approximation problems on a finite grid. Examples are provided to show the use of the generalized IRLS method in collective investment and in decision making under model uncertainty.

Multi-reservoir echo state network with five-elements cycle

Echo state network (ESN) is reservoir computing model that effectively replace recurrent neural network (RNN). However, building reservoir in traditional ESN often has randomness, making it difficult to effectively determine the reservoir that matches a given task. Therefore, a multi-reservoir ESN based on five-elements cycle (FEC-MRESN) is proposed to design the reservoir automatically in this paper. First, FEC-MRESN designs a pruning algorithm using a top-down strategy to remove redundant neurons from the reservoir based on the generation and restriction relations between elements in the five-elements cycle. Second, based on the reservoir neurons retained by the pruning algorithm, an exponential weight assignment method is studied to achieve deterministic assignment of reservoir weights. Finally, FEC-MRESN is tested on some time series benchmark datasets. The experimental results show that FEC-MRESN not only improves prediction accuracy, but also removes redundant reservoir neurons, improves network generalization performance and training efficiency.

Analysis of Influential Elements and Performance Evaluation of the Development of New Business Subjects in the Perspective of Rural Revitalization

Abstract This study deeply explores the development influencing factors and performance evaluation of new agricultural management subjects under the perspective of rural revitalization, provides data support through empirical analysis, and provides guidance for promoting rural economic development and optimizing agrarian management system. A performance evaluation model containing four dimensions of technology, finance, market and society is constructed using the hierarchical analysis method (AHP), multiplicative exponential weights (MEW) and entropy value method. The study results show that among the technical indicators, the member learning ability scores the highest (0.06575), while among the social indicators, the social responsibility and radiation ability scores are the same (both 0.087). Among the financial indicators, operational capacity scored the highest (0.07025) and customer acquisition rate scored the highest (0.07575) among the market indicators. The comprehensive evaluation shows that the technical indicators have the most significant impact on the development performance of new agricultural business entities. This study provides a quantitative analysis of the development of new farm business subjects, which is effective for promoting the rural revitalization strategy.

MPC-Based Exponential Weight Laguerre Function With Non-Singular Terminal SMC for Four-Wheel Independent Drive Electric Vehicles

MPC-Based Exponential Weight Laguerre Function With Non-Singular Terminal SMC for Four-Wheel Independent Drive Electric Vehicles

Uneven time series forecasting using a modified exponential smoothing method

The article is devoted to the problem of forecasting time series with an uneven distribution of observations over time. The exponential smoothing model is used as the basic forecasting model, in which the variable weights of observations decrease exponentially. The exponential smoothing model allows us to take into account the attenuation of the correlation of cross sections of a random process of time series change over time. However, this does not take into account the factors of temporal unevenness of the results of observations and the finiteness of the sample of observations. The article describes a method for predicting an uneven time series based on a modified exponential smoothing model, in which the transition from exponential smoothing to decreasing non-exponential smoothing is carried out. The modified sequence of the weights of the observations is determined by adjusting the classically calculated exponential weights, taking into account the actual irregularity of the observations.

HFSWR Clutter Suppression and Target Detection Method Based on RRN and Exponential Weight Control

HFSWR Clutter Suppression and Target Detection Method Based on RRN and Exponential Weight Control

Lagrange Interpolation Polynomials with Exponential Weights

Let Wρ be an exponential weight of the form Wρ (t):=|t|ρ exp(-Q(t)) on ℝ := (-∞,∞), and let Ln,ρ (F,t) for F ∈ C(ℝ) be the Lagrange interpolation polynomial at the zeros {tj,n,ρ}j=1)n of the orthonormal polynomial of degree n with respect to Wρ. A new Lp -norm convergence of Ln,ρ (F,t) is discussed.

Linear Classifiers Under Infinite Imbalance

Understanding Linear Classifiers in the Face of Severe Data Imbalance In “Linear Classifiers Under Infinite Imbalance,” Paul Glasserman and Mike Li tackle the challenge of binary classification when data are severely imbalanced—a common dilemma in fields like healthcare and finance. They build upon the work of Owen by examining the behavior of logistic regression and extending the analysis to a broader class of linear discriminant functions. Their key contribution is the proof of infinite-imbalance limits for these functions’ coefficient vectors, providing explicit expressions for these limits and distinguishing between classifiers with subexponential and exponential weight functions. This distinction allows for a better understanding of how to adjust classifiers in the context of extreme imbalance, ultimately leading to improved specificity or sensitivity in predictions. The authors also link their findings to the concepts of robustness and conservatism in classification decisions, offering insight into optimal classifier design against the most challenging alternatives. The practical implications of their theoretical work are illustrated through numerical examples and a credit risk case study, offering a new perspective on managing classification tasks in the face of infinite imbalance.

Local well-posedness for the compressible Navier–Stokes–BGK model in Sobolev spaces with exponential weight

Sprays are complex flows constituted of dispersed particles in an underlying gas. In this paper, we are interested in the equations for moderately thick sprays consisting of the compressible Navier–Stokes (NS) equations and Boltzmann BGK equation. Here the coupling of two equations is through a friction (or drag) force which depends on the density of compressible fluid and the relative velocity between particles and fluid. For the NS–BGK system, we establish the existence and uniqueness of solutions in Sobolev spaces with exponential weight.

Unsupervised feature selection by learning exponential weights

Unsupervised feature selection has gained considerable attention for extracting valuable features from unlabeled datasets. Existing approaches typically rely on sparse mapping matrices to preserve local neighborhood structures. However, this strategy favors large-weight features, potentially overlooking smaller yet valuable ones and distorting data distribution and feature structure. Besides, some methods focus on local structure information, failing to explore global information. To address these limitations, we introduce an exponential weighting mechanism to induce a rational feature distribution and explore data structure in the feature subspace. Specifically, we propose a unified framework incorporating local structure learning and exponentially weighted sparse regression for optimal feature combinations, preserving global and local information. Experimental results demonstrate the superiority of our approach over existing unsupervised feature selection methods.

Simple Proof of the Risk Bound for Denoising by Exponential Weights for Asymmetric Noise Distributions

Simple Proof of the Risk Bound for Denoising by Exponential Weights for Asymmetric Noise Distributions