Smooth Function Research Articles

An Improved Nonlinear Active Disturbance Rejection Controller via Sine Function and Whale Optimization Algorithm for Permanent Magnet Synchronous Motors Speed Control

Permanent magnet synchronous motors (PMSMs) speed control has gained wide application in various fields. Specifically, there is a disadvantage that nonlinear functions in the conventional active disturbance rejection controller (ADRC) is non‐differentiable at the piecewise points. Thus, an improved nonlinear active disturbance rejection controller (NLADRC) for permanent magnet synchronous motor speed control via sine function and whale optimization algorithm (WOA), abbreviated as NLADRC‐sin‐IWOA, is proposed to overcome this drawback. Considering the unsatisfactory control effect caused by the poor active disturbance resisting ability of the traditional PMSM controllers, this paper proposes an improved NLADRC for PMSM, that reconstructs a novel differentiable and smooth nonlinear function, the novel nonlinear function grounded on primitive function by the function of inverse hyperbolic, sine, square functions, and with difference fitting approach; and designs an improved whale optimization algorithm via convergence factor nonlinear decreasing, Gaussian variation and adaptive cross strategies. The experimental results findings show that the improved NLADRC‐sin‐IWOA has the advantages of response fast, small steady‐state error and tiny overshoot. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Differential Operators on Non-compact Harmonic Manifolds

We study the algebra of differential operators on non-compact simply connected harmonic manifolds and provide sufficient conditions for them to have a radial fundamental solution and be surjective on the space of smooth function. Furthermore, we show that the algebra of differential operators that commute with taking averages over geodesic spheres is generated by the Laplacian. As an application of this, we show that the heat-semi group is dense in the radial L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1$$\\end{document} space of a non-compact simply connected harmonic manifold. In the process, we provide a characterisation of the eigenfunctions of the Laplacian and therefore of the eigenfunctions of all differential operators commuting with taking spherical averages.

Compressed sensing with smooth L0 constraints for moving force identification from bridge response measurements

Abstract Compressed sensing (CS), as an emerging information sampling technique, has been successfully applied in the field of moving force identification (MFI). However, existing MFI CS models often fail to obtain the optimal sparse solutions and frequently underestimate the amplitude of local impact forces. To effectively address this issue, a new CS method is proposed for MFI based on smooth L0 norm constraints and bridge response measurements. Firstly, a smooth function is used to approximate the L0 norm, establishing a noise CS reconstruction model for MFI. The introduction of the smoothing function can locally convexify the original MFI problem and enhance the smoothness and differentiability of the objective function, making the optimization problem easier to solve. Subsequently, the Polak–Ribiere–Polyak formula is adopted to point the descent direction of the new objective function, and the sparse solution is iteratively advanced through the conjugate gradient algorithm. Finally, the applicability and feasibility of the proposed method is confirmed by numerical simulations and vehicle–bridge interaction tests, respectively. The results show that the proposed method can accurately identify moving forces from limited measurements of bridge responses. Compared with existing methods, it can provide more precise sparse solutions with higher robustness to measurement noises, and address the issue of underestimating on the amplitude of local impact forces, which is expected to enhance the performance and in-situ applicability of MFI.

Examining Teacher Willingness and the Labyrinth of Challenges in Implementing Professional Learning Communities at the Senior High School Level in Builsa South District

Aim: This study aimed to examine teacher willingness and the labyrinth of challenges in implementing Professional Learning Communities at the senior high school level in the Builsa South District. Methods: The study was purely quantitative and employed a descriptive correlational design with a questionnaire as the data collection instrument. A census technique was used allowing for the total accessible population, 79 senior high school teachers participate in the data collection process. Data was analyzed using descriptive statistics and a simple linear regression model. Results: The results showed that the regression model predicting willingness to participate in Professional Learning Community (PLC) activities from attitudes was statistically significant, F(1, 77) = 66.56, p < .001, meaning that more positive attitudes are associated with greater willingness to engage in PLC activities. Additionally, challenges such as time constraints, lack of leadership support, and resistance from teachers were reported as key obstacles faced in the implementation of Professional Learning Communities. Recommendation: The study strongly recommends that schools should prioritize providing adequate support and resources for Professional Learning Communities (PLCs) to address teachers' dissatisfaction in this area. This can include allocating sufficient time, funding, and administrative support to ensure the smooth functioning of PLC activities. By enhancing support and resources, schools can create a more conducive environment for collaboration and professional development within PLCs.

Micro-extrusion foaming fabricating porous polyester elastomeric fiber for using in radiative cooling fabrics

Climate change has unleashed relentless global heatwaves, posing grave threats to the physical and mental well-being of outdoor laborers and the smooth functioning of society. Porous polymeric fibers exhibit promising potential in personal thermal management for wearable fabrics. Nevertheless, the absence of an environmentally friendly, cost-effective, and efficient method for producing the desired porous fibers remains a formidable challenge. Here, we introduce a pioneering micro-extrusion foaming technique for crafting elastic porous fibers endowed with dense longitudinally oriented cell morphologies, remarkable porosity of 69 % and elongation of 668 %. The technique enabled the continuous production of porous fibers exceeding 3000 m in length in a single operation, with fiber diameters controlled to approximately 0.25–0.55 mm. Fabrics woven from the elastic porous fiber offered a soft touch, proficiently reflecting more than 90.0 % of incident solar radiation and emitting 91.9 % of absorbed heat radiation, thereby achieving a theoretical radiant cooling power of 111.46 W/m2 on sunlit days. Leveraging the controllable and scalable attributes of micro-extrusion foaming, the porous fiber is primed for practical deployment and expansion into diverse wearable applications.

Assessment of structural and functional profile of dental centers for people with disabilities.

People with disabilities (PWD) often face more significant oral healthcare needs than the general population. This study, conducted in response to the urgent and pressing need for improved dental care for PWD, aims to assess the infrastructural and work process flow of dental centers in Delhi that provide specialized dental care for PWD. A descriptive cross-sectional study was conducted across primary, secondary, and tertiary healthcare centers in Delhi, evaluating their infrastructure adaptations and work processes in delivering oral healthcare to PWD. The findings, which highlight the disparities in adaptations and work processes among different healthcare centers, are crucial for understanding the current state of oral healthcare for PWD in Delhi. The study reveals that while secondary and tertiary healthcare centers exhibit better adaptations for PWD than primary centers, challenges persist with insufficient accessibility and smooth functioning of the work process. This study underscores the need for dentists to be equipped with the competence to address the unique needs of PWD. It also highlights the significant potential for improvement in oral healthcare for PWD, as dentists should become more aware of the importance of designing clinics that are accessible for PWD.

Enhancing electromagnetic interference mitigation: A comprehensive study on the synthesis and shielding capabilities of polypyrrole/cobalt ferrite nanocomposites

In a society increasingly infiltrated by digital and networking technologies, designing electromagnetic interference (EMI) shielding materials is critical for safeguarding sensitive electronic equipment and ensuring the smooth functioning of essential communication networks. This study focuses on the optimization of the properties of cobalt ferrite (CoFe2O4)/polypyrrole (PPy) nanocomposites made by in-situ polymerization used for electromagnetic (EM) shielding based on their magnetic and dielectric losses. X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), transmission electron microscopy (TEM), vibrating sample magnetometer (VSM), and vector network analyzer (VNA) were employed to study the materials' physical and chemical characteristics. The findings demonstrate that the magnetic and electric properties of the materials composed of CoFe2O4 and PPy are substantially altered by the integration of CoFe2O4 and PPy. Adding PPy to CoFe2O4 reduces the real and imaginary parts of magnetic permeability, and the conductivity, dielectric constant, and dielectric loss are increased. These effects are advantageous for EM shielding applications. The high electromagnetic shielding performance mainly results from the enhanced interfacial polarization induced by interface region among CoFe2O4 and PPy molecules. The influence of the PPy matrix in altering the dielectric and magnetic loss factors (tanδE and tanδM) of the embedded ferrite particles is pronounced. Although CoFe2O4 shows excellent attenuation characteristics, it cannot optimally match impedance with free space, particularly at higher frequencies. In addition, material thickness and shielding efficiency adjust the reflection loss (RL) performance. The prepared composites can attenuate more than 95 % of the incident electromagnetic waves. This study emphasizes the benefits of employing composite materials in EMI shielding designs and the combined advantages of conductive and magnetic materials.

"Timely help" or "one disaster after another": The impact of potential and transition interim CEO succession on corporate performance.

The succession mode of interim CEO is highly uncertain. The smooth transition function of interim CEO is particularly important in the process of enterprise reform. We divide interim CEOs into potential successors and transition successors. Then we empirically analyze the heterogeneous impact and mechanism of interim CEOs on firm performance. The results show that compared with transition CEO, potential CEO has less negative impact on corporate performance. Interim CEO has a negative impact on enterprise performance by reducing agency efficiency. The mechanism analysis of this paper are as follows. For the potential CEO, strong incentive constraints can effectively mitigate the negative impact of the succession on corporate performance. For a transitional CEO, superior personal capabilities coupled with an effective oversight mechanism represent more optimal solutions. In today's corporate landscape, the frequencies of executive changes and interim successions are on the rise annually. Our research is tailored to aid enterprises in navigating these transitions seamlessly and in expediting their recovery processes.

The Lavrentiev Phenomenon

The basic problem of the calculus of variations consists of finding a function that minimizes an energy, like finding the fastest trajectory between two points for a point mass in a gravity field or finding the best shape of a wing. The existence of a solution may be established in quite abstract spaces, much larger than the space of smooth functions. An important practical problem is that of being able to approach the value of the infimum of the energy. However, numerical methods work with very “concrete” functions and sometimes they are unable to approximate the infimum: this is the surprising Lavrentiev phenomenon. The papers that ensure the nonoccurrence of the phenomenon form a recent saga, and the most general result formulated in the early ’90s was actually fully proved just recently, more than 30 years later. Our aim here is to introduce the reader to the calculus of variations, to illustrate the Lavrentiev phenomenon with the simplest known example, and to give an elementary proof of the nonoccurrence of the phenomenon.

Cardioprotection by Preconditioning with Intralipid Is Sustained in a Model of Endothelial Dysfunction for Isolated-Perfused Hearts.

Endothelial dysfunction (ED) is closely associated with most cardiovascular diseases. Experimental models are needed to analyze the potential impact of ED on cardioprotection in constant pressure Langendorff systems (CPLS). One cardioprotective strategy against ischemia/reperfusion injury (I/RI) is conditioning with the lipid emulsion Intralipid (IL). Whether ED modulates the cardioprotective effect of IL remains unknown. The aim of the study was to transfer a protocol using a constant flow Langendorff system for the induction of ED into a CPLS, without the loss of smooth muscle cell functionality, and to analyze the cardioprotective effect of IL against I/RI under ED. In isolated hearts of male Wistar rats, ED was induced by 10 min perfusion of a Krebs-Henseleit buffer containing 60 mM KCl (K+), and the vasodilatory response to the vasodilators histamine (endothelial-dependent) and sodium-nitroprusside (SNP, endothelial-independent) was measured. A CPLS was employed to determine cardioprotection of pre- or postconditioning with 1% IL against I/RI. The constant flow perfusion of K+ reduced endothelial response to histamine but not to SNP, indicating reduced vasodilatory functionality of endothelial cells but not smooth muscle cells. Preconditioning with IL reduced infarct size and improved cardiac function while postconditioning with IL had no effect. The induction of ED neither influenced infarct size nor affected the cardioprotective effect by preconditioning with IL. This protocol allows for studies of cardioprotective strategies under ED in CLPS. The protection by preconditioning with IL seems to be mediated independently of a functional endothelium.

Smooth Sigmoid Surrogate (SSS): An Alternative to Greedy Search in Decision Trees

Greedy search (GS) or exhaustive search plays a crucial role in decision trees and their various extensions. We introduce an alternative splitting method called smooth sigmoid surrogate (SSS) in which the indicator threshold function used in GS is approximated by a smooth sigmoid function. This approach allows for parametric smoothing or regularization of the erratic and discrete GS process, making it more effective in identifying the true cutoff point, particularly in the presence of weak signals, as well as less prone to the inherent end-cut preference problem. Additionally, SSS provides a convenient means of evaluating the best split by referencing a parametric nonlinear model. Moreover, in many variants of recursive partitioning, SSS can be reformulated as a one-dimensional smooth optimization problem, rendering it computationally more efficient than GS. Extensive simulation studies and real data examples are provided to evaluate and demonstrate its effectiveness.

Well-Posedness of the generalised Dean–Kawasaki Equation with correlated noise on bounded domains

In this paper, we extend the notion of stochastic kinetic solutions introduced in Fehrman and Gess (2024) to establish the well-posedness of stochastic kinetic solutions of generalised Dean–Kawasaki equations with correlated noise on bounded, C2-domains with Dirichlet boundary conditions. The results apply to a wide class of non-negative boundary data, which is based on certain a priori estimates for the solutions, that encompasses all non-negative constant functions including zero and all smooth functions bounded away from zero.

YOLOrot2.0: A novel algorithm for high-precision rice seed size measurement with real-time processing

We present YOLOrot2.0, an automated algorithm for measuring the dimensions of rice seeds, which holds significant importance in evaluating grain quality and genetic breeding research. The current methods for rice seed measurement exhibit various limitations, such as the need for seed preprocessing and selection, specialized equipment for measurement, and prolonged measurement time. To address these issues, YOLOrot2.0 introduces the following improvements: Firstly, it utilizes an anchor-free detection algorithm to optimize the detection of rotated targets. Secondly, the utilization of the Kalman Filter IoU loss function, which combines the horizontal bounding box and smooth L1 loss function, accelerates the convergence speed of the network. Moreover, the YOLOv8 architecture was adjusted by modifying certain convolutional layers and the Context to Fusion module to enhance the detection capabilities for smaller targets. Finally, YOLOrot2.0 enables direct processing of the entire image, eliminating the need for image partitioning and resulting in substantial time and processing savings. Experimental results demonstrate that YOLOrot2.0 achieves an mAP (mean average precision) score of 0.95, surpassing other comparative algorithms. Additionally, YOLOrot2.0 provides highly accurate measurements of seed length and width, closely aligned with ground truth values. Notably, YOLOrot2.0 achieves real-time detection by achieving an average detection time of only 11.5 ms for images sized 3000×4000 pixels.

Correction: Translational perspectives on the therapeutic potential of Hyptis crenata essential oil terpenes in smooth muscle function.

Correction: Translational perspectives on the therapeutic potential of Hyptis crenata essential oil terpenes in smooth muscle function.

Deep learning as Ricci flow.

Deep neural networks (DNNs) are powerful tools for approximating the distribution of complex data. It is known that data passing through a trained DNN classifier undergoes a series of geometric and topological simplifications. While some progress has been made toward understanding these transformations in neural networks with smooth activation functions, an understanding in the more general setting of non-smooth activation functions, such as the rectified linear unit (ReLU), which tend to perform better, is required. Here we propose that the geometric transformations performed by DNNs during classification tasks have parallels to those expected under Hamilton's Ricci flow-a tool from differential geometry that evolves a manifold by smoothing its curvature, in order to identify its topology. To illustrate this idea, we present a computational framework to quantify the geometric changes that occur as data passes through successive layers of a DNN, and use this framework to motivate a notion of 'global Ricci network flow' that can be used to assess a DNN's ability to disentangle complex data geometries to solve classification problems. By training more than 1500 DNN classifiers of different widths and depths on synthetic and real-world data, we show that the strength of global Ricci network flow-like behaviour correlates with accuracy for well-trained DNNs, independently of depth, width and data set. Our findings motivate the use of tools from differential and discrete geometry to the problem of explainability in deep learning.

Optimising seismic imaging design parameters via bilevel learning

Abstract Full waveform inversion (FWI) is a standard algorithm in seismic imaging. It solves the inverse problem of computing a model of the physical properties of the earth’s subsurface by minimising the misfit between actual measurements of scattered seismic waves and numerical predictions of these, with the latter obtained by solving the (forward) wave equation. The implementation of FWI requires the a priori choice of a number of ‘design parameters’, such as the positions of sensors for the actual measurements and one (or more) regularisation weights. In this paper we describe a novel algorithm for determining these design parameters automatically from a set of training images, using a (supervised) bilevel learning approach. In our algorithm, the upper level objective function measures the quality of the reconstructions of the training images, where the reconstructions are obtained by solving the lower level optimisation problem—in this case FWI. Our algorithm employs (variants of) the BFGS quasi-Newton method to perform the optimisation at each level, and thus requires the repeated solution of the forward problem—here taken to be the Helmholtz equation. This paper focuses on the implementation of the algorithm. The novel contributions are: (i) an adjoint-state method for the efficient computation of the upper-level gradient; (ii) a complexity analysis for the bilevel algorithm, which counts the number of Helmholtz solves needed and shows this number is independent of the number of design parameters optimised; (iii) an effective preconditioning strategy for iteratively solving the linear systems required at each step of the bilevel algorithm; (iv) a smoothed extraction process for point values of the discretised wavefield, necessary for ensuring a smooth upper level objective function. The algorithm also uses an extension to the bilevel setting of classical frequency-continuation strategies, helping avoid convergence to spurious stationary points. The advantage of our algorithm is demonstrated on a problem derived from the standard Marmousi test problem.

First mixed Laplace eigenfunctions with no hot spots

The hot spots conjecture of J. Rauch states that the second Neumann eigenfunction of the Laplace operator on a bounded Lipschitz domain in R n \mathbb {R}^n attains its extrema only on the boundary of the domain. We present an analogous problem for domains with mixed Dirichlet-Neumann boundary conditions. We then solve this problem for Euclidean triangles and a class of planar domains bounded by the graphs of certain piecewise smooth functions.

Generalized Additive Models

Generalized additive models are generalized linear models in which the linear predictor includes a sum of smooth functions of covariates, where the shape of the functions is to be estimated. They have also been generalized beyond the original generalized linear model setting to distributions outside the exponential family and to situations in which multiple parameters of the response distribution may depend on sums of smooth functions of covariates. The widely used computational and inferential framework in which the smooth terms are represented as latent Gaussian processes, splines, or Gaussian random effects is reviewed, paying particular attention to the case in which computational and theoretical tractability is obtained by prior rank reduction of the model terms. An empirical Bayes approach is taken, and its relatively good frequentist performance discussed, along with some more overtly frequentist approaches to model selection. Estimation of the degree of smoothness of component functions via cross validation or marginal likelihood is covered, alongside the computational strategies required in practice, including when data and models are reasonably large. It is briefly shown how the framework extends easily to location-scale modeling, and, with more effort, to techniques such as quantile regression. Also covered are the main classes of smooths of multiple covariates that may be included in models: isotropic splines and tensor product smooth interaction terms.

A Wasserstein perspective of Vanilla GANs

The empirical success of Generative Adversarial Networks (GANs) caused an increasing interest in theoretical research. The statistical literature is mainly focused on Wasserstein GANs and generalizations thereof, which especially allow for good dimension reduction properties. Statistical results for Vanilla GANs, the original optimization problem, are still rather limited and require assumptions such as smooth activation functions and equal dimensions of the latent space and the ambient space. To bridge this gap, we draw a connection from Vanilla GANs to the Wasserstein distance. By doing so, existing results for Wasserstein GANs can be extended to Vanilla GANs. In particular, we obtain an oracle inequality for Vanilla GANs in Wasserstein distance. The assumptions of this oracle inequality are designed to be satisfied by network architectures commonly used in practice, such as feedforward ReLU networks. By providing a quantitative result for the approximation of a Lipschitz function by a feedforward ReLU network with bounded Hölder norm, we conclude a rate of convergence for Vanilla GANs as well as Wasserstein GANs as estimators of the unknown probability distribution.

Analytical Neural Network System for the Helicopter Turboshaft Engines Operating Modes Classification

A novel neural network-based analytical system has been developed for classifying helicopter turboshaft engine operating modes during flight operations. This system utilizes a neural network architecture comprising an input layer with three neurons, two fully connected hidden layers, and an output layer with two neurons. The proposed approach demonstrates an exceptional recognition accuracy of 0.997 (99.7%) across steady-state, unsteady, and transient operating modes of helicopter turboshaft engines. A new method for training this neural network has been introduced, employing forward propagation, loss calculation, backpropagation, and weight updates, enhanced by an adaptive learning rate and the cross-entropy function as the loss criterion. The method also incorporates a novel modified Smooth ReLU activation function for hidden layer neurons. This innovation led to a near-perfect accuracy in network training and reduced the loss to 0.025 (2.5%), highlighting the high quality and reliability of the neural network in classifying engine operating modes during flight. Furthermore, it has been empirically shown that the application of this neural network significantly reduces type I errors by a factor of 2.09 to 2.14 and type II errors by 2.05 to 2.21 times compared to traditional classifiers based on ART-1 and BAM networks. This advancement marks a substantial improvement in classification accuracy and error minimization for helicopter turboshaft engine operating modes.