Search Results (15)

In this study, we examine a length preserving geodesic curvature difference flow for smooth strictly horocyclically convex simple closed curves in the hyperbolic plane ${\mathbb{H}}^2$. Given an initial curve ${\gamma }_1$ and a target curve ${\gamma }_2$ of the same hyperbolic length, we evolve ${\gamma }_1$ by a normal speed given by the difference of the reciprocals of geodesic curvatures evaluated at points with the same outward unit normal, together with a time-dependent scalar term $\mathrm{\Gamma }\left(t\right)$ chosen to preserve the hyperbolic length. Using Leichtweiβ’s hyperbolic support function and Howe’s curvature formula, the flow is reformulated as a quasilinear uniformly parabolic equation on ${\mathbb{S}}^1$ with a nonlocal term $\mathrm{\Gamma }\left(t\right)$. We prove short-time existence, uniqueness, and preservation of strict horocyclic convexity. Linearizing the support function equation at the target support function yields a uniformly elliptic operator whose kernel contains the infinitesimal isometry directions. Under a spectral gap assumption on a normalized slice transverse to the isometry orbit, we prove global existence and exponential convergence for initial data sufficiently close to the target curve. In the last section, this assumption is verified explicitly when the target curve is a geodesic circle. Full article

We present a geodesic dynamics framework for discrete-time state evolution on the unit sphere $S^{N-1}$ that maintains exact unit-norm constraints through Riemannian exponential mapping. Given an input sequence and an initial state, the method constructs trajectories by projecting inputs to tangent spaces and updating states along geodesics, incorporating temporal memory via approximate parallel transport of velocity directions. Unlike traditional approaches requiring post hoc normalization of linear updates, the geodesic formulation preserves $\parallel {\mathbf{x}}_t\parallel =1$ to machine precision while eliminating explicit $N\times N$ transition matrices in favor of $D\times N$ input embeddings when the intrinsic input dimension D is much smaller than the ambient dimension N. The update corresponds to a first-order exponential integrator on the sphere. We establish local Lipschitz continuity of the exponential map on positively curved manifolds with careful treatment of basepoint dependence, derive perturbation bounds showing linear-to-exponential growth transitions via Grönwall-type estimates, and we prove third-order asymptotic equivalence with normalized linear systems under appropriate scaling. Numerical experiments on synthetic data validate exact norm preservation over extended time horizons, confirm theoretical perturbation growth predictions, and demonstrate the effectiveness of the temporal memory mechanism in reducing long-horizon prediction errors. The framework provides a principled geometric approach for applications requiring exact directional or compositional constraints. Full article

The proliferation of next-generation Internet infrastructures and the Internet of Things (IoT) has exponentially increased network traffic complexity. While deep learning (DL)-based intrusion detection systems (IDSs) show immense potential, they persistently suffer from challenges including high computational overhead, vanishing gradients in deep architectures, and acute sensitivity to noise. Consequently, these issues impede their real-time deployment in resource-constrained edge computing environments. To overcome these limitations, we propose a novel, lightweight, and robust intrusion detection framework based on deep neural networks (DNNs). Initially, we employ a Robust Scaler-based statistical preprocessing strategy to supersede traditional Z-score standardization, effectively mitigating the adverse impacts of outliers and burst traffic noise. Subsequently, we design an advanced architecture that integrates self-normalizing residual blocks with a channel attention mechanism. Leveraging compressed hidden layers alongside the Scaled Exponential Linear Unit (SELU) activation function, this architecture not only mitigates the vanishing gradient problem but also amplifies critical traffic features. Concurrently, it achieves a substantial reduction in both parameter count and inference latency. Furthermore, we introduce a cosine annealing strategy to dynamically adjust the learning rate during training, thereby facilitating the model’s escape from local optima and accelerating convergence. Extensive experiments on standard benchmark datasets demonstrate that our proposed framework achieves superior detection accuracy while maintaining exceptional computational efficiency compared to state-of-the-art baselines. Full article

Generative Adversarial Networks (GANs) have emerged as a promising tool for augmenting medical image datasets used by AI solutions. However, GANs trained on small datasets (300–500 images) frequently encounter mode collapse, overfitting, and instability, which hinder their practical application. Many GAN-generated images look unrealistic. The Enhanced Deep Convolutional GAN (EDCGAN) is introduced to generate high-quality synthetic images of breast US (BUS). The model includes an experimental design for the Discriminator and Generator. The main components are spectral normalization (SN), the Squeeze-and-Excitation (SE) block, and the Scaled Exponential Linear Unit (SELU). One of the basic versions of DCGAN is considered for the proposed modifications. The stopping criteria are based on the convergence of the smoothed loss function and the constraints imposed on the Discriminator. The contribution is a combination of the above modifications and postprocessing based on the visual evaluation by radiologists and selected image processing metrics. The Inception Score (IS), the Structural Similarity Index (SSIM), and the Mean Squared Error (MSE) comply with the results obtained in the preceding works. The efficiency of augmenting the US data has been verified on a DL classification based on ResNet-18. The tests against training on a non-augmented data outperform ResNet by 5% and by the data augmented by the previous DCGAN by 3%. These numbers are substantial since this variant of ResNet has been pre-trained on 1000 categories by ImageNet-1K, including 1.28 million images. Additionally, the model wins the “Guess-the-real-image” game, competing with seven preceding GANs. Full article

The hydro-upgrading reaction behavior of model compound 1-hexene and FCC middle gasoline was investigated using a fixed-bed hydrogenation microreactor with a prepared La-Ni-Zn/H-ZSM-5 catalyst. The catalyst was prepared by wetness impregnation method, using hydrothermal treated H-ZSM-5 zeolite blended with alumina as the support, and La, Ni, Zn as the active metals. The reaction tests were carried out at 300–380 °C, 1.0 MPa, 1.5–3.0 h⁻¹ (LSHV), and 300:1 v/v (H₂/oil). Analyzing the changes in hydrocarbon components before and after hydro-upgrading elucidated the mechanistic pathways of olefin hydroisomerization and hydroaromatization. Based on these findings, a seven-lump kinetic model was established for the FCC middle gasoline hydro-upgrading process. Given the diversity and complexity of reaction products, they were grouped into seven lumps: normal paraffins, isoparaffins, linear olefins, branched olefins, cycloolefins, naphthenes, and aromatics. Kinetic parameters were estimated using the Levenberg–Marquardt algorithm and validated against experimental data. The results showed that the conversion of naphthenes to aromatics exhibited the highest activation energy and pre-exponential factor, resulting in the largest reaction rate increase within the 320–380 °C range. The model accurately predicted the product yields of FCC gasoline hydro-upgrading, with a relative error of less than 5%. These findings provide valuable guidance for the optimization, design, and operation of FCC gasoline hydro-upgrading units, as well as for catalyst development, with the aim of improving process efficiency and fuel quality. Full article

This paper investigated the relationships of some physical and mechanical parameters of sediments and a typical clay during a natural dewatering process. Four sediments from different French river dams sampled by the Électricité De France group (EDF group) and a commercial kaolin clay used for comparative purposes were the focus of this study. Continuous dewatering was monitored in a laboratory by quantifying the percentage of water remaining in sediments or clay, drained and evaporated. Undrained shear strength was also assessed during the sediment or clay dewatering process, using the laboratory vane shear test. The samples were controlled along different dimensions during the dewatering process throughout the whole experiment. The results showed a certain interdependence between the physical parameters and the water content (ω), which was normalized by the liquidity limit (ω/L_L) over time. This led to sigmoidal and exponential correlations when considering the percentage of water drained. The percentage of water remaining in the sediments or clay was characterized using the normalized water content, leading to exponential and power correlations. Both exponential and linear correlations were perfect for describing the evolution of the percentage of water evaporated. Other correlations were established for variations in void index, dry unit weight/solid unit weight ratio and undrained shear strength during the dewatering process. Full article

A neural network method has been developed for helicopter turboshaft engine residual life determination, the basis of which is a hierarchical system, which is represented in neural network model form, consisting of four layers, which determines the numerical value of the residual life. To implement a hierarchical system, a justified multilayer perceptron is used. A multilayer perceptron training algorithm has been developed, which, by introducing an initial parameter to the output layer, yields a prediction accuracy of up to 99.3%, and the adaptive Adam training rate ensures an accuracy of up to 99.4% in helicopter turboshaft engine residual life determination. A method for constructing a degradation curve has been developed that takes into account both the parameter predictions and similarities with past patterns, allowing you to determine the range of possible values of the residual life estimate, with a probability of up to 95%. The article considers an example of solving the task of determining the thermally stressed state of helicopter turboshaft engine compressor turbine blades and assessing their residual life. A computational experiment was carried out to determine the residual life of helicopter turboshaft engine compressor turbine blades, and the results, with 160 training epochs, recorded an accuracy of 99.3%, with a reduction in losses from 2.5% to 0.5% thanks to training process optimization by applying an adaptive training rate. The comparative analysis results showed that use of the multilayer perceptron as a hierarchical system gives better results than the classical RBF network and the least squares method. The first and second types of error were reduced by 2.23 times compared to the RBF network and by 4.74 times compared to the least squares method. Full article

The L-fractional derivative is defined as a certain normalization of the well-known Caputo derivative, so alternative properties hold: smoothness and finite slope at the origin for the solution, velocity units for the vector field, and a differential form associated to the system. We develop a theory of this fractional derivative as follows. We prove a fundamental theorem of calculus. We deal with linear systems of autonomous homogeneous parts, which correspond to Caputo linear equations of non-autonomous homogeneous parts. The associated L-fractional integral operator, which is closely related to the beta function and the beta probability distribution, and the estimates for its norm in the Banach space of continuous functions play a key role in the development. The explicit solution is built by means of Picard’s iterations from a Mittag–Leffler-type function that mimics the standard exponential function. In the second part of the paper, we address autonomous linear equations of sequential type. We start with sequential order two and then move to arbitrary order by dealing with a power series. The classical theory of linear ordinary differential equations with constant coefficients is generalized, and we establish an analog of the method of undetermined coefficients. The last part of the paper is concerned with sequential linear equations of analytic coefficients and order two. Full article

Generalized linear mixed models are commonly used in repeated measurement studies and account for the dependence between observations obtained from the same experimental unit. The designs of repeated measurements in which each experimental unit (e.g., subject) is proven in more than one experimental condition are widespread in psychology, neuroscience, medicine, social sciences and agricultural research. Estimation in generalized linear mixed models is often based on the maximum likelihood theory, which assumes that the assumptions about the underlying probability model are correct. These assumptions include the specification of the distribution of random effects. This research study aimed to identify the impact of the incorrect specification of this distribution on the probability of a type I error and the statistical power of the Wald test. This was achieved through a simulation study where different distributions were considered for random effects in generalized linear mixed models with Poisson and negative binomial responses. Evidence of the impact of the incorrect specification was presented in distributions for random effects different from the normal ones. Lognormal was used for random intercepts and bivariate exponential and Tukey for random intercepts and slopes. Lognormal has positive asymmetry and high kurtosis. Exponential has moderate asymmetry and kurtosis, and Tukey has moderate asymmetry and high kurtosis. Full article

The vibration signals for offshore wind-turbine high-speed bearings are often contaminated with noises due to complex environmental and structural loads, which increase the difficulty of fault detection and diagnosis. In view of this problem, we propose a fault-diagnosis strategy with good noise immunity in this paper by integrating the two-dimensional convolutional neural network (2DCNN) with random forest (RF), which is supposed to utilize both CNN’s automatic feature-extraction capability and the robust discrimination performance of RF classifiers. More specifically, the raw 1D time-domain bearing-vibration signals are transformed into 2D grayscale images at first, which are then fed to the 2DCNN-RF model for fault diagnosis. At the same time, three procedures, including exponential linear unit (ELU), batch normalization (BN), and dropout, are introduced in the model to improve feature-extraction performance and the noise immune capability. In addition, when the 2DCNN feature extractor is trained, the obtained feature vectors are passed to the RF classifier to improve the classification accuracy and generalization ability of the model. The experimental results show that the diagnostic accuracy of the 2DCNN-RF model could achieve 99.548% on the CWRU high-speed bearing dataset, which outperforms the standard CNN and other standard machine-learning and deep-learning algorithms. Furthermore, when the vibration signals are polluted with noises, the 2DCNN-RF model, without retraining the model or any denoising process, still achieves satisfying performance with higher accuracy than the other methods. Full article

We consider an optimization design for the alpha power exponential (APE) distribution as asymmetrical probability distributions under progressive type-I censoring for a step-stress accelerated life test. In this study, two stress variables are taken into account. To save the time and cost of lifetime testing, progressive censoring and accelerated life testing are utilized. The test units’ lifespans are supposed to follow an APE distribution. A cumulative exposure model is used to study the impact of varying stress levels. A log-linear relationship between the APE distribution’s scale parameter and stress is postulated. The maximum likelihood estimators, Bayesian estimators of the model parameters based on the symmetric loss function, approximate confidence intervals (CIs) and credible intervals are provided. Under normal operating conditions, an ideal test plan is designed by minimizing the asymptotic variance of the percentile life. Full article

Fixed and rotary-wing unmanned aircraft systems (UASs), originally developed for military purposes, have widely spread in scientific, civilian, commercial, and recreational applications. Among the most interesting and challenging aspects of small UAS technology are endurance enhancement and autonomous flight; i.e., mission management and control. This paper proposes a practical method for estimation of true and calibrated airspeed, Angle of Attack (AOA), and Angle of Sideslip (AOS) for small unmanned aerial vehicles (UAVs, up to 20 kg mass, 1200 ft altitude above ground level, and airspeed of up to 100 knots) or light aircraft, for which weight, size, cost, and power-consumption requirements do not allow solutions used in large airplanes (typically, arrays of multi-hole Pitot probes). The sensors used in this research were a static and dynamic pressure sensor (“micro-Pitot tube” MPX2010DP differential pressure sensor) and a 10 degrees of freedom (DoF) inertial measurement unit (IMU) for attitude determination. Kalman and complementary filtering were applied for measurement noise removal and data fusion, respectively, achieving global exponential stability of the estimation error. The methodology was tested using experimental data from a prototype of the devised sensor suite, in various indoor-acquisition campaigns and laboratory tests under controlled conditions. AOA and AOS estimates were validated via correlation between the AOA measured by the micro-Pitot and vertical accelerometer measurements, since lift force can be modeled as a linear function of AOA in normal flight. The results confirmed the validity of the proposed approach, which could have interesting applications in energy-harvesting techniques. Full article

Heart disease is the leading cause of death for men and women globally. The residual network (ResNet) evolution of electrocardiogram (ECG) technology has contributed to our understanding of cardiac physiology. We propose an artificial intelligence-enabled ECG algorithm based on an improved ResNet for a wearable ECG. The system hardware consists of a wearable ECG with conductive fabric electrodes, a wireless ECG acquisition module, a mobile terminal App, and a cloud diagnostic platform. The algorithm adopted in this study is based on an improved ResNet for the rapid classification of different types of arrhythmia. First, we visualize ECG data and convert one-dimensional ECG signals into two-dimensional images using Gramian angular fields. Then, we improve the ResNet-50 network model, add multistage shortcut branches to the network, and optimize the residual block. The ReLu activation function is replaced by a scaled exponential linear units (SELUs) activation function to improve the expression ability of the model. Finally, the images are input into the improved ResNet network for classification. The average recognition rate of this classification algorithm against seven types of arrhythmia signals (atrial fibrillation, atrial premature beat, ventricular premature beat, normal beat, ventricular tachycardia, atrial tachycardia, and sinus bradycardia) is 98.3%. Full article

Fetal fractional limb volume is a useful measure for predicting birth weight and newborn adiposity; however, a normal growth curve has been reported solely in the United States. As the birth weight of neonates in Japan is significantly lower than that in the US, fetal fractional limb volume is likely to be smaller in the Japanese population. This study aimed to define the normal growth curve of fractional arm volume (AVol) and thigh volume (TVol) in the Japanese population. Ultrasound scans of 453 AVol and TVol pairs were obtained; each AVol and TVol percentile at each gestational age was calculated. The measured AVol and TVol at each gestational week were also converted to z-scores based on a previous report. The growth curves increased linearly until the second trimester and exponentially in the third trimester. Linear regression showed a significant negative correlation between gestational age and AVol and TVol z-scores. The growth pattern of fetal fractional limb volume in the Japanese population is consistent with, but smaller than, that reported in the US; this difference becomes greater as the gestational age progresses. Full article

Data security technology is of great significance for the effective use of high-resolution remote sensing (HRRS) images in GIS field. Integrity authentication technology is an important technology to ensure the security of HRRS images. Traditional authentication technologies perform binary level authentication of the data and cannot meet the authentication requirements for HRRS images, while perceptual hashing can achieve perceptual content-based authentication. Compared with traditional algorithms, the existing edge-feature-based perceptual hash algorithms have already achieved high tampering authentication accuracy for the authentication of HRRS images. However, because of the traditional feature extraction methods they adopt, they lack autonomous learning ability, and their robustness still exists and needs to be improved. In this paper, we propose an improved perceptual hash scheme based on deep learning (DL) for the authentication of HRRS images. The proposed method consists of a modified U-net model to extract robust feature and a principal component analysis (PCA)-based encoder to generate perceptual hash values for HRRS images. In the training stage, a training sample generation method combining artificial processing and Canny operator is proposed to generate robust edge features samples. Moreover, to improve the performance of the network, exponential linear unit (ELU) and batch normalization (BN) are applied to extract more robust and accurate edge feature. The experiments have shown that the proposed algorithm has almost 100% robustness to format conversion between TIFF and BMP, LSB watermark embedding and lossless compression. Compared with the existing algorithms, the robustness of the proposed algorithm to lossy compression has been improved, with an average increase of 10%. What is more, the algorithm has good sensitivity to detect local subtle tampering to meet the high-accuracy requirements of authentication for HRRS images. Full article