It is known, that proper parameterizations of rational curves in reduced form are unique up to bilinear reparameterizations, i.e., projective transformations of its parameter domain. This observation ...has been used in a series of papers by Alcázar et al. to formulate algorithms for detecting Euclidean equivalences and symmetries as well as similarities. We generalize this approach to projective equivalences of rationally parametrized surfaces. More precisely, we observe that a birational base-point free parameterization of a surface is unique up to projective transformations of the domain. Furthermore, we use this insight to find all projective equivalences between two given surfaces. In particular, we formulate a polynomial system of equations whose solutions specify the projective equivalences, i.e., the reparameterizations associated with them.
Furthermore, we investigate how this system simplifies for the special case of affine equivalences for polynomial surfaces and how we can use our method to detect projective symmetries of surfaces. This method can be used for classifying the generic cases of quadratic surfaces.
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Deep learning techniques have been widely adopted in landslide detection by offering powerful feature extraction capabilities and automated processes. However, the pursuit of higher accuracy has led ...to increasingly complex network structures, which limits the efficiency of models in landslide detection. To tackle this challenge, we have developed a dynamic module, called Five-branch Feature Extraction Module (FFEM), based on the theory of structural reparameterization. This module is designed to reconstruct the encoder of the U-shaped network. Our novel network, Re-Net, effectively integrates information from multiple scales during training by utilizing its multi-branch structure, which is facilitated by the FFEM. During inference, leveraging the structural reparameterization, the FFEM in Re-Net transforms as a convolutional layer, achieving an impressive 52.9% reduction in parameters, and 34.98% reduction in FLOPs. the efficiency improvement of Re-Net does not come at the expense of sacrificing landslide recognition accuracy. In the public dataset (Bijie dataset), Re-Net achieved improvements of 2.81% in IoU(Intersection over Union) and 1.93% in F1-Score. In post-earthquake landslide detection tasks (Luding Dataset), Re-Net exhibited respective improvements of 2.29% and 1.52%. Moreover, in the task of Landslide Detection, Re-Net demonstrates superior segmentation accuracy compared to other CNNs, such as Unet++. when compared to other reparameterization modules, FFEM shows significant improvements in IoU and F1-Score in the Bijie dataset, with an average increase of 0.65% and 0.45%, respectively. Similarly, in the Luding dataset, FFEM demonstrates average improvements of 1.56% in IoU and 1.04% in F1-Score.
Using Bayesian methods for extreme value analysis offers an alternative to frequentist ones, with several advantages such as easily dealing with parametric uncertainty or studying irregular models. ...However, computations can be challenging and the efficiency of algorithms can be altered by poor parametrization choices. The focus is on the Poisson process characterization of univariate extremes and outline two key benefits of an orthogonal parameterization. First, Markov chain Monte Carlo convergence is improved when applied on orthogonal parameters. This analysis relies on convergence diagnostics computed on several simulations. Second, orthogonalization also helps deriving Jeffreys and penalized complexity priors, and establishing posterior propriety thereof. The proposed framework is applied to return level estimation of Garonne flow data (France).
•An orthogonal parameterization is beneficial for Bayesian inference of extreme value models.•Convergence diagnostics (autocorrelation, ESS, and local Rˆ) are superior in the three maximum domains of attraction.•Jeffreys and PC priors can be computed for the Poisson process model for extremes, and the corresponding posterior is proper.•The return level credible interval length can be reduced by adding prior information on the extreme value index.
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With the proliferation of wireless technologies in vehicular networks, robust automatic modulation classification (AMC) has become crucial for optimizing spectrum utilization and maintaining ...reliability. However, AMC in dynamic vehicular channels poses significant challenges for traditional machine learning techniques. This paper proposes a novel CNN-based approach named Reparameterization Causal Convolutional Network (RepCCNet) to achieve highly accurate and noise-robust AMC performance. RepCCNet incorporates causal convolutions and structural reparameterization techniques to extract long-term time-domain features. A bottleneck structure with channel attention dynamically calibrates feature channels, retaining only helpful information. Multi-sample dropout is integrated during training to improve generalization capability. We demonstrate RepCCNet's state-of-the-art classification accuracy on the two widely used datasets, RadioML 2016.10a and RadioML 2018.01a, across varying signal-to-noise ratios. Compared to existing methods, RepCCNet achieves highly competitive results compared to state-of-the-art approaches, utilizing fewer than 40 k parameters. Ablation studies validate the contributions of the proposed architectural innovations. This work represents a significant advancement toward developing deep learning solutions for robust wireless signal classification tasks.
The weights of rational Bézier curves cannot be regarded as true independent shape factors since they do not enjoy invariance with respect to Moebius (i.e., rational linear) reparametrizations, which ...do not change the curve shape. However, the existence of such shape factors, also called shape invariants, is well-known. They are associated with each inner control point and are computed as the ratio of weight ratios for three consecutive control points. We show that these shape factors, in addition to their invariance to Moebius reparameterization, provide a more convenient shape control than the customary weights since they exert a more localized push/pull. Each shape factor amounts to that of the conic defined by a triplet of consecutive control points and weights. Thus, shape factors can be controlled in a geometric way using existing techniques for conics by setting the conic rho-factor via moving the associated shoulder point. Each shoulder point moves along a radial direction through its corresponding control point, furnishing a more practical shape handle than sliding the traditional weight points (aka Farin points) on the polygon legs.
•Shape factors of rational Bézier curves must be invariant to Moebius reparameterization.•They are defined as the ratio of weight ratios for three consecutive control points.•They provide a more convenient shape control (localized push/pull) than the weights.•Each factor is that of the conic defined by three consecutive control points and weights.•They can be controlled via the conic rho-factor, moving the associated shoulder point.
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Understanding the role that molecular interactions play on physicochemical properties of ionic solutions is of fundamental importance to design novel electrolytes used in devices to storage energy, ...such as lithium ion batteries. Several salts containing propylene carbonate are studied. The propylene carbonate and TFSI− anion force fields were previously parametrized by our group. Those of lithium (Li+), hexafluorophosphate (PF6−) and tetrafluoroborate (BF4−) are developed in this work with ions carrying a charge of ±1e. The calculated properties are liquid density, dielectric constant, self-diffusion coefficient and viscosity. The results are in excellent agreement with experimental data at different salt concentrations and temperatures. The dielectric constant of PC/LiBF4 is greater than that of the other two electrolytes because the ions form large clusters and the solvent molecules behave as a pure liquid. The predictions with the new parameters improve those from a polarizable model for PC/LiTFSI and those from a machine learning force field for PC/LiPF6.
•The Li+, PF6- and BF4- force field parameters are developed in this work carrying charges of ±1e.•The dielectric constant of electrolytes at the same salt concentration decreases with molecular size of anions.•Calculated properties are in excellent agreement with experimental data at different salt concentrations and temperatures.•The results show that the used parametrization procedure is helpful to study new electrolytes for lithium-ion batteries.
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Underwater images suffer from low contrast and color distortion. In order to improve the quality of underwater images and reduce storage and computational resources, this paper proposes a lightweight ...model Rep-UWnet to enhance underwater images. The model consists of a fully connected convolutional network and three densely connected RepConv blocks in series, with the input images connected to the output of each block with a Skip connection. First, the original underwater image is subjected to feature extraction by the SimSPPF module and is processed through feature summation with the original one to be produced as the input image. Then, the first convolutional layer with a kernel size of 3 × 3, generates 64 feature maps, and the multi-scale hybrid convolutional attention module enhances the useful features by reweighting the features of different channels. Second, three RepConv blocks are connected to reduce the number of parameters in extracting features and increase the test speed. Finally, a convolutional layer with 3 kernels generates enhanced underwater images. Our method reduces the number of parameters from 2.7 M to 0.45 M (around 83% reduction) but outperforms state-of-the-art algorithms by extensive experiments. Furthermore, we demonstrate our Rep-UWnet effectively improves high-level vision tasks like edge detection and single image depth estimation. This method not only surpasses the contrast method in objective quality, but also significantly improves the contrast, colorimetry, and clarity of underwater images in subjective quality.
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•Proposed a novel convolutional neural network approach for classification of EEG signals.•Using local reparameterize trick to obtain an efficient estimator.•Classification accuracy of greater than ...92% was achieved by a global classifier.•The model can be used in handling individual variability issue.
Deep learning (DL) method has emerged as a powerful tool in studying the behavior of Electroencephalogram (EEG)-based motor imagery (MI). Although prospective studies have demonstrated promising performance, most of these studies have been affected by the lack of research between groups and individual subjects, and the accuracy of MI classification still has room for improvement. Due to the inter-individual variability in the EEG classification, enhancing the adaptability and robustness between different individuals is especially critical.
We developed a novel DL model based on the EEG signals to improve MI classification performance by introducing the local reparameterization trick into convolutional neural networks (LRT-CNN). 109 subjects from PhysioNet Dataset were used to test the proposed model. Firstly, a global classifier was evaluated by four groups. Secondly, individual variability was examined by testing individual subjects.
The classification accuracy of global classifier in 20 subjects, 50 subjects, 80 subjects, and 109 subjects are 93.86%, 98.94%, 93.04%, and 92.41%, respectively. The maximum classification accuracy of one individual subject is 99.79%, which is better than the state-of-the-art method and proves the proposed method can handle the challenge of individual variability.
We conclude that introducing the local reparameterization trick into convolutional neural networks can significantly improve the accuracy of the MI tasks based on the EEG signals without any complicated and tedious feature engineering works. Besides, encouraging results were obtained both between groups (multiple subjects) and on a single subject.
The experimental results add to the rapidly expanding field of brain science and contribute to our understanding of applying the DL method to address EEG-based classification problems (not limited to MI classification issues).
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