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The rapid development of renewable energy presents challenges to the security and stability of power systems. Aiming at addressing the power system scheduling problem with load demand and wind power uncertainty, this paper proposes the establishment of different error fuzzy sets based on the Wasserstein probability distance to describe the uncertainties of load and wind power separately. Based on these Wasserstein fuzzy sets, a distributed robust chance-constrained scheduling model was established. In addition, the scheduling model was transformed into a linear programming problem through affine transformation and CVaR approximation. The simplex method and an improved differential evolution algorithm were used to solve the model. Finally, the model and algorithm proposed in this paper were applied to model and solve the economic scheduling problem for the IEEE 6-node system with a wind farm. The results show that the proposed method has better optimization performance than the traditional method. [ABSTRACT FROM AUTHOR]

Invariant relations are used to analyze while loops; while their primary application is to derive the function of a loop, they can also be used to derive loop invariants, weakest preconditions, strongest postconditions, sufficient conditions of correctness, necessary conditions of correctness, and termination conditions of loops. In this paper we present two generic invariant relations that capture the semantics of loops whose loop body applies affine transformations on numeric variables. [ABSTRACT FROM AUTHOR]

In this paper, we take an axiomatic approach to the design of ecological footprint indices. Our focus is put on the heterogeneity of land with respect to types and regions, at the core of an inherent aggregation problem. We propose an axiomatic characterization of the ecological footprint index with two fundamentally new axioms, symmetry and independence, which can resolve the problem of land heterogeneity. It is shown that a unique index, up to an affine transformation, exists meeting the axiom system. This index simplifies the aggregation procedure considerably and avoids the need for a synthetic unit of measurement, like global hectares, as well as complex transformations of variables by means of weighting schemes. Our findings reveal differences with the Global Footprint Network (GFN) index, in particular with regard to the treatment of land heterogeneity. Finally, the axiomatic methodology employed may open up perspectives for the development of ecological measures in general, and especially of measures for sustainability and tipping points. [ABSTRACT FROM AUTHOR]

To study the fruit image fusion technology in the case of thermal infrared and visible heterogeneous sources and the method of online defect detection on fruit fusion images, this paper takes apple as the research object and proposes a registration algorithm for thermal infrared and visible images of apple based on the registration of feature points with an active contour model. First, by designing a thermal infrared and visible image acquisition system, thermal infrared and visible images of apple in the same scene are obtained simultaneously. Then, the improved Chan-vese model is adopted to obtain the active contour segmentation curves of the thermal infrared and visible images of apple respectively. Next, the average Euclidean distance of all adjacent edge points on the active contour segmentation curve is calculated, and the alignment feature point set is constructed by the linear interpolation method based on the obtained average distance, and the optimal scale transformation factor and the optimal horizontal transformation factor are obtained by calculating the partial Hausdorff distance between the two feature point sets. Finally, the registered visible image is acquired based on the obtained affine transformation matrix, thus realizing the registration of the thermal infrared and visible images of apple. The experimental results on the self-built image dataset indicate that the algorithm proposed in this paper can accurately match the heterogeneous images of intact fruit, calyx/stems, and defective fruit, and it performs excellently in terms of precise matching rate and root mean square error, and the high alignment success rate of 96%. Also, it has much better performance than other methods. The proposed registration algorithm can accurately match thermal infrared and visible images of apple, and lays the foundation for further research on the image fusion of thermal infrared and visible, apple surface defect detection, as well as the construction of online dual-light apple grading systems. [ABSTRACT FROM AUTHOR]

This paper focuses on optimizing the Zuker RNA folding algorithm, a bioinformatics task with non-serial polyadic dynamic programming and non-uniform loop dependencies. The intricate dependence pattern is represented using affine formulas, enabling the automatic application of tiling strategies via the polyhedral method. Three source-to-source compilers—PLUTO, TRACO, and DAPT—are employed, utilizing techniques such as affine transformations, the transitive closure of dependence relation graphs, and space–time tiling to generate cache-efficient codes, respectively. A dedicated transpose code technique for non-serial polyadic dynamic programming codes is also examined. The study evaluates the performance of these optimized codes for speed-up and scalability on multi-core machines and explores energy efficiency using RAPL. The paper provides insights into related approaches and outlines future research directions within the context of bioinformatics algorithm optimization. [ABSTRACT FROM AUTHOR]

In this paper, we determine the set S of straight lines L 0 that have intersections with four given distinct lines L 1 , ... , L 4 in R 3. If any two of the four given lines are skew, i.e., not co-planar, Bielinski and Lapinska used techniques in projective geometry to show that there are either zero, one, or two elements in the set S. Using linear algebra techniques, we determine S and show that there are no, one, two or infinitely many elements L 0 in S , where the last case was overlooked in the earlier paper. For the sake of completeness, we provide a comprehensive determination of all the elements L 0 in S if at least two of the four given lines are co-planar. In this scenario, there may also be zero, one, two, or infinitely many solutions. [ABSTRACT FROM AUTHOR]

The novelty of this work is that it is the first to introduce complex-valued suprametric spaces and apply it to Fractal Generation and mixed Volterra–Fredholm Integral Equations. In the realm of fuzzy logic, complex-valued suprametric spaces provide a robust framework for quantifying the similarity between fuzzy sets; for instance, utilizing a complex-valued suprametric approach, we compared the similarity between fuzzy sets represented by complex-valued feature vectors, yielding quantitative measures of their relationships. Thereafter, we establish related fixed point results and their applications in algorithmic and numerical contexts. The study then delves into the generation of fractals, exemplified by the Barnsley Fern fractal, utilizing sequences of affine transformations within complex-valued suprametric spaces. Moreover, this article presents two algorithms for soft computing and fractal generation. The first algorithm uses complex-valued suprametric similarity for fuzzy clustering, iteratively assigning fuzzy sets to clusters based on similarity and updating cluster centers until convergence. The distinctive pattern of the Barnsley Fern fractal is produced by the second algorithm's repetitive affine transformations, which are chosen at random. These techniques demonstrate how well complex numbers cluster and how simple procedures can create complicated fractals. Moving beyond fractal generation, the paper addresses the solution of mixed Volterra–Fredholm integral equations in the complex plane using our results, demonstrating numerical illustrations of complex-valued integral equations. [ABSTRACT FROM AUTHOR]

Eye movements offer precious information about persons’ state. Video surveillance, marketing, driver fatigue as well as medical diagnosis assistance applications manage eye behavior. We propose a new method for efficiently detecting eye movement. In this paper, we combine circle eye model with eye feature method to improve the accuracy. A set of detectors estimate the eyes centers to increase the localization rate. As a pre-processing stage, the mean of the edges yields the center of the two eye regions. Image treatment operations reduce the ROI. A Circle Hough Transform (CHT) algorithm is adopted in a modified version as a detector to find the circle eye in the image; the circle center found represents the eye's pupil estimation. We introduced the Maximally Stable Extremal Region (MSER) as a second detector, which has never been used for eye localization. Invariant to continuous geometric transformations and affine intensity changes and detected at several scales, MSERs efficiently detect regions of interest, in our case eye regions, and precisely, their centers. Ellipses fit MSERs, and their centroid estimation match eyes center. We demonstrate that the true eye centers can be found by combining these methods. The validation of the proposed method is performed on a very challenging BioID base. The proposed approach compares well with existing state-of-the-art techniques and achieves an accuracy of 82.53% on the BioID database when the normalized error is less than 0.05, without prior knowledge or any learning model. [ABSTRACT FROM AUTHOR]

The primary source of food is extracted from the plant. Take care of and maintain the plants in real-time to enhance human survival. Diseases in plants can directly lead to a reduction in the industrial economy. Automatic detection of plant diseases is crucial for effective disease control. Vitis vinifera (Grapes) is an essential crop with rich vitamin C nutrients. This paper targets to classify the major diseases in Vitis vinifera leaves using Capsule Network (CapsNet), that prevails over the significant CNN limitations by discarding the pooling layers and adding capsule layers. Dynamic routing techniques of CapsNet make are more robust for the affine transformation of the leaves dataset. It is capable of learning large datasets effectively with vital image transformations such as rotations and transitions. Implementing CapsNet for Vitis vinifera leaf disease classification, which utilizes dynamic routing between capsules, is a novel method. The proposed CapsNet for disease classification is trained with augmented and non-augmented datasets. The performance metrics highlight that the proposed method can effectively classify the Vitis vinifera plant leaves with 98.7% of validation accuracy. The results highlight that the proposed model performs well in detecting and classifying the diseases of Vitis vinifera plant leaves on two benchmark datasets. [ABSTRACT FROM AUTHOR]

The short-term power variations of renewable energy sources result in system state fluctuations and deviations from the scheduled operating point. Tracking short-term power variations and maintaining the system's optimality is challenging for traditional optimization methods due to their highly time-consuming nature. This paper proposes a short-timescale self-adaptive optimization strategy based on the nonlinear affine transformation to deal with this problem. Firstly, the multi-period optimization model is established and solved by considering static power-frequency characteristics to obtain an optimal operating point on a longer temporal scale, with the state security margins reserved using chance constraint programming. Next, analogously with the Taylor series, the nonlinear relationship between the system state variable and short-term power fluctuations is revealed through an analytic expression of the nonlinear affine transformation. Then, a self-adaptive optimization algorithm based on the nonlinear affine transformation is proposed to achieve frequency and voltage optimizations on a shorter temporal scale. With less communication, self-adaptive optimization is implemented at the local bus level to achieve more optimal states for short-term renewable power variations rapidly. Finally, simulations demonstrate that the proposed optimization strategy can effectively enhance frequency and voltage qualities, and decrease objective function, thereby improving the operation safety and economy. [ABSTRACT FROM AUTHOR]

The accurate and rapid prediction of wake flow characteristics is of great significance for the design of underwater vehicles. This paper develops a data driven Bayesian deep learning framework, named WakeNet, to accurately and quickly predict the wake velocity field on the paddle disk surface of the DARPA SUBOFF model under varying geometry configurations. Specifically, (i) the proposed WakeNet presents a coordinate affine transformation technique to address the issue of handling unstructured wake flow data with varying geometries; (ii) it develops a residual modeling strategy built upon a modern version of the U-net architecture to capture the multi-scale wake flow characteristics; and finally, (iii) it exploits the MC dropout method to achieve uncertainty quantification of the prediction, and builds the uncertainty based active learning framework to effectively update the model. Numerical experiments have verified the capability of the proposed WakeNet model for the accurate prediction and uncertainty quantification of the wake flow field with varying geometries. Besides, the proposed model yields a speed up factor of 7000 × compared to the conventional numerical simulation solver. • A novel Bayesian deep learning method for fast prediction of the wake field of DARPA SUBOFF. • A coordinate affine transformation method for tackling the unstructured wake flow data under varying geometries. • A residual modeling strategy built on the U-net architecture to capture the multi-scale wake flow characteristics. • A Monte Carlo (MC) dropout based uncertainty quantification and active learning framework have been built. • The proposed model achieves comparable yet 7000 × faster wake field predictions in comparison to the CFD solver. [ABSTRACT FROM AUTHOR]

Human pose transfer aims to synthesize referred human images with target pose, bringing the substantial economic potential for E-commerce or virtual reality. In this paper, we propose a novel method, the Attentional Pixel-wise Deformation Network (APD-Net), for synthesizing human images with guided pose and referred images. Specifically, we leverage attention-based spatial transformation modules and affine transformation modules to generate accurate appearance and extract pixel-wise details in local regions to generate intermediate results. Additionally, we introduce a confidence map to refine spatial information during the final image synthesis. Domain alignment loss, cycle loss, perceptual and feature matching loss and contextual loss are applied to constrain the synthesized images while attention loss and fusion loss benefit warp images generation. We verify the efficacy of the model on the Market-1501 and DeepFashion datasets, using quantitative and qualitative measures. Our approach surpasses all previously published state-of-the-art results on most evaluation metrics, e.g., achieving 0.780 SSIM score, 9.55 Sliced Wasserstein Distance score, and a 0.963 Semantic Consistency score on DeepFashion and obtaining 0.303 SSIM score, 16.971 Sliced Wasserstein Distance score and 0.729 Semantic Consistency score on Market-1501 Code and pretrained models are available at: https://github.com/LiaoFJ/APD-Net/. • A model with attention and deformation is proposed for human pose transfer. • The novel attention-based operation can assist the final image synthesis. • The model can generate accurate images while preserving the details. [ABSTRACT FROM AUTHOR]

This research tackles the challenge of dynamic formation control and collision avoidance in underactuated surface vessels (USVs). Firstly, an affine transformation is employed to implement arbitrary configuration transformations within the multi-USV system. Secondly, by considering both distances and velocities between USVs and obstacles, a novel collision avoidance scheme is proposed based on conventional distance-based artificial potential field methods. This method, building on traditional distance-based artificial potential fields, offers a more precise assessment of collision risks, thereby notably shrinking the potential collision zones. Such refinement leads to reduced energy consumption and minimizes disruption to formation integrity. Thirdly, an anti-perturbation formation maneuver safety control scheme is introduced to achieve a time-varying target formation without collisions, ensuring that local position tracking errors remain bounded. The effectiveness of the proposed approaches is substantiated through comprehensive theoretical analysis and extensive numerical simulations, underscoring their practical applicability. • This paper proposes a practical distributed USV formation framework designed to address challenges posed by model uncertainties and environmental disturbances encountered during environmental surveys. • An anti-perturbation formation maneuver safety controller is proposed to compensate for the lumped disturbances and achieve maneuver control without collision. • The proposed potential field function serves as a dynamic mechanism for tuning repulsive forces, leveraging real-time data on the relative distances and velocities between USVs and obstacles. [ABSTRACT FROM AUTHOR]

An ellipse can be uniquely determined by five tangents. Given a convex quadrilateral, there are infinitely many ellipses inscribed in it, but the one with maximum area is unique. In this paper, we give a concise and effective solution of this problem. Our solution is composed of three steps: First, we transform the problem from the maximal ellipse construction problem into the minimal quadrilateral construction problem by an affine transformation. And then, we convert the construction problem into a conditional extremum problem by analyzing the key angles. At last, we derive the solution of the conditional extremum problem with Lagrangian multiplier. Based on the conclusion, we designed an algorithm to achieve the construction. The numerical experiment shows that the ellipse constructed by our algorithm has the maximum area. It is interesting and surprising that our constructions only need to solve quadratic equations, which means the geometric information of the ellipse can even be derived with ruler and compass constructions. The solution of this problem means all the construction problems of conic with extremum area from given pure tangents are solved, which is a necessary step to solve more problems of constructing ellipses with extremum areas. Our work also provides a useful conclusion to solve the maximal inscribed ellipse problem for an arbitrary polygon in Computational Geometry. • We find a method to transform the maximal inscribed ellipse for an arbitrary quadrilateral to a conditional extremum problem. • We derive the solution for the conditional extremum problem with elementary operations. • We design the construction algorithm for constructing the maximal ellipse inscribed in an arbitrary quadrilateral. [ABSTRACT FROM AUTHOR]

Many routing algorithms in capsule networks (CapsNets) suffer seriously from a large amount of parameter training during iterations. To address this issue, a non-iterative CapsNet with interdependent agreement routing (IAR-CapsNet) is proposed in this paper, which relieves the parameter redundancy by reducing the pose dimensionality as well as obtains desired performance by introducing descriptive subcomponents. A dual attention mechanism is developed to pay special attention to equivariant pose information and invariant descriptor information. To be specific, the key information weights are assigned to different components separately through a multi-branch attention mechanism to fulfill the information transfer between the capsule layers. Then, a reciprocal agreement routing without iterations is designed to enhance such information transfer between layers. Finally, the experiments show that the proposed IAR-CapsNet achieves the best classification accuracy with only a 1.36% error rate on the smallNORB dataset and the best robustness performance in robustness experiments. • A novel capsule network with non-iterative and interdependent agreement routing. • A dual-attention mechanism is developed to respectively concentrate to pose and descriptor information. • Capsule with equivariant pose and invariant descriptor. • Theoretical analysis for the necessity of the squashing function. [ABSTRACT FROM AUTHOR]

It is essential to guarantee product quality by detecting defects in industrial printed labels. Defect detection based on reference comparison is a common method to achieve this task. However, this method yields poor performance under large deformations of printed labels, due to the lack of accurate registration ability between testing images and reference images. Therefore, it is an urgent task to achieve accurate image registration for printed label defect detection. In this paper, a coarse-to-fine end-to-end registration network, named APPR-Net, is proposed to deal with the large deformation. First, we adopt a strategy of image patch splitting and stitching to improve the scalability of image resolution. Second, we design a four-stream affine transformation module followed by a multi-scale pyramid registration network, where a coarse registration is obtained by the former module and then gradually refined by the later network in a coarse-to-fine manner. Third, we introduce a distortion loss function to constrain the text distortion of the warped image after image registration. Finally, to simulate printed labels with defects and large deformation, we build a synthetic database based on real-world industrial printed labels for performance comparison. The results demonstrate that the proposed APPR-Net significantly outperforms other compared methods. • Propose a coarse-to-fine registration network to deal with large deformation. • Take advantages of image patch splitting and stitching strategy. • Design a four-stream affine transformation module followed by a pyramid network. • Introduce a distortion loss function to constrain text distortions. • Build a synthetic database based on real-world printed labels. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive element Subdivision Method based on the Affine transformations and Partitioning techniques (APSM) is presented for evaluating the weakly singular integrals with arbitrary shape of elements. The basic idea consists in partitioning the input surface element via affine transformation and then in generating a set of high-quality patches by adaptive binary-tree subdivision. The proposed method has some advantages over the conventional methods based on elements subdivision, i.e. the adaptive element subdivision, an improvement of the accuracy and a straight-forward implementation. By using the domain partitioning technique, the surface element can be divided into several element projection and subdivision regions under affine transformations. It is far more efficient to separately perform the element subdivision for different regions where the desirable patches are required. The ultimate patches in the vicinity of the singular point are calculated numerically by the coordinate transformation technique, while the remaining patches are evaluated accurately by the standard Gaussian quadrature. Several numerical examples are presented in order to validate the accuracy, efficiency and availability of the proposed method. [ABSTRACT FROM AUTHOR]

This paper focuses on the challenge of time-varying formation control for underactuated autonomous underwater vehicles (AUVs). To tackle this challenge, an average consensus time-varying formation control based on event triggering decoupling mechanism (ETDM-ACTVF) is proposed. Firstly, the average consensus time-varying formation (ACTVF) based on the affine transformation are introduced, and the control objective considering the dynamic characteristics of underactuated AUVs is proposed. The trajectory tracking controller is designed by the back stepping method. Secondly, an event triggering decoupling mechanism (ETDM) achieves the state decoupling to constrain the uncontrollable state. Moreover, a dynamic event triggering mechanism is employed to reduce the execution frequency of actuators. Finally, the excellent performance of the proposed algorithm in addressing both the underactuated AUV time-varying formation control and decoupling control problems is demonstrated through simulation results. • Average consensus time-varying formation control was first proposed for underactuated AUVs. • The control objective provides a new direction for controller design of underactuated AUVs. • The event triggering decoupled mechanism achieved the decouple control of underactuated AUVs. • Dynamic event triggering mechanism reduces actuator and energy consumption. [ABSTRACT FROM AUTHOR]

The identical nature of unmanned vessels in a homogeneous formation imposes limitations on their adaptability to diverse task demands in complex environmental conditions or constantly evolving task requirements, hindering their ability to achieve optimal performance. This paper presents the heterogeneous formation comprising fully actuated and underactuated vessels to overcome these limitations. Firstly, an affine transformation is employed to implement arbitrary configuration transformations within the formation system. Secondly, a composite learning formation controller is proposed for the underactuated vessels acting as the leaders to track the arbitrary formation transformation. Thirdly, considering that certain followers have access to the state information of the leaders, a new virtual leader–follower structure is constructed to achieve formation maneuver control by designing distributed estimators to estimate the state information of the virtual leader. Finally, simulation results validate the proposed control law's effectiveness. • Synthesizing the attributes of fully actuated and underactuated vessels establishes a class of heterogeneous formation systems. • Considering the offshore application scenarios of vessels and various factors affecting formation control, we propose a composite learning algorithm-based formation maneuver controller to compensate for the lumped disturbances and achieve maneuver control. • In the follower subsystem, a new virtual leader-follower structure is constructed to achieve formation maneuver control by designing distributed estimators to estimate the state information of the virtual leader. [ABSTRACT FROM AUTHOR]