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Symmetry, in particular permutational symmetry, of a potential energy surface (PES) is a useful property in quantum chemical calculations. It facilitates, in particular, state labelling and identification of degenerate states. In many practically important applications, however, these issues are unimportant. The imposition of exact symmetry and the perception that it is necessary create additional methodological requirements narrowing or complicating algorithmic choices that are thereby biased against methods and codes that by default do not incorporate symmetry, including most off-the-shelf machine learning methods that cannot be directly used if exact symmetry is demanded. By introducing symmetric and unsymmetric errors into the PES of H2CO in a controlled way and computing the vibrational spectrum with collocation using symmetric and nonsymmetric collocation point sets, we show that when the deviations from an ideal PES are random, imposition of exact symmetry does not bring any practical advantages. Moreover, a calculation ignoring symmetry may be more accurate. We also compare machine-learned PESs with and without symmetrization and demonstrate that there is no advantage of imposing exact symmetry for the accuracy of the vibrational spectrum. [ABSTRACT FROM AUTHOR]

We introduce the abstract notion of a chain, which is a sequence of n points in the plane, ordered by xcoordinates, so that the edge between any two consecutive points is unavoidable as far as triangulations are concerned. A general theory of the structural properties of chains is developed, alongside a general understanding of their number of triangulations. We also describe an intriguing new and concrete configuration, which we call the Koch chain due to itssimilarities to the Koch curve. A specific construction based on Koch chains is then shown to have Ω(9.08n ) triangulations. This is a significant improvement over the previous and long-standing lower bound of Ω(8.65n ) for the maximum number of triangulations of planar point sets. [ABSTRACT FROM AUTHOR]

Deep learning models struggle to effectively capture data features and make accurate predictions because of the strong non-linear characteristics of arbitrage data. Therefore, to fully exploit the model performance, researchers have focused on network structure and hyperparameter selection using various swarm intelligence algorithms for optimization. Sparrow Search Algorithm (SSA), a classic heuristic method that simulates the sparrows' foraging and anti-predatory behavior, has demonstrated excellent performance in various optimization problems. Hence, in this study, the Multi-Strategy Modified Sparrow Search Algorithm (MSMSSA) is applied to the Long Short-Term Memory (LSTM) network to construct an arbitrage spread prediction model (MSMSSA-LSTM). In the modified algorithm, the good point set theory, the proportion-adaptive strategy, and the improved location update method are introduced to further enhance the spatial exploration capability of the sparrow. The proposed model was evaluated using the real spread data of rebar and hot coil futures in the Chinese futures market. The obtained results showed that the mean absolute percentage error, root mean square error, and mean absolute error of the proposed model had decreased by a maximum of 58.5%, 65.2%, and 67.6% compared to several classical models. The model has high accuracy in predicting arbitrage spreads, which can provide some reference for investors. [ABSTRACT FROM AUTHOR]

What is the most favorite and original chemistry developed in your research group? We originally proposed the design principle for molecular ferroelectrics: ferroelectrochemistry, including quasi‐spherical theory, the introduction of homochirality, and H/F substitution. Ferroelectrochemistry changed the blind search for molecular ferroelectrics into targeted chemical design, which will develop into a new discipline. How do you get into this specific field? Could you please share some experiences with our readers? I have been devoted to the field of molecular ferroelectrics for more than 20 years. In the early stage, I worked on non‐centrosymmetric metal‐organic complexes, which are potential molecular ferroelectrics. This laid a foundation for my further study of molecular ferroelectrics. Non‐centrosymmetric crystal symmetry is only one of the necessary requirements for ferroelectrics, which must adopt one of the 10 polar crystallographic point groups and should also generally undergo symmetry‐breaking phase transitions. Due to the lack of a feasible method, the discovery of molecular ferroelectrics has long depended on blindly searching. This process is like finding a needle in a haystack. After years of exploration in this field, I fully understood the Landau phase transition phenomenological theory, Curie symmetry, and Neumann principle from a chemical perspective, and proposed the design principle for molecular ferroelectrics: ferroelectrochemistry, transforming the discovery of molecular ferroelectrics from blind search to targeted chemical design. Never give up no matter how much difficulty you have met, because maybe there is an opportunity the next second. What is the most important personality for scientific research? Curiosity, divergent thinking, perseverance, team spirit, and gratitude. How do you supervise your students? Emphasis on independent problem‐solving abilities. Encourage students to read professional books frequently while doing research. What are your hobbies? What's your favorite book(s)? Jogging, reading, and swimming. My favorite book is The Journey to the West. Comprehensive Summary: Molecular ferroelectrics have attracted tremendous attention in the past decades due to their excellent ferroelectric performance and superiorities of easy processability, mechanical flexibility, and good biocompatibility. However, the discovery of molecular ferroelectrics is a great challenge and has long relied on blind search. This situation changed recently, with the development of ferroelectrochemistry proposed by our group. As a major design approach in ferroelectrochemistry, introducing homochirality, which facilitates the crystallization of materials in polar crystallographic point groups, greatly improves the probability of being ferroelectrics. Various new molecular ferroelectrics with splendid properties have been precisely synthesized by using this efficient and universal strategy. In this review, we summarize the advances in the chemical design of molecular ferroelectrics through the strategy of introducing homochirality. Key Scientists: [ABSTRACT FROM AUTHOR]

In 1935, the introduction of the norm of a group by Reinhold Baer is a turning point in group theory. In fact, Baer proved that there is a very strong relationship between the structure of the norm and that of the whole group (see [1] , [2] , [3] , [4] , [5]). Since then, the norm has been playing a very significant roles in many aspects of group theory and its applications: it has been used in [43] to describe the connection between Hopf–Galois structures and skew braces; it has been used in [23] to describe some special types of profinite groups; and it has been fundamental in the theory of subgroup lattices of groups (see [40]). In this paper, we weaken the original definition of norm by taking into account only those subgroups that are "large" in some sense. Depending on the chosen concept of largeness, the resulting norm can have an impact on the structure of the whole group that is even greater than that of Baer's norm. This is exactly what happens with the non-polycyclic norm , and in fact, Theorem 4.17 gives a precise description of generalized soluble groups in which the non-polycyclic norm is non-Dedekind (and can be considered as the main result of the paper). Other times, the resulting norms have their own peculiar behaviour; this is the case if "large" means "infinite", "having infinite rank", "being non-Černikov", or "having cardinality m " for some given uncountable cardinal number m. [ABSTRACT FROM AUTHOR]

Background: Osteoarthritis (OA) is a complex, age-related multifactorial degenerative disease of diarthrodial joints marked by impaired mobility, joint stiffness, pain, and a significant decrease in quality of life. Among other risk factors, such as genetics and age, hyper-physiological mechanical cues are known to play a critical role in the onset and progression of the disease (Guilak in Best Pract Res Clin Rheumatol 25:815–823, 2011). It has been shown that post-mitotic cells, such as articular chondrocytes, heavily rely on methylation at CpG sites to adapt to environmental cues and maintain phenotypic plasticity. However, these long-lasting adaptations may eventually have a negative impact on cellular performance. We hypothesize that hyper-physiologic mechanical loading leads to the accumulation of altered epigenetic markers in articular chondrocytes, resulting in a loss of the tightly regulated balance of gene expression that leads to a dysregulated state characteristic of the OA disease state. Results: We showed that hyper-physiological loading evokes consistent changes in CpGs associated with expression changes (ML-tCpGs) in ITGA5, CAV1, and CD44, among other genes, which together act in pathways such as anatomical structure morphogenesis (GO:0009653) and response to wound healing (GO:0042060). Moreover, by comparing the ML-tCpGs and their associated pathways to tCpGs in OA pathophysiology (OA-tCpGs), we observed a modest but particular interconnected overlap with notable genes such as CD44 and ITGA5. These genes could indeed represent lasting detrimental changes to the phenotypic state of chondrocytes due to mechanical perturbations that occurred earlier in life. The latter is further suggested by the association between methylation levels of ML-tCpGs mapped to CD44 and OA severity. Conclusion: Our findings confirm that hyper-physiological mechanical cues evoke changes to the methylome-wide landscape of chondrocytes, concomitant with detrimental changes in positional gene expression levels (ML-tCpGs). Since CAV1, ITGA5, and CD44 are subject to such changes and are central and overlapping with OA-tCpGs of primary chondrocytes, we propose that accumulation of hyper-physiological mechanical cues can evoke long-lasting, detrimental changes in set points of gene expression that influence the phenotypic healthy state of chondrocytes. Future studies are necessary to confirm this hypothesis. [ABSTRACT FROM AUTHOR]

Due to the widespread applications of curves on n‐dimensional spheres, fitting curves on n‐dimensional spheres has received increasing attention in recent years. However, due to the non‐Euclidean nature of spheres, curve fitting methods on n‐dimensional spheres often struggle to balance fitting accuracy and curve fairness. In this paper, we propose a new fitting framework, GLS‐PIA, for parameterized point sets on n‐dimensional spheres to address the challenge. Meanwhile, we provide the proof of the method. Firstly, we propose a progressive iterative approximation method based on geodesic least squares which can directly optimize the geodesic least squares loss on the n‐sphere, improving the accuracy of the fitting. Additionally, we use an error allocation method based on contribution coefficients to ensure the fairness of the fitting curve. Secondly, we propose an adaptive knot placement method based on geodesic difference to estimate a more reasonable distribution of control points in the parameter domain, placing more control points in areas with greater detail. This enables B‐spline curves to capture more details with a limited number of control points. Experimental results demonstrate that our framework achieves outstanding performance, especially in handling imbalanced data points. (In this paper, "sphere" refers to n‐sphere (n ≥ 2) unless otherwise specified.) [ABSTRACT FROM AUTHOR]

We introduce a Delaunay‐based algorithm for reconstructing the underlying surface of a given set of unstructured points in 3D. The implementation is very simple, and it is designed to work in a parameter‐free manner. The solution builds upon the fact that in the continuous case, a closed surface separates the set of maximal empty balls (medial balls) into an interior and exterior. Based on discrete input samples, our reconstructed surface consists of the interface between Voronoi balls, which approximate the interior and exterior medial balls. An initial set of Voronoi balls is iteratively processed, merging Voronoi‐ball pairs if they fulfil an overlapping error criterion. Our complete open‐source reconstruction pipeline performs up to two quick linear‐time passes on the Delaunay complex to output the surface, making it an order of magnitude faster than the state of the art while being competitive in memory usage and often superior in quality. We propose two variants (local and global), which are carefully designed to target two different reconstruction scenarios for watertight surfaces from accurate or noisy samples, as well as real‐world scanned data sets, exhibiting noise, outliers, and large areas of missing data. The results of the global variant are, by definition, watertight, suitable for numerical analysis and various applications (e.g., 3D printing). Compared to classical Delaunay‐based reconstruction techniques, our method is highly stable and robust to noise and outliers, evidenced via various experiments, including on real‐world data with challenges such as scan shadows, outliers, and noise, even without additional preprocessing. [ABSTRACT FROM AUTHOR]

To solve the problem of poor localization accuracy and robustness of visual simultaneous localization and mapping (SLAM) systems in highly dynamic environments, this paper proposes a dynamic visual SLAM algorithm called FFD-SLAM that fuses the target detection network with the optical flow method. The algorithm considers ORB-SLAM2 as the basic framework, joins the semantic thread in parallel with its tracking thread, initially obtains the set of feature points through the real-time detection of dynamic objects in the environment through YOLOv5 in the semantic thread, then filters the set of feature points obtained in the semantic thread through the optical flow module, and finally utilizes the remaining static feature points for the matching calculation. Experiments showed that the proposed algorithm showed an improvement of approximately 97% in the localization accuracy compared with the ORB-SLAM2 algorithm in a highly dynamic environment, which effectively improves the localization accuracy and robustness of the system. The proposed algorithm also showed a higher real-time performance compared with some excellent dynamic SLAM algorithms. [ABSTRACT FROM AUTHOR]

We establish a necessary and sufficient condition for pairs of integers to arise as the weights at the fixed points of an effective circle action on a compact almost complex 4-manifold with a discrete fixed point set. As an application, we provide a necessary and sufficient condition for a pair of integers to arise as the Chern numbers of such an action, answering negatively a question by Sabatini whether |$c_{1}^{2}[M] \leq 3 c_{2}[M]$| holds for any such manifold |$M$|⁠. We achieve this by demonstrating that pairs of integers that arise as weights of a circle action also arise as weights of a restriction of a |$\mathbb {T}^{2}$| -action. Furthermore, we discuss applications to circle actions on complex/symplectic 4-manifolds and semi-free circle actions with discrete fixed point sets. [ABSTRACT FROM AUTHOR]

In this work, we propose a novel framework for large-scale Gaussian process (GP) modeling. Contrary to the global, and local approximations proposed in the literature to address the computational bottleneck with exact GP modeling, we employ a combined global-local approach in building the approximation. Our framework uses a subset-of-data approach where the subset is a union of a set of global points designed to capture the global trend in the data, and a set of local points specific to a given testing location to capture the local trend around the testing location. The correlation function is also modeled as a combination of a global, and a local kernel. The predictive performance of our framework, which we refer to as TwinGP, is comparable to the state-of-the-art GP modeling methods, but at a fraction of their computational cost. [ABSTRACT FROM AUTHOR]

Object detection in remote sensing images poses great challenges due to the dense distribution, arbitrary orientation, and aspect ratio variations of objects. Most of the existing methods rely on aligned convolutional features, which fail to capture the geometric information of objects effectively and result in the inconsistency between the classification score and localization accuracy. Moreover, densely packed objects suffer from spatial feature aliasing caused by the intersection of reception fields between objects. To address this issue, a deformable convolution‐based method named rotated points is proposed, which consists of two modules: a point set loss module and a high‐quality sample assignment module. The point set loss module can extract geometric features of objects in arbitrary directions with fine‐grained point sets for feature representation and introduce outlier penalties to penalize outlier points. The high‐quality sample assignment module measures the classification and localization ability, orientation quality, and point‐wise correlation of point sets comprehensively to enhance the consistency of classification and regression significantly. Experiments on the DOTA and FAIR1M datasets demonstrate that the proposed method achieves significant improvements over the benchmark model. [ABSTRACT FROM AUTHOR]

How does the moral calculus of gentrification change for self-conscious newcomers in neighborhoods with a reputation deemed unworthy of preserving? In pointing to a set of practices distinct from "pioneering" accounts of gentrification, Brown-Saracino (2007) identified social preservationists as figures who seek to preserve authentic community and the marginalized old-timers who embody it. Using the deviant case of Bridgeport—a historically White neighborhood in Chicago with a deeply historical and persistent reputation for racism —we examine how self-conscious newcomers orient themselves to the gentrification process when the old-timers are not considered a marginalized group worth protecting, but rather a powerful group with problematic racial views. Whereas Brown-Saracino identified the importance of "selecting the old-timer" among a set of potential representatives of a valorized past, we suggest that in this case, newcomers fight to redefine a neighborhood based on a socially desirable future. Drawing on two distinct sets of ethnographic and interview-based data, we outline how this process has unfolded. We conclude that Bridgeport's story points to the importance of examining how gentrification ideologies emerge from the collision of personal commitments and neighborhood context, as neighborhood newcomers balance their ethics, concerns over personal reputation, and salient aspects of their new homes, including place reputation. [ABSTRACT FROM AUTHOR]

The aim of this study is the determination of the best fit ellipsoid to given points by quaternions. The problem of the fitting ellipsoid is frequently encountered in image processing, computer games, medicine, engineering and science applications, geodesy, etc. The ellipsoid fitting problem is the process of determining the ellipsoid that best fits a given set of points in 3D. In the fitting process, it is generally done over two models. The first of these is the algebraic method and the second one is orthogonal (geometric) method. In this study, we tried to solve the problem of algebraic and orthogonal ellipsoid fitting based on Euler angles for the first time over quaternions. The superiority of quaternions over Euler rotation angles is well known. In addition, the variance–covariance matrix of the parameters of the fitted ellipsoid will also be calculated. Numerical applications show that the proposed method can be used successfully. [ABSTRACT FROM AUTHOR]

Multimodal is the prominent characteristic of Lamb waves, which means a variety of Lamb wave modes propagate in the structure and each of them has unique propagation behaviour. For a wideband multimodal Lamb wave signal, it is possible that many different modes share the same group velocity at some frequency points, while their dispersion behaviours change differently to thickness variation. In this study, the diversity and difference of the interaction between the corrosion and Lamb wave modes are investigated. On this basis, a corrosion index (CI) is established to evaluate the time gap between two modes at their identical group velocity points. The simulation results show that the CI value of a corroded path is obviously larger than that of a healthy path, indicating the presence of the damage, which is independent of any base-line signal. Furthermore, the new reconstruction algorithm for the probabilistic inspection of damage (RAPID) was proposed, where the signal difference coefficient was replaced by the CI to visualise damage location. The experimental results demonstrate the effectiveness of the proposed multimodal Lamb wave baseline-free damage detection method. [ABSTRACT FROM AUTHOR]

In this work, we analyse the class of strictly pseudocontractive mappings in general metric spaces by providing a comprehensive and appropriate definition of a strictly pseudocontractive mapping, which serves as a natural extension of the existing notion. Moreover, we establish its various characterizations and explore several significant properties of these mappings in relation to fixed point theory in CAT(0) spaces. Specifically, we establish that these mappings are Lipschitz continuous, satisfying the demiclosedness-type property, and possessing a closed convex fixed point set. Furthermore, we show that the fixed points of the mappings can be effectively approximated using an iterative scheme for fixed points of nonexpansive mappings. The results in this work contribute to a deeper understanding of strictly pseudocontractive mappings and their applicability in the context of fixed point theory in metric spaces. [ABSTRACT FROM AUTHOR]

This paper addresses the optimal control problem with sparse controls of a Timoshenko beam, its numerical approximation using the finite element method, and the numerical solution via nonsmooth methods. Incorporating sparsity‐promoting terms in the cost function is practically useful for beam vibration models and results in the localization of the control action that facilitates the placement of actuators or control devices. We consider two types of sparsity‐inducing penalizers: the L1$$ {L}^1 $$‐norm and the L0$$ {L}^0 $$‐penalizer, which measures function support. We analyze discretized problems utilizing linear finite elements with a locking‐free scheme to approximate the states and adjoint states. We confirm that this approximation has the looking‐free property required to achieve a linear convergence linear order of approximation for L1$$ {L}^1 $$ control case and depending on the set of switching points in the L0$$ {L}^0 $$ controls. This is similar to the purely L2$$ {L}^2 $$‐norm penalized optimal control, where the order of approximation is independent of the thickness of the beam. [ABSTRACT FROM AUTHOR]

This paper proposes a novel graphical approach to control the liquid levels of the different variable area coupled tank systems using a decentralized H∞$$ {H}_{\infty } $$ controller. The coupled tank systems are common benchmark systems that consist of two tanks interconnected with each other. The primary goal is to maintain the liquid level in the tank at the desired set point by controlling the flow rate. This is attained with a decentralized method wherein the controller values are obtained from the KP,KI$$ {\mathcal{K}}_{\mathcal{P}},{\mathcal{K}}_{\mathcal{I}} $$ plane. Besides, the H∞$$ {H}_{\infty } $$ robust criteria ||UT(jω)F(jω)||∞≤1$$ {\left\Vert {\mathcal{U}}_{\mathcal{T}}\left(j\omega \right)\mathcal{F}\left(j\omega \right)\right\Vert}_{\infty}\le 1 $$ is enforced to guarantee the robustness. The proposed controller design approach aims to improve the performance of the system in terms of disturbance rejection and tracking. The decentralized control structure uses a distributed control strategy, thereby reducing the computational load which leads to improving the control performance. The loop interactions are minimized with decouplers. Furthermore, first‐order plus dead‐time (FOPDT) models are derived for each of the decoupled subsystems. Besides, the servo and regulatory responses of the controller are verified with input and output disturbances. Additionally, the response of the controller to system uncertainties and parameter variations is also studied. The simulation results demonstrate the effectiveness and robustness of the proposed approach. [ABSTRACT FROM AUTHOR]

The recently proposed semantic-aligned matching detection transformer (SAM–DETR model) accelerates the convergence of the detection transformer (DETR) by mapping object queries into an identical embedding space as the encoder's output feature map. However, SAM–DETR model has the problem of low detection accuracy compared to other DETR variants. We observe that the lower detection accuracy of SAM–DETR model is caused by the insufficient number of sample points and the inaccurate localization of the sample points during re-sampling, which blurs the generated attention map. This paper proposes an object detector based on a feature correction and double sampling DETR (FCDS-DETR) to solve this problem. FCDS-DETR takes SAM–DETR model as a baseline and builds on it by adding a feature correction module and a double sampling mechanism to achieve further improvement in detection accuracy with a limited number of additional parameters without sacrificing convergence speed. Firstly, FCDS-DETR improves the sampling point localization accuracy by adding a feature correction module to model the inter-channel dependence of the feature maps to be sampled. Secondly, the number of sampled points is increased by the double sampling mechanism, and attention fusion is used to fuse the attention weight maps corresponding to the two sets of sampled points to improve the recognizability of the attention weight maps. The experimental results show that the average precision is improved by +0.7 on the COCO dataset compared with the SAM–DETR model, and the number of parameters is increased by only 10.34 % , which improves the detection performance of the model very well. [ABSTRACT FROM AUTHOR]

Understanding elevation changes on the Tibetan Plateau is crucial to comprehend the changes in topography, landscape, climate, environmental conditions, and water resources. However, some of the current products that track elevation changes only cover specific surface types or limited areas, and others have low spatial resolution. We propose an algorithm to extract ICESat-2 crossover points dataset for the Tibetan Plateau, and form a dataset. The crossover points dataset has a density of 2.015 groups/km², and each group of crossover points indicates the amount of change in elevation before and after a period of time over an area of approximately 17 meters in diameter. Comparing ICESat-2 crossover points data with existing studies on glaciers and lakes, we demonstrated the reliability of the derived elevation changes. The ICESat-2 crossover points provide a refined data source for understanding high-spatial-resolution elevation changes on the Tibetan Plateau. This dataset can provide validation data for various studies that require high-precision or high-resolution elevation change data on the Tibetan Plateau. [ABSTRACT FROM AUTHOR]

As a city undergoes large-scale construction and expansion, there is an urgent need to monitor the stability of the ground and infrastructure. The time-series InSAR technique is an effective tool for measuring surface displacements. However, interpreting these displacements in a built environment, where observed displacements consist of mixed signals, poses a challenge. This study uses principal component analysis (PCA) and the k-means clustering method for exploring deformation series within an unsupervised learning context. The PCA method extracts the dominant components in deformation series, whereas the clustering method identifies similar deformation series. This method was tested on Kunming City (KMC) using C-band Sentinel-1, X-band TerraSAR-X, and L-band ALOS-2 PALSAR-2 data acquired between 2017 to 2022. The experiment demonstrated that the suggested unsupervised learning approach can group PS points with similar kinematic characteristics. Five types of deformation kinematic characteristics were discovered in the three SAR datasets: upward, slight upward, stability, slight downward, and downward. According to the results, less than 20% of points exhibit significant motion trends, whereas 50% show small velocity values but still demonstrate movement trends. The remaining 30% are relatively stable. Similar clustering results were obtained from the three datasets using unsupervised methods, highlighting the effectiveness of identifying spatial–temporal patterns over the study area. Moreover, It was found that clustering based on kinematic characteristics enhances the interpretation of InSAR deformation, particularly for points with small deformation velocities. Finally, the significance of PCA decomposition in interpreting InSAR deformation was discussed, as it can better represent series with noise, enabling their accurate identification. [ABSTRACT FROM AUTHOR]

Simple Summary: The volume of a pig, a new phenotype feature, can be used to estimate its weight due to its high correlation with body weight. The proportions of different body parts, such as the head and legs, can be determined through point cloud segmentation, providing new phenotype information for breeding pigs with smaller heads and stouter legs. However, due to the irregular shape and potential missing parts of the pig point cloud, it is challenging to form a closed surface for volume calculation. The study addresses this challenge by using an improved Poisson reconstruction algorithm, which provides smoother, more continuous, and complete reconstruction results, and its accuracy and reliability have been confirmed. The study also found that the correlation coefficient between pig body volume and weight was 0.95, indicating a strong relationship. This research could be valuable for improving the efficiency and accuracy of livestock weight estimation and breeding. Pig point cloud data can be used to digitally reconstruct surface features, calculate pig body volume and estimate pig body weight. Volume, as a pig novel phenotype feature, has the following functions: (a) It can be used to estimate livestock weight based on its high correlation with body weight. (b) The volume proportion of various body parts (such as head, legs, etc.) can be obtained through point cloud segmentation, and the new phenotype information can be utilized for breeding pigs with smaller head volumes and stouter legs. However, as the pig point cloud has an irregular shape and may be partially missing, it is difficult to form a closed loop surface for volume calculation. Considering the better water tightness of Poisson reconstruction, this article adopts an improved Poisson reconstruction algorithm to reconstruct pig body point clouds, making the reconstruction results smoother, more continuous, and more complete. In the present study, standard shape point clouds, a known-volume Stanford rabbit standard model, a measured volume piglet model, and 479 sets of pig point cloud data with known body weight were adopted to confirm the accuracy and reliability of the improved Poisson reconstruction and volume calculation algorithm. Among them, the relative error was 4% in the piglet model volume result. The average absolute error was 2.664 kg in the weight estimation obtained from pig volume by collecting pig point clouds, and the average relative error was 2.478%. Concurrently, it was determined that the correlation coefficient between pig body volume and pig body weight was 0.95. [ABSTRACT FROM AUTHOR]

Pour point depressant (PPD) is a crucial addition in the petroleum industry which can significantly enhance the flow properties of crude oil by preventing wax from precipitating out of it. The flow assurance effect of PPD on crude oil is impacted by its molecular structure. As a result, we concentrate on the PPD with various molecular structures, such as carboxyl and benzene rings, to investigate its impact on the flow behavior of crude oil. Then, FTIR and contact angle test were used to describe the characteristics of PPD (SAF-n and SAFS-m). The Karamay crude oil was tested using the following items: pour point, rheology, viscosity, viscoelasticity, and POM. When the crude oil was treated with 1000 ppm SAFS-1, the pour point decreased from 12 to −14 °C and the viscosity decreased from 40.1 to 6.3 pa·s at 0 °C. Meanwhile, the results show that the more variety polar groups PPD has, the more its dispersion increases and the stronger its interactions with crude oil are when its molar ratio of non-polar groups are suitable. These effects may be caused by the PPD changing the crystallization characteristics of wax and the aggregate state of resin and asphalt. [ABSTRACT FROM AUTHOR]

The wavefront reconstruction is a crucial step in determining the performance of wavefront detection instruments. The wavefront reconstruction algorithm is primarily evaluated in three dimensions: accuracy, speed, and noise immunity. In this paper, we propose a hybrid zonal reconstruction algorithm that introduces slope and curvature information in the diagonal, anti-diagonal, horizontal, and vertical directions by dividing the neighbor sampling points into subregions in groups of four. By canceling the same parameters in integration equations, an algorithm using multi-directional slope–curvature information is achieved with only two sets of integration equations in each subregion, reducing the processing time. Simulation experiments show that the relative root-mean-square reconstruction error of this algorithm is improved by about 4 orders of magnitude compared with existing algorithms that use multi-directional slope information or slope–curvature information alone. Compared with the hybrid multi-directional slope–curvature algorithm, the proposed algorithm can reduce computation time by about 50% as well as provide better noise immunity and reconstruction accuracy. Finally, the validity of the proposed algorithm is verified by the null test experiment. [ABSTRACT FROM AUTHOR]

The core and the Shapley value stand out as the most renowned solutions for addressing sharing problems in cooperative game theory. These concepts are widely acknowledged for their effectiveness in tackling negotiation, resource allocation, and power dynamics. The present study aims to extend various notions of cooperative games from the standard set N to a new class of cooperative games defined on the cartesian product N x N' (utilizing the specific coalition A * B). This extension encompasses fundamental concepts such as rationality, core, and Shapley value. The findings presented in this study demonstrate that the core concept as a solution yields a set of imputations without favoring any specific point within the set, in contrast to the Shapley value, which offers a singular solution. Moreover, the results confirm that the Shapley value satisfies the conditions defining the core of a game. Through both theoretical analysis and numerical findings, employing a practical example, it becomes evident that the Shapley value offers a more distinct solution to the sharing problem compared with the core solution. [ABSTRACT FROM AUTHOR]

Let φ be a function in the complex Sobolev space W ∗ (U) , where U is an open subset in ℂ k . We show that the complement of the set of Lebesgue points of φ is pluripolar. The key ingredient in our approach is to show that | φ | α for α ∈ [ 1 , 2) is locally bounded from above by a plurisubharmonic function. [ABSTRACT FROM AUTHOR]

The commonly used high utility itemsets mining method for massive data is the intelligent optimization algorithm. In this paper, the WHO (Whale-Hawk Optimization) algorithm is proposed by integrating the harris hawk optimization (HHO) algorithm with the beluga whale optimization (BWO) algorithm. Additionally, a whale initialization strategy based on good point set is proposed. This strategy helps to guide the search in the initial phase and increase the diversity of the population, which in turn improve the convergence speed and algorithm performance. By applying this improved algorithm to the field of high utility itemsets mining, it provides new solutions to optimization problems and data mining problems. To evaluate the performance of the proposed WHO, a large number of experiments are conducted on six datasets, chess, connect, mushroom, accidents, foodmart, and retail, in terms of convergence, recall rates, and runtime. The experimental results show that the convergence of the proposed WHO is optimal in five datasets and has the shortest runtime in all datasets. Compared to PSO, AF, BA, and GA, the average recall rate in the six datasets increased by 32.13%, 49.95%, 12.15%, and 16.24%, respectively. [ABSTRACT FROM AUTHOR]

Dendritic hydrogels based on carbosilane crosslinkers are promising drug delivery systems, as their amphiphilic nature improves the compatibility with poorly water-soluble drugs. In this work, we explored the impact of the complementary polymer on the amphiphilic properties of the dendritic network. Different polymers were selected as precursors, from the highly lipophilic propylene glycol (PPG) to the hydrophilic polyethylene glycol (PEG), including amphiphilic Pluronics L31, L35 and L61. The dithiol polymers reacted with carbosilane crosslinkers through UV-initiated thiol–ene coupling (TEC), and the resultant materials were classified as non-swelling networks (for PPG, PLUL31 and PLUL61) and high-swelling hydrogels (for PEG and PLUL35). The hydrogels exhibited thermo-responsive properties, shrinking at higher temperatures, and exhibited an intriguing drug release pattern due to internal nanostructuring. Furthermore, we fine-tuned the dendritic crosslinker, including hydroxyl and azide pendant groups in the focal point, generating functional networks that can be modified through degradable (ester) and non-degradable (triazol) bonds. Overall, this work highlighted the crucial role of the amphiphilic balance in the design of dendritic hydrogels with thermo-responsive behavior and confirmed their potential as functional networks for biomedical applications. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the novel concept of generalized distance denoted as J θ and call it an extended b-generalized pseudo-distance. With the help of this generalized distance, we define a generalized point to set distance J θ (u , H ★) , a generalized Hausdorff type distance and a P J θ -property of a pair (H ★ , K ★) of nonempty subsets of extended b-metric space (U ★ , ρ θ). Additionally, we establish several best proximity point theorems for multi-valued contraction mappings of Nadler type defined on b-metric spaces and extended b-metric spaces. Our findings generalize numerous existing results found in the literature. To substantiate the introduced notion and validate our main results, we provide some concrete examples. [ABSTRACT FROM AUTHOR]

We investigate the zero-error coding for computing problems with encoder side information. An encoder provides access to a source X and is furnished with side information g (Y) . It communicates with a decoder that possesses side information Y and aims to retrieve f (X , Y) with zero probability of error, where f and g are assumed to be deterministic functions. In previous work, we determined a condition that yields an analytic expression for the optimal rate R * (g) ; in particular, it covers the case where P X , Y is full support. In this article, we review this result and study the side information design problem, which consists of finding the best trade-offs between the quality of the encoder's side information g (Y) and R * (g) . We construct two greedy algorithms that give an achievable set of points in the side information design problem, based on partition refining and coarsening. One of them runs in polynomial time. [ABSTRACT FROM AUTHOR]

In this article we look at the geometric structure of the feet of an orthogonal Buekenhout–Metz unital 퓤 in PG(2, q2). We show that the feet of each point form a set of type (0, 1, 2, 4). Further, we discuss the structure of any 4-secants, and determine exactly when the feet form an arc. [ABSTRACT FROM AUTHOR]

The classical Ham Sandwich theorem states that any |$d$| point sets in |${\mathbb {R}}^{d}$| can be simultaneously bisected by a single affine hyperplane. A generalization of Dolnikov asserts that any |$d$| families of pairwise intersecting compact, convex sets in |${\mathbb {R}}^{d}$| admit a common hyperplane transversal. We extend Dolnikov's theorem by showing that families of compact convex sets satisfying more general non-disjointness conditions admit common transversals by multiple hyperplanes. In particular, these generalize all known optimal results to the long-standing Grünbaum–Hadwiger–Ramos measure equipartition problem in the case of two hyperplanes. Our proof proceeds by establishing topological Radon-type intersection theorems and then applying Gale duality in the linear setting. For a single hyperplane, this gives a new proof of Dolnikov's original result via Sarkaria's non-embedding criterion for simplicial complexes. [ABSTRACT FROM AUTHOR]

For the actual collected point cloud data, there are widespread challenges such as semantic inconsistency, density variations, and sparse spatial distribution. A network called PointMM is developed in this study to enhance the accuracy of point cloud semantic segmentation in complex scenes. The main contribution of PointMM involves two aspects: (1) Multi-spatial feature encoding. We leverage a novel feature encoding module to learn multi-spatial features from the neighborhood point set obtained by k-nearest neighbors (KNN) in the feature space. This enhances the network's ability to learn the spatial structures of various samples more finely and completely. (2) Multi-head attention pooling. We leverage a multi-head attention pooling module to address the limitations of symmetric function-based pooling, such as maximum and average pooling, in terms of losing detailed feature information. This is achieved by aggregating multi-spatial and attribute features of point clouds, thereby enhancing the network's ability to transmit information more comprehensively and accurately. Experiments on publicly available point cloud datasets S3DIS and ISPRS 3D Vaihingen demonstrate that PointMM effectively learns features at different levels, while improving the semantic segmentation accuracy of various objects. Compared to 12 state-of-the-art methods reported in the literature, PointMM outperforms the runner-up by 2.3% in OA on the ISPRS 3D Vaihingen dataset, and achieves the third best performance in both OA and MioU on the S3DIS dataset. Both achieve a satisfactory balance between OA, F1, and MioU. [ABSTRACT FROM AUTHOR]

In this article I map a set of points that could begin to tell the story of inertia's trajectory from physics and physiology to figurations of psychic life in Freudian psychoanalytic theory. Both preceding and contemporaneous with Freud's use of the concept of inertia to describe an element of psychic life, work was taking place in other intellectual and geographical contexts to translate this law of physics and physiology to a property of mental life. As a particular illustration of this, I examine a lecture given by British scientist Michael Faraday in 1818, wherein he makes the leap from the inertia of matter to 'mental inertia' and is arguably the first recorded thinker to do so in the English language. I then explore the use of the phrase 'psychic inertia' in 1900 by Scottish physiologist D.F. Harris and argue that Harris's work is not only emerging at the same time as Freud's discoveries, but that he prefigures Freud's ideas about the relationship between inertia and the death drive in interesting ways. The final part of the paper returns to sketch out Freud's engagement with the concept in several of his papers. [ABSTRACT FROM AUTHOR]

Effective point cloud denoising is critical in 3D plant phenotyping applications, which reduces interference in subsequent algorithms and improves the accuracy of plant phenotypes measurement. Deep learning-based point cloud denoising algorithms have shown excellent denoising performance on simple CAD models. However, these algorithms suffer from issues including over-smoothing or shrinkage and low efficiency when applied on density uneven, incomplete, various types of noise and complex plant point clouds. We proposed a plant point cloud denoising network (PDN) based on point cloud density gradient field learning, which can effectively address the challenges posed by plant point clouds. PDN consists of three main modules: point density feature (PDF) exception module, umbrella operator feature (UOF) computation module, and point density gradient (DG) estimation module. The performance of PDN was evaluated in experiments using point clouds of multiple plant species with noise of different types. Under different levels of Gaussian noise, our method achieved a relative performance improvement of 7.6%-19.3% compared to the state-of-the-art baseline methods, reaching state-of-the-art denoising performance. For noise of different types, the majority of our denoising results outperformed the baseline methods. In addition, our method was 0.5 and 8.6 times faster than the baseline methods when processing point clouds with low and high noise level, respectively. The good robustness, generalization, and computational efficacy of PDN are expected to facilitate the acquisition of high-precision 3D point clouds for various plant species, enhance the versatility of 3D phenotyping methods, improve the accuracy of the measurement of structural phenotypes, and increase the throughput of data processing, therefore facilitate the development of modern breeding research. The source code and the datasets used in this study is available on GitHub at https://github.com/suetme/PDN-plant-denoising-net. [ABSTRACT FROM AUTHOR]

In 2015, Haviv introduced the Remote set problem (RSP) and studied the complexity of the covering radius problem (CRP), which is a classical problem in lattices. The RSP aims to identify a set containing a point that is sufficiently distant from a given lattice L . It introduced a new method for analyzing the complexity of CRP. An open question in RSP is whether we can obtain the approximation factor γ = 1 / 2 . This paper investigates this question and proposes a probabilistic polynomial-time algorithm for RSP with an approximation factor of 1 / 2 - 1 / (c λ n (p)) , where c ∈ Z + and λ n (p) is the n-th successive minima in lattice under l p -norm. For a given lattice L with rank n and positive integer d, our algorithm outputs a set S of size d in polynomial time. This set S includes a point at least (1 2 - 1 c λ n (p) ) ρ (p) (L) from lattice L with a probability greater than 1 - 1 / 2 d . Here, c is a positive integer and ρ (p) (L) denotes the covering radius of L in l p -norm( 1 ≤ p ≤ ∞ ). Based on this, we obtain that GAPCRP 2 + 1 / 2 O (n) belongs to the complexity class coRP, and we provide new reductions from GAPCRP to GAPCVP. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to derive effective discrepancy estimates for the distribution of rational points on general semisimple algebraic group varieties, in general families of subsets and at arbitrarily small scales. We establish mean-square, almost sure and uniform estimates for the discrepancy with explicit error bounds. We also prove an analogue of W. Schmidt's theorem, which establishes effective almost sure asymptotic counting of rational solutions to Diophantine inequalities in the Euclidean space. We formulate and prove a version of it for rational points on the group variety, with an effective bound which in some instances can be expected to be the best possible. [ABSTRACT FROM AUTHOR]

The clustered and generalized vehicle routing problem (CGVRP) extends the well-known vehicle routing problem by grouping the demand points into multiple distinct zones, and within each zone, further separation is made by forming clusters. The objective of the CGVRP is to determine the optimal routes for a fleet of vehicles dispatched from a depot, visiting all zones within each cluster. This requires making two simultaneous optimization decisions. Firstly, each zone must be visited by exactly one node, and secondly, all zones within a cluster must be visited by the same vehicle. In this paper, we introduce two mixed-integer linear programming formulations for the CGVRP, aimed at solving a joint order batching and picker routing problem with alternative locations in a warehouse environment featuring mixed-shelves configuration. Both formulations are tested on three scenarios of randomly generated small- and medium-sized instances. Additionally, we propose a general rule approach for calculating a cost matrix in a rectangular environment. The results demonstrate the effectiveness of the proposed mathematical formulations in efficiently solving problems with up to 180 nodes. [ABSTRACT FROM AUTHOR]

Sparrow Search Algorithm (SSA) has recently received more attention in the intelligent optimization group. However, the high randomness and local optimal problems of the algorithm limit the application of the algorithm. In this paper, a novel sparrow search algorithm (NSSA) combined with spawning technology is proposed, which effectively improves the problem of the algorithm falling into local optimization. First of all, it is proposed to replace the traditional stochastic method with the good point set theory to find the initial individual, so that the initial population is more evenly distributed in the search space and improve the quality of the initial solution. Secondly, the spawning strategy of the cuckoo algorithm is integrated into the discoverer stage, which improves the search method of the discoverer and enhances the global search ability, which makes the algorithm avoids the sudden decline of population diversity and premature convergence. Finally, Levy flight and Brownian motion are used to disturb the position of the sparrow dimension by dimension to improve the ability of the algorithm to jump out of the local optimal value in subsequent iterations. By comparing and analyzing NSSA and SSA, DE, ALO, GOA, DOA, HSSA and XSSA algorithms in 12 common evaluation functions and CEC-2017 test functions, and apply NSSA to the TSP problem. The simulation results show the effectiveness and superiority of the proposed scheme. [ABSTRACT FROM AUTHOR]

We proceed with the current comprehension of asymptotic properties of multiclass support vector machine (MSVM) in high-dimensional, low-sample-size (HDLSS) settings. We show that MSVM is biased under HDLSS settings and point out inconsistency problems for MSVM. We propose a bias-corrected MSVM (BC-MSVM) which works well even for HDLSS data set. We give simulation studies and discuss the performance of the BC-MSVM. Finally, we evaluate the performance of the BC-MSVM using microarray data set. [ABSTRACT FROM AUTHOR]

A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of scattered points along with the corresponding classification algorithm to construct a representation of a decision curve by points with prescribed maximal distance to the true decision curve. Hereby, our algorithm ensures that the representing point set covers the decision curve in its entire extent and features local refinement based on the geometric properties of the decision curve. We demonstrate applications of our method to problems related to the detection of faults, to multi-criteria decision aid and, in combination with Kirsch's factorization method, to solving an inverse acoustic scattering problem. In all applications we considered in this work, our method requires significantly less pointwise classifications than previously employed algorithms. [ABSTRACT FROM AUTHOR]

We investigate for which metric spaces the performance of distance labeling and of ℓ ∞ -embeddings differ, and how significant can this difference be. Recall that a distance labeling is a distributed representation of distances in a metric space (X, d), where each point x ∈ X is assigned a succinct label, such that the distance between any two points x , y ∈ X can be approximated given only their labels. A highly structured special case is an embedding into ℓ ∞ , where each point x ∈ X is assigned a vector f(x) such that ‖ f (x) - f (y) ‖ ∞ is approximately d(x, y). The performance of a distance labeling or an ℓ ∞ -embedding is measured via its distortion and its label-size/dimension. We also study the analogous question for the prioritized versions of these two measures. Here, a priority order π = (x 1 , ⋯ , x n) of the point set X is given, and higher-priority points should have shorter labels. Formally, a distance labeling has prioritized label-size α (·) if every x j has label size at most α (j) . Similarly, an embedding f : X → ℓ ∞ has prioritized dimension α (·) if f (x j) is non-zero only in the first α (j) coordinates. In addition, we compare these prioritized measures to their classical (worst-case) versions. We answer these questions in several scenarios, uncovering a surprisingly diverse range of behaviors. First, in some cases labelings and embeddings have very similar worst-case performance, but in other cases there is a huge disparity. However in the prioritized setting, we most often find a strict separation between the performance of labelings and embeddings. And finally, when comparing the classical and prioritized settings, we find that the worst-case bound for label size often "translates" to a prioritized one, but also find a surprising exception to this rule. [ABSTRACT FROM AUTHOR]

We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in R d where the edge cost between two points is given by a pth power of their Euclidean distance. This includes e.g. the travelling salesperson problem and the bounded degree minimum spanning tree. We establish in particular almost sure convergence, as n grows, of a suitable renormalization of the random minimum cost, if the points are uniformly distributed and d ≥ 3 , 1 ≤ p < d . Previous results were limited to the range p < d / 2 . Our proofs are based on subadditivity methods and build upon new bounds for random instances of the Euclidean bipartite matching problem, obtained through its optimal transport relaxation and functional analytic techniques. [ABSTRACT FROM AUTHOR]

A CAT(0) space has rank at least n if every geodesic lies in an n-flat. Ballmann's Higher Rank Rigidity Conjecture predicts that a CAT(0) space of rank at least 2 with a geometric group action is rigid – isometric to a Riemannian symmetric space, a Euclidean building, or splits as a metric product. This paper is the first in a series motivated by Ballmann's conjecture. Here we prove that a CAT(0) space of rank at least n≥2 is rigid if it contains a periodic n-flat and its Tits boundary has dimension (n−1). This does not require a geometric group action. The result relies essentially on the study of flats which do not bound flat half-spaces – so-called Morse flats. We show that the Tits boundary ∂TF of a periodic Morse n-flat F contains a regular point – a point with a Tits-neighborhood entirely contained in ∂TF. More precisely, we show that the set of singular points in ∂TF can be covered by finitely many round spheres of positive codimension. [ABSTRACT FROM AUTHOR]

We classify Chabauty limits of groups fixed by various (abstract) involutions over SL (2 , F) , where F is a finite field-extension of Q p , with p ≠ 2 . To do so, we first classify abstract involutions over SL (2 , F) with F a quadratic extension of Q p , and prove p-adic polar decompositions with respect to various subgroups of p-adic SL 2 . Then we classify Chabauty limits of: SL (2 , F) ⊂ SL (2 , E) where E is a quadratic extension of F, of SL (2 , R) ⊂ SL (2 , C) , and of H θ ⊂ SL (2 , F) , where H θ is the fixed point group of an F-involution θ over SL (2 , F) . [ABSTRACT FROM AUTHOR]

This paper attempts to prove the Lipschitz continuity of the resolvent operator associated with a (P , η) -accretive mapping and compute an estimate of its Lipschitz constant. This is done under some new appropriate conditions that are imposed on the parameter and mappings involved in it; with the goal of approximating a common element of the solution set of a system of generalized variational-like inclusions and the fixed point set of a total asymptotically nonexpansive mapping in the framework of real Banach spaces. A new iterative algorithm based on the resolvent operator technique is proposed. Under suitable conditions, we prove the strong convergence of the sequence generated by our proposed iterative algorithm to a common element of the two sets mentioned above. The final section is dedicated to investigating and analyzing the notion of a generalized H(.,.)-accretive mapping introduced and studied by Kazmi et al. (Appl Math Comput 217:9679–9688, 2011). In this section, we provide some comments based on the relevant results presented in their work. [ABSTRACT FROM AUTHOR]