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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]

A number field K is primitive if K and Q are the only subextensions of K. Let C be a curve defined over Q . We call an algebraic point P ∈ C (Q ¯) primitive if the number field Q (P) is primitive. We present several sets of sufficient conditions for a curve C to have finitely many primitive points of a given degree d. For example, let C / Q be a hyperelliptic curve of genus g, and let 3 ≤ d ≤ g - 1 . Suppose that the Jacobian J of C is simple. We show that C has only finitely many primitive degree d points, and in particular it has only finitely many degree d points with Galois group S d or A d . However, for any even d ≥ 4 , a hyperelliptic curve C / Q has infinitely many imprimitive degree d points whose Galois group is a subgroup of S 2 ≀ S d / 2 . [ABSTRACT FROM AUTHOR]

We prove new upper bounds on the smallest size of affine blocking sets, that is, sets of points in a finite affine space that intersect every affine subspace of a fixed codimension. We show an equivalence between affine blocking sets with respect to codimension‐2 subspaces that are generated by taking a union of lines through the origin, and strong blocking sets in the corresponding projective space, which in turn are equivalent to minimal codes. Using this equivalence, we improve the current best upper bounds on the smallest size of a strong blocking set in finite projective spaces over fields of size at least 3. Furthermore, using coding theoretic techniques, we improve the current best lower bounds on a strong blocking set. Our main motivation for these new bounds is their application to trifferent codes, which are sets of ternary codes of length n$n$ with the property that for any three distinct codewords there is a coordinate where they all have distinct values. Over the finite field F3$\mathbb {F}_3$, we prove that minimal codes are equivalent to linear trifferent codes. Using this equivalence, we show that any linear trifferent code of length n$n$ has size at most 3n/4.55$3^{n/4.55}$, improving the recent upper bound of Pohoata and Zakharov. Moreover, we show the existence of linear trifferent codes of length n$n$ and size at least 139/5n/4$\frac{1}{3}{\left(9/5 \right)}^{n/4}$, thus (asymptotically) matching the best lower bound on trifferent codes. We also give explicit constructions of affine blocking sets with respect to codimension‐2 subspaces that are a constant factor bigger than the best known lower bound. By restricting to F3$\mathbb {F}_3$, we obtain linear trifferent codes of size at least 323n/312$3^{23n/312}$, improving the current best explicit construction that has size 3n/112$3^{n/112}$. [ABSTRACT FROM AUTHOR]

Let G be the complete Euclidean graph on a set of points embedded in the plane. Given a constant t > 1 , a spanning subgraph G ′ of G is said to be a t -spanner, or simply a spanner, if for any pair of nodes p , q in G there exists a t -path in G ′ , i.e., a path between p and q whose length is at most t times their distance in G. Gap-greedy spanner, proposed by Arya and Smid, is a light weight and bounded degree spanner in which a pair of points p , q is guaranteed to have a t -path, if there exists at least one edge with some special criteria in the spanner. Existing algorithms for computing the gap-greedy spanner determine the existence of such an edge for each pair of points by examining the edges of the spanner, which takes O (n) time, however in this paper, we have presented a method by which this task can be done in O (1) time. Using the proposed method and well-separated pair decomposition, we have proposed a linear-space algorithm that can compute the gap-greedy spanner in O (n 2) time. How to use the well-separated pair decomposition to compute this spanner was proposed by Bakhshesh and Farshi, however using an example, we have shown that one of the algorithms they have proposed for this purpose is incorrect. We have performed various experiments to measure the duration and amount of memory used by the algorithms for computing this spanner. The results of these experiments showed that the proposed method, without a significant effect on the amount of memory consumed compared to previous algorithms, leads to a significant acceleration in the construction time of this spanner. [ABSTRACT FROM AUTHOR]

Currently, the digitization of environment objects (vegetation, terrain, architectural structures, etc.) in the form of point clouds is actively being developed. The integration of such digitized objects into virtual environment systems allows the quality of the modeled environment to be improved, but requires efficient methods and algorithms for real-time visualization of large point volumes. In this paper the solution of this task on modern multicore GPUs with support of hardware-accelerated ray tracing is researched. A modified method is proposed where the original unordered point cloud is split up into point groups whose visualization is effectively parallelized on ray tracing cores. The paper describes an algorithm for constructing such groups using swapping arrays of point indices, which works faster than alternative solutions based on linked lists, and also has lower memory overhead. The proposed method and algorithm were implemented in point cloud visualization software complex and approbated on a number of digitized environment objects. The results of the approbation confirmed the efficiency of proposed solutions as well as their applicability for virtual environment systems, video simulators, geoinformation systems, virtual laboratories, etc. [ABSTRACT FROM AUTHOR]

Diffusion models have been successfully applied to point cloud generation tasks recently. The main notion is using a forward process to progressively add noises into point clouds and then use a reverse process to generate point clouds by denoising these noises. However, since point cloud data is high-dimensional and exhibits complex structures, it is challenging to adequately capture the surface distribution of point clouds. Moreover, point cloud generation methods often resort to sampling methods and local operations to extract features, which inevitably ignores the global structures and overall shapes of point clouds. To address these limitations, we propose a latent diffusion model based on Transformers for point cloud generation. Instead of directly building a diffusion process based on the points, we first propose a latent compressor to convert original point clouds into a set of latent tokens before feeding them into diffusion models. Converting point clouds as latent tokens not only improves expressiveness, but also exhibits better flexibility since they can adapt to various downstream tasks. We carefully design the latent compressor based on an attention-based auto-encoder architecture to capture global structures in point clouds. Then, we propose to use transformers as the backbones of the latent diffusion module to maintain global structures. The powerful feature extraction ability of transformers guarantees the high quality and smoothness of generated point clouds. Experiments show that our method achieves superior performance in both unconditional generation on ShapeNet and multi-modal point cloud completion on ShapeNet-ViPC. Our code and samples are publicly available at https://github.com/Negai-98/LDT. [ABSTRACT FROM AUTHOR]

Combining the Lagrange multiplier method, the Uzawa algorithm, and the least square progressive and iterative approximation (LSPIA), we proposed the constrained least square progressive and iterative approximation (CLSPIA) to solve the problem of B-spline curve and surface fitting with constraint on data interpolation, i.e., computing the control points of a B-spline curve or surface which interpolates one set of input points while approximating the other set of given points. Compared with the method of solving the linear system directly, CLSPIA has some advantages as it inherits all the nice properties of LSPIA. Because of the data reuse property of LSPIA, CLSPIA reduces a great amount of computation. Using the local property of LSPIA, we can get shape preserving fitting curves by CLSPIA. CLSPIA is efficient for fitting large-scale data sets due to the fact that its computational complexity is linear to the scale of the input data. The many numerical examples in this paper show the efficiency and effectiveness of CLSPIA. [ABSTRACT FROM AUTHOR]

The registration performance determines the widespread indoor application of 3D models acquired by depth sensors. Many advanced registration methods lack comprehensive feature aggregation and poor generalization capabilities, which improves the mismatching ratio. Here, a dual graph network is proposed by incorporating irregular shape factors to make point cloud features more expressive. At first, we transform point cloud sets into the stellar graph within the local neighbourhood of each point. The deep feature and shape factor of each point are combined in the directional‐connected irregular projection space. Subsequently, the combined features are modelled as the second graph. By the attention mechanism computation, feature information is continuously aggregated with intra‐graph and inter‐graph. Finally, a loss function is utilized to confirm point correspondence and perform the registration through singular value decomposition. Extensive experiments validate that the proposed point cloud registration method achieves state‐of‐the‐art performance. [ABSTRACT FROM AUTHOR]

This text explores the relationship between mathematicians Georg Cantor and Richard Dedekind and their differing perspectives on set theory. Cantor saw sets as vast and infinite, while Dedekind viewed them as closed and finite. Cantor sought Dedekind's support for his ideas on inconsistent sets, but Dedekind was not interested. Cantor's mental health declined, and he sought a position outside of academia. Despite their differences, both mathematicians made important contributions to the field of set theory. [Extracted from the article]

To tackle the issue of lack of semantic consistency between ground and non-ground points, as well as the damage to the integrity of terrain boundary information during network downsampling, we developed a Semantic Consistency-Convolutional Neural Network (SC-CNN) to improve the precision of point cloud filtering under complex terrain conditions. The novel aspects include: (1) farthest point sampling (FPS) with slope constraints, which enhances terrain contour preservation through adaptive subblock partitioning and slope-based sampling; (2) intra-class feature enhancement via copula correlation and attention mechanisms, improving the network's ability to distinguish between ground and non-ground points by focusing on intra-class feature consistency and inter-class differences; and (3) filter error correction using copula correlation and confidence intervals. refining filtering accuracy by adjusting for negatively correlated point sets. Tested on the ISPRS and 3D Vaihingen datasets, SC-CNN notably outperformed existing methods, reducing the mean total error (MT.E) by 0.17% and 1.93%, respectively, thereby significantly enhancing point-cloud filtering accuracy under complex terrain conditions. [ABSTRACT FROM AUTHOR]

In this article, we discuss the relation theoretic aspects of multivalued weakly contractive mappings to prove fixed point results in the setting of metric spaces endowed with a certain binary relation. Our newly proved results generalize, extend, unify, enrich, sharpen and improve some well-known fixed point theorems of existing literature to the case of multivalued and contractive notion. We also incorporated an example and an application to find the solution of a Volterra-type integral inclusion. [ABSTRACT FROM AUTHOR]

In this paper, we study some Krasnoselskii-Mann type dynamical systems in solving fixed point problems. The first one can be regarded as a continuous version of the Krasnoselskii-Mann iterations. We prove that the solution of this dynamical system converges weakly to a fixed point of the involving mapping. Next, we focus our attention on a regularized Krasnoselskii-Mann type dynamical system. Besides proving existence and uniqueness of strong global solutions, we show that the generated trajectories converge strongly to a unique solution of a variational inequality over the fixed point set. Also, we provide a convergence rate analysis for the regularized dynamical system. [ABSTRACT FROM AUTHOR]

The complex projective plane ℂ P 2 contains certain Lagrangian CW-complexes called pinwheels, which have interesting rigidity properties related to solutions of the Markov equation, see for example [J. Evans and I. Smith, Markov numbers and Lagrangian cell complexes in the complex projective plane, Geom. Topol. 22 (2018) 1143–1180]. We compute the Gromov width of the complement of pinwheels and show that it is strictly smaller than the Gromov width of ℂ P 2 , meaning that pinwheels are Lagrangian barriers in the sense of [P. Biran, Lagrangian barriers and symplectic embeddings, Geom. Funct. Anal. 11 (2001) 407–464]. The accumulation points of the set of these Gromov widths are in a simple bijection with the Lagrange spectrum below 3. [ABSTRACT FROM AUTHOR]

The vector information of mountainous roads is great significance, including regional economics, emergency response, disaster management, among others. Nevertheless, there are irregular deformations in existing vector data, coupled with incomplete extraction results for mountainous roadways. These issues pose challenges in establishing a matching model between road extraction results and existing vector data, significantly reducing the efficiency of automated updates for the current vector data. Targeting roads as a distinct artificial feature and leveraging their topological connectivity, we propose a vector data updating method based on matching point pair grouping. Firstly, we employ the SDUNet model to extract mountainous road and utilize the Superglue model to match road binary images with vector binary images, resulting in sets of initial matching point pairs. Subsequently, we propose a road line extraction model that groups matching point pairs, eliminates misaligned pairs based on road topological connectivity, and establishes a mapping relationship between road lines and vector lines. Ultimately, through road line optimization and vector line optimization methods, we accomplish the automatic updating of vector data for mountainous roadways. Through a comprehensive analysis of over 2600 vector data, our method demonstrates substantial advantages in terms of both F1 and IoU compared to alternative methods. [ABSTRACT FROM AUTHOR]

Classical jittered sampling partitions [ 0 , 1 ] d into m d cubes for a positive integer m and randomly places a point inside each of them, providing a point set of size N = m d with small discrepancy. The aim of this note is to provide a construction of partitions that works for arbitrary N and improves straight-forward constructions. We show how to construct equivolume partitions of the d-dimensional unit cube with hyperplanes that are orthogonal to the main diagonal of the cube. We investigate the discrepancy of such point sets and optimise the expected discrepancy numerically by relaxing the equivolume constraint using different black-box optimisation techniques. [ABSTRACT FROM AUTHOR]

For a nonautonomous stochastic discrete plate equation driven by multiplicative noise, we prove the unique existence of a pullback random attractor, which is a family of pullback‐attracting random compact sets parameterized by time and samples. We then establish the residual dense continuity of the pullback random attractor on the time‐sample plane with respect to the Hausdorff metric. Even without the Cantor continuum hypothesis, we show that the set of all points of continuity of the pullback random attractor is an uncountable set with the continuity cardinality. These results explain both nonexplosive and nonimplosive phenomena for the random plate lattice system. [ABSTRACT FROM AUTHOR]

Building Information Modeling (BIM) data has the advantages of high quality, operability, and parametric capabilities. In recent years, the application of BIM in construction planning for building robots has been increasing. Task planning for rebar binding is an important aspect of construction, and there is a growing trend of using robots to improve the accuracy and efficiency of binding operations. However, the complex and dynamic construction site environment poses significant challenges for task planning in rebar binding. Therefore, this paper proposes a new BIM-based task planning method for a wheeled-legged rebar binding robot, which can quickly generate an optimal task sequence. Firstly, an initial set of rebar intersection points is generated based on BIM data. Then, considering the execution dead zone of the robot and the variable workspace of the binding mechanism, the rebar intersection points set is decomposed and filtered using morphological opening operations. Finally, a constrained genetic algorithm is employed to sort the set of task points. Simulation and real-world experiments were conducted using a wheeled-legged rebar binding robot as the research subject. The results demonstrate that, compared to manual planning, the average binding efficiency is approximately 1500 points per hour, which is 1.97 times higher than manual operation. This validates the applicability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this study, a diffusion operator is investigated on a star graph with nonhomogeneous edges. First, the behaviors of sufficiently large eigenvalues are learned, and then the solution of the inverse problem is given to determine the potential functions and parameters of the boundary condition on the star graph with the help of a dense set of nodal points and to obtain a constructive solution to the inverse problems of this class. [ABSTRACT FROM AUTHOR]

We present data and analysis of a set of balloon‐borne sounding profiles, which includes co‐located O3, CO, CH4, and particles, over the northern Tibetan Plateau during an Asian summer monsoon (ASM) season. These novel measurements shed light on the ASM transport behavior near the northern edge of the anticyclone. Joint analyses of these species with the temperature and wind profiles and supported by back trajectory modeling identify three distinct transport processes that dominate the vertical chemical structure in the middle troposphere, upper troposphere (UT), and the tropopause region. The correlated changes in profile structures in the middle troposphere highlight the influence of the strong westerly jet. Elevated constituent concentrations in the UT identify the main level of convective transport at the upstream source regions. Observed higher altitude maxima for CH4 characterize the airmasses' continued ascent following convection. These data complement constituent observations from other parts of the ASM anticyclone. Plain Language Summary: Asian summer monsoon deep convection transports surface pollutants to the stratosphere. Although satellite data have provided clear evidence of this transport, in situ measurements are critical for characterizing how monsoon is vertically re‐distributing the regional emissions. We report new balloon‐borne measurements over the Tibetan Plateau that provide a unique data set on the northern edge of the anticyclone, complementing other observations. Key Points: A novel set of in‐situ profile measurements of O3, CO, CH4 and particles from Tibetan Plateau during Asian summer monsoon are presentedJoint analyses of the profiles provide insights into transport processes controlling the northern edge of the Asian monsoon anticycloneObserved CO profile maxima at 13–14 km (∼360–370 K) identify the level of convective transport at the upstream source regions [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]

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]

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]

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]

Building on work of Ruelle and Putnam in the Smale space case, Thomsen defined the homoclinic and heteroclinic C^\ast-algebras for an expansive dynamical system. In this paper we define a class of expansive dynamical systems, called synchronizing dynamical systems, that exhibit hyperbolic behavior almost everywhere. Synchronizing dynamical systems generalize Smale spaces (and even finitely presented systems). Yet they still have desirable dynamical properties such as having a dense set of periodic points. We study various C^\ast-algebras associated with a synchronizing dynamical system. Among other results, we show that the homoclinic algebra of a synchronizing system contains an ideal which behaves like the homoclinic algebra of a Smale space. [ABSTRACT FROM AUTHOR]

For a set Q of points in the plane and a real number δ ≥ 0 , let G δ (Q) be the graph defined on Q by connecting each pair of points at distance at most δ .We consider the connectivity of G δ (Q) in the best scenario when the location of a few of the points is uncertain, but we know for each uncertain point a line segment that contains it. More precisely, we consider the following optimization problem: given a set P of n - k points in the plane and a set S of k line segments in the plane, find the minimum δ ≥ 0 with the property that we can select one point p s ∈ s for each segment s ∈ S and the corresponding graph G δ (P ∪ { p s ∣ s ∈ S }) is connected. It is known that the problem is NP-hard. We provide an algorithm to exactly compute an optimal solution in O (f (k) n log n) time, for a computable function f (·) . This implies that the problem is FPT when parameterized by k. The best previous algorithm uses O ((k !) k k k + 1 · n 2 k) time and computes the solution up to fixed precision. [ABSTRACT FROM AUTHOR]

The centred simplex gradient (CSG) is a popular gradient approximation technique in derivative-free optimization. Its computation requires a perfectly symmetric set of sample points and is known to provide an accuracy of |$\mathcal {O}(\varDelta ^2)$|⁠ , where |$\varDelta $| is the radius of the sampling set. In this paper, we consider the situation where the set of sample points is not perfectly symmetric. By adapting the formula for the CSG to compensate for the misaligned points, we define a new Adapted-CSG. We study the error bounds and the numerical stability of the Adapted-CSG. We also present numerical examples to demonstrate its properties relative to each new parameter and make a comparison to an alternative method. [ABSTRACT FROM AUTHOR]

We show that independent and uniformly distributed sampling points are asymptotically as good as optimal sampling points for the approximation of functions from Sobolev spaces |$W_p^s(\varOmega)$| on bounded convex domains |$\varOmega \subset{\mathbb{R}}^d$| in the |$L_q$| -norm if |$q

To tackle the problem of the brain storm optimization (BSO) algorithm's suboptimal capability for avoiding local optima, which contributes to its inadequate optimization precision, we developed a flock decision mutation approach that substantially enhances the efficacy of the BSO algorithm. Furthermore, to solve the problem of insufficient BSO algorithm population diversity, we introduced a strategy that utilizes the good point set to enhance the initial population's quality. Simultaneously, we substituted the K-means clustering approach with spectral clustering to improve the clustering accuracy of the algorithm. This work introduced an enhanced version of the brain storm optimization algorithm founded on a flock decision mutation strategy (FDIBSO). The improved algorithm was compared against contemporary leading algorithms through the CEC2018. The experimental section additionally employs the AUV intelligence evaluation as an application case. It addresses the combined weight model under various dimensional settings to substantiate the efficacy of the FDIBSO algorithm further. The findings indicate that FDIBSO surpasses BSO and other enhanced algorithms for addressing intricate optimization challenges. [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]

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]

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]

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]

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]

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]

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]

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 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]

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]

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]

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]

The Tukey (or halfspace) depth extends nonparametric methods toward multivariate data. The multivariate analogues of the quantiles are the central regions of the Tukey depth, defined as sets of points in the d-dimensional space whose Tukey depth exceeds given thresholds k. We address the problem of fast and exact computation of those central regions. First, we analyze an efficient Algorithm (A) from Liu, Mosler, and Mozharovskyi, and prove that it yields exact results in dimension d = 2, or for a low threshold k in arbitrary dimension. We provide examples where Algorithm (A) fails to recover the exact Tukey depth region for d > 2, and propose a modification that is guaranteed to be exact. We express the problem of computing the exact central region in its dual formulation, and use that viewpoint to demonstrate that further substantial improvements to our algorithm are unlikely. An efficient C++ implementation of our exact algorithm is freely available in the R package TukeyRegion. [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]

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]

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]