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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]

Intersection polygons are an important component of road data. To address the challenge of extracting the microstructure of roads, we propose a method of extracting intersection polygons based on centerline junctions. The method involves the following steps: (1) topological preprocessing of the road centerline to extract dangling nodes and converting road polygon data into line rings, (2) matching the nearest line ring within a certain threshold range of dangling nodes to obtain splitting points, (3) calculating the set of splitting points associated with the line rings and dividing the line rings to obtain boundary arcs, (4) extracting the boundary arcs associated with the current intersection from the intersection nodes of the road centerline, and (5) calculating the primary nearest point set and the secondary nearest point set in turn, and using the secondary nearest point set to extract the resulting intersection polygons. Experimental results indicate that the method can effectively generate the required intersection polygons at road intersections. [ABSTRACT FROM AUTHOR]

Objective: To evaluate the adjunctive use of the probiotic Bifidobacterium animalis subsp. lactis HN019 (B. lactis HN019) to conventional therapy on clinical and microbiological parameters in patients with generalized gingivitis. Methods: Sixty systemically healthy individuals with untreated generalized gingivitis were submitted to periodontal therapy and allocated to receive Placebo (n = 30) or Probiotic (n = 30) lozenges, twice a day for 8 weeks. Bleeding on Marginal Probing (BOMP) was evaluated at baseline, after 2 and 8 weeks. Supra and subgingival biofilm were obtained at baseline and 8 weeks post-therapy for analyses by 16S rRNA gene sequencing. Differences between therapeutic groups were analyzed by non-parametric tests (p<0.05). Results: The Placebo and Probiotic groups showed a significant reduction in BOMP at 8 weeks compared to baseline (p<0.05). The Probiotic group had a lower percentage of BOMP when compared with the Placebo group at 8 weeks (p<0.0001). Alpha and beta-diversity showed no statistical significance between groups and time points. At phylum level, no significant differences were observed between groups and time points. At genus level, an increase in the relative abundances of Bergeyella and Corynebacterium were significantly associated with a greater reduction in bleeding in the Placebo group and with less reduction in bleeding in the Probiotic group, respectively. At species level, Schaalia spp., Streptococcus gordonii, and Leptotrichia wadei increased in Placebo and decreased in the Probiotic group after treatment. Granulicatella adiacens decreased significantly after the probiotic therapy, while Saccharibacteria (TM7) spp., Solobacterium moorei, and Catonella morbi increased significantly. In the Placebo group, Bergeyella sp. HMT-322 was associated with a greater percentage of reduction in bleeding. In both groups, Actinomyces species were related to less reduction in bleeding. Conclusion: The adjuvant use of B. lactis HN019 alongside conventional therapy enhanced the reduction in BOMP and promoted greater changes in the microbiological profile of patients with generalized gingivitis. Trial registration: The study was registered at Brazilian Clinical Trials Registry (ReBEC; protocol number: RBR-59v2yb). [ABSTRACT FROM AUTHOR]

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Chambert-Loir and Tschinkel constructed a framework for a geometric interpretation of the density of integral points on certain varieties, which was refined by Wilsch. By using harmonic analysis and the circle method, it was proved for some partial equivariant compactifications of vector groups over arbitrary number fields and high-dimensional complete intersections over Q . Further, there are some examples of using the torsor method for singular del Pezzo surfaces over Q . In this paper, we generalise the torsor method for integral points from Q to imaginary quadratic number fields. As a first representative example, we characterise integral points of bounded log-anticanonical height on a quartic del Pezzo surface of singularity type A 3 over imaginary quadratic fields with respect to its singularity and its lines. Furthermore, we count these integral points of bounded height by using universal torsors and interpret the count geometrically to prove an analogue of Manin's conjecture for the set of integral points with respect to the singularity and to a line. Our results coincide with the predicted framework. [ABSTRACT FROM AUTHOR]

Purpose: The objective of the current pilot trial was to evaluate whether ghost ileostomy is a safe alternative to the current standard of care in terms of a conventional loop ileostomy in patients undergoing low anterior resection with total mesorectal excision (LAR/TME) for rectal cancer. Methods: This randomized controlled pilot trial included patients undergoing LAR/TME, randomly assigning them to ghost ileostomy or conventional loop ileostomy intraoperatively. Follow-up spanned 6 months, evaluating the following endpoints: comprehensive complication index (CCI), postoperative morbidity, transformation of ghost ileostomy, presence of ostomy at 6 months, Wexner score, and quality of life (EORTC QLQ-C30 & CR29). Exploratory statistical analysis based on the intention-to-treat principle was conducted. Results: Recruiting 30 patients from May 2018 to September 2022, the trial was prematurely stopped due to slow recruitment. The mean CCI was comparable between groups at any point of time (at 6 months: 30.7 vs. 29.7, p = 0.889). There was no mortality and no need for creation of a terminal ostomy. Anastomotic leakage rates were similar in ghost ileostomy and loop ileostomy groups (p > 0.99). The ghost ileostomy was converted into a conventional loop ileostomy in 6 of 15 (40.0%) patients. Neither postoperative function, nor the overall quality of life showed significant differences. Conclusion: Ghost ileostomy appears as a viable and safe option for selectively deciding ileostomy creation in LAR/TME for rectal cancer. However, challenges in patient selection, excluding those at high risk for anastomotic leakage, limit widespread application and call for optimization in future research. Trial-registration: German Clinical Trials Register (https://drks.de/): DRKS00013997; date of registration: April 9th 2018. [ABSTRACT FROM AUTHOR]

With the continuous progress of information acquisition technology, the volume of LiDAR point cloud data is also expanding rapidly, which greatly hinders the subsequent point cloud processing and engineering applications. In this study, we propose a point cloud simplification strategy utilizing probabilistic membership to address this challenge. The methodology initially develops a feature extraction scheme based on curvature to identify the set of feature points. Subsequently, a combination of k-means clustering and Possibilistic C-Means is employed to partition the point cloud into subsets, and to simultaneously acquire the probabilistic membership information of the point cloud. This information is then utilized to establish a rational and efficient simplification scheme. Finally, the simplification results of the feature point set and the remaining point set are merged to obtain the ultimate simplification outcome. This simplification method not only effectively preserves the features of the point cloud while maintaining uniformity in the simplified results but also offers flexibility in balancing feature retention and the degree of simplification. Through comprehensive comparative analysis across multiple point cloud models and benchmarking against various simplification methods, the proposed approach demonstrates superior performance. Finally, the proposed algorithm was critically discussed in light of the experimental results. [ABSTRACT FROM AUTHOR]

AbstractIdeal point estimation methods in the social sciences lack a principled approach for identifying multidimensional ideal points. We present a novel method for estimating multidimensional ideal points based on ℓ1 distance. In the Bayesian framework, the use of ℓ1 distance transforms the invariance problem of infinite rotational turns into the signed perpendicular problem, yielding posterior estimates that contract around a small area. Our simulation shows that the proposed method successfully recovers planted multidimensional ideal points in a variety of settings including non-partisan, two-party, and multi-party systems. The proposed method is applied to the analysis of roll call data from the United States House of Representatives during the late Gilded Age (1891-1899) when legislative coalitions were distinguished not only by partisan divisions but also by sectional divisions that ran across party lines. [ABSTRACT FROM AUTHOR]

Exploring the underinvestigated area of instruction during study abroad, this article offers a quantitative study of linguistic development among second language university learners of Chinese during a semester in China. A comparison is made between learners following task‐based language teaching and a comparison group following a traditional approach at two proficiency levels. Spoken task data are analyzed within the framework of complexity, accuracy, and fluency. Quantitative findings point to enhanced linguistic development on the various measures used over the course of instruction abroad across the groups irrespective of instructional treatment and proficiency level. However, relative differences between the two groups point to an advantage of task‐based learning in a study‐abroad context. The findings are discussed in relation to the insights they allow into the role of different instructional treatments during study abroad, along with some directions for future research. [ABSTRACT FROM AUTHOR]

The robust counterpart of a given conic linear program with uncertain data in the constraints is defined as the robust conic linear program that arises from replacing the nominal feasible set by the robust feasible set of points that remain feasible for any possible perturbation of the data within an uncertainty set. Any minor changes in the size of the uncertainty set can result in significant changes, for instance, in the robust feasible set, robust optimal value and the robust optimal set. The concept of quantifying the extent of these deviations is referred to as the stability of robustness. This paper establishes conditions for the stability of robustness under which minor changes in the size of the uncertainty sets lead to only minor changes in the robust feasible set of a given linear program with cone constraints and ball uncertainty sets. [ABSTRACT FROM AUTHOR]

OBJECTIVE: Slow hoof growth poses a clinical challenge when hoof wear exceeds natural growth. Many treatment options have been reported without controlled prospective trials. The objective of this study was to evaluate the effect of transdermal CO2 on the rate of growth in treated hooves. METHODS: A prospective, randomized, blinded, crossover study of 14 Warmblood mares. Horses were randomly assigned a number and allocated for treatment of the front feet with room air or CO2 for 30 minutes 3 times per week, and groups were switched after 5 weeks. Hoof growth was measured on the dorsal midline and the quarters of each front foot. The distance from coronary band to lines made on the hoof wall was measured at the beginning, middle, and end of the study. The percentage of change in length at each location relative to baseline was evaluated at 5 weeks and 10 weeks using nonparametric analyses. RESULTS: All treatments were successfully administered. The left front medial (P = .028) and right front lateral (P = .03) sites of the CO2-treated hooves increased growth compared to the room air group at the 5-week point. CONCLUSIONS: The Results of this study suggest that repeated, noninvasive transdermal application of CO2 may accelerate hoof growth in normal horses over a 5-week treatment period. CLINICAL RELEVANCE: This study suggests that transdermal CO2 may increase the rate of hoof growth in normal horses. The mechanism of action of this treatment is unclear, and further studies are required to fully elucidate the potential effects. [ABSTRACT FROM AUTHOR]

In order to enhance the generalization ability of the network and improve the precision of the part segmentation, a point cloud part segmentation method which takes into account the optimal allocation and the optimal mask is proposed. Firstly, the optimal allocation between two point clouds is defined according to earth mover's distance. Then the farthest point sampling is used to group the point cloud, and the saliency of each point in the group is calculated. Finally, a new mixed sample is generated by replacing a partial subset of another point cloud sample with a local neighborhood in one point cloud sample. In this paper, the ShapeNet dataset was verified and the enhanced data was transferred to PointNet, Pointnet ++ and DGCNN models using this method. The mIoU increased from 83.7%, 85.1% and 85.1% to 84.6%, 85.9% and 85.7%, respectively. Effectively improve the effect of part segmentation. [ABSTRACT FROM AUTHOR]

We show that the recent relaxed-inertial proximal point algorithm due to Attouch and Cabot remains convergent when the function to be minimized is not convex, being only endowed with certain generalized convexity properties. Numerical experiments showcase the improvements brought by the relaxation and inertia features to the standard proximal point method in this setting, too. [ABSTRACT FROM AUTHOR]

Trade-offs between quality and quantity arise in an abundance of contexts concerning group decision making. With the starting point being that group members provide more accurate evidence when they are involved with fewer tasks, team managers often encounter the following dilemma: Should they assign their group members with many tasks (attempting to gather more evidence with lower quality), or with fewer tasks (aiming at receiving less, but more high-quality evidence)? Secondly, what is the optimal way to aggregate the collected evidence from a group, which may be contrasting and varying in accuracy? Should more weight be given to the more accurate group members, or to the larger number of those who provide the same answer? This topic is already studied within the mathematical framework of Terzopoulou and Endriss (2019). In this paper we complement it experimentally, by investigating to what extent people's decision-making patterns are in accordance with the optimal ones proposed by the normative model. Our findings suggest that people understand the task at hand and generally opt for optimal choices, especially in conflict-free cases. Still, a tendency towards overvaluing the importance of additional evidence, despite their accuracy, is observed; this translates into choosing options that align with the majority rule in aggregation problems. [ABSTRACT FROM AUTHOR]

High precision requirements in mechanical products have led machine tools to continuously improve their machining accuracy. However, the existence of geometric errors significantly affects the accuracy of machine tools. On-machine measurement (OMM) has become increasingly available for machine tools, offering an alternative method for identifying geometric errors as compared to the commonly applied traditional interferometry-based techniques. A method to identify the geometric errors based on on-machine measurement of a calibrated artefact is proposed. The mapping relation between the multiple sets of reference points on the artefact and the various types of geometric errors is elaborated on in detail. Geometric error identification experiments and the verification experiment by a laser tracer are conducted. The experiments indicate that the identification results from the proposed method and verification match well with each other, which confirms the effectiveness of the proposed identification method. Moreover, the impact of setup errors on the identification is analyzed, which suggests that the influence induced by setup errors on the identification result can be reasonably controlled. Periodic verification of machine tool geometric errors, as described in ISO 230–2, suggests continuous monitoring of machine tool accuracy and prompt detection of any degradation in accuracy. The OMM-based identification method is more easily automated and more efficient for periodic verification of machine tool accuracy. [ABSTRACT FROM AUTHOR]

Given a finite set of distinct points in R n and a positive weight for each point, primal and dual algorithms are developed for finding the Euclidean ball of minimum radius so that the weighted Euclidean distance between the center of the ball and each point is less than or equal to the radius of the ball. Each algorithm is based on a directional search method in which the search path at each iteration is either a ray or a two-dimensional circular arc in R n . At each iteration, a search path is constructed by intersecting bisectors of pairs of points, where the bisectors are either hyperplanes or n-dimensional spheres. Each search path preserves complementary slackness and primal (dual) feasibility for the primal (dual) algorithm. The step size along each search path is determined explicitly. Test problems up to 1000 dimensions and 10,000 points were solved to optimality by both primal and dual algorithms. Computational results also show that these algorithms outperform several open-source SOCP codes. [ABSTRACT FROM AUTHOR]

A 2- (v , k , λ) design is additive (or strongly additive) if it is possible to embed it in a suitable abelian group G in such a way that its block set is contained in (or coincides with) the set of all zero-sum k-subsets of its point set. Explicit results on the additivity or strong additivity of symmetric designs and subspace 2-designs are presented. In particular, the strong additivity of PG d (n , q) , which was known to be additive only for q = 2 or d = n - 1 , is always established. [ABSTRACT FROM AUTHOR]

We prove that multiplicative chaos measures can be constructed from extreme level sets or thick points of the underlying logarithmically correlated field. We develop a method which covers the whole subcritical phase and only requires asymptotics of suitable exponential moments for the field. As an application, we establish that these estimates hold for the logarithm of the absolute value of the characteristic polynomial of a Haar distributed random unitary matrix (CUE), using known asymptotics for Toeplitz determinant with (merging) Fisher–Hartwig singularities. Hence, this proves a conjecture of Fyodorov and Keating concerning the fluctuations of the volume of thick points of the CUE characteristic polynomial. [ABSTRACT FROM AUTHOR]

The problem of describing invariant extensions of the 3D Schrödinger operator H with finite number of point interactions leads to the need for studying matrices of a special type, the permutation matrices. A large class of such extensions considered in a certain boundary triplet is in one-to-one correspondence with a set of the so-called boundary operators (matrices). The extension of H with point interactions concentrated on X = {x1,... , xm} ⊂ R 3 is invariant under the symmetry group of X (or its subgroup) if and only if the corresponding boundary matrix commutes with the set of m-by-m permutation matrices induced by the symmetry group, i.e., belongs to its commutant. The bicommutant theorem for such a set of matrices is proven for an arbitrary finite point set. For the special cases of regular polygon, tetrahedron, and cube, the basis of the bicommutant, considered as a vector space, is specified explicitly. [ABSTRACT FROM AUTHOR]

Aiming at the problems of low convergence accuracy and easy to fall into local optimization of Harris hawk optimization (HHO) algorithm, a nonlinear Harris hawk optimization (SCNHHO) algorithm based on sine-cosine is proposed. Firstly, a good point set strategy is adopted to initialize the population, so as to make the population distribution more uniform and improve the convergence speed and accuracy of the algorithm; secondly, a positive cosine strategy is introduced in the exploration stage, which makes use of the oscillatory property of the positive cosine function to expand the search range and seek for more potential high-quality solutions; and lastly, a nonlinear parameter is introduced in the exploitation stage to balance the exploration and exploitation, so as to prevent the algorithm from falling into the local optimum. Performance tests are conducted for benchmark test functions of different dimensions, and the algorithm is analyzed with five other comparison algorithms by combining the results of Wilcoxon rank sum test and Friedman test. The results show that the performance of the improved algorithm is greatly improved over the original HHO algorithm, and it outperforms the zebra optimization algorithm (ZOA), the whale optimization algorithm (WOA), and the two variations of the Harris hawk algorithm (MHHO and IHHO), which verifies the effectiveness of the improved strategy. Finally, the practicality of SCNHHO is further verified by a three-bar truss design problem. [ABSTRACT FROM AUTHOR]

Spt4 and Spt5 form the DRB sensitivity inducing factor (DSIF) complex that regulates transcription elongation at multiple steps including promotorproximal pausing, processivity and termination. Although this implicated a general role in transcription, several studies pointed to smaller sets of target genes and indicated a more specific requirement in certain cellular contexts. To unravel common or distinct functions of Spt4 and Spt5 in vivo, we generated knock-out alleles for both genes in Drosophila melanogaster. Using the development of the mushroom bodies as a model, we provided evidence for two common functions of Spt4 and Spt5 during mushroom body development, namely control of cell proliferation of neural progenitor cells and remodeling of axonal projections of certain mushroom body neurons. This latter function is not due to a general requirement of Spt4 and Spt5 for axon pathfinding of mushroom body neurons, but due to distinct effects on the expression of genes controlling remodeling. [ABSTRACT FROM AUTHOR]

The kNN classifier is the most popular, supervised machine-learning technique, but the main disadvantage of this algorithm is that it has restricted access to the class distributions in a training point set and treats all the instances equally. In kNN classification, fuzzy sets are used to obtain the membership degrees of each point to the classes known as fuzzy kNN (FkNN) classification. Although the FkNN classifier enhances the performance of the kNN, it does not consider the effect of noisy and redundant instances, which makes it ineffective. Moreover, the performance of kNN is dependent on the value of k (number of nearest neighbours). Considering these issues, we present a novel algorithm that simultaneously tunes the class-dependent feature weights and k value using an effective meta-heuristic algorithm, the Enhanced Equilibrium Optimization technique. Several experiments have been conducted on different biomedical datasets, and the proposed approach has outperformed the other standard classifiers in terms of accuracy. [ABSTRACT FROM AUTHOR]

The income–happiness nexus is paradoxical. One dataset shows that happiness tracks income, while another shows that, in rich countries, happiness does not. This paper focuses on the limits of set point theory (known also ‘hedonic treadmill’ or ‘hedonic adaptation’) to solve the income–happiness paradox. To keep it manageable, it focuses on Daniel Kahneman's attempt to solve the paradox. He first employs his distinction between ‘the experiencing self’ and ‘the remembering self’ to solve the paradox. While the distinction is useful for the study of heuristics, it is irrelevant for the question at hand, the solution of the income–happiness paradox. Sensing such irrelevance, Kahneman turns his attention to the ‘life evaluation’ measure. This measure ironically shows that happiness tracks income. However, Kahneman disputes such tracking, arguing instead that happiness tracks income only if people, when they were teenagers, designate income as a life goal. The appeal to ‘goals’ or ‘life plans’, however, is an endorsement of a sophisticated version of set point theory. Kahneman argues that happiness varies with the variation of the designated goal or life plan, not with income per se. However, if happiness varies with the designated goals or life plans, it ultimately means that happiness cannot be conceived as a set point. Thus, Kahneman's arguments effectively sends us back to square one, failing to solve the income–happiness paradox. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the split feasibility problem with multiple output sets and fixed point problem in the class of demicontractive mappings and propose relaxed inertial self-adaptive algorithms that do not use the least squares method. Under some appropriate assumptions, we establish a strong convergence result for the sequence generated by the proposed algorithm. Our result generalizes and extends several results existing in the literature. Finally, we illustrate the convergence of the proposed algorithm by using a numerical example. [ABSTRACT FROM AUTHOR]

The friction and initial setting position of preform have an important influence on the metal flow and cavity filling during die forging process of large-scale component, especially for closed-die forging with flash of large-scale titanium alloy strut. This paper studies the influence of processing parameters on the die forging process of large-scale strut by targeting the filling difference (f) between right and left cavities, and some relational models such as relationship between friction and preform position were established. The results indicated that the friction amplitude (m) and initial setting position (x) of preform have notable influence on the filling states of right and left cavities, but the loading speed (v) of upper die and initial temperature ( T d ) of dies have little influence on the filling state; with the initial position of preform moving to right cavity (head of strut), the fluence of m on f reduces, but the fluence of x increases; the established relationship between m and x can obtain the feasible region with an optimal point for initial setting position of preform, and the feasible region with a linear range for the initial setting position of preform can be obtained by considering the expected accuracy of filling difference f, and then the feasible region with an areal range for the initial setting position of preform can be obtained by considering the fluctuation of frictional condition in further. [ABSTRACT FROM AUTHOR]

The pressure decaying test is traditionally used to detect leakage in pneumatic actuators; however, it is time-consuming as it is performed between cycles of actuation. To date, there is a notable lack of real-time, data-driven machine learning methods to detect such leakages. Such leakage prediction is important to determine the lifecycle of the actuator and the exerting force to seal the vacuum chamber. This study aims to employ machine learning techniques to predict the categories of normal and leaked pressure loss ratio (PLR) in real-time during different number of pneumatic actuators cycles. The data was collected using a two-way factorial design with center points for the cycle test setting parameters. Seven parameters were recorded and undergo the training and test phase. Additionally, multiple model architecture was employed, each performing binary classification for each class to predict the PLR. Correlation analysis shows that pressure reading of each "open" and "close" inlets have better correlation for predicting the leakage with 0.216 and 0.183 respectively. The top performing model for each class is K-Nearest Neighbors (KNN) and Multilayer Perceptron (MLP). For the model 1, the KNN model achieved the highest accuracy of 93.86%, with an AUC of 0.94 in ROC analysis. Meanwhile, for the Model 2, utilizing MLP model attained an accuracy of 89.36% and an 84.87% mean-harmonic score. This study demonstrates that real-time machine learning can effectively predict leakage in pneumatic actuators, with the potential for further improvement through the inclusion of more data and increased setting points in the cycle test. [ABSTRACT FROM AUTHOR]

We apply the Fixed Point Theorem for the actions of finite groups on Bruhat–Tits buildings and their products to establish two results concerning the groups of points of reductive algebraic groups over polynomial rings in one variable, assuming that the base field is of characteristic zero. First, we prove that for a reductive k -group G , every finite subgroup of G (k [ t ]) is conjugate to a subgroup of G (k). This, in particular, implies that if k is a finite extension of the p -adic field Q p , then the group G (k [ t ]) has finitely many conjugacy classes of finite subgroups, which is a well-known property for arithmetic groups. Second, we give a short proof of the theorem of Raghunathan–Ramanathan [26] about G -torsors over the affine line. [ABSTRACT FROM AUTHOR]

Elliptic curves are considered highly secure due to their complex mathematical structure and are widely used in cryptographic key exchange algorithms. This study aimed to construct a confusion component for a symmetric block cipher using a hybrid approach that involves elliptic curve points and an algebraic group structure. Generally, elliptic curve points do not generate much randomness, so they are not recommended for constructing a highly nonlinear S-box. In this study, we first randomized the elliptic curve points to the maximum possible level and generate initial S-boxes. These initial S-boxes were then evolved through algebraic group action to enhance their nonlinearity. The strength of the proposed substitution box was assessed using various tests, including nonlinearity, bit independence criterion, strict avalanche criterion, and differential and linear probabilities. Using this approach, we designed an S-box with a nonlinearity value of 114, which is higher than the standard value presented by AES. We compared the results of other cryptographic tests with well-known S-boxes to validate the effectiveness of the suggested confusion component. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we investigate iterative methods for solving generalized mixed equilibrium problems, split feasibility problems, and fixed point problems in Banach spaces. We introduce a new extragradient algorithm using the generalized metric projection and prove a strong convergence theorem for finding a common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of solutions to the split feasibility problem, the set of fixed points of a resolvent operator, and the set of solutions of the generalized mixed equilibrium problem. The algorithm is analyzed in a real 2-uniformly convex and uniformly smooth Banach space, taking into account computational errors. A numerical example is provided to illustrate the applicability and performance of the proposed method. [ABSTRACT FROM AUTHOR]

A new family of fourth‐order iterative methods for solving nonlinear equations is proposed using the weight function procedure. This family is optimal in the sense of the Kung–Traub conjecture, as it requires three function evaluations per iteration. Due to its flexible structure, the new family offers a variety of options, demonstrating that it includes several well‐known and recent methods as special cases. In particular, three new specific methods are designed to achieve better results compared to existing methods within the same family. Various nonlinear functions and engineering problems are used to illustrate the performance of these new specific methods, comparing them with existing ones. Furthermore, the analysis of complex dynamics and basins of attraction shows that the newly proposed methods yield the best results, with wider sets of initial points that lead to convergence. [ABSTRACT FROM AUTHOR]

Let X be a compact metric space, G be a countable discrete infinite amenable group continuously acting on X and $ \mathcal {F} $ F be a Følner sequence of G. In this paper, we acquire some ergodic properties of the discrete amenable group action $ (X, G) $ (X,G). By virtue of these properties, we prove the existence of syndetic sensitivity of the minimal $ \mathcal {F} $ F-centre of attraction of a point $ x\in X $ x∈X provided that the minimal $ \mathcal {F} $ F-centre of attraction of x is not S-generic and admits a dense set of quasi-weakly almost periodic points relative to $ \mathcal {F} $ F of $ (X, G) $ (X,G). The presented results enhance some main results of [Z. Chen and X. Dai, Chaotic dynamics of minimal centre of attraction of discrete amenable group actions, J. Math. Anal. Appl. 456 (2017), pp. 1397–1414.]. [ABSTRACT FROM AUTHOR]

Taking inspiration from what is commonly done in single-objective optimization, most local algorithms proposed for multiobjective optimization extend the classical iterative scalar methods and produce sequences of points able to converge to single efficient points. Recently, a growing number of local algorithms that build sequences of sets has been devised, following the real nature of multiobjective optimization, where the aim is that of approximating the efficient set. This calls for a new analysis of the necessary optimality conditions for multiobjective optimization. We explore conditions for sets of points that share the same features of the necessary optimality conditions for single-objective optimization. On the one hand, from a theoretical point of view, these conditions define properties that are necessarily satisfied by the (weakly) efficient set. On the other hand, from an algorithmic point of view, any set that does not satisfy the proposed conditions can be easily improved by using first-order information on some objective functions. We analyse both the unconstrained and the constrained case, giving some examples. [ABSTRACT FROM AUTHOR]

This paper reports the development of a process for leaching Pt, Pd, and Rh from simulated spent auto-catalyst material using ozone and hydrochloric acid in order to produce a pregnant leach solution that could be fed to an industrial precious metal refinery. The effects of O3 mass flow, initial acid concentration, and temperature were investigated using a Box–Behnken experimental design with three centre-point runs and a total leach time of 6 h. Set points of 3.34, 5.01, and 6.68 g/h; 1.0 M, 3.0 M, and 5.0 M; and 30, 60, and 90 °C were used for O3 mass flow, hydrochloric acid concentration, and temperature, respectively. The optimal extractions for Pt, Pd, and Rh were 80%, 85%, and 42%, respectively, at 5.01 g/h O3, 5.0 M HCl, and 90 °C. Statistical analyses indicated high dependencies of Pd and Rh on hydrochloric acid concentration and temperature, with only Pt displaying a significant dependence on O3 mass flow. [ABSTRACT FROM AUTHOR]

This study introduces a novel, iterative algorithm that achieves fourth-order convergence for solving nonlinear equations. Satisfying the Kung–Traub conjecture, the proposed technique achieves an optimal order of four with an efficiency index (I) of 1.587 , requiring three function evaluations. An analysis of convergence is presented to show the optimal fourth-order convergence. To verify the theoretical results, in-depth numerical comparisons are presented for both real and complex domains. The proposed algorithm is specifically examined on a variety of polynomial functions, and it is shown by the efficient and accurate results that it outperforms many existing algorithms in terms of speed and accuracy. The study not only explores the proposed method's convergence properties, computational efficiency, and stability but also introduces a novel perspective by considering the count of black points as an indicator of a method's divergence. By analyzing the mean number of iterations necessary for methods to converge within a cycle and measuring CPU time in seconds, this research provides a holistic assessment of both the efficiency and speed of iterative methods. Notably, the analysis of basins of attraction illustrates that our proposed method has larger sets of initial points that yield convergence. [ABSTRACT FROM AUTHOR]

Recently, a surge of interest has been given to quantifying epistemic uncertainty (EU), the reducible portion of uncertainty due to lack of data. We propose a novel EU estimator in the binary classification setting, as the posterior expected value of the empirical gain in accuracy between the current prediction and the optimal prediction. In order to validate the performance of our EU estimator, we introduce an experimental procedure where we take an existing dataset, remove a set of points, and compare the estimated EU with the observed change in accuracy. Through real and simulated data experiments, we demonstrate the effectiveness of our proposed EU estimator. [ABSTRACT FROM AUTHOR]

Two subsets A, B of the plane are betweenness isomorphic if there is a bijection f : A → B such that, for every x, y, z ∈ A, the point f(z) lies on the line segment connecting f(x) and f(y) if and only if z lies on the line segment connecting x and y. In general, it is quite difficult to tell whether two given subsets of the plane are betweenness isomorphic. We concentrate on the case when each of the sets A, B is of the form C ∪ D where C is a circle and D is a finite set. We fully characterize the betweenness isomorphism classes in the family of all circles with three collinear points inside. In particular, we show that there are only countably many isomorphism classes, for which we provide an algebraic description. [ABSTRACT FROM AUTHOR]

Deformation is the most direct indicator of structural state changes in arch dams. Therefore, numerous deformation monitoring points are typically arranged on arch dams to obtain deformation data from each point. Considering the complex relationships between the deformation at each monitoring point, this study focuses on the internal structural relationships and information fusion within the dam. The Pearson correlation coefficient is used as a similarity index to determine significant linear correlations between the measuring points. Ward's cluster analysis method is then applied to group these points based on their similarities. To identify measuring points with strong nonlinear correlations, the Maximum Information Coefficient (MIC) method is employed. By integrating these linear and nonlinear correlations, a model is constructed to characterize the deformation at specific measurement points using data from strongly correlated points. The effectiveness of this model is verified through a concrete engineering case study, offering a novel approach for analyzing arch dam deformations. [ABSTRACT FROM AUTHOR]

In the production of high-definition maps, it is necessary to achieve the three-dimensional instantiation of road furniture that is difficult to depict on traditional maps. The development of mobile laser measurement technology provides a new means for acquiring road furniture data. To address the issue of traffic marking extraction accuracy in practical production, which is affected by degradation, occlusion, and non-standard variations, this paper proposes a 3D reconstruction method based on energy functions and template matching, using zebra crossings in vehicle-mounted LiDAR point clouds as an example. First, regions of interest (RoIs) containing zebra crossings are obtained through manual selection. Candidate point sets are then obtained at fixed distances, and their neighborhood intensity features are calculated to determine the number of zebra stripes using non-maximum suppression. Next, the slice intensity feature of each zebra stripe is calculated, followed by outlier filtering to determine the optimized length. Finally, a matching template is selected, and an energy function composed of the average intensity of the point cloud within the template, the intensity information entropy, and the intensity gradient at the template boundary is constructed. The 3D reconstruction result is obtained by solving the energy function, performing mode statistics, and normalization. This method enables the complete 3D reconstruction of zebra stripes within the RoI, maintaining an average planar corner accuracy within 0.05 m and an elevation accuracy within 0.02 m. The matching and reconstruction time does not exceed 1 s, and it has been applied in practical production. [ABSTRACT FROM AUTHOR]

Discrepancy is a well-known measure for the irregularity of the distribution of a point set. Point sets with small discrepancy are called low discrepancy and are known to efficiently fill the space in a uniform manner. Low-discrepancy points play a central role in many problems in science and engineering, including numerical integration, computer vision, machine perception, computer graphics, machine learning, and simulation. In this work, we present a machine learning approach to generate a new class of low-discrepancy point sets named Message-Passing Monte Carlo (MPMC) points. Motivated by the geometric nature of generating low-discrepancy point sets, we leverage tools from Geometric Deep Learning and base our model on graph neural networks. We further provide an extension of our framework to higher dimensions, which flexibly allows the generation of custom-made points that emphasize the uniformity in specific dimensions that are primarily important for the particular problem at hand. Finally, we demonstrate that our proposed model achieves state-of-the-art performance superior to previous methods by a significant margin. In fact, MPMC points are empirically shown to be either optimal or near-optimal with respect to the discrepancy for low dimension and small number of points, i.e., for which the optimal discrepancy can be determined. [ABSTRACT FROM AUTHOR]

Chronic kidney disease (CKD), which has a significant prevalence of 15.7 % in Turkey, is a global health problem that particularly affects elderly. It is difficult to distinguish between age-related and CKD-related declines in kidney function with current glomerular filtration rate (GFR) estimation methods. The “HUGE” formula, incorporating haematocrit, urea, and gender, offers improved differentiation, targeting individuals over 40. This study aims to evaluate the effectiveness of the HUGE formula in estimating GFR in this demographic group and to establish a better diagnostic threshold.A retrospective study of 500 participants over 40 years was conducted and divided into CKD (252) and non-CKD (248) based on demographics, laboratory tests and ultrasound evaluation. Renal function was classified by the HUGE equation (HUGE<0 for age-related decline; ≥ 0 for CKD) and GFR estimates were compared with KDIGO guidelines via CKD-EPI, FAS and BIS1.We observed significant discrepancies in estimated glomerular filtration rate (eGFR) and its staging among different formulas. The HUGE formula showed better agreement with eGFR staging after the cut-off point was set as “−1.58” and improved diagnostic accuracy, especially in stages 3a and 3b.The study validates the HUGE formula improved accuracy in diagnosing CKD, especially for stages 3a and 3b, with a new cut-off value of “−1.58”. It supports the inclusion of the HUGE formula into current diagnostic practices to improve the identification and staging of CKD in individuals over the age of 40, while also demonstrating the necessity for further clinical evaluations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the partial regularity of suitable weak solution to the 3D simplify Ericksen–Leslie system modeling the hydrodynamical motion of nematic liquid crystal flow, which is a coupled system with the Navier–Stokes equations for the velocity field and kinematic transport equations for the molecular orientation field. We present a new regularity criteria for suitable weak solutions to the 3D simplified Ericksen–Leslie system. Moreover, under the condition ∥u∥Ltp,∞Lxq([−1,0]×R3)+∥∇d∥Ltp,∞Lxq([−1,0]×R3):=K<∞,with2p+3q=1and3

A comprehensive analysis of Bi2O2CO3 nanosheets, which were synthesized using nanosecond‐pulsed discharges in water between bismuth electrodes, was conducted in order to investigate the crystallographic features of this material. Electron diffraction, X‐ray diffraction and electron energy‐loss spectrometry techniques revealed the presence of a stoichiometric tetragonal Bi2O2CO3 structure, labelled BOC in this study. It crystallizes in the body‐centred tetragonal Bravais lattice and belongs to the I4/mmm space group (No. 139), with the following lattice parameters: a = 3.91, c = 13.77 Å. The nanosheets adopt square shapes. This shape is dictated by the symmetry elements of its point group (4/mmm) under the prevailing local conditions. From the energetic point of view, this shape, dictated by the 4/m2/m2/m point group and therefore a pinacoid, corresponds to an absolute extremum, an indicator of the stability of these BOC nanosheets. Most nanosheets are crossed by equal‐inclination fringes or bend contours. These bend contours reflect the fact that the BOC nanosheets contain crystal defects and/or are so thin that they bend elastically, leading to rotation of the lattice planes towards the diffracting Bragg position. The diffraction patterns corresponding to bend contours intersecting along the [001] zone axis have been studied in detail. Extra reflections are superimposed on the diffraction pattern of the BOC crystallographic structure. These extra reflections are essentially attributed to two phenomena: multiple diffraction and local disorder–order transformations of the BOC crystal structure, passing from a body‐centred tetragonal to a primitive Bravais lattice. A mechanism related to the ledge mechanism (kinks and jogs), explaining the formation of nanosheets in a metallic matrix, has been adapted and proposed for the formation of BOC nanosheets in water. When the nanosheets are removed from the water, they become carbonated once in the air, leading to the formation of BOC that inherits the nanosheet morphology. [ABSTRACT FROM AUTHOR]

The mathematical structure, description and classification of magnetic space groups is briefly reviewed, with special emphasis on the recently proposed notation, the so‐called UNI symbols [Campbell et al. (2022). Acta Cryst. A78, 99–106]. As illustrative examples, very simple magnetic space groups from each of the four possible types are described in detail. [ABSTRACT FROM AUTHOR]

This paper presents the notion of multiset-multiset frame (mm-frame for short), a frame equipped with a relation between (finite) multisets over the set of points which satisfies the condition called compositionality. This notion is an extension of Restall and Standefer's multiset frame, a frame that relates a multiset to a single point. While multiset frames serve as frames for the positive fragments of relevant logics RW and R, mm-frames are for the full RW and R with negation. We show this by presenting a way of constructing an mm-frame from any GS-frame, a frame with two dual ternary relations in which the Routley star is definable. [ABSTRACT FROM AUTHOR]

The proposed RMS-FlowNet++ is a novel end-to-end learning-based architecture for accurate and efficient scene flow estimation that can operate on high-density point clouds. For hierarchical scene flow estimation, existing methods rely on expensive Farthest-Point-Sampling (FPS) to sample the scenes, must find large correspondence sets across the consecutive frames and/or must search for correspondences at a full input resolution. While this can improve the accuracy, it reduces the overall efficiency of these methods and limits their ability to handle large numbers of points due to memory requirements. In contrast to these methods, our architecture is based on an efficient design for hierarchical prediction of multi-scale scene flow. To this end, we develop a special flow embedding block that has two advantages over the current methods: First, a smaller correspondence set is used, and second, the use of Random-Sampling (RS) is possible. In addition, our architecture does not need to search for correspondences at a full input resolution. Exhibiting high accuracy, our RMS-FlowNet++ provides a faster prediction than state-of-the-art methods, avoids high memory requirements and enables efficient scene flow on dense point clouds of more than 250K points at once. Our comprehensive experiments verify the accuracy of RMS-FlowNet++ on the established FlyingThings3D data set with different point cloud densities and validate our design choices. Furthermore, we demonstrate that our model has a competitive ability to generalize to the real-world scenes of the KITTI data set without fine-tuning. [ABSTRACT FROM AUTHOR]

We investigate the Möbius groups theory in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero-divisors. In this paper, we first generalize classical conjugacy classification to bicomplex analysis. Then we have a discussion of the iterates of a bicomplex Möbius transformation and study the attractive and repulsive fixed points in bicomplex setting. Finally, we shall prove two useful results concerning fixed point. [ABSTRACT FROM AUTHOR]

This paper is concerned with a recursive algorithm as a preprocessing step to find the convex hull of n random points uniformly distributed in the plane. For such a set of points, it is shown that eliminating all but O (log n) of points can derive the same convex hull as the input set. Finally it will be shown that the running time of the algorithm is O (n). [ABSTRACT FROM AUTHOR]

Sufficient conditions are given for planar cooperative maps to have the qualitative global dynamics determined solely on local stability information obtained from fixed and minimal period-two points. The results are given for a class of strongly cooperative planar maps of class $ C^1 $ C 1 on an order interval. The maps are assumed to have a finite number of strongly ordered fixed points, and also the strongly ordered minimal period-two points. Some applications are included. [ABSTRACT FROM AUTHOR]

We study the dynamics of the piecewise planar rotations $ F_{\lambda }(z)=\lambda (z-H(z)), $ F λ (z) = λ (z − H (z)) , with $ z\in {\mathbb C} $ z ∈ C , $ H(z)=1 $ H (z) = 1 if $ \mathrm {Im}(z)\ge 0, $ Im (z) ≥ 0 , $ H(z)=-1 $ H (z) = − 1 if $ \mathrm {Im}(z) \lt 0, $ Im (z) < 0 , and $ \lambda =\mathrm {e}^{i \alpha } \in {\mathbb C} $ λ = e iα ∈ C , being α a rational multiple of π. Our main results establish the dynamics in the so called regular set, which is the complementary of the closure of the set formed by the preimages of the discontinuity line. We prove that any connected component of this set is open, bounded and periodic under the action of $ F_\lambda $ F λ , with a period ℓ, that depends on the connected component. Furthermore, $ F_\lambda ^\ell $ F λ ℓ restricted to each component acts as a rotation with a period which also depends on the connected component. As a consequence, any point in the regular set is periodic. Among other results, we also prove that for any connected component of the regular set, its boundary is a convex polygon with certain maximum number of sides. [ABSTRACT FROM AUTHOR]