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To perform computations with the efficiency necessary for animal survival, neocortical microcircuits must be capable of reconfiguring in response to experience, while carefully regulating excitatory and inhibitory connectivity to maintain stable function. This dynamic fine-tuning is accomplished through a rich array of cellular homeostatic plasticity mechanisms that stabilize important cellular and network features such as firing rates, information flow, and sensory tuning properties. Further, these functional network properties can be stabilized by different forms of homeostatic plasticity, including mechanisms that target excitatory or inhibitory synapses, or that regulate intrinsic neuronal excitability. Here we discuss which aspects of neocortical circuit function are under homeostatic control, how this homeostasis is realized on the cellular and molecular levels, and the pathological consequences when circuit homeostasis is impaired. A remaining challenge is to elucidate how these diverse homeostatic mechanisms cooperate within complex circuits to enable them to be both flexible and stable. [ABSTRACT FROM AUTHOR]

The Jacobi set of a bivariate scalar field is the set of points where the gradients of the two constituent scalar fields align with each other. It captures the regions of topological changes in the bivariate field. The Jacobi set is a bivariate analog of critical points, and may correspond to features of interest. In the specific case of time-varying fields and when one of the scalar fields is time, the Jacobi set corresponds to temporal tracks of critical points, and serves as a feature-tracking graph. The Jacobi set of a bivariate field or a time-varying scalar field is complex, resulting in cluttered visualizations that are difficult to analyze. This paper addresses the problem of Jacobi set simplification. Specifically, we use the time-varying scalar field scenario to introduce a method that computes a reduced Jacobi set. The method is based on a stability measure called robustness that was originally developed for vector fields and helps capture the structural stability of critical points. We also present a mathematical analysis for the method, and describe an implementation for 2D time-varying scalar fields. Applications to both synthetic and real-world datasets demonstrate the effectiveness of the method for tracking features. [ABSTRACT FROM AUTHOR]

The formation of intelligent platforms is a multi-objective constraint problem. It is necessary for the multi-agent to automatically generate the path from the initial position to the specified end point, and at the same time meet the constraints of space collision avoidance on the multi-target intersection path and the constraint of the agent's motion ability, and pursue the shortest formation time of the whole formation as much as possible. In this paper, we propose an improved method for obtaining the starting set of multi-agent formation based on particle swarm optimization. First, the starting point set of the formation is defined, and then the particle swarm optimization algorithm is selected as the optimization algorithm to find the best starting point of the formation. Then the turning performance of the intelligent platform is studied, and the assembly route of each agent is designed by combining the Dubins curve. The simulation results show that the proposed method avoids collision between agents, shortens the time of agent formation assembly, and effectively ensures the reliability of the assembly route. [ABSTRACT FROM AUTHOR]

Let Ω be a set equipped with an equivalence relation ∼ ; we refer to the equivalence classes as blocks of Ω. A permutation group G ≤ Sym ⁢ (Ω) is 푘-by-block-transitive if ∼ is 퐺-invariant, with at least 푘 blocks, and 퐺 is transitive on the set of 푘-tuples of points such that no two entries lie in the same block. The action is block-faithful if the action on the set of blocks is faithful. In this article, we classify the finite block-faithful 2-by-block-transitive actions. We also show that, for k ≥ 3 , there are no finite block-faithful 푘-by-block-transitive actions with nontrivial blocks. [ABSTRACT FROM AUTHOR]

For the quadratic family f_{c}(z) = z^2+c with c in a hyperbolic component of the Mandelbrot set, it is known that every point in the Julia set moves holomorphically. In this paper we give a uniform derivative estimate of such a motion when the parameter c converges to a parabolic parameter {\hat {c}} radially; in other words, it stays within a bounded Poincaré distance from the internal ray that lands on {\hat {c}}. We also show that the motion of each point in the Julia set is uniformly one-sided Hölder continuous at {\hat {c}} with exponent depending only on the petal number. This paper is a parabolic counterpart of the authors' paper "From Cantor to semi-hyperbolic parameters along external rays" [Trans. Amer. Math. Soc. 372 (2019), pp. 7959–7992]. [ABSTRACT FROM AUTHOR]

In this paper, a multi-fidelity Bayesian optimization approach is presented to tackle computationally expensive constrained multiobjective optimization problems (MOPs). The proposed approach consists of a three-stage optimization framework designed to search for promising candidate points. In the first stage, an acquisition function is proposed to identify a feasible solution if none is available in the current set of sampling points. Subsequently, a new multi-fidelity weighted expected hypervolume improvement function is developed to find better solutions. In the third stage, a constrained weighted lower confidence bound acquisition function is presented to enhance the constraint predictions and refine the solutions near the constraint boundary. Additionally, a filter strategy is suggested to determine whether constraint updating is necessary, aiming to save computational resources and improve optimization efficiency. Moreover, to expedite the optimization process, a parallel optimization approach is further developed based on the suggested three-stage optimization framework. To achieve this, a multi-fidelity influence function is introduced, allowing the proposed approach to determine a desired number of candidate points within a single iteration. Lastly, the proposed approach is demonstrated through six numerical benchmark examples, which verifies its significant advantages in addressing expensive constrained MOPs. Besides, the proposed approach is applied to the multiobjective optimization of a metamaterial vibration isolator, resulting in the attainment of satisfactory solutions. [ABSTRACT FROM AUTHOR]

The dividing‐wall column (DWC) stands as an energy‐efficient distillation technology designed to efficiently separate ternary systems into their pure components within a single column. Despite its efficiency, integrating two towers into a DWC poses challenges in controllability. Published studies have focused on developing controllers for disturbance rejection but have not addressed the issue of servo control. Addressing this, our study proposes a servo controller problem and a methodical approach to strategically select controlled variables that undergo consecutive set point step changes, aiming to track the purity of key products obtained from the DWC. To achieve this goal, we developed a dynamic model specifically tailored to the DWC. Determining the design parameters involved employing a genetic algorithm optimization technique, minimizing the total annual cost. Subsequently, we implemented three servo parallel proportional‐integral (PI) feedback controllers for three distinct product streams. The fine‐tuning of their controller gain and reset time is carried out by minimizing the integrated square error while adhering to valve opening constraints. Our investigation revealed a limitation: the introduction of simultaneous step changes in all three controlled variables proved unfeasible with the three active PI controllers. As an alternative, our findings recommend prioritizing two variables: the lightest (distillate) and heaviest (bottom) key components, alongside the middle component (side stream) and either the lightest or heaviest key component. This research underscores the complexities of implementing step changes in multiple controlled variables within a DWC, offering insights into optimal control strategies for enhancing the efficiency of this innovative distillation technology. [ABSTRACT FROM AUTHOR]

Discovered as an apparent pattern, a universal relation between geometry and information called the holographic principle has yet to be explained. This relation is unfolded in the present paper. As it is demonstrated there, the origin of the holographic principle lies in the fact that a geometry of physical space has only a finite number of points. Furthermore, it is shown that the puzzlement of the holographic principle can be explained by a magnification of grid cells used to discretize geometrical magnitudes such as areas and volumes into sets of points. To wit, when grid cells of the Planck scale are projected from the surface of the observable universe into its interior, they become enlarged. For that reason, the space inside the observable universe is described by the set of points whose cardinality is equal to the number of points that constitute the universe's surface. [ABSTRACT FROM AUTHOR]

In this paper, as the main contribution, three sensorless control structures are presented for the control of the grid-connected PMSG-based Wind Turbine (WT) employing boost converter and diode rectiffer as the machine-side converter. Then, detailed control structures of the boost converter and grid-side converter at the three mentioned control strategies are extracted, and next, features of the abovementioned control strategies are investigated and compared against wind speed variation and grid voltage dip. The boost converter, in the first control strategy, controls the generator speed at the Maximum Power Point Tracking (MPPT) mode, and in the second control strategy, it regulates the Permanent Magnet Synchronous Generator (PMSG) active power to its set point value. Also, the boost converter, in the third control strategy, adjusts the voltage of the dc-link capacitor to its set point value. In this paper, steady-state performance and transient/LVRT behavior of the WT system are examined for each mentioned control strategy in the MATLAB-Simulink environment. It is shown that WT steady-state responses are relatively identical for all three control strategies. However, as an interesting result, at the fault conditions, the third control strategy has superior performance, and thus, the WT fault ride-through behavior enhances significantly with the third control structure without any hardware protection. [ABSTRACT FROM AUTHOR]

This article aimed to cluster districts and cities in West Sumatra Province based on various indicators of people’s welfare using the fuzzy clustering technique. The approach involved both Fuzzy C-Means and Spatial Fuzzy C-Means algorithms. The former assigns data points to groups based on membership degrees, while the latter incorporates spatial information.The analysis revealed that two clusters were optimal. Fuzzy C-Means identified nine regions in Cluster 1 and ten in Cluster 2. Spatial Fuzzy C-Means, on the other hand, assigned eight regions to Cluster 1 and eleven to Cluster 2. Notably, Spatial Fuzzy C-Means outperformed Fuzzy C-Means in terms of Modified Partition Coefficient (MPC) validity index values.In conclusion, leveraging sophisticated algorithms like Spatial Fuzzy C-Means enhances the accuracy of clustering districts and cities in West Sumatra Province based on welfare indicators. This study provides valuable insights for researchers seeking to group regions effectively while considering the nuances of people’s well-being. [ABSTRACT FROM AUTHOR]

In the separability problem of bichromatic point sets. given two sets of points colored as blue and red, we want to put a special geometric shape in a manner that includes the blue points while avoiding the red ones. This problem has various applications in data mining and other fields. Separability by various shapes, including L-shaped polygons. has been studied in the literature. In this paper. the separability of bichromatic point sets by C-shaped polygons, which are more general than L-shaped polygons, is studied and an 0(n log n)-time algorithm is presented. where n is the total number of points. [ABSTRACT FROM AUTHOR]

In this paper, we extend the work of Pollington and Velani [Selecta Math. 11(2005)] to an S$S$‐arithmetic set‐up, where S$S$ is a finite set of valuations of Q$\mathbb {Q}$. In particular, for an absolutely friendly measure μ$\mu$ supported on a compact set in QSd$\mathbb {Q}_S^d$, we give a summation condition on an approximating function ψ$\psi$ such that μ$\mu$ almost no point in the compact set is ψ$\psi$ approximable. The crucial ingredient is a version of the simplex lemma that we prove dynamically. [ABSTRACT FROM AUTHOR]

In this paper, we study the properties of the lattice of c-structures. We define the concept of simple expansion and examine some of its properties. Additionally, we determine the automorphism group of the lattice of c-structures and explore the fixed points of the group of automorphisms. [ABSTRACT FROM AUTHOR]

This study introduces the concept of nonlocal effect into a monoatomic mass–spring periodic structure, leading to unique characteristics of dispersion curves. Through the incorporation of the second neighboring nonlocal effect, we have observed the emergence of negative group velocity and specific points with zero group velocity (ZGV) within the dispersion curves. By harnessing the distinctive property of ZGV, we successfully attained the localization of transmission at specific frequencies, leading to a rainbow trapping effect. Notably, with the appropriate tuning of the third neighboring nonlocal effect, we observe that multi-frequency can be localized at predetermined positions. Waves under these frequencies are trapped at the same location, demonstrating a multi-frequency rainbow trapping phenomenon. The results from this research provide a novel perspective on elastic wave manipulation in periodic structures, with potential implications for the design of advanced materials and devices. [ABSTRACT FROM AUTHOR]

As the world is more focused on developing products and services, which are sustainable, special attention is needed in the design and manufacture of machine tools. There is a multitude of elements that contribute to the sustainability of machine tools. Moreover, the elements are interdependent with each other. The presence and absence of each element can be measured by different indicators. This paper analyzes the influence of elements and their indicators on the sustainability of machine tools. Sustainability elements and their indicators have been identified first. Further, a new hybrid model was developed to find the interdependencies between the sustainability elements for machine tools and determine the priorities of the indicators. Two structural models, i.e., Decision-Making Trial and Evaluation Laboratory and Analytic Network Process, have been combined to establish levels and intensities of interdependence as well as the relative weight of selected indicators. The results classify the indicators into the receiver, dispatcher, and neutral groups and also point out the indicators with feedback dependencies, i.e., indicators that depend on themselves. The methodology can be applied for evaluating as well as comparing the sustainability of different machines. The observations would be helpful to the designers of machine tools to make strategies for improving the sustainability of their machines. [ABSTRACT FROM AUTHOR]

The set of critical points of a simple mechanical device undergoing static or quasi-static evolution is investigated. When the system is fully elastic open bifurcation problems in the static case remain only for special structures or loadings. But the state of the art is different in the case of elastic-plasticity when addressing general solids or structures and general loadings where many difficult problems remain and where a relatively complete bifurcation diagram has been obtained only for a very simple mechanical system. The present paper focuses on the same simple system but in the case of damage which turns out to be very different since a part of the static equilibrium equations turns to be non-local. [ABSTRACT FROM AUTHOR]

In this article we give an explicit construction of the moduli space of trigonal superelliptic curves with level 3 structure. The construction is given in terms of point sets on the projective line and leads to a closed formula for the number of connected (and irreducible) components of the moduli space. The results of the article generalise the description of the moduli space of hyperelliptic curves with level 2 structure, due to Dolgachev and Ortland, Runge and Tsuyumine. [ABSTRACT FROM AUTHOR]

In order to solve the problem of low tracking accuracy of the traditional group target tracking algorithms in point-group coexistence scenarios, a trajectory Poisson multi--Bernoulli mixture (TPMBM) filtering algorithm is proposed, which can track both point target and group target simultaneously. The algorithm expands the state space of the target, introduces probability information about the target class based on the standard point target and the group target models, and achieves the judgment of the target class and the estimation of the target motion state through the prediction and update process of the TPMBM filter. Simulation results show that, compared with the existing algorithms, the proposed algorithm has significantly lower miss detection error and better tracking performance when point target and group target coexist. [ABSTRACT FROM AUTHOR]

Autonomous collision avoidance decision making for maritime autonomous surface ships (MASS), as one of the key technologies for MASS autonomous navigation, is a research hotspot focused on by relevant scholars in the field of navigation. In order to guarantee the rationality, efficacy, and credibility of the MASS autonomous collision avoidance scheme, it is essential to design the MASS autonomous collision avoidance algorithm under the stipulations of the Convention on the International Regulations for Preventing Collisions at Sea (COLREGs). In order to enhance the autonomous collision avoidance decision-making capability of MASS in accordance with the relevant provisions of COLREGs, an improved NSGA-II autonomous collision avoidance decision-making algorithm based on the good point set method (GPS-NSGA-II) is proposed, which incorporates the collision hazard and the path cost of collision avoidance actions. The experimental results in the four simulation scenarios of head-on situation, overtaking situation, crossing situation, and multi-ship encounter situation demonstrate that the MASS autonomous collision avoidance decision making based on the GPS-NSGA-II algorithm under the constraints of COLREGs is capable of providing an effective collision avoidance scheme that meets the requirements of COLREGs in common encounter situations and multi-ship avoidance scenarios promptly, with a promising future application. [ABSTRACT FROM AUTHOR]

Copyright of Baghdad Science Journal is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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

Copyright of Baghdad Science Journal is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

Apollonius defined the circle as the set of points that have a given ratio μ of distances from two given points, where the ratio is not equal to one. In a more general sense, consider two 0-symmetric, bounded, convex bodies K and K ′ , which define two norms. Their unit balls are K and K ′ . The surface of Apollonius is defined as the set of points equidistant from the centres of bodies K and K ′ with respect to the aforementioned norms. In this paper we demonstrate that the surface of Apollonius of two ellipsoids is a quadratic surface. We also examine the circumstances under which this surface becomes a sphere. [ABSTRACT FROM AUTHOR]

In this paper, we have presented rough statistical convergence of sequence on neutrosophic normed spaces as an important convergence criterion. As neutrosophication can handle partially dependent components, partially independent components and even independent components involved in real-world problems. By examining some properties related to rough convergence in these spaces we provide some useful functional tools in the situations of inconsistency and indeterminacy in the real world. Further, we have established some equivalent conditions on the set of statistical limit points as well as on the set of cluster points in these spaces for rough statistically convergent sequences. [ABSTRACT FROM AUTHOR]

A two-way segmentation model is proposed in this article. The model is used to solve the problem that the objective contour can not be completely extracted from image due to occlusion between objects within similar image groups or image sequences. The proposed model first decomposes incomplete contours into sub-segments using local features identified by seed points set along each path. Then, locate the occluded part of the target object and reconstruct the target. Finally, a new vector field is generated based on the reconstructed object from the proposed model, followed by iterative evolution. The experimental results show that the proposed algorithm can better handle the problem of occlusion or misleading features of targets in composite images and medical images. Not only does it facilitate subsequent measurement and analysis, but it also preserves the original shape of the object during the segmentation process without prior information. It is worth noting that the accuracy of the proposed model is robust to our initialization strategy. [ABSTRACT FROM AUTHOR]

Using traditional algorithms to identify persistent scatterer (PS) points is challenging during bridge construction because of short-term changes at construction sites, such as earthworks, as well as the erection and dismantling of temporary structures. To address this issue, this study proposes a PS point selection method based on statistical theory and Gaussian Mixture Model-Expectation Maximization (GMM-EM) algorithm. This method adopts amplitude information as an incoherence evaluation indicator. Furthermore, the statistical median of the amplitude dispersion index and amplitude mean is screened twice to extract a set of candidate points, including PS points that exhibit stable backscattering over long durations. Temporal coherence is simultaneously used as the coherence evaluation indicator. Another candidate point set is obtained by extracting high-coherence PS points using the GMM-EM algorithm. These sets of candidate points are then combined to obtain a final PS points set. In the experiment, the deformation monitoring of the under-construction Shenzhen-Zhongshan Cross-Sea Bridge in China was selected as a case study, with 28 Sentinel-1A images used as the data source for PS selection and deformation information extraction. The results show that the proposed method enhanced the density and quality of PS points on the under-construction cross-sea bridge compared to existing PS selection methods, thus offering higher reliability. Deformation analysis further revealed fluctuating deformation trends at characteristic points of the Shenzhen-Zhongshan Cross-Sea Bridge, indicating the occurrence of elastic deformation during its construction. [ABSTRACT FROM AUTHOR]

Geodesic coalescence, or the tendency of geodesics to merge together, is a hallmark phenomenon observed in a variety of planar random geometries involving a random distortion of the Euclidean metric. As a result of this, the union of interiors of all geodesics going to a fixed point tends to form a tree-like structure that is supported on a vanishing fraction of the space. Such geodesic trees exhibit intricate fractal behaviour; for instance, while almost every point in the space has only one geodesic going to the fixed point, there exist atypical points that admit two such geodesics. In this paper, we consider the directed landscape, the recently constructed [ 18 ] scaling limit of exponential last passage percolation (LPP), with the aim of developing tools to analyse the fractal aspects of the tree of semi-infinite geodesics in a given direction. We use the duality [ 39 ] between the geodesic tree and the interleaving competition interfaces in exponential LPP to obtain a duality between the geodesic tree and the corresponding dual tree in the landscape. Using this, we show that problems concerning the fractal behaviour of sets of atypical points for the geodesic tree can be transformed into corresponding problems for the dual tree, which might turn out to be easier. In particular, we use this method to show that the set of points admitting two semi-infinite geodesics in a fixed direction a.s. has Hausdorff dimension |$4/3$|⁠ , thereby answering a question posed in [ 12 ]. We also show that the set of points admitting three semi-infinite geodesics in a fixed direction is a.s. countable. [ABSTRACT FROM AUTHOR]

AbstractPhenomenon: With the proliferation of pass/fail grading practices in the pre-clerkship phase of undergraduate medical education, questions arise about the transparency and variability of grading and grade reporting practices, raising issues of equity in assessment, particularly regarding residency matching. The purpose of this survey was to determine the remediation and academic performance reporting practices of United States (U.S.) allopathic medical schools in the pre-clerkship phase of their curricula. Approach: After an extensive literature search and feedback from curriculum deans and learning experts, we developed a survey that we sent in the Spring of 2022 to pre-clerkship curriculum officials at all 154 accredited U.S. allopathic medical schools. It addressed curriculum content and structure; pre-clerkship remediation (e.g., course retakes) and reporting (e.g., permanency of transcript notation) practices; documentation and reporting of nonacademic competencies; and participant opinions and recommendations regarding reporting, transparency, and equity. We generated descriptive statistics and did manifest coding of open-ended responses. Findings: We had a response rate of 40% (62/155), with over 71% indicating mainly organ systems-based curricula. Depending on the situation, there were a wide range of remediation approaches for single- and multiple-course failures, including tutoring or learning support, re-exams, and referrals to a promotion board. Professionalism concerns were a top priority to report to residency directors, with significant variability in respondent opinions and practices in reporting remedial activities. Respondents were concerned about equity, both in terms of flexible grading practices and transparency of reporting practices. Insights: The variability in reporting practices across schools, while allowing holistic and individualized approaches to academic support, also creates potential inequities. More work is needed to understand how different reporting practices across institutions may disadvantage marginalized and minoritized student groups at different points in their preparation. [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]

In this article, we take a view of ignorance in relation to the new meaning of rationality, including the specific perspectives of limited rationality. We begin by suggesting that the problem of ignorance is far from the implied clarity of everyday expression, and there is a risk of inappropriate use of the concept. We show that not understanding what ignorance is, is part of ignorance, trying to avoid the situation of ignorance over ignorance. We propose a definition of ignorance by reference to the possible accessible and useful knowledge at a given time, suggesting that the understanding of ignorance is dependent on three variables: time, knowledge accessible at each moment of the present and utility. We analyze some asymmetries, including the one caused by the fact that we are often rigorous (but, nevertheless, interested) judges of others ignorance and very biased (that is, somewhat ignorant) about ourselves. We assess responsibility for our own ignorance by suggesting some limitations to the forms of ignorance for which we are responsible. We suggest that some variants of the unknown meet the definition of ignorance, and if we consider that most human decisions are made in conditions of information poverty, we can find that ignorance is frequently part of our cognitive strategies. Ignorance can be intentionally included in some of our cognitive strategies, one of which is provided by the principle of cognitive economics. The article can be one of the starting points for a set of recommendations on what can be ignored, what should and should not be ignored, when we are ignorant with no considerable effect and where/when we should not be. [ABSTRACT FROM AUTHOR]

This study explores the anharmonic local mode vibrational frequencies of the cyclohexane (C6H12) molecule, classified under the D3d point group, up to the second overtone. We use a vibrational Hamiltonian model based on U(2) Lie algebras. Our Lie algebraic method is characterized by integrating minimized algebraic parameters precisely adapted for cyclohexane. This process involves substituting each bond in the molecule with a corresponding Lie algebra, leading to the development of a Hamiltonian that includes interacting operators. Through this detailed analysis, we illuminate the anharmonic vibrational behavior of cyclohexane, providing significant insights into its molecular dynamics within a framework that respects symmetry adaptation. [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]

We investigate how the complexity of Euclidean TSP for point sets P inside the strip (- ∞ , + ∞) × [ 0 , δ ] depends on the strip width δ . We obtain two main results. For the case where the points have distinct integer x-coordinates, we prove that a shortest bitonic tour (which can be computed in O (n log 2 n) time using an existing algorithm) is guaranteed to be a shortest tour overall when δ ⩽ 2 2 , a bound which is best possible. We present an algorithm that is fixed-parameter tractable with respect to δ . Our algorithm has running time 2 O (δ) n + O (δ 2 n 2) for sparse point sets, where each 1 × δ rectangle inside the strip contains O(1) points. For random point sets, where the points are chosen uniformly at random from the rectangle [ 0 , n ] × [ 0 , δ ] , it has an expected running time of 2 O (δ) n . These results generalise to point sets P inside a hypercylinder of width δ . In this case, the factors 2 O (δ) become 2 O (δ 1 - 1 / d) . [ABSTRACT FROM AUTHOR]

For any given full rank lattice Λ and natural number K, we consider the point set P (K) = Λ / K ∩ (0 , 1) 2 , with N = # P (K) ≈ K 2 , and bound the spherical cap discrepancy of the projection of these points under the Lambert map to the unit sphere. The bound is of order 1 / N , with leading coefficient given explicitly and depending on Λ only. The proof is established using a lemma that bounds the number of intersections of certain curves with fundamental domains that tile R 2 , and even allows for local perturbations of Λ without affecting the bound, proving to be suitable for numerical applications. A special case yields the smallest constant for the leading term of the cap discrepancy for deterministic algorithms up to date. [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]

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]

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]

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]

Precision agriculture benefits from point set registration, which can monitor plant health and growth in real time, promote the precise application of fertilizers and pesticides, and provide technical support for achieving sustainable development of agriculture. In this work, we propose a robust point set registration method for precision agriculture based on L*a*b* color guidance, bidirectional search and Cauchy distribution. First, the L*a*b* color guidance is applied to establish accurate correspondences between agricultural RGB‐D data. Second, the bidirectional nearest neighbor search strategy between point sets improves the reliability of establishing correspondences and broadens the convergence domain of the algorithm. Third, Cauchy distribution is utilized as an energy function for noise suppression, which further improves the robustness of the algorithm in dealing with complex vegetation scenes. Finally, results of ablation and simulation experiments indicate that the proposed registration algorithm can achieve more accurate and robust alignment results than other classic and state‐of‐the‐art point cloud registration algorithms to achieve monitoring and comparison of plant growth. [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]

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]

In this paper, we introduce the notion of the semi-symmetric metric connection in the Heisenberg group. Moreover, by using the method of Riemannian approximations, we define the notions of intrinsic curvature for regular curves, the intrinsic geodesic curvature of regular curves on a surface, and the intrinsic Gaussian curvature of the surface away from characteristic points in the Heisenberg group with the semi-symmetric metric connection. Finally, we derive the expressions of those curvatures and prove the Gauss–Bonnet theorem related to the semi-symmetric metric connection in the Heisenberg group. [ABSTRACT FROM AUTHOR]