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Arising from the harmonic approximation in solving the vibrational Schrödinger equation, normal modes dissect molecular vibrations into distinct degrees of freedom. Normal modes are widely used as they give rise to descriptive vibrational notations and are convenient for expanding anharmonic potential energy surfaces as an alternative to higher-order Taylor series representations. Usually, normal modes are expressed in Cartesian coordinates, which bears drawbacks that can be overcome by switching to internal coordinates. Considering vibrational notations, normal modes with delocalized characters are difficult to denote, but internal coordinates offer a route to clearer notations. Based on the Hessian, normal mode decomposition schemes for a given set of internal coordinates can describe a normal mode by its contributions from internal coordinates. However, choosing a set of internal coordinates is not straightforward. While the Hessian provides unique sets of normal modes, various internal coordinate sets are possible for a given system. In the present work, we employ a normal mode decomposition scheme to choose an optimal set. Therefore, we screen reasonable sets based on topology and symmetry considerations and rely on a metric that minimizes coupling between internal coordinates. Ultimately, the Nomodeco toolkit presented here generates internal coordinate sets to find an optimal set for representing molecular vibrations. The resulting contribution tables can be used to clarify vibrational notations. We test our scheme on small to mid-sized molecules, showing how the space of definable internal coordinate sets can significantly be reduced. [ABSTRACT FROM AUTHOR]

Atomistic simulations of biological processes offer insights at a high level of spatial and temporal resolution, but accelerated sampling is often required for probing timescales of biologically relevant processes. The resulting data need to be statistically reweighted and condensed in a concise yet faithful manner to facilitate interpretation. Here, we provide evidence that a recently proposed approach for the unsupervised determination of optimized reaction coordinate (RC) can be used for both analysis and reweighting of such data. We first show that for a peptide interconverting between helical and collapsed configurations, the optimal RC permits efficient reconstruction of equilibrium properties from enhanced sampling trajectories. Upon RC-reweighting, kinetic rate constants and free energy profiles are in good agreement with values obtained from equilibrium simulations. In a more challenging test, we apply the method to enhanced sampling simulations of the unbinding of an acetylated lysine-containing tripeptide from the bromodomain of ATAD2. The complexity of this system allows us to investigate the strengths and limitations of these RCs. Overall, the findings presented here underline the potential of the unsupervised determination of reaction coordinates and the synergy with orthogonal analysis methods, such as Markov state models and SAPPHIRE analysis. [ABSTRACT FROM AUTHOR]

We construct an electrical-network version of the twist map for the positive Grassmannian, and use it to solve the inverse problem of recovering conductances from the response matrix. Each conductance is expressed as a biratio of Pfaffians as in the inverse map of Kenyon and Wilson; however, our Pfaffians are the more canonical |$B$| variables instead of their tripod variables, and are coordinates on the positive orthogonal Grassmannian studied by Henriques and Speyer. [ABSTRACT FROM AUTHOR]

Our starting point is the covariant coordinate transformation equation of a relativistic positioning system in Minkowski space–time that maps the receiver's emission coordinates (proper times broadcast by the emitters) to its coordinates in some inertial reference frame. Bancroft's analytical (closed-form) solution to the basic pseudorange navigation equations with four emitters is recovered, and the subjacent elements are geometrically interpreted. The case of four static beacons is analysed as a clarifying situation. [ABSTRACT FROM AUTHOR]

Generally, performing multiple scans is necessary to cover entire scanning area, and multiple point clouds are thus obtained. These point clouds need to be registered together, which is the focus of our work. However, influenced by the noise, point density variation, partial overlap and so on, the success rate of registration is still low. For this reason, a pairwise registration method is first proposed. It includes two main components: the triple local coordinate image (TriLCI) descriptor and a new 3D transformation estimation technique. The descriptor has high descriptiveness and strong robustness, by which more right correspondences can be achieved. The 3D transformation estimation technique is employed to calculate the rotation matrix and translation vector under the condition that most of correspondences are false. In this technique, a new geometric distance constraint is developed, and is then applied to eliminate incorrect correspondences. The robust estimation based on the median is introduced to calculate the rotation matrix and translation vector. For multi-view registration, the connected graph algorithm and shape growing based method are applied. A comparative study is presented. The experimental results well demonstrate that the proposed pairwise registration method has high success rate. The comparative study gives the merits and demerits of the two multi-view registration methods. [ABSTRACT FROM AUTHOR]

The paper is organized to study some mathematical properties and dynamics of a simple Cournot duopoly game based on a computed quadratic cost. The time evolution of this game is described by a two-dimensional noninvertible discrete time map using the bounded rationality mechanism. For this map, some dynamic characteristics such as multistability and synchronization are investigated. Its equilibrium points are obtained for the asymmetric case, and their conditions of stability are obtained. Our results investigate that the Nash equilibrium point may be unstable due to flip bifurcation and under certain parameter values, and Neimark–Sacker bifurcation is born after the period-4 cycle. Through some restrictions, the coordinate axes of the map construct an invariant manifold, and therefore, their dynamics can be analyzed by using a one-dimensional map. In the symmetric case, both firms behave identically, and this implies that the diagonal set forms an invariant manifold, and hence the synchronization phenomena take place. Furthermore, the global bifurcation of the map is confirmed through contact between critical curves and the boundaries of infeasible domains. [ABSTRACT FROM AUTHOR]

Recent progress in autoencoder-based sparse identification of nonlinear dynamics (SINDy) under ℓ1 constraints allows joint discoveries of governing equations and latent coordinate systems from spatio-temporal data, including simulated video frames. However, it is challenging for ℓ1 -based sparse inference to perform correct identification for real data due to the noisy measurements and often limited sample sizes. To address the data-driven discovery of physics in the low-data and high-noise regimes, we propose Bayesian SINDy autoencoders, which incorporate a hierarchical Bayesian Spike-and-slab Gaussian Lasso prior. Bayesian SINDy autoencoder enables the joint discovery of governing equations and coordinate systems with uncertainty estimate. To resolve the challenging computational tractability of the Bayesian hierarchical setting, we adapt an adaptive empirical Bayesian method with Stochastic Gradient Langevin Dynamics (SGLD) which gives a computationally tractable way of Bayesian posterior sampling within our framework. Bayesian SINDy autoencoder achieves better physics discovery with lower data and fewer training epochs, along with valid uncertainty quantification suggested by the experimental studies. The Bayesian SINDy autoencoder can be applied to real video data, withaccurate physics discovery which correctly identifies the governing equation and provides a close estimate for standard physics constants like gravity g , for example, in videos of a pendulum. [ABSTRACT FROM AUTHOR]

The increasing frequency of technological events has resulted in significant damage to the environment, human health, social stability, and economy, driving ongoing scientific development and interest in emergency management (EM). Traditional EM approaches are often inadequate because of incomplete and imprecise information during crises, making fast and effective decision-making challenging. Computational Intelligence techniques (CI) offer decision-supporting capabilities that can effectively address these challenges. However, there is still a need for deeper integration of emerging computational intelligence techniques to support evidence-based decision-making while also addressing gaps in metrics, standards, and protocols for emergency response and scalability. This study presents a coordinated decision-making system for multiple types of emergency case scenarios for technological disaster management based on CI techniques, including an Improved Genetic Algorithm (IGA), and Multi-objective Particle Swarm Optimization (MOPSO). The IGA enhances emergency performance by optimizing the task assignment for multiple agents involved in emergency response with coordination mechanisms, resulting in an approximately 15% improvement compared to other state-of-the-art methods. Ultimately, this study offers a promising foundation for future research to develop effective strategies for mitigating the impact of technological disasters on society and the environment. [ABSTRACT FROM AUTHOR]

Starting from a general transformation for spherically symmetric metrics where g_11=-1/g_00, we analyze coordinates with the common property of conformal flatness at constant solid angle element. Three general possibilities arise: one where tortoise coordinate appears as the unique solution, other that includes Kruskal-Szekeres coordinates as a very specific case, but that also allows other similar transformations, and finally a new set of coordinates with very different properties than the other two. In particular, it represents any causal patch of the spherically symmetric metrics in a compactified form. We analyze general properties of the new proposed "pulsating coordinates", and then proceed to apply the transformation for the Schwarzschild spacetime, as well as for several cosmological solutions, contrasting properties with the Kruskal case. In particular, Anti-de-Sitter solution presents interesting features. [ABSTRACT FROM AUTHOR]

The current challenging problems of learning a robust 6D pose lie in noise in RGB/RGBD images, sparsity of point cloud and severe occlusion. To tackle the problems, object geometric information is critical. In this work, we present a novel pipeline for 6DoF object pose estimation. Unlike previous methods that directly regressing pose parameters and predicting keypoints, we tackle this challenging task with a point-pair based approach and leverage geometric information as much as possible. Specifically, at the representation learning stage, we build a point cloud network locally modeling CNN to encode point cloud, which is able to extract effective geometric features while the point cloud is projected into a high-dimensional space. Moreover, we design a coordinate conversion network to regress point cloud in the object coordinate system in a decoded way. Then, the pose could be calculated through point pairs matching algorithm. Experimental results show that our method achieves state-of-the-art performance on several datasets. [ABSTRACT FROM AUTHOR]

The dynamics of the spring-pendulum system with two degrees of freedom were studied. The motion of this system is restricted to be in a vertical plane so that the chosen generalized coordinates are the increased length of the spring and the swing angle of pendulum. Hamiltonian of the system is obtained from the Legendre transformation of Lagrangian. Hamilton's equation yields four differential equations that represent the dynamic of the system. The obtained results were visualized in configuration space and phase space trajectories. It is shown that generally the greater the initial swing angle, the more complex pattern will occur followed by the appearance of chaotic phenomena. [ABSTRACT FROM AUTHOR]

The target coordinate measurement system features an extensive range of key applications. In many highprecision measurement systems wide scope, high precision and multiple cameras are used. However, the objective of this paper is to enhance the measurement accuracy and range of a monocular target owing to its portability and convenience. A systematic simulation of linear, planar and stereo target structures was carried out to investigate target structures. Based on our simulation results, the 3D target is more accurate and robust to tilt due to rich information available from 3D locations of the markers. To overcome the limitation in the measurement range for the monocular target, ideas of coded stereo target are presented in this paper. The measured coordinates can be calculated from only part of the markers, effectively enlarging the measurement range at short object distances. A stereo coded target system is designed based on this method and is compared to an ordinary monocular target. Stability experiments were conducted under different object distances and poses, which have shown that the Z direction accuracy of the stereo target is at least 23.8% or 10% higher than that of the 1D or 2D target, respectively. Additionally, the ranging experiment revealed that the measurement accuracy of the coded stereo target is 23.5% or 59.2% higher than that of the non-coded 1D or 2D target when measuring the Z direction and the distance of the far field. [ABSTRACT FROM AUTHOR]

Objective: The study analyzes the adoption of the Ecological ICMS in the states located in the Legal Amazon and the instruments mobilized by these regulatory state policies to coordinate the environmental actions in their municipalities. Methodology: The relevant legislation was reviewed and a bibliographical analysis of the Ecological ICMS was carried out in the six states where the policy is in force as they contain part of the Amazon forest: Amapá, Pará, Tocantins, Mato Grosso, Rondônia, and Acre. Originality/Relevance: The originality of the article lies in its comparison of the instruments for coordinating the ICMS-E legislation and its results in the states of the Legal Amazon to improve current legislation while encouraging other states in the country to adhere to this policy. Results: Regulatory and financial coordination instruments guide ICMS-E policies in the Legal Amazon as the essence of this policy is resource allocation according to environmental criteria stipulated by state legislation. However, greater clarity in the ICMS-E objectives could help municipalities adapt their actions to the practices expected by the states. Higher transfer percentages and coordination instruments related to management were also factors identified that could improve the policy's performance. Social/management contributions: The article contributes to the field of regional planning by offering recommendations for improving ICMS-E policies in states that have already adopted it and for those that have not yet implemented it. The study showed that the more coordination instruments used in the ICMS-E policy, the greater the possibility for states to affect municipal choices for improving environmental management. [ABSTRACT FROM AUTHOR]

Aiming at the problems of low accuracy, false detection, missed detection, and low real-time detection of current traffic sign detection, this paper proposes an improved traffic sign detection algorithm based on the YOLOv8s algorithm. Firstly, this paper proposes a double-layer semicomposite backbone network structure (DSCB), which uses the auxiliary backbone network to extract features, and then transmits the extracted features to the backbone network to enhance the ability of the backbone network to extract target features. At the same time, the deformable convolution is integrated into the DC2f structure of the auxiliary backbone network to enhance the generalization performance of the network. Secondly, the coordinate attention mechanism is used after the SPPF layer. The coordinate attention mechanism can better retain the coordinate position information of small targets, reduce the miss rate of the model, and increase detection accuracy. Finally, this paper introduces a new CAB module to learn and aggregate the output of each layer of the feature pyramid for global spatial context to enhance the feature representation ability further. The experimental results show that the improved algorithm achieves 90.51% detection accuracy, 82.00% recall rate, 89.51% mAP@0.5 on the TT100K dataset, and the FPS reaches 106. Compared with the original algorithm model, the detection accuracy is increased by 2.27%, and the recall rate is increased by 2.48%. mAP@0.5 is increased by 2.01%, and FPS is increased by 1. The improved traffic sign detection algorithm meets the requirements in detection accuracy and real-time detection. [ABSTRACT FROM AUTHOR]

We investigate the Teukolsky equation in horizon-penetrating coordinates to study the behavior of perturbation waves crossing the outer horizon. For this purpose, we use the null ingoing/outgoing Eddington–Finkelstein coordinates. The first derivative of the radial equation is a Fuchsian differential equation with an additional regular singularity to the ones the radial one has. The radial functions satisfy the physical boundary conditions without imposing any regularity conditions. We also observe that the Hertz-Weyl scalar equations preserve their angular and radial signatures in these coordinates. Using the angular equation, we construct the metric perturbation for a circularly orbiting perturber around a black hole in Kerr spacetime in a horizon-penetrating setting. Furthermore, we completed the missing metric pieces due to the mass M and angular momentum J perturbations. We also provide an explicit formula for the metric perturbation as a function of the radial part, its derivative, and the angular part of the solution to the Teukolsky equation. Finally, we discuss the importance of the extra singularity in the radial derivative for the convergence of the metric expansion. [ABSTRACT FROM AUTHOR]

The search for equilibrium in a two-stage traffic flow model reduces to the solution of a special nonsmooth convex optimization problem with two groups of different variables. For numerical solution of this problem, it is proposed to use the accelerated block-coordinate Nesterov–Stich method with a special choice of block probabilities at each iteration. Theoretical estimates of the complexity of this approach can appreciably improve the estimates of previously used approaches. However, in the general case they do not guarantee faster convergence. Numerical experiments with the proposed algorithms are carried out. [ABSTRACT FROM AUTHOR]

In this paper, a novel multi-node plate element with absolute node coordinate formulation (ANCF) is proposed. The nodes of the element are collocated to coincide with the in-plane integral quadrature points, which are used to calculate the elastic and inertia functions. The unevenly distributed nodes of the element are the zero points of the second-order derivative of Legendre polynomial and the boundary ends of the element. The tensor product of the two-direction univariate Lagrange interpolation is used to define the displacement field. To alleviate the locking problem, the gradient deficient setup and the second-order gradient of the thickness direction are used as the nodal coordinates. The standard continuum mechanic formulation is used to deduce the elastic forces. The proposed plate element based on the ANCF with collocated nodes is denoted as ANCF _ C element. The performance of the ANCF _ C element is verified by static, eigenfrequency and dynamic examples. The results show that the ANCF _ C element is more accurate and computationally efficient. [ABSTRACT FROM AUTHOR]

This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors resulting from numerical approximation. To construct our approximation, we decompose the stable manifold into three components: a finite dimensional slow component, a fast-but-finite dimensional component, and a strongly contracting infinite dimensional "tail". We employ the parameterization method in a finite dimensional projection to approximate the slow-stable manifold, as well as the attached finite dimensional invariant vector bundles. This approximation provides a change of coordinates which largely removes the nonlinear terms in the slow stable directions. In this adapted coordinate system we apply the Lyapunov-Perron method, resulting in mathematically rigorous bounds on the approximation errors. As a result, we obtain significantly sharper bounds than would be obtained using only the linear approximation given by the eigendirections. As a concrete example we illustrate the technique for a 1D Swift-Hohenberg equation. [ABSTRACT FROM AUTHOR]

Chirality was traditionally considered a binary property of periodic lattices and crystals. However, the classes of two‐dimensional lattices modulo rigid motion form a continuous space, which was recently parametrized by three geographic‐style coordinates. The four non‐oblique Bravais classes of two‐dimensional lattices form low‐dimensional singular subspaces in the full continuous space. Now, the deviations of a lattice from its higher symmetry neighbors can be continuously quantified by real‐valued distances satisfying metric axioms. This article analyzes these and newer G‐chiral distances for millions of two‐dimensional lattices that are extracted from thousands of available two‐dimensional materials and real crystal structures in the Cambridge Structural Database. [ABSTRACT FROM AUTHOR]

This paper addresses the challenge of protecting electrical networks in the presence of distribution generators (DGs). The use of DGs affects fault currents, leading to miscoordination between protection relays and causing constraints on network reliability. To tackle this issue, the authors propose an adaptive protection scheme (APS) based on a modified pelican optimization algorithm (MPOA) and active database management system (ADBMS). The APS coordinates directional overcurrent relays and distance relays, while the MPOA simulates a pelican mating strategy and includes a modified internal equation. The proposed APS is further upgraded with ADBMS to save system resources by storing relay settings in the database and calling them when the state of DGs changes without running optimization algorithms. The effectiveness of the proposed APS is validated on the Institute of Electrical and Electronics Engineers (IEEE) eight‐bus test system and the IEEE 14‐bus distribution network. Results indicate that the APS can effectively protect electrical networks in the presence of DGs, while the ADBMS upgrade saves system resources. [ABSTRACT FROM AUTHOR]

This study proposes an algebraic method of regional green wave coordinated control (AM-RGWCC) that can operate efficiently. The research on regional green wave coordinated control (RGWCC) has gradually become a hot spot, improving the overall operational efficiency of the control area more comprehensively and systematically. We usually encounter the difficulties of many constraints, high complexity, and low efficiency when using the modeling method to solve the RGWCC problem. AM-RGWCC is developed in this study to overcome these challenges. The overall coordinated effect is assured by realizing the comprehensive optimization of phase sequence, offset, and common signal cycle. A step-by-step design of AM-RGWCC is established to reduce the complexity by analyzing the comprehensive influence of offset difference and bias distance on the green wave bandwidth. Finally, the case study shows that for a three-by-three road network, an ideal scheme can be obtained by AM-RGWCC to maximize the green wave bandwidth in one second. The green wave bandwidth of each intersection accounts for more than 84%. The results illustrate that the coordinated effect and solving efficiency are significantly improved. The proposed algebraic method will have certain advantages in the RGWCC design of a large-scale road network. [ABSTRACT FROM AUTHOR]

A drone was used to map an area of 18.99 hectares with millimeter accuracy. The mapping process involved creating eight targets on the ground that were visible to the drone at a height of 60 meters. The coordinates of the targets were determined using GPS methods. Classical topographic methods have also been used to calibrate the drone's GPS for further correction and accuracy. A flight plan was created using DJI software, which determined the flight area, height, time, frame rate, camera tilt, battery level, direction of flight, wind speed, latitude, longitude, and flight speed. The flight plan was uploaded to the drone's memory, and the drone was flown according to the established parameters. This technology allows to make high-resolution digital maps (orthophotoplans), as well as 3D models of some objectives - historical monuments, buildings, land. A drone can be defined as an unmanned aircraft capable of autonomous navigation without external control using autopilot or that can be controlled by a remote control device. This technology allows the creation of high-resolution digital maps. With the help of UAV technology it is possible to provide topographic support for the revision of General Urban Plans (GUP), elaboration of Zonal Urban Plans (PUZ), feasibility studies for investment works, such as road infrastructure, railways, electrical networks. etc. [ABSTRACT FROM AUTHOR]

This paper is focused on the data description of the railway infrastructure. Its aim is to present the possibilities of constructing of linear elements representing tracks in 2D and their subsequent transformation into 3D using the parametric description of horizontal and vertical curves. The transformation is based on determining the spatial coordinates of the newly emerging 3D linear elements. This process is supposed to be implemented in such a graphical editor environment that allows the relevant data to be transferred to the the database based on the Multipurpose Railway Infrastructure Model. With the use of this data, it is possible to perform, among other things, the visualization of the railway infrastructure. [ABSTRACT FROM AUTHOR]

Surveyors are occasionally tasked to with determining the coordinates of inaccessible locations or points in civil engineering applications, ground control points for photogrammetry or LiDAR data acquisition, among others. The present work outlines and investigates a novel method for estimating the GNSS coordinates of an inaccessible location where a surveying instrument cannot be set up. The procedure is based on the well-known surveying intersection method and data extracted from an Earth Gravity Model (e.g., EGM 2008). The location's coordinates are obtained from the least-squares adjustment of the angles and distances measured from at least two sites to the unknown point using a total station, within the framework of the Gauss–Helmert method. Field tests confirmed that the accuracy of the determined coordinates of the inaccessible point is at the level of 1 cm. The proposed method bypasses standard coordinate transformation steps performed with the traditional approach, directly producing geocentric coordinates of the unknown points. [ABSTRACT FROM AUTHOR]

Optimal power flow (OPF) is one of the most widely studied problems in the field of operations research, as it applies to the optimal and efficient operation of the electric power system. Both the problem formulation and solution techniques have attracted significant research interest over the decades. A wide range of OPF problems have been formulated to cater for the various operational objectives of the power system and are mainly expressed either in polar or rectangular voltage coordinates. Many different solution techniques falling into the two main categories of classical/deterministic optimization and heuristic/non-deterministic optimization techniques have been explored in the literature. This study considers the Volt/VAR optimization (VVO) variant of the OPF problem formulated in rectangular voltage coordinates, which is something of a departure from the majority of the studies, which tend to use the polar coordinate formulation. The heuristic particle swarm optimization (PSO) and the classical primal-dual interior-point method (PDIPM) are applied to the solution of the VVO problem and a comparative analysis of the relative performance of the two algorithms for this problem is presented. Four case studies based on the 6-bus, IEEE 14-bus, 30-bus, and 118-bus test systems are presented. The comparative performance analysis reveals that the two algorithms have complementary strengths, when evaluated on the basis of the solution quality and computational efficiency. Particularly, the PSO algorithm achieves greater power loss minimization, whereas the PDIPM exhibits greater speed of convergence (and, thus, better computational efficiency) relative to the PSO algorithm, particularly for higher-dimensional problems. An additional distinguishing characteristic of the proposed solution is that it incorporates the Newton–Raphson load flow computation, also formulated in rectangular voltage coordinates, which adds to the efficiency and effectiveness of the presented solution method. [ABSTRACT FROM AUTHOR]

There is a long-standing problem of repeated patterns in correspondence problems, where mismatches frequently occur because of inherent ambiguity. The unique position information associated with repeated patterns makes coordinate representations a useful supplement to appearance representations for improving feature correspondences. However, the issue of appropriate coordinate representation has remained unresolved. In this study, we demonstrate that geometric-invariant coordinate representations, such as barycentric coordinates, can significantly reduce mismatches between features. The first step is to establish a theoretical foundation for geometrically invariant coordinates. We present a seed matching and filtering network (SMFNet) that combines feature matching and consistency filtering with a coarse-to-fine matching strategy in order to acquire reliable sparse correspondences. We then introduce Degree, a novel anchor-to-barycentric (A2B) coordinate encoding approach, which generates multiple affine-invariant correspondence coordinates from paired images. Degree can be used as a plug-in with standard descriptors, feature matchers, and consistency filters to improve the matching quality. Extensive experiments in synthesized indoor and outdoor datasets demonstrate that Degree alleviates the problem of repeated patterns and helps achieve state-of-the-art performance. Furthermore, Degree also reports competitive performance in the third Image Matching Challenge at CVPR 2021. This approach offers a new perspective to alleviate the problem of repeated patterns and emphasizes the importance of choosing coordinate representations for feature correspondences. [ABSTRACT FROM AUTHOR]

The unit vectors transformation between the Cartesian and the novel similar oblate spheroidal coordinates, and vice versa, is derived. It facilitates transformation of vector fields between these two types of orthogonal coordinates and can advantageously simplify solutions of problems exhibiting oblate spheroidal geometry. Several examples demonstrate the use of the derived relations. Generalized sine and cosine applicable in the similar oblate spheroidal coordinate system are introduced as well. [ABSTRACT FROM AUTHOR]

Radiative heat transport involving complex geometries is an important area of investigation. The formulation of the transport phenomenon is more involved and consideration of the proper treatment of the irregular geometry becomes necessary for accurate estimation of heat transfer rates. Therefore, the present study focuses on the modeling and the solution of the radiative transfer equation (RTE) in an absorbing, emitting, and isotropically scattering, participating media for complex geometries using the body-fitted coordinates. The RTE in an orthogonal coordinate system is formulated and is then numerically solved in conjunction with a numerically generated, body-fitted, curvilinear coordinate system. The geometries are considered to be opaque and, in the analysis, both the radiative as well as the non-radiative equilibrium cases are considered. The formulation is validated through the previously published results. Notable agreement is observed between the results and those reported earlier for different complex geometries and various properties of the participating media. [ABSTRACT FROM AUTHOR]

The theory of hierarchical equations of motion (HEOM) is one of the standard methods to give exact evaluations of the dynamics as coupled to harmonic oscillator environments. However, the theory is numerically demanding due to its hierarchy, which is the set of auxiliary elements introduced to capture the non-Markovian and non-perturbative effects of environments. When system–bath coupling becomes relatively strong, the required computational resources and precision move beyond the regime that can be currently handled. This article presents a new representation of HEOM theory in which the hierarchy is mapped into a continuous space of a collective bath coordinate and several auxiliary coordinates as the form of the quantum Fokker–Planck equation. This representation gives a rigorous time evolution of the bath coordinate distribution and is more stable and efficient than the original HEOM theory, particularly when there is a strong system–bath coupling. We demonstrate the suitability of this approach to treat vibronic system models coupled to environments. [ABSTRACT FROM AUTHOR]

We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and collate useful vector calculus identities for these coordinates. These results and provided code enable consistent accounting of geometric effects to arbitrary order for boundary layer asymptotics in a wide range of physical systems. [ABSTRACT FROM AUTHOR]

Object localization has been the focus of research in Fine-Grained Visual Categorization (FGVC). With the aim of improving the accuracy and precision of object localization in multi-branch networks, as well as the robustness and universality of object localization methods, our study mainly focus on how to combine coordinate attention and feature activation map for target localization. The model in this paper is a three-branch model including raw branch, object branch and part branch. The images are fed directly into the raw branch. Coordinate Attention Object Localization Module (CAOLM) is used to localize and crop objects in the image to generate the input for the object branch. Attention Partial Proposal Module (APPM) is used to propose part regions at different scales. The three classes of input images undergo end-to-end weakly supervised learning through different branches of the network. The model expands the receptive field to capture multi-scale features by Selective Branch Atrous Spatial Pooling Pyramid (SB-ASPP). It can fuse the feature maps obtained from the raw branch and the object branch with Selective Branch Block (SBBlock), and the complete features of the raw branch are used to supplement the missing information of the object branch. Extensive experimental results on CUB-200-2011, FGVC-Aircraft and Stanford Cars datasets show that our method has the best classification performance on FGVC-Aircraft and also has competitive performance on other datasets. Few parameters and fast inference speed are also the advantages of our model. [ABSTRACT FROM AUTHOR]

The β‐barrel assembly machinery (Bam) complex facilitates the assembly of outer membrane proteins (OMPs) in gram‐negative bacteria. The Bam complex is conserved and essential for bacterial viability and consists of five subunits, BamA‐E. BamA is the transmembrane component, and its β‐barrel domain opens laterally to allow folding and insertion of incoming OMPs. The remaining components are regulatory, among which only BamD is essential. Previous studies suggested that BamB regulates BamA directly, while BamE and BamC serve as BamD regulators. However, specific molecular details of their functions remain unknown. Our previous research demonstrated that BamE plays a specialized role in assembling the complex between the lipoprotein RcsF and its OMP partners, required for the Regulator of Capsule Synthesis (Rcs) stress response. Here, we used RcsF/OmpA as a model substrate to investigate BamE function. Our results challenge the current view that BamE only serves as a BamD regulator. We show that BamE also directly interacts with BamA. BamE interaction with both BamA and BamD is important for function. Our genetic and biochemical analysis shows that BamE stabilizes the Bam complex and promotes bidirectional signaling interaction between BamA and BamD. This BamE function becomes essential when direct BamA/BamD communication is impeded. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to show that the (multi-homogeneous) coordinate ring of a partial flag variety C [ G / P K − ] contains a cluster algebra if G is any semisimple complex algebraic group. We use derivation properties and a special lifting map to prove that the cluster algebra structure A of the coordinate ring C [ N K ] of a Schubert cell constructed by Goodearl and Yakimov can be lifted, in an explicit way, to a cluster structure A ˆ living in the coordinate ring of the corresponding partial flag variety. Then we use a minimality condition to prove that the cluster algebra A ˆ is equal to C [ G / P K − ] after localizing some special minors. [ABSTRACT FROM AUTHOR]

Conditions of a nonlocal solvability of the Cauchy problem in original coordinates are obtained for a system of two quasilinear first-order partial differential equations with constant terms. The investigation is based on the method of an additional argument. The proof of the nonlocal solvability of the Cauchy problem in original coordinates relies on global estimates. [ABSTRACT FROM AUTHOR]

Prey species that form groups gain a range of benefits from associating with conspecifics, including access to social information. Groups typically coordinate collective movement through local interactions, where individuals copy their nearest neighbours' behaviour to generate group level decisions. However, individuals in a group may not always make 'correct' decisions, and blind copying of behaviour can lead to the spread of poor information and maladaptive cascades. To impede the spread of poor information, many animals that form groups have developed information-dampening mechanisms such as consensus decision making through the quorum response. In this study we monitored flocks of roosting Eurasian oystercatchers with a view to understanding the mechanics of group departure decisions and to test for the presence of a quorum response. Nearing high tide, oystercatchers would leave the roosting site en masse, where the timing of departure of many individuals was coordinated. Coordinating the timing of mass departures was a complex task as single birds and small groups frequently joined and departed from the roosting site, meaning individuals had to decide which departures to copy and which to ignore. Individual oystercatchers were more likely to depart within 10 s of another bird if they were closer together in the group, suggesting that departure information may be transferred locally between neighbouring birds. While single departures were very common, most individuals departed in groups of 10 or more, showing that single departures were a relatively weak departure cue and were frequently ignored by the rest of the group. The probability of an individual joining a departure event was higher with increasing departure group size in a nonlinear (sigmoidal) relationship. This trend is consistent with a quorum response with the propensity to copy the departure of groupmates sharply increasing at a quorum threshold of about 10 birds. • Roosting oystercatchers departed en masse in response to the rising tide. • Departure information flows locally between close neighbouring birds. • The likelihood of joining a departure sharply rises at departing group sizes of >10. • Oystercatchers may use consensus decision making to regulate mass departures. [ABSTRACT FROM AUTHOR]

The rapidly drop of frequency in the microgrid (MG) system when it operates under island operation has caused frequency stability problems. In case, generators and renewable energy sources cannot supply enough power to restore the frequency, the load shedding will be proceeded. This paper proposes the load shedding method based on the coordinate multiple load shedding factors when the MG system operates in island mode. This proposed method carries out an approach through two main steps. Firstly, the optimal amount of load shedding power considering renewable energy sources and the ability to adjust the primary and secondary frequencies of the generator is calculated to restore the frequency to the allowed range. Next, distributing the optimal load shedding power for each bus is based on the combination of different criteria to meet the economic and technical goals. On the technical side, this paper also considers two criteria about the voltage distance, and the voltage sensitivity index. These two criteria contribute to reducing voltage drop and improving voltage stability when the microgrid operates in island mode. From the economic perspective, it considers the load importance factor, thereby minimizing the economic losses caused by load shedding. The AHP algorithm is applied in this paper to determine the importance of loads and the importance of the different criteria when they are combined. The effectiveness of the proposed method is demonstrated through simulation of IEEE 16-bus microgrid with 6-source. [ABSTRACT FROM AUTHOR]

Diagnosing Parkinson's disease (PD) in its early stages is a significant challenge in medicine. Hand tremors and dysgraphia, which are typical early motor symptoms of PD, can manifest for decades before a formal diagnosis is made. Therefore, handwriting analysis has become an important tool for detecting PD. While many machine learning algorithms have been applied in this area, they struggle to capture the subtle changes in handwriting and must describe features from various perspectives. To address these issues, this paper proposes a Coordinate Attention Enhanced Swin Transformer (CAS Transformer) model for PD handwriting recognition. It establishes the long‐term dependence of features on the joint coordinate attention application, which enables the model to more accurately localize the important features of handwriting data and also extract the fuzzy edge features of handwriting images.These characteristics of the CAS Transformer enable it to outperform current advanced deep learning methods in classification, with an accuracy of 92.68% in experiments conducted on two handwritten datasets. [ABSTRACT FROM AUTHOR]

The application of directional overcurrent relays (DOCRs) plays an important role in protecting power systems and ensuring their safe, reliable, and efficient operation. However, coordinating DOCRs involves solving a highly constrained and nonlinear optimization problem. The primary objective of optimization is to minimize the total operating time of DOCRs by determining the optimal values for decision variables such as the time multiplier setting (TMS) and plug setting (PS). This article presents an efficient hybrid optimization algorithm that combines the modified firefly algorithm and genetic algorithm to achieve improved solutions. First, this study modifies the firefly algorithm to obtain a global solution by updating the firefly's brightness and to prevent the distance between the individual fireflies from being too far. Additionally, the randomized movements are controlled to produce a high convergence rate. Second, the optimization problem is solved using the genetic algorithm. Finally, the solution obtained from the modified firefly algorithm is used as the initial population for the genetic algorithm. The proposed algorithms have been tested on the IEEE 3-bus, 8-bus, 9-bus and 15-bus networks. The results indicate the effectiveness and superiority of the proposed algorithms in minimizing the total operating time of DOCRs compared with other optimization methods presented in the literature. [ABSTRACT FROM AUTHOR]

Control of geodetic parameters is very important for traffic safety on the railways. Such control must be performed regularly because of the deviation of the track axis due to train traffic. The purpose of the article is the development of a mathematical rationale for the placement of railway benchmarks for the creation of the 'own' conditional benchmark network of the railway. These permanent repers are the basic points for both the construction stage and operation stage. The method is described and the curve coordinates from any point of the conditional benchmark network of the railway have been obtained. [ABSTRACT FROM AUTHOR]

We describe the projective superspace approach to supersymmetric models with off-shell (0, 4) supersymmetry in two dimensions. In addition to the usual superspace coordinates, projective superspace has extra bosonic variables — one doublet for each SU(2) in the R-symmetry SU(2) × SU(2) which are interpreted as homogeneous coordinates on CP1 × CP1. The superfields are analytic in the CP1 coordinates and this analyticity plays an important role in our description. For instance, it leads to stringent constraints on the interactions one can write down for a given superfield content of the model. As an example, we describe in projective superspace Witten's ADHM sigma model — a linear sigma model with non-derivative interactions whose target is R4 with a Yang-Mills instanton solution. The hyperkähler nature of target space and the twistor description of instantons by Ward, and Atiyah, Hitchin, Drinfeld and Manin are natural outputs of our construction. [ABSTRACT FROM AUTHOR]

Geocoordinates are difficult to generate and interpret and many users rely on academic articles for such data. However, their accuracy has not been assessed, and their continued use could have negative consequences. This paper assessed the accuracy of geocoordinates used to describe study areas in academic articles. The PRISMA methodology was used to select 87 articles. The results revealed that 77 (82.8%) geocoordinates had errors. The study concluded that majority of the articles misinformed the readers about the geocoordinates of their study areas. Hence, authors, editors and reviewers should pay attention to geocoordinates during the writing and review process. [ABSTRACT FROM AUTHOR]

Multi-configurational time-dependent Hartree (MCTDH) calculations using time-dependent grid representations can be used to accurately simulate high-dimensional quantum dynamics on general ab initio potential energy surfaces. Employing the correlation discrete variable representation, sets of direct product type grids are employed in the calculation of the required potential energy matrix elements. This direct product structure can be a problem if the coordinate system includes polar and azimuthal angles that result in singularities in the kinetic energy operator. In the present work, a new direct product-type discrete variable representation (DVR) for arbitrary sets of polar and azimuthal angles is introduced. It employs an extended coordinate space where the range of the polar angles is taken to be [−π, π]. The resulting extended space DVR resolves problems caused by the singularities in the kinetic energy operator without generating a very large spectral width. MCTDH calculations studying the F·CH4 complex are used to investigate important properties of the new scheme. The scheme is found to allow for more efficient integration of the equations of motion compared to the previously employed cot-DVR approach [G. Schiffel and U. Manthe, Chem. Phys. 374, 118 (2010)] and decreases the required central processing unit times by about an order of magnitude. [ABSTRACT FROM AUTHOR]

In autonomous driving, LiDAR (light detection and ranging) data are acquired over time. Most existing 3D object detection algorithms propose the object bounding box by processing each frame of data independently, which ignores the temporal sequence information. However, the temporal sequence information is usually helpful to detect the object with missing shape information due to long distance or occlusion. To address this problem, we propose a temporal sequence information fusion 3D point cloud object detection algorithm based on the Ada-GRU (adaptive gated recurrent unit). In this method, the feature of each frame for the LiDAR point cloud is extracted through the backbone network and is fed to the Ada-GRU together with the hidden features of the previous frames. Compared to the traditional GRU, the Ada-GRU can adjust the gating mechanism adaptively during the training process by introducing the adaptive activation function. The Ada-GRU outputs the temporal sequence fusion features to predict the 3D object in the current frame and transmits the hidden features of the current frame to the next frame. At the same time, the label uncertainty of the distant and occluded objects affects the training effect of the model. For this problem, this paper proposes a probability distribution model of 3D bounding box coordinates based on the Gaussian distribution function and designs the corresponding bounding box loss function to enable the model to learn and estimate the uncertainty of the positioning of the bounding box coordinates, so as to remove the bounding box with large positioning uncertainty in the post-processing stage to reduce the false positive rate. Finally, the experiments show that the methods proposed in this paper improve the accuracy of the object detection without significantly increasing the complexity of the algorithm. [ABSTRACT FROM AUTHOR]

We present the results of determining the coordinates of the vertices of various stellar systems, the centroids of which are located in the Galactic plane. To do this, the positions, parallaxes, proper motions, and radial velocities of red giants and subgiants contained in the Gaia  DR3 catalogue have been used. When determining the components of the deformation velocity tensors in local coordinate systems, we found the coordinates of the vertices of the stellar systems under study. It turned out that there is a complex dependence of vertex deviations lxy in Galactocentric cylindrical (R, θ) and Galactic rectangular (X, Y) coordinates. Based on the approach proposed in this paper, heliocentric distances to vertices have been determined for the first time. The results obtained show that in addition to the fact that the angular coordinates of the Galactic Centre and the vertices of stellar systems do not coincide, their heliocentric distances do not coincide as well. This presumably indicates that there are structures in the Galaxy that noticeably affect its axisymmetry. [ABSTRACT FROM AUTHOR]

The integration of the agricultural and tourism industries is important for transforming and improving the agricultural industry and the revitalizing the rural economy. In terms of innovative development, Fujian leads the country in ecological construction, and it has a certain representativeness in ecological construction and coordinated economic and social development. In this paper, the relevant statistical yearbook data of Fujian Province from 2009 to 2019 were selected. Based on the production-living-ecological function theory, this paper adopted the combination weighting method to construct the evaluation index system for integrating agriculture and tourism, and ArcGIS, Geoda, and STATA were used to analyze the coupling development level, spatial correlation, and spatial aggregation characteristics of the agricultural tourism industry spatiotemporally as well as explore the coupling factors and influencing mechanisms of the agricultural and tourism industries. The results showed that the overall coordination degree of agriculture – tourism coupling had a positive impact on development in a zigzag direction and gradually followed the six levels of mildly dissonance-nearly dissonance-barely coordinated-slightly coordinated-intermediately coordinated-well coordinated. The integration effect of the agricultural and tourism industries of prefecture-level cities in Fujian Province exists local spatial autocorrelation, and the local space Moran index shows a“W” shape fluctuation change. In addition, the aggregation type changed from a low-low to low-high aggregation, then to a high-high aggregation, and finally to the low-low state, after which a new cycle began. In terms of factors affecting the integration of the agricultural and tourism industries, resources supply, talent factors, science and technology, government support, industry drive, living standards, and demand upgrades all have significant impacts on the integration of the agricultural and tourism industries. During the process of promoting the integration of the agricultural tourism industry, through balancing the coordination of the agricultural and tourism industries, paying attention to the construction of modern agriculture, and properly coordinating the spatial planning of agriculture and tourism, the integration of element resources can be promoted and the integration mechanism of agricultural tourism can well coordinated, thereby strengthening internal and external positive factors and allowing for the implementation of appropriate measures. [ABSTRACT FROM AUTHOR]