Symmetry Of Problem Research Articles

Algorithmic Efficiency in Convex Hull Computation: Insights from 2D and 3D Implementations

This study examines various algorithms for computing the convex hull of a set of n points in a d-dimensional space. Convex hulls are fundamental in computational geometry and are applied in computer graphics, pattern recognition, and computational biology. Such convex hulls can also be useful in symmetry problems. For instance, when points are arranged symmetrically, the convex hull is also likely to be symmetrically shaped, which can be useful for object recognition in computer vision or pattern recognition. The focus is primarily on two-dimensional algorithms, including well-known methods like Gift Wrapping, Graham Scan, Divide and Conquer, QuickHull, TORCH, Kirkpatrick–Sediel, and Chan’s algorithms. These algorithms vary in terms of time complexity and scalability to higher dimensions. This study is extended to three-dimensional convex hull algorithms, such as NAW, randomized insertion, and parallelized versions, such as CudaHull and CudaChain. This study aimed to elucidate the operational principles, step-by-step procedures, and comparative time complexities of each algorithm. The implementation in Python facilitates a detailed comparison of the algorithmic performance through stepwise analysis and graphical outputs. The ultimate goal is to provide insights into the strengths and weaknesses of each algorithm under various scenarios, thereby offering a comprehensive guide for practical implementation.

Finite-Time Control for Automatic Berthing of Pod-Driven Unmanned Surface Vessel with an Event-Triggering Mechanism

Coastal water accidents have occurred frequently in recent years, and human factors are still the main cause of these accidents. The purpose of this study is to provide a better and safer solution for the symmetry problem of unmanned surface vessels during automatic berthing in coastal waters. In automatic berthing, the symmetry problem refers to whether the USVs can maintain a stable state during motion and positioning, including dynamic symmetry and environmental symmetry. A finite-time controller based on a global nonsingular terminal sliding mode is designed to improve response speed and state consistency. Dynamic uncertainty and disturbance are considered in the design process, which can optimize the control law and effectively ensure the symmetry of the vessel in different states. Then, an event-triggering mechanism based on a dynamic threshold is adopted. In practice, there is excessive operation of the actuator. This mechanism ensures that the actuator is triggered only when the threshold is reached. USVs can adaptively adjust control strategies based on the real-time status, thereby improving symmetry during berthing. In simulation analysis, a pod-driven unmanned surface vessel with good maneuverability is taken as the research object. The results indicate that this control strategy can ensure rapid and consistent response of the vessel when subjected to external disturbances, which helps to maintain the symmetry of the automatic berthing motion under different conditions.

A Knowledge-Guided Multi-Objective Shuffled Frog Leaping Algorithm for Dynamic Multi-Depot Multi-Trip Vehicle Routing Problem

Optimization algorithms have a wide range of applications in symmetry problems, such as graphs, networks, and pattern recognition. In this paper, a dynamic periodic multi-depot multi-trip vehicle routing model for scheduling test samples is constructed, which considers the differences in testing unit price and testing capacity of various agencies and introduces a cross-depot collaborative transport method. Both the cost and the testing time are minimized by determining the optimal sampling routes and testing agencies, subjecting to the constraints of vehicle capacity, number of vehicles, and delivery time. To solve the model, a knowledge-guided multi-objective shuffled frog leaping algorithm (KMOSFLA) is proposed. KMOSFLA adopts a convertible encoding mechanism to realize the diversified search in different search spaces. Three novel strategies are designed: the population initialization with historical information reuse, the leaping rule based on the greedy crossover and genetic recombination, and the objective-driven enhanced search. Systematic experimental studies are implemented. First, feasibility analyses of the model are carried out, where effectiveness of the cross-depot collaborative transport is validated and sensitivity analyses on two parameters (vehicle capacity and proportion of the third-party testing agencies) are performed. Then, the proposed algorithm KMOSFLA is compared with five state-of-the-art algorithms. Experimental results indicate that KMOSFLA can provide a set of non-dominated schedules with lower cost and shorter testing time in each scheduling period, which provides a reference for the dispatcher to make a final decision.

VSHPIC: a particle-in-cell algorithm based on vector spherical harmonics expansion

The particle-in-cell (PIC) method has been widely used for studying plasma physics. However, fully three-dimensional PIC simulations always require huge computational resources. For problems with near azimuthal symmetry, recent work (Lifschitz et al 2009 J. Comput. Phys. 228 1803–14, Davidson et al 2015 J. Comput. Phys. 281 1063–77, Li et al 2021 Comput. Phys. Commun. 261 107784, Li et al 2022 J. Comput. Phys. 470 111599) has shown that expanding all the quantities defined on the grid in azimuthal harmonics and truncating the expansion can improve the code efficiency. In this paper, we describe a novel parallel algorithm for efficiently simulating three-dimensional near-spherical symmetry problems. Our approach expands all physical quantities in the θ and ϕ directions in spherical coordinates using vector spherical harmonics. The code is capable of simulating three-dimensional asymmetric scenarios by accurately tracking the evolution of distinct individual modes while preserving the charge conservation law. The fundamental dispersion relation of EM waves in the plasma has been obtained using VSHPIC simulation results. The code also shows a well strong scalability up to more than 1000 cores.

Active Filters for Standard-Compliant Power Quality in Electrical Networks

The article is devoted to the analysis of three circuits of modular multilevel converters (MMCS) with cascade connection of single-phase bridge and half-bridge voltage converters, each of which operates in pulse width modulation (PWM) mode. The main feature of active filters based on MMS is the possibility of selective high-speed harmonic filtering in on–line mode: AF allows the suppression of any given set of harmonics, including the negative harmonic of the fundamental frequency (reverse sequence), with a given degree of suppression - to zero or a normalized value - by an appropriate task in the control program. For the practical implementation of MMS in solving problems of normalization of electricity quality indicators, the so-called DSB control algorithm of MMS was developed, based on the traditional "classical" theory of automatic control and the theory of three-phase circuits. A comparative assessment of the use of various MMC schemes for symmetry and reactive power compensation has been carried out. It is shown that the problem of voltage symmetry using MMS is a special one, requiring the use of special algorithms to solve it, ensuring the reactive nature of branches of MMS circuits.

Dark Radiation Constraints on Heavy QCD Axions

The naturalness problem of PQ symmetry motivates study of the heavy QCD axion, with masses ma> 1 MeV generated at scales above the QCD scale, and low values of the PQ symmetry breaking scale, fa. We compute the abundance of such axions in a model-independent way, assuming only that they freeze-out after reheating from inflation, and are not subsequently diluted by new physics. If these axions decay between neutrino decoupling and the last scatter era of the Cosmic Microwave Background (CMB), they dilute the neutrinos and their abundance is constrained by CMB measurements of the energy density in dark radiation, Neff. We accurately compute this bound using a numerical code to evolve the axion momentum distribution, including many key processes and effects previously ignored. We assume that the only relevant axion decays are to final states involving Standard Model particles. We determine regions of (ma, fa) that will give a signal in Neff at CMB Stage 4 experiments. We similarly compute the Neff bound and CMB Stage 4 signal for heavy axions that can decay to light mirror photons. Finally, we compute the bounds on heavy axions with mass below 1 MeV that decay after the era of CMB last scatter, from their contribution to cold or hot dark matter or Neff at this era.

Analytical Model of an E-core Driver-pickup Coils Probe Applied to Eddy Current Testing of Multilayer Conductor

An analytical model of an E-core driver-pickup coils probe located above a multilayer conductor containing a hidden cylindrical conductor is presented. The truncated region eigenfunction expansion (TREE) method is used to deal with the axial symmetry problem, and the closed-form final expression of the induced voltage in the pickup coil is derived. The changes of the induced voltage in the pickup coil due to the hidden cylindrical conductor are examined and calculated in Mathematica. Experiments and finite element simulations are performed and the results are compared with the analytical results, and they are in good agreement.

Identifying the Heat Source in Radially Symmetry and Axis-Symmetry Problems

This paper solves the inverse source problem of heat conduction in which the source term only varies with time. The application of the discrete regularization method, a kind of effective radial symmetry and axisymmetric heat conduction problem source identification that does not involve the grid integral numerical method, is put forward. Taking the fundamental solution as the fundamental function, the classical Tikhonov regularization method combined with the L-curve criterion is used to select the appropriate regularization parameters, so the problem is transformed into a class of ill-conditioned linear algebraic equations to solve with an optimal solution. Several numerical examples of inverse source problems are given. Simultaneously, a few numerical examples of inverse source problems are given, and the effectiveness and superiority of the method is shown by the results.

OPTICAL FEEDBACK. I STATIC EFFECTS.

Feedback is a common phenomenon. This paper gives examples of feedback in computer science (iterations). The primary aim of this paper is to observe the effects of optical feedback in a monitor-camera system. The static effects of optical feedback are presented in this paper. The problem of symmetry of the obtained images is discussed. It is explained how a multiple three-lens copying machine generates the Sierpinski triangle, which is a basic and very well-known fractal. In the next paper ( Part II ) the dynamic effects of optical feedback will be discussed.

From crack line field analysis method to symmetric line analysis method: Elastic-plastic analysis of symmetry problems

The mathematical difficulty encountered in the elastic–plastic analysis of solids lies in solving the partial differential equations analytically in the theory of plasticity. Such a mathematical dilemma has existed for decades and analytical solutions are still waiting to be obtained. This paper extends the crack line field analysis method and puts forward a symmetric line analysis method, which uses the parity of the Taylor series expansion of the plastic stress field near the symmetric line to transform the problem of solving partial differential equations into ordinary ones, and so obtain the general Taylor series solution of the plastic stress field near the symmetric line. The symmetric line analysis method can give elastic–plastic solutions to plane and anti-plane symmetry problems that have not been analytically solved before, which achieves an essential leap forward in the analytical analysis of elastic–plastic solids in the theory of plasticity. In this paper, three types of symmetry problems are defined, and examples are given for the elastic–plastic analysis and solution of each type of symmetry problems of elastic-perfectly plastic solids with the symmetric line analysis method.

Selves, Persons, and the Neo-Lucretian Symmetry Problem

The heavily discussed (neo-)Lucretian symmetry argument holds that as we are indifferent to nonexistence before birth, we should also be indifferent to nonexistence after death. An important response to this argument insists that prenatal nonexistence differs from posthumous nonexistence because we could not have been born earlier and been the same ‘thick’ psychological self. As a consequence, we can’t properly ask whether it would be better for us to have had radically different lives either. Against this, it’s been claimed we can form preferences as to which ‘thick’ (psychological) self our ‘thin’ (metaphysical) self would be better off ‘associated’ with. I argue that these discussions draw the right distinction, but do so in the wrong place: understanding the ‘thin’ self phenomenally instead of metaphysically allows us to understand how we can rationally form preferences to have been somebody else.

Invariants of magnetic lines for Yang-Mills solutions

We construct a new Yang-Mills 3D-solution on the space of negative scalar curvature. We discuss a problem of non-abelian gauge symmetry is broken with the assumption that a scalar curvature of the domain is a negative small parameter. In this case we use the following fact: a geometrical scale related with Vassiliev's discriminant of magnetic lines coincides with a phisical Kolmogorov scale. This gives an estimation of α-effect by the dispersion of the asymptotic ergodic Hopf invariant in the asymptotic limit with a negative scalar curvature parameter.

Experimental measurement of the quality factor of a Fabry-Pérot open-cavity axion haloscope

The axion is a hypothetical boson arising from the most natural solution to the problem of charge and parity symmetry in the strong nuclear force. Moreover, this pseudoscalar emerges as a dark matter candidate in a parameter space extending several decades in mass. The Dark-photons & Axion-Like particles Interferometer (DALI) is a proposal to search for axion dark matter in a range that remains under-examined. Currently in a design and prototyping phase, this haloscope is a multilayer Fabry-Pérot interferometer. A proof-of-principle experiment is performed to observe the resonance in a prototype. The test unveils a quality factor per layer of a few hundred over a bandwidth of the order of dozens of megahertz. The result elucidates a physics potential to find the, so far elusive, axion, in a sector which can simultaneously solve the symmetry problem in the strong interaction and the enigma of dark matter.

Comments and remarks on symmetry and asymmetry problems in the design of plated/shell composite structures–Laminates, nanostructures and functionally graded materials

Symmetry requires that the material configuration, geometry, restraints, loads, and material properties are symmetrical. It is generally not recommended to use symmetry for buckling and frequency studies. Symmetry can be used to model a portion of a construction instead of the entire model. Results in unmodeled fragments are derived from modeled fragments. In justified situations, the use of symmetry can reduce the size of the problem and increase the accuracy of the results. The analysis of symmetry of composite plated/shell 2D structures is connected with the description of deformations, failure modes and the scale of considerations (nano-, micro-, meso‑ and macro/global scale). For composites made with the use of filament winding method the cyclic symmetry is usually adopted.Due to the anisotropy of composite materials, the assumption of symmetry is related to the accuracy of the description of deformation and damage of the structure in relation to the results obtained experimentally. Typically, the analysis of composite structures is associated with the introduction of high values ​​of safety factors. It is necessary to determine how and when it is necessary and possible to introduce material property dispersion values ​​even when using a linear approach in geometric or physical approach. The description options are related to the use of statistical analysis, fuzzy set methods or the introduction of anti-optimization.

Test for diagonal symmetry in high dimension

Utilizing the energy distance and energy statistics, Sang and Dang (2020) proposed a test statistic as a difference of two U-statistics for the diagonal symmetry test of a p-vector X. Under the regular setting where the dimensionality of the random vector is fixed, the test statistic is a degenerate U-statistic and hence converges to a mixture of chi-squared distributions. In this paper, we test the diagonal symmetry of X in a more realistic setting where both the sample size and the dimensionality are diverging to infinity. Our theoretical results reveal that the degenerate U-statistic admits a central limit theorem in the high dimensional setting and the accuracy of normal approximation can increase with dimensionality. We then construct a powerful and consistent test for the diagonal symmetry problem based on the asymptotic normality. Simulation studies are conducted to illustrate the performances of the test.

CIPS-3D++: End-to-End Real-Time High-Resolution 3D-Aware GANs for GAN Inversion and Stylization.

Style-based GANs achieve state-of-the-art results for generating high-quality images, but lack explicit and precise control over camera poses. Recently proposed NeRF-based GANs have made great progress towards 3D-aware image generation. However, the methods either rely on convolution operators which are not rotationally invariant, or utilize complex yet suboptimal training procedures to integrate both NeRF and CNN sub-structures, yielding un-robust, low-quality images with a large computational burden. On top of our open-source CIPS-3D framework 1https://github.com/PeterouZh/CIPS-3D, this paper presents an upgraded version called CIPS-3D++, aiming at high-robust, high-resolution and high-efficiency 3D-aware GANs. On the one hand, our basic model CIPS-3D, encapsulated in a style-based architecture, features a shallow NeRF-based 3D shape encoder as well as a deep MLP-based 2D image decoder, achieving robust image generation/editing with rotation-invariance. On the other hand, our proposed CIPS-3D++, inheriting the rotational invariance of CIPS-3D, together with geometric regularization and upsampling operations, encourages high-resolution high-quality image generation/editing with great computational efficiency. Trained on raw single-view images, without any bells and whistles, CIPS-3D++ sets new records for 3D-aware image synthesis, with an impressive FID of 3.2 on FFHQ at the 1024×1024 resolution. In the meantime, CIPS-3D++ runs efficiently and enjoys a low GPU memory footprint so that it can be trained end-to-end on high-resolution images directly, in contrast to previous alternate/progressive methods. Based on the infrastructure of CIPS-3D++, we propose a 3D-aware GAN inversion algorithm named FlipInversion, which can reconstruct the 3D object from a single-view image. We also provide a 3D-aware stylization method for real images based on CIPS-3D++ and FlipInversion. In addition, we analyze the problem of mirror symmetry suffered in training, and solve it by introducing an auxiliary discriminator for the NeRF network. Overall, CIPS-3D++ provides a strong base model that can serve as a testbed for transferring GAN-based image editing methods from 2D to 3D. Our open-source project as well as accompanying demo videos can be found online 2https://github.com/PeterouZh/CIPS-3Dplusplus.

Symmetry in Quantum and Computational Chemistry: Volume 2

The problem of symmetry in quantum and computational chemistry is a paradigm of development in this field of knowledge [...]

Symmetries of κ-Minkowski space-time: a possibility of exotic momentum space geometry?

The quest for a quantum gravity phenomenology has inspired a quantum notion of space-time, which motivates us to study the fate of the relativistic symmetries of a particular model of quantum space-time, as well as its intimate connection with the plausible emergent curved “physical momentum space”. We here focus on the problem of Poincare symmetry of κ-Minkowski type non-commutative (quantum) space-time, where the Poincare algebra, on its own, remains undeformed, but in order to preserve the structure of the space-time non-commutative (NC) algebra, the actions of the algebra generators on the operator-valued space-time manifold must be enveloping algebra valued that lives in entire phase space i.e. the cotangent bundle on the space-time manifold (at classical level). Further, we constructed a model for a spin-less relativistic massive particle enjoying the deformed Poincare symmetry, using the first order form of geometric Lagrangian, that satisfies a new deformed dispersion relation and explored a feasible regime of a future Quantum Gravity theory in which the momentum space becomes curved. In this scenario there is only a mass scale (Planck mass mp), but no length scale. Finally, we relate the deformed mass shell to the geodesic distance in this curved momentum space, where the mass of the particle gets renormalized as a result of noncommutativity. We show, that under some circumstances, the Planck mass provides an upper bound for the observed renormalized mass.

Fast Image Block Matching for Image Detection and MPEG Encoding Based on Underlying Symmetries

Image block matching is one of the representative methods for image detection and motion compensation in MPEG. Block matching between two images is a problem of finding symmetry between two images by matching macro blocks that are symmetrical to each other in two given images. The greater the PSNR value, the greater the symmetry of the two images. In the given two images, the two macro blocks with the minimum matching error values are regarded as symmetrical to each other. The classical method of calculating the matching error function for every pixel in the entire search area and choosing the smallest of them guarantees global convergence but requires a lot of computation, especially for large intensities. For this reason, many sparse search methods have been developed to reduce the amount of computation. In this paper, we introduce a gradient descent vector optimization algorithm with guaranteed global convergence to the image block matching problem by utilizing the conceptual symmetry of the vector optimization problem, which is a continuous variable, and the image block matching problem, which is a discrete variable. By blurring the image, we transform the matching cost function closer to being unimodal so that the descent-type algorithm works well. As a result, although the proposed method is simple, it can reduce the amount of computation remarkably and has more robustness for the large displacement of image blocks compared to existing sparse search methods.

Symmetry of solutions to semilinear PDEs on Riemannian domains

This paper deals with symmetry phenomena for solutions to the Dirichlet problem involving semilinear PDEs on Riemannian domains. We shall present a rather general framework where the symmetry problem can be formulated and provide some evidence that this framework is completely natural by pointing out some results for stable solutions. The case of manifolds with density, and corresponding weighted Laplacians, is inserted in the picture from the very beginning.