Search Results (326)

Many challenges in solving large graph coloring through parallel strategies remain unresolved. Previous algorithms based on Pregel-like frameworks, such as Apache Giraph, encounter parallelism bottlenecks due to sequential execution and the need for a full graph traversal in certain stages. Additionally, GPU-based algorithms face the dilemma of costly and time-consuming processing when moving complex graph applications to GPU architectures. In this study, we propose Spardex, a novel parallel and distributed graph coloring optimization algorithm designed to overcome and avoid these challenges. We design a symmetry-driven optimization approach wherein the EdgePartition1D strategy in GraphX induces partitioning asymmetry, leading to overlapping locally symmetric regions. This structure is leveraged through asymmetric partitioning and symmetric reassembly to reduce the search space. A two-stage pipeline consisting of partitioned repaint and core conflict detection is developed, enabling the precise correction of conflicts without traversing the entire graph as in previous algorithms. We also integrate symmetry principles from combinatorial optimization into a distributed computing framework, demonstrating that leveraging locally symmetric subproblems can significantly enhance the efficiency of large-scale graph coloring. Combined with Spark-specific optimizations such as AQE skew join optimization, all these techniques contribute to an efficient parallel graph coloring optimization in Spardex. We conducted experiments using the Aliyun Cloud platform. The results demonstrate that Spardex achieves a reduction of 8–72% in the number of colors and a speedup of 1.13–10.27 times over concurrent algorithms. Full article

Energy generation from renewable sources has increased exponentially worldwide, particularly wind energy, which is converted into electricity through wind turbines. The growing demand for renewable energy has driven the development of horizontal-axis wind turbines with larger dimensions, as the energy captured is proportional to the area swept by the rotor blades. In this context, the dynamic loads typically observed in wind turbine towers include vibrations caused by rotating blades at the top of the tower, wind pressure, and earthquakes (less common). In offshore wind farms, wind turbine towers are also subjected to dynamic loads from waves and ocean currents. Vortex-induced vibration can be an undesirable phenomenon, as it may lead to significant adverse effects on wind turbine structures. This study presents a two-dimensional transient model for a rigid body anchored by a torsional spring subjected to a constant velocity flow. We applied a coupling of the Fourier pseudospectral method (FPM) and immersed boundary method (IBM), referred to in this study as IMERSPEC, for a two-dimensional, incompressible, and isothermal flow with constant properties—the FPM to solve the Navier–Stokes equations, and IBM to represent the geometries. Computational simulations, solved at an aspect ratio of $\varphi =4.0$, were analyzed, considering Reynolds numbers ranging from $Re=150$ to Re = 1000 when the cylinder is stationary, and $Re=250$ when the cylinder is in motion. In addition to evaluating vortex shedding and Strouhal number, the study focuses on the characterization of space–time symmetry during the galloping response. The results show a spatial symmetry breaking in the flow patterns, while the oscillatory motion of the rigid body preserves temporal symmetry. The numerical accuracy suggested that the IMERSPEC methodology can effectively solve complex problems. Moreover, the proposed IMERSPEC approach demonstrates notable advantages over conventional techniques, particularly in terms of spectral accuracy, low numerical diffusion, and ease of implementation for moving boundaries. These features make the model especially efficient and suitable for capturing intricate fluid–structure interactions, offering a promising tool for analyzing wind turbine dynamics and other similar systems. Full article

Bilinear systems can be developed from the point of view of time-varying linear differential equations or from the symmetry of Lie theory, in particular Lie algebras, Lie groups, and Lie semigroups. For bilinear control systems with bounded control range, we analyze when a unique control set (i.e., a maximal set of approximate controllability) with nonvoid interior exists, for the induced system on projective space. We use the system semigroup by considering piecewise constant controls and use spectral properties to extend the result to bilinear systems in ${\mathbb{R}}^d$. The contribution of this paper highlights the relationship between all the existent control sets. We show that the controllability property of a bilinear system is equivalent to the existence and uniqueness of a control set of the projective system. Full article

This paper introduces a novel and flexible class of continuous probability distributions, termed the Alpha Power Survival Ratio-X (APSR-X) family. Unlike many existing transformation-based families, the APSR-X class integrates an alpha power transformation with a survival ratio structure, offering a new mechanism for enhancing shape flexibility while maintaining mathematical tractability. This construction enables fine control over both the tail behavior and the symmetry properties, distinguishing it from traditional alpha power or survival-based extensions. We focus on a key member of this family, the two-parameter Alpha Power Survival Ratio Exponential (APSR-Exp) distribution, deriving essential mathematical properties including moments, quantile functions and hazard rate structures. We estimate the model parameters using eight frequentist methods: the maximum likelihood (MLE), maximum product of spacings (MPSE), least squares (LSE), weighted least squares (WLSE), Anderson–Darling (ADE), right-tailed Anderson–Darling (RADE), Cramér–von Mises (CVME) and percentile (PCE) estimation. Through comprehensive Monte Carlo simulations, we evaluate the estimator performance using bias, mean squared error and mean relative error metrics. The proposed APSR-X framework uniquely enables preservation or controlled modification of the symmetry in probability density and hazard rate functions via its shape parameter. This capability is particularly valuable in reliability and survival analyses, where symmetric patterns represent balanced risk profiles while asymmetric shapes capture skewed failure behaviors. We demonstrate the practical utility of the APSR-Exp model through three real-world applications: economic (tax revenue durations), engineering (mechanical repair times) and medical (infection durations) datasets. In all cases, the proposed model achieves a superior fit over that of the conventional alternatives, supported by goodness-of-fit statistics and visual diagnostics. These findings establish the APSR-X family as a unique, symmetry-aware modeling framework for complex lifetime data. Full article

Energy-aware scheduling plays a critical role in modern computing and manufacturing systems, where energy consumption often increases with job execution order or resource usage intensity. This study investigates a scheduling problem in which a sequence of heterogeneous jobs—classified as either heavy or light—must be assigned to multiple identical machines with monotonically increasing slot costs. While the machines are structurally symmetric, the fixed job order and cost asymmetry introduce significant challenges for optimal job allocation. We formulate the problem as an integer linear program and simplify the objective by isolating the cumulative cost of heavy jobs, thereby reducing the search for optimality to a position-based assignment problem. To address this challenge, we propose a structured assignment model termed monotonic machine assignment, which enforces index-based job distribution rules and restores a form of functional symmetry across machines. We prove that any feasible assignment can be transformed into a monotonic one without increasing the total energy cost, ensuring that the global optimum lies within this reduced search space. Building on this framework, we first present a general dynamic programming algorithm with complexity $O\left(n^2{m}^2\right)$. More importantly, by introducing a structural correction scheme based on misaligned assignments, we design an iterative refinement algorithm that achieves global optimality in only $O\left(n{m}^2\right)$ time, offering significant scalability for large instances. Our results contribute both structural insight and practical methods for optimal, position-sensitive, energy-aware scheduling, with potential applications in embedded systems, pipelined computation, and real-time operations. Full article

Lorentz invariance is such a basic principle in fundamental physics that it must be constantly tested and any proposal of its violation and breakdown of CPT symmetry that might characterize some approaches to quantum gravity should be treated with care. In this review, we examine, among other scenarios, such instances in supercritical (Liouville) string theory, particularly in some brane models for “quantum foam”. Using the phenomenological formalism introduced here, we analyze the observational hints of Lorentz violation in time-of-flight lags of cosmic photons and neutrinos which fit excellently stringy space–time foam scenarios. We further demonstrate how stringent constraints from other astrophysical data, including the recent first detections of multi-TeV events in $\gamma$-ray burst 221009A and PeV cosmic photons by the Large High Altitude Air Shower Observatory (LHAASO), are satisfied in this context. Such models thus provide a unified framework for all currently observed phenomenologies of space–time symmetry breaking at Planckian scales. Full article

In complex electromagnetic environments, spatial coupling uncertainties—position errors and timing jitter—increase false target information entropy, reducing strategy effectiveness and posing challenges for robust UAV swarm track deception. This paper proposes an error-constrained entropy-minimizing compensation framework to model radar/UAV errors and their spatial coupling. The framework establishes closed-form gate association conditions based on the principle of entropy minimization, ensuring mutual consistency of false target measurements across multiple radars. Two strategies are proposed to reduce false target information entropy: 1. Zonal track compensation forms dense “information entropy bands” around each preset false target by inserting auxiliary deception echoes, enhancing mutual information concentration in the measurement space; 2. Formation jamming compensation adaptively reshapes the UAV swarm into regular polygons, leveraging geometric symmetry to suppress spatial diffusion of position errors. Simulation results show that compared with traditional methods, the proposed approach reduces the spatial inconsistency entropy by 50%, improving false target consistency and radar deception reliability. Full article

Stellar radiation simulation is critical in the space industry; however, with the current simulation methods, only a single color temperature and magnitude can be modulated at a time. Furthermore, star sensors rely on star observation tests for accurate calibration; this seriously restricts their development. This paper presents a novel star spectral information multi-partition mapping simulation method to closely simulate real sky star map information, thus replacing non-scenario-specific field stargazing experiments. First, using the stellar spectral simulation principle, a multi-partition mapping principle based on a digital micro-mirror device is proposed, and the theoretical basis of sub-region division is provided. Second, multi-component mapping simulation of stellar spectral information is expounded, and a general architecture for the same based on a double-prism symmetry structure is presented. Next, the influence of peak spectral half-peak width and peak interval on spectral simulation accuracy is analyzed, and a pre-collimated beam expansion system, multi-dimensional slit, and spectral splitting system are designed accordingly. Finally, a test platform is set up, and single-region simulation results and multi-region consistency experiments are conducted to verify the feasibility of the proposed method. Our method can realize high-precision simulation and independently control the output of various color temperatures and magnitudes. It provides a theoretical and technical basis for the development of star sensor ground calibration tests and space target detection light environment simulation. Full article

In the context of coal mine operations, the assurance of work safety relies heavily on efficient autonomous navigation for rescue robots, yet traditional path planning algorithms such as A and RRT exhibit significant deficiencies in a coal mine environment. Traditional path planning algorithms (such as Dijkstra and PRM) have certain deficiencies in dynamic Spaces and narrow environments. For example, the Dijkstra algorithm has A relatively high computational complexity, the PRM algorithm has poor adaptability in real-time obstacle avoidance, and the A* algorithm is prone to generating redundant nodes in complex terrains. In recent years, research on underground mine scenarios has also pointed out that there are many difficulties in the integration of global planning and local planning. This paper proposes an enhanced A* algorithm in conjunction with the Dynamic Window Approach (DWA) to enhance the efficiency, search accuracy, and obstacle avoidance capability of path planning by optimizing the target function and eliminating redundant nodes. This approach enables path smoothing to be performed. In order to ensure that the requirement of multiple target point detection is realized, an RRT algorithm is proposed to reduce the element of randomness and uncertainty in the path planning process, leading to an increase in the convergence rate and overall performance of the algorithm. The solution to the problem of determining the global optimal path is proposed to be simplified by means of the optimal path planning algorithm based on the gradient coordinate rotation method. In this study, we not only focus on the efficiency of mobile robot path planning and real-time dynamic obstacle avoidance capabilities but also pay special attention to the symmetry of the final path. The findings of simulation experiments conducted within the MATLAB environment demonstrate that the proposed algorithm exhibits a substantial enhancement in terms of three key metrics: path planning time, path length, and obstacle avoidance efficiency, when compared with conventional methodologies. This study provides a theoretical foundation for the autonomous navigation of mobile robots in coal mines. Full article

Probability models are instrumental in a wide range of applications by being able to accurately model real-world data. Over time, numerous probability models have been developed and applied in practical scenarios. This study introduces the AAP-X family of distributions—a novel, flexible framework for continuous data analysis named after authors Aadil Ajaz and Parvaiz. The proposed family effectively accommodates both symmetric and asymmetric characteristics through its shape-controlling parameter, an essential feature for capturing diverse data patterns. A specific subclass of this family, termed the “AAP Exponential” (AAPEx) model is designed to address the inflexibility of classical exponential distributions by accommodating versatile hazard rate patterns, including increasing, decreasing and bathtub-shaped patterns. Several fundamental mathematical characteristics of the introduced family are derived. The model parameters are estimated using six frequentist estimation approaches, including maximum likelihood, Cramer–von Mises, maximum product of spacing, ordinary least squares, weighted least squares and Anderson–Darling estimation. Monte Carlo simulations demonstrate the finite-sample performance of these estimators, revealing that maximum likelihood estimation and maximum product of spacing estimation exhibit superior accuracy, with bias and mean squared error decreasing systematically as the sample sizes increases. The practical utility and symmetric–asymmetric adaptability of the AAPEx model are validated through five real-world applications, with special emphasis on cancer survival times, COVID-19 mortality rates and reliability data. The findings indicate that the AAPEx model outperforms established competitors based on goodness-of-fit metrics such as the Akaike Information Criteria (AIC), Schwartz Information Criteria (SIC), Akaike Information Criteria Corrected (AICC), Hannan–Quinn Information Criteria (HQIC), Anderson–Darling (A*) test statistic, Cramer–von Mises (W*) test statistic and the Kolmogorov–Smirnov (KS) test statistic and its associated p-value. These results highlight the relevance of symmetry in real-life data modeling and establish the AAPEx family as a powerful tool for analyzing complex data structures in public health, engineering and epidemiology. Full article

We quantify the advantages of a recently proposed data processing technique to search for continuous gravitational wave (GW) signals from isolated rotating asymmetric neutron stars in data measured by ground-based GW interferometers. This technique relies on the symmetry of the motion around the Sun of an Earth-bound gravitational wave interferometer. By multiplying the measured data time series with a half-year time-shifted copy of it, we obtain two advantages: (i) the main Doppler phase modulation of a monochromatic gravitational wave signal is exactly removed, and (ii) the signal in the product data are located at twice the GW signal frequency. The first significantly reduces the size of the signal’s parameter space over which a search is to be performed. The second is advantageous at low frequencies; we find that, with currently available computer processing speeds, this technique is capable of achieving sensitivity that is comparable to or even better than coherent and other possibly non-coherent methods. Further, since our proposed method is implemented over a year-long data segment, it requires processing time comparable to the data acquisition time of currently available computers. Full article

This paper reports an interesting phenomenon in which fractional-order effects can be induced by the mismatch of the differential orders of space and time; that is, fractional-order effects can be induced by space–time symmetry breakage. Classical mathematical equations can be transformed into differential equations of undetermined operators. We confirmed that the presence of fractional-order operator solutions in operator differential equations is contingent upon the mismatch of differential orders of space and time, which can induce both fractional operators in the time domain and fractional operators in the space domain. The introduction of symmetry breakage and operators of space and time offers novel insights into understanding nonlocal phenomena within the space–time continuum. Full article

Gravity water waves in the shallow-ocean scenario described by generalized Boussinesq–Broer–Kaup–Whitham (gBBKW) equations are discussed. The residual symmetry and Bäcklund transformation associated with the gBBKW equations are systematically constructed. The time and space evolution of wave velocity and height are explored. Additionally, it is demonstrated that the gBBKW equations are solvable through the consistent Riccati expansion method. Leveraging this property, a novel Bäcklund transformation, solitary wave solution, and soliton–cnoidal wave solution are derived. Furthermore, miscellaneous novel solutions of gBBKW equations are obtained using the modified Sardar sub-equation method. The impact of variations in the diffusion power parameter on wave velocity and height is quantitatively analyzed. The exact solutions of gBBKW equations provide precise description of propagation characteristics for a deeper understanding and the prediction of some ocean wave phenomena. Full article

This study sought to deepen our understanding of the dynamical properties of the newly extended $(3+1)$-dimensional integrable Kadomtsev–Petviashvili (KP) equation, which models the behavior of ion acoustic waves in plasmas and nonlinear optics. This paper aimed to perform Lie symmetry analysis and derive lump, breather, and soliton solutions using the extended hyperbolic function method and the generalized logistic equation method. It also analyzed the dynamical system using chaos detection techniques such as the Lyapunov exponent, return maps, and the fractal dimension. Initially, we focused on constructing lump and breather soliton solutions by employing Hirota’s bilinear method. Secondly, employing Lie symmetry analysis, symmetry generators were utilized to satisfy the Lie invariance conditions. This approach revealed a seven-dimensional Lie algebra for the extended $(3+1)$-dimensional integrable KP equation, incorporating translational symmetry (including dilation or scaling) as well as translations in space and time, which were linked to the conservation of energy. The analysis demonstrated that this formed an optimal sub-algebraic system via similarity reductions. Subsequently, a wave transformation method was applied to reduce the governing system to ordinary differential equations, yielding a wide array of exact solitary wave solutions. The extended hyperbolic function method and the generalized logistic equation method were employed to solve the ordinary differential equations and explore closed-form analytical solitary wave solutions for the diffusive system under consideration. Among the results obtained were various soliton solutions. When plotting the results of all the solutions, we obtained bright, dark, kink, anti-kink, peak, and periodic wave structures. The outcomes are illustrated using 2D, 3D, and contour plots. Finally, upon introducing the perturbation term, the system’s behavior was analyzed using chaos detection techniques such as the Lyapunov exponent, return maps, and the fractal dimension. The results contribute to a deeper understanding of the dynamic properties of the extended KP equation in fluid mechanics. Full article

Recent work has demonstrated a correspondence that bridges quantum information processing and high-energy physics: discrete quantum cellular automata (QCA) can, in the continuum limit, reproduce quantum field theories (QFTs). This QCA/QFT correspondence raises fundamental questions about how matter/energy, information, and the nature of spacetime are related. Here, we show that free QED is equivalent to the continuous-space-and-time limit of Fermi and Bose QCA theories on the cubic lattice derived from quantum random walks satisfying simple symmetry and unitarity conditions. In doing so, we define the Fermi and Bose theories in a unified manner using the usual fermion internal space and a boson internal space that is six-dimensional. We show that the reduction to a two-dimensional boson internal space (two helicity states arising from spin-1 plus the photon transversality condition) comes from restricting the QCA theory to positive energies. We briefly examine common symmetries of QCAs and how time-reversal symmetry demands the existence of negative-energy solutions. These solutions produce a tension in coupling the Fermi and Bose theories, in which the strong locality of QCAs seems to require a non-zero amplitude to produce negative-energy states, leading to an unphysical cascade of negative-energy particles. However, we show in a 1D model that, by extending interactions over a larger (but finite) range, it is possible to exponentially suppress the production of negative-energy particles to the point where they can be neglected. Full article