Search Results (171)

Software maintenance is one of the most expensive phases in software development, especially when complex source code is the only available artifact. Clustering software modules and generating a structured architectural model can significantly reduce the effort and cost of maintenance. This study aims to achieve high-quality modularization by maximizing intra-cluster cohesion, minimizing inter-cluster coupling, and optimizing overall modular quality. Since finding optimal clustering is an NP-complete problem, many existing methods suffer from poor modular structures, instability, and inconsistent results. To overcome these limitations, this paper proposes a module clustering method using a discrete bedbug optimizer. In software architecture, symmetry refers to the balanced and structured arrangement of modules. In the proposed method, module clustering aims to identify and group related modules based on structural and behavioral similarities, reflecting symmetrical properties in the source code. Conversely, asymmetries, such as modules with irregular dependencies, can indicate architectural flaws. The method was evaluated on ten widely used real-world software datasets. The experimental results show that the proposed algorithm consistently delivers superior modularization quality, with an average score of 2.806 and a well-balanced trade-off between cohesion and coupling. Overall, this research presents an effective solution for software module clustering and provides better architecture recovery and more maintainable systems. Full article

Code generation is a critical task in software engineering, enabling the automation of transforming natural language descriptions into executable code. Recent advancements in large language models (LLMs) have demonstrated their potential to significantly enhance code generation capabilities by leveraging complex reasoning processes. However, the large size of these models poses challenges for deployment in resource-constrained environments, as they require substantial computational resources and memory. The challenge lies in transferring the sophisticated problem-solving strategies of LLMs to smaller, more efficient models without sacrificing performance, while maintaining symmetry between the reasoning steps and final code generation. This task is further complicated by the need to preserve high code generation accuracy while reducing the resource demands of deployment. Although distillation methods have been proposed, efficiently transferring both the reasoning process and final code generation remains an underexplored area. In this work, we propose a novel distillation framework that extracts intermediate reasoning steps, such as pseudocode, from LLMs and transfers them to smaller models. Our approach enables smaller models to replicate the problem-solving strategies of larger models through a multi-task learning framework, which includes both pseudocode and code generation tasks, thus maintaining the symmetry between reasoning and output. We conducted comprehensive experiments on the CodeSearchNet dataset, comparing our distillation framework across four student models (Tranx, CodeT5, NatGen, and SPT-Code) distilled from four large language models (CodeLlama-7B, CodeQwen-7B, DeepSeek, and GPT-4). Results show that our approach consistently improves code generation performance, with the best case (CodeT5 distilled from GPT-4) achieving up to 74% improvement in Top-1 accuracy over the baseline. Full article

Herein, a matrix representation of the Hamilton quaternion group by 4 × 4 square matrices with entries equal to −1, 0, or 1 is defined. It is proven that this group, denoted as $\left({\mathrm{Q}}_{\mathrm{M}},\circ \right)$, is a group of rotational symmetries of the four-dimensional hypercube ${\mathbb{Z}}_2^4,$ that is, a subgroup of the special orthogonal group ${\mathrm{SO}}_4\left(\mathbb{Z}\right).$ As a consequence, $\left({\mathrm{Q}}_{\mathrm{M}},\circ \right)$ is a group of rotational symmetries for each of the biological hypercubes RNY, YNY, YNR, and RNR. It is also proven that $\left({\mathrm{Q}}_{\mathrm{M}},\circ \right)$ is a group of permutations of the eight cubes contained in the four-dimensional hypercube ${\mathbb{Z}}_2^4.$ The latter is a novel result. It is also proven that the matrix quaternion group $\left({\mathrm{Q}}_{\mathrm{M}},\circ \right)$ is a normal subgroup of ${\mathrm{SO}}_4\left(\mathbb{Z}\right)$ and that the latter is a semidirect product of $\left({\mathrm{Q}}_{\mathrm{M}},\circ \right)$ with a copy of the special orthogonal group ${\mathrm{SO}}_3\left(\mathbb{Z}\right),$ also called an octahedral group because it is a group of rotational symmetries of a regular octahedron or of a three-dimensional cube. Full article

We propose Observer-Linked Branching (OLB), a mathematically rigorous extension of quantum theory in which an observer’s cognitive commitment actively modulates collapse dynamics at macroscopic scales. The OLB framework rests on four axioms, employing a norm-preserving nonlinear Schrödinger evolution and Lüders-type projection triggered by crossing a cognitive commitment threshold. Our expanded formalism provides five main contributions: (1) deriving Lie symmetries of the observer–environment interaction Hamiltonian; (2) embedding OLB into the Consistent Histories and path-integral formalisms; (3) multi-agent network simulations demonstrating intentional synchronisation toward shared macroscopic outcomes; (4) detailed statistical power analyses predicting measurable biases (up to ~5%) in practical experiments involving traffic delays, quantum random number generators, and financial market sentiment; and (5) examining the conceptual, ethical, and neuromorphic implications of intent-driven reality selection. Full reproducibility is ensured via the provided code notebooks and raw data tables in the appendices. While the theoretical predictions are precisely formulated, empirical validation is ongoing, and no definitive field results are claimed at this stage. OLB thus offers a rigorous, norm-preserving and falsifiable framework to empirically test whether cognitive engagement modulates macroscopic quantum outcomes in ways consistent with—but extending—standard quantum predictions. Full article

Medium- and large-scale heat sinks are critical for thermal load management in high-performance systems. However, their high heat flux densities and limited space complicate cooling, leading to risks of overheating, performance degradation, or failure. This study employs the Cascaded Lattice Boltzmann Method (CLBM) to enhance their thermal performance. This numerical approach is known for being stable, accurate when dealing with complex boundaries, and efficient when computing in parallel. The numerical code was validated against a benchmark configuration and an experimental setup to ensure its reliability and accuracy. While previous studies have explored mixed convection in cavities or heat sinks, few have addressed configurations involving side air injection and boundary conditions periodicity in the transition-to-turbulent regime. This gap limits the understanding of realistic cooling strategies for compact systems. Focusing on mixed convection in the transition-to-turbulent regime, where buoyancy and forced convection interact, the study investigates the impact of Rayleigh number values ($5\times {10}^7$ to $5\times {10}^8$) and Reynolds number values (${10}^3$ to $3\times {10}^3$) on heat transfer. Simulations were conducted in a rectangular cavity with periodic boundary conditions on the vertical walls. Two heat sources are located on the bottom wall ($T_h$ = 50 °C). Two openings, one on each side of the two hot sources, force a jet of fresh air in from below. An opening at the level of the cavity ceiling’s axis of symmetry evacuates the hot air. Mixed convection drives the flow, exhibiting complex multicellular structures influenced by the control parameters. Calculating the average Nusselt number (Nu) across the surfaces of the heat sink reveals significant dependencies on the Reynolds number. The proposed correlation between Nu and Re, developed specifically for this configuration, fills the current gap and provides valuable insights for optimizing heat transfer efficiency in engineering applications. Full article

Deep neural video compression codecs have shown great promise in recent years. However, there are still considerable challenges for ultra-low bitrate video coding. Inspired by recent diffusion models for image and video compression attempts, we attempt to leverage diffusion models for ultra-low bitrate portrait video compression. In this paper, we propose a predictive portrait video compression method that leverages the temporal prediction capabilities of diffusion models. Specifically, we develop a temporal diffusion predictor based on a conditional latent diffusion model, with the predicted results serving as decoded frames. We symmetrically integrate a temporal diffusion predictor at the encoding and decoding side, respectively. When the perceptual quality of the predicted results in encoding end falls below a predefined threshold, a new frame sequence is employed for prediction. While the predictor at the decoding side directly generates predicted frames as reconstruction based on the evaluation results. This symmetry ensures that the prediction frames generated at the decoding end are consistent with those at the encoding end. We also design an adaptive coding strategy that incorporates frame quality assessment and adaptive keyframe control. To ensure consistent quality of subsequent predicted frames and achieve high perceptual reconstruction, this strategy dynamically evaluates the visual quality of the predicted results during encoding, retains the predicted frames that meet the quality threshold, and adaptively adjusts the length of the keyframe sequence based on motion complexity. The experimental results demonstrate that, compared with the traditional video codecs and other popular methods, the proposed scheme provides superior compression performance at ultra-low bitrates while maintaining competitiveness in visual effects, achieving more than 24% bitrate savings compared with VVC in terms of perceptual distortion. Full article

Dynamic scheduling in hybrid flexible job shops (HFJSs) presents a critical challenge in modern manufacturing systems, particularly under dynamic and uncertain conditions. These systems often exhibit inherent structural and behavioral symmetry, such as uniform machine–job relationships and repeatable event response patterns. To leverage this, we propose a time Petri nets (TPNs) model that integrates time and logic constraints, capturing symmetric processing and setup behaviors across machines as well as dynamic job and machine events. A transition select coding mechanism is introduced, where each transition node is assigned a normalized priority value in the range [0, 1], preserving scheduling consistency and symmetry during decision-making. Furthermore, we develop a symmetry-aware time Petri nets-based improved genetic algorithm (TPGA) to solve both static and dynamic scheduling problems in HFJSs. Experimental evaluations show that TPGA significantly outperforms classical dispatching rules such as Shortest Job First (SJF) and Highest Response Ratio Next (HRN), achieving makespan reductions of 23%, 10%, and 13% in process, discrete, and hybrid manufacturing scenarios, respectively. These results highlight the potential of exploiting symmetry in system modeling and optimization for enhanced scheduling performance. Full article

We present a theoretical framework for designing optical masks, which are useful for implementing nonconventional Schlieren techniques. We revisit the use of effective transfer functions, which emphasize the role of symmetries in the design of coded masks. The proposed technique implements an optical autocorrelation of a mask, which is coded with the Barker sequences. For the same purpose, one can also use masks coded with the pseudorandom sequences. For the sake of completeness, we link our deterministic theoretical framework with a simple statistical model. The proposed technique may be useful for the automatic sensing of phase gradients. Full article

In recent years, hashing-based algorithms have garnered significant attention as vital technologies for cross-modal retrieval tasks. They leverage the inherent symmetry between different data modalities (e.g., text, images, or audio) to bridge their semantic gaps by embedding them into a unified representation space. This symmetry-preserving approach would greatly enhance retrieval performance. However, challenges persist in mining and enriching multi-modal semantic feature information. Most current methods use pre-trained models for feature extraction, which limits information representation during hash code learning. Additionally, these methods map multi-modal data into a unified space, but this mapping is sensitive to feature distribution variations, potentially degrading cross-modal retrieval performance. To tackle these challenges, this paper introduces a novel method called Attention-based Multi-scale Graph Fusion Hashing (AMGFH). This approach first enhances the semantic representation of image features through multi-scale learning via an image feature enhancement network. Additionally, graph convolutional networks (GCNs) are employed to fuse multi-modal features, where the self-attention mechanism is incorporated to enhance feature representation by dynamically adjusting the weights of less relevant features. By optimizing a combination of loss functions and addressing the diverse requirements of image and text features, the proposed model demonstrates superior performance across various dimensions. Extensive experiments conducted on public datasets further confirm its outstanding performance. For instance, AMGFH exceeds the most competitive baseline by 3% and 4.7% in terms of mean average precision (MAP) when performing image-to-text and text-to-image retrieval tasks at 32 bits on the MS COCO dataset. Full article

This paper continues the subject of symmetry breaking of fractional-order maps, previously addressed by one of the authors. Several known planar classes of curves of integer order are considered and transformed into their fractional order. Several known planar classes of curves of integer order are considered and transformed into their fractional order. For this purpose, the Grunwald–Letnikov numerical scheme is used. It is shown numerically that the aesthetic appeal of most of the considered curves of integer order is broken when the curves are transformed into fractional-order variants. The considered curves are defined by parametric representation, Cartesian representation, and iterated function systems. To facilitate the numerical implementation, most of the curves are considered under their affine function representation. In this way, the utilized iterative algorithm can be easily followed. Besides histograms, the entropy of a curve, a useful numerical tool to unveil the characteristics of the obtained fractional-order curves and to compare them with their integer-order counterparts, is used. A Matlab code is presented that can be easily modified to run for all considered curves. Full article

Let $\mathcal{R}={\displaystyle \frac{{\mathbb{F}}_{p^m}[u,v]}{⟨u^2,v^2,uv-vu⟩}}$, where p is an odd prime and m is a positive integer. For a unit $\alpha$ in $\mathcal{R}$, $\alpha$-constacyclic codes of length $2p^s$ over $\mathcal{R}$ are ideals of ${\displaystyle \frac{\mathcal{R}\left[x\right]}{⟨x^{2p^s}-\alpha ⟩}}$, where s is a positive integer. The structure of $\alpha$-constacyclic codes are classified on the distinct cases for the unit $\alpha$: when $\alpha$ is a square in $\mathcal{R}$ and when it is not. In this paper, for all such $\alpha$-constacyclic codes, the Hamming distances are determined using this structure. In addition, their symbol-pair distances are obtained. The symmetry property of Hamming and symbol-pair distances makes analysis easier and maintains consistency by guaranteeing that the distance between codewords is the same regardless of their order. As symmetry preserves invariant distance features across transformations, it improves error detection and correction. Full article

The computational complexity of existing multi-symbol detection (MSD) algorithms grows exponentially as the observation intervals increase, resulting in difficulties in algorithm implementation for detecting pulse code modulation/frequency modulation (PCM/FM) signals, especially for multi-channel signals. To address the challenges, we proposed a low-complexity MSD algorithm based on the averaged matched filtering. The proposed algorithm groups the local reference signals based on the different importance levels of the middle and edge bits in the correlation operations and averages the edge bits, leading to a considerable decrease in matching branches. Furthermore, it leverages the phase symmetry, and the proposed algorithm retains half of the averaged local reference signals for the matching operation, thus further reducing the matching branches. The proposed algorithm reduces the storage of the local signals and correlation operations to one-eighth compared to the traditional MSD algorithm under different observation lengths. Additionally, based on the structure of multiplexed FIR filters, the proposed algorithm optimizes single-channel single-coefficient FIR filters into four-channel double-coefficient FIR filters, further reducing the hardware resource consumption by approximately 25%. The simulation results showed that the proposed algorithm achieved demodulation performance comparable to the traditional MSD algorithms while reducing the computational complexity by 87.5%. Compared to the decision-feedback MSD algorithm, it achieves higher demodulation gain with a 75% complexity reduction. The Field Programmable Gate Array (FPGA) platform implementation results showed that the proposed algorithm reduces hardware resource consumption by nearly 90% compared with the traditional algorithm, and the hardware demodulation performance loss is less than 1 dB compared with the simulation results. Full article

In this paper, we present mathematical geometric models and recursive algorithms to generate and design complex patterns using fractal structures. By applying analytical, iterative methods, iterative function systems (IFS), and L-systems to create geometric models of complicated fractals, we developed fractal construction models, visualization tools, and fractal measurement approaches. We introduced a novel recursive fractal modeling (RFM) method designed to generate intricate fractal patterns with enhanced control over symmetry, scaling, and self-similarity. The RFM method builds upon traditional fractal generation techniques but introduces adaptive recursion and symmetry-preserving transformations to produce fractals with applications in domains such as medical imaging, textile design, and digital art. Our approach differs from existing methods like Barnsley’s IFS and Jacquin’s fractal coding by offering faster convergence, higher precision, and increased flexibility in pattern customization. We used the RFM method to create a mathematical model of fractal objects that allowed for the viewing of polygonal, Koch curves, Cayley trees, Serpin curves, Cantor set, star shapes, circulars, intersecting circles, and tree-shaped fractals. Using the proposed models, the fractal dimensions of these shapes were found, which made it possible to create complex fractal patterns using a wide variety of complicated geometric shapes. Moreover, we created a software tool that automates the visualization of fractal structures. This tool may be used for a variety of applications, including the ornamentation of building items, interior and exterior design, and pattern construction in the textile industry. Full article

In the face of escalating environmental degradation and dwindling resources, the imperatives of prioritizing environmental protection, and conserving resources have come sharply into focus. Therefore, remanufacturing processing, as the core of remanufacturing, becomes a key step in solving the above problems. However, with the increasing number of failing products and the advent of Industry 5.0, there is a heightened request for remanufacturing in the context of environmental protection. In response to these shortcomings, this study introduces a novel remanufacturing process planning model to address these gaps. Firstly, the failure characteristics of the used parts are extracted by the fault tree method, and the failure characteristics matrix is established by the numerical coding method. This matrix includes both symmetry and asymmetry, thereby reflecting each attribute of each failure feature, and the remanufacturing process is expeditiously generated. Secondly, a multi-objective optimization model is devised, encompassing the factors of time, cost, energy consumption, and carbon emission. This model integrates considerations of failure patterns inherent in used parts and components, alongside the energy consumption and carbon emissions entailed in the remanufacturing process. To address this complex optimization model, an improved teaching–learning-based optimization (TLBO) algorithm is introduced. This algorithm amalgamates Pareto and elite retention strategies, complemented by local search techniques, bolstering its efficacy in addressing the complexities of the proposed model. Finally, the validity of the model is demonstrated by means of a single worm gear. The proposed algorithm is compared with NSGA-III, MPSO, and MOGWO to demonstrate the superiority of the algorithm in solving the proposed model. Full article

This work effectively modifies APSM-jSO (a novel jSO variant with an adaptive parameter selection mechanism and a new external archive updating mechanism) to offer a new jSO (single objective real-parameter optimization: Algorithm jSO) version called NLAPSMjSO-EDA. There are three main distinctions between NLAPSMjSO-EDA and APSM-jSO. Firstly, in the linear population reduction strategy, the number of individuals eliminated in each generation is insufficient. This results in a higher number of inferior individuals remaining, and since the total number of iterations is fixed, these inferior individuals will also consume iteration counts for their evolution. Therefore, it is essential to allocate more iterations to the elite population to promote the emergence of superior individuals. The nonlinear population reduction strategy effectively addresses this issue. Secondly, we have introduced an Estimation of Distribution Algorithm (EDA) to sample and generate individuals from the elite population, aiming to produce higher-quality individuals that can drive the iterative evolution of the population. Furthermore, to enhance algorithmic diversity, we increased the number of individuals in the initial population during subsequent experiments to ensure a diverse early population while maintaining a constant total number of iterations. Symmetry plays an essential role in the design and performance of NLAPSMjSO-EDA. The nonlinear population reduction strategy inherently introduces a form of asymmetry that mimics natural evolutionary processes, favoring elite individuals while reducing the influence of inferior ones. This asymmetric yet balanced approach ensures a dynamic equilibrium between exploration and exploitation, aligning with the principles of symmetry and asymmetry in optimization. Additionally, the incorporation of EDA utilizes probabilistic symmetry in sampling from the elite population, maintaining structural coherence while promoting diversity. Such applications of symmetry in algorithm design not only improve performance but also provide insights into balancing diverse algorithmic components. NLAPSMjSO-EDA, evaluated on the CEC 2017 benchmark suite, significantly outperforms recent differential evolution algorithms. In conclusion, NLAPSMjSO-EDA effectively enhances the overall performance of APSM-jSO, establishing itself as an outstanding variant combining jSO and EDA algorithms. The algorithm code has been open-sourced. Full article