Search Results (868)

The transition toward renewable-dominated power systems introduces significant complexity and nonlinearity, rendering traditional mechanism-based modeling computationally prohibitive for real-time security assessment. While data-driven approaches offer computational efficiency, they fundamentally lack physical interpretability and often exhibit generalization failures under rare, large-signal disturbances due to the absence of intrinsic physical constraints. To bridge this gap, this paper proposes a Physics-Guided Symbolic Regression (PGSR) framework for constructing interpretable and robust dynamic equivalent models. The methodology embeds domain knowledge via topological masks and dimensional consistency rules to restrict the evolutionary search space to physically admissible manifolds. A multi-resolution extraction strategy based on the Pareto frontier is developed to autonomously identify both linear small-signal models and nonlinear large-signal formulations adaptable to varying analytical requirements. Furthermore, a post hoc verification stage based on Lyapunov stability theory ensures the dynamic validity and energy dissipation properties of the generated equations. A case study on the WSCC 9-bus system demonstrates that the proposed method accurately recovers the underlying Taylor-series structure of swing equations and significantly outperforms four data-driven baselines—including polynomial, kernel, and neural network models—in out-of-distribution generalization, achieving 12–42× lower trajectory error under unseen large perturbations. Full article

Pseudorandom number generators (PRNGs) used in deoxyribonucleic acid (DNA)-oriented computational workflows often generate outputs in the bit domain and then map them to DNA symbols. This indirect strategy may treat DNA-specific constraints, including GC balance, homopolymer limits, and short-range sequence dependencies, as separate from generation. This study proposes a constraint-aware, dual-head decoder-only Transformer framework for DNA-local PRNG generation directly in the adenine/cytosine/guanine/thymine (A/C/G/T) alphabet. The model generates the next DNA base and derives the bitstream through dynamic selection among eight equivalent DNA-to-bit coding rules. The framework was evaluated under R1 based on real genomic data, R1-ext as independent validation, R2 based on synthetic data, and R3 without training or reference data. For each setting, 10 independent runs were performed, each producing a 500,000-base DNA sequence and a 1,000,000-bit stream. Bit-level evaluation used NIST SP 800-22, SP 800-90B-inspired min-entropy/health indicators, and ENT, while DNA-level evaluation used GC balance, homopolymer control, and symbolic structural metrics. The reported NIST tests satisfied the acceptance criterion, t-tuple min-entropy lower bounds ranged from 0.9955 to 0.9964 bit/bit, and core DNA-compatibility constraints were preserved. Multi-stream and exact-match k-mer leakage analyses indicated no systematic bit-level dependence or direct long-fragment copying. Overall, the framework supports reproducible DNA-local PRNG generation and multilayer validation. Full article

Landscape Visual Assessment (LVA) has long examined how landscape elements influence visual perception and aesthetic response, yet the question of which elements attract attention remains underexplored in historic parks. Compared with urban parks, streetscapes, or natural landscapes, historic parks are shaped by a distinctive combination of natural features, cultural structures, and historically embedded symbolic meanings. In this study, we categorize landscape elements in historic parks into Natural Landscape Elements (NLE) and Cultural Landscape Elements (CLE), and investigate their relative visual salience in three historic parks in Beijing: Taoranting Park, the Summer Palace, and Beihai Park. We adopt a multi-method exploratory framework integrating cognitive maps, eye-tracking experiments, computational vision analysis, and GIS/UGC-based spatial analysis. The study draws on 30 cognitive maps, participant-level eye-tracking data from 30 valid participants, supplementary heatmap-based computational image analysis, and large-scale geotagged photo-density data. The results show that, within the exploratory sample, CLE were more frequently associated with strong memory impressions than NLE. In the pooled eye-tracking analysis, CLE showed higher attention scores overall, but this pattern was not stable across all parks and was strongly context-dependent. The computational and spatial analyses further suggest that attention distribution is influenced not only by the presence of specific elements, but also by color contrast, the spatial coupling of CLE and NLE, and the broader organization of park scenes and visitor activity zones. Rather than proposing a universal model of visual attention in historic parks, this study offers an exploratory, context-sensitive account of how cultural and natural landscape elements jointly shape attention across perceptual and spatial scales. The findings contribute to landscape visual assessment research by extending it into the specific setting of historic parks and by demonstrating the value of combining perceptual, computational, and spatial methods in a complementary framework. Full article

Euclidean plane geometry problem solving is a challenging benchmark for artificial intelligence because it requires complex diagram understanding, symbolic deduction, and multi-step reasoning. Constructing effective datasets for this task requires geometric instances that are realizable, non-degenerate, structurally diverse, and paired with human-like proofs. However, existing random or template-based generation pipelines often produce redundant, singular, or infeasible candidates, causing substantial computation to be spent before useful reasoning trajectories can be extracted. To address these limitations, we present FGeo-GCG, a hybrid geometric data synthesis framework built on the FormalGeo-V2 deductive engine. It formulates Geometric Configuration Generation as an incremental linear construction process that decomposes global constraint satisfaction into local construction steps, thereby pruning invalid branches during the generation process. To improve reliability and efficiency, FGeo-GCG combines two validation stages: a safe stochastic Jacobian-rank filter estimates whether local candidate constraints contribute independent algebraic restrictions, and progressive geometric validation checks whether the resulting partial construction remains realizable and non-degenerate. By encoding incidence-, metric-, and symmetry-related dependencies within unified constraint graphs, the framework also connects geometric data synthesis with structural symmetry analysis. Validated constraint graphs are then converted into problem instances through forward deduction, goal decomposition, and multi-dimensional complexity filtering, producing proof targets without manual annotation. Experiments show that the full validation pipeline reduces the failure rate for highly constrained instances. The resulting FGeo-GCG dataset contains more than 50,000 formally validated plane geometric configurations and provides engine-derived reasoning traces and targets for future training and evaluation of neuro-symbolic geometry problem-solving systems. Full article

Understanding advanced pre-tertiary mathematics, particularly three-dimensional vectors, demands robust spatial reasoning skills that many students find challenging to develop through traditional pedagogical methods. This study proposes and evaluates an innovative educational tool that leverages large vision models to automate the conversion of handwritten vector equations into accurate 3D graphical representations. By interpreting students’ handwritten input using advanced computer vision, the system provides immediate, interactive visual feedback to bridge the cognitive gap between abstract symbolic notation and tangible geometric concepts. We evaluated the system using a dataset of 1000 handwritten vector equations typical of the Singapore-Cambridge GCE ‘A’ Level H2 Mathematics syllabus. Our findings demonstrate that while GPT-4o serves as a capable baseline, achieving 84.6% accuracy with multi-shot prompting, newer variants such as GPT-4.1-mini offer superior performance, reaching 91.4% accuracy with significantly higher computational efficiency. The results confirm that AI-powered visualisation tools can effectively interpret complex spatial mathematical layouts when guided by optimal prompt engineering. Implementing such technology in educational settings presents a viable, scalable, and cost-effective method to democratise learning support, fostering independent study and enhancing students’ conceptual comprehension of spatial mathematics. Full article

Binary Waring decomposition seeks to express a homogeneous binary form as a minimal sum of powers of linear forms. In the binary setting, Sylvester’s theorem gives a classical algebraic route for rank determination and parameter recovery through structured Hankel/catalecticant matrices. Although this procedure is exact and interpretable in ideal arithmetic, practical rank identification may become unstable when the input coefficients are contaminated by noise or when the underlying roots are close to degenerate configurations. This paper develops a data-driven rank inference framework coupled with certified Sylvester reconstruction for robust binary Waring decomposition. The proposed method first converts the coefficient sequence into a Hankel-aware graph that captures recurrence-induced dependencies among polynomial coefficients. A graph neural network is then used to infer plausible rank candidates from this structured representation. Instead of accepting a single prediction directly, the framework performs explicit Sylvester reconstruction and algebraic residual verification for candidate ranks. To further improve decision reliability, a lightweight meta-verification module integrates reconstruction residuals, model confidence scores, and stability-related indicators to select the most credible rank. Experiments on large-scale synthetic binary forms show that the proposed meta-guided variant improves rank identification and verified reconstruction success relative to the one-shot hybrid solver under low-to-moderate noise while maintaining the transparency and auditability of classical symbolic–numeric computation. Additional stress tests indicate that performance can degrade under shifted sampling regimes; so, the method should be interpreted as a robust decision layer within the modeled problem class rather than as unconstrained real-world validation. Full article

We show that a single Hodgkin–Huxley (HH) neuron with Pyragas-type delayed feedback control (DFC) can store multiple symbols as stable periodic orbits, where the specific orbit is selected by tuning the DFC gain K and time delay $\tau$. Sweeping the $(K,\tau )$ parameter plane at fixed bias current $I_{\mathrm{bias}}$ = 10.0 μA/cm² reveals 207 orbit types across 12 topological categories, with inter-spike interval (ISI) means from 5.9 to 56.9 ms. We establish: (i) a write protocol that reliably locks orbits with 13.9 ms median settling time; (ii) a novel Pattern-Oriented Limit-cycle Decoder (POLD) that reads orbits at 100% accuracy from only five observed ISIs (1200 trials across 12 orbits; Wilson 95% CI: 99.7–100%); (iii) a complete single-symbol write–read–erase (W–R–E) cycle with 100% read accuracy, 92% erase verification, and no decay over hold durations up to 50 s; and (iv) a fully validated 12-symbol memory capacity with a read-discriminable upper bound of 67 symbols (11.2× over rate coding; write viability confirmed only for the conservative 12-symbol subset). Reliable orbit addressing needs delay precision of ±2%, which constitutes a write-precision specification and not a fundamental capacity limit. These findings show that parametric delayed feedback is a viable mechanism for limit-cycle-based information storage in conductance-based spiking neurons. The biological interpretation is analogical, not direct: the ±2% delay-precision requirement exceeds what has been demonstrated for biological autaptic variability, and the orbit-coded memory framing is best understood as a computational proof-of-principle aimed at neuromorphic engineering, not as a claim about biological working memory. Full article

This article studies the nonlinear wave dynamics of the recently introduced integrable combined Kairat-II-X (K-II-X) equation, which combines dynamical features of the Kairat-II and Kairat-X models. The considered model possesses relevance in nonlinear wave propagation, geometric curve dynamics, and localized optical pulse evolution, thereby providing a mathematical framework for describing curvature-driven nonlinear phenomena in higher-dimensional systems. To obtain exact analytical solutions, a symbolic neural analytical framework based on the improved Riccati neural networks (IRNNs) method is employed. The proposed framework integrates trial functions within multilayer neural network structures, where each neuron in the first hidden layer is constructed through solutions of the improved Riccati equation. The symbolic outputs obtained from the neural network computations are subsequently employed as trial functions for the integrable combined K-II-X equation. Using this framework, several classes of exact wave solutions are derived in the form of hyperbolic, trigonometric, rational, including localized solitary waves and interaction-type structures. In particular, the symbolic neural representation produces both single- and multisoliton wave profiles exhibiting nonlinear localization and interaction behavior. Furthermore, representative wave structures are illustrated through two-dimensional, three-dimensional, contour, and density visualizations to examine the qualitative influence of governing parameters on wave amplitude, localization, propagation behavior, and interaction patterns. The reported results demonstrate the capability of the IRNNs framework to generate diverse nonlinear wave structures in integrable higher-dimensional systems and provide a useful analytical reference for future investigations in nonlinear science and applied mathematical physics. Full article

Controllable symbolic music generation must preserve a reference melody while remaining responsive to style prompts. Existing hierarchical diffusion systems typically reuse a shared condition vector across harmony, rhythm, and timbre stages, which can entangle stylistic factors and weaken melody preservation. We present HCDMG++, a hierarchical diffusion framework that addresses these two limitations through stage-aware style routing and differentiable melody regularization. The routing module uses a residual multi-layer perceptron (MLP) with zero-initialized scalar gates to project text-derived style embeddings into harmony-, rhythm-, and timbre-specific subspaces, whereas the regularization branch aligns soft pitch histograms and contour trajectories with the conditioning melody during training without breaking the differentiable computation graph. We evaluate the integrated system on a 384-sample benchmark covering four melodies, eight styles, four random seeds, and three denoising budgets, supplemented by a matched legacy-compatible reference and inference-time component ablation that contrasts legacy behavior, silenced gates, an automated uniform gamma routing sweep, and the full forward pass. HCDMG++ produces valid four-track outputs in all 384 runs, reaches a peak pitch histogram similarity score of 0.508 under a 64-step budget, and improves pitch histogram alignment over Legacy-HCDMG by roughly two orders of magnitude on the matched slice, while attaining a positive Fisher-style style separability score where the legacy benchmark is too sparse to support one. These results indicate that stage-specific conditioning and differentiable structural guidance jointly improve controllability in symbolic music diffusion, while also exposing the remaining limitations in long-form generalization and perceptual validation, which motivate the future work outlined at the end of this paper. Full article

Delays are among air transport’s main operational challenges, with significant economic, societal and environmental consequences, and many methodological alternatives have been used in their study. Here we explore the use of symbolic regression, a data-driven technique that searches a space of analytic expressions to identify compact and interpretable models explaining a given set of data. We specifically use symbolic regression to characterise delays at the busiest European airports, how they evolve in time and depend on their own past, up to how they propagate across airports. This is done with the aim of evaluating the feasibility of using this approach, and the added value when compared to standard statistical and causal models. Results of this proof of concept point to a nuanced picture: while symbolic regression demonstrates clear potential for uncovering interpretable functional relationships in delay dynamics, its applicability is hindered by the significant computational cost and its stochastic nature. Full article

Music genre classification is an important task in the music information retrieval community that aims to categorize music samples by genre; it can help to retrieve music more easily and efficiently from huge digital music resources. There is an extensive literature on music genre classification, and in this study, we solve the problem using multi-modal information, especially based on music audio and text. We propose a deep multi-modal kernel map network that learns discriminative features in a high-dimensional kernel Hilbert space by fusing the multi-modal features. For the music audio, Mel Frequency Cepstral Coefficients (MFCCs) are extracted and a pre-trained ResNet is applied to extract the features. For the texts, the pre-trained RoBERTa model is applied to extract the semantic symbolic features. In the network’s input layer, we calculate four exact/approximated elementary kernel maps from the audio and text features; in the intermediate and final layer, we progressively compute the nonlinear combination of preceding kernel maps of different modalities, followed by a fully connected layer for classification. The network can be trained end-to-end to jointly learn the combination weights between modalities and classifier parameters. We apply the proposed network on the public GTZAN dataset, multi-modal piano genre dataset, and 4MuLA dataset, and the experimental results validate the effectiveness of the proposed deep multi-modal kernel map network for music genre classification. Full article

In the present work, we introduce and study a new two-parameter generalization of Legendre-based Appell polynomials, defined through an explicit representation that unifies classical Legendre structures with the Appell polynomial framework. Starting from a generating function, we derive a three-term recurrence relation, a degree-lowering operator, an integro-partial degree-raising operator, and a corresponding integro-partial differential equation satisfied by the new family. A determinant representation is established via Cramer’s rule applied to the Cauchy-product expansion of the generating function. Several subfamilies of independent interest arise naturally as special cases, namely, Legendre-based Hermite–Frobenius–Euler polynomials, Legendre-based Miller–Lee polynomials, and both the probabilist’s and physicist’s variants of Legendre-based bi-variate Hermite polynomials. For each subfamily we record the corresponding recurrence relations, shift operators, differential equations, and determinant forms, and we illustrate the behavior of selected members through three-dimensional surface plots and real-root distribution diagrams. The framework presented here extends several constructions available in the recent literature and points to natural directions for future work, including connections with q-series, combinatorial identities, and symbolic-computation methods, which are outlined in the concluding section. Full article

As global markets navigate the dual transition of digitalization and sustainability, the risk of “digital greenwashing” has emerged as a critical corporate governance challenge. Utilizing a comprehensive dataset of Chinese A-share listed firms from 2018 to 2024—an ideal laboratory characterized by rapid regulatory shifts and unique state-market dynamics that provide highly generalizable insights for other emerging economies—this study empirically investigates whether corporate digital transformation acts as a genuine driver for Environmental, Social, and Governance (ESG) enhancement or merely serves as a symbolic disclosure tool. Fortified by rigorous identification strategies, including Propensity Score Matching and Lewbel heteroskedasticity-based instrumental variable estimations, the results confirm that digitalization serves as an incremental yet statistically significant driver for corporate sustainability. Crucially, mechanism analyses reveal a “full moderation” effect: the positive impact of digitalization on ESG performance is completely activated only in the presence of premium external assurance (e.g., Big 4 audits). Without high-quality IT auditing to act as a credibility enforcer and verify the substance of digital signals, technological adoption alone fails to yield significant ESG improvements. Furthermore, a nuanced structural asymmetry is identified: foundational data infrastructures (Cloud Computing and Big Data) directly enhance quantifiable Environmental and Governance metrics, whereas premium audits are strictly required to activate the “soft,” qualitative Social dimension. Finally, the synergy exhibits distinct boundary conditions. It is heavily concentrated within high-pollution industries where digital transition acts as a regulatory survival imperative rather than mere market expansion, and its reliance on external assurance is fundamentally driven by the market-signaling needs of non-State-Owned Enterprises (non-SOEs) rather than the policy-distorted mandates of SOEs. These findings offer critical theoretical extensions and policy implications for standardizing digital-audit infrastructures globally. Full article

This article examines the evolution of computational paradigms in architecture through the articulation of a diachronic framework and a comparative analytical matrix. Moving beyond linear narratives centred on technological progress, the study proposes an interpretation of architectural computation as a layered ecology in which distinct regimes—symbolic, representational, informational, generative, and probabilistic— interact simultaneously. Based on a critical review of historical, theoretical, and technical sources, the study comparatively examines five major paradigmatic moments in the development of architectural computation. Instead of proposing these paradigms as discrete or sequential stages, the article interprets them as interdependent computational layers that continue to coexist within contemporary architectural practice. The findings indicate that the transition from rule-based deterministic systems to learning-based systems introduces a fundamental shift in the nature of architectural computation, moving design processes from controlled execution toward probabilistic exploration. In this context, artificial intelligence does not merely extend existing technical capabilities but reconfigures the relationships between designer, tool, and knowledge. The article concludes that contemporary architecture operates within a layered computational ecology in which multiple paradigms overlap and interact. This perspective allows computation to be understood not only as a set of tools but as an epistemological infrastructure that profoundly transforms architectural practice, its processes, and its critical frameworks. Full article

This study examines the dynamical behavior of the dual-mode nonlinear Schrödinger equation (d-mNLSE), which describes the interaction, amplification, and attenuation of two coexisting wave modes in nonlinear media. The model incorporates key physical parameters including the nonlinearity coefficient, interaction phase velocity, and dispersion parameter, which significantly influence the evolution of nonlinear waves. By applying the modified Sardar sub-equation method (mSS-EM), a wide spectrum of exact analytical solutions is derived. These solutions include mixed trigonometric waves, shock-type structures, singular solutions, complex dark–bright solitons, multi-peak solitons, periodic and mixed-periodic waves, as well as mixed hyperbolic structures. The analytical findings provide useful insight into nonlinear wave propagation phenomena arising in fluid mechanics, water wave dynamics, ocean engineering, and related physical systems. Moreover, the conservation laws of the d-mNLSE are established, which leads to the conserved quantities of impulse power, momentum, and energy and describes the invariant characteristics of the soliton solutions during their propagation. The bifurcation analysis of the reduced dynamical model is carried out to explore the qualitative characteristics of the obtained solutions. The equilibrium points of the considered model are calculated, and their stability properties are analyzed systematically. To demonstrate the physical characteristics of the obtained solutions, different kinds of two-dimensional, three-dimensional, and contour plots are plotted using symbolic computations software. These findings confirm that the analytical method used to obtain the soliton solutions can be used to obtain a variety of soliton solutions of nonlinear evolution equations that appear in applied sciences and engineering. Full article