Search Results (328)

Parametric tiered-seating design can be framed as a constrained multi-objective optimization problem in which a low-dimensional decision vector is evaluated by a deterministic operator with sequential feasibility rejection and visibility constraints. This study introduces an oracle-preserving, learning-assisted screening workflow, where a multi-output multilayer perceptron (MLP) is used only to prioritize candidates for evaluation. Here, multi-output denotes a single network trained to predict the full objective vector jointly. Candidates are sampled within bounded decision ranges and evaluated by an operator that propagates section-coupled geometric state and enforces hard clearance thresholds through a Vertical Sightline System (VSS), i.e., a deterministic row-wise sightline/clearance evaluator that enforces hard clearance thresholds. The oracle-evaluated set is reduced to its mixed-direction Pareto-efficient subset and filtered by feature-space proximity to a fixed validation reference using nearest-neighbor distances in standardized 11-dimensional features, yielding a robustness-oriented pool. A compact shortlist is derived via TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution; used here strictly as a post-Pareto decision-support ranking rule), and preference uncertainty is assessed by Monte Carlo weight sampling from a symmetric Dirichlet distribution. In an archived run under a fixed oracle budget, 1235 feasible designs are evaluated, producing 934 evaluated Pareto solutions; proximity filtering retains 187 robust candidates and TOPSIS reports a traceable top-30 shortlist. Stability is supported by concentrated top-k frequencies under weight perturbations and by audits under single-feature-drop ablations and tested rounding precisions. Overall, the workflow enables reproducible multi-objective screening and reporting for feasibility-dominated seating design. Full article

Feed formulation is a typical multi-objective optimization problem that aims to minimize cost while satisfying multiple nutritional constraints. However, existing methods often suffer from limitations in handling nonlinear constraints, high-dimensional decision spaces, and solution feasibility. To address these challenges, this study proposes a multi-objective feed formulation method based on an improved Non-dominated Sorting Genetic Algorithm II (NSGA-II). A hybrid Dirichlet–Latin Hypercube Sampling (Dirichlet-LHS) strategy is introduced to generate an initial population with high feasibility and diversity, together with an iterative normalization-based dynamic repair operator to efficiently handle ingredient proportion and nutritional constraints. In addition, an adaptive termination mechanism based on the hypervolume improvement rate (Hypervolume Termination, HVT) is designed to avoid redundant computation while ensuring effective convergence of the Pareto front. Experimental results demonstrate that the Dirichlet–LHS strategy outperforms random sampling, Dirichlet sampling, and Latin hypercube sampling in terms of hypervolume and solution diversity. Under identical nutritional constraints, the improved NSGA-II reduces formulation cost by 1.52% compared with multi-objective Bayesian optimization and by 2.17% relative to conventional feed formulation methods. In a practical application to meat sheep diet formulation, the optimized feed cost is reduced to 1162.23 CNY per ton, achieving a 4.83% cost reduction with only a 1.09 s increase in computation time. These results indicate that the proposed method effectively addresses strongly constrained multi-objective feed formulation problems and provides reliable technical support for precision feeding in intelligent livestock production. Full article

This paper presents a finite element methodology for generating continuous digital elevation models (DEMs) from discrete terrain data using the Poisson equation under steady-state conditions. Unlike conventional DEM interpolation techniques, the proposed methodology formulates terrain reconstruction as a constrained harmonic problem, solved directly on scattered point sets using standard finite element procedures, without requiring structured grids or intermediate interpolation stages. The approach interprets the elevation field as a harmonic scalar function whose smoothness is enforced by the variational formulation of the Poisson problem. The governing equation is solved using standard finite element procedures with Dirichlet boundary conditions applied at the measurement points, ensuring that the reconstructed surface passes exactly through the known elevations. The isotropic conductivity coefficient is set to unity and the source term to zero, which simplifies the formulation and yields a harmonic interpolation independent of any physical parameters. The resulting surfaces exhibit continuous slopes and reduced sensitivity to irregular data distributions. Numerical tests comprising two analytical examples and a real terrain case show that, compared with thin-plate FEM and RBF–NURBS reconstructions, the proposed Poisson-based approach yields smoother and more stable surfaces, with global errors of the same order of magnitude and reduced computational cost. Full article

The numerical solution of space-fractional diffusion problems is investigated focusing on stability and non-negativity issues. The extension of classical schemes is analyzed for the case of the spectral fractional Dirichlet Laplacian operator. For the spatial discretization, both finite differences and finite elements are used. The finite element case needs special care and is discussed in detail. Both spatial discretizations are combined with the matrix transformation method, leading to fractional powers of matrices in the discretized problems. In the time stepping, $\theta$-methods are utilized with $\theta =0,{\displaystyle \frac{1}{2}}$ and 1. In the analysis, it is pointed out that the stability condition in the case of $\theta =0$ depends on the fractional power $\alpha \in (0,1]$, which results in a weaker condition on the time discretization compared to the conventional diffusion. In this case, we also obtain non-negativity preservation. Also, unconditional stability is established for $\theta ={\displaystyle \frac{1}{2}}$ and $\theta =1$, where for the spatial discretization rather general conditions are posed. The results containing stability conditions are also confirmed in a series of numerical experiments. In the course of the corresponding algorithms, an efficient matrix power–vector product procedure is employed to keep simulation time at an affordable level. The associated computational algorithm is also described in detail. Full article

The rapid proliferation of artificial intelligence (AI) systems across high-stakes domains—with global AI adoption accelerating since 2023—has created an urgent need to identify which AI challenges and issues are materializing into real-world harms so that policymakers can develop targeted regulations, organizations can implement effective risk management, and accountability mechanisms can address actual rather than speculative problems. Public concern has risen sharply: 52% of Americans now feel more concerned than excited about AI (up from 38% in 2022), and 80% believe government should maintain AI safety rules even if development slows. Yet existing approaches exhibit critical limitations that impede evidence-based governance. Ethics frameworks, while establishing normative principles across 84+ published guidelines, remain aspirational rather than empirical. Survey-based studies capture perceptions from over 48,000 respondents globally but measure expectations rather than documented harms. Incident databases catalog over 1200 AI failures but depend on media coverage, systematically overrepresenting high-profile cases while underrepresenting routine organizational problems. This study addresses this gap by analyzing 347 AI-related U.S. litigation cases using machine learning text analytics, providing empirical evidence of AI problems that have crossed the threshold from abstract concern into documented legal conflict. Employing Latent Dirichlet Allocation (LDA) and Non-negative Matrix Factorization (NMF) topic modeling with coherence validation (NMF achieving 0.276 NPMI vs. LDA’s 0.164), the analysis identifies nine distinct AI issue areas with specific case distributions: cybersecurity vulnerabilities and data breaches (116 cases, 33.4%), intellectual property and AI ownership (61 cases, 17.6%), AI misrepresentation and inflated claims (59 cases, 17.0%), criminal justice and algorithmic due process (37 cases, 10.7%), employment automation (33 cases, 9.5%), privacy and surveillance (31 cases, 8.9%), platform accountability (21 cases, 6.1%), algorithmic bias (19 cases, 5.5%), and government AI deployment (6 cases, 1.7%). The findings reveal a systematic mismatch between AI ethics discourse—which emphasizes fairness and transparency—and litigation patterns, where data security (33.4%) and intellectual property (17.6%) dominate while algorithmic bias comprises only 5.5% of cases. Most disputes are addressed through existing legal frameworks (First Amendment, Lanham Act, FOIA, Title VII) rather than AI-specific regulation, underscoring the urgent need for governance mechanisms aligned with empirically documented AI challenges. Full article

Europe is dealing with environmental problems that require cooperation beyond national and regional borders. Air pollution, water pollution, biodiversity loss, and waste management are the major issues that are not only complex but also cross borders. Therefore, it is necessary to provide collaborative responses that go beyond the capacity of individual countries. This inquiry centers on the question of what the best way is to set up and govern the transnational cooperation in Europe to confront these major environmental challenges. A systematic bibliographic review of the research conducted between 2010 and 2025 forms the basis of this work. The research combines semantic analysis and Latent Dirichlet Allocation (LDA) modeling to study 80 selected publications to find the tenets of the themes discussed. The identified topics are urban climate change adaptation and mitigation, climate policy and management, adaptation and vulnerability frameworks, land use and biodiversity impacts, and future climate projections and assessment. The findings show that there are strong synergies between biodiversity and climate adaptation, resilience, and environmental governance, as well as the great influence of climate change on the water management sector. The study has unveiled the significance of institutional policy frameworks in bringing about environmental cooperation across borders. In addition, it depicts the relationship between local urban projects and supra-regional policy strategies, in which the two can merge and function efficiently as long as they are working towards the common goal of environmental sustainability. This study is meant to shed more light on the area of environmental governance research, discovering areas that need more exploration, and providing some signposts on how to improve environmental involvement in Europe. Full article

The paper deals with the Dirichlet problem for the nonstationary Stokes system in a bounded two- or three-dimensional domain with angular or conical points on the boundary. The author proves the existence and uniqueness of solutions in weighted Sobolev spaces. The main result can also be used to obtain existence and uniqueness results in non-weighted spaces. Full article

The sixth-generation (6G) system has been attracting increasing attention from both industry and academia, with the space–air–ground integrated network (SAGIN) identified as one of its key applications. This study investigates a SAGIN framework tailored for deployment in remote areas. To address the differing needs of users with emergency and routine tasks, an offloading strategy is proposed that enables direct offloading for emergency tasks and optimized UAV-assisted offloading for routine tasks. Additionally, considering the limited satellite coverage duration, a reliability mechanism for task offloading is designed. The study formulates a task offloading optimization problem aimed at maximizing the completion rate of routine tasks—while reducing their energy consumption and latency—under the premise of guaranteeing the completion of emergency task offloading. The problem is modeled as a Markov Decision Process (MDP). To solve it, a D-MAPPO reinforcement learning algorithm is proposed, which integrates the Dirichlet distribution with the Multi-Agent Proximal Policy Optimization (MAPPO) framework. Simulation results show that, compared with the MAPPO and PPO algorithms, the delay is reduced by 38% and 31%, respectively, while the energy consumption is reduced by 7% and 48%, respectively. Full article

Background/Objectives: Loneliness and social isolation are common among older adults and linked to adverse health outcomes. Videoconferencing can support social connections, but the role of aging-in-place organizations (AIPOs), such as senior centers and Area Agencies on Aging, in facilitating adoption is poorly understood. This review examined how AIPOs use relational videoconferencing to promote social engagement among older adults. Methods: We applied a hybrid methodology combining a scoping review with latent topic modeling to contextualize and analyze the evidence base. Exploratory searches revealed limited literature specifically addressing AIPO involvement; therefore, we first conducted latent topic modeling of the broader literature on social videoconferencing among older adults to establish a thematic foundation for the subsequent PRISMA-guided scoping review. Thematic analysis of this broader corpus, identified through 2021 database searches, applied Latent Dirichlet Allocation (LDA) to a collection of peer-reviewed articles. Subsequent refinement of this corpus by removing non-primary research and non-AIPO records produced the narrower PRISMA subset used for the scoping review. The scoping review followed JBI guidelines and was based on database searches (EBSCOhost: MEDLINE, AgeLine, SocINDEX, Health Source: Nursing/Academic Edition, and Family & Society Studies Worldwide; ProQuest Social Science Premium Collection; and PubMed, including MEDLINE, PMC, and in-process content) for peer-reviewed studies published between 2011 and 2025. Inclusion criteria required primary research involving adults aged 65 years or older, use of videoconferencing technology for social engagement, and reference to AIPOs or analogous community-based aging services. The protocol was post-registered with the Open Science Framework. Results: The LDA analysis of 101 peer-reviewed articles identified six latent themes describing the broader research landscape: problem of isolation, character of socialization, physical health, technology as intervention, technology as social medium, and supportive environments. This thematic framework informed the scoping review, which screened 1908 records and retained 25 publications (representing 24 unique studies) explicitly referencing AIPO involvement in relational videoconferencing. Only one study predated COVID-19. Mapping these studies to the LDA-derived themes revealed the least consistent coverage to be in supportive environments and physical health, particularly among AIPOs other than senior or community centers. Conclusions: Relational videoconferencing has potential to sustain and expand older adults’ social connections, but evidence mapped through the scoping review shows that documentation of how AIPOs support adoption is sparse. The hybrid approach advances understanding of videoconferencing in aging contexts and identifies priorities for documenting, comparing, and refining AIPO practices to inform future interventions and policy. Full article

The Steklov–Zaremba problem for the Laplace operator in a bounded domain with a strictly Lipschitz boundary is considered. A homogeneous Dirichlet condition is specified on the closed part of the boundary of the domain, and the Steklov boundary condition with a spectral parameter is assumed to be satisfied on the complement to the closed part. This problem is a natural generalization of the classical Steklov problem. With respect to a closed set on the boundary of the domain, where the homogeneous Dirichlet boundary condition is specified, its Wiener capacity is assumed to be positive. It follows from this condition on the capacity that it is natural to consider the problem in the Sobolev space of functions that are square-integrable together with all generalized (weak) first-order derivatives. The aim of the paper is to find an estimate for the maximum modulus of normalized eigenfunctions to the problem under consideration. The proofs of the main results make substantial use of the iterative technique of Jurgen Moser. Full article

We derive an analytical solution to the one-dimensional linearized Boussinesq equation with mixed boundary conditions (Dirichlet–Neumann), formulated to describe drainage in porous media. The solution is obtained via the unified transform method (Fokas method), extending its previous applications in infiltration problems and illustrating its utility in soil hydrology. An explicit integral representation is constructed, considering different types of initial conditions. Numerical examples are presented to demonstrate the accuracy of the solution, with direct comparisons to the classical Fourier series approach. Full article

Complex fractal dimensions, defined as poles of appropriate fractal zeta functions, describe the geometric oscillations in fractal sets. In this work, we show that the same possible complex dimensions in the geometric setting also govern the asymptotics of the heat content on self-similar fractals. We consider the Dirichlet problem for the heat equation on bounded open regions whose boundaries are self-similar fractals. The class of self-similar domains we consider allows for non-disjoint overlap of the self-similar copies, provided some control over the separation. The possible complex dimensions, determined strictly by the similitudes that define the self-similar domain, control the scaling exponents of the asymptotic expansion for the heat content. We illustrate our method in the case of generalized von Koch snowflakes and, in particular, extend known results for these fractals with arithmetic scaling ratios to the generic (in the topological sense), non-arithmetic setting. Full article

Non-IID is one of the key challenges in federated learning. Data heterogeneity may lead to slower convergence, reduced accuracy, and more training rounds. To address the common Non-IID data distribution problem in federated learning, we propose a comprehensive dynamic optimization approach based on existing methods. It leverages MAP estimation of the Dirichlet parameter $\beta$ to dynamically adjust the regularization coefficient $\mu$ and introduces orthogonal gradient coefficients ${\mathbf{\Delta }}_i$ to mitigate gradient interference among different classes. The approach is compatible with existing federated learning frameworks and can be easily integrated. Achieves significant accuracy improvements in both mildly and severely Non-IID scenarios while maintaining a strong performance lower bound. Full article

This study focuses on a class of perturbed Dirichlet–Neumann tridiagonal (PDNT) Toeplitz matrices, mainly exploring their eigenvalue sensitivity and inverse problems. By the explicit expressions for eigenvalues and eigenvectors of PDNT Toeplitz matrices, an analytical formula for the eigenvalue condition number is proposed, and numerical experiments are presented based on the theoretical results. Meanwhile, the stability of eigenvalues is analyzed with respect to structured perturbations and pseudospectral properties, and finally, two inverse eigenvalue problems are discussed. Full article