Accurate and layout-consistent reconstruction remains a key challenge in indoor simultaneous localization and mapping (SLAM) due to the prevalence of planar and axis-aligned structures. Traditional visual and RGB-D SLAM methods often suffer from incomplete geometry and weak structural reasoning, while NeRF-based SLAM improves fidelity but is computationally expensive and unsuitable for real-time use. 3D Gaussian splatting offers improved efficiency but lacks structural priors, often resulting in distortions in structured scenes. To address these issues, we propose a structure-aware SLAM framework based on 2D Gaussian splatting, which provides efficient, view-consistent mapping. We introduce a lightweight regularization scheme under the Manhattan-world assumption to align Gaussian orientations and positions with dominant axes, improving layout consistency and geometric fidelity. Extensive experiments on Replica and TUM-RGBD datasets demonstrate that our method consistently outperforms existing SLAM baselines in terms of geometric accuracy and edge preservation across multiple indoor scenes.

The convective Allen-Cahn equation generalizes the classical Allen-Cahn equation by introducing an additional convective term associated with a solenoidal velocity field while maintaining the maximum bound principle (MBP). However, developing high-order numerical schemes that are accurate in both time and space and preserve the MBP unconditionally has remained a significant challenge. In this paper, we address this by first defining new auxiliary variables to reformulate the interaction of the velocity field with the phase field. We then transform the convective Allen-Cahn equation into a generalized Fokker-Planck form using an exponential transformation, enabling the development of MBP-preserving linear numerical schemes. Subsequently, we propose first- and second-order in time numerical schemes for the reformulated equations with a second-order quasi-symmetric finite difference discretization in space. In this approach, the auxiliary variables are replaced with known functions related to the velocity field, simplifying the numerical implementation. For the first-order in time scheme, we derive its optimal error estimate and prove its unconditional MBP-preservation. For the second-order in time scheme, we show its MBP-preservation under mild constraints on the mesh and time step sizes. Some numerical experiments in two and three dimensions are also presented to validate the theoretical findings and illustrate the accuracy and efficiency of our proposed schemes.

Corruption remains a major barrier to development in Africa, undermining public trust, weakening service delivery, and hindering economic growth. Defined as the abuse of public power for personal gain, it appears in forms such as bribery, embezzlement, nepotism, and cronyism, affecting both public and private sectors. Despite various anti-corruption efforts, the problem persists. This study presents a non-linear system of differential equations to evaluate the impact of corruption on productivity and service delivery, incorporating both constant and time-dependent control strategies. The basic reproduction number ($R_0$) is calculated using the next-generation matrix method. Model behaviour is further analysed through sensitivity analysis and stability assessments using the Routh-Hurwitz criterion and Lyapunov functions. An optimal control framework, based on Pontryagin’s maximum principle, assesses the effectiveness and cost-efficiency of preventative and punitive interventions. Numerical simulations, using the fourth-order Runge-Kutta method, indicate that strong enforcement of punitive measures is the most effective and cost-efficient strategy to combat corruption. These measures significantly improve productivity and public service delivery. The key policy recommendation is that governments and institutions should prioritize robust punitive controls as the primary approach to reducing corruption and promoting sustainable development.

Families of slowly changing nonsingular large sparse linear systems arise frequently in many simulation problems in science and engineering. We consider iterative solution with recycling techniques for a general case where both left-hand sides and right-hand sides of the systems change from one family to the next. We firstly develop a generalized product-type method in the framework of recycling biconjugate gradient method (RBiCG), referred to as RGPBiCG, which can also be considered as a recycling variant of GPBiCG. However, as the same situation in RBiCG stabilized method (RBiCGSTAB), the construction of recycling spaces in RGPBiCG requires expensive computational costs due to invoking other algorithms (like RBiCG) to compute approximate eigenspaces. In order to further reduce such computational costs, we alternatively form the recycling spaces in RGPBiCG with difference vectors of approximate solutions, as employed for loose GMRES (LGMRES), resulting in a more promising algorithm termed as LR-GPBiCG. Numerical experiments on both a set of academic problems and engineering simulation problems demonstrate the efficiency of our proposed algorithms.

In this paper, we introduce a neural network-based method to address the high-dimensional dynamic unbalanced optimal transport (UOT) problem. Dynamic UOT focuses on the optimal transportation between two densities with unequal total mass, however, it introduces additional complexities compared to the traditional dynamic optimal transport problem. To efficiently solve the dynamic UOT problem in high-dimensional space, we first relax the original problem by using the generalized Kullback-Leibler divergence to constrain the terminal density. Next, we adopt the Lagrangian discretization to address the unbalanced continuity equation and apply the Monte Carlo method to approximate the high-dimensional spatial integrals. Moreover, a carefully designed neural network is introduced for modeling the velocity field and source function. Numerous experiments demonstrate that the proposed framework performs excellently in high-dimensional cases. Additionally, this method can be easily extended to more general applications, such as crowd motion problem.

Polygonal meshes are a fundamental surface representation, yet their resolution can vary significantly. Establishing a smooth, bijective projection between meshes of different resolutions is crucial for consistent attribute transfer but becomes challenging when handling sharp bends and complex geometric features. This paper presents a novel approach to address this challenge by implicitly representing the shell enclosing two polygonal meshes using a cubic trivariate B-spline function, where the inner and outer bounding surfaces are formulated as level sets of a single cubic B-spline function. Our method enforces the bijective projection requirements on the cubic B-spline function, ensuring that the resulting gradient field naturally defines a robust bijective projection. Leveraging the favorable properties of cubic B-spline functions – namely, 1) sufficient smoothness while maintaining expressive representation, and 2) computational efficiency and ease of implementation, our approach efficiently computes a smooth and bijective projection even for challenging cases. Compared to existing shell-based bijective projection methods, our method consistently produces valid bijective projections, even in complex scenarios, outperforming state-of-the-art techniques. We further demonstrate its effectiveness in robust attribute transfer and precision-controlled shape manipulation.

We provide a sufficient and necessary condition in terms of the stoichiometric coefficients for a bi-reaction network to admit multistability. Also, this result completely characterizes the bi-reaction networks according to if they admit multistability.

Data- and mechanism-driven hybrid computing refers to the integration of traditional mechanism-based computing with data-driven methods. In this article, we present three typical patterns of this emerging paradigm: (1) mechanism-driven model optimization via data-driven refinement, (2) data-driven model construction with physical constraints, and (3) alternating optimization of mechanism-driven and data-driven models. We present several concrete examples to illustrate how hybrid computing improves accuracy, efficiency, and robustness across a variety of computational tasks.

The practice of incorporating extra parameters into standard models is a common technique in statistical analysis. Adding an extra parameter enables the formation of a new model by applying the modified alpha-power transformation, employing the Nadarajah-Haghighi model as the baseline. Numerous characteristics of the said model are acquired, like the mode, quantiles, entropies, stochastic orders, mean residual life function, and order statistics. The maximum likelihood estimation method has been employed to estimate the parameters of the suggested model. To show how well the suggested distributions will function in a real-world setting, a simulation study has also been carried out and data has been examined. It is attained that the proposed model outperforms several other cutting-edge, current models as well as the baseline.

This study develops a mathematical model for contaminant transport from two industrial sources and one natural source through a heterogeneous aquifer featuring fracture networks with variable apertures, faults of heterogeneous width, and a complex rock matrix. Key innovations include: (1) A nonlinear Darcy’s law with concentration-dependent conductivity; (2) Three coupled advection-dispersion equations with nonlinear dispersion and reaction terms for multispecies interactions; (3) Seasonal recharge dynamics integrated into flow-transport coupling. Non-dimensional analysis reveals advection-dominated regimes governed by Péclet and Damköhler numbers. Bifurcation analysis identifies stability thresholds for ternary chemical reactions. Numerical solutions via the Crank-Nicolson scheme demonstrate fracture-controlled contaminant pathways and recharge-modulated plume evolution. The framework provides critical insights for pollution management in geologically complex aquifers.