CSIAM Transactions on Applied Mathematics
The CSIAM Transactions on Applied Mathematics (CSIAM-AM) is the flagship journal of the Chinese Society for Industrial and Applied Mathematics. It publishes original research articles of high quality on a topic in applied mathematics or computational mathematics or scientific computing. Papers should address mathematically and computationally interesting and challenging problems. Manuscripts applying known methods to previously solved problems will not be accepted.
Optimal Strong Convergence Rate of Spectral Galerkin Exponential Euler Scheme for Parabolic SPDEs
We provide a new approach to strong error analysis of the spatial-spectral Galerkin and temporal exponential Euler scheme for a family of second-order parabolic stochastic partial differential equations (SPDEs) driven by multiplicative noise. Applying these results to the stochastic advection-diffusion-reaction equation with a gradient term driven by white noise indicates that this scheme achieves optimal strong convergence order exactly 1/2 in space, which removes an infinitesimal factor in the literature, and 1/4 in time. Numerical experiments support our theoretical analysis.
Parabolic stochastic partial differential equation
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Optimal Control for Maximum Instantaneous Convergence in Collective Migration Models
This paper studies consensus tracking of collective migration models that involve the alignment force gathering agents and the tracking force matching target. Each agent's dynamics is controlled by the tracking strategy, which establishes a trade-off between the two forces through a convex combination. In order to drive the system to achieve consensus tracking with the maximum instantaneous convergence speed, an optimal control strategy is proposed that the agents whose alignment force is weaker than, or counteracts its tracking force sense only the target, and become leaders, while the others sense only their neighbours, and become followers. Interestingly, there exist some initial frameworks such that the optimal control strategy consists of letting all agents become followers, which is called ``inactivation principle'' in [Piccoli, Duteil and Scharf, Math. Models Methods Appl. Sci., 26(2), 2016] and means that the leaderless is better than the leader-follower structure for certain conditions. Both asymptotic and finite-time consensus tracking are investigated. Several numerical simulations show the effect of the optimal control strategy.
Curvilinear Mask Optimization for Inverse Lithography Based on B-splines and Constrained Delaunay Triangulation
In this paper, we propose a gradient-based method to optimize curvilinear masks in optical lithography. The mask pattern is represented by periodic B-spline curves. We apply constrained Delaunay triangulation to discretize the domains circled by the spline curves. Subsequently, we establish an explicit relationship between the integral points and the control points of the boundary spline curve. Based on the relationship, we derive explicit formulas of the gradient of the optimization objective function with respect to the coordinates of the control points. Then we propose an inverse lithography algorithm to optimize the curvilinear mask pattern. Finally, the results of the numerical experiments demonstrate the feasibility and extensive adaptability of our method.
Random Regularity of the Vlasov-Poisson System with Random Initial Inputs in the Quasineutral Regime
The Vlasov-Poisson system is widely used in plasma physics and other related fields. In this paper, we study the Vlasov-Poisson system with initial uncertainty in the quasineutral regime. First, we prove the uniform convergence in the Wasserstein distance between the uncertain Vlasov-Poisson system in the quasineutral regime and its quasineutral limit system with random initial inputs. This is achieved by deriving an upper bound for the Wasserstein distance and rigorously estimating each component of this bound. Furthermore, by defining a new norm with respect to the quasineutral parameter and estimating the distribution function as well as the electric field in this norm using a variable substitution, we establish the random regularity of the solutions in the quasineutral regime. This work develops a novel framework for quantifying the propagation of the initial uncertainty of the Vlasov-Poisson system in the quasineutral regime, providing a theoretical basis for designing high-performance numerical algorithms.
High-Efficiency and Positivity-Preserving Stabilized SAV Methods for Gradient Flows
The scalar auxiliary variable (SAV)-type methods are very popular techniques for solving various nonlinear dissipative systems. Compared to the semi-implicit method, the baseline SAV method can keep a modified energy dissipation law but doubles the computational cost. The general SAV approach does not add additional computation but needs to solve a semi-implicit solution in advance, which may potentially compromise the accuracy and stability. In this paper, we construct a novel first- and second-order unconditional energy stable and positivity-preserving stabilized SAV (PS-SAV) schemes for $L^2$ and $H^{−1}$ gradient flows. The constructed schemes can reduce nearly half computational cost of the baseline SAV method and preserve its accuracy and stability simultaneously. Meanwhile, the introduced auxiliary variable is always positive while the baseline SAV cannot guarantee this positivity-preserving property. Unconditionally energy dissipation laws are derived for the proposed numerical schemes. In addition we propose an energy optimization technique to optimize the modified energy close to the original energy. Several interesting numerical examples are presented to demonstrate the accuracy and effectiveness of the proposed methods. Finally, we establish a rigorous error analysis of the fully discrete PS-SAV scheme.
Efficient Two-Dimensional Randomized Progressive Iterative Approximation for Large-Scale B-Spline Fitting
The randomized progressive iterative approximation (RPIA) is a local and approximate geometric iteration method designed for large-scale data fitting. At each iteration, RPIA updates only the control points indexed by a specific set, leaving the others unchanged. In this work, we introduce a two-dimensional RPIA (D2RPIA) for fitting B-spline curves and surfaces. Unlike RPIA, D2RPIA updates the control points with an adaptive step-size, which is determined by imposing a constraint on the new control points. This adaptive step-size allows D2RPIA to achieve the current optimal result, thereby enhancing the convergence rate compared to RPIA. We prove that D2RPIA converges linearly in the mean square to the least-squares solution. Several numerical studies are presented to validate our theoretical results.
2D High-Order Cage-Based Deformation by Polygonal Surface Patches
This paper presents a novel method for 2D high-order cage-based deformation using polygonal surface patches, providing a unified framework that supports various types of polygonal patches. The proposed deformation process comprises two main components: the contribution from the cage corner points and the influence of the middle control points along each boundary curve. First, a coarse deformation is reconstructed using generalized barycentric coordinates derived from the deformed cage corners. Then, displacement curves defined by the middle control points on each cage edge are employed to refine the deformation, precisely relocating the transition points to their final positions. Extensive experimental results demonstrate that our method produces high-quality results across diverse 2D deformation scenarios.
Real-Time Simulation of Hydraulic Erosion Based on Soil and Water Conservation Theory and Physical Calculation
Hydraulic erosion stands as one of the most critical influencing factors in geological transformation processes. However, current hydraulic erosion simulations still face several challenges. First, existing computer-based simulations prioritize visual realism while inadequately accounting for authentic physical phenomena and complex environmental factors during hydraulic erosion processes, resulting in insufficient accuracy of simulation outcomes. Secondly, hydraulic erosion involves fluid-solid coupling calculations. Physical-particles-based fluid simulation methods, such as the smoothed particle hydrodynamics (SPH) and position based fluids (PBF) methods, have relatively low computational efficiency in this interaction process. This paper addresses these two challenges. Regarding accuracy, we comprehensively integrate theoretical frameworks and research achievements from soil and water conservation studies, achieving for the first time a complete hydraulic erosion simulation process encompassing splash erosion and lateral erosion. The simulation system also incorporates multiple environmental factors to enhance accuracy. For efficiency improvement, we introduced an efficient fluid-solid interaction method based on volume maps. This innovation enhances computational efficiency in fluid particle-terrain interactions, making our system one of the first to achieve real-time hydraulic erosion simulation using the PBF particle method. The proposed method successfully simulates various hydraulic erosion phenomena including splash erosion, vertical incision erosion, lateral erosion, sedimentation and other related phenomena. It achieves real-time computational efficiency in medium-scale scenarios.
An Optimization Process for p-Curves in Surface-to-Surface Intersection to Improve Accuracy and Reduce Redundancy
The problem of surface-to-surface intersection (SSI) is among the most fundamental challenges encountered in computer-aided geometric design. In industrial applications, the execution of an SSI operation usually demands a high degree of precision while maintaining a concise representation of the intersection curve. We present a post-processing scheme for refining the intersection curve in the parameter domain (p-curves), achieving an improvement in accuracy without additional control points inserted. Moreover, by adjusting the parameterization, a one-to-one correspondence is created between a pair of p-curves. The proposed methodology is grounded on the minimization of an objective function that describes both accuracy and parameterization. The effectiveness of our method is illustrated through examples in comparison with the open-source NURBS library SISL and commercial software ACIS.
Reconstructing Dynamic Scenes with Topologically-Varying Neural Implicit Fields
This paper addresses the challenge of reconstructing dynamic scenes from monocular videos with dynamic neural implicit fields. Previous methods combine a single canonical template with a per-frame deformation field or optimize a hyperspace of templates to cover the variance of the scenes with a large amount of templates. However, single-template based methods cannot recover scenes with topology changes, while hyperspace template approaches may fail to be optimized under large-scale topology changes or motions without any constraints over the high-dimensional space. To address these issues, we propose a topologically-varying neural implicit fields by deforming the sum of multiple canonical templates and recovering large-scale motion and topology changes with a video segmentation strategy. Specifically, multiple templates are defined in canonical space, i.e. a primary template and sparse auxiliary templates. The primary template represents parts that do not change significantly during movement, while the auxiliary templates are combined linearly to represent topological changes. To reconstruct large-scale topologically-varying scenes, a dynamic segmentation strategy is adopted to divide the entire video into multiple segments, and each segment is modeled with its own templates. Compared to existing reconstruction methods for topologically changing objects, our method uses sparse auxiliary templates to form a continuous hyperspace, which is easier to optimize even under large topology changes and motions. Experimental results on various datasets demonstrate that our method outperforms previous works in both geometric reconstruction and novel-view synthesis.
topologically-varying neural implicit fields
Structure-Aware Indoor RGB-D SLAM via Manhattan-Constrained 2D Gaussian Splatting
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.
Linear Maximum Bound Principle Preserving Finite Difference Schemes for the Convective Allen-Cahn Equation
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.
Generalized Product-Type Variants of RBiCG for Solving Families of Linear Systems
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.
difference vectors of approximate solutions
A Mathematical Perspective on Corruption’s Effect on Productivity and Service Efficiency with Cost-Effective Control Strategies
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.
An Accelerated Spectral Perry-Type Conjugate Gradient Projection Method for Unconstrained Nonlinear Equations with Applications
In this paper, we propose an accelerated spectral Perry-type conjugate gradient projection method for solving systems of unconstrained nonlinear equations. The spectral parameter is generated using an accelerated gradient-descent method, which ensures that the proposed search direction always satisfies the sufficient descent condition. By incorporating a self-adaptive strategy into the optimal Perry conjugate parameter, the proposed search direction possesses the trust region property independent of any line search. Additionally, the proposed method incorporates an inertial extrapolation step to enhance computational performance. The global convergence of the proposed method is theoretically established without requiring monotonicity or pseudo-monotonicity of the underlying mapping. Numerical experiments on systems of unconstrained nonlinear equations and image de-blurring problems demonstrate the effectiveness of the proposed method.
Biharmonic Distance Driven Voronoi Diagrams Restricted on Curved Surfaces
Computing surface-based Voronoi diagrams is a fundamental operation in geometry processing, typically relying on either geodesic or straight-line distances as solvers. However, when the input is a 3D model containing thin-plate structures, geodesic distances incur significant computational overhead, whereas straight-line distances can result in ownerless regions. To address this issue, we propose integrating biharmonic embedding distances into the SurfaceVoronoi framework. Specifically, mesh vertices can be embedded into a high-dimensional spectral space, ensuring that the embedding distance closely approximates the straight-line distance between sufficiently close points. In contrast, when points reside on opposite sides of a thin plate, the embedding distance significantly exceeds the straight-line distance, effectively preventing dominance from penetrating through to the opposite side. Our proposed framework offers several advantages: 1) It operates efficiently, as the embedding distance can be rapidly evaluated as a straight-line distance in high-dimensional space. 2) It guarantees the “one site, one region” property, even for models consisting of thin-plate structures. 3) It enables high-quality triangulation through iterative repositioning of each site to the centroid of its dominant region. Extensive experiments conducted on benchmark meshes demonstrate these benefits.
A Neural Network Framework for High-Dimensional Dynamic Unbalanced Optimal Transport
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.
Smooth Bijective Projection of Polygonal Meshes via a Cubic B-Spline Shell
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: A New Paradigm for Scientific and Engineering Computation
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.
Tackling Challenge of Masked and Unmasked Face for Facial Recognition Through Dimensionality Reduction and Deep Learning
Facial recognition systems face considerable performance degradation in the presence of occlusions, particularly face masks, which are increasingly common in public setting. This research examines the impact of such occlusions by employing dimensionality reduction techniques: principal component analysis (PCA) and auto-encoders, combined with convolutional neural networks for classification. Through experiments on custom-built dataset comprising masked, unmasked, and mixed facial images, we observe that PCA consistently outperforms auto-encoders across all evaluation metrics, including accuracy, precision, recall and F1-score. However, PCA is more sensitive to occlusion variability, while auto-encoders exhibit more stable, though generally lower performance. Notably, performance declines significantly when models are evaluated on mixed datasets, emphasizing the complexity of real-world scenarios. Data augmentation yields only marginal improvement, underscoring the limitation of current approaches in handling diverse occlusions. The study also explores the potential of advanced mathematical tools such as higher-order tensor decomposition and fractional differentiation to enhance feature representation and model robustness. Overall, this research directions involving diverse training sets, sophisticated feature extraction and hybrid architectures to enhance model generalization in dynamic environments. Hence, contributing to the development of more reliable biometric systems.
Optimizing Interdisciplinarity in Data Analysis with the Adapted Alpha-Power Transformation of the Nadarajah-Haghighi Distribution
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.
Transport of Contaminant Release by Three Different Sources: A Medium with Complex Geometry
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.
The Poisson-Garima Distribution: Additional Key Features and Its Significance on Statistical Process Control in Agriculture
This study primarily advances the theoretical development of the Poisson-Garima (PSNG) distribution by establishing several novel properties not previously addressed in existing literature. These theoretical enrichments enhance the model’s statistical foundation and extend its applicability to overdispersed count data commonly observed in fields such as agriculture, biology, and medicine. As a secondary contribution, the improved PSNG model is applied to statistical process control through the development of PSNG-based control charts for monitoring count data. The proposed charts are evaluated via simulation studies and validated with an empirical agricultural dataset, where their performance is benchmarked against eight competing models. Additionally, comparisons between PSNG- and Poisson-based control charts demonstrate the superiority of the proposed approach in detecting process shifts under overdispersion. This integrated approach reinforces the PSNG distribution’s theoretical depth while demonstrating its practical relevance in quality monitoring contexts.
Thermodynamics of Freshwater Production via CuS-Infused Porous Membrane Solar Absorber in Seawater Desalination
In our advanced modern world, ensuring the availability and access to freshwater resources remains a significant global challenge. Seawater desalination is viewed as one of the most promising solutions to address the increasing human demand for freshwater. This study theoretically examines the thermodynamics of a novel desalination system that integrates a copper sulfide (CuS) nanomaterial-porous membrane solar absorber for freshwater production. The governing partial differential equations for energy and mass balance in the model were derived from conservation laws and solved numerically using the method of lines. The impact of various parameters on steam temperature and freshwater production rate was analyzed in two scenarios: (i) under constant solar radiation flux in a controlled laboratory setting, and (ii) as a time-dependent function under typical daily solar radiation conditions. The pertinent results were presented graphically and discussed. It was found that the Nusselt number at the surface of the porous membrane solar absorber increases with the infusion of CuS nanomaterial. The desalination system reached a steady state with steam temperature, and the rate of freshwater production improved as the volume fraction of CuS nanomaterial in the porous membrane solar absorber increased. Additionally, an increase in steam generation and condensation Biot numbers further boosted the freshwater production rate.
Superconvergence Points of Several Polynomial and Nonpolynomial Hermite Spectral Interpolations
In this paper, we analyze the superconvergence properties for spectral interpolations by Hermite polynomials and mapped Hermite functions. At the superconvergence points, the $(N−k)$-th term in the Hermite spectral interpolation remainder for the $(k+1)$-th derivatives vanish. To solve multi-point weakly singular nonlocal problems, we previously introduced mapped Hermite functions (MHFs), which are constructed by applying a mapping to the Hermite polynomials. We prove that the superconvergence points of the spectral interpolations based on MHFs for the $(k+1)$-th derivatives are the zero points of the $(N−k)$-th term. Additionally, due to the rapid growth of the logarithmic function at the endpoints 0 and 1, we further propose generalized mapped Hermite functions (GMHFs). We develop basic approximation theory for these new orthogonal functions and prove the projection error and interpolation error in the $L^2$-weighted space using the pseudo-derivative. We demonstrate that the superconvergence points of the spectral interpolations based on both MHFs and GMHFs for the $(k+1)$-th derivative are the zero points of the $(N−k)$-th term. Numerical experiments confirm our theoretical results.
An Efficient Iterative Convolution-Thresholding Method for Image Inpainting
Variational methods have been developed for image inpainting, which involve minimizing an objective functional consisting of the regularization term and the fidelity term. The fidelity term controls the consistency of the restored region with the original image, while the regularization term smooths the boundary of the region. In this paper, we develop an efficient iterative convolution-thresholding method to solve variational approach-based image inpainting problems. In the proposed method, the region is represented by its indicator function, and the regularization term is approximated by the heat kernel convolution with the indicator function. Based on this approximation, we derive an efficient iterative method to update the indicator function only within the damaged region by alternating the convolution and thresholding steps, relying on a relaxation and linearization procedure. Extensive numerical experiments demonstrate the simplicity and efficiency of the proposed method.
Iterative convolution-thresholding method
Double-Domain Driven Unet for Selective Segmentation of Medical Image
Selective segmentation has been a notable increase in interest in the use of interactive deep learning-based methods. However, developing an efficient and accurate segmentation method for medical applications remains a formidable challenge, primarily due to the inherent complexity and diversity of medical image structures. To address these challenges, we introduce a novel deep learning approach, termed the double-domain driven Unet method (DDUM), designed for the selective segmentation of medical images. Our approach utilizes a threshold geodesic distance in conjunction with the original images as input to construct a parallel Unet architecture that captures information from both the image domain and the geodesic distance domain. To further enhance the accuracy and efficacy of the segmentation process, we employ soft threshold dynamics as a replacement for the sigmoid activation function in the final layer. The efficacy of our proposed DDUM is substantiated through extensive experiments conducted on multiple medical image datasets. In particular, the DDUM method exhibits exceptional performance in terms of both segmentation accuracy and robustness.
Assessment and Evaluation of Surface Water Quality and Human Health Risk in the Inkomati River Catchment Basin, South Africa
Multivariate statistical methods, dimensionality reduction, clustering techniques, water quality indices (WQIs) of the Canadian Council of Ministers of the Environment (CCME), comprehensive pollution index (CPI), and human health risk assessment indices for carcinogenic risk of heavy metals, using the hazard index (HI), are utilized in this work to assess the surface water quality of the Inkomati catchment. Six physicochemical parameters – ${\rm EC},$ ${\rm pH},$ ${\rm SO_4},$ ${\rm Fe},$ ${\rm Mn},$ and ${\rm Cu}$ were measured monthly from January 2015 to June 2019 from two sites Crocodile and Sabie rivers. The outcomes were compared to standard regulatory guidelines values. Recommended parameter values from US-EPA and peer-reviewed literature were used for the HI. The findings indicated that the river water was turbid and suffered from EC, specifically distressed due to trace metals. The US-WQI range (103.15-431.38) showed that the water quality level of the catchment was in the poor category but excellent during the winter. Water quality improved from marginal to good, according to the CCME-WQI scores, whereas the CPI scores (2.359-8.459) showed that the catchment’s water quality was in a very poor condition. The US-WQI suggested that the overall quality of the basin has declined in both the upper and lower portions. The hazard quotient through ingestion exposure did not exceed the threshold limit of 1 for children. This implies there is no potential carcinogenic health risk from trace elements via ingestion of drinking water for children. However, cancer risk for children was computed in relation to ${\rm Cu},$ ${\rm Fe},$ ${\rm Mn},$ and levels. It did not exceed the carcinogenic threshold limit of $10^{-4}$ for both sites.
Bifurcation and Crossover Processes in the Dynamics of a Marburg Haemorrhagic Fever Model
Just like Ebola disease, the Marburg virus disease (MVD) remains a constant threat to people’s live, not only in Africa, but also in the other parts of the globe. Recorded past outbreaks occurred in Europe, America and of course Africa, especially in places where inhabitants come into contact with wild animal products or live alongside wild animals such as apes, monkeys and fruit bats on a daily basis. Therefore, studying the dynamics of the Marburg virus and making some epidemiological assessments remain relevant and important in preventing future outbreaks. In this paper, we analyze a Marburg epidemic model in which the transmission is nonlinear. The well-posedness result is established as well as conditions for boundedness and dissipativity results. Then, we intensively analyze the stability of the Marburg model’s equilibria. The bifurcation dynamics indicate the existence of both transcritical (exchange of stability between the endemic equilibrium (EE) point and the disease free equilibrium (DFE)) and backward bifurcation where the classical epidemiological condition for the MVD to die out $(\mathcal{R}_0<1)$ is not sufficient anymore, but remains necessary. Lastly, some numerical simulations show convergence of the trajectories to both the EE and the DFE. Some adequate preventive measures are provided.