Implicit Function Research Articles

Bifurcation analysis and global sensitivity index for malaria disease transmission dynamics: Information and treated bed nets control

Malaria is known globally as the foremost cause of death in children and adults. Several intervention strategies and controls have been implemented and proposed, among which is Long Lasting Insecticide Treated Nets (LLINs). Malaria cases have been reported to reduce by [Formula: see text] due to the use of LLINs. However, the laid-back behaviors of humans negatively impact its effective use through improper handling and exposure to direct sunlight. To this end, a mathematical model is formulated to investigate the influence of individual response to information on the transmission dynamics of malaria infection in both human and mosquito populations. The threshold for the effective reduction of the prevalence of malaria through a behavioral change in the use of LLINs in response to the created awareness is determined in this study. The point of departure of this study from other studies is that it incorporates information/awareness as a dynamic variable to investigate the impact of LLINs on malaria. The equilibrium points of the model are analyzed using stability theory and the associated basic reproduction number [Formula: see text]. The implicit function theorem is used to determine the direction of bifurcation. We use Latin hypercube sampling (LHS) to test the most sensitive parameters in the basic reproduction number. The correlation between the [Formula: see text] and parameters is displayed using Scatter plots. The mathematical analysis shows that the direction of bifurcation is supercritical, which suggests that we only need to bring [Formula: see text] below unity for disease eradication. The study also revealed that an increase in awareness of the use of LLINs has an impact on reducing malaria transmission.

Statistical Modeling of Implicit Functional Relations

This study considers the statistical estimation of relations presented by implicit functions. Such structures define mutual interconnections of variables rather than outcome variable dependence by predictor variables considered in regular regression analysis. For a simple case of two variables, pairwise regression modeling produces two different lines of each variable dependence using another variable, but building an implicit relation yields one invertible model composed of two simple regressions. Modeling an implicit linear relation for multiple variables can be expressed as a generalized eigenproblem of the covariance matrix of the variables in the metric of the covariance matrix of their errors. For unknown errors, this work describes their estimation by the residual errors of each variable in its regression by the other predictors. Then, the generalized eigenproblem can be reduced to the diagonalization of a special matrix built from the variables’ covariance matrix and its inversion. Numerical examples demonstrate the eigenvector solution’s good properties for building a unique equation of the relations between all variables. The proposed approach can be useful in practical regression modeling with all variables containing unobserved errors, which is a common situation for the applied problems.

Multi-Objective Parametric Shape Optimisation of Body-Centred Cubic Lattice Structures for Additive Manufacturing

There has been significant interest in additively manufactured lattice structures in recent years due to their enhanced mechanical and multi-physics properties, making them suitable candidates for various applications. This study presents a multi-parameter implicit equation model for designing body-centred cubic (BCC) lattice structures. The model is used in conjunction with a multi-objective genetic algorithm (MOGA) approach to maximise the stiffness of the BCC lattice structure while minimising von-Mises stress within the structure under a specific loading condition. The selected design from the MOGA at a specific lattice density is compared with the classical BCC lattice structure and the designs generated by a single-objective genetic algorithm, which focuses on maximising stiffness or minimising von-Mises stress alone. By conducting a finite element analysis on the optimised samples and performing mechanical testing on the corresponding 3D-printed specimens, it was observed that the optimised lattice structures exhibited a substantial improvement in mechanical performance compared to the classical BCC model. The suitability of multi-objective and single-objective optimisation approaches for designing lattice structures was further investigated by comparing the corresponding designs in terms of their stiffness and maximum von-Mises stress values. The results from the numerical analysis and experimental testing demonstrate the significance of the application of an appropriate optimisation strategy for designing lattice structures for additive manufacturing.

Slope stability analysis based on improved radial movement optimization considering seepage effect

Among various effecting factors, groundwater is commonly known as one of the major triggers for slope failures. Thus, it is great significant of considering the contribution from groundwater seepage in slope stability analysis. In this study, the effect from groundwater seepage are considered as the interaction force (infiltration force) between water and soil materials for static and moment equilibrium analysis. Based on Rigorous Janbu method, the implicit equations are determined for estimating the minimum factor of safety and locating the non-circular critical failure surface. A new metaheuristic algorithm, Improved Radial Movement Optimization (IRMO), was adopted to figure out such complex, nonlinear and constrained optimization problem due to its high precision and stability. The effectiveness of the proposed methodology is validated by four different cases including homogeneous and inhomogeneous slopes from the literature. Comparative studies in different optimization algorithms have been carried out to validate the stability and efficiency of proposed IRMO algorithm accordingly. The results indicate that proposed approaches could acquire a more acceptable and stable result with more efficient way in slope stability analysis considering seepage effect over several existing methods.

Adaptive design of the magnetron injection gun using constrained multiobjective optimization

The design of the magnetron injection gun (MIG) is an inverse problem with implicit objective functions and complex constraints. The computer-aided design using an optimization algorithm is a promising method to improve the performance of the MIG and reduce design complexity and time consumption. However, the dependence on the initial structure makes it difficult to realize the real sense of using algorithms to design. To address this issue, this paper proposes an adaptive design method for the MIG. The design problem is equivalent to a constrained multiobjective optimization problem. A pseudo-random structure generation algorithm is developed based on the geometric constraints and the first-order MIG design trade-off equations. The fully parameterized MIG structure is randomly generated by the decision variables composed of the scale coefficients ranging from (0,1) and the other structural parameters. This transformation can increase the effectiveness of the randomly generated MIG structures and make it easier to set the value range of decision variables. The proposed adaptive design method is further verified by successfully designing the MIG for an 800 GHz gyrotron via the co-simulation of MATLAB and CST.

Reflections of STEAM Education on Children According to Early Childhood and Primary School Teachers

In this study, we examined STEAM education's reflections and implicit functions on children according to the views of early childhood and primary school teachers who applied STEAM education. We conducted the study within the scope of phenomenology design, one of the qualitative research designs. The participants were ten teachers who had previously received STEAM education and applied STEAM education in their classroom and were determined by the snowball sampling method. We collected the data with semi-structured interviews and analyzed them with content analysis. We explained our findings with three themes: 1) opportunities for collaborative learning with peers, 2) values, and 3) opportunities for skill development. According to the results, STEAM education encouraged children to make friends, work together, have fun, develop positive commitment, and take responsibility. STEAM education enabled children to cooperate, share, take responsibility, and develop friendships among children. In addition, STEAM education contributed to many skills of children, such as empathy, problem-solving, scientific process, analytical thinking, aggressiveness, self-control, and critical thinking. In this respect, the study provides evidence for the illusions of STEAM education for children.

DAWTran: dynamic adaptive windowing transformer network for pneumothorax segmentation with implicit feature alignment

Objective. This study aims to address the significant challenges posed by pneumothorax segmentation in computed tomography images due to the resemblance between pneumothorax regions and gas-containing structures such as the trachea and bronchus. Approach. We introduce a novel dynamic adaptive windowing transformer (DAWTran) network incorporating implicit feature alignment for precise pneumothorax segmentation. The DAWTran network consists of an encoder module, which employs a DAWTran, and a decoder module. We have proposed a unique dynamic adaptive windowing strategy that enables multi-head self-attention to effectively capture multi-scale information. The decoder module incorporates an implicit feature alignment function to minimize information deviation. Moreover, we utilize a hybrid loss function to address the imbalance between positive and negative samples. Main results. Our experimental results demonstrate that the DAWTran network significantly improves the segmentation performance. Specifically, it achieves a higher dice similarity coefficient (DSC) of 91.35% (a larger DSC value implies better performance), showing an increase of 2.21% compared to the TransUNet method. Meanwhile, it significantly reduces the Hausdorff distance (HD) to 8.06 mm (a smaller HD value implies better performance), reflecting a reduction of 29.92% in comparison to the TransUNet method. Incorporating the dynamic adaptive windowing (DAW) mechanism has proven to enhance DAWTran’s performance, leading to a 4.53% increase in DSC and a 15.85% reduction in HD as compared to SwinUnet. The application of the implicit feature alignment (IFA) further improves the segmentation accuracy, increasing the DSC by an additional 0.11% and reducing the HD by another 10.01% compared to the model only employing DAW. Significance. These results highlight the potential of the DAWTran network for accurate pneumothorax segmentation in clinical applications, suggesting that it could be an invaluable tool in improving the precision and effectiveness of diagnosis and treatment in related healthcare scenarios. The improved segmentation performance with the inclusion of DAW and IFA validates the effectiveness of our proposed model and its components.

ImplicitPCA: Implicitly-proxied parametric encoding for collision-aware garment reconstruction

The emerging remote collaboration in a virtual environment calls for quickly generating high-fidelity 3D humans with cloth from a single image. To estimate clothing geometry and topology, parametric models are widely used but often lack details. Alternative approaches based on implicit functions can generate accurate details but are limited to closed surfaces and may not produce physically correct reconstructions, such as collision-free human avatars. To solve these problems, we present ImplicitPCA, a framework for high-fidelity single-view garment reconstruction that bridges the good ends of explicit and implicit representations. The key is a parametric SDF network that closely couples parametric encoding with implicit functions and thus enjoys the fine details brought by implicit reconstruction while maintaining correct topology with open surfaces. We further introduce a collision-aware regression network to ensure the physical correctness of cloth and human. During inference, an iterative routine is applied to an input image with 2D garment landmarks to obtain optimal parameters by aligning the cloth mesh projection with the 2D landmarks and fitting the parametric implicit fields with the reconstructed cloth SDF. The experiments on the public dataset and in-the-wild images demonstrate that our result outperforms the prior works, reconstructing detailed, topology-correct 3D garments while avoiding garment-body collisions.

Alternately denoising and reconstructing unoriented point sets

We propose a new strategy to bridge point cloud denoising and surface reconstruction by alternately updating the denoised point clouds and the reconstructed surfaces. In Poisson surface reconstruction, the implicit function is generated by a set of smooth basis functions centered at the octnodes. When the octree depth is properly selected, the reconstructed surface is a good smooth approximation of the noisy point set. Our method projects the noisy points onto the surface and alternately reconstructs and projects the point set. We use the iterative Poisson surface reconstruction (iPSR) to support unoriented surface reconstruction. Our method iteratively performs iPSR and acts as an outer loop of iPSR. Considering that the octree depth significantly affects the reconstruction results, we propose an adaptive depth selection strategy to ensure an appropriate depth choice. To manage the oversmoothing phenomenon near the sharp features, we propose a λ-projection method, which means to project the noisy points onto the surface with an individual control coefficient λi for each point. The coefficients are determined through a Voronoi-based feature detection method. Experimental results show that our method achieves high performance in point cloud denoising and unoriented surface reconstruction within different noise scales, and exhibits well-rounded performance in various types of inputs. The source code is available at https://github.com/Submanifold/AlterUpdate.

Time-variant reliability of interlayer damage of CRTS-II slab track by combining the second-order fourth-moment and outcrossing method

This study proposes the combining second-order fourth-moment and outcrossing method for evaluating the time-variant reliability of slab tracks’ interlayer damage. The merit of the method is to improve significantly the computing efficiency and accuracy for the implicit and strong nonlinear limit state function. Furthermore, the effects of narrow joints damage and temperature load on the time-variant reliability of slab tracks’ interlayer damage are investigated. Narrow joints damage is an inducement for the decrease of time-variant reliability index of slab tracks’ interlayer damage, and the index decreases more violently with the increase of temperature rise than that of positive temperature gradient.

Active learning-based structural reliability evaluation Kriging model and sequential importance sampling

The efficient analysis of structural system reliability with multiple failure modes and small failure probabilities presents significant challenges for active Kriging methods. This paper proposes a novel method, PAK-SEIS, which combines the Parallel Active learning Kriging model and the Sequential Importance Sampling method to overcome these challenges. The proposed method includes a new sequential importance sampling method that integrates the sequential Monte Carlo simulation (MCS) and kernel density estimation to construct the optimal importance density. Additionally, the proposed parallel learning strategy allows for the selection of multiple new training samples, reducing performance function calls and refining iterations of Kriging models. The PAK-SEIS method gradually approximates the optimal importance density by updating multiple new training samples and failure modes in parallel at each iteration based on a small number of candidate samples. Candidate samples generated in the final sequence can cover all limit state surfaces, and all Kriging models are accurately constructed. The PAK-SEIS method can effectively address system reliability problems with small failure probability, multiple failure regions, and implicit functions. Two examples demonstrate the efficiency and accuracy of the proposed PAK-SEIS method.

Joint Real-Time Identification for Mutual Inductance and Load Charging Parameters of IPT System

Accurate and fast identification for mutual inductance and load charging parameters of inductive wireless power transfer (IPT) system is essential for impedance matching, and the output control of communication-free IPT system. A joint real-time identification method for mutual inductance and load charging parameters of IPT system is proposed in this paper. Only via measuring the RMS value of fundamental voltage and current on primary side, the double equivalent impedance modulus equations about mutual inductance and equivalent load resistance are established. To obtain real-time identification results of mutual inductance and equivalent load resistance from the high-order implicit function equations, an improved adaptive filtering algorithm based on Least Mean Squares (LMS) is proposed. Then, the identification values of load charging parameters are obtained according to the identified mutual inductance and equivalent load resistance. Finally, a 3.6kW platform is built to verify the validity of the proposed method. And the experiment results show that, compared with other existing achievements, the proposed method can identify <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U_Bat</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I_Bat</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_L</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> simultaneously in real-time without changing the system operation, and it has faster rate and higher accuracy of identification.

Bumble bee pollination and the wildflower/crop trade-off: When do wildflower enhancements improve crop yield?

Populations of wild insect pollinators such as bumble bees are threatened worldwide, which compromises pollinator-dependent crop yields. Intentionally planting wildflower patches in agricultural landscapes can support these populations and increase the pollination of nearby crops via the “spillover effect” (i.e., the exporter hypothesis), but may also distract bees from the crops and reduce their pollination via the “Circe principle” (i.e., the aggregation hypothesis). Considering the potentially high costs of these management strategies and the necessity to support wild insect pollinators in the Anthropocene, there is a pressing need to provide simulation tools that can inform best practices for wildflower plantings in agro-ecosystems. We developed a spatially implicit ordinary differential equations (ODEs) model specifically designed to determine the optimal wildflower-to-crop ratio as a function of wildflower patch (i) attractiveness, (ii) nutritional benefits, and (iii) blooming period relative to the crop. The model represents the population dynamics of a bumble bee colony and floral resources (crop and wildflower) in the landscape and nest during one harvesting season. We conduct a full factorial simulation experiment to identify the optimal characteristics of the wildflower patch (i.e., blooming period, attractiveness, relative abundance) that maximise crop yield via the enhancement of the number of bees pollinating crop flowers in a fictional blueberry farm. Our results suggest that providing highly attractive and nutritive wildflower resources before and not during the crop blooming season is the most beneficial strategy. When both flower types are in competition, pollination services can decrease, either when wildflowers are too attractive, or if they provide less benefits to the bees than the crop due to a trade-off between resources quality versus quantity.

Temporally consistent reconstruction of 3D clothed human surface with warp field

Implicit functions are widely used in 3D human surface reconstruction due to their advantage to represent details. However, human reconstruction based on implicit functions struggles to maintain the integrity (unbroken body structure) and accuracy (no non-human parts) of human models. To address these issues, we propose a method, called TCR, for temporally consistent reconstruction of 3D clothed human surface with warp field. The fact that the general shape of a person does not change largely over time inspires us to exploit the temporally consistent shape information from previous frames to refine the human model of current frame. Therefore, we construct a canonical space and then store the shape information by updating the canonical model. To align the observed space with the canonical space, a warp field is firstly estimated for the forward and inverse warping of the human model. A probabilistic fusion strategy is then used to update the canonical model. In addition, the reconstructed result is further refined through the orthogonality constraints between the surface and its normal, which fully exploits the detailed information of estimated normal maps. Experiments on the Adobe and MonoPerfCap datasets show that TCR achieves the state-of-the-art performance. Furthermore, TCR is more robust and can maintain the integrity and accuracy of the reconstructed human body even with extreme poses and partial occlusions.

Numerical study on the anisotropy in thermo-fluid behavior of triply periodic minimal surfaces (TPMS)

Porous structures are frequently utilized as thermal conductivity enhancers in the realm of heat transfer enhancement. Triply Periodic Minimal Surface (TPMS) has gained significant attention in recent years due to its favorable performance in many fields including mechanics and thermodynamic. The exceptionally large specific surface area grants it promising performance in heat transfer enhancement. However, the angular effect on thermal-fluid characteristics are not understood and requires further investigation. In this work, Gyroid and Diamond with various rotating angles used as sandwich cores were designed utilizing the implicit function method. Then, the discussions on thermal and hydraulic behaviors in the TPMS-based sandwich panels under an isothermal condition were systematically conducted by means of computational fluid dynamics. After that, the fluid flow mechanisms and heat transfer properties were visually investigated according to the comparative analysis of velocity fields, pressure drops, vortices inducing, and Nusselt number distribution. The results showed that the flow field characteristics and the heat transfer performance exhibited an apparent 45° symmetry in both Gyroid and Diamond. Moreover, the pressure gradient exhibited evident dependence on the rotating angle in both Gyroid and Diamond groups. The 45° rotated Gyroid structure case had the most extensive pressure gradient of 11.4 kPa/m; to the contrary, the 45° rotated Diamond structure had the smallest one of 9.9 kPa/m in their respective group. Nonetheless, the angular difference in heat transfer rate (HTR) is not significant, and the maximum total HTR in Gyroid and Diamond groups was 8.25 W and 9.43 W, respectively. Overall, this work contributes to a better understanding of the angular behavior of TPMS-based sandwich panels and provides valuable information for their potential applications in various industries.

Effects of shear strength variability on the peak and residual horizontal resistance of on-bottom subsea pipelines in clay

Subsea production pipelines in deep water oil and gas fields are susceptible to a phenomenon called lateral buckling which is a major pipeline design concern. Accurate estimation of lateral buckle formation and the additional stresses generated are of particular importance for High-Temperature High-Pressure (HTHP) pipelines resting on soft clay and is the subject of pipe-soil interaction studies (PSI). Variability in pipe embedment and soil resistances constitute the largest uncertainty in PSI analyses. Best practice methods for PSI studies constitute multi-step strategies that involve finding solutions to nonlinear and implicit equations. In the present study, the impact of soil strength variability on embedment and subsequently peak (Hpeak/V) and residual (Hres/V) lateral friction factors are evaluated. An R code, PSI-Lateral, is developed and verified against published case studies. It is used to calculate the pipeline embedment and horizontal resistances mobilized in a parametric study on three pipe diameters (0.6, 0.8 m and 1.0 m) with three different wall thicknesses. For each pipe diameter-weight combination, embedment and lateral friction factors (peak and residual) are calculated for a series of mean shear strengths ranging from 2 kPa to 8 kPa and COV ranging from 5% to 37.5%. The high estimate and low estimate shear strengths, suHE and suLE, correspond to values that are +/- two standard deviations from the mean. Hence, the range of strengths encompassed between these two extremes represents approximately 95% of the shear strength distribution. The results of the parametric runs conducted are presented in the form of graphical charts where high and low embedment and lateral friction factors can be read-off for any selected pair of mean shear strength and COV. Similar trends are observed in the charts for all pipelines evaluated. It is found that the range of normalized embedment, z/D, increases with increasing COV and decreases with increasing mean shear strength for all pipelines tested. A similar trend is observed for the residual horizontal resistance. The expected range of peak horizontal resistance Hpeak/V shows the same trend but only for soils with mean strengths less than 4 kPa. For soils with higher mean strengths, the range of Hpeak/V is found to be mostly insensitive to variations in COV and further increases in the mean strength.

Stochastic quantization of laser propagation models

This paper identifies certain interesting mathematical problems of stochastic quantization type in the modeling of Laser propagation through turbulent media. In some of the typical physical contexts, the problem reduces to stochastic Schrödinger equation with space–time white noise of Gaussian or Poisson or Lévy type. We identify their mathematical resolution via stochastic quantization. Nonlinear phenomena such as Kerr effect can be modeled by a stochastic nonlinear Schrödinger equation in the focusing case with space–time white noise. A treatment of stochastic transport equation, the Korteweg–De Vries equation as well as a number of other nonlinear wave equations with space–time white noise is also given. The main technique is the S-transform (we will actually use the closely related Hermite transform) which converts the stochastic partial differential equation (PDE) with space–time white noise to a deterministic PDE defined on the Hida–Kondratiev white noise distribution space. We then utilize the inverse S-transform/Hermite transform known as the characterization theorem combined with the infinite-dimensional implicit function theorem for analytic maps to establish local existence and uniqueness theorems for path-wise solutions of this class of problems. The particular focus of this paper on singular white noise distributions is motivated by practical situations where the refractive index fluctuations in the propagation medium in space and time are intense due to turbulence, ionospheric plasma turbulence, marine-layer fluctuations, etc. Since a large class of PDEs, that arise in nonlinear wave propagation, have polynomial-type nonlinearities, white noise distribution theory is an effective tool in studying these problems subject to different types of white noises.

Existence, uniqueness, and stability analysis of fractional Langevin equations with anti‐periodic boundary conditions

This paper is devoted to studying the system of switched coupled implicit fractional Langevin equations of nonlinear form with anti‐periodic boundary conditions. In the first step, problem's equivalence and the corresponding integral equation by applying fractional calculus tools are established, and a fixed point problem is defined. For mixed monotone mappings, we have used coupled fixed point theorems to achieve the existence and uniqueness of solutions of these equations. In the next step, by using Banach's fixed point theorem, Ulam–Hyers, Ulam–Hyers–Rassias, generalized Ulam–Hyers and generalized Ulam–Hyers–Rassias stabilities of our considered model are discussed. An example is given at the end for the verification of our results.

MixNet: Mix different networks for learning 3D implicit representations

We introduce a neural network, MixNet, for learning implicit representations of 3D subtle models with large smooth areas and exact shape details in the form of interpolation of two different implicit functions. Our network takes a point cloud as input and uses conventional MLP networks and SIREN networks to predict different implicit fields. We use a learnable interpolation function to combine the implicit values of these two networks and achieve the respective advantages of them. The network is self-supervised with only reconstruction loss, leading to faithful 3D reconstructions with smooth planes, correct details, and plausible spatial partition without any ground-truth segmentation. We evaluate our method on ABC, the largest and most diverse CAD dataset, and some typical shapes to test in terms of geometric correctness and surface smoothness to demonstrate superiority over current alternatives suitable for shape reconstruction.

Scale-Aware Frequency Attention network for super-resolution

Scale-arbitrary super-resolution (SASR) has recently gained widespread attention in the community, which aims to super-resolve an image to arbitrary desired resolutions. Existing SASR methods always use a fixed convolution neural network (CNN) as the backbone to share the same image features for different resolutions, leading to limited reconstruction performance due to the lack of distinctive feature extraction for individual resolutions. Meanwhile, these CNN-based methods always tend to overfit low-frequency components while losing high-frequency ones. This frequency gap leads to blurred structures in the reconstructed image. To address these issues, we propose a Scale Aware Frequency Attention network (SAFANet), which consists of Scale-Aware Frequency Attention (SAFA) modules and a Scale-Guided Continuous Reconstruction (SGCR) module. Additionally, frequency-domain attention learning is introduced to optimize the scale-adapted features to explicitly focus on high-frequency components, thereby overcoming the frequency restoration gap. Finally, the SGCR module combines the input scale as guidance with the optimized features to reconstruct images with arbitrary resolutions by using an implicit reconstruction function, thus adaptively achieving continuous image restoration. Our proposed SAFANet can be easily incorporated into existing CNN-based SR networks to achieve interactive SR at arbitrary scales. Extensive experiments demonstrate that SAFANet achieves superior performance, which is competitive with or even better than the state-of-the-art methods across a vast scale range (×1∼×30) via a single model.