Level Set Research Articles

Confidence sets for a level set in linear regression.

Regression modeling is the workhorse of statistics and there is a vast literature on estimation of the regression function. It has been realized in recent years that in regression analysis the ultimate aim may be the estimation of a level set of the regression function, ie, the set of covariate values for which the regression function exceeds a predefined level, instead of the estimation of the regression function itself. The published work on estimation of the level set has thus far focused mainly on nonparametric regression, especially on point estimation. In this article, the construction of confidence sets for the level set of linear regression is considered. In particular, level upper, lower and two-sided confidence sets are constructed for the normal-error linear regression. It is shown that these confidence sets can be easily constructed from the corresponding level simultaneous confidence bands. It is also pointed out that the construction method is readily applicable to other parametric regression models where the mean response depends on a linear predictor through a monotonic link function, which include generalized linear models, linear mixed models and generalized linear mixed models. Therefore, the method proposed in this article is widely applicable. Simulation studies with both linear and generalized linear models are conducted to assess the method and real examples are used to illustrate the method.

Relationship between sensory processing patterns and gross motor function of children and adolescents with Down syndrome and typical development: a cross-sectional study.

Children and adolescents with Down syndrome (DS) may experience impairments in sensory and motor skills that can be interrelated. The purposes of this study were (i) to compare the sensory processing patterns and gross motor function between children and adolescents with DS and with typical development (TD) and (ii) to explore associations between these areas in both DS and TD groups. This cross-sectional study involved a sample size of 25 participants with DS (mean age 10.24±2.04years) and 25 participants with TD (mean age 10.04±2.82years). The sensory processing patterns were assessed using the Sensory Profile Second Version questionnaire, and the gross motor function was measured with the Gross Motor Function Measure (GMFM-88) dimensions (D) standing, and (E) walking, running, and jumping. Differences between groups were tested using the Mann-Whitney test, and the relationship between the variables was examined using Spearman's correlation tests, with a significance level set at 5%. Children with DS showed greater difficulties with sensory processing than TD children in Seeker (P<0.001), Avoider (P<0.001), Sensitivity (P<0.001), Registration (P<0.001), Auditory (P<0.001), Touch (P=0.001), Movements (P=0.001), Oral (P=0.028), Conduct (P=0.005), Socioemotional (P<0.001), and Attentional (P<0.001) domains. Additionally, children with DS presented lower gross motor function than TD in GMFM-88, standing (P<0.001) and walking, running, and jumping (P<0.001). Correlations were found between greater difficulties with sensory processing in Touch and lower gross motor function in walking, running, and jumping for the DS group. Our results suggest there are more difficulties in sensory processing patterns and gross motor function in children with DS than in TD. Also, there is a single association between more difficulties in sensory processing and less well-developed motor function in the DS group. Therefore, a comprehensive assessment of all these aspects should be performed in children and adolescents with DS, along with the provision of relevant interventions addressing specific needs.

Effect of Ball Inclusion in Drop Vertical Jump Test on Performance and Movement Variability in Basketball Players

The aim of this study was to assess and compare performance and movement variability (MV) in both bilateral and unilateral vertical drop jumps (DVJs) under conditions involving the incorporation or exclusion of ball catching. Twelve amateur basketball players were recruited for participation in the study (seven females and five males). Participants performed three jumps in each of the six conditions analyzed in randomized order: bilateral DVJ without (BNB) and with ball (BB); unilateral DVJ right leg without (RNB) and with ball (RB); and unilateral DVJ left leg without (LNB) and with ball (LB). MV and DVJ performance parameters were analyzed with an accelerometer and a force platform. MV was quantified using the sample entropy (sample entropy; SampEn) derived from the acceleration of the lower back. Differences between the different DVJ conditions were determined with the Wilcoxon test, with a significance level set at p &lt; 0.05. The comparisons were also assessed via standardized mean differences (Cohen’s d). No significant differences were observed in jump height, contact time and reactive strength index between conditions. However, the RB condition reported higher MV compared to RNB (effect size = 0.79; p = 0.016). Similarly, LNB showed greater MV compared to RNB (effect size = −0.62; p = 0.042). The inclusion of the ball in the DVJ increased the MV in the bilateral condition and in the right leg, but not in the unilateral condition with the left leg. The asymmetry between legs (right vs. left) in MV values in NOBALL conditions was higher (≈15%) compared to the BALL condition (≈5%).

On the Impacts of the Global Sea Level Dynamics

The temporal evolution of the global mean sea level (GMSL) is investigated in the present analysis using the monthly mean values obtained from two sources: a reconstructed dataset and a satellite altimeter dataset. To this end, we use two well-known techniques, detrended fluctuation analysis (DFA) and multifractal DFA (MF-DFA), to study the scaling properties of the time series considered. The main result is that power-law long-range correlations and multifractality apply to both data sets of the global mean sea level. In addition, the analysis revealed nearly identical scaling features for both the 134-year and the last 28-year GMSL-time series, possibly suggesting that the long-range correlations stem more from natural causes. This demonstrates that the relationship between climate change and sea-level anomalies needs more extensive research in the future due to the importance of their indirect processes for ecology and conservation.

A variational level set model based on local-global function approximation for image segmentation

The variational level set model is widely used in image segmentation tasks due to its sound theoretical basis and reliable performance. However, it often faces limitations when dealing with images that contain intensity inhomogeneity and noise. To address this challenge, a novel variational level set model based on local-global function approximation (LSM-LGA) is proposed in this paper. In this approach, an approximation function space is first introduced for the input image. This space defines the function as a linear combination of a local approximation image and a global one, weighted by two coefficients and two complementary characteristic functions defined by a level set function. To achieve the optimal representation of the input image within this approximation function space, a hybrid-metric strategy that combines Euclidean distance and Jeffreys divergence is introduced. An alternating direction method of multiplier (ADMM) based on Euclidean distance is developed to solve for the optimal weight coefficients of the local and global approximation images. Additionally, gradient descent based on Jeffreys divergence is utilized to solve for the optimal level set function. Furthermore, the existence and uniqueness of the optimal approximation function are proven using the theory of projection onto convex sets. Extensive numerical experiments on natural and synthetic images with intensity inhomogeneity, textures, and noise validate that the LSM-LGA exhibits superior performance compared with several state-of-the-art models in terms of segmentation quality and computational efficiency.

Low-Carbon Optimal Scheduling of Integrated Energy System Considering Multiple Uncertainties and Electricity–Heat Integrated Demand Response

To realize the low-carbon operation of integrated energy systems (IESs), this paper proposes a low-carbon optimal scheduling method. First of all, considering the integrated demand response of price-based electricity and heating, an economic scheduling model of the IES integrated demand response based on chance-constrained programming is proposed to minimize the integrated operating cost in an uncertain environment. Through the comprehensive demand response model, the impact of the demand response ratio on the operating economy of the IES is explored. Afterward, the carbon emission index is introduced, and gas turbines and energy storage devices are used as the actuators of multi-energy coupling to further explore the potential interactions between the coupling capacities of various heterogeneous energy sources and carbon emissions. Finally, the original uncertainty model is transformed into a mixed-integer linear-programming model and solved using sequence operation theory and the linearization method. The results show that the operating economy of the IES is improved by coordinating the uncertainty of the integrated demand response and renewable energy. In addition, the tradeoff between the working economy and reliability of the EIS can be balanced via the setting of an appropriate confidence level for the opportunity constraints.

Ensemble Kalman inversion of induced polarization data

SUMMARY This paper explores the applicability of ensemble Kalman inversion (EKI) with level-set parametrization for solving geophysical inverse problems. In particular, we focus on its extension to induced polarization (IP) data with uncertainty quantification. IP data may provide rich information on characteristics of geological materials due to its sensitivity to characteristics of the pore–grain interface. In many IP studies, different geological units are juxtaposed and the goal is to delineate these units and obtain estimates of unit properties with uncertainty bounds. Conventional inversion of IP data does not resolve well sharp interfaces and tends to reduce and smooth resistivity variations, while not readily providing uncertainty estimates. Recently, it has been shown for DC resistivity that EKI is an efficient solver for inverse problems which provides uncertainty quantification, and its combination with level set parametrization can delineate arbitrary interfaces well. In this contribution, we demonstrate the extension of EKI to IP data using a sequential approach, where the mean field obtained from DC resistivity inversion is used as input for a separate phase angle inversion. We illustrate our workflow using a series of synthetic and field examples. Variations with uncertainty bounds in both DC resistivity and phase angles are recovered by EKI, which provides useful information for hydrogeological site characterization. Although phase angles are less well-resolved than DC resistivity, partly due to their smaller range and higher percentage data errors, it complements DC resistivity for site characterization. Overall, EKI with level set parametrization provides a practical approach forward for efficient hydrogeophysical imaging under uncertainty.

Compact SOI Dual-Mode (De)multiplexer Based on the Level Set Method

Mode (de)multiplexer is an essential device in integrated multimode photonic systems. Here, we present a dual-mode (de)multiplexer that separates two input modes, TE0 and TE1, into two output ports while converting TE1 to TE0 mode. Based on the adjoint and level set method, the device features a small footprint of 9.4 μm × 2.9 μm, and a minimum feature size over 200 nm is achieved, affirming stable and reliable fabrication. Through simulations, we observed insertion losses of less than 0.28 dB for TE0 mode and 0.35 dB for TE1 mode within the wavelength range of 1500–1600 nm, accompanied by crosstalk levels lower than −30 dB. In our experimental tests, we achieved insertion losses of less than 0.89 dB for TE0 mode and 0.44 dB for TE1 modes within the 1530 nm to 1570 nm range, with crosstalk maintained below −25 dB. Furthermore, we conducted an experimental verification of the differences between the standard device and the boundary dilation/erosion device, observing an insertion loss degradation by 0.61 dB within a deviation range of ±40 nm, which demonstrates the device’s robustness to the fabrication. The proposed devices exhibit exceptional performance and feature a compact structure, thus holding significant potential for the development of future multimode integrated photonic circuits.

On the role of advection in a spatial epidemic model with general boundary conditions

This paper is concerned with a reaction-diffusion-advection model for vector-borne disease with general boundary conditions and general incidences. Due to the boundary conditions, we first apply the eigenvalue theory of elliptic system to prove the existence and uniqueness of steady state for the model. The well-posedness of the model is established using an induction argument. By overcoming the difficulty of the associated elliptic eigenvalue problem, we originally derive the variational expression of the basic reproduction ratio R0. The asymptotic profiles and monotonicity of R0 with respect to the mobility and advection rates are investigated following the variational characterization of R0. Furthermore, the spatial dynamics of the model with Robin type boundary condition are categorized via classifying the level set of R0. This work provides new clues for further research on the spread of epidemics in open advective environments.

Numerical investigation into effects of rheological properties on grout flow in rock fracture using Herschel-Bulkley model

Grouting is an essential technique for reducing the hydraulic conductivity and enhancing the strength of rock mass used in the Dongzhuang hydro-junction project. The rheological properties of grout are not to be disregarded during grouting. In this study, a numerical grouting model is established by combining a modified Herschel–Bulkley (HB) rheology model with the level set method. The effects of rheological parameters (power-law index n, consistency coefficient k, and yield stress τ0) on distribution pattern and flow characteristics of the grout are investigated. The HB model is more effective and precise than the Bingham model for predicting rheological characteristics. Numerical results indicated that distribution pattern and grout volume are primarily determined by n. A low shear rate inhibits the horizontal distribution and reduces the filling capacity of the grout, thus resulting in minimal deposition in the fracture. Grouts with a higher n and k require higher pressure to distribute around the fracture. The reduction in water volume in the fracture is calculated to provide comprehensive understanding into the sealing efficiency of the grout by varying the rheological parameters. This study provides valuable guidance regarding the different rheological parameter of grout in fractures, in addition to a novel concept for the optimal design of grouting distribution.

Predicting intraoperative hemorrhage during curettage treatment of cesarean scar pregnancy using free-breathing GRASP DCE-MRI

ObjectiveTo explore the feasibility of the golden-angle radial sparse parallel (GRASP) dynamic magnetic resonance imaging (MRI) technique in predicting the intraoperative bleeding risk of scar pregnancy.MethodsA total of 49 patients with cesarean scar pregnancy (CSP) who underwent curettage and GRASP-MRI imaging were retrospectively selected between January 2021 and July 2022. The pharmacokinetic parameters, including Wash-in, Wash-out, time to peck (TTP), initial area under the curve (iAUC), the transfer rate constant (Ktrans), constant flow rate (Kep), and volume of extracellular space (Ve), were calculated. The amount of intraoperative bleeding was recorded by a gynecologist who performed surgery, after which patients were divided into non-hemorrhage (blood loss ≤ 200 mL) and hemorrhage (blood loss > 200 mL) groups. The measured pharmacokinetic parameters were statistically compared using the t-test or Mann–Whitney U test with a significant level set to be p < 0.05. The receiver operating characteristic (ROC) curve was constructed, and the area under the curve (AUC) was calculated to evaluate each parameter’s capability in intraoperative hemorrhage subgroup classification.ResultsTwenty patients had intraoperative hemorrhage (blood loss > 200 mL) during curettage. The hemorrhage group had larger Wash-in, iAUC, Ktrans, Ve, and shorter TTP than the non-hemorrhage group (all P > 0.05). Wash-in had the highest AUC value (0.90), while Ktrans had the lowest value (0.67). Wash-out and Kep were not significantly different between the two groups.ConclusionGRASP DCE-MRI has the potential to forecast intraoperative hemorrhage during curettage treatment of CSP, with Wash-in exhibiting the highest predictive performance. This data holds promise for advancing personalized treatment. However, further study is required to compare its effectiveness with other risk factors identified through anatomical MRI and ultrasound.

Factors influencing sex ratio at birth in Krosno, Poland

The secondary sex ratio (SSR) is a widely used descriptor that reflects the living conditions and health status during pregnancy. The aim of study was to assess the impact of maternal factors, season of birth, and air pollution with the heating season on the sex ratio at birth in the Subcarpathian population from the Krosno district, Poland. A retrospective study involving 11,587 births was occurred at the John Paul II Podkarpackie Province Hospital in Krosno between 2016 and 2020. Sex of the newborn, the season of their birth, as well as the maternal age, birth order, the interval between births, and the season of birth were analysed. Furthermore, the relationship between the SSR and the level of air pollution during the heating season was investigated. To determine the significance of differences in sex ratios, chi-square analysis and multifactorial regression were used, with a significance level set at p < 0.05. At the chi-square level, all the studied factors indicated a statistically significant relationship with the SSR. However, the regression model used shows that maternal age and birth order were the most important factors in shaping the SSR in the study group.

WDLS: Deep Level Set Learning for Weakly Supervised Aeroengine Defect Segmentation

With the rapid development of the aviation industry, videoscope inspection of aeroengines has become crucial for ensuring aircraft flight safety. Recently, deep learning, particularly convolutional neural networks (CNNs), have shown remarkable efficacy in videoscope inspection tasks. However, these methods usually require large-scale training labels with accurate annotation. In videoscope images, defects are often present at the micrometer level and require manual labeling by professional inspection personnel, posing further challenges to model training. To address these issues, Weakly-Supervised Deep Level Set (WDLS), a fully automatic framework for aeroengine defect segmentation, was proposed in this work. WDLS employs a multi-branch structure and an iterative learning strategy to combine a high-performance CNN architecture with level set evolution. First, the Similarity-Guided Region (SGR) detector was designed to generate class-specific segmentation proposals and initialize the level set function. Second, the Adaptive Local Parameter Prediction (ALPP) algorithm was proposed to integrate local priors and constraints into the energy function and optimize the iterative process. Finally, a self-supervised objective function named Convexified Level Set (CLS) was introduced to represent an improved level set formulation and obtain the final segmentation. The proposed framework is continuously differentiable and unified. Thus, it can be seamlessly embedded in any CNN without postprocessing. Furthermore, the method was evaluated on a new aeroengine dataset Turbo19 and a benchmark dataset. Experimental results demonstrated that the proposed framework meets real-time requirements and achieves better performance than state-of-the-art methods.

Extending the concepts of complex interval valued neutrosophic subbisemiring of bisemiring

The objective of this paper is to investigate the innovative concept of complex neutrosophic subbisemiring. The novelty of the complex neutrosophic subbisemiring lies in its wide range of truth, indeterminacy, and false function values. It goes beyond the range of [0,1] in the complex plane in contrast to the traditional range [0,1]. Therefore, these three functions can be described mathematically using a complex number in the complex neutrosophic subbisemiring. We develop and analyze the concept of complex interval-valued neutrosophic subbisemiring (CIVNSBS). Moreover, we study homomorphic characteristics and important properties of CIVNSBS. We propose the level sets of CIVNSBS and complex interval valued neutrosophic normal subbisemiring (CIVNNSBS) of bisemirings. Moreover, we introduce CIVNNSBS of bisemiring. Let ¡ be a complex neutrosophic subset of bisemiring S. Then is a CIVNSBS of S if and only if all non empty level set is a subbisemiring, where . Let ¡be a CIVNSBS of bisemiring S and V be the strongest complex neutrosophic relation of bisemiring S. Then ¡ is a CIVNSBS of bisemiring S if and only if V is a CIVNSBS of . We illustrate that homomorphic images of every CIVNSBS is a CIVNSBS and homomorphic pre-images of every CIVNSBS is a CIVNSBS. Examples are provided to illustrate our results.\\

Mean value formulas for classical solutions to some degenerate elliptic equations in Carnot groups

&lt;p style='text-indent:20px;'&gt;We prove surface and volume mean value formulas for classical solutions to uniformly elliptic equations in divergence form with Hölder continuous coefficients. The kernels appearing in the integrals are supported on the level and superlevel sets of the fundamental solution relative the adjoint differential operator. We then extend the aforementioned formulas to some subelliptic operators on Carnot groups. In this case we rely on the theory of finite perimeter sets on stratified Lie groups.&lt;/p&gt;

Adherence to Practice Guidelines in the Implementation of Emergency Obstetric and Newborn Care in Referral Hospitals in Osun State, Nigeria.

While practice guidelines support clinical decision-making for optimal patient outcomes, there is often nonadherence to practice guidelines in implementing evidence-based interventions. This article aimed to assess adherence to practice guidelines in emergency obstetric and newborn care (EmONC) and the outcome of pregnancy in cases of obstetric complications in referral hospitals. The study employed a descriptive design. A purposive sampling technique was used to select the three tertiary hospitals and six out of nine state hospitals in Osun State. A data extraction form developed based on a fidelity framework was used to collect data on Adherence from 264 cases of obstetric complications. Descriptive statistics, such as frequency and percentage, and inferential statistics, such as chi-square, were done with the significance level set as p < .05. Findings showed low adherence to practice guidelines in 70.8% of hemorrhage care, 52.0% of fetal distress care, 60.0% of prolonged obstructed labor care, and 44.4% of preeclampsia/eclampsia care. The study's findings also showed that 64.3% of cases of prolonged/obstructed labor, 54.9% of cases of fetal distress, and 46.7% of all cases of obstetric complications were referred out at the state hospitals. Neonatal mortality in state and tertiary hospitals was 3.7% and 21.7%, respectively, which was significantly different (p < .001). There was low adherence to practice guidelines for the implementation of EmONC in state and tertiary hospitals, and a significant number of cases of obstetric complications were referred out in the state hospitals. The low adherence to practice guidelines and numerous referrals truncate the successful implementation of EmONC and hinder women and newborns from receiving optimal care for obstetric complications. There is a need to develop strategies that promote adherence to practice guidelines in implementing EmONC.

Description of random level sets by polynomial chaos expansions

Description of random level sets by polynomial chaos expansions

Topology optimization for additive manufacturing of CFRP structures

Combining design optimization and additive manufacturing (AM) enables the full exploitation of the potential for heightening the performance of carbon fiber reinforced plastic (CFRP) structures. This study simultaneously conducts topology optimization and fiber path design by employing the radial basis function (RBF) based level set function (LSF). Fiber paths are determined instinctively for the inherent advantages of the LSF, and fiber orientations are parameterized accordingly. Manufacturing drawbacks such as gaps and overlaps can be avoided by introducing a fast-marching method. To verify the effectiveness of the optimization method, three groups of optimized and empirical designs are fabricated by the AM technique, respectively, and the experimental tests are further carried out. Finite element (FE) models are also reconstructed based on the printing schemes, and then the FE simulation is validated by the experimental tests. With the proposed optimization method, stiffnesses for all three groups of the optimal samples are significantly improved compared with the empirical counterparts. The FE modeling technique is capable of reproducing the experimental results. This study paves a new way to develop an integrated framework of optimization, additive manufacturing, experimentation, and validation to deliver high-performance CFRP structures.

Accurate and Automatic Dental Crown Components Segmentation With Multi-Scale Attention Based U-Net and Hybrid Level Set Models

Accurate and Automatic Dental Crown Components Segmentation With Multi-Scale Attention Based U-Net and Hybrid Level Set Models

A Level Set Method With Heterogeneity Filter for Side-Scan Sonar Image Segmentation

A Level Set Method With Heterogeneity Filter for Side-Scan Sonar Image Segmentation