Towards better predicting the settling velocity of film-shaped microplastics based on experiment and simulation data.

The properties of microplastics determine their settling velocities and affect the fates and migration pathways of microplastics. This paper has simulated the settling velocities of film-shaped microplastics, which are present in natural aquatic environments. The numerical results provided more data to fit the terminal settling velocities of film-shaped microplastics. Comparison between the particle definition and the equivalent spherical diameter confirmed that the particle definition is more suitable for film-shaped microplastics. In the transitional flow regime, CD decreases linearly with Re. As Re further increases, CD gradually converges at approximately 1.20. By integrating the experimental and simulated data, a new explicit formula for predicting the settling velocity of film-shaped microplastics has been presented with the optimal shape parameter f. The presented formula achieves better performance (MAPE = 6.6 %, RMSE = 16.8 %, and R2 = 0.99) than the existing formulas for settling velocity for film-shaped microplastics, closely rivaling that of the ensemble learning algorithm.

Study on the space field reconstruction method of the radial basis function of electromagnetic radiation under optimal parameters.

Electromagnetic radiation (EM) pollution has a certain impact on human life and health, and the reconstruction of the EM space field in this paper is of great practical significance for EM analysis and research. The radial basis function (RBF) sufficiently considers the influence of each sampling point and is more suitable for reconstructing the EM space field than other spatial interpolation methods. Currently, when RBF is used to reconstruct the EM space field, the optimal determination of the basis function and shape parameter (SP) is rarely considered. This ultimately leads to low reconstruction accuracy of the EM space field. Therefore, in this paper, the particle swarm optimization (PSO) is used to calculate the optimal SP of the RBF. On this basis, reliable EM space field reconstruction is performed, which helps people understand the EM distribution characteristics in actual situations from a visual perspective. The EM sampling data of a region on the Yunnan Normal University campus are used as the data source, and the RBF under the optimal parameters is used for EM reconstruction. The accuracy of its interpolation results is evaluated and compared and analyzed with inverse distance weighting (IDW) after distance index optimization. The results show that the RBF under optimal parameters reconstructs the EM space field with high accuracy and good effect, which can truly reflect the actual distribution of EM.

Electromagnetic radiation (EM) pollution has a great impact on the surrounding environment. Therefore, EM space field reconstruction can help us analyze the characteristics of the electromagnetic environment in a visual way. Radial Basis Function (RBF) is a method more suitable for EM space field reconstruction than other methods because it fully considers the influence of each sampling point. However, when currently using RBF to reconstruct the EM space field, few researchers consider how to choose the most appropriate basis function and shape parameter (SP). This results in low reconstruction accuracy. Therefore, this study uses particle swarm optimization (PSO) to find the optimal SP parameters for reliable EM space field reconstruction. The study used the EM sampling data of an area within the campus of Yunnan Normal University as the study material, and a parameter-optimized RBF method was adopted for the reconstruction of the EM space field. The reconstruction results were then evaluated for accuracy and compared and analyzed with the IDW method optimized with a distance index. Research results show that using RBF with optimal parameters to reconstruct the EM space field has high accuracy and can effectively reflect the actual EM distribution, thereby helping people better understand the characteristics of the electromagnetic environment.

Machine learning-based prediction for settling velocity of microplastics with various shapes.

Microplastics can easily enter the aquatic environment and be transported between water bodies. The terminal settling velocity of microplastics, which affects their transport and distribution in the aquatic environment, is mainly influenced by their size, density, and shape. Due to the difficulty in accurately predicting the terminal settling velocity of microplastics with various shapes, this study focuses on establishing high-performance prediction models and understanding the importance and effect of each feature parameter using machine learning. Based on the number of principal dimensions, the shapes of microplastics are classified into fiber, film, and fragment, and their thresholds are identified. The microplastics of different shape categories have different optimal shape parameters for predicting the terminal settling velocity: Corey shape factor, flatness, elongation, and sphericity for the fragment, film, fiber, and mixed-shape MPs, respectively. By including the dimensionless diameter, relative density and optimal shape parameter in the input parameter combination, the machine learning models can well predict the terminal settling velocity for the microplastics of different shape categories and mixed-shape with R2 > 0.867, achieving significantly higher performance than the existing theoretical and regression models. The interpretable analysis of machine learning reveals the highest importance of the microplastic size and its marginal effect when the dimensionless diameter D* = dn(g/v2)1/3 > 80, where dn is the equivalent diameter, g is the gravitational acceleration, and ν is the fluid kinematic viscosity. The effect of shape is weak for small microplastics and becomes significant when D* exceeds 65.

An image-based shape analysis approach and its application to young women's waist-hip-leg position.

Digital image processing has been widely used for researches in the fashion industry. This study presented a method to classify women's waist-hip-leg position based on body images. 135 healthy female students were selected as the experimental subjects, and then photo and 3D body measuring methods were used to obtain 40 shape parameters. Through factor analysis, five factors were extracted for the waist-hip position and eight factors for the leg position. The waist-hip and leg were separately classified into four categories after clustering analysis with optimised factors. The distribution of waist-hip-leg shape was analysed by combining the waist-hip and leg classification results. The results showed that 12.31% of the subjects had prominent abdomens, flat buttocks, and round and thin legs. The landmarks and parameters were automatically extracted for waist-hip-leg shape identification. The image-based shape analysis approach (ISA) was finally verified with an accuracy rate of over 90% with 30 new subjects.Practitioner summary: This study will propose an image-based shape analysis approach (ISA) to realise the quick automatic shape identification of the waist-hip-leg position based on body images. In addition, the method can be applied to pants' pattern alteration for different body types by analysing the relationship between the waist-hip-leg shape and pants.

Tissue Characterization of Puborectalis Muscle From 3-D Ultrasound.

Pelvic floor (PF) muscles have the role of preventing pelvic organ descent. The puborectalis muscle (PRM), which is one of the female PF muscles, can be damaged during child delivery. This damage can potentially cause irreversible muscle trauma and even lead to an avulsion, which is disconnection of the muscle from its insertion point, the pubic bone. Ultrasound imaging allows diagnosis of such trauma based on comparison of geometric features of a damaged muscle with the geometric features of a healthy muscle. Although avulsion, which is considered severe damage, can be diagnosed, microdamage within the muscle itself leading to structural changes cannot be diagnosed by visual inspection through imaging only. Therefore, we developed a quantitative ultrasound tissue characterization method to obtain information on the state of the tissue of the PRM and the presence of microdamage in avulsed PRMs. The muscle was segmented as the region of interest (ROI) and further subdivided into six regions of interest (sub-ROIs). Mean echogenicity, entropy and shape parameter of the statistical distribution of gray values were analyzed on two of these sub-ROIs nearest to the bone. The regions nearest to the bones are also the most likely regions to exhibit damage in case of disconnection or avulsion. This analysis was performed for both the muscle at rest and the muscle in contraction. We found that, for PRMs with unilateral avulsion compared with undamaged PRMs, the mean echogenicity (p = 0.02) and shape parameter (p < 0.01) were higher, whereas the entropy was lower (p < 0.01). This method might be applicable to quantification of PRM damage within the muscle.

Statistical Analysis of Ultrasonic Scattered Echoes Enables the Non-invasive Measurement of Temperature Elevations inside Tumor Tissue during Oncological Hyperthermia.

Non-invasive monitoring of temperature elevations inside tumor tissue is imperative for the oncological thermotherapy known as hyperthermia. In the present study, two cancer patients, one with a developing right renal cell carcinoma and the other with pseudomyxoma peritonei, underwent hyperthermia. The two patients were irradiated with radiofrequency current for 40 min during hyperthermia. We report the results of our clinical trial study in which the temperature increases inside the tumor tissues of patients with right renal cell carcinoma and pseudomyxoma peritonei induced by radiofrequency current irradiation for 40 min could be detected by statistical analysis of ultrasonic scattered echoes. The Nakagami shape parameter m varies depending on the temperature of the medium. We calculated the Nakagami shape parameter m by statistical analysis of the ultrasonic echoes scattered from the tumor tissues. The temperature elevations inside the tumor tissues were expressed as increases in brightness on 2-D hot-scale maps of the specific parameter αmod, indicating the absolute values of the percentage changes in m values. In the αmod map for each tumor tissue, the brightness clearly increased with treatment time. In quantitative analysis, the mean values of αmod were calculated. The mean value of αmod for the right renal cell carcinoma increased to 1.35 dB with increasing treatment time, and the mean value of αmod for pseudomyxoma peritonei increased to 1.74 with treatment time. The increase in both αmod brightness and the mean value of αmod implied temperature elevations inside the tumor tissues induced by the radiofrequency current; thus, the acoustic method is promising for monitoring temperature elevations inside tumor tissues during hyperthermia.

Kansa Method for Unsteady Heat Flow in Nonhomogenous Material with a New Proposal of Finding the Good Value of RBF's Shape Parameter.

New engineering materials exhibit a complex internal structure that determines their properties. For thermal metamaterials, it is essential to shape their thermophysical parameters' spatial variability to ensure unique properties of heat flux control. Modeling heterogeneous materials such as thermal metamaterials is a current research problem, and meshless methods are currently quite popular for simulation. The main problem when using new modeling methods is the selection of their optimal parameters. The Kansa method is currently a well-established method of solving problems described by partial differential equations. However, one unsolved problem associated with this method that hinders its popularization is choosing the optimal shape parameter value of the radial basis functions. The algorithm proposed by Fasshauer and Zhang is, as of today, one of the most popular and the best-established algorithms for finding a good shape parameter value for the Kansa method. However, it turns out that it is not suitable for all classes of computational problems, e.g., for modeling the 1D heat conduction in non-homogeneous materials, as in the present paper. The work proposes two new algorithms for finding a good shape parameter value, one based on the analysis of the condition number of the matrix obtained by performing specific operations on interpolation matrix and the other being a modification of the Fasshauer algorithm. According to the error measures used in work, the proposed algorithms for the considered class of problem provide shape parameter values that lead to better results than the classic Fasshauer algorithm.

Approximations for the inverse cumulative distribution function of the gamma distribution used in wireless communication.

The use of quantile functions of probability distributions whose cumulative distribution is intractable is often limited in Monte Carlo simulation, modeling, and random number generation. Gamma distribution is one of such distributions, and that has placed limitations on the use of gamma distribution in modeling fading channels and systems described by the gamma distribution. This is due to the inability to find a suitable closed-form expression for the inverse cumulative distribution function, commonly known as the quantile function (QF). This paper adopted the Quantile mechanics approach to transform the probability density function of the gamma distribution to second-order nonlinear ordinary differential equations (ODEs) whose solution leads to quantile approximation. Closed-form expressions, although complex of the QF, were obtained from the solution of the ODEs for degrees of freedom from one to five. The cases where the degree of freedom is not an integer were obtained, which yielded values closed to the R software values via Monte Carlo simulation. This paper provides an alternative for simulating gamma random variables when the degree of freedom is not an integer. The results obtained are fast, computationally efficient and compare favorably with the machine (R software) values using absolute error and Kullback-Leibler divergence as performance metrics.

Rate of Entropy Production in Evolving Interfaces and Membranes under Astigmatic Kinematics: Shape Evolution in Geometric-Dissipation Landscapes.

This paper presents theory and simulation of viscous dissipation in evolving interfaces and membranes under kinematic conditions, known as astigmatic flow, ubiquitous during growth processes in nature. The essential aim is to characterize and explain the underlying connections between curvedness and shape evolution and the rate of entropy production due to viscous bending and torsion rates. The membrane dissipation model used here is known as the Boussinesq-Scriven fluid model. Since the standard approaches in morphological evolution are based on the average, Gaussian and deviatoric curvatures, which comingle shape with curvedness, this paper introduces a novel decoupled approach whereby shape is independent of curvedness. In this curvedness-shape landscape, the entropy production surface under constant homogeneous normal velocity decays with growth but oscillates with shape changes. Saddles and spheres are minima while cylindrical patches are maxima. The astigmatic flow trajectories on the entropy production surface, show that only cylinders and spheres grow under the constant shape. Small deviations from cylindrical shapes evolve towards spheres or saddles depending on the initial condition, where dissipation rates decrease. Taken together the results and analysis provide novel and significant relations between shape evolution and viscous dissipation in deforming viscous membrane and surfaces.

Assessing accuracy of Weibull shape parameter estimate from historical studies for subsequent sample size calculation in clinical trials with time-to-event outcome.

BACKGROUND: Recent developments in literature on sample size calculations for time-to-event outcomes involve assumption of Weibull distributed times. These methods require a point estimate of the Weibull shape parameter obtained from historical studies. However, very limited guidance exists in published literature to assess how reliable this point estimate is when it is obtained from published results of a historical study. METHODS: We conduct simulations to assess how accurate and reliable the point estimate of the Weibull shape parameter is when it is estimated from published results of median survival time and/or corresponding interquartile range. Accuracy of this estimate is assessed using the criteria of average relative bias, root mean square error, and coefficient of variation for various combinations of sample sizes and censoring rates. Sensitivity of these calculations is assessed first, by increasing the number of survival quantiles used to calculate accuracy, and second, by using the full Kaplan Meier (KM) curve from the historical study. RESULTS: Our simulations suggest that point estimate of the shape parameter is reasonably accurate when estimated from historical studies with sample size ≥ 50 with censoring rate approximately 20%. Knowledge of the median and inter-quartile range seems to be adequate for this purpose. For historical studies with small sample sizes or higher censoring rates, more information needs to be abstracted from the published KM curves to improve accuracy. CONCLUSIONS: We conclude that assessing the accuracy of Weibull shape parameter estimate is important before it can be used to conduct sample size calculations for a subsequent trial.

Size-Based Differentiation of Cancer and Normal Cells by a Particle Size Analyzer Assisted by a Cell-Recognition PC Software.

Detection of anomalous cells such as cancer cells from normal blood cells has the potential to contribute greatly to cancer diagnosis and therapy. Conventional methods for the detection of cancer cells are usually tedious and cumbersome. Herein, we report on the use of a particle size analyzer for the convenient size-based differentiation of cancer cells from normal cells. Measurements made using a particle size analyzer revealed that size parameters for cancer cells are significantly greater (e.g., inner diameter and width) than the corresponding values for normal cells (white blood cells (WBC), lymphocytes and splenocytes), with no significant difference in shape parameters (e.g., circularity and convexity). The inner diameter of many cancer cell lines is greater than 10 µm, in contrast to normal cells. For the detection of WBC having similar size to that of cancer cells, we developed a PC software "Cancer Cell Finder" that differentiates them from cancer cells based on brightness stationary points on a cell surface. Furthermore, the aforementioned method was validated for cancer cell/clusters detection in spiked mouse blood samples (a B16 melanoma mouse xenograft model) and circulating tumor cell cluster-like particles in the cat and dog (diagnosed with cancer) blood samples. These results provide insights into the possible applicability of the use of a particle size analyzer in conjunction with PC software for the convenient detection of cancer cells in experimental and clinical samples for theranostics.

G2 continuity conditions for generalized Bézier-like surfaces with multiple shape parameters.

In order to tackle the problem of shape design and shape adjustment of complex surfaces in engineering, continuity conditions between generalized Bézier-like surfaces with multiple shape parameters are studied in this paper. Firstly, the geometric model of the generalized Bézier-like surfaces is built by blending a number of Bézier-like curves with independent shape parameters. Secondly, based on the terminal properties and linear independence of Bernstein-like basis functions, the conditions for G2 continuity between two adjacent generalized Bézier-like surfaces are derived, and then simplified by choosing appropriate shape parameters. Finally, some properties and applications of the smooth continuity between generalized Bézier-like surfaces are discussed. The modeling examples show that the proposed method is effective and easy to implement, which can greatly improve the ability to construct complex surfaces by using the generalized Bézier-like surfaces.

Application of the Weibull Distribution with a Non-Constant Shape Parameter for Identifying Risk Factors in Pharyngeal Cancer Patients

Background: In its standard form, the parametric survival model assumes that the shape parameter is constant and the scaling parameter is not. This article focuses on how a model with a non-constant shape parameter could make differences in oncology studies and lead to more precise results. Materials and Methods: Online data for part of a large clinical trial conducted by the Radiation Oncology Group in the United States available online on UMass Amherst`s website were employed. The full study included patients with squamous cell carcinoma from fifteen sites in the mouth and throat, although only data on three sites in the oropharynx reported by the six largest institutions were considered here. To identify clinical, pathological and biological characteristics of patients which might have had an effect on their survival, we compared Weibull distributions once with a constant shape parameter and again with a non-constant shape parameter. Analyzes were performed using SAS university edition. The level of significance was set at P ≤ 0.05. Results: Based on the model with a constant shape parameter only the patient status was identified as a risk factor and the AIC of this model was 2152.4, but based on the model with a non-constant shape parameter, sex, patient status, stage of the tumor and the institute at which the patient had been treated were significant, with an AIC of 2150.1. Conclusion: On the basis of the AIC, the second model with a non-constant shape parameter was suggested to be more accurate for identifying risk factors, leading to more precise results.

Continuity conditions for Q-Bézier curves of degree n.

As a new method of representing curves, Q-Bézier curves not only exhibit the beneficial properties of Bézier curves but also allow effective shape adjustment by changing multiple shape parameters. In order to resolve the problem of not being able to construct complex curves using a single curve, we study the geometric continuity conditions for Q-Bézier curves of degree n. Following the analysis of basis functions and terminal properties of Q-Bézier curves of degree n, the continuity conditions of [Formula: see text] and [Formula: see text] between two adjacent Q-Bézier curves are proposed. In addition, we discuss the specific steps of smooth continuity for Q-Bézier curves and analyze the influence rules of shape parameters for Q-Bézier curves. The modeling examples show that the proposed method is effective and easy to achieve, making it useful for constructing complex curves for engineering design.

Adaptive independent vector analysis for multi-subject complex-valued fMRI data.

BACKGROUND: Complex-valued fMRI data can provide additional insights beyond magnitude-only data. However, independent vector analysis (IVA), which has exhibited great potential for group analysis of magnitude-only fMRI data, has rarely been applied to complex-valued fMRI data. The main challenges in this application include the extremely noisy nature and large variability of the source component vector (SCV) distribution. NEW METHOD: To address these challenges, we propose an adaptive fixed-point IVA algorithm for analyzing multiple-subject complex-valued fMRI data. We exploited a multivariate generalized Gaussian distribution (MGGD)- based nonlinear function to match varying SCV distributions in which the MGGD shape parameter was estimated using maximum likelihood estimation. To achieve our de-noising goal, we updated the MGGD-based nonlinearity in the dominant SCV subspace, and employed a post-IVA de-noising strategy based on phase information in the IVA estimates. We also incorporated the pseudo-covariance matrix of fMRI data into the algorithm to emphasize the noncircularity of complex-valued fMRI sources. RESULTS: Results from simulated and experimental fMRI data demonstrated the efficacy of our method. COMPARISON WITH EXISTING METHOD(S): Our approach exhibited significant improvements over typical complex-valued IVA algorithms, especially during higher noise levels and larger spatial and temporal changes. As expected, the proposed complex-valued IVA algorithm detected more contiguous and reasonable activations than the magnitude-only method for task-related (393%) and default mode (301%) spatial maps. CONCLUSIONS: The proposed approach is suitable for decomposing multi-subject complex-valued fMRI data, and has great potential for capturing additional subject variability.

Axisymmetric Drop Shape Analysis (ADSA): An Outline.

Drop shape techniques for the measurement of interfacial tension are powerful, versatile and flexible. The shape of the drop/bubble depends on the balance between surface tension and external forces, e.g. gravity. This balance is reflected mathematically in the Laplace equation of capillarity. Axisymmetric Drop Shape Analysis (ADSA) is a commonly used drop shape technique. A streamlined version of the development of ADSA over the past several decades is presented to illustrate its validity and range of utility. Several configurations of interest will be considered and presented systematically. Shape and surface tension will be linked to a shape parameter based on proper concepts of differential geometry. The resulting shape parameter will be shown to allow determination of the range of applicability of such a drop shape method.

Dilute solution properties of canary seed (Phalaris canariensis) starch in comparison to wheat starch.

Dilute solution properties of an unknown starch are important to understand its performance and applications in food and non-food industries. In this paper, rheological and molecular properties (intrinsic viscosity, molecular weight, shape factor, voluminosity, conformation and coil overlap parameters) of the starches from two hairless canary seed varieties (CO5041 & CDC Maria) developed for food use were evaluated in the dilute regime (Starch dispersions in DMSO (0.5g/dl)) and compared with wheat starch (WS). The results showed that Higiro model is the best among five applied models for intrinsic viscosity determination of canary seed starch (CSS) and WS on the basis of coefficient of determination (R(2)) and root mean square error (RMSE). WS sample showed higher intrinsic viscosity value (1.670dl/g) in comparison to CSS samples (1.325-1.397dl/g). Berry number and the slope of master curve demonstrated that CSS and WS samples were in dilute domain without entanglement occurrence. The shape factor suggested spherical and ellipsoidal structure for CO5041 starch and ellipsoidal for CDC Maria starch and WS. The molecular weight, coil radius and coil volume of CSSs were smaller than WS. The behavior and molecular characterization of canary seed starch showed its unique properties compared with wheat starch.

A geometrical model for testing bilateral symmetry of bamboo leaf with a simplified Gielis equation.

The size and shape of plant leaves change with growth, and an accurate description of leaf shape is crucial for describing plant morphogenesis and development. Bilateral symmetry, which has been widely observed but poorly examined, occurs in both dicot and monocot leaves, including all nominated bamboo species (approximately 1,300 species), of which at least 500 are found in China. Although there are apparent differences in leaf size among bamboo species due to genetic and environmental profiles, bamboo leaves have bilateral symmetry with parallel venation and appear similar across species. Here, we investigate whether the shape of bamboo leaves can be accurately described by a simplified Gielis equation, which consists of only two parameters (leaf length and shape) and produces a perfect bilateral shape. To test the applicability of this equation and the occurrence of bilateral symmetry, we first measured the leaf length of 42 bamboo species, examining >500 leaves per species. We then scanned 30 leaves per species that had approximately the same length as the median leaf length for that species. The leaf-shape data from scanned profiles were fitted to the simplified Gielis equation. Results confirmed that the equation fits the leaf-shape data extremely well, with the coefficients of determination being 0.995 on average. We further demonstrated the bilateral symmetry of bamboo leaves, with a clearly defined leaf-shape parameter of all 42 bamboo species investigated ranging from 0.02 to 0.1. This results in a simple and reliable tool for precise determination of bamboo species, with applications in forestry, ecology, and taxonomy.

Laplacian drop shapes and effect of random perturbations on accuracy of surface tension measurement for different drop constellations.

Theoretical drop shapes are calculated for three drop constellations: pendant drops, constrained sessile drops, and unconstrained sessile drops. Based on total Gaussian curvature, shape parameter and critical shape parameter are discussed as a function of different drop sizes and surface tensions. The shape parameter is linked to physical parameters for every drop constellation. The as yet unavailable detailed dimensional analysis for the unconstrained sessile drop is presented. Results show that the unconstrained sessile drop shape depends on a dimensionless volume term and the contact angle. Random perturbations are introduced and the accuracy of surface tension measurement is assessed for precise and perturbed profiles of the three drop constellations. It is concluded that pendant drops are the best method for accurate surface tension measurement, followed by constrained sessile drops. The unconstrained sessile drops come last because they tend to be more spherical at low and moderate contact angles. Of course, unconstrained sessile drops are the only option if contact angles are to be measured.

Total Gaussian curvature, drop shapes and the range of applicability of drop shape techniques.

Drop shape techniques are used extensively for surface tension measurement. It is well-documented that, as the drop/bubble shape becomes close to spherical, the performance of all drop shape techniques deteriorates. There have been efforts quantifying the range of applicability of drop techniques by studying the deviation of Laplacian drops from the spherical shape. A shape parameter was introduced in the literature and was modified several times to accommodate different drop constellations. However, new problems arise every time a new configuration is considered. Therefore, there is a need for a universal shape parameter applicable to pendant drops, sessile drops, liquid bridges as well as captive bubbles. In this work, the use of the total Gaussian curvature in a unified approach for the shape parameter is introduced for that purpose. The total Gaussian curvature is a dimensionless quantity that is commonly used in differential geometry and surface thermodynamics, and can be easily calculated for different Laplacian drop shapes. The new definition of the shape parameter using the total Gaussian curvature is applied here to both pendant and constrained sessile drops as an illustration. The analysis showed that the new definition is superior and reflects experimental results better than previous definitions, especially at extreme values of the Bond number.