B-spline Model Research Articles

A new algorithm for fitting semi-parametric variance regression models

Variance regression allows for heterogeneous variance, or heteroscedasticity, by incorporating a regression model into the variance. This paper uses a variant of the expectation–maximisation algorithm to develop a new method for fitting additive variance regression models that allow for regression in both the mean and the variance. The algorithm is easily extended to allow for B-spline bases, thus allowing for the incorporation of a semi-parametric model in both the mean and variance. Although there are existing methods to fit these types of models, this new algorithm provides a reliable alternative approach that is not susceptible to numerical instability that can arise in this constrained estimation context. We utilise the developed algorithm with a series of simulation studies and analyse illustrative data. Various simulation studies show that the algorithm can recover the true model for a variety of scenarios. We also study automatic selection of model complexity based on information-based criteria, and show that the Akaike information criterion is useful for choosing the optimal number of knots in a B-spline model. An R package is available for implementing these methods.

Pemodelan Pola Produktivitas Cabai Rawit di Kabupaten Magelang

The objective of this study was to determine the best model that describe the pattern of cayenne pepper productivity in Magelang Regency. This study uses primary data which was obtained from the results of a survey of cayenne pepper production by the General Director of Horticulture on several sample plots in Magelang District, Central Java Province in 2018. The process of data analysis was divided into two parts: grouping the sample plots based on the similarity in productivity pattern and then fitting models in each group. The models used to fit data were Logistic Growth Model, Monomolecular Growth Model, Exponential Growth Model, Polynomial Model and Linear B-Spline Model. The best model was determined based on R2 and MAPE. The results showed that the pattern of cayenne pepper productivity in Magelang District had eight different characteristics. Characteristics of each groups were illustrated by the similarity of their productivity pattern. The best model in each group was B-Spline Linear Model.

B-spline modelling of inspiratory drive in NAVA-ventilated patients

Abstract Model-based approaches are often used to estimate mechanical properties of lungs, such as elastance (E) and airway resistance (R), during invasive and non-invasive mechanical ventilation (MV). Current models are less effective when spontaneous breathing is present. This analysis utilises b-spline functions within a single compartment model framework to identify patient-specific inspiratory driving pressure. A series of 2nd-order, constrained b-spline basis functions are used to identify inspiratory driving pressure breath to breath alongside single E and R using inspiration and expiration data from n=20 breaths for 10 patients ventilated using NAVA. Median [IQR] per patient RMS error for n = 20 breaths was 0.75 [0.6 – 0.9] cmH2O, with elastance ranging from 2.1 – 29.8 cmH20/L, and per-patient median peak driving pressure ranging from -1.9 to -7.9 cmH2O. Inspiratory driving pressure profiles matched esophageal pressures from literature and its value at peak nervous signal to the diaphragm (Eadi) was correlated with peak Eadi (R2=0.25-0.86). Average trans-pulmonary pressure remained consistent between breaths for each patient, despite differences in peak Eadi and peak airway pressure. Overall, the model-based approach resulted in physiologically reasonable inspiratory driving pressures, with trends with electrical activity and matched literature data showing neuro-muscular decoupling as a function of pressure and/or volume.

Imposing implicit feasibility constraints on deformable image registration using a statistical generative model.

Purpose: Deformable registration problems are conventionally posed in a regularized optimization framework, where balance between fidelity and prescribed regularization usually needs to be tuned for each case. Even so, using a single weight to control regularization strength may be insufficient to reflect spatially variant tissue properties and limit registration performance. In this study, we proposed to incorporate a spatially variant deformation prior into image registration framework using a statistical generative model. Approach: A generator network is trained in an unsupervised setting to maximize the likelihood of observing the moving and fixed image pairs, using an alternating back-propagation approach. The trained model imposes constraints on deformation and serves as an effective low-dimensional deformation parametrization. During registration, optimization is performed over this learned parametrization, eliminating the need for explicit regularization and tuning. The proposed method was tested against SimpleElastix, DIRNet, and Voxelmorph. Results: Experiments with synthetic images and simulated CTs showed that our method yielded registration errors significantly lower than SimpleElastix and DIRNet. Experiments with cardiac magnetic resonance images showed that the method encouraged physical and physiological feasibility of deformation. Evaluation with left ventricle contours showed that our method achieved a dice of ( ) with significant improvement over all SimpleElastix options, DIRNet, and VoxelMorph. Mean average surface distance was on millimeter level, comparable to the best SimpleElastix setting. The average 3D registration time was 12.78s, faster than 24.70s in SimpleElastix. Conclusions: The learned implicit parametrization could be an efficacious alternative to regularized B-spline model, more flexible in admitting spatial heterogeneity.

Pemodelan Pola Produktivitas Cabai Rawit di Kabupaten Magelang

The objective of this study was to determine the best model that describe the pattern of cayenne pepper productivity in Magelang Regency. This study uses primary data which was obtained from the results of a survey of cayenne pepper production by the General Director of Horticulture on several sample plots in Magelang District, Central Java Province in 2018. The process of data analysis was divided into two parts: grouping the sample plots based on the similarity in productivity pattern and then fitting models in each group. The models used to fit data were Logistic Growth Model, Monomolecular Growth Model, Exponential Growth Model, Polynomial Model and Linear B-Spline Model. The best model was determined based on R2 and MAPE. The results showed that the pattern of cayenne pepper productivity in Magelang District had eight different characteristics. Characteristics of each groups were illustrated by the similarity of their productivity pattern. The best model in each group was B-Spline Linear Model.

High-Resolution Ionosphere Corrections for Single-Frequency Positioning

The ionosphere is one of the main error sources in positioning and navigation; thus, information about the ionosphere is mandatory for precise modern Global Navigation Satellite System (GNSS) applications. The International GNSS Service (IGS) and its Ionosphere Associated Analysis Centers (IAAC) routinely provide ionospheric information in terms of global ionosphere maps (final GIM). Typically, these products are modeled using series expansion in terms of spherical harmonics (SHs) with a maximum degree of n=15 and are based on post processed observations from Global Navigation Satellite Systems (GNSS), as well as final satellite orbits. However, precise applications such as autonomous driving or precision agriculture require real-time (RT) information about the ionospheric electron content with high spectral and spatial resolution. Ionospheric RT-GIMs are disseminated via Ntrip protocol using the SSR VTEC message of the RTCM. This message can be streamed in RT, but it is limited for the dissemination of coefficients of SHs of lower degrees only. It allows the dissemination of SH coefficients up to a degree of n=16. This suits to most the SH models of the IAACs, but higher spectral degrees or models in terms of B-spline basis functions, voxels, splines and many more cannot be considered. In addition to the SHs, several alternative approaches, e.g., B-splines or Voxels, have proven to be appropriate basis functions for modeling the ionosphere with an enhanced resolution. Providing them using the SSR VTEC message requires a transfer to SHs. In this context, the following questions are discussed based on data of a B-spline model with high spectral resolution; (1) How can the B-spline model be transformed to SHs in order to fit to the RTCM requirements and (2) what is the loss of detail when the B-spline model is converted to SHs of degree of n=16? Furthermore, we discuss (3) what is the maximum necessary SH degree n to convert the given B-spline model and (4) how can the transformation be performed to make it applicable for real-time applications? For a final assessment, we perform both, the dSTEC analysis and a single-frequency positioning in kinematic mode, using the transformed GIMs for correcting the ionospheric delay. The assessment shows that the converted GIMs with degrees n≥30 coincide with the original B-spline model and improve the positioning accuracy significantly.

A fast technique for hyper-echoic region separation from brain ultrasound images using patch based thresholding and cubic B-spline based contour smoothing

Ultrasound image guided brain surgery (UGBS) requires an automatic and fast image segmentation method. The level-set and active contour based algorithms have been found to be useful for obtaining topology-independent boundaries between different image regions. But slow convergence limits their use in online US image segmentation. The performance of these algorithms deteriorates on US images because of the intensity inhomogeneity. This paper proposes an effective region-driven method for the segmentation of hyper-echoic (HE) regions suppressing the hypo-echoic and anechoic regions in brain US images. An automatic threshold estimation scheme is developed with a modified Niblack’s approach. The separation of the hyper-echoic and non-hyper-echoic (NHE) regions is performed by successively applying patch based intensity thresholding and boundary smoothing. First, a patch based segmentation is performed, which separates roughly the two regions. The patch based approach in this process reduces the effect of intensity heterogeneity within an HE region. An iterative boundary correction step with reducing patch size improves further the regional topology and refines the boundary regions. For avoiding the slope and curvature discontinuities and obtaining distinct boundaries between HE and NHE regions, a cubic B-spline model of curve smoothing is applied. The proposed method is 50–100 times faster than the other level-set based image segmentation algorithms. The segmentation performance and the convergence speed of the proposed method are compared with four other competing level-set based algorithms. The computational results show that the proposed segmentation approach outperforms other level-set based techniques both subjectively and objectively.

Nonlinear system identification with regularized Tensor Network B-splines

This article introduces the Tensor Network B-spline (TNBS) model for the regularized identification of nonlinear systems using a nonlinear autoregressive exogenous (NARX) approach. Tensor network theory is used to alleviate the curse of dimensionality of multivariate B-splines by representing the high-dimensional weight tensor as a low-rank approximation. An iterative algorithm based on the alternating linear scheme is developed to directly estimate the low-rank tensor network approximation, removing the need to ever explicitly construct the exponentially large weight tensor. This reduces the computational and storage complexity significantly, allowing the identification of NARX systems with a large number of inputs and lags. The proposed algorithm is numerically stable, robust to noise, guaranteed to monotonically converge, and allows the straightforward incorporation of regularization. The TNBS-NARX model is validated through the identification of the cascaded watertank benchmark nonlinear system, on which it achieves state-of-the-art performance while identifying a 16-dimensional B-spline surface in 4 s on a standard desktop computer. An open-source MATLAB implementation is available on GitHub.

Determining the refractive index and the dielectric constant of PPDT2FBT thin film using spectroscopic ellipsometry

Despite the recent increase in PPDT2FBT polymer thin film applications for optoelectronic devices, a comprehensive study of this material's optical dispersion properties is unavailable. The optical properties of the PPDT2FBT thin film is investigated using variable-angle spectroscopic ellipsometry (VASE) at ambient conditions. Knowledge of optical dispersion properties is essential for designing and fabricating optoelectronic devices such as solar cells, photodetectors, and photodiodes. In this research, we determined the dielectric function of PPDT2FBT thin film using the B-spline model and then reproduced the dielectric function using Psemi-Tri oscillators. We estimated the refractive index (n) of the thin film to be between 2.00 and 2.15 and the extinction coefficient (k) to be in the range of 1.14–1.39 at a wavelength of 632.8 nm. We further verified the estimated optical properties from the model using directly measured quantities such as transmission and absorption data obtained using the ultraviolet–visible (UV–Vis) spectrometer and thicknesses obtained using a surface profilometer. In addition, we determined the optical band gap of PPDT2FBT using the absorption coefficient. • The optical properties such as n, k of the PPDT2FBT polymer thin film are determined. • It was determined in a nondestructive way using variable-angle spectroscopic ellipsometry at ambient conditions. • We applied analytical methods to verify the determined optical properties.

Splipy: B-Spline and NURBS Modelling in Python

Splipy is a pure Python library for the creation, evaluation and manipulation of B-spline and NURBS geometries. It supports n-variate splines of any dimension, but emphasis is placed on the use of curves, surfaces and volumes. The library is designed primarily for analysis use, and therefore allows fine-grained control over many aspects which cannot be achieved with conventional CAD tools. It is packaged and distributed through Python Package Index: PyPi which gives easy installation.

A Genetic Algorithm Application in Planning Path Using B-Spline Model for Autonomous Underwater Vehicle (AUV)

This paper proposes a method of using the B-spline mathematical model to plan high smoothness curve trajectories with heading condition through given waypoints for autonomous underwater vehicles (AUVs) in particular and ships with rudder systems in general. In addition, this paper examines some of the physical limitations of this vehicle, which lead to some binding conditions of the trajectory. Besides, the paper applies B-spline approximation method to reduce the curvature of the trajectory, when waypoints are too close and we do not need to go through exactly these waypoints in the 2D plane. Finally, this paper also proposes the genetic algorithm application with some modifications to solve the optimization of B-spline path length with constraint in turning radius of the vehicle.

PEMODELAN KASUS PNEUMONIA PADA BALITA DI PROVINSI BALI MENGGUNAKAN METODE REGRESI NONPARAMETRIK B-SPLINE

Pneumonia is an inflammatory lung disease caused by bacterium Streptococcus pneumonia, Chlamydophila pneumonia bacteria, influenza virus, and fungi. Bali Provincial Health Service data in 2018 shows that one of the diseases that causes many deaths in children under five is pneumonia. This study aims to model the number of pneumonia cases in children under five in Bali Province in 2018 with six research variables, namely percentage of low birth weight, percentage of coverage of infants who receive vitamin A, percentage of infants who receive exclusive breastfeeding, percentage of under-five health services, percentage of villages that implement community-based total sanitation, and percentage of neonatal complications management. In the B-Spline function there are connecting points called knots. The best estimation of the B-Spline regression model is obtained from selecting the optimum knot point with the criteria for the value of generalized cross validation (GCV) and the selected mean square error (MSE) having the minimum value. The B-Spline regression model that is formed is the quadratic B-Spline model (order 3) with five knots resulting in an value of 87.79%.

Pemodelan Data Time Series dengan Pendekatan Regresi Nonparametrik B-Spline

Spline is one of the nonparametric approach, to adjust data so the final model has good flexibility. The purpose of this research is to model the time series data in the form of currency exchange rates by using the nonparametric B-spline approach. In B-spline modelling, determination of the order for the model, and the number and the placement of the knot are the criteria that must be considered. The best B-spline model obtained based on the selection of the optimal knot points with minimum Generalized Cross Validation (GCV) criteria. The modelling in this research use data on the exchange rate of the rupiah toward the US dollar in the period January 2014 - December 2018. The best B-spline model obtained by the 2 point knot approach, at points 11935.10 and 12438.29, with GCV valueequals to 55683.09.Keywords: Nonparametric Regression; B-Spline; Generalized Cross Validation

Automatic Shape Control of Deformable Wires Based on Model-Free Visual Servoing

In this letter, we propose a novel approach to automatically control the 3D shape of deformable wires using robots. Our approach proposes a novel visual feature along with a novel shape servoing method to enable dual arm manipulation of deformable wires. The visual feature relies on a geometric B-spline model and the use of Sequential Importance Resampling (SIR) particle filtering to track the 3D deformed shape of a wire over time. The shape servoing method is an adaptive model-free method that iteratively updates the deformation Jacobian matrix using weighted least-squares minimization with sliding window and an eigenvalue-based confidence criterion. We performed several experiments on wires with different mechanical properties. The results show that our approach succeeded to control the 3D shape of various wires for many different desired deformations, while working at an interactive time. It has also been shown that the shape servoing method can be used to handle large deformations by subdividing the task in successive intermediary targets to reach. These promising results pave the way for automatic control of the 3D shapes of deformable wires in many fields such as catheter insertion in medicine or wire manipulation in industry.

Examining the Impact of the SDLMI and Whose Future Is It? Over a Two-Year Period With Students With Intellectual Disability.

The purpose of this study was to examine self-determination outcome data in the year following a one-year cluster randomized controlled trial (C-RCT) comparing the impacts of a Self-Determined Learning Model of Instruction (SDLMI) only condition to a SDLMI + Whose Future Is It? (SDLMI + WF) condition. Using multilevel B-spline model analysis with Bayesian estimation, we examined ongoing patterns of growth after the trial ended and all students were exposed to SDLMI + WF. The findings suggest that the inclusion of an additional year of outcome data provided additional insight into the impact of more intensive intervention conditions over time. Specifically, after the initial year of implementation, the SDLMI + WF condition predicted greater annual gains than the SDLMI only condition, unlike findings in the first year which reflected the opposite pattern. This evidence suggests a nonlinear growth pattern over multiple years of intervention with more intensive interventions. Implications for future research and practice are discussed.

Laser-based Thickness Control in a Double-Side Polishing System for Silicon Wafers.

Thickness control is a critical process of automated polishing of large and thin Si wafers in the semiconductor industry. In this paper, an elaborate double-side polishing (DSP) system is demonstrated, which has a polishing unit with feedback control of wafer thickness based on the scan data of a laser probe. Firstly, the mechanical structure, as well as the signal transmission and control of the DSP system, are discussed, in which the thickness feedback control is emphasized. Then, the precise positioning of the laser probe is explored to obtain the continuous and valid scan data of the wafer thickness. After that, a B-spline model is applied for the characterization of the wafer thickness function to provide the thickness control system with credible thickness deviation information. Finally, experiments of wafer-thickness evaluation and control are conducted on the presented DSP system. With the advisable number of control points in B-spline fitting, the thickness variation can be effectively controlled in wafer polishing with the DSP system, according to the experimental results of curve fitting and the statistical analysis of the experimental data.

B-spline sectional model for general 3D effects in reinforced concrete elements

In this paper, an efficient sectional model for the nonlinear analysis of reinforced concrete elements sensible to 3D stress-components effects is presented. The classic plane-sections kinematic hypothesis is enhanced with a warping-distortion displacement field, which enables the model to reproduce the interaction between normal and tangential forces. The complementary field is obtained explicitly considering the inter-fiber equilibrium. This is solved using b-splines interpolation on the cross-section domain. The proposed method significantly reduces the number of unknowns compared with a finite element solution. The model is able to reproduce the interaction of longitudinal and transverse reinforcement with the concrete matrix. The validation shows that the presented model reproduces accurately complex failure modes as pure shear and coupling between bending and torsion. Further, as the transverse reinforcement is considered explicitly, confinement can be simulated in an objective manner. The presented model is an efficient tool for nonlinear analysis of reinforced concrete sections under general loading.

Blood pressure reaction to negative stimuli: Insights from continuous recording and analysis.

Individuals with a tendency toward abnormally enhanced cardiovascular responses to stress are at greater risk of developing essential hypertension later in life. Accurate profiling of continuous blood pressure (BP) reactions in healthy populations is crucial for understanding normal and abnormal emotional reaction patterns. To this end, we examined the continuous time course of BP reactions to aversive pictures among healthy participants. In two experiments, we showed participants negative and neutral pictures while simultaneously measuring their continuous BP and heart rate (HR) reactions. In this study, BP reactions were analyzed continuously, in contrast to previous studies, in which BP responses were averaged across blocks. To compare time points along a temporal continuum, we applied a multi‐level B‐spline model, which is innovative in the context of BP analysis. Additionally, HR was similarly analyzed in order to examine its correlation with BP. Both experiments revealed a similar pattern of BP reactivity and association with HR. In line with previous studies, a decline in BP and HR levels was found in response to negative pictures compared to neutral pictures. In addition, in both conditions, we found an unexpected elevation of BP toward the end of the stimuli exposure period. These findings may be explained by the recruitment of attention resources in the presence of negative stimuli, which is alleviated toward the end of the stimulation. This study highlights the importance of continuous measurement and analysis for characterizing the time course of BP reactivity to emotional stimuli.

A Physical Process Driven Digital Terrain Model Generating Method Based on D-NURBS

Airborne light detection and ranging (LiDAR) technology is becoming the primary method for generating high-resolution digital terrain models (DTMs), which is essential for commercial and scientific uses. In order to generate DTMs, non-ground features as buildings, vehicles, and vegetation must be recognized and distinguished from the LiDAR point cloud. However, various degrees of errors may accumulate in the separated filtering and modeling processes. In this paper, a novel physical process driven DTM generating method for airborne LiDAR measurement is proposed, which combines the point cloud classification and surface fitting process simultaneously. Actually, the physical dynamic process is integrated with the common non-uniform rational b-splines (NURBS) model under the corresponding parameter mediation. The experimental results show that the proposed method is efficacious in reducing errors and have a nice performance in terrain fitting.

Multiuser Detection for Nonlinear MIMO Uplink

For the multiple-input multiple-output (MIMO) uplink employing high-order quadrature amplitude modulation (QAM) signaling and with nonlinear high power amplifiers (HPAs) at mobile users’ transmitters, the existing multiuser detection methods can no longer be applied. We propose a novel nonlinear multiuser detection scheme for the nonlinear MIMO uplink. Specifically, we adopt an effective B-spline parameterization of the nonlinear transmit HPAs and derive an efficient and accurate algorithm to identify the nonlinear MIMO uplink channel, including the nonlinear B-spline model of the nonlinear transmit HPAs and the estimate of the linear MIMO channel matrix. Moreover, as the direct result of this nonlinear MIMO channel identification, the B-spline inverse model of nonlinear transmit HPAs can readily be identified. The nonlinear multiuser detection can be effectively implemented by the zero-forcing linear detection based on the estimated linear MIMO channel and followed by compensating the nonlinear distortion of the nonlinear transmit HPAs based on the estimated B-spline inverse model. An extensive simulation investigation is performed to demonstrate the effectiveness of our proposed nonlinear multiuser detection scheme for nonlinear MIMO uplink with high-order QAM signaling.