Use Of Splines Research Articles

An adaptation of Random Forest to estimate convex non‐parametric production technologies: an empirical illustration of efficiency measurement in education

AbstractThis paper presents a novel approach to conduct non‐parametric estimations of production technologies that adhere to the basic assumptions of production theory axioms, including free disposability in inputs and outputs and convexity. The methodology is rooted in adapting the highly effective machine learning techniques associated with Random Forest and the use of splines. The new method features a piecewise linear estimator analogous to data envelopment analysis (DEA); however, it distinguishes itself by addressing DEA's overfitting and lack of robustness via randomization of data and input variables in the construction of the models. In this paper, the virtues of employing machine learning techniques for assessing the efficiency of public services, particularly in the realm of educational institutions, are underscored. The new approach has the capability to predict outputs based on inputs, even for units not included in the observed sample. Furthermore, it enables the identification of the most relevant inputs in relation to output production. To demonstrate the advantages of our method, an estimation of the educational production function is conducted for Spanish regions utilizing data sourced from the Program for International Student Assessment.

Analysis of the calculated and observed X-X ro-vibrational transition intensities in molecular hydrogen

The potential-energy and quadrupole-moment functions of the H2 ground electronic state are well known in literature (Komasa et al., 2019; Wolniewicz et al., 1998), and the line list of the vibrational–rotational transitions was calculated (Roueff et al., 2019). In this paper, we analyze the calculated intensities in order to learn how the intensities will change when analytic quadrupole-moment functions fitted to the ab initio and experimental data are used instead of spline-interpolated functions. We found that the use of splines does not deteriorate the intensities and does not lead to nonphysical saturation, as in heavier molecules, owing to the high precision of the ab initio data and the high density of the grid. The accuracy of the calculated intensities is estimated up to high overtones. Extraction of new spectroscopic information from the observational data that supplements the laboratory measurements is performed. The laboratory and observational data do not help increase the quality of the analytic functions. Numerous anomalies resulting from the destructive interference are identified in the calculated line lists, some of them being situated within the recently observed spectral regions, 1.5–2.5μm. The intensities of these anomalies can be sensitive to the form of the molecular functions as well as to the proton-to-electron mass ratio. In this connection, the similar Le Roy anomalies (Brown and LeRoy, 1973; Le Roy and Vrscay, 1975) also arising due to the destructive interference in the Lyman and Werner systems are discussed.

Maternal Vitamin D Insufficiency Early in Pregnancy Is Associated with Increased Risk of Preterm Birth in Ethnic Minority Women in Canada

BackgroundMaternal vitamin D insufficiency (plasma 25-hydroxyvitamin D [25(OH)D] <75 nmol/L) may play a role in ethnic disparities in rates of preterm and spontaneous preterm births. ObjectiveWe explored the relation between maternal plasma 25(OH)D concentration in the first trimester (8–14 wk of gestation) and the risk of preterm and spontaneous preterm births (<37 wk of gestation) by ethnicity. MethodsWe designed a case-control study that included 120 cases of preterm birth (<37 wk of gestation) and 360 term controls (≥37 wk of gestation) of singleton pregnancies from the 3D cohort, a multicenter study in 2456 pregnant women in Quebec, Canada. Plasma 25(OH)D was measured by LC–mass spectrometry. We compared the distribution of vitamin D status between cases and controls for 8 ethnic minority subgroups. We explored the association between maternal plasma 25(OH)D concentration and preterm and spontaneous preterm births with the use of splines in logistic regression by ethnicity. ResultsThe distributions of maternal vitamin D status (<50, 50–75, and >75 nmol/L) were different in preterm and spontaneous preterm birth cases compared with controls but only in women of ethnic minority (P-trend = 0.003 and 0.024, respectively). Among ethnic subgroups, sub-Saharan Africans (P-trend = 0.030) and Arab-West Asians (P-trend = 0.045) showed an inverse relation between maternal vitamin D status and the risk of preterm birth. Maternal plasma 25(OH)D concentrations of 30 nmol/L were associated with 4.05 times the risk of preterm birth in the total ethnic minority population (95% CI: 1.16, 14.12; P = 0.028) relative to participants with a concentration of 75 nmol/L. In contrast, there was no such association among nonethnic women (OR: 0.94; 95% CI: 0.48, 1.82; P = 0.85). There was no association when we considered only spontaneous preterm births in the total ethnic minority population (OR: 1.75; 95% CI: 0.39, 7.79; P = 0.46). ConclusionVitamin D insufficiency is associated with an increased risk of preterm birth in ethnic minority women in Canada.

Nonlinear Seasonal and Long-Term Trends in a Twentieth-Century Meteorological Drought Index across the Continental United States

Abstract Analyzing gradual trends in meteorological drought has become increasingly important as anthropogenic climate change and natural climate variability interact to complicate measurement of drought severity. Complex seasonality and long-term trends pose a limitation in understanding spatial trends in nonstationary changes of meteorological drought in the United States. This study seeks to address this issue by simultaneously analyzing recurring seasonal patterns (stationary component) and long-term drought trends (nonstationary component), with a unique focus on nonlinear trends and common regional patterns. We analyzed 696 instrumental precipitation gauges with long historical records in the continental United States, using a novel spline-based model to disaggregate a 3-month meteorological drought index (SPI) into its seasonal and long-term components. The disaggregated components for each gauge were then clustered into subregions with similar seasonality and groupings with similar long-term trends using a two-step process. Our results identify clearly defined regions based on precipitation seasonality, while long-term trends are not spatially coherent with the seasonality. Instead, these findings support prior findings of an increasingly drier western United States and an increasingly wetter eastern United States over the last century, but with more nuanced spatial and temporal patterns. The new clustering analysis based on nonstationary meteorological drought trends can contribute to informing and adapting current water management strategies to long-term drought trends. Significance Statement This study considered 656 precipitation gauges across the continental United States to find regions with similar precipitation seasonality and then to group records with similar long-term climate trends. The study focused on 3-month average precipitation, a key indicator for drought monitoring. We identified eight regions across the United States with similar precipitation seasonality. From 1920 to the present, we found continuous drying trends throughout the western United States, continuously wetter trends in the northern plains, and an overall wetter trend interrupted by a midcentury dry period (1930–50) for much of the central Plains and Midwest. This study’s use of splines, or fitted curves, allowed these nonlinear patterns, which we believe better capture the nuances and intensification of climate change effects on precipitation.

Certain topics in ellipsometric data modeling with splines: a review of recent developments

AbstractDielectric function representation by a variety of polynomial spline functions provides a consistent and efficient method for accurate modeling of the material optical properties in the context of spectroscopic ellipsometry data interpretation. Splines as an elegant and purely mathematical way for such modeling task were introduced about three decades ago. In the following years the use of splines in the area of ellipsometric data analysis became widely utilized. The goal of this review is to provide a self-contained presentation on the current status of the dielectric function modeling by splines for advanced industrial ellipsometry users but, hopefully, it can be useful for some scholarly users as well. It is also intended to promote more extended recognition of the spline-based modeling among optical metrology professionals. Here, a brief description of different ways, – ordinary polynomials, piecewise polynomials (splines), and B(asis)-spline functions, – is presented to parameterize an arbitrary function which can be used as an analytic representation of the dielectric-function curves. A number of particular polynomial-based models for the optical functions of materials and how they may be used in applications are also discussed. Particular attention is paid to different concepts of the efficient and optimal spline construction.

Accuracy and Reproducibility of Myocardial Blood Flow Quantification by Single Photon Emission Computed Tomography Imaging in Patients With Known or Suspected Coronary Artery Disease.

Single photon emission computed tomography (SPECT) has limited ability to identify multivessel and microvascular coronary artery disease. Gamma cameras with cadmium zinc telluride detectors allow the quantification of absolute myocardial blood flow (MBF) and myocardial flow reserve (MFR). However, evidence of its accuracy is limited, and of its reproducibility is lacking. We aimed to validate 99mTc-sestamibi SPECT MBF and MFR using standard and spline-fitted reconstruction algorithms compared with 13N-ammonia positron emission tomography in a cohort of patients with known or suspected coronary artery disease and to evaluate the reproducibility of this technique. Accuracy was assessed in 34 participants who underwent dynamic 99mTc-sestamibi SPECT and 13N-ammonia positron emission tomography and reproducibility in 14 participants who underwent 2 99mTc-sestamibi SPECT studies, all within 2 weeks. A rest/pharmacological stress single-day SPECT protocol was performed. SPECT images were reconstructed using a standard ordered subset expectation maximization (OSEM) algorithm with (N=21) and without (N=30) application of spline fitting. SPECT MBF was quantified using a net retention kinetic model' and MFR was derived as the stress/rest MBF ratio. SPECT global MBF with splines showed good correlation with 13N-ammonia positron emission tomography (r=0.81, P<0.001) and MFR estimates (r=0.74, P<0.001). Correlations were substantially weaker for standard reconstruction without splines (r=0.61, P<0.001 and r=0.34, P=0.07, for MBF and MFR, respectively). Reproducibility of global MBF estimates with splines in paired SPECT scans was good (r=0.77, P<0.001), while ordered subset expectation maximization without splines led to decreased MBF (r=0.68, P<0.001) and MFR correlations (r=0.33, P=0.3). There were no significant differences in MBF or MFR between the 2 reproducibility scans independently of the reconstruction algorithm (P>0.05 for all). MBF and MFR quantification using 99mTc-sestamibi cadmium zinc telluride SPECT with spatiotemporal spline fitting improved the correlation with 13N-ammonia positron emission tomography flow estimates and test/retest reproducibility. The use of splines may represent an important step toward the standardization of SPECT flow estimation.

Method for QOE monitoring and increasing in cellular networks based on QOE-to-QOS mapping using spline approximation

The current level of development of the cellular services market, qualitative changes in the means and methods of providing services, and the increased volume and diversity of information circulating in cellular networks have evoked the need for service quality assessment system improvement. To maintain competitiveness, the main efforts of operators are aimed at improving quality and increasing the service life of subscribers in the network by ensuring the required level of customer satisfaction in high-quality services through a system of organizational–technical and socioeconomic measures to bring the achieved level of quality-of-service (QoS) provision in accordance with the existing, emerging, or projected needs of subscribers. To achieve improved QoS provision, a functional relationship between network parameters has been established: The impact of key performance indicators on a key quality indicator through the use of cubic Hermitian splines (CHS) has been determined. The use of splines, as a signal model, can significantly improve the quality of signal processing due to the continuity of values and partial derivatives in the joints of spline gluing. CHS are characterized by calculation simplicity, as they provide high-speed computing, which, in turn, is important for real-time work when processing large data sets. Experimentally, it was shown that the use of splines allows for the ability to calculate statistical estimates of the required parameters of spline approximations, but also their confidence intervals, which increases the accuracy and probability of further calculations and is a distinct advantage of this approach. Also, the methods of service quality management through machine learning have been improved, which are effective tools for modeling integrated indicators of communication services quality control, monitoring their condition in terms of final copies of services, determining the causes of degradation, and reporting. It monitors the service performance provided by the cellular operator. Finally, the method checks the readiness and availability of services, detects network nodes through which quality degradation occurs, collects various quality metrics, and compares them with pre-installed quality indicators.

AUTOMATION OF CONTROL OF ROOM DEEP OIL PUMP USINGTRACE MODE SCADA SYSTEMS

The issues of automation of technological processes are relevant for all industries. The article discusses the issues of automating the control of the operation of oil pumping units widely used in oil production using the TRACE MODE SCADA system from AdAstrA Research Group.&#x0D; &#x0D; To control the operation of a sucker rod pump of an oil pumping unit, the use of dynamometers is widespread in world practice. Technically, it is easier to carry out a more generalized control of the operation of an oil pumping unit using a wattmetergram, which displays the dependence of the active power consumed by the drive on time or the position of the polished rod. The results of power measurements are transmitted via communication channels to the computer of the SCADA system. Further, preliminary processing of the results of the control of the wattmeter diagram and the calculation of parameters characterizing the operation of the oil pumping unit are performed.&#x0D; &#x0D; At the stage of data preprocessing, noise filtering is performed using TRACE MODE tools that provide data exchange with MS Excel, MS Access, MS Visual Basic packages. The use of moving average, median filtering, and B-splines methods for this is considered. It is shown that cubic B-splines are an effective method of analytical description and graphical representation of experimental data, reducing the total mean square of the error. The use of splines in comparison with the polynomial approximation gives a slightly better approximation. The results of filtering and calculations by means of the SCADA system are displayed on the dispatcher’s monitor, archived, documented, etc. Thus, the related software products SCADA TRACE MODE and MS allow you to effectively implement complex data processing algorithms.

Predicting personalised absolute treatment effects in individual participant data meta-analysis: An introduction to splines.

Modelling non-linear associations between an outcome and continuous patient characteristics, whilst investigating heterogeneous treatment effects, is one of the opportunities offered by individual participant data meta-analysis (IPD-MA). Splines offer great flexibility, but guidance is lacking. To introduce modelling of nonlinear associations using restricted cubic splines (RCS), natural B-splines, P-splines, and smoothing splines in IPD-MA to estimate absolute treatment effects. We describe the pooling of spline-based models using pointwise and multivariate meta-analysis (two-stage methods) and one-stage generalised additive mixed effects models (GAMMs). We illustrate their performance on three IPD-MA scenarios of five studies each: one where only the associations differ across studies, one where only the ranges of the effect modifier differ and one where both differ. We also evaluated the approaches in an empirical example, modelling the risk of fever and/or ear pain in children with acute otitis media conditional on age. In the first scenario, all pooling methods showed similar results. In the second and third scenario, pointwise meta-analysis was flexible but showed non-smooth results and wide confidence intervals; multivariate meta-analysis failed to converge with RCS, but was efficient with natural B-splines. GAMMs produced smooth pooled regression curves in all settings. In the empirical example, results were similar to the second and third scenario, except for multivariate meta-analysis with RCS, which now converged. We provide guidance on the use of splines in IPD-MA, to capture heterogeneous treatment effects in presence of non-linear associations, thereby facilitating estimation of absolute treatment effects to enhance personalized healthcare.

Splines of the Fourth Order Approximation and the Volterra Integral Equations

This paper is a continuation of a series of papers devoted to the numerical solution of integral equations using local interpolation splines. The main focus is given to the use of splines of the fourth order of approximation. The features of the application of the polynomial and non-polynomial splines of the fourth order of approximation to the solution of Volterra integral equation of the second kind are discussed. In addition to local splines of the Lagrangian type, integro-differential splines are also used to construct computational schemes. The comparison of the solutions obtained by different methods is carried out. The results of the numerical experiments are presented.

Image Compression and Enlargement Algorithms

In some cases, there are problems associated with the compression and enlargement of images. The use of splines is quite effective in some cases. In this paper, a new image compression algorithm is presented. The features of increasing the size of an image when using local polynomial or non-polynomial splines are considered. The main method for enlarging an image is based on the use of splines of the second and third order of approximation. Polynomial and trigonometric splines are considered. To speed up the process of enlarging the image, we used the parallelization techniques

Method for Solving the Inverse Problem of the Chemical Kinetics of Multistage Reactions

A method for solving the inverse problem of chemical kinetics based on the data of non-stationary experiments for multistage reactions is described. The method is based on the use of splines, which take into account the relaxation features of reactions with monotone kinetics. Examples of using the method to determine the intervals of physical values of the rate constants of two- and three-stage reactions are given. The influence of the spline structure on error in the determination of rate constants of stages is estimated. The effectiveness of the method for solving the inverse problem of chemical kinetics for multistage reactions is shown with consideration for errors in the determination of experimental data.

Determination of the Relationship between Cell Network Parameters with a Cubic Hermite Spline

One of the most urgent tasks during the organization of cellular networks is the task of improving the quality of service provision by the cellular operator. The paper presents a method for determining the relationship between the cellular network parameters KPI and KQI by using cubic Hermite spline. First of all, the theoretical principle of calculating and constructing a cubic Hermite spline is given in satisfaction of the conditions of the least squares’ method. The use of splines, as a signal model, can significantly improve the quality of signal processing due to the continuity of values and part of the derivatives in the nodes of spline gluing. Cubic Hermite splines, in turn, differ in their simplicity of calculations from the global one, which ensures high performance in computing, which is important for real-time operation when processing large amounts of data.On the basis of this, to evaluate the use of this spline an experimental study was conducted to establish the functional dependence between KPI and KQI network parameters. Namely, within the framework of the work, the Internet access service has been tested on the basis of the use of 3G cellular technology. The experiment consists of 50 experiments. Data was obtained under constant external conditions to ensure the purity of the experiment. On the basis of the measured data for each parameter, the ordinates vector of the spline bonding nodes was calculated and an approximation of the parameters was made using Cubic Hermite splines.The next step is to establish the influence degree of each KPI parameter on the single KQI parameter. The analytical connection coefficients were found taking into account that the mean square error of the KQI parameter prediction from the KPI parameters would be minimal. As a result, on the above data basis, the statistical alignment of the time series of the KQI parameter was performed, that is, it was leveled the KQI physics process using already found KPI approximated parameters.The use of splines allows us to find not only statistical estimates of the desired parameters of the spline approximations, but also their confidence intervals, which increases the accuracy and reliability of the results and it is undoubtedly the advantage of the chosen approach. In our case, this allows you to get a KQI forecast from KPI.In the future, research under such conditions will be followed by the implementation of a specific KPI parameter choice in order to its improvement to improve the quality of service provided to users of the cellular communication operator.Ref. 11, fig. 10.

Bayesian semiparametric modeling for HIV longitudinal data with censoring and skewness.

In biomedical studies, the analysis of longitudinal data based on Gaussian assumptions is common practice. Nevertheless, more often than not, the observed responses are naturally skewed, rendering the use of symmetric mixed effects models inadequate. In addition, it is also common in clinical assays that the patient's responses are subject to some upper and/or lower quantification limit, depending on the diagnostic assays used for their detection. Furthermore, responses may also often present a nonlinear relation with some covariates, such as time. To address the aforementioned three issues, we consider a Bayesian semiparametric longitudinal censored model based on a combination of splines, wavelets, and the skew-normal distribution. Specifically, we focus on the use of splines to approximate the general mean, wavelets for modeling the individual subject trajectories, and on the skew-normal distribution for modeling the random effects. The newly developed method is illustrated through simulated data and real data concerning AIDS/HIV viral loads.

Maternal Vitamin D Insufficiency Early in Pregnancy Is Associated with Increased Risk of Preterm Birth in Ethnic Minority Women in Canada

BackgroundMaternal vitamin D insufficiency (plasma 25-hydroxyvitamin D [25(OH)D] <75 nmol/L) may play a role in ethnic disparities in rates of preterm and spontaneous preterm births. ObjectiveWe explored the relation between maternal plasma 25(OH)D concentration in the first trimester (8–14 wk of gestation) and the risk of preterm and spontaneous preterm births (<37 wk of gestation) by ethnicity. MethodsWe designed a case-control study that included 120 cases of preterm birth (<37 wk of gestation) and 360 term controls (≥37 wk of gestation) of singleton pregnancies from the 3D cohort, a multicenter study in 2456 pregnant women in Quebec, Canada. Plasma 25(OH)D was measured by LC–mass spectrometry. We compared the distribution of vitamin D status between cases and controls for 8 ethnic minority subgroups. We explored the association between maternal plasma 25(OH)D concentration and preterm and spontaneous preterm births with the use of splines in logistic regression by ethnicity. ResultsThe distributions of maternal vitamin D status (<50, 50–75, and >75 nmol/L) were different in preterm and spontaneous preterm birth cases compared with controls but only in women of ethnic minority (P-trend = 0.003 and 0.024, respectively). Among ethnic subgroups, sub-Saharan Africans (P-trend = 0.030) and Arab-West Asians (P-trend = 0.045) showed an inverse relation between maternal vitamin D status and the risk of preterm birth. Maternal plasma 25(OH)D concentrations of 30 nmol/L were associated with 4.05 times the risk of preterm birth in the total ethnic minority population (95% CI: 1.16, 14.12; P = 0.028) relative to participants with a concentration of 75 nmol/L. In contrast, there was no such association among nonethnic women (OR: 0.94; 95% CI: 0.48, 1.82; P = 0.85). There was no association when we considered only spontaneous preterm births in the total ethnic minority population (OR: 1.75; 95% CI: 0.39, 7.79; P = 0.46). ConclusionVitamin D insufficiency is associated with an increased risk of preterm birth in ethnic minority women in Canada.

Spline Based Numerical Method for Heat Conduction Nonlinear Problems Solution

There are many cases in engineering practice when one needs to calculate the transient temperature field in a flat plate. This paper obtains the spline-method grade 3 defect 1 for solve such problems. This method allows simulating the process of thermal conductivity for the infinitely extended plate with temperature-dependent material properties. To conduct an accuracy evaluation of the spline-method the standard problem has been created for one-dimensional infinite flat plane with temperature-dependent material properties, which has the exact analytical solution.This paper shows that the use of splines allows obtaining solutions of transient heat conduction problems with thermal properties dependent on temperature at a relative error less than 1•10-5 that is quite enough in solving many practical problems.

Fitting Cox Models with Doubly Censored Data Using Spline-Based Sieve Marginal Likelihood.

In some applications, the failure time of interest is the time from an originating event to a failure event, while both event times are interval censored. We propose fitting Cox proportional hazards models to this type of data using a spline-based sieve maximum marginal likelihood, where the time to the originating event is integrated out in the empirical likelihood function of the failure time of interest. This greatly reduces the complexity of the objective function compared with the fully semiparametric likelihood. The dependence of the time of interest on time to the originating event is induced by including the latter as a covariate in the proportional hazards model for the failure time of interest. The use of splines results in a higher rate of convergence of the estimator of the baseline hazard function compared with the usual nonparametric estimator. The computation of the estimator is facilitated by a multiple imputation approach. Asymptotic theory is established and a simulation study is conducted to assess its finite sample performance. It is also applied to analyzing a real data set on AIDS incubation time.

Scalable Dynamic Bid Prices for Network Revenue Management in Continuous Time

This study develops an approximate optimal control problem to produce time‐dependent bid prices for the airline network revenue management problem. The main contributions of our study are the analysis of time‐dependent bid prices in continuous time and the use of splines to modify the problem into an approximate second‐order cone program (ASOCP). The spline representation of bid prices permits the number of variables to depend solely on the number of resources and not on the size of the booking horizon. The advantage of this framework is the ASOCP's scalability, which we demonstrate by solving for bid prices on an industrial‐sized network. The numerical experiments highlight the ASOCP's ability to solve industrial sized problems in seconds.

Global optimization with spline constraints: a new branch-and-bound method based on B-splines

This paper discusses the use of splines as constraints in mathematical programming. By combining the mature theory of the B-spline and the widely used branch-and-bound framework a novel spatial branch-and-bound (sBB) method is obtained. The method solves nonconvex mixed-integer nonlinear programming (MINLP) problems with spline constraints to global optimality. A broad applicability follows from the fact that a spline may represent any (piecewise) polynomial and accurately approximate other nonlinear functions. The method relies on a reformulation---convexification technique which results in lifted polyhedral relaxations that are efficiently solved by an LP solver. The method has been implemented in the sBB solver Convex ENvelopes for Spline Optimization (CENSO). In this paper CENSO is compared to several state-of-the-art MINLP solvers on a set of polynomially constrained NLP problems. To further display the versatility of the method a realistic pump synthesis problem of class MINLP is solved with exact and approximated pump characteristics.

Bayesian nonlinear model selection for gene regulatory networks.

Gene regulatory networks represent the regulatory relationships between genes and their products and are important for exploring and defining the underlying biological processes of cellular systems. We develop a novel framework to recover the structure of nonlinear gene regulatory networks using semiparametric spline-based directed acyclic graphical models. Our use of splines allows the model to have both flexibility in capturing nonlinear dependencies as well as control of overfitting via shrinkage, using mixed model representations of penalized splines. We propose a novel discrete mixture prior on the smoothing parameter of the splines that allows for simultaneous selection of both linear and nonlinear functional relationships as well as inducing sparsity in the edge selection. Using simulation studies, we demonstrate the superior performance of our methods in comparison with several existing approaches in terms of network reconstruction and functional selection. We apply our methods to a gene expression dataset in glioblastoma multiforme, which reveals several interesting and biologically relevant nonlinear relationships.