Fitting Approach Research Articles

Allometry and biomass dynamics in temperate mixed and monospecific stands: Contrasting response of Scots pine (Pinus sylvestris L.) and sessile oak (Quercus petraea (Matt.) Liebl.)

Mixed forests generally outperform monospecific forests in terms of productivity, stability, and resilience and are becoming increasingly important for sustainable forest management. However, accurate estimates of tree biomass allocation, as well as aboveground and component biomass in mixed forests, remain scarce. Our study addressed three different objectives to identify differences in biomass between mixed and monocultures and develop biomass models: (1) identification of biomass growth patterns in mixed and monoculture stands using analysis of covariance (ANCOVA), (2) investigation of the best fitting approach to modeling aboveground biomass using logarithmic regression and nonlinear mixed-effects models, and (3) fitting compartment biomass proportion models by Dirichlet regression, considering the additivity property. We analyzed 52 harvested trees from six plots within an experimental triplet in northern Spain, consisting of mixed and single-species stands of Scots pine (Pinus sylvestris L.) and sessile oak (Quercus petraea (Matt.) Liebl.). Moreover, diameter at breast height and tree height were used as covariate variables to determine the most accurate and unbiased models. The research findings showed that (i) allometric patterns of individual-tree biomass in mixed stands significantly differed from those in monospecific stands for sessile oak, while those in Scots pine did not change; (ii) nonlinear mixed-effect models demonstrated a better fit – indicated by lower Furnival index values – than logarithmic regression models in predicting aboveground biomass; and (iii) the fitted biomass equations provided good performance and accurate estimates of biomass component proportions compared to those of existing models. Consequently, our results offer a better understanding of biomass and carbon storage within mixed and monoculture forests in the context of climate change.

Improving standardization and accuracy of in vivo omega plot exchange parameter determination using rotating-frame model-based fitting of quasi-steady-state Z-spectra.

Although Ω-plot-driven quantification of in vivo amide exchange properties has been demonstrated, differences in scan parameters may complicate the fidelity of determination. This work systematically evaluated the use of quasi-steady-state (QUASS) Z-spectra reconstruction to standardize in vivo amide exchange quantification across acquisition conditions and further determined it in vivo. Simulation and in vivo rodent brain chemical exchange saturation transfer (CEST)data at 4.7 T were fit with and without QUASS reconstruction using both multi-Lorentzian and model-based fitting approaches. pH modulation was accomplished both in simulation and in vivo by inducing global ischemia via cardiac arrest. Amide parameters were determined via Ω-plots and compared across methods. Simulation showed that Ω-plots using multi-Lorentzian fitting could underestimate the exchange rate, with error increasing as conditions diverged from the steady state. In comparison, model-based fitting using QUASS estimated the same exchange rate within 2%. These results aligned with in vivo findings where multi-Lorentzian fitting of native Z-spectra resulted in an exchange rate of 64 ± 13 s-1 (38 ± 16 s-1 after cardiac arrest), whereas model-based fitting of QUASS Z-spectra yielded an exchange rate of 126 ± 25 s-1 (49 ± 13 s-1). The model-based fitting of QUASS CEST Z-spectra enables consistent and accurate quantification of exchange parameters through Ω-plot construction by reducing error due to signal overlap and nonequilibrium CEST effects.

Total, Between-, and Within-Item Attribute Person Fit Analysis Using Mokken Scaling Techniques: An Exploratory Nonparametric Approach to Person Fit

The purpose of this study was to consider how researchers can incorporate item attributes into nonparametric person fit analysis for the purpose of providing additional insight into person fit beyond what is available using typical total-scale person fit approaches. Inspired by parametric person fit statistics that consider patterns of residuals at the total-scale, between-item-attribute, and within-item-attribute levels, we proposed simple adaptations to standard Mokken Scale Analysis (MSA) person fit analysis techniques to reflect these three levels of person fit analysis. We demonstrated the technique using a secondary analysis of survey data related to learning motivation and considered how the results may be interpreted in an affective assessment context. We used a simple exploratory simulation study to consider the techniques under a wider range of conditions. Overall, the results suggested that it is possible to incorporate item attributes into MSA person fit analysis at the total-scale, between-item-attribute, and within-item attribute levels, and that each set of analyses provides a unique perspective on person fit.

Reward shaping via expectation maximization method

Reinforcement Learning (RL) has found widespread applications in various decision making tasks. However, it still faces challenges such as the deadly triad, slow convergence, and rewards drop, which limit its practical scope. This paper primarily addresses the issues of slow convergence and rewards drop observed during RL training. Our proposed solution involves a reward shaping method composed of two distinct components, each serving a specific purpose: speeding up training and enhancing stability. These two components are interconnected through hyper-parameters, and it has been observed that the choice of hyper-parameters plays a critical role in determining the final performance of the RL algorithm. To optimize these hyper-parameters effectively, we employ a discrete sampling technique to cover the value ranges of these parameters. This discrete sampling creates a sparse set of data points within the reward matrix. Subsequently, we introduce a fitting approach based on the Expectation Maximization (EM) algorithm to estimate the global maximum of the reward matrix along with the corresponding hyper-parameters combination. This EM method significantly reduces computational complexity. Our extensive experimental results across various RL environments have demonstrated the effectiveness of our proposed method. It successfully mitigates the issue of rewards drop while simultaneously accelerating the convergence speed of the RL algorithm.

Interpretation of complex x-ray photoelectron peak shapes. II. Case study of Fe 2p3/2 fitting applied to austenitic stainless steels 316 and 304

In this paper, a review of the analysis of Fe 2p3/2 peak and other transition metals in the austenitic stainless steel literature is presented. It reveals the significant shortcomings of the most widely used approaches, based on the principle of “chemistry fitting,” where single symmetric peaks are used to represent either individual oxidation states or specific compounds. No meaningful conclusions can be drawn from these commonly employed two- or three-component peak fitting (2C and 3C) approaches; the implication being that a large portion of the literature that relies on this approach is flawed. As a significantly more accurate and reliable alternative to “chemistry fitting,” we also assess “envelope fitting” (using empirical multiplet structures) and examine its limitations when applying the approach to austenitic stainless steel data. A detailed comparison of these two fitting approaches is described in Part I. For other elements such as Cr 2p, the problems associated with using single components to represent oxidation states or compounds are not as severe. It was found that it does not impact binding energy measurements, but does influence relative intensities, which will have a flow-on effect for oxide thickness calculations and obtaining a correct understanding of the surface more broadly.

Interpretation of complex x-ray photoelectron peak shapes. I. Case study of Fe 2p3/2 spectra

Analyzing transition metal XPS peaks is widely used to determine surface composition and chemistry. However, these peaks have a complex structure, which is still the subject of investigation. Fe 2p analysis is a case in point where the multiplet structure and many-electron-effects lead to peak shapes that cannot be analyzed using standard approaches. Examination of the literature reveals that one of the most widely used approaches to data reduction when processing Fe 2p3/2 spectra involves using symmetric two- or three-component peak fitting with each peak effectively acting to capture a single chemical species (chemistry fit) in the complex spectra. Herein, this approach is compared to an envelope fit approach using Biesinger multiplet components of known iron oxides to determine how effective these methods are in reproducing iron oxide composition. Mixed oxide and metal XPS Fe 2p spectra were synthesized using reference spectra collected experimentally. For the first time, the accuracy and differences between the two approaches are reported. It is demonstrated that no meaningful conclusions can be drawn using single symmetric peaks to analyze complex Fe 2p3/2 spectra, implying that a large portion of the literature is flawed. The envelope fit approach, however, is shown to provide useful information regarding oxide ratios in mixed iron oxide materials, though limitations do exist. A methodology for evaluating the quality of XPS analysis of Fe 2p3/2 spectra is proposed for benchmarking new submissions so that reviewers, authors, and editors can assess these submissions.

Accurate two-step random phase retrieval approach without pre-filtering based on hyper ellipse fitting

In this work, we propose a hyper ellipse fitting-based high-precision random two-frame phase shifting algorithm to improve the accuracy of phase retrieval. This method includes a process of Gram-Schmidt orthonormalization, followed by a hyper ellipse fitting procedure. The Gram-Schmidt orthonormalization algorithm constructs a quadrature fringe pattern relative to the original fringe pattern. These two quadrature fringe patterns are then fed into the hyper ellipse fitting procedure, which reconstructs the phase map and refines the background light to produce the final accurate phase of interest. Due to the hyper ellipse fitting procedure, the demodulation results are significantly improved in many cases. This method allows us to design a two-shot phase reconstruction algorithm without the need for least squares iteration or pre-filtering, effectively mitigating residual background to the greatest extent. It combines the advantages of both the Gram-Schmidt orthonormalization method and the Lissajous ellipse fitting method, making our hyper ellipse fitting approach a simple, flexible, and accurate phase retrieval algorithm. Experiments show that by using the weighted least squares method and adjusting the weights, this method can prioritize data points with more significant information or higher reliability, ensuring more accurate estimation of the ellipse parameters.

Determining the thickness of a thin aluminum sheet using the transmission measurement of X-rays with varying energies: A comparative analysis between calibration curve fitting and artificial neural network approaches

This study proposes an innovative configuration for thickness measurement based on X-ray transmission, intending to improve the precision of measuring thin aluminum sheets. In this configuration, an activation sample containing Zr, Sb, and Ba elements is irradiated by 59.54 keV gamma rays emitted from three 241Am radioactive sources with a total activity of 1.78 GBq. Subsequently, the activation sample emits fluorescent X-rays at energy levels of 15.78 keV (Zr-Kα1,2), 17.67 keV (Zr-Kβ1), 26.36 keV (Sb-Kα1,2), 29.73 keV (Sb-Kβ1), 32.2 keV (Ba-Kα1,2), and 36.38 keV (Ba-Kβ1). These X-rays are collimated into a narrow beam, which then penetrates through an absorbing sample, and is ultimately recorded by a Si(Li) detector. Two different approaches are investigated to determine the thickness of absorbing samples including Calibration Curve Fitting (CCF) and Artificial Neural Network (ANN). The CCF approach requires constructing linear calibration curves for establishing the relationship between lnR (R is the ratio of the peak areas in measurements with and without absorbing sample) and the thickness of the absorbing sample at each X-ray energy level. The sample thickness is then determined by calculating a weighted average of the measured thicknesses associated with all analyzed energy levels. This approach requires in-depth understanding of radiation physics and proficiency in X-ray spectrum analysis. Meanwhile, the ANN approach uses raw spectra obtained by the Si(Li) detector to predict the thickness of aluminum sheets, facilitating analysis without requiring human intervention. The reliability of these approaches is evaluated through experimental measurements on aluminum sheets with thicknesses ranging from 0.064 cm to 1.074 cm. The results indicate that using X-rays with many different energies leads to superior accuracy in thickness measurements compared to using X-rays with a single energy. Besides, both the CCF and ANN approaches yield relative deviations of less than 3% between the predicted and reference thicknesses. It is important to emphasize that the ANN approach represents a promising solution for automated analysis without the intervention of experts.

Isothermal crystallization kinetics of commercial PA66 and PA11

AbstractThis study is aimed at investigating the crystallization kinetics of two structurally related polymers, Nylon 6,6 (PA66) and Nylon 11 (PA11), by differential scanning calorimetry (DSC) in the scope of a logistic-based model using a model fitting approach. By this method, the values of the rate parameters for each specific temperature are obtained from fitting all points of the crystallization exotherm that were accurately recorded at that temperature. This method differs from Arrhenius-based model fitting approaches, in which the initial and final parts of the exotherm do not usually match the shape of Arrhenius-based models and are therefore discarded for fitting. Furthermore, in other kinetic approaches that fall outside the scope of this article, kinetic parameters are typically obtained from specific points in the crystallization exotherm, and good fits cannot generally be obtained nor is that the goal of those approaches. The DSC curves of both polymers obtained at different temperatures are analysed to determine the crystallization kinetics. One of the most insightful parameters of the model is the crystallization rate. Its dependence on temperature is analysed for both polymers and compared to others. The other parameters can also help to better understand some of the crystallization features of these polymers. In addition, the information retrieved from this study can be useful to adjust processing conditions.

(Invited) Evolution of the Solid Electrolyte Interphase in Si Nanoparticle Based Li-Ion Battery Anodes: Insights from Ab Initio Simulations of Core-Level Spectroscopies

Silicon nanoparticles (c-Si NPs) are considered promising candidates for the active material in Si-based anodes, offering high gravimetric capacity and helping to mitigate volume expansion effects. However, the formation of an unstable Solid Electrolyte Interphase (SEI) around the nanoparticles leads to increased irreversible lithium consumption, resulting in reduced capacity and poor cycling stability. In this context, core-level spectroscopies are established techniques to assess the evolution and composition of the SEI. While X-ray spectroscopies provide valuable insights into atomic and electronic structures, interpreting them in complex systems could be challenging, highlighting the need of theoretical insights from ab-initio approaches. Our study focuses on the changes occurring in c-Si NPs and the SEI during the initial charge cycle, leveraging post-mortem core-level spectra at various states of charge (SOC). We employ a multi-edge analysis coupled with a fitting approach based on known experimental references and theoretical simulations. Additionally, we demonstrate how comparing experimental spectra with theoretical references allows tracking changes at the NP level, including amorphization and surface oxidation. Finally, we discuss some of the limitations of our theoretical description and propose addressing them through machine learning approaches. This work is supported by the European Union’s Horizon 2020 research and innovation program (BIG-MAP, Grant No. 957189, also part of the BATTERY 2030+ initiative, Grant No. 957213).

Minimum spouting velocity of fine particles in fountain confined conical spouted beds using machine learning and least square fitting approaches

AbstractThe present study concerns the development of new models to estimate the minimum spouting velocity (Ums) in various configurations of fountain‐confined conical spouted beds (FC‐CSBs) with fine particles. Existing literature correlations were found to be inaccurate for FC‐CSBs. Therefore, smart modelling techniques were employed to design more accurate predictive tools. The radial basis function (RBF) approach provided the best predictions for systems without draft tubes as well as those with open‐sided draft tubes. Additionally, the Gaussian process regression (GPR) approach yielded the best predictions for systems with nonporous draft tubes. The mean absolute percentage error (MAPE) values for the testing phase were 5.80%, 5.67%, and 5.59%, respectively. These models consider how bed shape and particle properties affect Ums. The sensitivity analysis was conducted to determine the factors with more importance in controlling Ums. Finally, simpler correlations were derived for Ums prediction in different FC‐CSB configurations, with accuracy around 12% error.

Exploring Entropy Measures with Topological Indices on Subdivided Cage Networks via Linear Regression Analysis

ABSTRACT In this study, we investigate entropy measurements for subdivided cage networks based on topological indices. We specifically calculate different entropy, redefining Zagreb entropy, HM ( G ) , M 1 ( G ) , M 2 ( G ) entropy, atom bond connection entropy, and Randic entropy. We examine the graphical behavior of various entropy measures using the line fit approach. The results highlight patterns in the distribution of entropy values and interactions between them, which shed light on the intricate connectivity and structural properties of segmented cage networks. This work improves our understanding of cage network dynamics and provides a visual framework for interpreting their behavior.

On curve fitting between topological indices and Gibb’s energy for semiconducting carbon nitrides network

Quantitative structure relationships linked to a chemical structure that shed light on its properties and chemical reactions are called topological indices. This structure is upset by the addition of silicon (Si) doping, which changes the electrical and optical characteristics. In this article, we examine the connection between a chemical structure’s Gibbs energy (GE) and K-Banhatti indices. In this article, we compute the K-Banhatti indices and then show the correlation between the indices and Gibb’s energy of the molecule using curve fitting. Through the curve fitting, we see that there is a strong correlation between indices and Gibb’s energy of a molecule. We use the polynomial curve fitting approach to see the correlation between indices and Gibb’s energy.

Examination of nonlinear associations between pulse pressure index and incident prediabetes susceptibility: a 5-year retrospective cohort investigation

Prediabetes and related complications constitute significant public health burdens globally. As an indicator closely associated with abnormal glucose metabolism and atherosclerosis, the utility of Pulse Pressure Index (PPI) as a prediabetes risk marker has not been explored. We performed a retrospective cohort analysis to investigate this putative association between PPI and prediabetes hazard. Our analysis encompassed 183,517 Chinese adults ≥ 20 years registered within the Rich Healthcare Group 2010–2016. PPI was defined as (systolic blood pressure − diastolic blood pressure)/systolic blood pressure. The relationship between PPI and prediabetes risk was assessed via Cox proportional hazards regression modeling. Non-linearity evaluations applied cubic spline fitting approaches alongside smooth curve analysis. Inflection points of PPI concerning prediabetes hazard were determined using two-piecewise Cox models. During a median follow-up of 3 years (2.17–3.96 years), new-onset prediabetes was documented in 20,607 patients (11.23%). Multivariate regression analysis showed that PPI was an independent risk factor for prediabetes, and the risk of prediabetes increased by 0.6% for every 1% increase in PPI (Hazard Ratio [HR]: 1.006, 95% Confidence Interval [CI] 1.004–1.008, P < 0.001). This association was non-significant for PPI ≤ 37.41% yet exhibited a sharp upsurge when PPI surpassed 37.41% (HR: 1.013, 95% CI 1.005–1.021, P = 0.0029). Our analysis unveils a positive, non-linear association between PPI and future prediabetes risk. Within defined PPI ranges, this relationship is negligible but dramatically elevates beyond identified thresholds.

Integrating Genomic Insights with Vocational Interests: A Gene-Occupation Fit Approach

Integrating Genomic Insights with Vocational Interests: A Gene-Occupation Fit Approach

A novel method for fitting the electric field inside a hemispherical radon monitor to accurately estimate the collection efficiency of 218Po

The collection efficiency of the hemispherical radon monitors based on electrostatic collection is strongly influenced by the electric field distribution and the relative humidity. Previous studies have been restricted to fitting the electric field using a single-segment, resulting in poor fitting optimality and accuracy. Overestimating or underestimating the fitted value relative to the true value can lead to inaccuracies in estimating the collection efficiency. To address this problem, the aim of this paper is to accurately characterize the electrostatic field of the hemispherical radon monitors using COMSOL software and to fit the potential in a segmented fitting approach. The two-segment fitting method was employed to divide the electric field inside the hemispherical radon monitor into two distinct parts for fitting. The improved fitting model increase the goodness-of-fit by 11.6% over the single-segment fitting model, and improves the accuracy of the collection efficiency of 218Po at different humidity levels. The saturation collection efficiency is also raised, especially when the humidity is greater than 10%, the saturation collection efficiency is increased by 9.2%. Through the improved method, the collection efficiency of 218Po in the hemispherical radon monitor can be accurately estimated and provide technical support for optimizing the electric field of the radon monitor.

Oceanic Mesoscale Eddy Fitting Using Legendre Polynomial Surface Fitting Model Based on Along-Track Sea Level Anomaly Data

Exploring the spatial distribution of sea surface height involves two primary methodologies: utilizing gridded reanalysis data post-secondary processing or conducting direct fitting along-track data. While processing gridded reanalysis data may entail information loss, existing direct fitting methods have limitations. Therefore, there is a pressing need for novel direct fitting approaches to enhance efficiency and accuracy in sea surface height fitting. This study demonstrates the viability of Legendre polynomial surface fitting, benchmarked against bicubic quasi-uniform B-spline surface fitting, which has been proven to be a well-established direct fitting method. Despite slightly superior accuracy exhibited by bicubic quasi-uniform B-spline surface fitting under identical order combinations, Legendre polynomial surface fitting offers a simpler structure and enhanced controllability. However, it is pertinent to note that significant expansion of the spatial scope of fitting often results in decreased fitting efficacy. To address this, the current research achieves the precise fitting of sea surface height across expansive spatial ranges through a regional stitching methodology.

Carbon fibre detection in polymer composites reinforced by chopped carbon fibres through digital image processing and machine learning

Mechanical and thermodynamical properties and thus machinability of carbon fibre reinforced polymer composites significantly depend on the fibre orientation relative to the load direction. However, the orientations of the fibre groups in polymer composites reinforced by chopped carbon fibres are stochastic; therefore, the properties and machinability of such composites are challenging to plan, predict and optimise. We developed four different and novel approaches for fibre detection in polymer composites reinforced by chopped carbon fibres: (i) detecting the fibres through naked eye supported manual drawing, (ii) digital image processing of optical images, (iii) machine learning-based fibre detection, and (iv) rectangle fitting on the outputs of the automated processes using the Chaudhuri and Samal method. The applicability of the novel approaches was tested through optically captured images of polymer composites reinforced by chopped carbon fibres. The developed methods are each capable of detecting fibre groups at the top and bottom of the composite plate with certain limitations. The rectangle fitting approaches performed the best from the point of view of correctly identifying of fibre groups, followed by the machine learning-based and the conventional digital image processed, respectively. As a result of this study, the machining process planning and condition monitoring of polymer composites reinforced by chopped carbon fibres is more deeply supported.

Error Correction of the RapidEye Sub-Pixel Correlation: A Case Study of the 2019 Ridgecrest Earthquake Sequence.

The optical image sub-pixel correlation (SPC) technique is an important method for monitoring large-scale surface deformation. RapidEye images, distinguished by their short revisit period and high spatial resolution, are crucial data sources for monitoring surface deformation. However, few studies have comprehensively analyzed the error sources and correction methods of the deformation field obtained from RapidEye images. We used RapidEye images without surface deformation to analyze potential errors in the offset fields. We found that the errors in RapidEye offset fields primarily consist of decorrelation noise, orbit error, and attitude jitter distortions. To mitigate decorrelation noise, the careful selection of offset pairs coupled with spatial filtering is essential. Orbit error can be effectively mitigated by the polynomial fitting method. To address attitude jitter distortions, we introduced a linear fitting approach that incorporated the coherence of attitude jitter. To demonstrate the performance of the proposed methods, we utilized RapidEye images to extract the coseismic displacement field of the 2019 Ridgecrest earthquake sequence. The two-dimensional (2D) offset field contained deformation signals extracted from two earthquakes, with a maximum offset of 2.8 m in the E-W direction and 2.4 m in the N-S direction. A comparison with GNSS observations indicates that, after error correction, the mean relative precision of the offset field improved by 92% in the E-W direction and by 89% in the N-S direction. This robust enhancement underscores the effectiveness of the proposed error correction methods for RapidEye data. This study sheds light on large-scale surface deformation monitoring using RapidEye images.

Empirical Model Variability: Developing a new global optimisation approach to populate compression and compaction mixture rules

This study systematically evaluated the predictive accuracy of common empirical models for pharmaceutical powder compaction. A dataset of nine placebo and twelve active pharmaceutical ingredient (API) loaded blend formulations (four APIs at three drug loadings) was fitted to the widely used empirical tablet compression (Gurnham, Heckel, and Kawakita) and compaction (Ryshkewitch-Duckworth and Leuenberger) models. At low API loadings (<20w/w%), all models achieved R2 above 90 % and RRMSE (relative root mean squared error) below 0.1. However, as API loads increased, overall model performance decreased, notably in the Heckel model. A parameter variability analysis identified multiple parameter pairs achieving acceptable fits. Consequently, a novel global optimization approach was developed populating arithmetic, geometric, and harmonic mixture rules for empirical tuning parameters. This method outperformed the traditional line of best fit approach. A cross validation study revealed that this method is capable of predicting tuning parameters which achieve an acceptable Goodness of Fit for new blends. Finally, with the restriction of maintaining consistent parameters for the placebo blend, the proposed method could substantially reduce the experimental requirements and API consumption for the exploration of new blends.