Quantification Model Research Articles

Estimating Extreme Drought Risk Through Classical and Bayesian Paradigms

ABSTRACTDrought poses significant challenges to both the environment and the economy, necessitating proactive mitigation strategies. This study introduces both classical and Bayesian Markov Chain Monte Carlo (MCMC) extreme value probabilistic models for quantifying drought risk. The models utilise the generalised extreme value (GEV) distribution to characterise the distribution of standardised precipitation index (SPI) and non‐stationary standardised precipitation index (NSSPI) variables. Drought risk is probabilistically assessed across five regions in Baluchistan (a drought‐prone area of Pakistan) over two 20‐year periods per region. The study presents a novel approach in probabilistic quantification models, demonstrating slight performance improvement with the Bayesian MCMC paradigm, as evaluated by the continuously ranked probability scoring. Moreover, the application of the presented methodology can be extended to other climatic zones using Bayesian MCMC with informative priors constructed from historical records of the neighbouring regions.

Machine learning materials properties with accurate predictions, uncertainty estimates, domain guidance, and persistent online accessibility

Abstract One compelling vision of the future of materials discovery and design involves the use of machine learning (ML) models to predict materials properties and then rapidly find materials tailored for specific applications. However, realizing this vision requires both providing detailed uncertainty quantification (model prediction errors and domain of applicability) and making models readily usable. At present, it is common practice in the community to assess ML model performance only in terms of prediction accuracy (e.g. mean absolute error), while neglecting detailed uncertainty quantification and robust model accessibility and usability. Here, we demonstrate a practical method for realizing both uncertainty and accessibility features with a large set of models. We develop random forest ML models for 33 materials properties spanning an array of data sources (computational and experimental) and property types (electrical, mechanical, thermodynamic, etc). All models have calibrated ensemble error bars to quantify prediction uncertainty and domain of applicability guidance enabled by kernel-density-estimate-based feature distance measures. All data and models are publicly hosted on the Garden-AI infrastructure, which provides an easy-to-use, persistent interface for model dissemination that permits models to be invoked with only a few lines of Python code. We demonstrate the power of this approach by using our models to conduct a fully ML-based materials discovery exercise to search for new stable, highly active perovskite oxide catalyst materials.

Study on quantitative interpretation of uranium spectral gamma-ray logging based on machine learning algorithm

Spectral gamma-ray logging stands out as an efficacious methodology in the exploration of uranium(U). In order to address the challenges associated with low statistical efficacy in spectral analysis and mitigate the impact of spectral drift, machine learning algorithms such as Back Propagation (BP) neural network, Generalized Regression Neural Network (GRNN), and Support Vector Machine (SVM) have been employed for the quantitative interpretation of uranium. A method rooted in machine learning algorithms for energy spectral analysis has been proposed, catering to the analysis of high-speed spectra logging and gamma-ray spectra characterized by spectral drift. Examinations conducted on standard model wells containing uranium revealed that the BP neural network exhibited commendable accuracy in uranium interpretation, achieving quantification accuracy rates of 86.986 % and 93.478 % for low-grade and medium-high-grade uranium ores in the Testing Set, respectively. Notably, marginal variations in the model's quantification errors were observed under diverse logging speeds and spectral drift conditions, underscoring the capacity of gamma-ray spectral quantitative interpretation through machine learning algorithms to effectively surmount the impacts of logging speed and spectral drift. This machine learning-based approach to energy spectral analysis proved instrumental in enhancing traditional logging speeds to 6 m/min, presenting a novel perspective for the quantitative interpretation of uranium spectral gamma-ray logging at heightened logging speeds.

Identification of perceptive users based on the graph convolutional network

In this paper, we introduce a pioneering approach titled Identifying Perceptive Users based on Graph Convolutional Networks (IPGCN), tailored specifically for user-object bipartite networks. Our methodology incorporates rating behavior into the graph convolutional network framework, crafting a feature matrix that encapsulates the intricacies of user preferences. This feature matrix is meticulously constructed using a breadth-first search algorithm, grounded in user rating attributes, effectively transforming the bipartite network into a compact, low-dimensional vector space. This transformation not only serves as the input for our graph convolutional network but also meticulously preserves the topological structure and interconnectivity of the nodes. Furthermore, we introduce a novel training paradigm by leveraging the classification outcomes from a perceptive user quantification model. This model discriminates between perceptive users, defined as the top q% (with 0 <q< 1) most insightful users based on their ratings, and non-perceptive users. This binary classification serves as the ground truth for training our IPGCN model. Through rigorous experimentation on three real-world datasets, we demonstrate that our IPGCN method outperforms traditional machine learning algorithms like SVM, XGBoost, and Random Forest, as well as state-of-the-art graph neural network approaches including GCN and GAT. Specifically, when q = 5%, our method achieves remarkable improvements of 25.28% in Accuracy, 23.34% in F1 Score, and 25.30% in AUC, highlighting the efficacy and superiority of our proposed IPGCN approach in identifying perceptive users within complex bipartite networks.

Research on the Construction and Application of a SVM-Based Quantification Model for Streetscape Visual Complexity

Visual complexity is a crucial criterion for evaluating the quality of urban environments and a key dimension in arousal theory and visual preference theory. Objectively quantifying visual complexity holds significant importance for decision-making support in urban planning. This study proposes a visual complexity quantification model based on a support vector machine (SVM), incorporating six key indicators, to establish a mapping relationship between objective image features and subjective complexity perception. This model can efficiently and scientifically predict street view complexity on a large scale. The research findings include the following: (1) the introduction of a new quantification dimension for the urban environment complexity—hierarchical complexity– which reflects the richness of street elements based on an in-depth semantic understanding of images; (2) the established complexity quantification model demonstrates high accuracy, with the indicators ranked by contribution for compression ratio, grayscale contrast, hierarchical complexity, fractal dimension, color complexity, and symmetry; and (3) the model was applied to predict and analyze the visual complexity of the Xiaobailou and Wudadao Districts in Tianjin, revealing that the visual complexity of most streets is moderate, and targeted recommendations were proposed based on different levels of visual complexity.

Deep learning-based algorithm for automatic quantification of nigrosome-1 and Parkinsonism classification using susceptibility map-weighted MRI.

To develop and validate a deep learning-based automatic quantification for nigral hyperintensity and a classification algorithm for neurodegenerative parkinsonism using susceptibility map-weighted imaging (SMwI). We retrospectively collected 450 participants (210 with idiopathic Parkinson's disease [IPD] and 240 individuals in the control group) for training data between November 2022 and May 2023, and 237 participants (168 with IPD, 58 with essential tremor, and 11 with drug-induced Parkinsonism) for validation data between July 2021 and January 2022. SMwI data were reconstructed from multi-echo GRE. Diagnostic performance for diagnosing IPD was assessed using deep learning-based automatic quantification (Heuron NI) and classification (Heuron IPD) model. Reference standard for IPD was based on 18F-FP-CIT PET finding. Additionally, the correlation between the H&Y stage and volume of nigral hyperintensity in patients with IPD was assessed. Quantification of nigral hyperintensity using Heuron NI showed AUC of 0.915 (95% CI, 0.872-0.947) and 0.928 (95% CI, 0.887-0.957) on the left and right, respectively. Classification of nigral hyperintensity abnormality using Heuron IPD showed AUC of 0.967 (95% CI, 0.881-0.991) and 0.976 (95% CI, 0.948-0.992) on the left and right, respectively. H&Y score ≥ 3 showed significant smaller nigral hyperintensity volume (1.43 ± 1.19 mm3) compared to H&Y score 1-2.5 (1.98 ± 1.63 mm3; p = 0.008). Our deep learning-based model proves rapid, accurate automatic quantification of nigral hyperintensity, facilitating IPD diagnosis, symptom severity prediction, and patient stratification for personalized therapy. Further study is warranted to validate the findings across various clinical settings. IPD = Idiopathic Parkinson's disease; SN = substantia nigra; SMwI = susceptibility map weighted imaging; QSM = quantitative susceptibility mapping; CNN = convolutional neural network; ICV = intracranial volume.

In-situ impedance diagnosis experiment and equivalent circuit modeling based on distribution of relaxation time method for unitized regenerative proton exchange membrane fuel cells

The Distribution of Relaxation Times (DRT) method provides a powerful approach for analyzing Electrochemical Impedance Spectroscopy (EIS) in electronic components, enabling clear separation of different impedance types and accurate equivalent circuit modeling. In this study, the DRT method was applied to unitized regenerative proton exchange membrane fuel cells (UR-PEMFCs) for the first time, establishing an impedance quantification model for in-situ diagnostics of multiple impedances. This foundational framework supports future durability testing efforts. In-situ impedance diagnostics were conducted in both Fuel Cell (FC) and Electrolytic Cell (EC) modes using a custom mode-switching platform. Results show that under constant electrode conditions, the bifunctional membrane electrode enhances round-trip efficiency by 15.75% compared to the constant gas mode. Through DRT imaging in FC and EC modes, impedance information corresponding to distinct relaxation peaks was extracted and assigned based on operational experiments. The three main peaks identified in both modes were attributed to proton transfer impedance, charge transfer impedance, and mass transfer impedance. Additionally, variations in operating conditions led to the appearance of new transport mechanisms within the charge transfer impedance. In FC mode, the DRT-based equivalent circuit model achieved precise fitting. Applying DRT to UR-PEMFCs improves water and bubble management, offering efficient optimization pathways and valuable guidance for cell design, operational parameter refinement, and durability monitoring.

Integrating Machine Learning and Traditional Models for Financial Risk Quantification

This study explores the integration of machine learning techniques with traditional financial risk measurement models to enhance the accuracy and robustness of risk quantification. By employing models such as Value at Risk (VaR) and GARCH alongside machine learning algorithms like Random Forest and Neural Networks, the research demonstrates improved prediction accuracy across various market conditions. The findings highlight the advantages of an integrated approach, which not only provides a comprehensive framework for financial risk assessment but also bridges the gap between theoretical models and practical applications. This work contributes to the evolving landscape of financial risk management by offering insights into effective model integration, thereby paving the way for future research in advanced risk quantification strategies.

Uncertainty Quantification in the Prediction of Remaining Useful Life Considering Multiple Failure Modes

Abstract Despite the substantive literature on remaining useful life (RUL) prediction, less attention is paid to the influence of epistemic uncertainty and aleatory uncertainty in multiple failure behaviors in the accuracy of RUL. The research question in this study was: can uncertainties be quantified in predicting the RUL of systems with multiple failure modes? The first objective was to quantify the uncertainties in the prediction of RUL, considering known multiple failure modes. This objective used vibration data from accelerated degradation experiments of rolling element bearings. The second objective was to calculate the uncertainties in the prediction of RUL, considering the multiple failure modes as unknown. The experimental data used in this objective were from run-to-failure tests of Li-ion batteries. An analysis was performed on how the uncertainties affect the RUL prediction in systems with known multiple failure modes and systems where the multiple failure modes were unknown. A Bayesian neural network (BNN) was used to quantify epistemic and aleatory uncertainty while predicting RUL. The results of the qualitative uncertainties on RUL in systems with multiple failure modes were presented and discussed. Also, the study yielded an RUL uncertainty quantification model for multiple failure modes. The proposed framework's performance in the RUL prediction was demonstrated. Finally, the epistemic and aleatory uncertainties were quantified in the system's RUL. It was shown that systems that fail due to the same failure mode tend to have similar uncertainty values over time. The results in this paper may lead to the design of more reliable systems that exhibit multiple failure modes.

A Space Mapping Augmented Compact Model for Uncertainty Quantification of GaN HEMT Devices and Circuits in the Presence of Trap Effects

A Space Mapping Augmented Compact Model for Uncertainty Quantification of GaN HEMT Devices and Circuits in the Presence of Trap Effects

Automatic 3-dimensional quantification of orthodontically induced root resorption in cone-beam computed tomography images based on deep learning

Orthodontically induced root resorption (OIRR) is a common and undesirable consequence of orthodontic treatment. Traditionally, studies employ manual methods to conduct 3-dimensional quantitative analysis of OIRR via cone-beam computed tomography (CBCT), which is often subjective and time-consuming. With advancements in computer technology, deep learning-based approaches have gained traction in medical image processing. This study presents a deep learning-based model for the fully automatic extraction of root volume information and the localization of root resorption from CBCT images. In this cross-sectional, retrospective study, 4534 teeth from 105 patients were used to train and validate an automatic model for OIRR quantification. The protocol encompassed several steps: preprocessing of CBCT images involving automatic tooth segmentation and conversion into point clouds, followed by segmentation of tooth crowns and roots via the Dynamic Graph Convolutional Neural Network. The root volume was subsequently calculated, and OIRR localization was performed. The intraclass correlation coefficient was employed to validate the consistency between the automatic model and manual measurements. The proposed method strongly correlated with manual measurements in terms of root volume and OIRR severity assessment. The intraclass correlation coefficient values for average volume measurements at each tooth position exceeded 0.95 (P<0.001), with the accuracy of different OIRR severity classifications surpassing 0.8. The proposed methodology provides automatic and reliable tools for OIRR assessment, offering potential improvements in orthodontic treatment planning and monitoring.

Leveraging pre-trained machine learning models for islet quantification in type 1 diabetes

Human islets display a high degree of heterogeneity in terms of size, number, architecture, and endocrine cell-type compositions. An ever-increasing number of immunohistochemistry-stained whole slide images (WSIs) are available through the online pathology database of the Network for Pancreatic Organ donors with Diabetes (nPOD) program at the University of Florida (UF). We aimed to develop an enhanced machine learning-assisted WSI analysis workflow to utilize the nPOD resource for analysis of endocrine cell heterogeneity in the natural history of type 1 diabetes (T1D) in comparison to donors without diabetes. To maximize usability, the user-friendly open-source software QuPath was selected for the main interface. The WSI data were analyzed with two pre-trained machine learning models (i.e., Segment Anything Model (SAM) and QuPath's pixel classifier), using the UF high-performance-computing cluster, HiPerGator. SAM was used to define precise endocrine cell and cell grouping boundaries (with an average quality score of 0.91 per slide), and the artificial neural network-based pixel classifier was applied to segment areas of insulin- or glucagon-stained cytoplasmic regions within each endocrine cell. An additional script was developed to automatically count CD3+ cells inside and within 20 μm of each islet perimeter to quantify the number of islets with inflammation (i.e., CD3+ T-cell infiltration). Proof-of-concept analysis was performed to test the developed workflow in 12 subjects using 24 slides. This open-source machine learning-assisted workflow enables rapid and high throughput determinations of endocrine cells, whether as single cells or within groups, across hundreds of slides. It is expected that use of this workflow will accelerate our understanding of endocrine cell and islet heterogeneity in the context of T1D endotypes and pathogenesis.

Laser-Induced Breakdown Spectroscopy Applied to the Quantification of K, Ca, Mg and Mn Nutrients in Organo-Mineral, Mineral P Fertilizers and Rock Fertilizers

A low-cost laser-induced breakdown spectroscopy (LIBS) instrument equipped with a charge-coupled device (CCD) was tested in the atmospheric environment for the quantification of K, Ca, Mg, and Mn in some organo–mineral fertilizers, mineral P fertilizers, and rock fertilizers of various compositions and origins, using flame atomic absorption spectrometry (FAAS) as the reference technique. The correlation analysis performed between each CCD pixel and the corresponding element concentration measured by FAAS allowed to choose the most appropriate K, Ca, Mg and Mn emission lines for LIBS analysis. The normalization process applied to LIBS spectra to correct physical matrix effects and small fluctuations was able to increase the linear correlation of the calibration curves between LIBS data and FAAS data by an average of 0.15 points of the R-value for all elements of interest. The R values of calibration curves were 0.97, 0.96, 0.86 and 0.84, for K, Ca, Mg and Mn, respectively. The limits of detection (LOD) were 66 mg/kg (K), 35 mg/kg (Ca), 5.4 mg/kg (Mg) and 0.8 mg/kg (Mn) when using LIBS in the quantification model. The cross-validation (leave-one-out) analysis yielded an absolute average error of 12% (K), 21% (Ca), 8% (Mg) and 13% (Mn) when LIBS data were correlated to FAAS ones. These results showed that the calibration models used were close to the optimization limit and satisfactory for K, Ca, Mg, and Mn quantification in the fertilizers and rocks examined.

Research on Tennis Score Based on Momentum Quantization Model

The paper goal is to investigate the significance, logic, and effects of momentum in tennis matches in order to offer logical advice to athletes and tennis coaches. the paper created a quantitative momentum model and mostly finished three tasks based on the research objectives. Firstly, the paper develop a momentum quantification model and set four essential indicators to quantify the momentum. By adding together these indicators, the paper may determine a player's momentum score at a given scoring point. And a shift curve of momentum scores is shown using the momentum scores acquired at each scoring point, providing the groundwork for determining the competition's turning point in the future. Secondly, the randomness of momentum is assessed by us. To evaluate coaches' skepticism about the impact of momentum, the paper conducted two randomized experiments to investigate this issue. The first test is a randomness test based on outcome correlation. The paper calculate the correlation between the winner and the player with the highest score on the final score. The second test is the permutation test, which involves generating a large number of random permutations by redistributing the labels of the data points. It then calculates the consistent distribution between the highest momentum scorer and the competition winner under these random permutations. The test results all indicate that the player with the highest momentum score is the winner of the game. The paper proves that momentum plays a crucial role in the matches, and predicting momentum can be utilized to anticipate pivotal moments in the game.

Toward quantitative CEST imaging of glutamate in the mouse brain using a multi-pool exchange model calibrated by 1H-MRS.

To develop a CEST quantification model to map glutamate concentration in the mouse brain at 11.7 T, overcoming the limitations of conventional glutamate-weighted CEST (gluCEST) contrast (magnetization transfer ratio with asymmetric analysis). 1H-MRS was used as a gold standard for glutamate quantification to calibrate a CEST-based quantitative pipeline. Joint localized measurements of Z-spectra at B1 = 5 μT and quantitative 1H-MRS were carried out in two voxels of interest in the mouse brain. A six-pool Bloch-McConnell model was found appropriate to fit experimental data. Glutamate exchange rate was estimated in both regions with this dedicated multi-pool fitting model and using glutamate concentration determined by 1H-MRS. Glutamate exchange rate was estimated to be ˜1300 Hz in the mouse brain. Using this calibrated value, maps of glutamate concentration in the mouse brain were obtained by pixel-by-pixel fitting of Z-spectra at B1 = 5 μT. A complementary study of simulations, however, showed that the quantitative model has high sensitivity to noise, and therefore, requires high-SNR acquisitions. Interestingly, fitted [Glu] seemed to be overestimated compared to 1H-MRS measurements, although it was estimated with simulations that the model has no intrinsic fitting bias with our experimental level of noise. The hypothesis of an unknown proton-exchanging pool contributing to gluCEST signal is discussed. High-resolution mapping of glutamate in the brain was made possible using the proposed calibrated quantification model of gluCEST data. Further studying of the in vivo molecular contributions to gluCEST signal could improve modeling.

A multi-scale uncertainty quantification model encompassing minimum-size unit cells for effective properties of plain woven composites

The uncertainty quantification is crucial to the high-precision prediction of composites’ effective properties. However, the unclear input uncertainties of multiscale parameters, complex uncertainty propagations of inter-scale correlations, and unaffordable computational cost of massive simulations are three primary problems at present. In this work, an innovative model with high accuracy and feasible cost for the mechanical property prediction of plain woven composites is developed encompassing minimum-size unit cells and multi-scale uncertainty quantification. For the accuracy holding, an uncertainty analysis process consists of the traceability description, inter-scale propagation and quantification is established. The uncertainties of geometry are described by uniform distributions for fiber, fiber bundle and composite scales, respectively; that of constituent properties is described by normal distributions for fiber and matrix, and its propagations to bundle and composite scales are realized by Nataf transformation methods with the consideration of parameter correlations. For the cost control, minimum-size unit cells are formulated by exhaustive analysis of structural symmetries to reduce the computational cost without accuracy compromising for the single simulation, and 1/8 and 1/16 unit cells compared with traditional full-size ones are obtained. The evolution convergence for statistical uncertainties of effective properties is finally obtained with totally reduced computational cost of 89%.

Theoretical framework for calibrating the depth-dependent optical scattering in layered human skin using spatially offset measurements.

Spatially offset spectroscopy offers an alternative non-invasive method for enabling deep probing of structures and chemical molecules, which is clinically significant for the characterization of chemical and physical alterations in human skin. However, a more precise depth-resolved quantification using the spatially offset measurements still remains a challenge due to the mixed inhomogeneous scattering. Herein, we report a Monte-Carlo-based quantification modeling platform combined with a novel, to the best of our knowledge, scattering spectrum decomposition method to explore the depth-dependent optical scattering contributions in human skin. In the simplified modeling, human skin was empirically set to be composed of multiple layers, and each layer possessed different photon weights for the spatially offset scattering intensity measurements. The modeling results of photon transportation in-and-out of the layered skin substantially discovered that the layer-dependent scattering contribution was compositely encoded into the spatially offset measurements and varied with the illumination incidence angle. For calibrating the layer-dependent scattering contribution, a modified nonlinear independent component processing algorithm was applied to the spatially offset measurements by decomposing the photon weights of each layer. The calibration results figured out the major scattering contribution of each layer along the offset axis under different incidence angles, which were consistent with previous experimental observations. The proposed theoretical framework establishes a feasible approach for spatially offset optical spectroscopies enabling non-invasive quantitative A-line characterization of the concentrations of skin components.

Raman spectroscopy for monitoring free sulfhydryl formation during monoclonal antibody manufacturing

During production, harvested cell culture fluid (HCCF) can degrade due to reductases breaking interchain disulfide bonds, forming low molecular weight (LMW) impurities that contain free sulfhydryl and high molecular weight (HMW) impurities through disulfide shuffling. Thus, detecting and quantifying the free sulfhydryl increase in HCCF is critical. Herein, Raman spectroscopy is implemented as a process analytical technology, and multivariate data analysis is applied to characterize and quantify sulfhydryl formation in HCCF with disulfide-containing indicator molecules. Raman spectra qualitatively probe the presence or absence of disulfide bond breakage in antibodies, consistent with offline non-reduced capillary electrophoresis sodium dodecyl sulfate results. Between two antibodies studied, mAb A was identified for a higher risk of antibody reduction where sulfhydryl formation was observed within 16 h, while mAb B did not show similar concerns even after 1 week. The offline measurement of redox potential is below –100 mV in HCCF for mAb A, while the stable mAb B HCCF shows redox potentials above +20 mV. A multivariate partial least squares (PLS) model for quantification is developed using an offline free sulfhydryl assay, applying Raman spectra to predict free sulfhydryl concentration with high accuracy (R2 > 0.98) and expected mean error of 0.677 mM from the offline Ellman’s Assay. This work confirms the use of Raman PAT to monitor real-time disulfide reduction, enabling improvements to process understanding and product quality.

MATES: a deep learning-based model for locus-specific quantification of transposable elements in single cell

Transposable elements (TEs) are crucial for genetic diversity and gene regulation. Current single-cell quantification methods often align multi-mapping reads to either ‘best-mapped’ or ‘random-mapped’ locations and categorize them at the subfamily levels, overlooking the biological necessity for accurate, locus-specific TE quantification. Moreover, these existing methods are primarily designed for and focused on transcriptomics data, which restricts their adaptability to single-cell data of other modalities. To address these challenges, here we introduce MATES, a deep-learning approach that accurately allocates multi-mapping reads to specific loci of TEs, utilizing context from adjacent read alignments flanking the TE locus. When applied to diverse single-cell omics datasets, MATES shows improved performance over existing methods, enhancing the accuracy of TE quantification and aiding in the identification of marker TEs for identified cell populations. This development facilitates the exploration of single-cell heterogeneity and gene regulation through the lens of TEs, offering an effective transposon quantification tool for the single-cell genomics community.

Moisture content determination along production line of ibuprofen soft gelatin capsule manufacturing by near infrared spectroscopy and ensemble deep neural networks

AbstractIn the manufacturing process of ibuprofen soft gelatin capsules, controlling moisture content at each production line stage, including in their components—gelatin, fill content, and shell—is vital to ensure quality and stability. This study developed and assessed an analytical method for rapid and non‐destructive moisture determination using near‐infrared spectroscopy (NIRS) coupled with deep neural networks (DNN) on all stages of the ibuprofen production line. The NIRS‐DNN classifier models were able to distinguish between the three components, achieving accuracy scores of up to 99%. The DNN models for moisture quantification also demonstrated high accuracy, with R2 values exceeding 0.997 across all production stages and prediction errors to those of previously reported models. A significant advantage of the NIRS‐DNN approach was its ability to maintain accuracy over a wide moisture concentration range, from 7% to 48%. The ensemble model, NIRS‐EDNN, seamlessly integrated classification and quantification, revealing its potential for real‐time process control in soft gel manufacturing. The comprehensive sampling approach ensured a diverse representation of moisture content, thereby enhancing the understanding of its impact on the final product stability, demonstrating that this methodology is potentially applicable to any soft gelatin capsule tracking worldwide.