Estimation Of Function Research Articles

Mean square convergence of functional conditional distribution estimators under twice censoring

In this work, we propose a novel kernel estimator for the conditional distribution in the twice censored model, with functional regressors. We next analyze its mean square convergence, with an explicit rate given in Theorem [t1]. To validate our theoretical result, we conduct a simulation study that demonstrates the estimator's accuracy and performance, further supporting the robustness of our method, even with twice censored data.

Deep learning enhances reliability of dynamic contrast-enhanced MRI in diffuse gliomas: bypassing post-processing and providing uncertainty maps.

To propose and evaluate a novel deep learning model for directly estimating pharmacokinetic (PK) parameter maps and uncertainty estimation from DCE-MRI. In this single-center study, patients with adult-type diffuse gliomas who underwent preoperative DCE-MRI from Apr 2010 to Feb 2020 were retrospectively enrolled. A spatiotemporal probabilistic model was used to create synthetic PK maps. Structural Similarity Index Measure (SSIM) to ground truth (GT) maps were calculated. Reliability was evaluated using the intraclass correlation coefficient (ICC) for synthetic and GT PK maps. For clinical validation, Area Under the Receiver Operating Characteristic Curve (AUROC) was obtained for predicting WHO low vs high grade and IDH-wildtype vs mutant. 329 patients (mean age, 55 ± 15 years, 197 men) were eligible. Synthetic Ktrans, Vp, Ve maps showed high SSIM (0.961, 0.962, 0.890) compared to the GT maps. The ICC of PK maps was significantly higher in synthetic PK maps compared to the conventional approach: 1.00 vs 0.68 (p < 0.001) for Ktrans, 1.00 vs 0.59 (p < 0.001) for Vp, 1.00 vs 0.64 (p < 0.001) for Ve. PK values of enhancing tumor portion obtained from synthetic and GT maps were comparable in AUROC: (1) Ktrans, 0.857 vs 0.842 (p = 0.57); Vp, 0.864 vs 0.835 (p = 0.31); and Ve, 0.835 vs 0.830 (p = 0.88) for mutation prediction. (2) Ktrans, 0.934 vs 0.907 (p = 0.50); Vp, 0.927 vs 0.899 (p = 0.24); and Ve, 0.945 vs 0.910 (p = 0.24) for glioma grading. Synthetic PK maps generated from DCE-MRI using a spatiotemporal probabilistic deep-learning model showed improved reliability without compromising diagnostic performance in glioma grading. Question Can a deep learning model enhance the reliability of dynamic contrast-enhanced MRI (DCE-MRI) for more consistent and clinically acceptable glioma imaging? Findings A spatiotemporal deep learning model outperformed the Tofts model in Ktrans reliability and preserved diagnostic performance for IDH mutation and glioma grade, bypassing arterial input function estimation. Clinical relevance Enhancing DCE-MRI reliability with deep learning improves imaging consistency, supports molecular tumor characterization through reproducible pharmacokinetic maps, and enables personalized treatment planning, which might lead to better clinical outcomes for patients with diffuse gliomas.

A comparison between radiomic biological age and chronological age in estimating kidney function

Accurate kidney function estimation hinges on essential markers of age and body size. The relative benefit of both markers has been debated with the emerging biological age and novel body size descriptors. We used radiomic biomarkers of age-related changes in body composition to construct new biological age indices as covariates of kidney function. A retrospective cohort of hospitalized patients with plasma concentrations of aminoglycosides and computed tomography images were evaluated. Aminoglycoside clearance served as a kidney function surrogate. A population pharmacokinetic model was constructed to determine whether biological age indices improved aminoglycoside clearance estimation compared to chronological age. The final dataset included 156 patients (51.92% female) with a median (minimum-maximum) age and body weight of 58 [21, 93] years and 81 [43.8, 139.3] Kg. A 1-compartment clearance model with linear elimination, incorporating biological index, serum creatinine, and drug type best fits the concentration-time data. The best radiomic biological age model included dorsal muscle group area, bone mineral density, visceral fat area, and subcutaneous fat density. The radiomic biological age model offered a modest improvement over the chronological age model. This work offers a proof-of-concept, highlighting the potential for more precise methods for aging-related kidney function estimation to aid personalized pharmacotherapy.

The ABO Blood System and Associated Implications for Hemostasis and Thrombosis.

The relationship between non-O blood groups and thromboembolic events has been suggested by several studies, although the exact underlying mechanisms are not fully elucidated. However, the correlation between ABO blood groups with the opposite pole of hemostasis, hemorrhage, has been investigated less thoroughly. Non-O blood groups confer an overall increased risk of single, recurrent, and provoked thromboembolic episodes. On the other hand, blood group O has been associated with more severe bleeding events and less favorable manifestations in individuals with hemorrhagic disorders. Therefore, ABO blood group screening may have a role in both thrombotic and hemorrhagic risk assessment and could potentially be added to available clinical prediction systems. This strong belief is supported by the ongoing research. Nevertheless, up to date, the majority of studies represent important heterogeneity, and given the frequency of non-O blood groups, a natural reluctance to incorporate blood groups in risk assessment models arises. Therefore, a more targeted approach should be considered to provide safe outcomes. The in vitro estimation of the thrombotic and hemorrhagic profile of each blood group separately, the quantitative estimation of VWF, FVIII, and platelet function in several disease settings and in well-organized studies, could be useful to establish a clear relationship of ABO blood types with hemostatic and thrombotic disorders. This may ensure a safe approach to categorizing a patient's risk, managing treatment, and influencing prognosis.

Towards a turnkey approach for unbiased Monte Carlo estimation of smooth functions of expectations

Summary Given a smooth function f, we develop a general approach to turn Monte Carlo samples with expectation m into an unbiased estimate of f (m). Specifically, we develop estimators that are based on randomly truncating the Taylor series expansion of f and estimating the coefficients of the truncated series. We derive their properties and propose a strategy to set their tuning parameters—which depend on m—automatically, with a view to make the whole approach simple to use. We develop our methods for the specific functions f (x) = log x and f (x) = 1/x, as they arise in several statistical applications such as maximum likelihood estimation of latent variable models and Bayesian inference for un-normalised models. Detailed numerical studies are performed for a range of applications to determine how competitive and reliable the proposed approach is.

Increasing the Accuracy of the Model for Predicting the Performance of University Students

This paper discusses approaches to preparing educational data on students' learning outcomes to improve the accuracy of predicting their academic performance over a given period. The rules for checking initial data for using them in a forecasting model are considered, implemented, and investigated. The rules help to work with poor-quality initial data and improve the accuracy of modeling. Modeling of students' learning outcomes is based on a nonparametric estimate of the Nadaraya-Watson regression function. The article presents some fragments of computational experiments that show acceptable results from a practical point of view.

Which behavioral patterns score points in taekwondo matches? An analysis of the Roma 2019 World Grand Prix finalists

IntroductionObservational methodology facilitates the study of situational factors in taekwondo matches, examines observable technical-tactical behaviors, and reveals various relationships, thus generating behavioral patterns. The aim of this study was to examine the technical-tactical scoring actions in the final matches of the Roma 2019 World Taekwondo Grand Prix, using polar coordinate analysis and function estimation.MethodsA point/nomothetic/multidimensional (P/N/M) observational design was applied, where the movements of all athletes were analyzed in relation to their behaviors and dimensions that align with the criteria of the observation instrument. Seven matches were observed (female, n = 3; male, n = 4) for a total of 1,382 registrations. The observation tool used for this study was designed “ad hoc” using the HOISAN tool. It consisted of five criteria (tactical action, technique type, strike area, sidedness, and scoring) and 30 categories. The tool was designed by three observers. Pearson's, Spearman's, and Kendall's tau-b interobserver and intraobserver correlation coefficients were estimated. Five focal categories related to the criterion “scoring” were considered: one point, two points, three points, four points, and five points. Relationships with a vector length ≥1.96 were considered significant (p &amp;lt; 0.05). A function estimation analysis was performed to validate the observed values (using linear, polynomial, exponential, and logarithmic regression, and polynomial interpolation) using Estimación de Funciones software.Results and discussionThe results allow for the development of new training and competition strategies based on the different technical-tactical actions that establish a significant pattern in the realization of a scoring action. Specifically, one point was obtained through a direct attack, a correction, or a subsequent counterattack. Two points were obtained through a simultaneous counterattack, while three points were obtained through an anticipation or a melee tactical action. Four points and five points were obtained through a direct attack or a simultaneous counterattack. Two points and three points were obtained with the left leg, while four points were obtained with the right leg. Moreover, three points and four points inhibited the right and left side of the body, respectively. Linear techniques were also inhibited when obtaining one point and five points, while circular techniques were used before or after one, two, and five points, showing that the circular technique was the most used.

Flexible modelling of demographic transition processes with a Bayesian hierarchical B-splines model

Abstract Several demographic and health indicators, including the total fertility rate (TFR) and modern contraceptive use rate (mCPR), evolve similarly over time, characterized by a transition between stable states. Existing approaches for estimation or projection of transitions in multiple populations have successfully used parametric functions to capture the relation between the rate of change of an indicator and its level. However, incorrect parametric forms may result in bias or incorrect coverage in long-term projections. We propose a new class of models to capture demographic transitions in multiple populations. Our proposal, the B-spline Transition Model (BTM), models the relationship between the rate of change of an indicator and its level using B-splines, allowing for data-adaptive estimation of transition functions. Bayesian hierarchical models are used to share information on the transition function between populations. We apply the BTM to estimate and project country-level TFR and mCPR and compare the results against those from extant parametric models. For TFR, BTM projections have generally lower error than the comparison model. For mCPR, while results are comparable between BTM and a parametric approach, the B-spline model generally improves out-of-sample predictions. The case studies suggest that the BTM may be considered for demographic applications.

ML Estimation of Intensity Function in Non-homogeneous Poisson Processes

ML Estimation of Intensity Function in Non-homogeneous Poisson Processes

Thematic coherence of innovation systems: a patent-based index

ABSTRACT We propose a novel measure of thematic coherence of national innovation systems, based on the comparison of distributions of patent applications submitted by business and academia. The index is calculated for a number of countries using data on more than 5 million priority filings from 1990 to 2016. Cluster analysis suggests a complex relationship of thematic coherence with other aspects of national innovation systems, with two quite different groups of countries showing high level of the index. The estimates of knowledge production function indicate that more coherent systems obtain more innovation outputs per unit of research input.

A New Approach to Estimate the Parameters of the Joint Distribution of the Wind Speed and the Wind Direction, Modelled with the Angular–Linear Model

In order to assess the potential and suitability of a location to deploy a wind farm, it is essential to have a model of the joint probability density function of the wind speed and direction, fV,Θ(v,θ). The angular–linear model is widely used to obtain the analytical expression of the joint density from the parametric estimation of the probability density functions of wind speed, fV(v), and wind direction, fΘ(θ). In previous studies, the parameters of the marginal distributions were obtained by fitting the wind measurements to the cumulative distribution function (CDF) using the least squares method and then calculating the probability density function (PDF). In this study, we propose to directly fit the probability density function and then calculate the cumulative distribution function. It is shown that it has both computational and goodness-of-fit advantages. In addition, previous studies have been expanded, analysing the effect of the number of intervals on which wind speed and direction ranges are divided. The new parameter fitting method is evaluated and compared with the original proposal in terms of goodness of fit, using the coefficient of determination R2 as an estimator both in the probability density function (R2pdf) and in the cumulative distribution function (R2cdf). The computational times required to estimate the parameters using both methods will also be compared. The new approach is faster, and the goodness of the fitting is satisfactory for both estimators: it produces a better R2pdf, without significantly affecting the R2cdf, in contrast to the initial one where the R2pdf is smaller.

'Neuropathological Function Estimations': A User-Friendly Module for Analyzing Neural Activity in Neurological Disorders

Abstract Motivation This work introduces the Neuropathological Function Estimations software, designed to facilitate the study of neuronal activity alterations in neurological disorders without requiring programming expertise. With its user-friendly interface, researchers can input various data types to generate subject-specific functional brain models and decode neuropathological influences. Results The software’s capabilities are validated through its application to Alzheimer’s disease, providing insights into neuronal excitability and disease mechanisms. This tool has the potential to enhance our understanding of the biological basis of in-vivo neural activity and contribute to the development of personalized therapeutic interventions. Availability and implementation The latest version of the software and support are freely available for noncommercial users through the Neuroinformatics for Personalized Medicine Lab (NeuroPM Lab) website at McGill University (https://www.neuropm-lab.com/neuropm-box.html). The software is maintained by the NeuroPM team. This publication is linked to version 1.0.

Effects of essential tremor on longevity and mortality rates in families.

Essential Tremor (ET) is a common movement disorder characterized by action tremors, primarily affecting the hands and head. lthough previous studies have suggested potential links between ET and aging-related diseases, its relationship with longevity remains unclear, with conflicting evidence in the literature. To investigate this association, we analyzed data from 1,493 individuals across 145 families, encompassing both ET-positive (ET+) and ET-negative (ET-) participants. Using comprehensive statistical methods, including survival function estimation and regression modeling, we examined the potential influence of ET on lifespan. The median age of our participants was 67 years (IQR 54-77). Among deceased individuals, those with ET had a higher median age at death (80 years, IQR 70-86) compared to their ET- counterparts (70 years, IQR 59-77). Living ET+ participants also demonstrated slightly higher median ages (63 years, IQR 53-74) than living ET- individuals (60 years, IQR 49-71). Survival analysis revealed a significantly prolonged lifespan for ET+ individuals compared to ET- individuals (log-rank p = 1.11 × 10 ⁻23). Furthermore, hazard ratio (HR) calculations indicated a reduced risk of mortality for the ET+ group (HR = 0.44, CI95% = 0.37-0.52), particularly among males. These findings suggest that ET may be associated with increased longevity, though the underlying biological mechanisms remain unclear. Further research is essential to elucidate the processes contributing to this relationship and to explore its implications for understanding aging and neurodegenerative disorders.

AI-based automatic estimation of single-kidney glomerular filtration rate and split renal function using non-contrast CT

Abstract Objectives To address SPECT’s radioactivity, complexity, and costliness in measuring renal function, this study employs artificial intelligence (AI) with non-contrast CT to estimate single-kidney glomerular filtration rate (GFR) and split renal function (SRF). Methods 245 patients with atrophic kidney or hydronephrosis were included from two centers (Training set: 128 patients from Center I; Test set: 117 patients from Center II). The renal parenchyma and hydronephrosis regions in non-contrast CT were automatically segmented by deep learning. Radiomic features were extracted and combined with clinical characteristics using multivariable linear regression (MLR) to obtain a radiomics-clinical-estimated GFR (rcGFR). The relative contribution of single-kidney rcGFR to overall rcGFR, the percent renal parenchymal volume, and the percent renal hydronephrosis volume were combined by MLR to generate the estimation of SRF (rcphSRF). The Pearson correlation coefficient (r), mean absolute error (MAE), and Lin’s concordance coefficient (CCC) were calculated to evaluate the correlations, differences, and agreements between estimations and SPECT-based measurements, respectively. Results Compared to manual segmentation, deep learning-based automatic segmentation could reduce the average segmentation time by 434.6 times to 3.4 s. Compared to single-kidney GFR measured by SPECT, the rcGFR had a significant correlation of r = 0.75 (p &lt; 0.001), MAE of 10.66 mL/min/1.73 m2, and CCC of 0.70. Compared to SRF measured by SPECT, the rcphSRF had a significant correlation of r = 0.92 (p &lt; 0.001), MAE of 7.87%, and CCC of 0.88. Conclusions The non-contrast CT and AI methods are feasible to estimate single-kidney GFR and SRF in patients with atrophic kidney or hydronephrosis. Critical relevance statement For patients with an atrophic kidney or hydronephrosis, non-contrast CT and artificial intelligence methods can be used to estimate single-kidney glomerular filtration rate and split renal function, which may minimize the radiation risk, enhance diagnostic efficiency, and reduce costs. Key Points Renal function can be assessed using non-contrast CT and AI. Estimated renal function significantly correlated with the SPECT-based measurements. The efficiency of renal function estimation can be refined by the proposed method. Graphical Abstract

Impact of Removing Race Coefficient from Glomerular Filtration Rate Estimation Equations on Antidiabetics Among Black Patients

Background: In 2021, the National Kidney Foundation–American Society of Nephrology (NKF-ASN) recommended the use of the 2021 refit equation without race; however, the effect of the removal is unclear. Our research aimed to examine the implications of antidiabetic dosing and eligibility on the new 2021 equation among Black patients. Methods: This is a retrospective analysis of patients receiving care at the diabetes treatment center (DTC) of an academic medical center. Estimated glomerular filtration rates (eGFRs) based on serum creatinine were calculated using the 2009 and 2021 CKD-EPI equations. A Monte Carlo simulation was performed to create 10,000 virtual patients. Dosing simulations based on each estimate of kidney function were performed for antidiabetics based on product labeling. The proportion and percentage of patients who were eligible based on the estimates were calculated. Results: The percentages of patients ineligible for metformin based on the estimates from the 2009 and 2021 CKD-EPI equations at the DTC were comparable (8.02% and 8.36%, respectively). In our 10,000 simulated virtual patients, the percentage of ineligibility increased only by 1%. For the GFR cut points of 20 mL/min and 25 mL/min, the rates of ineligibility were similar in our cohort and simulated patients. Conclusions: The exclusion of race from the 2021 CKD-EPI equation may slightly reduce medication eligibility among Black patients.

Unsupervised Deep Learning for Blood-Brain Barrier Leakage Detection in Diffuse Glioma Using Dynamic Contrast-enhanced MRI.

"Just Accepted" papers have undergone full peer review and have been accepted for publication in Radiology: Artificial Intelligence. This article will undergo copyediting, layout, and proof review before it is published in its final version. Please note that during production of the final copyedited article, errors may be discovered which could affect the content. Purpose To develop an unsupervised deep learning framework for generalizable blood-brain barrier (BBB) leakage detection using dynamic contrast-enhanced (DCE) MRI, without requiring pharmacokinetic (PK) models and arterial input function (AIF) estimation. Materials and Methods This retrospective study included data from patients who underwent DCE MRI between April 2010 and December 2020. An autoencoder-based anomaly detection (AEAD) identified 1D voxel-wise time-series abnormal signals through reconstruction residuals, separating them into residual leakage signals (RLS) and residual vascular signals (RVS). The RLS maps were evaluated and compared with the volume transfer constant (Ktrans) using the structural similarity index (SSIM) and correlation coefficient (r). Generalizability was tested on subsampled data, and IDH status classification performance was assessed using areas under the receiver operating characteristic curves (AUCs). Results A total of 274 patients were included (164 male; mean age 54.23 ± [SD] 14.66 years). RLS showed high structural similarity (SSIM = 0.91 ± 0.02) and correlation (r = 0.56, P < .001) with Ktrans. On subsampled data, RLS maps showed better correlation with RLS values from original data (0.89 versus 0.72, P < .001), higher PSNR (33.09 dB versus 28.94 dB, P < .001), and higher SSIM (0.92 versus 0.87, P < .001) compared with Ktrans maps. RLS maps also outperformed Ktrans maps in predicting IDH mutation status (AUC = 0.87 [95% CI: 0.83-0.91] versus 0.81 [95% CI: 0.76-0.85], P = .02). Conclusion The unsupervised framework effectively detected blood-brain barrier leakage without PK models and AIF. ©RSNA, 2025.

Time delay velocity estimation from a superposition of localized and uncorrelated pulses

This study investigates a method for estimating two-dimensional velocities from coarse-grained imaging data tailored for plasma diagnostics. The method utilizes measurements from three non-collinear points, and it is based on a stochastic model. The method yields exact time delay estimates for symmetric Gaussian pulse functions. We performed extensive simulations to evaluate the method's performance under varying process durations, degrees of pulse overlap, resolution, additive noise, and linear damping, including analysis of the barber pole effect. We propose safeguards to anticipate the applicability of the method based on parameters of the measurement data. Overall, this technique enhances precise velocity estimation in fusion plasma diagnostics and similar applications.

Efficient Bayesian source reconstruction and uncertainty quantification of atmospheric radionuclide releases by replacing release rate sampling with Maximum-A-Posteriori estimation of time-varying release rates.

Efficient Bayesian source reconstruction and uncertainty quantification of atmospheric radionuclide releases by replacing release rate sampling with Maximum-A-Posteriori estimation of time-varying release rates.

Estimation of kidney function in Graves' disease using creatinine and cystatin C.

There is no consensus regarding methods to estimate kidney function in hyperthyroidism. The aim was therefore to assess changes in filtration markers in patients with Graves' disease undergoing treatment with antithyroid drugs. Thirty patients with de novo Graves' disease were included. Blood sampling, including TSH, fT3, fT4, and creatinine, was performed at baseline, 6 weeks, 3, 6, 12, and 24 months. Cystatin C was measured from frozen samples. To calculate creatinine- and cystatin C-based eGFR the Lund-Malmö equation (LMR) and the CAPA formula were used. fT3 and fT4 normalized during treatment. Creatinine increased initially but stabilized after 6 months. eGFRLMR decreased until 12 months. Cystatin C decreased, while eGFRCAPA and eGFRCAPA/eGFRLMR increased until 6 months. The mean of eGFRLMR and eGFRCAPA remained stable. The % changes in creatinine and Cystatin C were associated with % changes in fT3 and fT4. In regression models including fT3 or fT4 with body weight (all % change), fT3 and fT4 were the strongest predictors of percentual changes in both creatinine and Cystatin C. The increase in creatinine and decrease in cystatin C during the treatment of Graves' disease was significantly associated with changes in thyroid hormones, and for Cr, also body weight. The mean of eGFRLMR and eGFRCAPA remained stable, suggesting that creatinine and Cystatin C were affected by different non-GFR-related factors. The potential use of eGFRLMR and eGFRCAPA to assess kidney function in patients with thyroid disorders should be further evaluated in studies measuring kidney function with state-of-the-art methods.

Deep Frequency Awareness Functional Maps for Robust Shape Matching.

Traditional deep functional map frameworks are widely used for 3D shape matching; however, many methods fail to adaptively capture the relevant frequency information required for functional map estimation in complex scenarios, leading to poor performance, especially under significant deformations. To address these challenges, we propose a novel unsupervised learning-based framework, Deep Frequency Awareness Functional Maps (DFAFM), specifically designed to tackle diverse shape-matching problems. Our approach introduces the Spectral Filter Operator Preservation constraint, which ensures the preservation of critical frequency information. These constraints promote frequency awareness by learning a set of spectral filters and incorporating them as a loss function to jointly supervise the functional maps, pointwise maps, and spectral filters. The spectral filters are constructed using orthonormal Jacobi polynomials with learnable coefficients, enabling adaptive and efficient frequency representation. Furthermore, we propose a refinement strategy that leverages the learned spectral filters and constraints to enhance the accuracy of the final pointwise map. Extensive experiments conducted on multiple benchmark datasets demonstrate that our method outperforms state-of-the-art approaches, particularly in challenging scenarios involving non-isometric deformations and inconsistent topology. Our code is available at https://github.com/LuoFeifan77/DeepFAFM.