Functional Principal Component Research Articles

Temporal Image Sandwiches Enable Link between Functional Data Analysis and Deep Learning for Single-Plant Cotton Senescence

Abstract Senescence is a highly ordered biological process involving resource redistribution away from aging tissues that affects yield and quality in annuals and perennials. Images from 14 unmanned / unoccupied / uncrewed aerial system (UAS, UAV, drone) flights captured the senescence window across two experiments while functional principal component analysis (FPCA) effectively reduced the dimensionality of temporal visual senescence ratings (VSRs) and two vegetation indices: the red chromatic coordinate index (RCC) and transformed normalized difference green and red index (TNDGR). Convolutional neural networks (CNNs) trained on temporally concatenated, or “sandwiched,” UAS images of individual cotton plants (Gossypium hirsutum L.), allowed single-plant analysis (SPA). The first functional principal component scores (FPC1) served as the regression target across six CNN models (M1-M6). Model performance was strongest for FPC1 scores from VSRs (R2 = 0.857 and 0.886 for M1 and M4), strong for TNDGR (R2 = 0.743 and 0.745 for M3 and M6), and strong-to-moderate for RCC (R2 = 0.619 and 0.435 for M2 and M5), with deep learning attention of each model confirmed by activation of plant pixels within saliency maps. Single-plant UAS image analysis across time enabled translatable implementations of high-throughput phenotyping by linking deep learning with functional data analysis (FDA). This has applications for fundamental plant biology, monitoring orchards or other spaced plantings, plant breeding, and genetic research.

Exploring Peak Concentric Force and Zero Velocity Synchronization in the Drop Jump.

The application of force is a key aspect of performance during athletic activities. In jumping, the timing and magnitude of force application are important performance factors. The relative timing of forces has only been investigated in the countermovement jump. This study aimed to explore if the synchronization of peak concentric force with the instance of zero velocity during a drop jump impacted performance and examine the relationship of force-time curve shape to performance. Sixty-six state-level athletes (24 males and 42 females) completed drop jumps from a 30 cm box onto dual force plates. The jump with the highest reactive strength index (RSI) score was taken for analysis and classified as synchronous or asynchronous based on the relative timing of peak concentric force and zero velocity. RSI and other force-time variables were compared between groups, and functional principal component analysis (fPCA) was performed on the force-time curves, which were used to perform functional principal component regression (fPCR). Synchronous jumpers exhibited greater RSI scores and shorter contact times compared to asynchronous jumpers. Performance differences were largely driven by improved concentric kinetics, which the fPCR model revealed to have the greatest influence on RSI. Sex was also found to be a significant factor for RSI in the fPCR model. fPCA revealed that greater force application preceding and throughout the amortization phase was positively associated with RSI. The timing of peak concentric force and the shape of the force-time curve are key factors for drop jump performance, and these concepts should be investigated further in other athletic activities.

Daily Engine Performance Trending using Common Flight Regime Identification

Abstract Accurate flight regime identification is critical for enhancing aircraft efficiency and safety. Traditionally, predictive models for aircraft operation have relied on complex, black-box machine learning techniques that lack transparency. This study introduces a more interpretable approach by leveraging the New Comprehensive Modular Aero-propulsion System Simulation (N-CMAPSS) dataset and combining expanding window classification, voting schemes, and spectral clustering to detect distinct flight regimes. The method applies elastic registration to align time-shifted patterns and Functional Principal Component Analysis (FPCA) to reduce dimensionality, capturing core dynamics across flight regimes. These transformed features are fed into a genetic algorithm-assisted orthogonal matching pursuit for sparse feature selection. Through evolutionary selection, crossover, and mutation, the most informative features are identified, enabling accurate predictions while maintaining transparency. This method outperforms more complex models in certain test cases, offering a balance between accuracy and interpretability that is essential for predictive maintenance and safety applications.

Association between autonomic dysfunction, 12-year mortality and 10-year incident cardiovascular disease

Abstract Background Standing from a supine position requires a co-ordinated response in peripheral and central haemodynamic signals to protect the brain and body from sudden drops in blood pressure (BP) and has previously been shown to be an important measure of neuro-cardiovascular health (1-3). Previous studies have found an association between BP and heart rate recovery (HRR) to standing with all-cause mortality, cardiovascular disease and other health outcomes (4-8). However, almost all of these studies have exclusively investigated the association of consensus-defined HR/BP phenotypes measured at specific timepoints during standing. Purpose We hypothesised that assessing information from the entire haemodynamic response to orthostasis - instead of discrete timepoints or consensus definitions - may uncover novel associations between BP/HR responses to active stand and neuro-cardiovascular health in older adults. This may afford better physiological understanding of the longitudinal relationships between the response to standing and both Cardiovascular Disease (CVD) and mortality. Methods We used functional Principal Components Analysis (FPCA) to examine the determinants of variability in the complete haemodynamic response to active stand and examine which components were related to mortality and incident CVD in >4500 community-dwelling adults aged 50+. Results Figure 1 shows the mean response curve according to mortality status and Figure 2 the mean curve for participants free of CVD at baseline who later have CVD vs those who remain CVD-free during 10 year follow-up. All-cause mortality was associated with functional principal components which discriminate higher baseline HR, blunted HR peak and impaired HRR up to ~25 seconds after standing. Components that discriminated high baseline and impaired recovery of SBP from the post-stand nadir to 60 seconds post stand were also associated with all-cause mortality. This association remained even after covariate adjustment. Interestingly, neither baseline SBP nor orthostatic hypotension (OH) were associated with mortality. Components which discriminate high baseline and blunted HR peak; elevated stroke volume index and impaired recovery of DBP from ~25 seconds post stand were associated with 10-year incident CVD. Conclusions To our knowledge this is the first study to incorporate data driven information over the entire trace of the haemodynamic response to standing to investigate associations with incident CVD and mortality. The fact that components which discriminated high BP and impaired recovery of BP were associated with 12-year mortality and 10-year incident CVD when traditional summary measures of OH and baseline BP were not; suggests that incorporating information across the entire response to standing allows for richer and more flexible associations with health outcomes to be uncovered and allows for a better understanding of the underlying physiology leading to such associations.Figure 1:Mean trace of Mortality StatusFigure 2:Mean Trace of CVD Status

Functional quantile principal component analysis.

This paper introduces functional quantile principal component analysis (FQPCA), a dimensionality reduction technique that extends the concept of functional principal components analysis (FPCA) to the examination of participant-specific quantiles curves. Our approach borrows strength across participants to estimate patterns in quantiles, and uses participant-level data to estimate loadings on those patterns. As a result, FQPCA is able to capture shifts in the scale and distribution of data that affect participant-level quantile curves, and is also a robust methodology suitable for dealing with outliers, heteroscedastic data or skewed data. The need for such methodology is exemplified by physical activity data collected using wearable devices. Participants often differ in the timing and intensity of physical activity behaviors, and capturing information beyond the participant-level expected value curves produced by FPCA is necessary for a robust quantification of diurnal patterns of activity. We illustrate our methods using accelerometer data from the National Health and Nutrition Examination Survey, and produce participant-level 10%, 50%, and 90% quantile curves over 24 h of activity. The proposed methodology is supported by simulation results, and is available as an R package.

Functional Principal Component Analysis for Continuous Non-Gaussian, Truncated, and Discrete Functional Data.

Mobile health studies often collect multiple within-day self-reported assessments of participants' behavior and well-being on different scales such as physical activity (continuous scale), pain levels (truncated scale), mood states (ordinal scale), and the occurrence of daily life events (binary scale). These assessments, when indexed by time of day, can be treated and analyzed as functional data corresponding to their respective types: continuous, truncated, ordinal, and binary. Motivated by these examples, we develop a functional principal component analysis that deals with all four types of functional data in a unified manner. It employs a semiparametric Gaussian copula model, assuming a generalized latent non-paranormal process as the underlying generating mechanism for these four types of functional data. We specify latent temporal dependence using a covariance estimated through Kendall's bridging method, incorporating smoothness in the bridging process. The approach is then extended with methods for handling both dense and sparse sampling designs, calculating subject-specific latent representations of observed data, latent principal components and principal component scores. Simulation studies demonstrate the method's competitive performance under both dense and sparse sampling designs. The method is applied to data from 497 participants in the National Institute of Mental Health Family Study of Mood Spectrum Disorders to characterize differences in within-day temporal patterns of mood in individuals with the major mood disorder subtypes, including Major Depressive Disorder and Type 1 and 2 Bipolar Disorder. Software implementation of the proposed method is provided in an R-package.

Non-linear dynamics of global liquidity and energy sector profitability

ABSTRACT This study examines how global liquidity influences the profitability of companies in the energy sector using a non-linear approach. Applying Functional Principal Component Analysis (FPCA) to sparse data, we reconstruct the profitability history of 497 energy companies in various subsectors, including coal, oil and gas, oil and gas-related equipment and services, renewable energy, and uranium. We use a Distributed Delay Nonlinear Model (DLNM) to estimate the impact of global liquidity on profitability. Our results reveal distinct nonlinear patterns in the response of these subsectors to changes in global liquidity. For example, in the oil and gas subsector, an extreme quantile (99%) of global liquidity is associated with a significant 5.19% increase in profitability in the first quarter after the shock. In contrast, in the renewable energy subsector, a lower quantile (25%), corresponding to a moderately downward trend, is associated with a 0.73% increase in profitability over the same period. These finings are crucial to improving risk management, investment and policy development strategies within the energy sector, offering a deeper understanding of the dynamics in the global financial and economic landscape.

Estimating Time-Varying Exposure Effects Through Continuous-Time Modelling in Mendelian Randomization.

Mendelian randomization is an instrumental variable method that utilizes genetic information to investigate the causal effect of a modifiable exposure on an outcome. In most cases, the exposure changes over time. Understanding the time-varying causal effect of the exposure can yield detailed insights into mechanistic effects and the potential impact of public health interventions. Recently, a growing number of Mendelian randomization studies have attempted to explore time-varying causal effects. However, the proposed approaches oversimplify temporal information and rely on overly restrictive structural assumptions, limiting their reliability in addressing time-varying causal problems. This article considers a novel approach to estimate time-varying effects through continuous-time modelling by combining functional principal component analysis and weak-instrument-robust techniques. Our method effectively utilizes available data without making strong structural assumptions and can be applied in general settings where the exposure measurements occur at different timepoints for different individuals. We demonstrate through simulations that our proposed method performs well in estimating time-varying effects and provides reliable inference when the time-varying effect form is correctly specified. The method could theoretically be used to estimate arbitrarily complex time-varying effects. However, there is a trade-off between model complexity and instrument strength. Estimating complex time-varying effects requires instruments that are unrealistically strong. We illustrate the application of this method in a case study examining the time-varying effects of systolic blood pressure on urea levels.

Functional data analysis to describe and classify southern resident killer whale calls

The Southern Resident Killer Whale (SRKW) is an endangered population of whales found in the northeast Pacific. They have a vocal dialect unique from other killer whales, having a repertoire of distinct stereotyped calls. A framework for distinguishing SRKW call types using the frequency traces of the amplitude ridges from their spectrograms (termed frequency ridges) is proposed. The first step is the extraction of these ridges of SRKW calls using an Sequential Monte Carlo approach. Next, they are converted into functional data using B-spline functions. They are analyzed with a functional principal component (FPC) analysis to characterise the intrinsic variability of frequency ridges within a call type. The FPCs are able to capture the general patterns in the frequency ridges of the different SRKW call types. The FPCs are also used as the basis for call classification. Using a cross-validation procedure to assess the robustness of the classification, this framework proves to be successful for classification with some call types having an F1-score ≥80%, but other calls less well discriminated. On balance, this approach showed reasonable performance given the small sample size available, and provides a useful contribution towards the development of a universal tool for call classification.

9318 Growth Response To Oral Growth Hormone Secretagogue LUM-201 In Children With Moderate GH Deficiency (GHD) Is Dependent On The Pattern Of Pulsatile GH Secretion Induced By LUM-201

Abstract Disclosure: A. Roslan: None. R. Roman: None. A. Avila: None. D. Said: None. I. Baier: None. E. Brincks: Employee; Self; Lumos Pharma, Inc.. Stock Owner; Self; Lumos Pharma, Inc. A. Bruchey: Employee; Self; Lumos Pharma, Inc.. Stock Owner; Self; Lumos Pharma, Inc. J. McKew: Employee; Self; Lumos Pharma, Inc.. Stock Owner; Self; Lumos Pharma, Inc. P. Pitukcheewanont: Employee; Self; Lumos Pharma, Inc.. Stock Owner; Self; Lumos Pharma, Inc.. M. Johnson: None. T. Garner: Consulting Fee; Self; Lumos Pharma, Inc.. Grant Recipient; Self; Novo Nordisk. M.O. Thorner: Consulting Fee; Self; Lumos Pharma, Inc.. Stock Owner; Self; Lumos Pharma, Inc. P.E. Clayton: Advisory Board Member; Self; Lumos Pharma, Inc.. Consulting Fee; Self; Lumos Pharma, Inc.. Grant Recipient; Self; Novo Nordisk. A. Stevens: Consulting Fee; Self; Lumos Pharma, Inc. F. Cassorla: Consulting Fee; Self; Lumos Pharma, Inc.. Background: Oral GH secretagogue, LUM-201, increases growth rates in children with moderate GHD in Phase 2 trials (OraGrowtH210 and 212) [ENDO 2023, OR21-06]. GH pulse profiles at baseline (D1) and 6 months (6M) were assessed in OraGrowtH212. This study aims to understand relationships between pulse profiles and growth response to LUM-201. Methods: The OraGrowtH212 trial is being conducted at a single site (Chile). 22 prepubertal children (M 14: F 8) with moderate GHD (peak GH level on two stimulation tests >3 and <10ng/ml), who had basal IGF-I >30ng/ml and an acute GH response to 0.8mg/kg LUM-201 of ≥5ng/ml, were randomised to receive LUM-201 1.6 or 3.2 mg/kg/day. 10min samples over 12hrs (08.00-20.00) were collected at D1 and M6 for measurement of GH concentration (ng/ml), with GH secretion rates (ng/ml/min) derived by deconvolution analysis. A univariate Spearman’s rank correlation matrix was used to screen for relationships (significant at p<0.05) between D1 characteristics, D1 height velocity, 6M annualised height velocity (AHV) and interpulse, pulsatile and total GH secretion at D1 and M6.The pattern of pulsatile GH secretion in the 12hr profile was characterised using Functional Principal Component Analysis (FPCA) - used to explore the dominant modes of variation in functional data, in this case the GH time series. Subjects were grouped into tertiles based on 6M AHV (High [mean 8.9cm/yr], Medium [7.7], and Low [6.7]), and the 12hr profiles were divided into three 4hr intervals. The interquartile range (IQR) for mean GH secretion (representing variation in amount) and principal components [PCs] (variation in pattern) for all subjects in each AHV tertile at D1 and M6 were generated. Results: All GH secretion parameters increased significantly from D1 to M6 (p<0.01). Age was negatively associated with 6m AHV (rs= -0.46), and D1 pulsatile GH secretion was positively associated with D1 AHV (rs = +0.51). However, GH secretion at D1 and M6 was not correlated with 6m AHV. In the FPCA, the difference in IQR for mean GH secretion from D1 to 6M was highest over 0-4hrs for subjects in the high and medium AHV tertiles (5- and 3.3-fold greater respectively compared to the other time intervals), while subjects with low AHV had the highest difference over 8-12hrs (42-fold greater). Using the first PC (which accounts for ∼50% of total variation), the change in IQR was highest over 0-4 and 4-8hrs in the high AHV tertile (3-fold greater compared to other time intervals), over 0-4hrs in the medium tertile (46-fold greater) and over 8-12hrs in the low tertile (3.4-fold greater). Conclusions: Oral LUM-201 stimulates significant increases in GH secretion over 6 months in children with moderate GH deficiency. Complex relationships exist between growth response and both the amount and pattern of GH secretion, with the highest growth responses to LUM-201 associated with the greatest pulsatile activity early in the profile. Presentation: 6/3/2024

Strain Patterns With Ultrasound for Assessment of Abdominal Aortic Aneurysm Vessel Wall Biomechanics

BackgroundAbdominal aortic aneurysms (AAAs) are an important cause of death. Small AAAs are surveyed with ultrasound (US) until a defined diameter threshold, often triggering a computer tomography scan and surgical repair. Nevertheless, 5%–10% of AAA ruptures are below threshold, and some large AAAs never rupture. AAA wall biomechanics may reveal vessel wall degradation with potential for patient-centred risk assessment. This clinical study investigated AAA vessel wall biomechanics and deformation patterns, including reproducibility. MethodsIn 50 patients with AAA, 183 video clips were recorded by two sonographers. Prototype software extracted AAA vessel wall principal strain characteristics and patterns. Functional principal component analysis (FPCA) derived strain pattern statistics. ResultsStrain patterns demonstrated reduced AAA wall strains close to the spine. The strain pattern “topography” (i.e., curve phases or “peaks” and “valleys”) had a 3.9 times lower variance than simple numeric assessment of strain amplitudes, which allowed for clustering in two groups with FPCA. A high mean reproducibility of these clusters of 87.6% was found. Median pulse pressure-normalised mean principal strain (PPPS) was 0.038%/mm Hg (interquartile range: 0.029–0.051%/mm Hg) with no correlation to AAA size (Spearman's ρ = 0.02, false discovery rate-p = 0.15). Inter-operator reproducibility of PPPS was poor (limits of agreement: ±0.031%/mm Hg). DiscussionStrain patterns challenge previous numeric stiffness measures based on anterior-posterior-diameter and are reproducible for clustering. This study's PPPS aligned with prior findings, although clinical reproducibility was poor. In contrast, US-based strain patterns hold promising potential to enhance AAA risk assessment beyond traditional diameter-based metrics.

Functional Data Analysis: An Introduction and Recent Developments.

Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are generally the same as for statistical analyses of scalar-valued or multivariate data, but FDA brings additional challenges due to the high- and infinite dimensionality of observations and parameters, respectively. This paper provides an introduction to FDA, including a description of the most common statistical analysis techniques, their respective software implementations, and some recent developments in the field. The paper covers fundamental concepts such as descriptives and outliers, smoothing, amplitude and phase variation, and functional principal component analysis. It also discusses functional regression, statistical inference with functional data, functional classification and clustering, and machine learning approaches for functional data analysis. The methods discussed in this paper are widely applicable in fields such as medicine, biophysics, neuroscience, and chemistry and are increasingly relevant due to the widespread use of technologies that allow for the collection of functional data. Sparse functional data methods are also relevant for longitudinal data analysis. All presented methods are demonstrated using available software in R by analyzing a dataset on human motion and motor control. To facilitate the understanding of the methods, their implementation, and hands-on application, the code for these practical examples is made available through a code and data supplement and on GitHub.

FAStEN: An Efficient Adaptive Method for Feature Selection and Estimation in High-Dimensional Functional Regressions

Functional regression analysis is an established tool for many contemporary scientific applications. Regression problems involving large and complex data sets are ubiquitous, and feature selection is crucial for avoiding overfitting and achieving accurate predictions. We propose a new, flexible and ultra-efficient approach to perform feature selection in a sparse high dimensional function-on-function regression problem, and we show how to extend it to the scalar-on-function framework. Our method, called FAStEN, combines functional data, optimization, and machine learning techniques to perform feature selection and parameter estimation simultaneously. We exploit the properties of Functional Principal Components and the sparsity inherent to the Dual Augmented Lagrangian problem to significantly reduce computational cost, and we introduce an adaptive scheme to improve selection accuracy. In addition, we derive asymptotic oracle properties, which guarantee estimation and selection consistency for the proposed FAStEN estimator. Through an extensive simulation study, we benchmark our approach to the best existing competitors and demonstrate a massive gain in terms of CPU time and selection performance, without sacrificing the quality of the coefficients’ estimation. The theoretical derivations and the simulation study provide a strong motivation for our approach. Finally, we present an application to brain fMRI data from the AOMIC PIOP1 study. Complete FAStEN code is provided at https://github.com/IBM/funGCN. Supplementary materials for this article are available online.

Diurnal timing of physical activity and risk of colorectal cancer in the UK Biobank

BackgroundPhysical activity reduces colorectal cancer risk, yet the diurnal timing of physical activity in colorectal cancer etiology remains unclear.MethodsThis study used 24-h accelerometry time series from UK Biobank participants aged 42 to 79 years to derive circadian physical activity patterns using functional principal component analysis. Multivariable Cox proportional hazard models were used to examine associations with colorectal cancer risk.ResultsAmong 86,252 participants (56% women), 529 colorectal cancer cases occurred during a median 5.3-year follow-up. We identified four physical activity patterns that explained almost 100% of the data variability during the day. A pattern of continuous day-long activity was inversely associated with colorectal cancer risk (hazard ratio (HR) = 0.94, 95% confidence interval (CI) = 0.89–0.99). A second pattern of late-day activity was suggestively inversely related to risk (HR = 0.93, 95% CI = 0.85–1.02). A third pattern of early- plus late-day activity was associated with decreased risk (HR = 0.89, 95% CI = 0.80–0.99). A fourth pattern of mid-day plus night-time activity showed no relation (HR = 1.02, 95% CI = 0.88–1.19). Our results were consistent across various sensitivity analyses, including the restriction to never smokers, the exclusion of the first 2 years of follow-up, and the adjustment for shift work.ConclusionsA pattern of early- plus late-day activity is related to reduced colorectal cancer risk, beyond the benefits of overall activity. Further research is needed to confirm the role of activity timing in colorectal cancer prevention.

Longitudinal activity monitoring and lifespan: quantifying the interface.

Understanding the relationship between activity over the entire lifespan and longevity is an important facet of aging research. We present a comprehensive framework for the statistical analysis of longitudinal activity and behavioral monitoring and their relationship with age-at-death at the individual level, highlighting the importance of advanced methodological approaches in aging research. The focus is on animal models, where continuous monitoring activity in terms of movement, reproduction and behaviors over the entire lifespan is feasible at the individual level. We specifically demonstrate the methodology with data on activity monitoring for Mediterranean fruit flies. Advanced statistical methodologies to explore the interface between activity and age-at-death include functional principal component analysis, concurrent regression, Fréchet regression and point processes. While the focus of this perspective is on relating age-at-death with data on movement, reproduction, behavior and nutrition of Mediterranean fruit flies, the methodology equally pertains to data from other species, including human data.

Functional Principal Component Analysis as an Alternative to Mixed-Effect Models for Describing Sparse Repeated Measures in Presence of Missing Data.

Analyzing longitudinal data in health studies is challenging due to sparse and error-prone measurements, strong within-individual correlation, missing data and various trajectory shapes. While mixed-effect models (MM) effectively address these challenges, they remain parametric models and may incur computational costs. In contrast, functional principal component analysis (FPCA) is a non-parametric approach developed for regular and dense functional data that flexibly describes temporal trajectories at a potentially lower computational cost. This article presents an empirical simulation study evaluating the behavior of FPCA with sparse and error-prone repeated measures and its robustness under different missing data schemes in comparison with MM. The results show that FPCA is well-suited in the presence of missing at random data caused by dropout, except in scenarios involving most frequent and systematic dropout. Like MM, FPCA fails under missing not at random mechanism. The FPCA was applied to describe the trajectories of four cognitive functions before clinical dementia and contrast them with those of matched controls in a case-control study nested in a population-based aging cohort. The average cognitive declines of future dementia cases showed a sudden divergence from those of their matched controls with a sharp acceleration 5 to 2.5 years prior to diagnosis.

Monitoring reaction time to digital device in the very-old to detect early cognitive decline

Early detection of cognitive decline is essential for timely intervention and effective management of age-related impairments. We monitored repetitive reaction times to a simple task on senior-friendly tablet computers among 72 functionally independent older adults, with a mean age of 82, ranging up to 100 years, within natural settings over two years. Functional principal component analyses revealed a consistent decrease in reaction time in line with their task experience among those without subjective cognitive decline. Conversely, individuals reporting subjective cognitive decline showed no consistent trend and exhibited wide variability over time. These distinctive reaction time trajectories in very old adults suggest the potential for monitoring as a non-invasive, convenient method for early detection of cognitive impairment.

Functional sufficient dimension reduction through distance covariance

Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has several advantages over existing methods. Unlike current techniques which require restrictive assumptions such as linear conditional mean and constant covariance, our method has mild requirements on the predictor. Additionally, our method does not involve the use of the unbounded inverse of the covariance operator. The link function between the response and predictor can be arbitrary, and our proposed method maintains the advantage of being model-free, without the need to estimate the link function. Furthermore, our method is naturally suited for sparse longitudinal data. We utilize functional principal component analysis with truncation as a regularization mechanism in the development of our method. We provide justification for the validity of our proposed method, and establish statistical consistency of the estimator under certain regularization conditions. To demonstrate the effectiveness of our proposed method, we conduct simulation studies and real data analysis. The results show improved performance compared to existing methods.

Multilevel Longitudinal Functional Principal Component Model.

Sensor devices, such as accelerometers, are widely used for measuring physical activity (PA). These devices provide outputs at fine granularity (e.g., 10-100Hz or minute-level), which while providing rich data on activity patterns, also pose computational challenges with multilevel densely sampled data, resulting in PA records that are measured continuously across multiple days and visits. On the other hand, a scalar health outcome (e.g., BMI) is usually observed only at the individual or visit level. This leads to a discrepancy in numbers of nested levels between the predictors (PA) and outcomes, raising analytic challenges. To address this issue, we proposed a multilevel longitudinal functional principal component analysis (mLFPCA) model to directly model multilevel functional PA inputs in a longitudinal study, and then implemented a longitudinal functional principal component regression (FPCR) to explore the association between PA and obesity-related health outcomes. Additionally, we conducted a comprehensive simulation study to examine the impact of imbalanced multilevel data on both mLFPCA and FPCR performance and offer guidelines for selecting optimal methods.

In Silico and In Vitro Investigation of Phytoconstituents from Flacourtia Jangomas as a Potential Candidate for the Treatment of Type 2 Diabetes Mellitus

AbstractFlacourtia jangomas is a plant used for centuries in Brazil, China, India, and the Malaya Peninsula to treat conditions such as diabetes, asthma, anaemia, and diarrhoea. Despite its therapeutic and economic benefits, the plant has not been popular among farmers due to its limited yield and lack of knowledge about its potential. Targeting PPARγ agonists is a promising approach for discovering and developing effective drugs to treat type 2 diabetes. Due to the activation of the PPARγ through PPARγ agonists, target genes implicated in inflammation, adipogenesis, lipid metabolism, and glucose metabolism are transcriptionally regulated. This study analysed the curated datasets of F. jangomas to identify the binding conformations of the phytoconstituents with different T2DM targets through molecular docking, molecular dynamics, and ADMET prediction approach. To determine the most favourable binding conformations of phytoconstituents that bind with the PPARγ receptors, density functional theory and principal component analysis were performed. The study reveals that the phytoconstituents of F. jangomas can act as PPARγ agonists and could be used to design and optimise the potential antidiabetic agents inspired by natural products. These findings provide a promising approach towards developing effective antidiabetic drugs.