Gradient synchronization for multivariate functional data, with application to brain connectivity.

Quantifying the association between components of multivariate random curves is of general interest and is a ubiquitous and basic problem that can be addressed with functional data analysis. An important application is the problem of assessing functional connectivity based on functional magnetic resonance imaging (fMRI), where one aims to determine the similarity of fMRI time courses that are recorded on anatomically separated brain regions. In the functional brain connectivity literature, the static temporal Pearson correlation has been the prevailing measure for functional connectivity. However, recent research has revealed temporally changing patterns of functional connectivity, leading to the study of dynamic functional connectivity. This motivates new similarity measures for pairs of random curves that reflect the dynamic features of functional similarity. Specifically, we introduce gradient synchronization measures in a general setting. These similarity measures are based on the concordance and discordance of the gradients between paired smooth random functions. Asymptotic normality of the proposed estimates is obtained under regularity conditions. We illustrate the proposed synchronization measures via simulations and an application to resting-state fMRI signals from the Alzheimer's Disease Neuroimaging Initiative and they are found to improve discrimination between subjects with different disease status.

Trajectories of brain volumes in young children are associated with maternal education.

Brain growth in early childhood is reflected in the evolution of proportional cerebrospinal fluid volumes (pCSF), grey matter (pGM), and white matter (pWM). We study brain development as reflected in the relative fractions of these three tissues for a cohort of 388 children that were longitudinally followed between the ages of 18 and 96 months. We introduce statistical methodology (Riemannian Principal Analysis through Conditional Expectation, RPACE) that addresses major challenges that are of general interest for the analysis of longitudinal neuroimaging data, including the sparsity of the longitudinal observations over time and the compositional structure of the relative brain volumes. Applying the RPACE methodology, we find that longitudinal growth as reflected by tissue composition differs significantly for children of mothers with higher and lower maternal education levels.

Latent deformation models for multivariate functional data and time-warping separability.

Multivariate functional data present theoretical and practical complications that are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are subject to mutual time warping. That is, the component processes exhibit a common shape but are subject to systematic phase variation across their domains in addition to subject-specific time warping, where each subject has its own internal clock. This motivates a novel model for multivariate functional data that connect such mutual time warping to a latent-deformation-based framework by exploiting a novel time-warping separability assumption. This separability assumption allows for meaningful interpretation and dimension reduction. The resulting latent deformation model is shown to be well suited to represent commonly encountered functional vector data. The proposed approach combines a random amplitude factor for each component with population-based registration across the components of a multivariate functional data vector and includes a latent population function, which corresponds to a common underlying trajectory. We propose estimators for all components of the model, enabling implementation of the proposed data-based representation for multivariate functional data and downstream analyses such as Fréchet regression. Rates of convergence are established when curves are fully observed or observed with measurement error. The usefulness of the model, interpretations, and practical aspects are illustrated in simulations and with application to multivariate human growth curves and multivariate environmental pollution data.

Autoregressive optimal transport models.

Series of univariate distributions indexed by equally spaced time points are ubiquitous in applications and their analysis constitutes one of the challenges of the emerging field of distributional data analysis. To quantify such distributional time series, we propose a class of intrinsic autoregressive models that operate in the space of optimal transport maps. The autoregressive transport models that we introduce here are based on regressing optimal transport maps on each other, where predictors can be transport maps from an overall barycenter to a current distribution or transport maps between past consecutive distributions of the distributional time series. Autoregressive transport models and their associated distributional regression models specify the link between predictor and response transport maps by moving along geodesics in Wasserstein space. These models emerge as natural extensions of the classical autoregressive models in Euclidean space. Unique stationary solutions of autoregressive transport models are shown to exist under a geometric moment contraction condition of Wu & Shao [(2004) Limit theorems for iterated random functions. Journal of Applied Probability 41, 425-436)], using properties of iterated random functions. We also discuss an extension to a varying coefficient model for first-order autoregressive transport models. In addition to simulations, the proposed models are illustrated with distributional time series of house prices across U.S. counties and annual summer temperature distributions.

Genome sequence of the progenitor of the wheat D genome Aegilops tauschii.

Aegilops tauschii is the diploid progenitor of the D genome of hexaploid wheat (Triticum aestivum, genomes AABBDD) and an important genetic resource for wheat. The large size and highly repetitive nature of the Ae. tauschii genome has until now precluded the development of a reference-quality genome sequence. Here we use an array of advanced technologies, including ordered-clone genome sequencing, whole-genome shotgun sequencing, and BioNano optical genome mapping, to generate a reference-quality genome sequence for Ae. tauschii ssp. strangulata accession AL8/78, which is closely related to the wheat D genome. We show that compared to other sequenced plant genomes, including a much larger conifer genome, the Ae. tauschii genome contains unprecedented amounts of very similar repeated sequences. Our genome comparisons reveal that the Ae. tauschii genome has a greater number of dispersed duplicated genes than other sequenced genomes and its chromosomes have been structurally evolving an order of magnitude faster than those of other grass genomes. The decay of colinearity with other grass genomes correlates with recombination rates along chromosomes. We propose that the vast amounts of very similar repeated sequences cause frequent errors in recombination and lead to gene duplications and structural chromosome changes that drive fast genome evolution.

Modeling sparse longitudinal data in early neurodevelopment.

Early childhood is a period marked by rapid brain growth accompanied by cognitive and motor development. However, it remains unclear how early developmental skills relate to neuroanatomical growth across time with no growth quantile trajectories of typical brain development currently available to place and compare individual neuroanatomical development. Even though longitudinal neuroimaging data have become more common, they are often sparse, making dynamic analyses at subject level a challenging task. Using the Principal Analysis through Conditional Expectation (PACE) approach geared towards sparse longitudinal data, we investigate the evolution of gray matter, white matter and cerebrospinal fluid volumes in a cohort of 446 children between the ages of 1 and 120 months. For each child, we calculate their dynamic age-varying association between the growing brain and scores that assess cognitive functioning, applying the functional varying coefficient model. Using local Fréchet regression, we construct age-varying growth percentiles to reveal the evolution of brain development across the population. To further demonstrate its utility, we apply PACE to predict individual trajectories of brain development.

Modeling sparse longitudinal data on Riemannian manifolds.

Modern data collection often entails longitudinal repeated measurements that assume values on a Riemannian manifold. Analyzing such longitudinal Riemannian data is challenging, because of both the sparsity of the observations and the nonlinear manifold constraint. Addressing this challenge, we propose an intrinsic functional principal component analysis for longitudinal Riemannian data. Information is pooled across subjects by estimating the mean curve with local Fréchet regression and smoothing the covariance structure of the linearized data on tangent spaces around the mean. Dimension reduction and imputation of the manifold-valued trajectories are achieved by utilizing the leading principal components and applying best linear unbiased prediction. We show that the proposed mean and covariance function estimates achieve state-of-the-art convergence rates. For illustration, we study the development of brain connectivity in a longitudinal cohort of Alzheimer's disease and normal participants by modeling the connectivity on the manifold of symmetric positive definite matrices with the affine-invariant metric. In a second illustration for irregularly recorded longitudinal emotion compositional data for unemployed workers, we show that the proposed method leads to nicely interpretable eigenfunctions and principal component scores. Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative database.

Structural variation and rates of genome evolution in the grass family seen through comparison of sequences of genomes greatly differing in size.

Homology was searched with genes annotated in the Aegilops tauschii pseudomolecules against genes annotated in the pseudomolecules of tetraploid wild emmer wheat, Brachypodium distachyon, sorghum and rice. Similar searches were performed with genes annotated in the rice pseudomolecules. Matrices of collinear genes and rearrangements in their order were constructed. Optical BioNano genome maps were constructed and used to validate rearrangements unique to the wild emmer and Ae. tauschii genomes. Most common rearrangements were short paracentric inversions and short intrachromosomal translocations. Intrachromosomal translocations outnumbered segmental intrachromosomal duplications. The densities of paracentric inversion lengths were approximated by exponential distributions in all six genomes. Densities of collinear genes along the Ae. tauschii chromosomes were highly correlated with meiotic recombination rates but those of rearrangements were not, suggesting different causes of the erosion of gene collinearity and evolution of major chromosome rearrangements. Frequent rearrangements sharing breakpoints suggested that chromosomes have been rearranged recurrently at some sites. The distal 4 Mb of the short arms of rice chromosomes Os11 and Os12 and corresponding regions in the sorghum, B. distachyon and Triticeae genomes contain clusters of interstitial translocations including from 1 to 7 collinear genes. The rates of acquisition of major rearrangements were greater in the large wild emmer wheat and Ae. tauschii genomes than in the lineage preceding their divergence or in the B. distachyon, rice and sorghum lineages. It is suggested that synergy between large quantities of dynamic transposable elements and annual growth habit have been the primary causes of the fast evolution of the Triticeae genomes.

Longitudinal associations between white matter maturation and cognitive development across early childhood.

From birth to 5 years of age, brain structure matures and evolves alongside emerging cognitive and behavioral abilities. In relating concurrent cognitive functioning and measures of brain structure, a major challenge that has impeded prior investigation of their time-dynamic relationships is the sparse and irregular nature of most longitudinal neuroimaging data. We demonstrate how this problem can be addressed by applying functional concurrent regression models (FCRMs) to longitudinal cognitive and neuroimaging data. The application of FCRM in neuroimaging is illustrated with longitudinal neuroimaging and cognitive data acquired from a large cohort (n = 210) of healthy children, 2-48 months of age. Quantifying white matter myelination by using myelin water fraction (MWF) as imaging metric derived from MRI scans, application of this methodology reveals an early period (200-500 days) during which whole brain and regional white matter structure, as quantified by MWF, is positively associated with cognitive ability, while we found no such association for whole brain white matter volume. Adjusting for baseline covariates including socioeconomic status as measured by maternal education (SES-ME), infant feeding practice, gender, and birth weight further reveals an increasing association between SES-ME and cognitive development with child age. These results shed new light on the emerging patterns of brain and cognitive development, indicating that FCRM provides a useful tool for investigating these evolving relationships.

Quantifying functionals of age distributions in the wild by solving an operator equation.

Residual demography is a recent concept that has proved to be a useful tool to gain insights about the age distributions of wild populations, especially insects. We develop an operator equation that permits the derivation of functionals of the age distribution in wild populations, such as mean age, within the framework of residual demography. Our method combines information from an observed captive cohort, which consists of subjects that are sampled from the wild with unknown ages and then raised in the laboratory until death, and from a reference cohort that consists of subjects raised in the laboratory since birth of the same population. Targeting functionals such as the mean of the wild age distribution has the advantage of avoiding strong assumptions such as stationarity and stability of the population that one would need when targeting the entire survival distribution in the wild. Our main result characterizes the existence of a solution of the operator equation that yields the functional of interest. The proposed method also enjoys straightforward and easy implementation. A data example is included illustrating an application, where one aims to attain the mean age of mosquitoes in the wild, based on seasonal captive cohorts from Greece and a simulated reference cohort, separately for various summer and fall months.

Daily activity profiles over the lifespan of female medflies as biomarkers of aging and longevity.

The relationship between the early-age activity of Mediterranean fruit flies (medflies) or other fruit flies and their lifespan has not been much studied, in contrast to the connections between lifespan and diet, sexual signaling, and reproduction. The objective of this study is to assess intra-day and day-to-day activity profiles of female Mediterranean fruit flies and their role as biomarker of longevity as well as to explore the relationships between these activity profiles, diet, and age-at-death throughout the lifespan. We use advanced statistical methods from functional data analysis (FDA). Three distinct patterns of activity variations in early-age activity profiles can be distinguished. A low-caloric diet is associated with a delayed activity peak, while a high-caloric diet is linked with an earlier activity peak. We find that age-at-death of individual medflies is connected to their activity profiles in early life. An increased risk of mortality is associated with increased activity in early age, as well as with a higher contrast between daytime and nighttime activity. Conversely, medflies are more likely to have a longer lifespan when they are fed a medium-caloric diet and when their daily activity is more evenly distributed across the early-age span and between daytime and nighttime. The before-death activity profile of medflies displays two characteristic before-death patterns, where one pattern is characterized by slowly declining daily activity and the other by a sudden decline in activity that is followed by death.

FTO variation and early frontostriatal brain development in children.

OBJECTIVE: Common obesity-associated genetic variants at the fat mass and obesity-associated (FTO) locus have been associated with appetitive behaviors and altered structure and function of frontostriatal brain regions. The authors aimed to investigate the influence of FTO variation on frontostriatal appetite circuits in early life. METHODS: Data were drawn from RESONANCE, a longitudinal study of early brain development. Growth trajectories of nucleus accumbens and frontal lobe volumes, as well as total gray matter and white matter volume, by risk allele (AA) carrier status on FTO single-nucleotide polymorphism rs9939609 were examined in 228 children (102 female, 126 male) using magnetic resonance imaging assessments obtained from infancy through middle childhood. The authors fit functional concurrent regression models with brain volume outcomes over age as functional responses, and FTO genotype, sex, BMI z score, and maternal education were included as predictors. RESULTS: Bootstrap pointwise 95% CI for regression coefficient functions in the functional concurrent regression models showed that the AA group versus the group with no risk allele (TT) had greater nucleus accumbens volume (adjusted for total brain volume) in the interval of 750 to 2250 days (2-6 years). CONCLUSIONS: These findings suggest that common genetic risk for obesity is associated with differences in early development of brain reward circuitry and argue for investigating dynamic relationships among genotype, brain, behavior, and weight throughout development.

Point process models for COVID-19 cases and deaths.

The study of events distributed over time which can be quantified as point processes has attracted much interest over the years due to its wide range of applications. It has recently gained new relevance due to the COVID-19 case and death processes associated with SARS-CoV-2 that characterize the COVID-19 pandemic and are observed across different countries. It is of interest to study the behavior of these point processes and how they may be related to covariates such as mobility restrictions, gross domestic product per capita, and fraction of population of older age. As infections and deaths in a region are intrinsically events that arrive at random times, a point process approach is natural for this setting. We adopt techniques for conditional functional point processes that target point processes as responses with vector covariates as predictors, to study the interaction and optimal transport between case and death processes and doubling times conditional on covariates.

Daily Activity Profiles over the Lifespan of Female Medflies as Biomarkers of Aging and Longevity.

The relationship between the early age activity of Mediterranean fruit flies or other fruit flies and their lifespan has not been much studied, in contrast to the connections between lifespan and diet, sexual signaling and reproduction. The objective of this study is to assess intraday and day-to-day activity profiles of female Mediterranean fruit flies and their role as biomarker of longevity as well as to explore the relationships between these activity profiles, diet and age-at-death throughout the lifespan. Three distinct patterns of activity variations in early age activity profiles can be distinguished. A low-caloric diet is associated with a delayed activity peak, while a high-caloric diet is linked with an earlier activity peak. We find that age-at-death of individual medflies is connected to their activity profiles in early life. An increased risk of mortality is associated with increased activity in early age, as well as with a higher contrast between daytime and nighttime activity. Conversely, medflies are more likely to have a longer lifespan when they are fed a medium caloric diet and when their daily activity is more evenly distributed across the early age span and between daytime and nighttime. The before-death activity profile of medflies displays two characteristic before-death patterns, where one pattern is characterized by slowly declining daily activity and the other by a sudden decline in activity that is followed by death.

Network evolution of regional brain volumes in young children reflects neurocognitive scores and mother's education.

The maturation of regional brain volumes from birth to preadolescence is a critical developmental process that underlies emerging brain structural connectivity and function. Regulated by genes and environment, the coordinated growth of different brain regions plays an important role in cognitive development. Current knowledge about structural network evolution is limited, partly due to the sparse and irregular nature of most longitudinal neuroimaging data. In particular, it is unknown how factors such as mother's education or sex of the child impact the structural network evolution. To address this issue, we propose a method to construct evolving structural networks and study how the evolving connections among brain regions as reflected at the network level are related to maternal education and biological sex of the child and also how they are associated with cognitive development. Our methodology is based on applying local Fréchet regression to longitudinal neuroimaging data acquired from the RESONANCE cohort, a cohort of healthy children (245 females and 309 males) ranging in age from 9 weeks to 10 years. Our findings reveal that sustained highly coordinated volume growth across brain regions is associated with lower maternal education and lower cognitive development. This suggests that higher neurocognitive performance levels in children are associated with increased variability of regional growth patterns as children age.

Gender and single nucleotide polymorphisms in MTHFR, BHMT, SPTLC1, CRBP2, CETP, and SCARB1 are significant predictors of plasma homocysteine normalized by RBC folate in healthy adults.

Using linear regression models, we studied the main and 2-way interaction effects of the predictor variables gender, age, BMI, and 64 folate/vitamin B-12/homocysteine (Hcy)/lipid/cholesterol-related single nucleotide polymorphisms (SNP) on log-transformed plasma Hcy normalized by RBC folate measurements (nHcy) in 373 healthy Caucasian adults (50% women). Variable selection was conducted by stepwise Akaike information criterion or least angle regression and both methods led to the same final model. Significant predictors (where P values were adjusted for false discovery rate) included type of blood sample [whole blood (WB) vs. plasma-depleted WB; P < 0.001] used for folate analysis, gender (P < 0.001), and SNP in genes SPTLC1 (rs11790991; P = 0.040), CRBP2 (rs2118981; P < 0.001), BHMT (rs3733890; P = 0.019), and CETP (rs5882; P = 0.017). Significant 2-way interaction effects included gender × MTHFR (rs1801131; P = 0.012), gender × CRBP2 (rs2118981; P = 0.011), and gender × SCARB1 (rs83882; P = 0.003). The relation of nHcy concentrations with the significant SNP (SPTLC1, BHMT, CETP, CRBP2, MTHFR, and SCARB1) is of interest, especially because we surveyed the main and interaction effects in healthy adults, but it is an important area for future study. As discussed, understanding Hcy and genetic regulation is important, because Hcy may be related to inflammation, obesity, cardiovascular disease, and diabetes mellitus. We conclude that gender and SNP significantly affect nHcy.

The dynamics of ideology drift among U.S. Supreme Court justices: A functional data analysis.

We study the U.S. Supreme Court dynamics by analyzing the temporal evolution of the underlying policy positions of the Supreme Court Justices as reflected by their actual voting data, using functional data analysis methods. The proposed fully flexible nonparametric method makes it possible to dissect the time-dynamics of policy positions at the level of individual Justices, as well as providing a comprehensive view of the ideology evolution over the history of Supreme Court since its establishment. In addition to quantifying individual Justice's policy positions, we uncover average changes over time and also the major patterns of change over time. Additionally, our approach allows for representing highly complex dynamic trajectories by a few principal components which complements other models of analyzing and predicting court behavior.

Learning delay dynamics for multivariate stochastic processes, with application to the prediction of the growth rate of COVID-19 cases in the United States.

Delay differential equations form the underpinning of many complex dynamical systems. The forward problem of solving random differential equations with delay has received increasing attention in recent years. Motivated by the challenge to predict the COVID-19 caseload trajectories for individual states in the U.S., we target here the inverse problem. Given a sample of observed random trajectories obeying an unknown random differential equation model with delay, we use a functional data analysis framework to learn the model parameters that govern the underlying dynamics from the data. We show the existence and uniqueness of the analytical solutions of the population delay random differential equation model when one has discrete time delays in the functional concurrent regression model and also for a second scenario where one has a delay continuum or distributed delay. The latter involves a functional linear regression model with history index. The derivative of the process of interest is modeled using the process itself as predictor and also other functional predictors with predictor-specific delayed impacts. This dynamics learning approach is shown to be well suited to model the growth rate of COVID-19 for the states that are part of the U.S., by pooling information from the individual states, using the case process and concurrently observed economic and mobility data as predictors.

Functional embedding for the classification of gene expression profiles.

MOTIVATION: Low sample size n high-dimensional large p data with n<

Response-adaptive regression for longitudinal data.

We propose a response-adaptive model for functional linear regression, which is adapted to sparsely sampled longitudinal responses. Our method aims at predicting response trajectories and models the regression relationship by directly conditioning the sparse and irregular observations of the response on the predictor, which can be of scalar, vector, or functional type. This obliterates the need to model the response trajectories, a task that is challenging for sparse longitudinal data and was previously required for functional regression implementations for longitudinal data. The proposed approach turns out to be superior compared to previous functional regression approaches in terms of prediction error. It encompasses a variety of regression settings that are relevant for the functional modeling of longitudinal data in the life sciences. The improved prediction of response trajectories with the proposed response-adaptive approach is illustrated for a longitudinal study of Kiwi weight growth and by an analysis of the dynamic relationship between viral load and CD4 cell counts observed in AIDS clinical trials.