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.

Genetic and methylation profiles distinguish benign, malignant and spitzoid melanocytic tumors.

Accurate classification of melanocytic tumors is important for prognostic evaluation, treatment and follow-up protocols of patients. The majority of melanocytic proliferations can be classified solely based on clinical and pathological criteria, however in select cases a definitive diagnostic assessment remains challenging and additional diagnostic biomarkers would be advantageous. We analyzed melanomas, nevi, Spitz nevi and atypical spitzoid tumors using parallel sequencing (exons of 611 genes and 507 gene translocation analysis) and methylation arrays (850k Illumina EPIC). By combining detailed genetic and epigenetic analysis with reference-based and reference-free DNA methylome deconvolution we compared Spitz nevi to nevi and melanoma and assessed the potential for these methods in classifying challenging spitzoid tumors. Results were correlated with clinical and histologic features. Spitz nevi were found to cluster independently of nevi and melanoma and demonstrated a different mutation profile. Multiple copy number alterations and TERT promoter mutations were identified only in melanomas. Genome-wide methylation in Spitz nevi was comparable to benign nevi while the Leukocytes UnMethylation for Purity (LUMP) algorithm in Spitz nevi was comparable to melanoma. Histologically difficult to classify Spitz tumor cases were assessed which, based on methylation arrays, clustered between Spitz nevi and melanoma and in terms of genetic profile or copy number variations demonstrated worrisome features suggesting a malignant neoplasm. Comprehensive sequencing and methylation analysis verify Spitz nevi as an independent melanocytic entity distinct from both nevi and melanoma. Combined genetic and methylation assays can offer additional insights in diagnosing difficult to classify Spitzoid tumors.

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.

Atypical fibroxanthoma and pleomorphic dermal sarcoma harbor frequent NOTCH1/2 and FAT1 mutations and similar DNA copy number alteration profiles.

Atypical fibroxanthomas and pleomorphic dermal sarcomas are tumors arising in sun-damaged skin of elderly patients. They have differing prognoses and are currently distinguished using histological criteria, such as invasion of deeper tissue structures, necrosis and lymphovascular or perineural invasion. To investigate the as-yet poorly understood genetics of these tumors, 41 atypical fibroxanthomas and 40 pleomorphic dermal sarcomas were subjected to targeted next-generation sequencing approaches as well as DNA copy number analysis by comparative genomic hybridization. In an analysis of the entire coding region of 341 oncogenes and tumor suppressor genes in 13 atypical fibroxanthomas using an established hybridization-based next-generation sequencing approach, we found that these tumors harbor a large number of mutations. Gene alterations were identified in more than half of the analyzed samples in FAT1, NOTCH1/2, CDKN2A, TP53, and the TERT promoter. The presence of these alterations was verified in 26 atypical fibroxanthoma and 35 pleomorphic dermal sarcoma samples by targeted amplicon-based next-generation sequencing. Similar mutation profiles in FAT1, NOTCH1/2, CDKN2A, TP53, and the TERT promoter were identified in both atypical fibroxanthoma and pleomorphic dermal sarcoma. Activating RAS mutations (G12 and G13) identified in 3 pleomorphic dermal sarcoma were not found in atypical fibroxanthoma. Comprehensive DNA copy number analysis demonstrated a wide array of different copy number gains and losses, with similar profiles in atypical fibroxanthoma and pleomorphic dermal sarcoma. In summary, atypical fibroxanthoma and pleomorphic dermal sarcoma are highly mutated tumors with recurrent mutations in FAT1, NOTCH1/2, CDKN2A, TP53, and the TERT promoter, and a range of DNA copy number alterations. These findings suggest that atypical fibroxanthomas and pleomorphic dermal sarcomas are genetically related, potentially representing two ends of a common tumor spectrum and distinguishing these entities is at present still best performed using histological criteria.

Activating cysteinyl leukotriene receptor 2 (CYSLTR2) mutations in blue nevi.

Blue nevi are common melanocytic tumors arising in the dermal layer of the skin. Similar to uveal melanomas, blue nevi frequently harbor GNAQ and GNA11 mutations. Recently, recurrent CYSLTR2 and PLCB4 mutations were identified in uveal melanomas not harboring GNAQ or GNA11 mutations. All four genes (GNAQ, GNA11, CYSLTR2, and PLCB4) code for proteins involved in the same signaling pathway, which is activated by mutations in these genes. Given the related functional consequences of these mutations and the known genetic similarities between uveal melanoma and blue nevi, we analyzed a cohort of blue nevi to investigate whether CYSLTR2 and PLCB4 mutations occur in tumors lacking GNAQ or GNA11 mutations (as in uveal melanoma). A targeted next-generation sequencing assay covering known activating mutations in GNAQ, GNA11, CYSLTR2, PLCB4, KIT, NRAS, and BRAF was applied to 103 blue nevi. As previously reported, most blue nevi were found to harbor activating mutations in GNAQ (59%, n=61), followed by less frequent mutations in GNA11 (16%, n=17). Additionally, one BRAF (1%) and three NRAS (3%) mutations were detected. In three tumors (3%) harboring none of the aforementioned gene alterations, CYSLTR2 mutations were identified. All three CYSLTR2 mutations were the same c.386T>A, L129Q mutation previously identified in uveal melanoma that has been shown to lead to increased receptor activation and signaling. In summary, our study identifies CYSLTR2 L129Q alterations as a previously unrecognized activating mutation in blue nevi, occuring in a mutually exclusive fashion with known GNAQ and GNA11 mutations. Similar to GNAQ and GNA11 mutations, CYSLTR2 mutations, when present, are likely defining pathogenetic events in blue nevi.

SF3B1 and BAP1 mutations in blue nevus-like melanoma.

Blue nevi are melanocytic tumors originating in the cutaneous dermis. Malignant tumors may arise in association with or resembling blue nevi, so called 'blue nevus-like melanoma', which can metastasize and result in patient death. Identifying which tumors will behave in a clinically aggressive manner can be challenging. Identifying genetic alterations in such tumors may assist in their diagnosis and prognostication. Blue nevi are known to be genetically related to uveal melanomas (eg, both harboring GNAQ and GNA11 mutations). In this study, we analyzed a large cohort (n=301) of various morphologic variants of blue nevi and related tumors including tumors diagnosed as atypical blue nevi (n=21), and blue nevus-like melanoma (n=12), screening for all gene mutations known to occur in uveal melanoma. Similar to published reports, we found the majority of blue nevi harbored activating mutations in GNAQ (53%) or GNA11 (15%). In addition, rare CYSLTR2 (1%) and PLCB4 (1%) mutations were identified. EIF1AX, SF3B1, and BAP1 mutations were also detected, with BAP1 and SF3B1 R625 mutations being present only in clearly malignant tumors (17% (n=2) and 25% (n=3) of blue nevus-like melanoma, respectively). In sequencing data from a larger cohort of cutaneous melanomas, this genetic profile was also identified in tumors not originally diagnosed as blue nevus-like melanoma. Our findings suggest that the genetic profile of coexistent GNAQ or GNA11 mutations with BAP1 or SF3B1 mutations can aid the histopathological diagnosis of blue nevus-like melanoma and distinguish blue nevus-like melanoma from conventional epidermal-derived melanomas. Future studies will need to further elucidate the prognostic implications and appropriate clinical management for patients with tumors harboring these mutation profiles.

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.

Clinicopathologic and molecular features in cutaneous extranodal natural killer-/T-cell lymphoma, nasal type, with aggressive and indolent course.

BACKGROUND: Extranodal natural killer-/T-cell lymphoma, nasal type (ENKTCL-NT) is a highly aggressive lymphoma and prognosis is usually poor. The genetic background of primary cutaneous cases is poorly understood. OBJECTIVE: We sought to evaluate the clinicopathologic features of cutaneous ENKTCL-NT, and the prognostic significance of genomic copy number alterations. METHODS: Eight cases of cutaneous ENKTCL-NT (5 primary, 2 secondary, 1 no staging performed), including 2 patients with an unusually prolonged course of 5 and 23 years, were investigated using array comparative genomic hybridization. RESULTS: All patients presented with typical clinicopathologic features. Epstein-Barr virus was found in neoplastic cells in all specimens. Copy number alterations were detected in all 8 cases with losses on 6q (37.5% of cases) and 7p (37.5% of cases), and gains on 7q (37.5% of cases) being the most frequent. Complexity of array comparative genomic hybridization profile did not correlate with the course of the disease. However, an increase of copy number alterations was detected in sequential biopsy specimens of 1 long-term survivor. LIMITATIONS: This was a small case series retrospective study. CONCLUSION: Clinicopathologic features of cutaneous ENKTCL-NT are distinctive. Lower number of copy number alterations cannot be used as predictor for prolonged survival in cutaneous ENKTCL-NT.

ORF virus infection in a hunter in Western Austria, presumably transmitted by game.

A variety of animals host parapoxviruses. Orf virus is prevalent in sheep and goats in the Tyrol region of Austria and Northern Italy. Zoonotic infections in humans mostly occur after occupational exposure. We report here a case of a hunter with a typical Orf lesion (contagious ecthyma) on the finger, with no history of direct contact with domestic animals. Three weeks previously he had been hunting chamois (Rupicapra rupicapra) and cut his finger while handling a carcass. Parapoxvirus infection was confirmed by electron microscopy and PCR, and the species was identified by DNA sequencing. The sequence was highly homologous with prevalent sheep Orf virus and rather distant from parapoxviruses found in red deer in Northern Italy. As this case indicated that the infection was acquired via game, we performed spot testing in the suspected area and detected several seropositive animals. This is a strong indication that Orf virus has been introduced into chamois in Western Austria. This probably occurred via roaming domestic sheep sharing the high alpine areas during the summer 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.