dataesr/scientific-paragraphs-categorization huggingface dataset:
Broadly, spatial process data can be split according to whether they exhibit asymptotic independence or asymptotic dependence. As mentioned, these can be characterized by whether the data display independence or dependence in the limiting distribution of pointwise maxima, but when considering threshold exceedances other definitions are more useful. Consider two spatial locations s, s+h ∈ S. For Y (s) ∼ F s , define the tail correlation function  (Strokorb et al. , 2015)  as χ(s, s + h) = lim q→1 Pr{F s+h (Y (s + h)) > q|F s (Y (s)) > q}. (1) If χ(s, s + h) = 0 for all h = 0 then Y is asymptotically independent, or asymptotically dependent where limit (1) is positive for all h. Intermediate scenarios of asymptotic dependence up to a certain distance are also possible. Asymptotic dependence is a minimum requirement for use of max-stable or Pareto process models, but in practice more rigid assumptions are imposed as these models do not allow for any weakening of dependence with the level of the event -a feature common in most environmental datasets.
Recent work on modeling of spatial extremes has focused on the twin challenges of incorporating flexible extremal dependence structures, and developing models and inference techniques that allow for large numbers of observation locations. Huser et al. (2017 Huser et al. ( , 2021) )  suggest Gaussian scale mixture models, for which both types of extremal dependence can be captured depending on the distribution of the scaling variable. The model of  Huser and Wadsworth (2019)  was the first to offer a smooth transition between dependence classes, meaning it is not necessary to make a choice before fitting the model. However, owing to complicated likelihoods, each of these models is limited in practice to datasets with tens of observation locations. Modifications in  Zhang et al. (2021)  suggest that hundreds of sites might be possible, but further scalability looks elusive for now.
Overview of paper The remainder of the paper is structured as follows. In Section 2, we provide flexible forms for the conditional spatial extremes model that are possible under the latent variable framework. We apply our inferential approach for modeling conditional spatial extremes to a dataset of Red Sea surface temperatures in Section 3, and consider a range of diagnostics to aid model selection and the assessment of model fit. A spatio-temporal extension is presented in Section 4. Section 5 is aimed at those readers interested in the specifics of implementation, and includes more detail on the stochastic partial differential equation (SPDE) approach used to generate numerically convenient approximations to the Matérn covariance and implementation in R-INLA. Section 6 concludes with a discussion.
Overview In this section, we propose specific model structures for the general model (5) and illustrate an application of our approach using a dataset of Red Sea surface temperatures, the spatio-temporal extremes of which have also been studied by  Hazra and Huser (2021)  and  Simpson and Wadsworth (2021) , for instance. We focus on the purely spatial case here, and consider further spatio-temporal modeling extensions for this dataset in Section 4. We begin with an introduction to the data, and a discussion of the transformation to exponential-tailed marginal distributions required for conditional extremes modeling. We then consider variants of the conditional spatial model, based on the possibilities introduced in Section 1. 3, and use a range of diagnostics to assess their relative suitability for modeling the Red Sea data.
Red Sea surface temperature data The surface temperature dataset comprises daily observations for the years 1985 to 2015 for 16703 locations across the Red Sea, corresponding to 0. 05 • × 0. 05 • grid cells. We focus only on the months of July to September to approximately eliminate the effects of seasonality. More information on the data, which were obtained from a combination of satellite and in situ observations, can be found in  Donlon et al. (2012). Extreme events in this dataset are of interest, since particularly high water temperatures can be detrimental to marine life, e. g. , causing coral bleaching, and in some cases coral mortality. Simpson and Wadsworth (2021)  apply their conditional spatio-temporal extremes model to a subset of 54 grid cells located across the north of the Red Sea.
In this paper, we instead focus on a southern portion of the Red Sea, where coral bleaching is currently more of a concern  (Fine et al. , 2019). We demonstrate our approach using datasets of two different spatial dimensions; the first dataset contains 6239 grid cells, corresponding to all available locations in our region of interest, while the second dataset is obtained by taking locations at every third longitude and latitude value in this region, leaving 678 grid cells to consider. These two sets of spatial locations are shown in Figure  2. Simpson and Wadsworth (2021)  consider their 54 spatial locations at five time-points, resulting in a lower dimensional problem than both the datasets we consider here. On the other hand,  Hazra and Huser (2021)  model the full set of 16703 grid cells, but they ensure computational feasibility by implementing so-called 'low-rank' modeling techniques using spatial basis functions given by the dominant empirical orthogonal functions, obtained from preliminary empirical estimation of the covariance matrix of the data.
That is, we assume the distribution function F (y) =      1 -λ v 1 + ξ(y-v) σv -1/ξ + , y ≥ v F (y), y < v, for λ v = 1 -F (v) , σ v > 0 and y + = max(y, 0). In practice, we take v to be the empirical 0. 95 quantile of Y , so that λ v = 0. 05. Having fitted this model, we obtain standard Laplace margins via the transformation X =    log {2F (Y )} , F (Y ) ≤ 1/2, -log [2{1 -F (Y )}] , F (Y ) > 1/2. This transformation is applied separately for each spatial location, with the parameters of the generalized Pareto distributions estimated using the ismev package in R  (Heffernan and Stephenson, 2018). It is possible to include covariate information in the marginal parameters and impose spatial smoothness on these, for instance by using flexible generalized additive models (see  Castro-Camilo et al.
Model 2 is also asymptotically dependent, but allows for weaker dependence than in Model 0 due to the drift that is captured by the γ(s -s 0 ) term, supposed to be negative in practice based on the remarks following equation (  5 ). In Model 6, the residual process has been removed, so that all variability is forced to be captured by the nugget process i in (5). Models 0 and 6 are meant to act as simple baselines to which we can compare the other models, but we would not expect them to perform sufficiently well in practice. As will be detailed in Section 5. 4, we focus on a residual process of the form {Z(s)} -Z(s 0 ) for all of these models. In the remainder of this section, we apply these models to the Red Sea data with the large spatial dataset in Figure  2 , and discuss model selection and diagnostic techniques.
For the conditioning site, we selected a location lying towards the centre of the spatial domain of interest. We discuss this choice further in Section 3. 8, where we present additional results based on the moderate dataset. In Appendix A, we provide an initial assessment of the spatial extremal dependence properties of the sea surface temperature data, based on the tail correlation function defined in (1). These results demonstrate that there is weakening dependence in the data at increasingly extreme levels, which indicates that models for asymptotic independence should be more appropriate here.
7% of the size of the large dataset, and similar in size to the moderate dataset. The mesh was generated using R-INLA, with the most dense region corresponding to the area where we have observations. The extension of the mesh beyond the study region is reasonably big, in order to avoid boundary effects of the SPDE for the sea surface temperatures, whose spatial dependence range is known to be relatively large; see  Simpson and Wadsworth (2021). We use a coarser resolution in the extension region to keep the number of latent Gaussian variables as small as reasonably possible. For specifying the prior distributions of the hyperparameters (e. g. , variances, spatial ranges, autocorrelation coefficients) we use the concept of penalized complexity (PC) priors  (Simpson et al. , 2017) , which has become the standard approach in the INLA framework.
Given the observations v i , i = 1,. , d, the WAIC is then estimated as We use the WAIC to compare each of the models in Table  1  applied to the large spatial dataset of Figure  2 , with smaller WAIC values being preferred. Models 1 and 3 are simplified versions of Models 5 and 4, respectively, in that the value of β is fixed to 0 rather than estimated directly in R-INLA. In both cases, the results are very similar whether β is estimated or fixed, suggesting the simpler models are still effective. d i=1 log 1 S S s=1 π(v i | θs ) - d i=1 V S s=1 log π(v i | θs ) , The estimated WAIC values suggest Models 3 and 4 provide the best fit for our data. The common structure in these models are the terms α(s -s 0 )x and γ(s -s 0 ), indicating that their inclusion is important. In Model 4, the value of β is estimated to be 0.
However, bootstrap methods are needed to assess parameter uncertainty, and as the composite likelihood is formed from the product of d full likelihoods, the approach scales poorly with the number of conditioning sites. Composite  scalability, and straightforward interpretation of parameter uncertainty, we focus on implementations with a single conditioning location. Sensitivity to the particular location can be assessed similarly to other modeling choices, such as the threshold above which the model is fitted. In particular, different conditioning sites may lead us to select different forms of the models described in Table  1 , as well as the resulting parameter estimates. To assess this, we fit all seven models to the moderate dataset, using 39 different conditioning sites on a grid across the spatial domain, with the mesh and prior distributions selected as previously.
Implementation using the R-INLA software While standard functionality available in the R-INLA library allows for straightforward implementation of the unconstrained SPDE model and auto-regressive structures for dimensions D = 1, 2, as presented in Sections 5. 3 and 5. 5, respectively, more specific extensions are required for imposing the condition Z 0 (s 0 , t 0 ) = 0. The R-INLA package provides the precision matrices of the unconstrained latent spatial process {Z(s)}. Spacetime processes {Z(s, t)}, and independent replications of spatial or spatio-temporal processes, are then handled internally by R-INLA. To estimate model components of type b (s,t)-(s0,t0) (x) [{Z(s, t)} -Z(s 0 , t 0 )], with a deterministic function b (s,t)-(s0,t0) that contains no parameters to be estimated through INLA, we can then simply modify the observation matrix A repl and give it as input to the estimation routine.
In all operations involving large precision matrices, it is crucial to use appropriate sparse matrix objects and sparse matrix operations in the R language. In Section 3. 6, we proposed a cross validation procedure that involved removing and subsequently predicting observations in a particular region of the spatial domain. We now highlight that in R-INLA, this is straightforward to achieve by replacing the data for the cross validation by missing data flags, since these values will automatically be estimated, e. g. , through the posterior mean of the "fitted values". We note that some potentially useful constructions are not possible with R-INLA because they violate the linear structure in the Gaussian predictor vector η as expressed through the latent Gaussian components of W. For instance, suppose we wish to construct a prior distribution for a term of the right-hand side in (5) as follows: h(A 1 W 1 ) × A 2 W 2 , with A 2 W 2 corresponding to the spatial residual process {Z 0 (s)} in equation (  4 ), and A 1 W 1 a Gaussian process prior for a spline function (D = 1) where an (arbitrary) function h is used to specify the scale function b s-s0 (x).
Such a transformation is not incorporated within the standard R-INLA set-up, but the anisotropy parameters could be estimated using a generic model. In the spatial setting,  Richards and Wadsworth (2021)  propose a deformation technique to deal with non-stationarity in extremal dependence features. This allows for anisotropy to be handled as a preliminary modeling step, which it would be possible to do in the context of conditional spatial extremes. Our approach is not fully Bayesian, since the marginal transformation of data at each spatial location to a standard Laplace distribution is carried out separately to the dependence modeling. This approach appears sufficient, particularly since simultaneous estimation of the margins and the dependence within the INLA framework would be intricate.
This would result in us resorting to MCMC estimation, but here we do not want to sacrifice the simplicity and speed of the INLA-implementation with big datasets. There are several aspects that we have had to consider as part of the implementation of the conditional extremes models in INLA, with some of these being more important than others. We found the priors of the hyperparameters to have minimal importance, as indicated by posteriors with small credible intervals. This is likely due to the large number of observations we had available. We also observed very similar results when setting the SPDE parameter to ζ = 1. 5 or ζ = 2, so for our data, the smoothness of the Gaussian field does not have a significant impact compared to other aspects of the model. As we may have expected, choosing appropriate normalizing functions is hugely important, and the forms of these may need to be tailored to the specific data application.
03 and P = 6. 0 × 10 -19 for clock 2 and HR = 1. 03, P = 5. 3 × 10 -11 for clock 3; Fig. 3a, b ), although less pronounced than specialized human clocks designed to estimate human mortality risk  22, 23, 28. We evaluated the cross-sectional associations of lifestyle factors and clinical biomarkers with clocks 2 and 3 in the same cohorts. Robust correlation analysis (biweight midcorrelation (bicor)  29  ) revealed associations of both clocks with inflammation (C-reactive protein, bicor = 0. 12, P = 9. 9  × 10 -16  ) and dyslipidemia (triglyceride as these traits are better established and explain over 69% of maximum lifespan variation on the log scale (Supplementary Data 2). This third clock is referred to as the universal log-linear age clock (clock 3). The non-linear mathematical function underlying the age transformation of clock 3 reflects the fact that epigenetic clocks tick faster during development, an observation that led to the establishment of the first pan-tissue clock for humans  4  (Extended Data Fig.
Performance of universal epigenetic clocks across species To evaluate the clocks' accuracy, we employed leave-one-fraction-out (LOFO) and leave-one-species-out (LOSO) cross-validation analyses. Each analysis divides the dataset differently for validation: LOFO into ten fractions with similar proportions of species and tissue types; LOSO excludes one species per iteration. The final models of the clocks use less than 1,000 CpG sites each (Supplementary Data 3. 1-3. 3), with 401 common genes proximal to CpG sites in both clock 2 and clock 3 (Supplementary Data 3. 5). LOFO cross-validation reveals the universal clocks as highly accurate estimators of chronological age (r ≈ 0. 96-0. 98) with a median absolute error (MAE) of <1 year between chronological age and DNA methylation (DNAm)-based age estimate (DNAmAge) and a relative error of <3.
Heritability analysis in humans To investigate whether genetic control within a species influences the epigenetic aging rates measured by pan-mammalian clocks, we used human pedigree data from the FHS. Pedigree-based polygenic models of epigenetic age, adjusted for age and sex, yielded significant   ). These heritability estimates for pan-mammalian clocks are on par with that of Horvath's human pantissue clock (h 2 = 0. 39, P = 4. 0 × 10 -7 )  4.
Epigenetic reprogramming reverses epigenetic age Epigenetic clocks, such as the human pan-tissue clock, suggest that cellular reprogramming based on the Yamanaka factors (collectively termed as OSKM: OCT4, SOX2, KLF4, and c-MYC) induces age reversal  4, 30. To examine whether the universal clocks show a similar age-reversal pattern during reprogramming, we applied clock 2 and clock 3 to a previously published reprogramming dataset in human dermal fibroblasts  31. We imputed the mammalian methylation array data on the basis of the existing human Infinium array data. Both clocks suggest age reversal after OSKM transduction (Fig. 3c, d ). Notably, universal clock 2 showed a decrease in epigenetic age in partially reprogrammed cells after 11 d (Fig. 3c ), mirroring observations with human epigenetic clocks  4, 30, 32.
8  and Supplementary Data 9). Notably, the top 1,000 negatively agerelated CpG sites overlap significantly with CpG sites that are both common PMDs and solo WCGW sites (hg19): skin (OR = 7. 9, P = 1. 6 × 10 -90 ), blood (OR = 5. 3, P = 1. 5 × 10 -50 ) and all tissues (OR = 7. 3, P = 4. 4 × 10 -81 ; For each species, the age groups were defined with respect to the average ASM obtained from the Animal Aging and Longevity Database (AnAge) (de Magalhaes et al. 86  ). We defined the three age groups using intervals defined by multiples of ASM: young age is defined as age <1. 4a ). The x axis denotes the distance to the closest TSS in a log 10 scale of bp. The positive TSS indicates the direction from 5′ to 3′, and the negative TSS indicates from the direction from 3′ to 5′. The horizontal phase is categorized into three regions: distal upstream → promoter → gene bodies.
8 × 10 -202 ), brain (P = 1. 4 × 10 -54 ) and cortex (P = 2. 7 × 10 -115 ; Fig. 7 ). As PRC2 plays a critical role in development, these results reinforce the epigenetic link between development and aging. This connection is supported by observations that developmentally compromised mice, due to growth hormone receptor (GHRKO) ablation or anterior pituitary gland removal (Snell mice), show reduced rates of epigenetic aging in multiple tissues, as measured by universal epigenetic age clocks (Fig. 3e ). While positively age-related CpG sites (across all tissues) were enriched in 2,961 GO or Molecular Signatures Database terms at a false discovery rate of 0. 05 (Supplementary Data 10. 1), negatively agerelated CpG sites were enriched in only three. Negatively age-related CpG sites in brain and muscle were enriched in genes associated with circadian rhythm (brain, P = 3.
8 × 10 -184 ), liver (P = 2. 7 × 10 -112 ), muscle (P = 6. 2 × 10 -5 ), skin (P = 9. 1 × 10 -84 ), combined brain tissues (P = 1. 2 × 10 -21 ) and the cerebral cortex (P = 5. 0 × 10 -50 ). As inflammation increases with aging, we assessed the overlap with inflammation-related gene sets (Supplementary Data 10. 4). Positively age-related CpG sites are enriched in the gene set associated with inflammation in the murine pancreas (all tissues, P = 8. 4 × 10 -21 and skin, P = 9. 4 × 10 -20 ). Negatively age-related CpG sites are enriched in Toll-like signaling (GO:0034121) genes (muscle, P = 9. 2 × 10 -8 ). Both positively and negatively age-related CpG sites are enriched in immunologic signature gene sets associated with interleukin (IL; for example, IL-6, IL-23) and transforming growth factor (TGF)-β1 exposure in type 17 helper T cells (Supplementary Data 10.
TF binding We used the CellBase  52  and ENCODE databases  53  to annotate CpG sites with binding sites for 68 TFs identified through chromatin immunoprecipitation followed by sequencing (ChIP-seq) in 17 cell types. If a CpG site overlapped with the binding site of a TF (hg19) in at least one cell type, it was assigned to that TF. Analysis of the most significant age-related CpG sites across mammals showed that the REST TF was the most significant TF for the top 1,000 positively age-related CpG sites across all tissues (OR = 8. 4, P = 3. 1 × 10 -54 ), especially in proliferative tissues such as blood (OR = 5. 8, P = 2. 7 × 10 -32 ), skin (OR = 8. 7, P = 6. 8 × 10 -59 ) and liver (OR = 5. 4, P = 1. 5 × 10 -28 ). REST TF enrichment was less significant in non-proliferative tissues such as muscle (OR = 1.
8, P = 2. 2 × 10 -3 ), cerebral cortex (OR = 1. 6, P = 0. 01) and brain (OR = 1. 4, P = 0. 09; Extended Data Fig. 9  and Supplementary Data 11). REST TF ChIP-seq analysis was performed on five cell lines, including a human embryonic stem cell line (Supplementary Data 11. 1). REST is known for repressing neuronal genes in non-neuronal tissues, which could explain the weak enrichments in brain regions. Notably, CpG cg12841266 near LHFPL4 is within the REST-binding region. Substantial binding enrichments were observed for transcription factor 12 (TCF12) and histone deacetylase 2 (HDAC2). TCF12 is part of the basic helix-loop-helix (bHLH) E-protein family, associated with neuronal differentiation, and top positively age-related CpG sites are proximal to another bHLH gene, NEUROD1 (Supplementary Table  3  and Supplementary Data 11).
Lower enrichments were noted for CCCTCbinding factor (CTCF) and Nanog homeobox (NANOG). For the top 1,000 negatively age-related CpG sites, fewer significant TF binding enrichments emerged, with JUN (c-Jun) in blood (OR = 2. 8, P = 2. 6 × 10 -9 ) and brain (OR = 1. 5, P = 0. 024; Extended Data Fig. 9 ) being exceptions.
Age-related CpG sites and age-related transcriptomic changes We studied whether the top 1,000 positively and negatively agerelated CpG sites neighbor genes with age-correlated mRNA levels. Using GenAge  54  and Enrichr  55, 56  databases, we scrutinized age-specific transcriptome-wide association studies (TWAS) in four mammalian species. The EWAS-TWAS overlap analysis (Fig. 7 , Extended Data Fig. 10a  and Supplementary Data 12) indicates significant overlaps between age-related CpG sites and transcriptomic age changes in several species, including Genotype-Tissue Expression (GTEx) human tibial nerve samples, normal monkey hippocampal samples (P = 9 × 10 -15 ) and various rat and mouse tissues. However, the age-related EWAS and TWAS overlap is generally weak and tissue specific.
Single-cell ATAC-seq analysis in human bone marrow Low-methylated regions distant from TSS correlate with open chromatin, TF binding and enhancers  57. Hence, our top positively age-related pan-mammalian CpG sites (initially low in methylation, gaining methylation with age) could imply a gradual loss of these open chromatin regions. To validate this, we examined the association between the top 35 positively age-related CpG sites (Supplementary Table  3 ) and chromatin accessibility in single cells from human bone marrow mononuclear cells (BMNCs). Single-cell assay for transposase-accessible chromatin with sequencing (scATAC-seq) data from a recent study  58  employed 10x Multiome technology to profile both ATAC and gene expression within the same cell across ten donors of varying age. Overlaying the genomic regions of the top 35 CpG sites (Supplementary Table  3 ) with the called ATAC peaks within the BMNC dataset identified 17 genes, including LHFPL4 (Supplementary Data 14.