SUMMARY: Admixed populations, with their unique and diverse genetic backgrounds, are often underrepresented in genetic studies. This oversight not only limits our understanding but also exacerbates existing health disparities. One major barrier has been the lack of efficient tools tailored for the special challenges of genetic studies of admixed populations. Here, we present admix-kit, an integrated toolkit and pipeline for genetic analyses of admixed populations. Admix-kit implements a suite of methods to facilitate genotype and phenotype simulation, association testing, genetic architecture inference, and polygenic scoring in admixed populations. AVAILABILITY AND IMPLEMENTATION: Admix-kit package is open-source and available at https://github.com/KangchengHou/admix-kit. Additionally, users can use the pipeline designed for admixed genotype simulation available at https://github.com/UW-GAC/admix-kit_workflow.

The number of variants that have a non-zero effect on a trait (i.e. polygenicity) is a fundamental parameter in the study of the genetic architecture of a complex trait. Although many previous studies have investigated polygenicity at a genome-wide scale, a detailed understanding of how polygenicity varies across genomic regions is currently lacking. In this work, we propose an accurate and scalable statistical framework to estimate regional polygenicity for a complex trait. We show that our approach yields approximately unbiased estimates of regional polygenicity in simulations across a wide-range of various genetic architectures. We then partition the polygenicity of anthropometric and blood pressure traits across 6-Mb genomic regions (N = 290K, UK Biobank) and observe that all analyzed traits are highly polygenic: over one-third of regions harbor at least one causal variant for each of the traits analyzed. Additionally, we observe wide variation in regional polygenicity: on average across all traits, 48.9% of regions contain at least 5 causal SNPs, 5.44% of regions contain at least 50 causal SNPs. Finally, we find that heritability is proportional to polygenicity at the regional level, which is consistent with the hypothesis that heritability enrichments are largely driven by the variation in the number of causal SNPs.

In this paper, we propose the first sketching system for interactively personalized and photorealistic face caricaturing. Input an image of a human face, the users can create caricature photos by manipulating its facial feature curves. Our system first performs exaggeration on the recovered 3D face model, which is conducted by assigning the laplacian of each vertex a scaling factor according to the edited sketches. The mapping between 2D sketches and the vertex-wise scaling field is constructed by a novel deep learning architecture. Our approach allows outputting different exaggerations when applying the same sketching on different input figures in term of their different geometric characteristics, which makes the generated results "personalized". With the obtained 3D caricature model, two images are generated, one obtained by applying 2D warping guided by the underlying 3D mesh deformation and the other obtained by re-rendering the deformed 3D textured model. These two images are then seamlessly integrated to produce our final output. Due to the severe stretching of meshes, the rendered texture is of blurry appearances. A deep learning approach is exploited to infer the missing details for enhancing these blurry regions. Moreover, a relighting operation is invented to further improve the photorealism of the result. These further make our results "photorealistic". The qualitative experiment results validated the efficiency of our sketching system.

While graph kernels (GKs) are easy to train and enjoy provable theoretical guarantees, their practical performances are limited by their expressive power, as the kernel function often depends on hand-crafted combinatorial features of graphs. Compared to graph kernels, graph neural networks (GNNs) usually achieve better practical performance, as GNNs use multi-layer architectures and non-linear activation functions to extract high-order information of graphs as features. However, due to the large number of hyper-parameters and the non-convex nature of the training procedure, GNNs are harder to train. Theoretical guarantees of GNNs are also not well-understood. Furthermore, the expressive power of GNNs scales with the number of parameters, and thus it is hard to exploit the full power of GNNs when computing resources are limited. The current paper presents a new class of graph kernels, Graph Neural Tangent Kernels (GNTKs), which correspond to \emph{infinitely wide} multi-layer GNNs trained by gradient descent. GNTKs enjoy the full expressive power of GNNs and inherit advantages of GKs. Theoretically, we show GNTKs provably learn a class of smooth functions on graphs. Empirically, we test GNTKs on graph classification datasets and show they achieve strong performance.