Visualizing population structure with variational autoencoders

Dimensionality reduction is a common tool for visualization and inference of population structure from genotypes, but popular methods either return too many dimensions for easy plotting (PCA) or fail to preserve global geometry (t-SNE and UMAP). Here we explore the utility of variational autoencoders (VAEs)—generative machine learning models in which a pair of neural networks seek to first compress and then recreate the input data—for visualizing population genetic variation. VAEs incorporate nonlinear relationships, allow users to define the dimensionality of the latent space, and in our tests preserve global geometry better than t-SNE and UMAP. Our implementation, which we call popvae, is available as a command-line python program at github.com/kr-colab/popvae. The approach yields latent embeddings that capture subtle aspects of population structure in humans and Anopheles mosquitoes, and can generate artificial genotypes characteristic of a given sample or population.

Global properties of toric nearly Kähler manifolds

We study toric nearly Kähler manifolds, extending the work of Moroianu and Nagy. We give a description of the global geometry using multi-moment maps. We then investigate polynomial and radial solutions to the toric nearly Kähler equation.

The local and global geometry of trabecular bone

The organization and shape of the microstructural elements of trabecular bone govern its physical properties, are implicated in bone disease, and can serve as blueprints for biomaterial design. To devise fundamental structure-property relationships, it is essential to characterize trabecular bone from the perspective of geometry, the mathematical study of shape. Here, we used the micro-computed tomography images of 70 donors at five different sites to characterize the local and global geometry of human trabecular bone, respectively quantified by surface curvatures and Minkowski functionals. We find that curvature density maps provide sensitive shape fingerprints for bone from different sites. Contrary to a common assumption, these curvature maps also show that bone morphology does not approximate a minimal surface but exhibits a much more intricate curvature landscape. At the global (or integral) perspective, our Minkowski analysis illustrates that trabecular bone exhibits other types of anisotropy/ellipticity beyond interfacial orientation, and that anisotropy varies substantially within the trabecular structure. Moreover, we show that the Minkowski functionals unify several traditional morphometric indices. Our geometric approach to trabecular morphometry provides a fundamental language of shape that could be useful for bone failure prediction, understanding geometry-driven tissue growth, and the design of complex tissue engineering scaffolds.

Visualizing Population Structure with Variational Autoencoders

Dimensionality reduction is a common tool for visualization and inference of population structure from genotypes, but popular methods either return too many dimensions for easy plotting (PCA) or fail to preserve global geometry (t-SNE and UMAP). Here we explore the utility of variational autoencoders (VAEs) – generative machine learning models in which a pair of neural networks seek to first compress and then recreate the input data – for visualizing population genetic variation. VAEs incorporate non-linear relationships, allow users to define the dimensionality of the latent space, and in our tests preserve global geometry better than t-SNE and UMAP. Our implementation, which we call popvae, is available as a command-line python program at github.com/kr-colab/popvae. The approach yields latent embeddings that capture subtle aspects of population structure in humans and Anopheles mosquitoes, and can generate artificial genotypes characteristic of a given sample or population.

Characterisation of Portuguese RC Precast Industrial Building Stock

The construction of a vulnerability model requires reliable information on the features of the buildings in the study. The purpose of this work is the characterisation of the precast industrial buildings in Portuguese industrial park, based on the survey of 73 design projects of existing buildings. The collected data are based on a previous study on the features that influence the seismic response of this type of buildings. The parameters collected are associated with the global geometry and specific elements characteristics (e.g., column dimensions, reinforcement ratios, and connections details), to the mechanical properties of the materials and other parameters that can give some important information in the characterisation of the buildings (e.g., construction year and localization). In the end, a comparison with other available databases, namely, from Italy and Turkey, is done in order to conclude about the similarity. This information is important to define representative experimental specimens and numerical simulation to conduce seismic risk analysis.

Global geometry on moduli of local systems for surfaces with boundary

We show that every coarse moduli space, parametrizing complex special linear rank-2 local systems with fixed boundary traces on a surface with nonempty boundary, is log Calabi–Yau in that it has a normal projective compactification with trivial log canonical divisor. We connect this to a novel symmetry of generating series for counts of essential multicurves on the surface.