A Weighted Edge-Count Two-Sample Test for Multivariate and Object Data

Single-cell transcriptomics unveils xylem cell development and evolution

BACKGROUND

Xylem, the most abundant tissue on Earth, is responsible for lateral growth in plants. Typical xylem has a radial system composed of ray parenchyma cells and an axial system of fusiform cells. In most angiosperms, fusiform cells comprise vessel elements for water transportation and libriform fibers for mechanical support, while both functions are performed by tracheids in other vascular plants such as gymnosperms. Little is known about the developmental programs and evolutionary relationships of these xylem cell types.

RESULTS

Through both single-cell and laser capture microdissection transcriptomic profiling, we determine the developmental lineages of ray and fusiform cells in stem-differentiating xylem across four divergent woody angiosperms. Based on cross-species analyses of single-cell clusters and overlapping trajectories, we reveal highly conserved ray, yet variable fusiform, lineages across angiosperms. Core eudicots Populus trichocarpa and Eucalyptus grandis share nearly identical fusiform lineages, whereas the more basal angiosperm Liriodendron chinense has a fusiform lineage distinct from that in core eudicots. The tracheids in the basal eudicot Trochodendron aralioides, an evolutionarily reversed trait, exhibit strong transcriptomic similarity to vessel elements rather than libriform fibers.

CONCLUSIONS

This evo-devo framework provides a comprehensive understanding of the formation of xylem cell lineages across multiple plant species spanning over a hundred million years of evolutionary history.

TWO-SAMPLE TESTS FOR MULTIVARIATE REPEATED MEASUREMENTS OF HISTOGRAM OBJECTS WITH APPLICATIONS TO WEARABLE DEVICE DATA

Repeated observations have become increasingly common in biomedical research and longitudinal studies. For instance, wearable sensor devices are deployed to continuously track physiological and biological signals from each individual over multiple days. It remains of great interest to appropriately evaluate how the daily distribution of biosignals might differ across disease groups and demographics. Hence, these data could be formulated as multivariate complex object data, such as probability densities, histograms, and observations on a tree. Traditional statistical methods would often fail to apply, as they are sampled from an arbitrary non-Euclidean metric space. In this paper we propose novel, nonparametric, graph-based two-sample tests for object data with the same structure of repeated measures. We treat the repeatedly measured object data as multivariate object data, which requires the same number of repeated observations per individual but eliminates any assumptions on the errors of the repeated observations. A set of test statistics are proposed to capture various possible alternatives. We derive their asymptotic null distributions under the permutation null. These tests exhibit substantial power improvements over the existing methods while controlling the type I errors under finite samples as shown through simulation studies. The proposed tests are demonstrated to provide additional insights on the location, inter- and intra-individual variability of the daily physical activity distributions in a sample of studies for mood disorders.

Visualization, benchmarking and characterization of nested single-cell heterogeneity as dynamic forest mixtures

A major topic of debate in developmental biology centers on whether development is continuous, discontinuous, or a mixture of both. Pseudo-time trajectory models, optimal for visualizing cellular progression, model cell transitions as continuous state manifolds and do not explicitly model real-time, complex, heterogeneous systems and are challenging for benchmarking with temporal models. We present a data-driven framework that addresses these limitations with temporal single-cell data collected at discrete time points as inputs and a mixture of dependent minimum spanning trees (MSTs) as outputs, denoted as dynamic spanning forest mixtures (DSFMix). DSFMix uses decision-tree models to select genes that account for variations in multimodality, skewness and time. The genes are subsequently used to build the forest using tree agglomerative hierarchical clustering and dynamic branch cutting. We first motivate the use of forest-based algorithms compared to single-tree approaches for visualizing and characterizing developmental processes. We next benchmark DSFMix to pseudo-time and temporal approaches in terms of feature selection, time correlation, and network similarity. Finally, we demonstrate how DSFMix can be used to visualize, compare and characterize complex relationships during biological processes such as epithelial-mesenchymal transition, spermatogenesis, stem cell pluripotency, early transcriptional response from hormones and immune response to coronavirus disease. Our results indicate that the expression of genes during normal development exhibits a high proportion of non-uniformly distributed profiles that are mostly right-skewed and multimodal; the latter being a characteristic of major steady states during development. Our study also identifies and validates gene signatures driving complex dynamic processes during somatic or germline differentiation.

A nonparametric approach to high-dimensional k-sample comparison problems

High-dimensional $k$-sample comparison is a common task in applications. We construct a class of easy-to-implement distribution-free tests based on new nonparametric tools and unexplored connections with spectral graph theory. The test is shown to have various desirable properties and a characteristic exploratory flavour that has practical consequences for statistical modelling. Numerical examples show that the proposed method works surprisingly well across a broad range of realistic situations.