Statistical analysis and modeling of the geometry and topology of plant roots

Coordinated variation in root and leaf functional traits of Hippophae rhamnoides treated at different stump heights in feldspathic sandstone areas of Inner Mongolia

This study was aimed to clarify the effects of stumping on root and leaf traits as well as the tradeoffs and synergies of decaying Hippophae rhamnoides in feldspathic sandstone areas, and to select the optimal stump height that contributed to the recovery and growth of H. rhamnoides. variations and coordination between leaf traits and fine root traits of H. rhamnoides were studied at different stump heights (0, 10, 15, 20 cm, and no stumping) in feldspathic sandstone areas. All functional traits of the leaves and roots, except the leaf C content (LC) and the fine root C content (FRC), were significantly different among different stump heights. The total variation coefficient was the largest in the specific leaf area (SLA), which is therefore the most sensitive trait. Compared to non-stumping, SLA, leaf N content (LN), specific root length (SRL) and fine root N content (FRN) all improved significantly at stump height of 15 cm, but leaf tissue density (LTD), leaf dry matter content (LDMC), leaf carbon to nitrogen ratio (LC : LN), fine root tissue density (FRTD), fine root dry matter content (FRDMC) and fine root carbon to nitrogen ratio (FRC : FRN) all decreased significantly. The leaf traits of H. rhamnoides at different stump heights follow the leaf economic spectrum, and the fine roots show a similar trait syndrome to the leaves. SLA and LN are positively correlated with SRL and FRN and negatively with FRTD and FRC : FRN. LDMC and LC : LN are positively correlated with FRTD and FRC : FRN, and negatively correlated SRL and RN. The stumped H. rhamnoides changes to the 'rapid investment-return type' resource trade-offs strategy, and the growth rate is maximized at the stump height of 15 cm. Our findings are critical to the prevention and control of vegetation recovery and soil erosion in feldspathic sandstone areas.

4D Atlas: Statistical Analysis of the Spatiotemporal Variability in Longitudinal 3D Shape Data

We propose a novel framework to learn the spatiotemporal variability in longitudinal 3D shape data sets, which contain observations of objects that evolve and deform over time. This problem is challenging since surfaces come with arbitrary parameterizations and thus, they need to be spatially registered. Also, different deforming objects, hereinafter referred to as 4D surfaces, evolve at different speeds and thus they need to be temporally aligned. We solve this spatiotemporal registration problem using a Riemannian approach. We treat a 3D surface as a point in a shape space equipped with an elastic Riemannian metric that measures the amount of bending and stretching that the surfaces undergo. A 4D surface can then be seen as a trajectory in this space. With this formulation, the statistical analysis of 4D surfaces can be cast as the problem of analyzing trajectories embedded in a nonlinear Riemannian manifold. However, performing the spatiotemporal registration, and subsequently computing statistics, on such nonlinear spaces is not straightforward as they rely on complex nonlinear optimizations. Our core contribution is the mapping of the surfaces to the space of Square-Root Normal Fields (SRNF) where the [Formula: see text] metric is equivalent to the partial elastic metric in the space of surfaces. Thus, by solving the spatial registration in the SRNF space, the problem of analyzing 4D surfaces becomes the problem of analyzing trajectories embedded in the SRNF space, which has a euclidean structure. In this paper, we develop the building blocks that enable such analysis. These include: (1) the spatiotemporal registration of arbitrarily parameterized 4D surfaces even in the presence of large elastic deformations and large variations in their execution rates; (2) the computation of geodesics between 4D surfaces; (3) the computation of statistical summaries, such as means and modes of variation, of collections of 4D surfaces; and (4) the synthesis of random 4D surfaces. We demonstrate the performance of the proposed framework using 4D facial surfaces and 4D human body shapes.

Toward a Three-Dimensional Chromosome Shape Alphabet

The study of the three-dimensional (3D) structure of chromosomes-the largest macromolecules in biology-is one of the most challenging to date in structural biology. Here, we develop a novel representation of 3D chromosome structures, as sequences of shape letters from a finite shape alphabet, which provides a compact and efficient way to analyze ensembles of chromosome shape data, akin to the analysis of texts in a language by using letters. We construct a Chromosome Shape Alphabet from an ensemble of chromosome 3D structures inferred from Hi-C data-via SIMBA3D or other methods-by segmenting curves based on topologically associating domains (TADs) boundaries, and by clustering all TADs' 3D structures into groups of similar shapes. The median shapes of these groups, with some pruning and processing, form the Chromosome Shape Letters (CSLs) of the alphabet. We provide a proof of concept for these CSLs by reconstructing independent test curves by using only CSLs (and corresponding transformations) and comparing these reconstructions with the original curves. Finally, we demonstrate how CSLs can be used to summarize shapes in an ensemble of chromosome 3D structures by using generalized sequence logos.