Title: Constrained Shape Analysis with Applications to RNA Structure Show Chinese title

Title: 受限形状分析及其在RNA结构中的应用

Abstract: In many applications of shape analysis, lengths between some landmarks are constrained. For instance, biomolecules often have some bond lengths and some bond angles constrained, and variation occurs only along unconstrained bonds and constrained bonds' torsions where the latter are conveniently modelled by dihedral angles. Our work has been motivated by low resolution biomolecular chain RNA where only some prominent atomic bonds can be well identified. Here, we propose a new modelling strategy for such constrained shape analysis starting with a product of polar coordinates (polypolars), where, due to constraints, for example, some radial coordinates should be omitted, leaving products of spheres (polyspheres). We give insight into these coordinates for particular cases such as five landmarks which are motivated by a practical RNA application. We also discuss distributions for polypolar coordinates and give a specific methodology with illustration when the constrained size-and-shape variables are concentrated. There are applications of this in clustering and we give some insight into a modified version of the MINT-AGE algorithm. Show Chinese abstract

Abstract: 在形状分析的许多应用中，某些标志点之间的长度受到约束。 例如，生物分子通常有一些键长和键角被约束，而变化仅发生在未受约束的键以及这些约束键的扭转上，后者可以通过二面角方便地建模。 我们的工作受到了低分辨率生物分子链RNA的启发，在这种情况下，只能很好地识别出一些突出的原子键。 在这里，我们提出了一种新的针对这种约束形状分析的建模策略，从极坐标乘积（多极坐标）开始，由于约束的存在，例如，一些径向坐标应被省略，从而留下球体的乘积（多球体）。 我们对这些坐标给出了特定情况下的见解，例如由实际RNA应用启发的五个标志点的情况。 我们还讨论了多极坐标的分布，并在约束大小-形状变量集中时提供了一种具体的方法论及实例说明。 这种方法在聚类中有应用，我们还对MINT-AGE算法的修改版本提供了部分见解。