[学术报告] DNA-Like Structure of Shapes
主讲人：Moody T. Chu教授 （North Carolina State University, ）
摘要：The importance of DNA to living organisms and its general structure of a double helix joined by base pairings whose sequences encode the genetic information are well known facts. Proposed in this work is a new computational and data analysis technique that exploits a remarkably similar structure underneath all smooth surfaces. Such a structure exists even in higher dimensional spaces, but the development of fundamental theory and novel algorithms for surfaces alone should be of great significance already. The crux at the center of this approach is our recent discovery that, analogous to the double helix structure with two (AT and CG) base parings in DNA, two strands of curves and eight base pairings would encode properties of an arbitrary surface. The idea is based on generalizing the common notion of gradient adaption from a scalar field to vector fields --- singular vectors of the Jacobian of any given function form a natural moving frame pointing in directions that capture the most critical infinitesimal deformation of the underlying map. Trajectories of these singular vectors, referred to as singular curves, unveil some interesting, perplexing, intriguing patterns per the given function. At points where two or more singular values coalesce, curious and complex behavior occurs, manifesting specific landmarks for the underlying function. Such an innate dynamical structure thus raises the curiosity of whether the double strands with base pairings would be the universal structure encoding all 3-dimensional entities, life or lifeless. We anticipate that the notion of a DNA genetics for surfaces might provide a unifying paradigm to such an extent that almost all surfaces can be genome sequenced and classified accordingly.