HLA class II antigens are heterodimeric cell surface glycoproteins that interact with antigenic peptides to form complexes recognizable by CD4-positive T cells. During their biosynthesis, class II antigens are retained in a post-Golgi compartment in association with the invariant chain, which dissociates before class II cell surface expression. To address whether the invariant chain mediates th...

In this paper, we have developed a new surface signature-based representation that is orientation-independent and can be used to match surfaces under rigid transformation including uniform scaling. In addition to surface matching, the proposed representation can be used to estimate the scaling factor between the surfaces. The proposed scheme represents the surface signatures as Extended Polar M...

Isometric surfaces share the same geometric structure, also known as the “first fundamental form.” For example, all possible bendings of a given surface that includes all length preserving deformations without tearing or stretching the surface are considered to be isometric. We present a method to construct a bending invariant signature for such surfaces. This invariant representation is an emb...

To a smooth, compact, oriented, properly-embedded surface in the $4$-ball, we define an invariant of its boundary-preserving isotopy class from Khovanov homology boundary link. Previous work showed that when link is empty, this determined by genus surface. We show relative invariant: can obstruct sliceness knots; detects pair slices for $9_{46}$; not hindered detecting connected sums with knott...

An efficient algorithm for isometry-invariant matching of surfaces is presented. The key idea is computing the minimum-distortion mapping between two surfaces. For this purpose, we introduce the generalized multidimensional scaling, a computationally efficient continuous optimization algorithm for finding the least distortion embedding of one surface into another. The generalized multidimension...

To each connected component in the space of semisimple representations from the orbifold fundamental group of the base orbifold of a Seifert fibered homology 3-sphere into the Lie group U(2, 1), we associate a real number called the “orbifold Toledo invariant.” For each such orbifold, there exists an elliptic surface over it, called a Dolgachev surface. Using the theory of Higgs bundles on thes...

The extremal and partly marginally trapped surfaces in Minkowski 4-space, which are invariant under the group of boost isometries, are classified. Moreover, it is shown that there do not exist extremal surfaces of this kind with constant Gaussian curvature. A procedure is given in order to construct a partly marginally trapped surface by gluing two marginally trapped surfaces which are invarian...