Birkhoff’s fundamental theorem on distributive lattices states that for every distributive lattice L there is a poset PL whose lattice of down-sets is order-isomorphic to L. Let G(L) denote the cover graph of L. In this paper, we consider the following problems: Suppose we are simply given PL. How do we compute the eccentricity of an element of L in G(L)? How about a center and the radius of G(...

In the ǫ-regime of QCD the main features of the spectrum of the low-lying eigenvalues of the (euclidean) Dirac operator are expected to be described by a certain universality class of random matrix models. In particular, the latter predict the joint statistical distribution of the individual eigenvalues in any topological sector of the theory. We compare some of these predictions with high-prec...

An intriguing observation of photosynthetic light-harvesting systems is the N-fold symmetry of light-harvesting complex 2 (LH2) of purple bacteria. We calculate the optimal rotational configuration of N-fold rings on a hexagonal lattice and establish two related mechanisms for the promotion of maximum excitation energy transfer (EET). (i) For certain fold numbers, there exist optimal basis cell...

Due to the recent advancement of computer graphics hardware and software algorithms, deformable characters have become more and more popular in real-time applications such as computer games. While there are mature techniques to generate primary deformation from skeletal movement, simulating realistic and stable secondary deformation such as jiggling of fats remains challenging. On one hand, tra...

This paper considers some classes of graphs which are easily seen to have many perfect matchings. Such graphs can be considered robust with respect to the property of having a perfect matching if under vertex deletions (with some mild restrictions), the resulting subgraph continues to have a perfect matching. It is clear that you can destroy the property of having a perfect matching by deleting...

A covering with dominoes of a rectilinear region is called tatami if no four dominoes meet at any point. We describe a reduction from planar 3SAT to Domino Tatami Covering. As a consequence it is NP-complete to decide whether there is a perfect matching of a graph that meets every 4-cycle, even if the graph is restricted to be an induced subgraph of the grid-graph. The gadgets used in the reduc...

In applications that require an input point cloud to be matched with a set of database point clouds present on a remote server, it is preferable to compress and transfer 3D feature descriptors online, rather than compressing and transferring the whole input point cloud. This is because the former would require much lesser bandwidth and does not require feature extraction on the server. Existing...

A brick is a 3-connected graph such that the graph obtained from it by deleting any two distinct vertices has a perfect matching. Bricks are building blocks of the matching decomposition procedure of Kotzig, Lovasz and Plummer, and therefore many matching-related problems can be reduced to bricks. We prove, roughly, that every brick other than the Petersen graph can be generated from a “matchin...