Graph representation learning (GRL) has become a prominent tool for furthering the understanding of complex networks providing tools network embedding, link prediction, and node classification. In this paper, we propose Hybrid Membership-Latent Distance Model (HM-LDM) by exploring how Latent (LDM) can be constrained to latent simplex. By controlling edge lengths corners simplex, volume space sy...

This paper is motivated by the concept of the signed k-domination problem and dedicated to the complexity of the problem on graphs. For any fixed nonnegative integer k, we show that the signed k-domination problem is NP-complete for doubly chordal graphs. For strongly chordal graphs and distance-hereditary graphs, we show that the signed k-domination problem can be solved in polynomial time. We...

Collision detection is an essential problem in many applications in computer graphics, CAD/CAM, and robotics. In this paper, a new method, called CD-Dual, for detecting collision between two convex polyhedra is proposed. The idea is based on a local search among the faces on the Minkowski difference (M) of the polyhedra. The local search is guided by a simple signed distance function defined on...

We propose a new method for the reconstruction of the signed distance function in the context of level set methods. The new method is a modification of the algorithm which makes use of the PDE equation for the distance function introduced by M. Sussman, P. Smereka, and S. Osher (1994, J. Comput. Phys. 119, 146). It is based mainly on the use of a truly upwind discretization near the interface. ...

We present a new method for computing the medial axis of a given closed smooth curve or surface. It is based on an algorithm for approximating the signed distance function using polynomial splines over hierarchical T-meshes, which has recently been presented in [36]. Since the signed distance function is not differentiable along the medial axis, the hierarchical T-meshes is automatically refine...

In this paper we present an efficient method to compute the signed distance field for a large triangle mesh, which can run interactively with GPU accelerated. Restricted by absence of flexible pointer addressing on GPU, we design a novel multi-layer hash table to organize the voxel/triangle overlap pairs as two-tuples, such strategy provides an efficient way to store and access. Based on the ge...

The problem of reconstructing signed permutations on n elements from their erroneous patterns distorted by reversal errors is considered in this paper.A reversal is the operation of taking a segment of the signed permutation, reversing it, and flipping the signs of its elements. The reversal metric is defined as the least number of reversals transforming one signed permutation into another. It ...

We present a method for generating shell-like objects such as surgical guides and plates from segmented computed tomography (CT) images, using signed distance fields and constructive solid geometry (CSG). We develop a userfriendly modeling tool which allows a user to quickly design such models with the help of stereo graphics, six degrees-of-freedom input, and haptic feedback, in our existing s...

Genome rearrangement is an important area in computational biology. There are three basic operations, reversal, translocation and transposition. Here we study the translocation operations. Multi-chromosomal genomes frequently evolve by translocation events that exchange genetic material between two chromosomes. We focus on the signed case, where the direction of each gene is known. The signed t...

A new redistancing method for piecewise polynomial finite element level set functions is introduced. The method directly computes the distance to the implicitly given discrete level set. Rigorous error bounds and numerical experiments are provided. Both show that, up to constants, the method is as good as the nodal interpolation of the computationally unavailable signed distance function of the...