The level set equation is a nonlinear advection equation, and standard finite-element and finitedifference strategies typically employ spatial stabilization techniques to suppress spurious oscillations in the numerical solution. We recast the level set equation in a simpler form by assuming that the level set function remains a signed distance to the front/interface being captured. As with the ...

This paper is motivated by the concept of nonnegative signed domination that was introduced by Huang, Li, and Feng in 2013 [15]. We study the non-negative signed domination problem from the theoretical point of view. For networks modeled by strongly chordal graphs and distance-hereditary graphs, we show that the non-negative signed domination problem can be solved in polynomial time. For networ...

Range nder devices are quite useful to measure the geometry of real world objects How ever the reconstruction of large and complicated objects often requires the acquisition of multiple range images showing di erent views of the object With our reconstruction method the relative orientations of all range images are determined via simultaneous registration of all range images The registration pr...

This paper presents two new types of fuzzy shortest-path network problems. We consider the edge weight of the network as uncertain, which means that it is either imprecise or unknown. Thus, the first type of fuzzy shortest-path problem uses triangular fuzzy numbers for the imprecise problem. The second type uses level (1 − β, 1 − α) interval-valued fuzzy numbers, which are based on past statist...

Let $W_n := \sum_{j=1}^n Z_j$ be a sum of independent integer-valued random variables. In this paper, we derive an asymptotic expansion for the probability $\mathbb{P}[W_n \in A]$ of an arbitrary subset $A \in \mathbb{Z}$. Our approximation improves upon the classical expansions by including an explicit, uniform error estimate, involving only easily computable properties of the distributions of...

The level set method is a popular technique used in medical image segmentation; however, the numerics involved make its use cumbersome. This paper proposes an approximate level set scheme that removes much of the computational burden while maintaining accuracy. Abandoning a floating point representation for the signed distance function, we use integral values to represent the signed distance fu...

We propose a left-to-right (i.e., from the most significant column to the least significant column) algorithm for computing a signed-binary (SB) representation of pairs of integers with minimum joint weight as well as maximum average length of zero-column runs. The proposed method speeds up the scalar multiplication of elliptic curve cryptosystems (ECC) by all known strategies, while at the sam...

We propose a novel surface-aware ray tracing method based on implicit model representation. Each horizon is represented by a signed distance field and the spatial relationships between horizons are described by a stratigraphic binary tree. With this kind of implicit representation, complex structural model (e.g., heavily faulted, intrusions and unconformities) are easily handled, and the veloci...