No abstract

Finding the roots of an equation is a fundamental problem in various fields, including numerical computing, social and physical sciences. Numerical techniques are used when an analytic solution is not available. There is not a single algorithm that works best for every function. We designed and implemented a new algorithm that is a dynamic blend of the bisection and regula falsi algorithms. The implementation results validate that the new algorithm outperforms both bisection and regula falsi algorithms. It is also observed that the new algorithm outperforms the secant algorithm and the Newton–Raphson algorithm because the new algorithm requires fewer computational iterations and is guaranteed to find a root. The theoretical and empirical evidence shows that the average computational complexity of the new algorithm is considerably less than that of the classical algorithms.

DNA sequence and structure design is very important for DNA nanoapplications. A computer-aided design tool is needed for exploring DNA sequence and structure of interests before experimental synthesis, which is a time- and labor-consuming process. In this paper, an interactive DNA sequence and structure design software tool called DNA shop is proposed and implemented. The visualization tool can generate DNA structures by specifying, selecting, and moving DNA sequences around and display corresponding structures. Using the tool, DNA sequence and structure can be visually inspected in three-dimensional space before experimental studies.

No abstract

VRCC-3D+ is an implementation of a region connection calculus that qualitatively determines the spatial relation between two 3D objects in terms of connectivity and obscuration. The eight connectivity relations are conceptually the same as RCC8, but calculated in 3D rather than 2D. The fifteen obscuration relations are calculated using the projection of the 3D objects on a particular 2D plane and the distance of the objects from the viewpoint. Herein we present a smaller, more precise set of VRCC-3D+ obscuration relations that retains the qualities of being jointly exhaustive and pairwise disjoint. However, this new set of relations overcomes two problems that existed in the previous set of fifteen relations: (1) lack of a precise mathematical definition for a key predicate, InFront, and (2) lack of an intuitive mapping of converse relations.