We propose an approach to constructing a new type of design, a sliced space-filling design, intended for computer experiments with qualitative and quantitative factors. The approach starts with constructing a Latin hypercube design based on a special orthogonal array for the quantitative factors and then partitions the design into groups corresponding to different level combinations of the qual...

Over the past few years, Deep learning (DL) has revolutionized field of data analysis. Not only are algorithmic paradigms changed, but also performance in various classification and prediction tasks been significantly improved with respect to state-of-the-art, especially area computer vision. The progress made vision produced a spillover many other domains, such as biomedical engineering. Some ...

This paper presents a general data-parallel formulation for a class of problems based on the divide and conquer strategy. A combination of three techniques—mapping vectors, index-digit permutations and space-filling curves—are used to reorganize the algorithmic dataflow, providing great flexibility to efficiently exploit data locality and to reduce and optimize communications. In addition, thes...

The solution of partial differential equations on a parallel computer is usually done by a data parallel approach. The grid is partitioned and mapped onto the processors. However, partitioning of unstructured meshes and adaptively refined meshes in general is an NP -hard problem and heuristics are needed. In this paper a parallelisable and cheap method based on space-filling curves is analysed....

Hilbert curves can be generated by using L-System concept. A theoretical intuitive method is suggested for manipulating the Hilbert space filling curve for simple coding to one dimension. Our method is aimed to code the Hilbert curve simply by observing the base Hilbert curve as generated. By simple observation one can code the Hilbert curve easily. The present work has been mainly inspired by ...

Competitive numerical simulation codes solving partial differential equations have to tap the full potential of both modern numerical methods – like multi-grid and adaptive grid refinement – and available computing resources. In general, these two are rival tasks. Typically, hierarchical data structures resulting from multigrid and adaptive grid refinement impede efficient usage of modern memor...

In this study, we investigate the semi-real quaternionic curves in the semi-Euclidean space E_4_2. Firstly, we introduce algebraic properties of semi-real quaternions. Then, we give some characterizations of semi-real quaternionic involute-evolute curves in the semi-Euclidean space E42 . Finally, we give an example illustrated with Mathematica Programme.

So far we have discussed only ‘local’ properties of (plane) curves. These properties depend only on the behavior of a curve near a given point, and not on the ‘global’ shape of the curve. Now let us look at some global results about curves. The most famous, and perhaps the oldest, of these is the ‘isoperimetric inequality’, which relates the length of a certain ‘closed’ curve to the area it con...

To evaluate left ventricular (LV) diastolic function and potential, LV filling curves for 18 patients with atrial fibrillation (Af) were constructed and their positions and appearance were evaluated quantitatively by analysis of 95% maximal filling volume points and maximal curvature alteration points. The LV filling curves of group A (Af only) lay left superiorly, while those of group B (impai...