Existence and Construction of Orthogonal and Nearly Orthogonal Latin Hypercube Designs with Eight Columns | Chapter 4 | Mathematics and Computer Science: Research Updates Vol. 1

Latin hypercube designs are widely used in computer experiments to study complex processes. Orthogonality and space-filling are important criteria used to select good Latin hypercube designs. Orthogonality allows to study of the main effect of each factor independently when a regression model is fitted. Designs with better space-filling properties are used to estimate the meta-model more efficiently. In this chapter, we have solved the problem of the existence and construction of orthogonal Latin hypercube designs (OLHD) with eight columns. In particular, the proposed method is used to construct OLHDs (whenever exist) with eight factors for n=8k+s runs, where k≥1 is an odd integer and 0≤s≤7. In addition, nearly orthogonal Latin hypercube designs have been constructed for some values of n for which OLHD(n,8) do not exist. We have also shown that an OLHD(2ut,u) and an OLHD(2ut+1,u) can always be constructed for u=8,16,32,64,96,128,160,192, if a Hadamard matrix of order 4t exists, where t>1 is an integer. All the designs constructed in this chapter can be optimized in terms of discrepancy measures.

 

Author (s) Details

 

Poonam Singh
Department of Statistics, University of Delhi, New Delhi 110007, India.

 

Nilesh Kumar
Department of Statistics, University of Delhi, New Delhi 110007, India.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v1/3435

The Development of a Method for Constructing Super Saturated Design and Nearly Orthogonal Design with Mixed Level Orthogonal Design | Chapter 4 | Current Topics on Mathematics and Computer Science Vol. 10

 For discovering significant aspects to increase the quality of an experiment, orthogonal arrays such as factorial and fractional factorial designs of experimental plans are used. In the early stages of scientific research, Super Saturated Designs are particularly cost-effective. Nearly-Orthogonal Arrays with good statistical features can create a variety of small-run designs with varied levels. Super Saturated Design and Nearly Orthogonal Design are created with Orthogonal Design in this work. The creation of factor screening experiments that are optimal or extremely efficient under the E (s2) and J2 criterion has sparked a lot of attention. We are primarily interested in finding a combinatorial solution to the experiment. Using Hadamard design on thalassemic children's data, we suggested a class of exceptional super saturated designs and produced mixed level orthogonal arrays and nearly orthogonal arrays.

Author(s) Details

Sunita Khurana
School of Statistics, Devi Ahilya University, Indore, M.P., India

Shakti Banerjee
School of Statistics, Devi Ahilya University, Indore, M.P., India

View Book :- https://stm.bookpi.org/CTMCS-V10/article/view/3743

Study on Grassmannian Constellation Based on Antipodal Points and Orthogonal Design and Its Simplified Detecting Algorithm | Chapter 5 | Theory and Practice of Mathematics and Computer Science Vol. 10

 Based on antipodal points on a Grassmannian manifold, this paper proposes a framework for the unitary space time modulation (USTM) constellation. The antipodal constellation allows for a more straightforward ML detection approach. The algebraic orthogonal USTM constellation is an antipodal constellation that, in addition to being adaptable to the antipodal simplified ML detector, also has a second simplified ML detector based on its self-indexing properties, which is simpler due to the elimination of the matrix operation. Under the provided framework, a searching orthogonal USTM constellation based on the grid search method is produced, and its minimal Frobenius chordal distance and simulation performance outperform the algebraic orthogonal USTM constellation.

Author(s) Details

Li Peng
School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan National Laboratory for Optoelectronics, Wuhan 430074, Hubei, China and Department of Electronics and Information, Research Institute of Huazhong University of Science and Technology in Shenzhen, Shenzhen 518057, Guangdong, China.

Dacong Hu
School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China.

Lin Zhang
School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China.

Zhen Qin
School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China.

View Book :- https://stm.bookpi.org/TPMCS-V10/article/view/1075