scholarly journals Simulations on the Combinatorial Structure of D-Optimal Designs

2018 ◽  
pp. 343-353
Author(s):  
Roberto Fontana ◽  
Fabio Rapallo
Keyword(s):  
Optimal Designs ◽  
Combinatorial Structure

Q-optimal experimental designs and close to them experimental designs for polynomial regression on the interval

2020 ◽  
Vol 86 (5) ◽  
pp. 65-72
Author(s):  
Yu. D. Grigoriev
Keyword(s):  
Optimal Design ◽  
Polynomial Regression ◽  
Direct Consequence ◽  
Experimental Designs ◽  
Optimal Designs ◽  
Software Systems ◽  
General Character ◽  
Support Points ◽  
Optimal Weights ◽  
Universal Expression

The problem of constructing Q-optimal experimental designs for polynomial regression on the interval [–1, 1] is considered. It is shown that well-known Malyutov – Fedorov designs using D-optimal designs (so-called Legendre spectrum) are other than Q-optimal designs. This statement is a direct consequence of Shabados remark which disproved the Erdős hypothesis that the spectrum (support points) of saturated D-optimal designs for polynomial regression on a segment appeared to be support points of saturated Q-optimal designs. We present a saturated exact Q-optimal design for polynomial regression with s = 3 which proves the Shabados notion and then extend this statement to approximate designs. It is shown that when s = 3, 4 the Malyutov – Fedorov theorem on approximate Q-optimal design is also incorrect, though it still stands for s = 1, 2. The Malyutov – Fedorov designs with Legendre spectrum are considered from the standpoint of their proximity to Q-optimal designs. Case studies revealed that they are close enough for small degrees s of polynomial regression. A universal expression for Q-optimal distribution of the weights pi for support points xi for an arbitrary spectrum is derived. The expression is used to tabulate the distribution of weights for Malyutov – Fedorov designs at s = 3, ..., 6. The general character of the obtained expression is noted for Q-optimal weights with A-optimal weight distribution (Pukelsheim distribution) for the same problem statement. In conclusion a brief recommendation on the numerical construction of Q-optimal designs is given. It is noted that in this case in addition to conventional numerical methods some software systems of symbolic computations using methods of resultants and elimination theory can be successfully applied. The examples of Q-optimal designs considered in the paper are constructed using precisely these methods.

Constrained optimal designs

1984 ◽  
Author(s):  
Moun-Shen Carl Lee
Keyword(s):  
Optimal Designs

Combinatorial Design of Molecule using Activity-Linked Substructural Topological Information as Applied to Antitubercular Compounds

2018 ◽  
Vol 15 (1) ◽  
pp. 67-81 ◽  
Author(s):  
Chandan Raychaudhury ◽  
Md. Imbesat Hassan Rizvi ◽  
Debnath Pal
Keyword(s):  
Biological Activities ◽  
Combinatorial Design ◽  
Combinatorial Structure ◽  
Potential Drug ◽  
Structure Generation ◽  
Topological Information ◽  
Active Compounds ◽  
Antitubercular Drugs ◽  
Topological Distance ◽  
Drug Molecules

Background: Generating a large number of compounds using combinatorial methods increases the possibility of finding novel bioactive compounds. Although some combinatorial structure generation algorithms are available, any method for generating structures from activity-linked substructural topological information is not yet reported. Objective: To develop a method using graph-theoretical techniques for generating structures of antitubercular compounds combinatorially from activity-linked substructural topological information, predict activity and prioritize and screen potential drug candidates. </P><P> Methods: Activity related vertices are identified from datasets composed of both active and inactive or, differently active compounds and structures are generated combinatorially using the topological distance distribution associated with those vertices. Biological activities are predicted using topological distance based vertex indices and a rule based method. Generated structures are prioritized using a newly defined Molecular Priority Score (MPS). Results: Studies considering a series of Acid Alkyl Ester (AAE) compounds and three known antitubercular drugs show that active compounds can be generated from substructural information of other active compounds for all these classes of compounds. Activity predictions show high level of success rate and a number of highly active AAE compounds produced high MPS score indicating that MPS score may help prioritize and screen potential drug molecules. A possible relation of this work with scaffold hopping and inverse Quantitative Structure-Activity Relationship (iQSAR) problem has also been discussed. The proposed method seems to hold promise for discovering novel therapeutic candidates for combating Tuberculosis and may be useful for discovering novel drug molecules for the treatment of other diseases as well.

Dynamic modeling and power optimization of a 4RPSP+PS parallel flight simulator machine

Robotica ◽  
2021 ◽  
pp. 1-26
Author(s):  
Soheil Zarkandi
Keyword(s):  
Power Consumption ◽  
Dynamic Modeling ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Pareto Front ◽  
Essential Role ◽  
Power Optimization ◽  
Optimal Designs ◽  
Flight Simulator ◽  
Lagrange Method

Abstract Reducing consumed power of a robotic machine has an essential role in enhancing its energy efficiency and must be considered during its design process. This paper deals with dynamic modeling and power optimization of a four-degrees-of-freedom flight simulator machine. Simulator cabin of the machine has yaw, pitch, roll and heave motions produced by a 4RPSP+PS parallel manipulator (PM). Using the Euler–Lagrange method, a closed-form dynamic equation is derived for the 4RPSP+PS PM, and its power consumption is computed on the entire workspace. Then, a newly introduced optimization algorithm called multiobjective golden eagle optimizer is utilized to establish a Pareto front of optimal designs of the manipulator having a relatively larger workspace and lower power consumption. The results are verified through numerical examples.

scholarly journals Asymptotic Inference for Optimal Rerandomization Designs

2021 ◽  
Vol 1 (1) ◽  
pp. 49-58
Author(s):  
Mårten Schultzberg ◽  
Per Johansson
Keyword(s):  
Experimental Design ◽  
Normal Distribution ◽  
Mahalanobis Distance ◽  
Design Strategy ◽  
Sampling Distribution ◽  
Optimal Designs ◽  
Asymptotic Inference ◽  
Optimal Allocations ◽  
Asymptotic Sampling

AbstractRecently a computational-based experimental design strategy called rerandomization has been proposed as an alternative or complement to traditional blocked designs. The idea of rerandomization is to remove, from consideration, those allocations with large imbalances in observed covariates according to a balance criterion, and then randomize within the set of acceptable allocations. Based on the Mahalanobis distance criterion for balancing the covariates, we show that asymptotic inference to the population, from which the units in the sample are randomly drawn, is possible using only the set of best, or ‘optimal’, allocations. Finally, we show that for the optimal and near optimal designs, the quite complex asymptotic sampling distribution derived by Li et al. (2018), is well approximated by a normal distribution.

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