The D-optimal design of blocked and split-plot experiments with mixture components.

So far, the optimal design of blocked and split-plot experiments involving mixture components has received scant attention. In this paper, an easy method to construct efficient blocked mixture experiments in the presence of fixed and/or random blocks is presented. The method can be used when qualitative variables are involved in a mixture experiment as well. It is also shown that orthogonally blocked mixture experiments are highly inefficient compared to D-optimal designs. Finally, the design of a split-plot mixture experiment with process variables is discussed.Design; Fixed and random blocks; Minimum support design; Mixture experiment; Optimal; Optimal design; Orthogonal blocking; Process variables; Processes; Qualitative variables; Split-plot experiment; Variables;

The optimal design of an experiment with blocks of size two for quadratic regression on one variable.

Exact D-optimal designs are derived for an optometry experiment for the estimation of a quadratic polynomial in one explanatory variable. Two observations are made for each subject participating in the experiment, such that each subject serves as a block of two possibly correlated observations. The exact D-optimal designs are compared to the best possible three-level designs and to the continuous D-optimal designs.Optimal;

Adaptive grid semidefinite programming for finding optimal designs

We find optimal designs for linear models using anovel algorithm that iteratively combines a semidefinite programming(SDP) approach with adaptive grid techniques.The proposed algorithm is also adapted to find locally optimaldesigns for nonlinear models. The search space is firstdiscretized, and SDP is applied to find the optimal designbased on the initial grid. The points in the next grid set arepoints that maximize the dispersion function of the SDPgeneratedoptimal design using nonlinear programming. Theprocedure is repeated until a user-specified stopping rule isreached. The proposed algorithm is broadly applicable, andwe demonstrate its flexibility using (i) models with one ormore variables and (ii) differentiable design criteria, suchas A-, D-optimality, and non-differentiable criterion like Eoptimality,including the mathematically more challengingcasewhen theminimum eigenvalue of the informationmatrixof the optimal design has geometric multiplicity larger than 1. Our algorithm is computationally efficient because it isbased on mathematical programming tools and so optimalityis assured at each stage; it also exploits the convexity of theproblems whenever possible. Using several linear and nonlinearmodelswith one or more factors, we showthe proposedalgorithm can efficiently find optimal designs

Trend-resistant and cost-efficient cross-over designs for mixed models.

A mixed model approach is used to construct optimal cross-over designs. In a cross-over experiment the same subject is tested at different points in time. Consider as an example an experiment to investigate the influence of physical attributes of the work environment such as luminance, ambient temperature and relative humidity on human performance of acceptance inspection in quality assurance. In a mixed model context, the subject effects are assumed to be independent and normally distributed. Besides the induction of correlated observations within the same inspector, the mixed model approach also enables one to specify the covariance structure of the inspection data. Here, several covariance structures are considered either depending on the time variable or not. Unfortunately, a serious drawback of the inspection experiment is that the results may be influenced by an unknown time trend because of inspector fatigue due to monotony of the inspection task. In other circumstances, time trend effects can be caused by learning effects of the test subjects in behavioural and life sciences, heating or aging of material in prototype experiments, etc. An algorithm is presented to construct cross-over designs that are optimally balanced for time trend effects. The costs for using the subjects and for altering the factor levels between consecutive observations can also be taken into account. A number of examples illustrate utility of the outlined design methodology.Optimal; Models; Model;

Computational aerodynamics and artificial intelligence

The general principles of artificial intelligence are reviewed and speculations are made concerning how knowledge based systems can accelerate the process of acquiring new knowledge in aerodynamics, how computational fluid dynamics may use expert systems, and how expert systems may speed the design and development process. In addition, the anatomy of an idealized expert system called AERODYNAMICIST is discussed. Resource requirements for using artificial intelligence in computational fluid dynamics and aerodynamics are examined. Three main conclusions are presented. First, there are two related aspects of computational aerodynamics: reasoning and calculating. Second, a substantial portion of reasoning can be achieved with artificial intelligence. It offers the opportunity of using computers as reasoning machines to set the stage for efficient calculating. Third, expert systems are likely to be new assets of institutions involved in aeronautics for various tasks of computational aerodynamics

Recent Developments in Nonregular Fractional Factorial Designs

Nonregular fractional factorial designs such as Plackett-Burman designs and other orthogonal arrays are widely used in various screening experiments for their run size economy and flexibility. The traditional analysis focuses on main effects only. Hamada and Wu (1992) went beyond the traditional approach and proposed an analysis strategy to demonstrate that some interactions could be entertained and estimated beyond a few significant main effects. Their groundbreaking work stimulated much of the recent developments in design criterion creation, construction and analysis of nonregular designs. This paper reviews important developments in optimality criteria and comparison, including projection properties, generalized resolution, various generalized minimum aberration criteria, optimality results, construction methods and analysis strategies for nonregular designs.Comment: Submitted to the Statistics Surveys (http://www.i-journals.org/ss/) by the Institute of Mathematical Statistics (http://www.imstat.org

What does semantic tiling of the cortex tell us about semantics?

Recent use of voxel-wise modeling in cognitive neuroscience suggests that semantic maps tile the cortex. Although this impressive research establishes distributed cortical areas active during the conceptual processing that underlies semantics, it tells us little about the nature of this processing. While mapping concepts between Marr's computational and implementation levels to support neural encoding and decoding, this approach ignores Marr's algorithmic level, central for understanding the mechanisms that implement cognition, in general, and conceptual processing, in particular. Following decades of research in cognitive science and neuroscience, what do we know so far about the representation and processing mechanisms that implement conceptual abilities? Most basically, much is known about the mechanisms associated with: (1) features and frame representations, (2) grounded, abstract, and linguistic representations, (3) knowledge-based inference, (4) concept composition, and (5) conceptual flexibility. Rather than explaining these fundamental representation and processing mechanisms, semantic tiles simply provide a trace of their activity over a relatively short time period within a specific learning context. Establishing the mechanisms that implement conceptual processing in the brain will require more than mapping it to cortical (and sub-cortical) activity, with process models from cognitive science likely to play central roles in specifying the intervening mechanisms. More generally, neuroscience will not achieve its basic goals until it establishes algorithmic-level mechanisms that contribute essential explanations to how the brain works, going beyond simply establishing the brain areas that respond to various task conditions

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners