Minimum aberration construction results for nonregular two-level fractional factorial designs

Nonregular two-level fractional factorial designs are designs which cannot be specified in terms of a set of defining contrasts. The aliasing properties of nonregular designs can be compared by using a generalisation of the minimum aberration criterion called minimum G2-aberration.Until now, the only nontrivial designs that are known to have minimum G2-aberration are designs for n runs and m n–5 factors. In this paper, a number of construction results are presented which allow minimum G2-aberration designs to be found for many of the cases with n = 16, 24, 32, 48, 64 and 96 runs and m n/2–2 factors.

Some theory for constructing minimum aberration fractional factorial designs

Minimum aberration is the most established criterion for selecting a regular fractional factorial design of maximum resolution. Minimum aberration designs for n runs and n/2 less than or equal to m < n factors have previously been constructed using the novel idea of complementary designs. In this paper, an alternative method of construction is developed by relating the wordlength pattern of designs to the so-called 'confounding between experimental runs'. This allows minimum aberration designs to be constructed for n runs and 5n/16 less than or equal to m less than or equal to n/2 factors as well as for n/2 less than or equal to m < n.

Fourier transform, null variety, and Laplacian's eigenvalues

We consider a quantity κ(Ω)—the distance to the origin from the null variety of the Fourier transform of the characteristic function of Ω. We conjecture, firstly, that κ(Ω) is maximised, among all convex balanced domains of a fixed volume, by a ball, and also that κ(Ω) is bounded above by the square root of the second Dirichlet eigenvalue of Ω. We prove some weaker versions of these conjectures in dimension two, as well as their validity for domains asymptotically close to a disk, and also discuss further links between κ(Ω) and the eigenvalues of the Laplacians.

Fractional order modeling of large three-dimensional RC networks

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.

Evaluating relative impact of virtual reality system variables on architectural design comprehension and presence - A variable-centered approach using fractional factorial experiment

The relative contributions of five variables (Stereoscopy, screen size, field of view, level of realism and level of detail) of virtual reality systems on spatial comprehension and presence are evaluated here. Using a variable-centered approach instead of an object-centric view as its theoretical basis, the contributions of these five variables and their two-way interactions are estimated through a 25-1 fractional factorial experiment (screening design) of resolution V with 84 subjects. The experiment design, procedure, measures used, creation of scales and indices, results of statistical analysis, their meaning and agenda for future research are elaborated.

Fractional order and non-linear system identification algorithms for biomedical applications

We discuss the modelling of dielectric responses of amorphous biological samples. Such samples are commonly encountered in impedance spectroscopy studies as well as in UV, IR, optical and THz transient spectroscopy experiments and in pump-probe studies. In many occasions, the samples may display quenched absorption bands. A systems identification framework may be developed to provide parsimonious representations of such responses. To achieve this, it is appropriate to augment the standard models found in the identification literature to incorporate fractional order dynamics. Extensions of models using the forward shift operator, state space models as well as their non-linear Hammerstein-Wiener counterpart models are highlighted. We also discuss the need to extend the theory of electromagnetically excited networks which can account for fractional order behaviour in the non-linear regime by incorporating nonlinear elements to account for the observed non-linearities. The proposed approach leads to the development of a range of new chemometrics tools for biomedical data analysis and classification.

Identification of fractional-order transfer functions using a step excitation

This brief proposes a new method for the identification of fractional order transfer functions based on the time response resulting from a single step excitation. The proposed method is applied to the identification of a three-dimensional RC network, which can be tailored in terms of topology and composition to emulate real time systems governed by fractional order dynamics. The results are in excellent agreement with the actual network response, yet the identification procedure only requires a small number of coefficients to be determined, demonstrating that the fractional order modelling approach leads to very parsimonious model formulations.