The p value line: a way to choose the tuning constant in tests based on the Huber {\varvec{M}}-estimator

In this paper, we propose a method to choose a test result from several competing ones. The choice is based on the p value under the alternative, i.e., the probability of obtaining an extreme or a more extreme result than the one actually observed, assuming that the alternative hypothesis is true. The function obtained, by moving the alternative, is called the p value line. Because this combines the power of a test and its sensitivity to outliers, it is considered to be the basis for the selection between several classical and/or robust test results. When we change the trimming fraction in the trimmed mean, or the tuning constant when we consider a test based on the Huber \(M\) -estimator, we obtain competing robust test results. For this reason, we can use the p value line to choose the trimming fraction or the tuning constant in an objective way. In this article, we shall focus on the second class of estimators. Because computing the distribution of the test statistic under the alternative could be a very hard problem, a linear approximation of the tail probability functional based on the von Mises expansion can be used to compute the p value line. Applications of the proposal to the one-sample location problem, generalized linear models and generalized additive models are considered in the article. We conclude the article with the random p value line to decide if the observed differences between p value lines are significant or not.     

Three dimensional finite element investigations into the effects of thickness and notch radius on the fracture toughness of polycarbonate

Fracture toughness of polycarbonate (PC), a commercially important glassy amorphous polymer, is known to be sensitively dependent on a number of factors including molecular weight, ageing time, loading rate and specimen geometry. In this work, we analyze the effect of notch radius and specimen thickness on the near tip fields and the consequence of these on the mode I fracture initiation. To this end, we have performed extensive three dimensional Finite Element simulations within the framework of large deformation elasto-plasticity based on a realistic constitutive model that has been carefully calibrated for PC. Using a simple set of criteria for fracture initiation by void nucleation or ductile tearing, we are able to reproduce experimentally observed brittle to ductile transitions that occur in PC with decrease in thickness and increase in notch radius.     

Further exploring rm metrics for validation of QSPR models

Quantitative structure-property relationship (QSPR) models are widely used for prediction of properties, activities and/or toxicities of new chemicals. Validation strategies check the reliability of predictions of QSPR models. The classical metrics like Q² and R²_pred (Q²_ext) are commonly used, besides other techniques, for internal validation (mostly leave-one-out) and external validation (test set validation) respectively. Recently, we have proposed a set of novel r_m² metrics which has been extensively used by us and other research groups for validation of QSPR models. In the present attempt, some additional variants of r_m² metrics have been proposed and their applications in judging the quality of predictions of QSPR models have been shown by analyzing results of the QSPR models obtained from three different data sets (n = 119, 90, and 384). In each case, 50 combinations of training and test sets have been generated, and models have been developed based on the training set compounds and subsequently applied for prediction of responses of the test set compounds. Finally, models for a particular data set have been ranked according to the quality of predictions. The role of different validation metrics (including classical metrics and different variants of r_m² metrics) in differentiating the “good” (predictive) models from the “bad” (low predictive) models has been studied. Finally, a set of guidelines has been proposed for checking the predictive quality of QSPR models.     

A linear-encoding model explains the variability of the target morphology in regeneration

A fundamental assumption of today''s molecular genetics paradigm is that complex morphology emerges from the combined activity of low-level processes involving proteins and nucleic acids. An inherent characteristic of such nonlinear encodings is the difficulty of creating the genetic and epigenetic information that will produce a given self-assembling complex morphology. This ‘inverse problem’ is vital not only for understanding the evolution, development and regeneration of bodyplans, but also for synthetic biology efforts that seek to engineer biological shapes. Importantly, the regenerative mechanisms in deer antlers, planarian worms and fiddler crabs can solve an inverse problem: their target morphology can be altered specifically and stably by injuries in particular locations. Here, we discuss the class of models that use pre-specified morphological goal states and propose the existence of a linear encoding of the target morphology, making the inverse problem easy for these organisms to solve. Indeed, many model organisms such as Drosophila, hydra and Xenopus also develop according to nonlinear encodings producing linear encodings of their final morphologies. We propose the development of testable models of regeneration regulation that combine emergence with a top-down specification of shape by linear encodings of target morphology, driving transformative applications in biomedicine and synthetic bioengineering.     

Numerical integration on the sphere and its effect on the material symmetry of constitutive equations—A comparative study

In the present paper, we consider a class of constitutive models based on numerical integration on the unit sphere. The directional behaviour of the quadrature schemes and its effect on the symmetry properties of these constitutive models are studied by subjecting the set of integration points on the sphere to arbitrary rigid rotations. We investigate a number of recently proposed integration schemes in application to a full network model of rubber elasticity and to an exponential model for soft tissues. In order to assess and compare these schemes, statistical methods are presented and applied. The analysis discloses a number of integration schemes that offer a good compromise between the numerical error and the number of integration points. However, as a general result it turns out that numerical integration is prone to introduce strong anisotropy into originally isotropic constitutive equations, in particular, for highly non‐linear integrand functions. The consequences for application of the investigated class of constitutive models in finite element calculations are highlighted in a benchmark‐like numerical example. Copyright © 2009 John Wiley & Sons, Ltd.     

A statistical engineering strategy for mixture problems with process variables

Experimenting with both mixture components and process variables, especially when there is likely to be interaction between these two sets of variables, is discussed. We consider both design and analysis questions within the context of addressing an actual mixture/process problem. We focus on a strategy for attacking such problems, as opposed to finding the best possible design or best possible model for a given set of data. In this sense, a statistical engineering framework is used. In particular, when we consider the potential of fitting parsimonious linear additive or nonlinear models as opposed to larger linearized models, we find potential to reduce the size of experimental designs. It is difficult in practice to know what type of model will best fit the resulting data. Therefore, an integrated, sequential design and analysis strategy is recommended. Using two published data sets and one new data set, we find that in some cases nonlinear models, or linear additive models —with no process/mixture interaction terms, enable reduction of experimentation on the order of 50%. In other cases, additive or nonlinear models will not suffice. We therefore provide guidelines as to when such an approach is likely to succeed, and propose an overall strategy for these types of problems.     

Metamer sets

If two different surfaces look the same when viewed under a particular light source, then they are called metamers. We show mathematically how one can solve for the whole set of physically realizable natural surface reflectances that relate to the same tristimulus, the metamer set. Our analysis is based on very general linear models of reflectances, coupled with constraints that reflectances should adhere to (e.g., positivity and boundedness). We show that we can recover metamer sets for linear models of an arbitrary high dimension. To illustrate our new algorithm, we provide an example of calculating the metamer set and its manifestation as a mismatch region. Given a single XYZ observed under illuminant D65, we can examine the set of XYZs that would be possible under illuminant A.     

Linear models for non-Gaussian processes and applications to linear random vibration

Linear models are finite sums of specified deterministic, continuous functions of time with random coefficients. It is shown that linear models provide (i) accurate approximations for real-valued non-Gaussian processes with continuous samples defined on bounded time intervals, (ii) simple solutions for linear random vibration problems with non-Gaussian input, and (iii) efficient techniques for selecting optimal designs from collections of proposed alternatives. Theoretical arguments and numerical examples are presented to establish properties of linear models, illustrate the construction of linear models, solve linear random vibration with non-Gaussian input, and propose an approach for optimal design of linear dynamic systems. It is shown that the proposed linear model provides an efficient tool for analyzing linear systems in non-Gaussian environment.     

Structural similitude for flutter of delaminated composite beam-plates

The main objective of this study is to demonstrate the applicability of similitude theory in designing scaled down models to predict the flutter pressure of delaminated composite beam-plate subjected to supersonic airflow. The linear plate theory is used for structural modeling, and linear piston theory is used for aerodynamic modeling. In this study, we consider only the procedure that is based on the direct use of the governing equations. Distorted models with different fiber orientation, delamination size, and axial position than those of prototype are studied. Results show that a set of scaling models can be found which can predict the flutter pressure of delaminated beam-plate accurately.     

Semi-parametric estimation in the compositional modeling of multicomponent systems from Raman spectroscopic data

Identification and quantification of molecular species are central applications of molecular spectroscopy. In complex multicomponent systems like tissue samples, linear parametric models are often used to estimate the relative concentrations of the biochemical components of the sample. In situations where not all of the components of the sample are known or modeled, such parametric models can suffer from omitted variable bias and result in skewed estimates of component concentrations. We propose a semi-parametric approach that tries to avoid this omitted variable bias by effectively including unknown covariates as a non-parametric term in the regression equation. Constituent concentrations estimated with such partial linear models should outperform strict parametric linear models when the user has limited information on the composition of a multi-constituent system.     

Certain investigations on the reduction of side lobe level of an uniform linear antenna array using biogeography based optimization technique with sinusoidal migration model and simplified-BBO

In this paper, we propose biogeography based optimization technique, with linear and sinusoidal migration models and simplified biogeography based optimization (S-BBO), for uniformly spaced linear antenna array synthesis to maximize the reduction of side lobe level (SLL). This paper explores biogeography theory. It generalizes two migration models in BBO namely, linear migration model and sinusoidal migration model. The performance of SLL reduction in ULA is investigated. Our performance study shows that among the two, sinusoidal migration model is a promising candidate for optimization. In our work, simplified – BBO algorithm is also deployed. This determines an optimum set value for amplitude excitations of antenna array elements that generate a radiation pattern with maximum side lobe level reduction. Our detailed investigation also shows that sinusoidal migration model of BBO performs better compared to the other evolutionary algorithms discussed in this paper.     

Space Research Program on Planarian Schmidtea Mediterranea’s Establishment of the Anterior-Posterior Axis in Altered Gravity Conditions

Planarians of the species Schmidtea mediterranea are a well-established model for regeneration studies. In this paper, we first recall the morphological characters and the molecular mechanisms involved in the regeneration process, especially focussing on the Wnt pathway and the establishment of the antero-posterior axial polarity. Then, after an assessment of a space-experiment (run in 2006 on the Russian Segment of the International Space Station) on planarians of the species Girardia tigrina, we present our experimental program to ascertain the effects that altered-gravity conditions may have on regeneration processes in S. mediterrnea at the molecular and genetic level.     

Assessing the effect of dynamics on the closed-loop protein-folding hypothesis

The closed-loop (loop-n-lock) hypothesis of protein folding suggests that loops of about 25 residues, closed through interactions between the loop ends (locks), play an important role in protein structure. Coarse-grain elastic network simulations, and examination of loop lengths in a diverse set of proteins, each supports a bias towards loops of close to 25 residues in length between residues of high stability. Previous studies have established a correlation between total contact distance (TCD), a metric of sequence distances between contacting residues (cf. contact order), and the log-folding rate of a protein. In a set of 43 proteins, we identify an improved correlation (r² = 0.76), when the metric is restricted to residues contacting the locks, compared to the equivalent result when all residues are considered (r² = 0.65). This provides qualified support for the hypothesis, albeit with an increased emphasis upon the importance of a much larger set of residues surrounding the locks. Evidence of a similar-sized protein core/extended nucleus (with significant overlap) was obtained from TCD calculations in which residues were successively eliminated according to their hydrophobicity and connectivity, and from molecular dynamics simulations. Our results suggest that while folding is determined by a subset of residues that can be predicted by application of the closed-loop hypothesis, the original hypothesis is too simplistic; efficient protein folding is dependent on a considerably larger subset of residues than those involved in lock formation.     

The Bayes linear approach to inference and decision-making for a reliability programme

In reliability modelling it is conventional to build sophisticated models of the probabilistic behaviour of the component lifetimes in a system in order to deduce information about the probabilistic behaviour of the system lifetime. Decision modelling of the reliability programme requires a priori, therefore, an even more sophisticated set of models in order to capture the evidence the decision maker believes may be obtained from different types of data acquisition.Bayes linear analysis is a methodology that uses expectation rather than probability as the fundamental expression of uncertainty. By working only with expected values, a simpler level of modelling is needed as compared to full probability models.In this paper we shall consider the Bayes linear approach to the estimation of a mean time to failure MTTF of a component. The model built will take account of the variance in our estimate of the MTTF, based on a variety of sources of information.     

Structural fatigue crack growth on a representative volume element under cyclic strain behavior

By introducing parameters λ and ω into the crack tip field, a unified cyclic stress and strain field was first formulated by using the Hutchinson-Rice-Rosengren (HRR) field and the Rice-Kujawski-Ellyin (RKE) field under plane stress states in the present study. On the basis of the plastic strain energy and the linear damage accumulation, two fatigue crack growth models without any artificial parameters were then proposed from a representative volume element of cyclic strain behavior. The fatigue crack growth model included parameters λ and ω which showed the effect of two singularity fields. In addition, a simplified structural fatigue crack growth model was eventually established in terms of the fatigue life of each point on the crack front and the non-self-similar shape evolution law. Finally, the predictions of models are compared with the experimental data and the agreement is found to be fairly good.     

Using reflectance models for color scanner calibration

We examine the use of linear spectral reflectance models for calibrating a color scanner to generate device-independent CIE XYZ values from scanner vectors. Polynomial regression approaches to color scanner calibration use parameterized functions to approximate the calibration mapping over a set of training colors. These approaches can perform poorly if the parameterized functions do not accurately model the structure of the desired calibration mapping. Several studies have shown that linear reflectance models accurately characterize a wide range of materials. By viewing color scanner calibration as reflectance estimation, we can incorporate linear reflectance models into the calibration process. We show that in most cases linear models do not constrain the calibration problem sufficiently to allow exact recovery of X, Y, Z from a scanner vector obtained with three filters. By examining a series of methods that exploit information about reflectance functions, however, we show that reflectance information can be used to improve the accuracy of calibration over that of standard methods applied to the same set of inputs.     

Revision on ‘Maximally permissive deadlock prevention via an Invariant Controlled Method’

All current design approaches of maximally permissive supervisors assume that forbidden and legal markings are linearly separable. Based on that implicit assumption, Liu et al. propose a novel method of optimal control of a problematic siphon to synthesise maximally permissive controllers. However, there are counter examples for which we could not produce optimal solutions. This occurs when forbidden and legal markings are not linearly separable even though it rarely happens. Verifying linear separability involves solving a large set of linear inequalities and is quite time consuming. This paper aims to relieve this problem via enhancing our critical-siphon approach. Specifically, we propose to: (1) find an efficient method to detect linear inseparability; (2) construct best suboptimal control models; (3) find all lost legal markings; and (4) identify the linear equations that violate linear separability. Each above contribution is unique and pioneering.