Efficient regression analysis with ranked-set sampling

This article is motivated by a lung cancer study where a regression model is involved and the response variable is too expensive to measure but the predictor variable can be measured easily with relatively negligible cost. This situation occurs quite often in medical studies, quantitative genetics, and ecological and environmental studies. In this article, by using the idea of ranked-set sampling (RSS), we develop sampling strategies that can reduce cost and increase efficiency of the regression analysis for the above-mentioned situation. The developed method is applied retrospectively to a lung cancer study. In the lung cancer study, the interest is to investigate the association between smoking status and three biomarkers: polyphenol DNA adducts, micronuclei, and sister chromatic exchanges. Optimal sampling schemes with different optimality criteria such as A-, D-, and integrated mean square error (IMSE)-optimality are considered in the application. With set size 10 in RSS, the improvement of the optimal schemes over simple random sampling (SRS) is great. For instance, by using the optimal scheme with IMSE-optimality, the IMSEs of the estimated regression functions for the three biomarkers are reduced to about half of those incurred by using SRS.

Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

Electron Mean Energy, Secondary Ionization Coefficients And (E/P)Crit In Binary-Mixtures Of Sf6-N2 And Ccl2f2-N2

Measurements of the ratio of diffusion coefficient to mobility (D/ mu ) of electrons in SF6-N2 and CCl2F2-N2 mixtures over the range 80mean energies epsilon c.mix corresponding to (E/p)c.mix, are found to vary with the percentage of the electronegative gas in the mixture (F) according to the following relationship: (E/p)c.mix=(E/p)c.N(2)+((E/p)c.A-(E/p)c.N(2)) (1-exp(- beta F/100-F)) and epsilon c.mix= epsilon c.N(2)+( epsilon c.A- epsilon c.N(2)) (1-exp(- beta F/100-F)) where A refers to the attaching gas, either SF6 or CCl2F2 and beta is a constant, equal to 2.43 for SF6 mixtures and 5.12 for CCl2F2 mixtures. In the present study, it has been possible to show that beta is indeed to a factor of synergism. Estimated gamma values (secondary ionisation coefficients) did not show any significant variation with F for F<50.

Error bounds for calculation of the Gittins indices

For a wide class of semi-Markov decision processes the optimal policies are expressible in terms of the Gittins indices, which have been found useful in sequential clinical trials and pharmaceutical research planning. In general, the indices can be approximated via calibration based on dynamic programming of finite horizon. This paper provides some results on the accuracy of such approximations, and, in particular, gives the error bounds for some well known processes (Bernoulli reward processes, normal reward processes and exponential target processes).

A quasi-likelihood approach for ordered categorical data with overdispersion

Quasi-likelihood (QL) methods are often used to account for overdispersion in categorical data. This paper proposes a new way of constructing a QL function that stems from the conditional mean-variance relationship. Unlike traditional QL approaches to categorical data, this QL function is, in general, not a scaled version of the ordinary log-likelihood function. A simulation study is carried out to examine the performance of the proposed QL method. Fish mortality data from quantal response experiments are used for illustration.

Non-stationary signal analysis by least mean fourth (LMF) adaptive algorithm

A modified least mean fourth (LMF) adaptive algorithm applicable to non-stationary signals is presented. The performance of the proposed algorithm is studied by simulation for non-stationarities in bandwidth, centre frequency and gain of a stochastic signal. These non-stationarities are in the form of linear, sinusoidal and jump variations of the parameters. The proposed LMF adaptation is found to have better parameter tracking capability than the LMS adaptation for the same speed of convergence.

Mean-field results of a lattice-gas model of multilayer adsorption

A lattice-gas model of multilayer adsorption has been solved in the mean-field approximation by a different numerical method. Earlier workers obtained a single solution for all values of temperature and pressure. In the present work, multiple solutions have been obtained in certain regions of temperature and pressure which give rise to bysteresis in the adsorption isotherm. In addition, we have obtained a parameter which behaves like an order parameter for the transition. The potential-energy function shows a double minimum in the region of bysteresis and a single maximum elsewhere.

Optimum choice of wavelengths in the anomalous scattering technique with synchrotron radiation

A formula has been derived for the mean-square error in the phases of crystal reflections determined through the multiwavelength anomalous scattering method.The error is written in terms of a simple function of the positions in the complex plane of the 'centres' corresponding to the different wavelengths. For the case of three centres, the mean-square error is inversely proportional to the area of the triangle formed by them.

Assessment of internal quality attributes of mandarin fruit. 2. NIR calibration model robustness

The robustness of multivariate calibration models, based on near infrared spectroscopy, for the assessment of total soluble solids (TSS) and dry matter (DM) of intact mandarin fruit (Citrus reticulata cv. Imperial) was assessed. TSS calibration model performance was validated in terms of prediction of populations of fruit not in the original population (different harvest days from a single tree, different harvest localities, different harvest seasons). Of these, calibration performance was most affected by validation across seasons (signal to noise statistic on root mean squared error of prediction of 3.8, compared with 20 and 13 for locality and harvest day, respectively). Procedures for sample selection from the validation population for addition to the calibration population (‘model updating’) were considered for both TSS and DM models. Random selection from the validation group worked as well as more sophisticated selection procedures, with approximately 20 samples required. Models that were developed using samples at a range of temperatures were robust in validation for TSS and DM.

Many-body effects in electrochemisorption : Part III. Beyond mean field and hartree-fock

Several channels provided by many-body couplings — both fermion-fermion and fermion-boson — for the evolution of the chemisorption system are discussed. This provides an opportunity of a systematic study of the effects of correlations reflected through the intricate pole structure of the absorbate Green functions. The results of Newns, Anda and others in the context of chemisorption are generalized.

The One and The Many : In the works of Heraclitus, Parmenides and Lao Zi

This paper concentrates on Heraclitus, Parmenides and Lao Zi. The focus is on their ideas on change and whether the world is essentially One or if it is composed of many entities. In the first chapter I go over some general tendences in Greek and Chinese philosophy. The differences in the cultural background have an influence in the ways philosophy is made, but the paper aims to show that two questions can be brought up when comparing the philosophies of Heraclitus, Parmenides and Lao Zi. The questions are; is the world essentially One or Many? Is change real and if it is, what is the nature of it and how does it take place? For Heraclitus change is real, and as will be shown later in the chapter, quite essential for the sustainability of the world-order (kosmos). The key-concept in the case of Heraclitus is Logos. Heraclitus uses Logos in several senses, most well known relating to his element-theory. But another important feature of the Logos, the content of real wisdom, is to be able to regard everything as one. This does not mean that world is essentially one for Heraclitus in the ontological sense, but that we should see the underlying unity of multiple phenomena. Heraclitus regards this as hen panta: All from One, One from All. I characterize Heraclitus as epistemic monist and an ontological pluralist. It is plausible that the views of Heraclitus on change were the focus of Parmenides’ severe criticism. Parmenides held the view that the world is essentially one and that to see it as consisting of many entities was the error of mortals, i.e. the common man and his philosophical predecessors. For Parmenides what-is, can be approached by two routes; The Way of Truth (Aletheia) and The Way of Seeming (Doxa). Aletheia essentially sees the world as one, where even time is an illusion. In Doxa Parmenides is giving an explanation of the world seen as consisting of many entities and this is his contribution to the line of thought of his predecessors. It should be noted that a strong emphasis is given to the Aletheia, whereas the world-view given is in Doxa is only probable. I go on to describe Parmenides as ontological monist, who gives some plausibility to pluralistic views. In the work of Lao Zi world can be seen as One or as consisting of Many entities. In my interpretation, Lao Zi uses Dao in two different senses; Dao is the totality of things or the order in change. The wu-aspect (seeing-without-form) attends the world as one, whereas the you-aspect attends the world of many entities. In wu-aspect, Dao refers to the totality of things, when in you-aspect Dao is the order or law in change. There are two insights in Lao Zi regarding the relationship between wu- and- you-apects; in ch.1 it is stated that they are two separate aspects in seeing the world, the other chapters regarding that you comes from wu. This naturally brings in the question whether the One is the peak of seeing the world as many. In other words, is there a way from pluralism to monism. All these considerations make it probable that the work attributed to Lao Zi has been added new material or is a compilation of oral sayings. In the end of the paper I will go on to give some insights on how Logos and Dao can be compared in a relevant manner. I also compare Parmenides holistic monism to Lao Zi’s Dao as nameless totality (i.e. in its wu-aspect). I briefly touch the issues of Heidegger and the future of comparative philosophy.

A study of the use of the Edinburgh postnatal depression scale with parent groups outside the postpartum period

The Edinburgh Postnatal Depression Scale (EPDS) was sent by post to 206 mothers and 201 fathers of toddlers (aged between 19 and 22 months). At the same time these parents also completed subscales of the Crown—Crisp Experiential Index (CCEI). The responses were used to assess the feasibility of postal completion of the EPDS and its acceptability to parents outside the postpartum year, particularly fathers for whom there have been no previous reports of its use. On a small sub-group, the sensitivity, specificity and predictive values of the measures were assessed using the Present. State Examination. Answers to the depression subscale of the CCEI to the EPDS and to the Present State Examination were compared to assess validity. Completion of the postally-administered EPDS was satisfactory, though some difficulties were experienced in a second postal administration to a subsample. The scale was completed without obvious error or omission and this, combined with positive comments from parents, suggests the acceptability of the scale to both mothers and fathers. The mean scores were higher for mothers than for fathers, but the pattern of distribution was similar with a marked positive skew and a distinct decline in scores above 10. Because the subsample of parents interviewed was small the calculation of sensitivity and specificity has to be treated with caution. However, the results for mothers suggest that the EPDS has satisfactory validity for this group and one superior to the depression subscale of the CCEI. Among the fathers interviewed there were insufficient cases to enable calculation of sensitivity and specificity. Other results were encouraging, however, and suggest the merit of further studies of the application and validity of the EPDS with fathers.

Parameterizing Unconditional Skewness in Models for Financial Time Series

In this paper we consider the third-moment structure of a class of time series models. It is often argued that the marginal distribution of financial time series such as returns is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate unconditional skewness. We consider modeling the unconditional mean and variance using models that respond nonlinearly or asymmetrically to shocks. We investigate the implications of these models on the third-moment structure of the marginal distribution as well as conditions under which the unconditional distribution exhibits skewness and nonzero third-order autocovariance structure. In this respect, an asymmetric or nonlinear specification of the conditional mean is found to be of greater importance than the properties of the conditional variance. Several examples are discussed and, whenever possible, explicit analytical expressions provided for all third-order moments and cross-moments. Finally, we introduce a new tool, the shock impact curve, for investigating the impact of shocks on the conditional mean squared error of return series.

An absolute method for the determination of surface tension of liquids using pendent drop profiles

Drop formation at conical tips which is of relevance to metallurgists is investigated based on the principle of minimization of free energy using the variational approach. The dimensionless governing equations for drop profiles are computer solved using the fourth order Runge-Kutta method. For different cone angles, the theoretical plots of XT and ZT vs their ratio, are statistically analyzed, where XT and ZT are the dimensionless x and z coordinates of the drop profile at a plane at the conical tip, perpendicular to the axis of symmetry. Based on the mathematical description of these curves, an absolute method has been proposed for the determination of surface tension of liquids, which is shown to be preferable in comparison with the earlier pendent-drop profile methods.

Understanding how axial loads on the spine influence segmental biomechanics for idiopathic scoliosis patients: A magnetic resonance imaging study

Background Segmental biomechanics of the scoliotic spine are important since the overall spinal deformity is comprised of the cumulative coronal and axial rotations of individual joints. This study investigates the coronal plane segmental biomechanics for adolescent idiopathic scoliosis patients in response to physiologically relevant axial compression. Methods Individual spinal joint compliance in the coronal plane was measured for a series of 15 idiopathic scoliosis patients using axially loaded magnetic resonance imaging. Each patient was first imaged in the supine position with no axial load, and then again following application of an axial compressive load. Coronal plane disc wedge angles in the unloaded and loaded configurations were measured. Joint moments exerted by the axial compressive load were used to derive estimates of individual joint compliance. Findings The mean standing major Cobb angle for this patient series was 46°. Mean intra-observer measurement error for endplate inclination was 1.6°. Following loading, initially highly wedged discs demonstrated a smaller change in wedge angle, than less wedged discs for certain spinal levels (+ 2,+1,− 2 relative to the apex, (p < 0.05)). Highly wedged discs were observed near the apex of the curve, which corresponded to lower joint compliance in the apical region. Interpretation While individual patients exhibit substantial variability in disc wedge angles and joint compliance, overall there is a pattern of increased disc wedging near the curve apex, and reduced joint compliance in this region. Approaches such as this can provide valuable biomechanical data on in vivo spinal biomechanics of the scoliotic spine, for analysis of deformity progression and surgical planning.