Properties of the space horopter.

For general points of fixation the space horopter has been found to be a twisted cubic curve, which, when fixation is in the median plane, degenerates into a conic curve inclined to the plane of fixation. The inclination of the plane of this conic is found to be a function of the angles of torsion of the two eyes. If these angles are zero and fixation is horizontal the space horopter reduces to the Vieth-Müller circle. Previous experimental techniques for plotting the horopter curve do not in fact determine the locus in space of those points that will stimulate corresponding points in the two retinae: they are, locate the position of certain chords of the space horopter. The Hering-Hillebrand deviation coefficient is found theoretically to be a linear function of the fixation distance. This had been shown experimentally by previous workers, but without any satisfactory explanation.     

Derivation of the space horopter.

The horopter--the locus of those points in space that would stimulate corresponding points on the retinae of the two eyes--has been previously considered to be a plane curve lying in the horizontal plane. The two-dimensional character of this curve arises as a consequence of limiting all considerations to two dimensions only. However, by considering the retina as a two-dimensional surface in 3-space, geometric analysis reveals the horopter to be a non-planar curve: a twisted cubic curve in space. The classical horopter experiments can then be seen to be plotting self-corresponding lines rather than self-corresponding points, and these lines are found to be the chords of this cubic curve. The equations determining the horopter curve in parametric form have been found expressing each point of the curve as a function of the coordinates of the point of fixation.     

Quantitative trait loci influencing β-glucan content in oat (Avena sativa, 2n=6x=42)

The β-glucan content of oat grain is of inter-est due to its positive human health role as a dietary component influencing serum cholesterol levels and its relation to the energy intake of livestock feed. Two recombinant inbred populations sharing a common parent (Kanota × Ogle and Kanota × Marion), and containing 137 individual lines each, were used to identify genomic regions that influence the β-glucan content in cultivated oat. Single-factor ANOVA, a backward elimination process, simple interval mapping (SIM) and simplified composite interval mapping (sCIM) were used to identify quantitative trait loci (QTLs). Regions on linkage groups 11 and 14 of the hexaploid oat RFLP map influenced β-glucan levels in both populations and over environments. Other genomic regions were identified whose effects varied depending on the genetic background, but were significant over measurements for a given population. Kanota and Ogle exhibit similar β-glucan levels and each parent contributed about the same number of positive β-glucan alleles in the Kanota × Ogle cross. Marion is higher in β-glucan content than Kanota and contributed all of the positive alleles in the Kanota × Marion cross. Three of the β-glucan QTL regions identified have been previously implicated as having a significant influence on the groat oil content in oat. These correlated QTL regions were either in coupling phase, with a region from one parent having the same effect on both traits, or were in repulsion phase. Identification of coupling- and repulsion-phase QTL regions for β-glucan and oil content facilitates the use of markers in manipulating these traits in oat breeding. Received: 8 September 1999 / Accepted: 25 March 2000     

The plasticity of correspondence: After-effects,illusions and horopter shifts in depth perception

Retinal disparity is the cue for stereoscopic depth perception. Disparity detection begins with cortical single units driven binocularly from the two eyes. A previous paper (Nelson, 1975) has shown that inhibitory and facilitatory interactions are essential to insure successful disparity detection, particularly with repeating stimulus patterns, and that such a system will display all the appropriate properties of sensory fusion. This paper shows that most depth illusions occur as by-products of the same domain interactions. Such illusion effects fall into two classes: those caused by shifts in the distribution of activity along the appropriate sensory domain (here, the disparity domain) and those caused by changes in the average activity level within the domain. Profile shifts cause depth contrast illusions. The most important profile level change is an activity lowering due to disparity domain inhibition. This adversely affects fusional range (Panum's area). It is postulated that all domain interactions persist following cessation of stimulation. Persistent profile shifts cause depth after-effect illusions; persistent profile lowering is responsible for threshold elevation after-effects.Sensory fusion, the coding errors seen in illusions, the induced effect, and widespread failure to perceive depth from disparity input show that retinal correspondence is not stable in the normal individual. Yet horopter research has attempted to specify one set of retinal points as corresponding. Not surprisingly, horopter research shows systematic shifts in retinal correspondence linked to eye position. Small, simple, tonic modulations of the domain interactions responsible for so many other stereopsis system properties provide a satisfactory cortical mechanism for horopter changes.     

New Ranked Set Sampling for One‐Parameter Family of Distributions

Bhoj (1997c) proposed a new ranked set sampling (NRSS) procedure for a specific two‐parameter family of distributions when the sample size is even. This NRSS procedure can be applied to one‐parameter family of distributions when the sample size is even. However, this procedure cannot be used if the sample size is odd. Therefore, in this paper, we propose a modified version of the NRSS procedure which can be used for one‐parameter distributions when the sample size is odd. Simple estimator for the parameter based on proposed NRSS is derived. The relative precisions of this estimator are higher than those of other estimators which are based on other ranked set sampling procedures and the best linear unbiased estimator using all order statistics.     

Qualitative and quantitative trait loci conditioning resistance to Puccinia coronata pathotypes NQMG and LGCG in the oat (Avena sativa L.) cultivars Ogle and TAM O-301

Mapping disease resistance loci relies on the type and precision of phenotypic measurements. For crown rust of oat, disease severity is commonly assessed based on visual ratings of infection types (IT) and/or diseased leaf area (DLA) of infected plants in the greenhouse or field. These data can be affected by several variables including; (i) non-uniform disease development in the field; (ii) atypical symptom development in the greenhouse; (iii) the presence of multiple pathogenic races or pathotypes in the field, and (iv) rating bias. To overcome these limitations, we mapped crown rust resistance to single isolates in the Ogle/TAM O-301 (OT) recombinant inbred line (RIL) population using detailed measurements of IT, uredinia length (UL) and relative fungal DNA (FDNA) estimates determined by q-PCR. Measurements were taken on OT parents and recombinant inbred lines (RIL) inoculated with Puccinia coronata pathotypes NQMG and LGCG in separate greenhouse and field tests. Qualitative mapping identified an allele conferred by TAM O-301 on linkage group (LG) OT-11, which produced a bleached fleck phenotype to both NQMG and LGCG. Quantitative mapping identified two major quantitative trait loci (QTL) originating from TAM O-301 on LGs OT-11 and OT-32 which reduced UL and FDNA of both isolates in all experiments. Additionally, minor QTLs that reduced UL and FDNA were detected on LGs OT-15 and OT-8, originating from TAM O-301, and on LG OT-27, originating from Ogle. Detailed assessments of the OT population using two pathotypes in both the greenhouse and field provided comprehensive information to effectively map the genes responsible for crown rust resistance in Ogle and TAM O-301 to NQMG and LGCG.     

Estimating average annual percent change for disease rates without assuming constant change

The annual percent change (APC) is often used to measure trends in disease and mortality rates, and a common estimator of this parameter uses a linear model on the log of the age-standardized rates. Under the assumption of linearity on the log scale, which is equivalent to a constant change assumption, APC can be equivalently defined in three ways as transformations of either (1) the slope of the line that runs through the log of each rate, (2) the ratio of the last rate to the first rate in the series, or (3) the geometric mean of the proportional changes in the rates over the series. When the constant change assumption fails then the first definition cannot be applied as is, while the second and third definitions unambiguously define the same parameter regardless of whether the assumption holds. We call this parameter the percent change annualized (PCA) and propose two new estimators of it. The first, the two-point estimator, uses only the first and last rates, assuming nothing about the rates in between. This estimator requires fewer assumptions and is asymptotically unbiased as the size of the population gets large, but has more variability since it uses no information from the middle rates. The second estimator is an adaptive one and equals the linear model estimator with a high probability when the rates are not significantly different from linear on the log scale, but includes fewer points if there are significant departures from that linearity. For the two-point estimator we can use confidence intervals previously developed for ratios of directly standardized rates. For the adaptive estimator, we show through simulation that the bootstrap confidence intervals give appropriate coverage.     

Darwin on Aristotle

Charles Darwin's famous 1882 letter, in response to a gift by his friend, William Ogle of Ogle's recent translation of Aristotle's Parts of Animals, in which Darwin remarks that his “two gods,” Linnaeus and Cuvier, were “mere school-boys to old Aristotle,” has been thought to be only an extravagantly worded gesture of politeness. However, a close examination of this and other Darwin letters, and of references to Aristotle in Darwin's earlier work, shows that the famous letter was written several weeks after a first, polite letter of thanks, and was carefully formulated and literally meant. Indeed, it reflected an authentic, and substantial, increase in Darwin's already high respect for Aristotle, as a result of a careful reading both of Ogle's Introduction and of more or less the portion of Ogle's translation which Darwin says he has read. Aristotle's promotion to the pantheon, as an examination of the basis for Darwin's admiration of Linnaeus and Cuvier suggests, was most likely the result specifically of Darwin's late discovery that the man he already knew as “one of the greatest ... observers that ever lived” (1879) was also the ancient equivalent both of the great modern systematist and of the great modern advocate of comparative functional explanation. It may also have reflected some real insight on Darwin's part into the teleological aspect of Aristotle's thought, indeed more insight than Ogle himself had achieved, as a portion of their correspondence reveals. This revised version was published online in July 2006 with corrections to the Cover Date.     

Genomic regions controlling vernalization and photoperiod responses in oat

Oat genotypes vary for photoperiod and vernalization responses. Vernalization often promotes earlier flowering in fall-sown but not spring-sown cultivars. Longer photoperiods also promote earlier flowering, and the response to longer photoperiods tends to be greater in cultivars from higher latitudes. To investigate the genetic basis of photoperiod and vernalization responses in oat, we mapped QTLs for flowering time under four combinations of photoperiod and vernalization treatments in the Ogle 2 TAM O-301 mapping population in growth chambers. We also mapped QTLs for flowering time in early spring and late-spring field plantings to determine the genetic basis of response to early spring planting in oat. Three major flowering-time QTLs (on linkage groups OT8, OT31 and OT32) were detected in most conditions. QTLs with smaller effects on flowering were less-consistently observed among treatments. Both vernalization-sensitive and insensitive QTLs were discovered. Longer photoperiod or vernalization alone tended to decrease the effects of flowering-time QTLs. Applied together, longer photoperiod and vernalization interacted synergistically, often on the same genomic regions. Earlier spring planting conferred an attenuated vernalization treatment on seeds. The major flowering-time QTLs mapped in this study matched those mapped previously in the Kanota 2 Ogle oat mapping population. Between these two studies, we found a concordance of flowering-time QTLs, segregation distortion, and complex genetic linkages. These effects may all be related to chromosomal rearrangements in hexaploid oat. Comparative mapping between oat and other grasses will facilitate molecular analysis of vernalization response in oat.     

IMPLICATIONS OF NON-LINEAR DENSITY DEPENDENCE

Abstract: Ranges of the ratio of maximum net productivity level (MNPL) to carrying capacity (K) are explored in general models for pinnipeds and odontocetes. MNPL/K is used in management of marine mammals but no empirical evidence exists to limit the range of values expected. Density dependent changes in age-specific birth and death rates have been used to infer MNPL/K. Non-linearities in these rates do not translate directly to population growth curves. The simple models demonstrate: (1) density dependence is likely to involve more than a single parameter (such as birth rate), (2) MNPL/K can be greatly reduced from that inferred from one strongly non-linear parameter when changes in other parameters are linear, (3) ranges of MNPL/K depend on biological limits on ranges of fecundity and survival rates, and (4) the magnitude and sign of bias incurred by inferring MNPL/K from functional forms of single parameters cannot be determined. Given current empirical evidence the range of MNPL/K for marine mammals as a group is large. Although MNPL/K should not be inferred from single parameter non-linearities, distributions of MNPL/K values can be generated through models which account for single species ranges for birth and death rates and maximum population growth rate.     

Clustering in linear‐mixed models with a group fused lasso penalty

A method is proposed that aims at identifying clusters of individuals that show similar patterns when observed repeatedly. We consider linear‐mixed models that are widely used for the modeling of longitudinal data. In contrast to the classical assumption of a normal distribution for the random effects a finite mixture of normal distributions is assumed. Typically, the number of mixture components is unknown and has to be chosen, ideally by data driven tools. For this purpose, an EM algorithm‐based approach is considered that uses a penalized normal mixture as random effects distribution. The penalty term shrinks the pairwise distances of cluster centers based on the group lasso and the fused lasso method. The effect is that individuals with similar time trends are merged into the same cluster. The strength of regularization is determined by one penalization parameter. For finding the optimal penalization parameter a new model choice criterion is proposed.     

A nonproportional hazards Weibull accelerated failure time regression model

We present a study of risk factors measured in mean before age 50 and subsequent incidence of heart disease over 32 years of follow-up. The data are from the Framingham Heart Study. The standard accelerated failure time model assumes the logarithm of time until an event has a constant dispersion parameter and a location parameter that is a linear function of covariates. Parameters are estimated by maximum likelihood. We reject a standard Weibull model for these data in favor of a model with the dispersion parameter depending on the location parameter. This model suggests that the cumulative hazard ratio for two individuals shrinks towards unity over the follow-up period. Thus, not only the standard Weibull, but also the semiparametric proportional hazards (Cox) model is inadequate for this data. The model improvement appears particularly valuable when estimating the difference in predicted outcome probabilities for two individuals.     

Forecasting flowering dates of lawn species with air temperature: Application boundaries of the linear approach

Summary A modelling analysis was performed on the phenological data collected for three years in a lawn located at the Operational Meteorological Centre of S. Pietro Capofiume, Bologna, Italy. The data concern the flowering of up to 56 wild species and were taken according to a seven-stage phenological key. The analysis was performed in order to verify the predictive limits of the degreeday model, an approach assuming a linear functional relationship between air temperature and the rate of phenological development. The procedure we followed consists in the heuristic assessment of the three parameters characterizing the linear model, that is the starting date before which the temperature has no influence on the anthesic development, the base temperature, and the temperature sum. With that in mind, we determined the temperature sums for all the pairs of parameter values taken in the range (– ÷ 15° C) for base temperatures, and in the range (January I^m ÷ flowering date) for starting dates. Not all the species examined produced stable parameter sets but a test of the latter against independent data showed data, where applicable, the linear approach provides a reliable forecasting tool. The linear approach was also applied in order to determine the existence of leading species, that is species whose flowering dates could represent the staring date of temperature accumulation in order to forecast the flowering date of later species. In this case the determination of base temperatures and temperature sums derives from the assumption that when the leading species attains flowering the predicted one has reached an unknown but fixed fraction of its own phenological development. We applied this procedure to all the possible pairs of species and in this case the stability test produced a drastic selection among them.     

Comparative AFLP mapping in two hexaploid oat populations

Amplified fragment length polymorphisms (AFLPs) can be used to quickly develop linkage maps in plant species and are especially useful for crops with large genomes like oat (Avena sativa L., 2n=6x=42). High reproducibility and consistency are crucial if AFLP linkage maps are employed for comparative mapping. We mapped AFLP markers in combination with restriction fragment length polymorphism (RFLP) markers in two recombinant inbred populations of hexaploid oat in two laboratories to test the consistency of AFLP markers in a polyploid crop. Eight primer combinations produced 102 and 121 scoreable AFLP markers in the respective populations. In a population from the cross Kanota×Ogle, AFLP markers were placed onto a RFLP reference map consisting of 32 linkage groups. Nineteen linkage groups from another population from the cross Kanota×Marion were assigned to the reference map using AFLP and RFLP markers homologous to those used in the Kanota× Ogle cross. Reproducibility of AFLP assays was high in both laboratories and between laboratories. The AFLP markers were well-distributed across the genome in both populations. Many AFLP markers tended to extend the distance between adjacent RFLP markers in linkage analysis. Of the 27 polymorphic AFLPs common in both populations, 20 mapped to homologous linkage groups, 4 were unlinked in at least one population, and 3 mapped to different linkage groups in the two crosses. We believe that 1 of the 3 markers that mapped to a different linkage group in the two populations mapped to homoeologous linkage groups. The linkage map of hexaploid oat is not yet complete, and genomic rearrangements such as translocations exist among cultivars and are likely to account for the remaining two non-syntenous mapping results. AFLPs provide not only a fast and powerful tool for mapping but could be useful in characterizing genomic structural variations among germplasms in hexaploid oat. Received: 17 December 1999 / Accepted: 28 July 2000     

An algorithm for finding globally identifiable parameter combinations of nonlinear ODE models using Gröbner Bases

The parameter identifiability problem for dynamic system ODE models has been extensively studied. Nevertheless, except for linear ODE models, the question of establishing identifiable combinations of parameters when the model is unidentifiable has not received as much attention and the problem is not fully resolved for nonlinear ODEs. Identifiable combinations are useful, for example, for the reparameterization of an unidentifiable ODE model into an identifiable one. We extend an existing algorithm for finding globally identifiable parameters of nonlinear ODE models to generate the ‘simplest’ globally identifiable parameter combinations using Gröbner Bases. We also provide sufficient conditions for the method to work, demonstrate our algorithm and find associated identifiable reparameterizations for several linear and nonlinear unidentifiable biomodels.     

Reduction of Linear Models Using Correct or Incorrect Prior Information

When there is no prior knowledge on the parameter vector β of the linear model then the LSE is most favourable at least in the class of linear unbiased estimators. On the other hand, in many practical problems one has some guessed estimate of β. Using this information leads to two-step estimation procedures which may or may not dominate the LSE with respect to MSE. The dominance depends on the degree of incorrectness of the guessed parameter and is analyzed numerically for the case of sample reduction.     

Permutation tests for random effects in linear mixed models

Inference regarding the inclusion or exclusion of random effects in linear mixed models is challenging because the variance components are located on the boundary of their parameter space under the usual null hypothesis. As a result, the asymptotic null distribution of the Wald, score, and likelihood ratio tests will not have the typical χ(2) distribution. Although it has been proved that the correct asymptotic distribution is a mixture of χ(2) distributions, the appropriate mixture distribution is rather cumbersome and nonintuitive when the null and alternative hypotheses differ by more than one random effect. As alternatives, we present two permutation tests, one that is based on the best linear unbiased predictors and one that is based on the restricted likelihood ratio test statistic. Both methods involve weighted residuals, with the weights determined by the among- and within-subject variance components. The null permutation distributions of our statistics are computed by permuting the residuals both within and among subjects and are valid both asymptotically and in small samples. We examine the size and power of our tests via simulation under a variety of settings and apply our test to a published data set of chronic myelogenous leukemia patients.     

Comparison of One‐Step and Two‐Step Meta‐Analysis Models Using Individual Patient Data

The problem of combining information from separate trials is a key consideration when performing a meta‐analysis or planning a multicentre trial. Although there is a considerable journal literature on meta‐analysis based on individual patient data (IPD), i.e. a one‐step IPD meta‐analysis, versus analysis based on summary data, i.e. a two‐step IPD meta‐analysis, recent articles in the medical literature indicate that there is still confusion and uncertainty as to the validity of an analysis based on aggregate data. In this study, we address one of the central statistical issues by considering the estimation of a linear function of the mean, based on linear models for summary data and for IPD. The summary data from a trial is assumed to comprise the best linear unbiased estimator, or maximum likelihood estimator of the parameter, along with its covariance matrix. The setup, which allows for the presence of random effects and covariates in the model, is quite general and includes many of the commonly employed models, for example, linear models with fixed treatment effects and fixed or random trial effects. For this general model, we derive a condition under which the one‐step and two‐step IPD meta‐analysis estimators coincide, extending earlier work considerably. The implications of this result for the specific models mentioned above are illustrated in detail, both theoretically and in terms of two real data sets, and the roles of balance and heterogeneity are highlighted. Our analysis also shows that when covariates are present, which is typically the case, the two estimators coincide only under extra simplifying assumptions, which are somewhat unrealistic in practice.     

High-precision three-dimensional photogrammetric calibration and object space reconstruction using a modified DLT-approach

Two modified DLT algorithms are presented that improve the accuracy of three-dimensional object space reconstruction by almost an order of magnitude when compared with conventional methods. The improvement in the linear modified DLT (MDLT) algorithm is achieved by satisfying certain orthogonality conditions in the form of a non-linear constraint, thereby effectively eliminating a redundant DLT parameter. In the non-linear MDLT algorithm, the improvement and computational stability results from the appropriate elimination of implicit variables from one side of the approximating relations and the corresponding reformulation of the objective function to be minimized. The highest reconstruction accuracy of 0.733 mm rms mean error was obtained with the non-linear MDLT algorithm. This corresponds to a spatial resolution of about one part in 2860 or 0.035% overall accuracy. The accuracy obtainable with the linear MDLT was found to be slightly less and about 0.041% (0.833 mm rms mean error).     

Absolute measurement of enhanced fluctuations in assemblies of biomolecules by ultrasonic techniques.

By expressing the fluctuation-dissipation theorem explicitly, equations are obtained for the ultrasonic relaxation amplitudes that contain one single molecular parameter, i.e., the fluctuation, or the sum of fluctuations. The absolute measurement of this parameter is therefore possible. The equations apply to a two-state system, to a multistate system and to a linear Ising chain as well. In an aqueous medium, where molar volume changes are important, the ultrasonic relaxation amplitudes are proportional to the volume fluctuations. For assemblies of biomolecules that exhibit enhanced ultrasonic absorption on assembly it is possible to measure the increase on assembly of the sum of fluctuations. In view of application to tobacco mosaic virus protein aggregates, examples are given in which the fluctuations associated with two normal modes of relaxation are equally enhanced when the difference of conformational stability of the states is reduced. The corresponding observable changes of the ultrasonic spectra are described.