{p=[Background, Current statistical methods for sib-pair linkage analysis of complex diseases include linear models, generalized linear models, and novel data mining techniques. The purpose of this study was to further investigate the utility and properties of a novel pattern recognition technique (step-wise discriminant analysis) using the chromosome 10 linkage data from the Framingham Heart Study and by comparing it with step-wise logistic regression and linear regression., Results, The three step-wise approaches were compared in terms of statistical significance and gene localization. Step-wise discriminant linkage analysis approach performed best; next was step-wise logistic regression; and step-wise linear regression was the least efficient because it ignored the categorical nature of disease phenotypes. Nevertheless, all three methods successfully identified the previously reported chromosomal region linked to human hypertension, marker GATA64A09. We also explored the possibility of using the discriminant analysis to detect gene × gene and gene × environment interactions. There was evidence to suggest the existence of gene × environment interactions between markers GATA64A09 or GATA115E01 and hypertension treatment and gene × gene interactions between markers GATA64A09 and GATA115E01. Finally, we answered the theoretical question "Is a trichotomous phenotype more efficient than a binary?" Unlike logistic regression, discriminant sib-pair linkage analysis might have more power to detect linkage to a binary phenotype than a trichotomous one., Conclusion, We confirmed our previous speculation that step-wise discriminant analysis is useful for genetic mapping of complex diseases. This analysis also supported the possibility of the pattern recognition technique for investigating gene × gene or gene × environment interactions.], h1=Abstract}

{p=[Background, Compared to model-based approaches, nonparametric methods for quantitative trait loci mapping are more robust to deviations in distributional assumptions. In this study, we modify a nonparametric regression method and the "contrast function"- based regression method to analyze total cholesterol level in the younger cohort (the offspring generation) of the Genetic Analysis Workshop 13 simulated data set., Results, We obtained significant evidence of linkage near four of the six non-sex-specific genes in at least 30% of the replicates., Conclusions, The proposed nonparametric method seems to be a powerful robust alternative to distribution-based methods.], h1=Abstract}

{p=[Background, Genetic studies of complex disorders such as hypertension often utilize families selected for this outcome, usually with information obtained at a single time point. Since age-at-onset for diagnosed hypertension can vary substantially between individuals, a phenotype based on long-term follow up in unselected families can yield valuable insights into this disorder for the general population., Methods, Genetic analyses were conducted using 2884 individuals from the largest 330 families of the Framingham Heart Study. A longitudinal phenotype was constructed using the age at an examination when systolic blood pressure (SBP) first exceeds 139 mm Hg. An interval for age-at-onset was created, since the exact time of onset was unknown. Time-fixed (sex, study cohort) and time-varying (body mass index, daily cigarette and alcohol consumption) explanatory variables were included., Results, Segregation analysis for a major gene effect demonstrated that the major gene effect parameter was sensitive to the choice for age-at-onset. Linkage analyses for age-at-onset were conducted using 1537 individuals in 52 families. Evidence for putative genes identified on chromosome 17 in a previous linkage study using a quantitative SBP phenotype for these data was not confirmed., Conclusions, Interval censoring for age-at-onset should not be ignored. Further research is needed to explain the inconsistent segregation results between the different age-at-onset models (regressive threshold and proportional hazards) as well as the inconsistent linkage results between the longitudinal phenotypes (age-at-onset and quantitative).], h1=Abstract}

A real-space representation of the current response of many-electron systems with possible applications to x-ray nonlinear spectroscopy and magnetic susceptibilities is developed. Closed expressions for the linear, quadratic and third-order response functions are derived by solving the adiabatic Time Dependent Current Density Functional (TDCDFT) equations for the single-electron density matrix in Liouville space.

{p=[Background, For analyzing longitudinal familial data we adopted a log-linear form to incorporate heterogeneity in genetic variance components over the time, and additionally a serial correlation term in the genetic effects at different levels of ages. Due to the availability of multiple measures on the same individual, we permitted environmental correlations that may change across time., Results, Systolic blood pressure from family members from the first and second cohort was used in the current analysis. Measures of subjects receiving hypertension treatment were set as censored values and they were corrected. An initial check of the variance and covariance functions proposed for analyzing longitudinal familial data, using empirical semi-variogram plots, indicated that the observed trait dispersion pattern follows the assumptions adopted., Conclusion, The corrections for censored phenotypes based on ordinary linear models may be an appropriate simple model to correct the data, ensuring that the original variability in the data was retained. In addition, empirical semi-variogram plots are useful for diagnosis of the (co)variance model adopted.], h1=Abstract}

{p=With the availability of longitudinal data, age-specific (stratified) or age-adjusted genetic analyses have the potential to localize different putative trait influencing loci. If age does not influence the locus-specific penetrance function within the range examined, age-stratified analyses will tend to yield comparable results for an individual trait. However, age-stratified results should vary across age strata when the locus-specific penetrance function is age dependent. In this paper, age-stratified and age-adjusted quantitative trait loci (QTL) linkage analyses were contrasted for height, weight, body mass index (BMI), and systolic blood pressure on a subset of the Framingham Heart Study. The strata comprised individuals with data present in each of three age groups: 31–49, 50–60, 61–79. Genome-wide QTL analyses were performed using SOLAR. Over all ages, a linkage signal for height was detected on chromosome 14q11.2 near marker GATA74E02A (LOD for ages 31–49 = 2.38, LOD for ages 50–60 = 1.84, LOD for ages 61–79 = 2.45). Evidence of linkage to BMI in the 31–49 age group was found on chromosome 3q22 (GATA3C02, LOD = 2.89, p = 0.0003) at the same location as the signal for weight (LOD = 3.10, p = 0.0002). Linkage was also supported on chromosome 1p22.1 for BMI (LOD = 2.21, p = 0.0014) and weight (LOD = 2.47, p = 0.0007) in the 31–49 age group. Our age-stratified results suggest that QTL that are expressed over long periods of time and affecting multiple, correlated traits may be identified using genome scan and variance-component methodology to help detect early and/or late gene expression., h1=Abstract}

{p=This paper presents a method of performing model-free LOD-score based linkage analysis on quantitative traits. It is implemented in the QMFLINK program. The method is used to perform a genome screen on the Framingham Heart Study data. A number of markers that show some support for linkage in our study coincide substantially with those implicated in other linkage studies of hypertension. Although the new method needs further testing on additional real and simulated data sets we can already say that it is straightforward to apply and may offer a useful complementary approach to previously available methods for the linkage analysis of quantitative traits., h1=Abstract}

A recent paper on quantum walks by Childs et al. [STOC'03] provides an example of a black-box problem for which there is a quantum algorithm with exponential speedup over the best classical randomized algorithm for the problem, but where the quantum algorithm does not involve any use of the quantum Fourier transform. They give an exponential lower bound for a classical randomized algorithm solving the black-box graph traversal problem defined in their paper. In this note we give an improved lower bound for this problem via a straightforward and more complete analysis.

Exploiting the SU(2) Skyrmion Lagrangian with second-class constraints associated with Lagrange multiplier and collective coordinates, we convert the second-class system into the first-class one in the Batalin-Fradkin-Tyutin embedding through introduction of the St\"uckelberg coordinates. In this extended phase space we construct the "canonical" quantum operator commutators of the collective coordinates and their conjugate momenta to describe the Schr\"odinger representation of the SU(2) Skyrmion, so that we can define isospin operators and their Casimir quantum operator and the corresponding eigenvalue equation possessing integer quantum numbers, and we can also assign via the homotopy class $\pi_{4}(SU(2))=Z_{2}$ half integers to the isospin quantum number for the solitons in baryon phenomenology. Different from the semiclassical quantization previously performed, we exploit the "canonical" quantization scheme in the enlarged phase space by introducing the St\"uckelberg coordinates, to evaluate the baryon mass spectrum having global mass shift originated from geometrical corrections due to the $S^{3}$ compact manifold involved in the topological Skyrmion. Including ghosts and anti-ghosts, we also construct Becci-Rouet-Stora-Tyutin invariant effective Lagrangian.

We investigate the infrared behaviour of gluon and ghost propagators in Landau gauge QCD by means of an exact renormalisation group equation. We explain how, in general, the infrared momentum structure of Green functions can be extracted within this approach. An optimisation procedure is devised to remove residual regulator dependences. In Landau gauge QCD this framework is used to determine the infrared leading terms of the propagators. The results support the Kugo-Ojima confinement scenario. Possible extensions are discussed.