Novel Methods for Multivariate Ordinal Data applied to Genetic Diplotypes, Genomic Pathways, Risk Profiles, and Pattern Similarity

Introduction: Conventional statistical methods for multivariate data (e.g., discriminant/regression) are based on the (generalized) linear model, i.e., the data are interpreted as points in a Euclidian space of independent dimensions. The dimensionality of the data is then reduced by assuming the components to be related by a specific function of known type (linear, exponential, etc.), which allows the distance of each point from a hyperspace to be determined. While mathematically elegant, these approaches may have shortcomings when applied to real world applications where the relative importance, the functional relationship, and the correlation among the variables tend to be unknown. Still, in many applications, each variable can be assumed to have at least an “orientation”, i.e., it can reasonably assumed that, if all other conditions are held constant, an increase in this variable is either “good” or “bad”. The direction of this orientation can be known or unknown. In genetics, for instance, having more “abnormal” alleles may increase the risk (or magnitude) of a disease phenotype. In genomics, the expression of several related genes may indicate disease activity. When screening for security risks, more indicators for atypical behavior may constitute raise more concern, in face or voice recognition, more indicators being similar may increase the likelihood of a person being identified. Methods: In 1998, we developed a nonparametric method for analyzing multivariate ordinal data to assess the overall risk of HIV infection based on different types of behavior or the overall protective effect of barrier methods against HIV infection. By using u-statistics, rather than the marginal likelihood, we were able to increase the computational efficiency of this approach by several orders of magnitude. Results: We applied this approach to assessing immunogenicity of a vaccination strategy in cancer patients. While discussing the pitfalls of the conventional methods for linking quantitative traits to haplotypes, we realized that this approach could be easily modified into to a statistically valid alternative to a previously proposed approaches. We have now begun to use the same methodology to correlate activity of anti-inflammatory drugs along genomic pathways with disease severity of psoriasis based on several clinical and histological characteristics. Conclusion: Multivariate ordinal data are frequently observed to assess semiquantitative characteristics, such as risk profiles (genetic, genomic, or security) or similarity of pattern (faces, voices, behaviors). The conventional methods require empirical validation, because the functions and weights chosen cannot be justified on theoretical grounds. The proposed statistical method for analyzing profiles of ordinal variables, is intrinsically valid. Since no additional assumptions need to be made, the often time-consuming empirical validation can be skipped.ranking; nonparametric; robust; scoring; multivariate

Towards Novel Nonparametric Statistical Methods and Bioinformatics Tools for Clinical and Translational Sciences

As the field of functional genetics and genomics is beginning to mature, we become confronted with new challenges. The constant drop in price for sequencing and gene expression profiling as well as the increasing number of genetic and genomic variables that can be measured makes it feasible to address more complex questions. The success with rare diseases caused by single loci or genes has provided us with a proof-of-concept that new therapies can be developed based on functional genomics and genetics. Common diseases, however, typically involve genetic epistasis, genomic pathways, and proteomic pattern. Moreover, to better understand the underlying biologi-cal systems, we often need to integrate information from several of these sources. Thus, as the field of clinical research moves toward complex diseases, the demand for modern data base systems and advanced statistical methods increases. The traditional statistical methods implemented in most of the bioinformatics tools currently used in the novel field of genetics and functional genomics are based on the linear model and, thus, have shortcomings when applied to nonlinear biological systems. The previous work on partially ordered data (Wittkowski 1988; 1992), when combined with theoretical results (Hoeffding 1948) and computational strategies (Deuchler 1914) has opened a new field of nonparametric statistics. With grid technology, new tools are now feasible when screening for interactions between genetics (Wittkowski, Liu 2002) and functional genomics (Wittkowski, Lee 2004). Having more complex study designs and more specific methods available increases the demand for decision support when selecting appropriate bioinformatics tools. With the advent of rapid prototyping systems for Web based database application, we have recently begun to complement previous work on knowledge based systems with graphical Web-based tools for acquisition of DESIGN and MODEL knowledge.Biostatistics Bioinformatics NIH NCRR ROADMAP

Radio and IR interferometry of SiO maser stars

Radio and infrared interferometry of SiO maser stars provide complementary information on the atmosphere and circumstellar environment at comparable spatial resolution. Here, we present the latest results on the atmospheric structure and the dust condensation region of AGB stars based on our recent infrared spectro-interferometric observations, which represent the environment of SiO masers. We discuss, as an example, new results from simultaneous VLTI and VLBA observations of the Mira variable AGB star R Cnc, including VLTI near- and mid-infrared interferometry, as well as VLBA observations of the SiO maser emission toward this source. We present preliminary results from a monitoring campaign of high-frequency SiO maser emission toward evolved stars obtained with the APEX telescope, which also serves as a precursor of ALMA images of the SiO emitting region. We speculate that large-scale long-period chaotic motion in the extended molecular atmosphere may be the physical reason for observed deviations from point symmetry of atmospheric molecular layers, and for the observed erratic variability of high-frequency SiO maser emissionComment: 8 pages, 4 figures, submitted to Proc. IAU Symp. 287 "Cosmic masers - from OH to H_0", R.S. Booth, E.M.L. Humphreys, W.H.T. Vlemmings (eds.), invited pape

New Statistical Paradigms Leading to Web-Based Tools for Clinical/Translational Science

As the field of functional genetics and genomics is beginning to mature, we become confronted with new challenges. The constant drop in price for sequencing and gene expression profiling as well as the increasing number of genetic and genomic variables that can be measured makes it feasible to address more complex questions. The success with rare diseases caused by single loci or genes has provided us with a proof-of-concept that new therapies can be developed based on functional genomics and genetics. Common diseases, however, typically involve genetic epistasis, genomic pathways, and proteomic pattern. Moreover, to better understand the underlying biologi-cal systems, we often need to integrate information from several of these sources. Thus, as the field of clinical research moves toward complex diseases, the demand for modern data base systems and advanced statistical methods increases. The traditional statistical methods implemented in most of the bioinformatics tools currently used in the novel field of genetics and functional genomics are based on the linear model and, thus, have shortcomings when applied to nonlinear biological systems. The previous work on partially ordered data (Wittkowski 1988; 1992), when combined with theoretical results (Hoeffding 1948) and computational strategies (Deuchler 1914) has opened a new field of nonparametric statistics. With grid technology, new tools are now feasible when screening for interactions between genetics (Wittkowski, Liu 2002) and functional genomics (Wittkowski, Lee 2004). Having more complex study designs and more specific methods available increases the demand for decision support when selecting appropriate bioinformatics tools. With the advent of rapid prototyping systems for Web based database application, we have recently begun to complement previous work on knowledge based systems with graphical Web-based tools for acquisition of DESIGN and MODEL knowledge

Fundamental properties and atmospheric structure of the red supergiant VY CMa based on VLTI/AMBER spectro-interferometry

We investigate the atmospheric structure and fundamental properties of the red supergiant VY CMa. We obtained near-infrared spectro-interferometric observations of VY CMa with spectral resolutions of 35 and 1500 using the AMBER instrument at the VLTI. The visibility data indicate the presence of molecular layers of water vapor and CO in the extended atmosphere with an asymmetric morphology. The uniform disk diameter in the water band around 2.0 mu is increased by \sim20% compared to the near-continuum bandpass at 2.20-2.25 mu and in the CO band at 2.3-2.5 mu it is increased by up to \sim50%. The closure phases indicate relatively small deviations from point symmetry close to the photospheric layer, and stronger deviations in the extended H2O and CO layers. Making use of the high spatial and spectral resolution, a near-continuum bandpass can be isolated from contamination by molecular and dusty layers, and the Rosseland-mean photospheric angular diameter is estimated to 11.3 +/- 0.3 mas based on a PHOENIX atmosphere model. Together with recent high-precision estimates of the distance and spectro-photometry, this estimate corresponds to a radius of 1420 +/- 120 Rsun and an effective temperature of 3490 +/- 90 K. VY CMa exhibits asymmetric, possibly clumpy, atmospheric layers of H2O and CO, which are not co-spatial, within a larger elongated dusty envelope. Our revised fundamental parameters put VY CMa close to the Hayashi limit of recent evolutionary tracks of initial mass 25 Msun with rotation or 32 Msun without rotation, shortly before evolving blueward in the HR-diagram.Comment: 5 pages, 5 figures, accepted for publication in Astronomy and Astrophysics (A&A) as a Lette

New insights into the dust formation of oxygen-rich AGB stars

We observed the AGB stars S Ori, GX Mon and R Cnc with the MIDI instrument at the VLTI. We compared the data to radiative transfer models of the dust shells, where the central stellar intensity profiles were described by dust-free dynamic model atmospheres. We used Al2O3 and warm silicate grains. Our S Ori and R Cnc data could be well described by an Al2O3 dust shell alone, and our GX Mon data by a mix of an Al2O3 and a silicate shell. The best-fit parameters for S Ori and R Cnc included photospheric angular diameters Theta(Phot) of 9.7+/-1.0mas and 12.3+/-1.0mas, optical depths tau(V)(Al2O3) of 1.5+/-0.5 and 1.35+/-0.2, and inner radii R(in) of 1.9+/-0.3R(Phot) and 2.2+/-0.3R(Phot), respectively. Best-fit parameters for GX Mon were Theta(Phot)=8.7+/-1.3mas, tau(V)(Al2O3)=1.9+/-0.6, R(in)(Al2O3)=2.1+/-0.3R(Phot), tau(V)(silicate)=3.2+/-0.5, and R(in)(silicate)=4.6+/-0.2R(Phot). Our model fits constrain the chemical composition and the inner boundary radii of the dust shells, as well as the photospheric angular diameters. Our interferometric results are consistent with Al2O3 grains condensing close to the stellar surface at about 2 stellar radii, co-located with the extended atmosphere and SiO maser emission, and warm silicate grains at larger distances of about 4--5 stellar radii. We verified that the number densities of aluminum can match that of the best-fit Al2O3 dust shell near the inner dust radius in sufficiently extended atmospheres, confirming that Al2O3 grains can be seed particles for the further dust condensation. Together with literature data of the mass-loss rates, our sample is consistent with a hypothesis that stars with low mass-loss rates form primarily dust that preserves the spectral properties of Al2O3, and stars with higher mass-loss rate form dust with properties of warm silicates.Comment: 20 pages, 10 figure

VLTI/AMBER spectro-interferometry of the late-type supergiants V766 Cen (=HR 5171 A), sigma Oph, BM Sco, and HD 206859

We add four warmer late-type supergiants to our previous spectro-interferometric studies of red giants and supergiants. V766 Cen (=HR 5171 A) is found to be a high-luminosity log(L/L_sun)=5.8+-0.4 source of Teff 4290+-760 K and radius 1490+-540 Rsun located close to both the Hayashi and Eddington limits; this source is consistent with a 40 Msun evolutionary track without rotation and current mass 27-36 Msun. It exhibits NaI in emission arising from a shell of radius 1.5 Rphot and a photocenter displacement of about 0.1 Rphot. V766 Cen shows strong extended molecular (CO) layers and a dusty circumstellar background component. This suggest an optically thick pseudo-photosphere at about 1.5 Rphot at the onset of the wind. V766 Cen is a red supergiant located close to the Hayashi limit instead of a yellow hypergiant already evolving back toward warmer Teff as previously discussed. The stars sigma Oph, BM Sco, and HD 206859 are found to have lower luminosities of about log(L/Lsun)=3.4-3.5 and Teff of 3900-5300 K, corresponding to 5-9 Msun tracks. They do not show extended molecular layers as observed for higher luminosity red supergiants of our sample. BM Sco shows an unusually strong contribution by an over-resolved circumstellar dust component. These stars are more likely high-mass red giants instead of red supergiants. This leaves us with an unsampled locus in the HR diagram corresponding to luminosities log(L/Lsun)~3.8-4.8 or masses 10-13 Msun, possibly corresponding to the mass region where stars explode as type II-P supernovae during the RSG stage. Our previously found relation of increasing strength of extended molecular layers with increasing luminosities is now confirmed to extend to double our previous luminosities and up to the Eddington limit. This might further point to steadily increasing radiative winds with increasing luminosity. [Abridged]Comment: 16 pages, 14 figures, accepted for publication in Astronomy and Astrophysics (A&A