A Geometric Model for Odd Differential K-theory

Odd $K$-theory has the interesting property that it admits an infinite number of inequivalent differential refinements. In this paper we provide a bundle theoretic model for odd differential $K$-theory using the caloron correspondence and prove that this refinement is unique up to a unique natural isomorphism. We characterise the odd Chern character and its transgression form in terms of a connection and Higgs field and discuss some applications. Our model can be seen as the odd counterpart to the Simons-Sullivan construction of even differential $K$-theory. We use this model to prove a conjecture of Tradler-Wilson-Zeinalian regarding a related differential extension of odd $K$-theoryComment: 36 page

The IRAS 1.2 Jy Survey: Redshift Data

We present the redshift data for a survey of galaxies selected from the data base of the Infrared Astronomical Satellite (IRAS). This survey extends the 1.936 Jy sample of Strauss et al. (1992) from a flux limit of 1.936 Jy at 60 microns to 1.2 Jy. The survey extension consists of 3920 sources in the flux interval 1.2 - 1.936 Jy, of which 2663 are galaxies with measured redshifts. Fourteen objects (0.52%) do not have redshifts. The survey covers 87.6% of the sky. The data for the complete 1.2 Jy survey (the data presented here in addition to that of Strauss \etal 1992) may be obtained in a machine-readable form from the National Space Science Data Center and from the anonymous ftp site given above.Comment: uuencoded postscript file. Figures, data tables, and machine readable data files can be obtained via anonymous ftp to (192.16.204.30) ftp://eku.ias.edu/pub/fisher/12jy/12jy.tar.Z (a compressed tar file)

On long-term boundedness of Galerkin models

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.We investigate linear–quadratic dynamical systems with energy-preserving quadratic terms. These systems arise for instance as Galerkin systems of incompressible flows. A criterion is presented to ensure long-term boundedness of the system dynamics. If the criterion is violated, a globally stable attractor cannot exist for an effective nonlinearity. Thus, the criterion can be considered a minimum requirement for control-oriented Galerkin models of viscous fluid flows. The criterion is exemplified, for example, for Galerkin systems of two-dimensional cylinder wake flow models in the transient and the post-transient regime, for the Lorenz system and for wall-bounded shear flows. There are numerous potential applications of the criterion, for instance, system reduction and control of strongly nonlinear dynamical systems

Detection of amplified DNA sequences by reverse chromosome painting using genomic tumor DNA as probe

A modification of reverse chromosome painting was carried out using genomic DNA from tumor cells as a complex probe for chromosomal in situ suppression hybridization to normal metaphase chromsome spreads. Amplified DNA sequences contained in such probes showed specific signals, revealing the normal chromosome positions from which these sequences were derived. As a model system, genomic DNAs were analyzed from three tumor cell lines with amplification units including the proto-oncogene c-myc. The smallest amplification unit was about 90 kb and was present in 16–24 copies; the largest unit was bigger than 600 kb and was present in 16–32 copies. Specific signals that co-localized with a differently labeled c-myc probe on chromosome band 8q24 were obtained with genomic DNA from each cell line. In further experiments, genomic DNA derived from primary tumor material was used in the case of a male patient with glioblastoma multiforme (GBM). Southern blot analysis using an epidermal growth factor receptor gene (EGFR) probe that maps to 7p13 indicated the amplification of sequences from this gene. Using reverse chromosome painting, signals were found both on band 7p13 and bands 12q13–q15. Notably, the signal on 12q13–q15 was consistently stronger. The weaker 7p13 signal showed co-localization with the major signal of the differently labeled EGFR probe. A minor signal of this probe was seen on 12q13, suggesting cross-hybridization to ERB3 sequences homologous to EGFR. The results indicate co-amplification of sequences from bands 12q13–q15, in addition to sequences from band 7p13. Several oncogenes map to 12q13–q15 providing candidate genes for a tumor-associated proto-oncogene amplification. Although the nature of the amplified sequences needs to be clarified, this experiment demonstrates the potential of reverse chromosome painting with genomic tumor DNA for rapidly mapping the normal chromosomal localization of the DNA from which the amplified sequences were derived. In addition, a weaker staining of chromosomes 10 and X was consistently observed indicating that these chromosomes were present in only one copy in the GBM genome. This rapid approach can be used to analyze cases where no metaphase spreads from the tumor material are available. It does not require any preknowledge of amplified sequences and can be applied to screen large numbers of tumors

Are Recent Peculiar Velocity Surveys Consistent?

We compare the bulk flow of the SMAC sample to the predictions of popular cosmological models and to other recent large-scale peculiar velocity surveys. Both analyses account for aliasing of small-scale power due to the sparse and non-uniform sampling of the surveys. We conclude that the SMAC bulk flow is in marginal conflict with flat COBE-normalized Lambda-CDM models which fit the cluster abundance constraint. However, power spectra which are steeper shortward of the peak are consistent with all of the above constraints. When recent large-scale peculiar velocity surveys are compared, we conclude that all measured bulk flows (with the possible exception of that of Lauer & Postman) are consistent with each other given the errors, provided the latter allow for `cosmic covariance'. A rough estimate of the mean bulk flow of all surveys (except Lauer & Postman) is ~400 km/s towards l=270, b=0.Comment: 8 pages, 3 figures. To appear in Proceedings of the Cosmic Flows Workshop, Victoria, B. C., Canada, July 1999, eds. S. Courteau, M. Strauss, and J. Willic