To an exact category with duality C,I will construct a spectrum K(C) with an action of Z/2 such that the fixed point spectrum is the K-theory of non singular hermitian forms when the category is the category of finitely generated projective modules with standard duality.
The construction uses a Real version of Waldhausen's S.-construction.There are Real versions of Waldhausen's basic theorems e.g.of the additivity theorems. The bigraded homotopy groups associated to the Z/2 spectrum generalizes earlier work of Karoubi and Schlichting.
Tha talk represents joint work with Lars Hesselholt.
In part 1, I will present some recent results with Olivier Gascuel on how accurately we can expect to predict ancestral states at the interior nodes of a phylogenetic tree from discrete character data at the extant leaves.
In part 2, I will describe a second project on species tree reconstruction when genes have evolved under a simple model of random lateral gene transfer (LGT). The aim is to answer questions such as: 'could we reconstruct a species tree on (say) 200 species from a large number of gene trees, if each gene has been laterally transferred into other lineages, on average, ten times?' and 'can LGT lead to inconsistent tree estimation?' Our analysis involves a curious connection to random walks on cyclic graphs.
In 1984 Andreas Dress published a paper entitled "Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups" in response to a question raised in the late 1970's by Manfred Eigen. At that time Manfred Eigen was trying to fit 20 distinct t-RNA sequences of the E.coli bacterium onto a tree. He realized that there was an obstruction to finding such a tree even for four sequences and wondered:
What could be used as a substitute for a tree if no globally fitting tree existed? In this talk, we will explore some consequences of Andreas Dress' response, which has led to a surprising number of new theorems, unsuspected applications, and unforseen relationships with other subjects in mathematics, a few of which we will present.
Next-generation deep-sequencing (NGS) has been revolutionizing eukaryotic and prokaryotic genome analyses. The technology can be used to address a wide variety of questions, such as the evolution of species by comparison of their genomes. When genomes are compared based on genomic positions typically a specific reference genome is assigned which acts as the coordinate system for the comparison. However, rearrangements and insertions or deletions lead to substantial architectural variations between genomes and therefore genomic regions, that cannot be aligned to the reference, are lost.
We have proposed the SuperGenome as a solution, which establishes a general global coordinate system for multiply aligned genomes. This enables the consistent placement of genome annotations in the presence of insertions, deletions, and rearrangements.
In my talk I will first formally introduce the SuperGenome concept and then turn to various applications. One is GenomeRing, a visualisation of a multiple genome alignment based on the SuperGenome. With GenomeRing, we won the most creative algorithm award at Illumina's iDEA challenge 2011. The second one explains how the SuperGenome can be used as a general support for genome annotation pipelines. In particular, I will point out how the Pan-genome, i.e., the full complement of genes in a species, can be nicely derived from the SuperGenome.
Finally I will show how the SuperGenome can also be used for comparative transcriptomic analyses, notably how we have used the SuperGenome for the cross-genome prediction of transcription start sites from RNA-seq data [2]. I will end my talk by pointing out open questions that we hope to be able to solve in future research work.
References:[1] Herbig A., Jäger G., Battke F. and Nieselt K. (2012), "GenomeRing: alignment visualization based on SuperGenome coordinates", Bioinformatics. Vol. 28(12), pp. i7-i15, doi:10.1093/bioinformatics/bts217.[2] Dugar G., Herbig A., Förstner K., Heidrich N., Reinhardt R., Nieselt K. and Sharma C. (2013), "High-resolution transcriptome maps reveal strain-specific regulatory features of multiple Campylobacter jejuni isolates", PLoS Genet 9(5):e1003495.
In phylogenetic data analysis, using different methods or different data sets frequently results in different trees with the same label set. Further, some heuristic optimization algorithms require the construction of a different but not too different tree from a given one, in order to find a (locally) optimal tree. Therefore, we have to quantify the dissimilarity between two phylogenetic trees with identical leaf sets.
One common measure for this is the quartet distance. It is defined to be the number of sets of exactly four taxa for which the trees have different restrictions. Bandelt and Dress showed in 1986 that the maximum distance between two binary trees, when normalized by the number of all 4-sets, is monotone decreasing with n. They conjectured that the limit of this ratio is 2/3 which corresponds to the distance between two random trees.
I will give a generalization of the conjecture to arbitrary X-trees and show some partial results. As a consequence, we find that quartets can be used to quantify the dependence between two real-valued random variables or between two data sets. In some sense, this measure of dependence corresponds to Kendall's tau to measure correlation.
I will speak about my three recent results (two applied, one theoretical) which all rely on the properties of the principal eigenvectors of (different) graph matrices.
Participants
Ingo Althöfer
FSU Jena, Germany
Jakob Lykke Andersen
University of Southern Denmark, Denmark
Miroslav Bačák
Max Planck Institute for Mathematics in the Sciences, Germany
Monika Balvociute
Ernst Moritz Arndt Universität Greifswald, Germany
Hans Jürgen Bandelt
Universität Hamburg, Germany
Sarah Bastkowski
University of East Anglia, United Kingdom
Philipp Benner
Max Planck Institute for Mathematics in the Sciences, Germany
Matthias Bernt
University of Leipzig, Germany
Damian Blasi
MPI MIS / MPI EVA, Germany
Pierre Yves Bourguignon
Isthmus SARL & MPI MiS, Germany
Gunnar Brinkmann
Ghent University, Belgium
Olaf Delgado-Friedrichs
The Australian National University (contractor), Australia
Andreas Deutsch
Technische Universität Dresden, Germany
Nikolay Dolbilin
Steklov Mathematical Institute, Russia
Philip Dowerk
Max Planck Institute for Mathematics in the Sciences, Germany
Heidi Dress
Andreas Dress
Manfred Eigen
Max-Planck-Institut für biophysikalische Chemie, Germany
Mareike Fischer
Ernst-Moritz-Arndt University Greifswald, Germany
Prasanth G. Narasimha-Shenoi
Government College, Chittur Palakkad - 678104, India
Alex Grossmann
Laboratoire Statistique et Génome, CNRS, France
Stefan Grünewald
CAS-MPG Partner Institute for Computational Biology (PICB), China
Jiao Gu
Max Planck Institute for Mathematics in the Sciences, Germany
Joachim Heinze
Springer-Verlag GmbH, Germany
Marc Hellmuth
Saarland University, Germany
Jelle Herold
Defekt BV, Netherlands
Bobo Hua
Max Planck Institute for Mathematics in the Sciences, Germany
Katharina Huber
University of East Anglia, United Kingdom
Mohammed Olanrewaju Ibrahim
University of Ilorin, Nigeria
Herbert Jäckle
Vicepresident, Max Planck Society, Germany
Li Felix Jin
Fudan University, China
Simon Johanning
Universität Leipzig, Germany
Jürgen Jost
Max Planck Institute for Mathematics in the Sciences, Germany
Enno Keßler
Max-Planck-Institut für Mathematik in den Naturwissenschaften, Germany
Matjaz Kovse
Leipzig University, Germany
Andreas Kübel
Max Planck Institute for Mathematics in the Sciences, Germany
Manfred Kuechler
Hunter College (City University of New York -- CUNY), USA
Jörg Lehnert
Max Planck Institute for Mathematics in the Sciences, Germany
Nela Lekic
Maastricht University, Netherlands
Xianqing Li-Jost
Max Planck Institute for Mathematics in the Sciences, Germany
Jian Lu
CAS-MPG Partner Institute for Computational Biiology, China
Ib Madsen
University of Copenhagen, Denmark
Daniel Merkle
University of Souther Denmark, Denmark
Petra Meyer
Goethe University Frankfurt, Germany
Burkhard Morgenstern
University of Göttingen, Germany
Vincent Moulton
University of East Anglia, United Kingdom
Eberhard Neumann
Universität Bielefeld, Germany
Kay Nieselt
Universität Tübingen, Germany
James Oldman
University of East Anglia, United Kingdom
Philipp-Jens Ostermeier
Max Planck Institute for Mathematics in the Sciences, Germany
Lydia Ostermeier
Leipzig University, Germany
Andrei-Alin Popescu
University of East Anglia, United Kingdom
Johannes Rauh
MPI MIS, Germany
Barbara Ringel
Universität Paderborn, Germany
Claus Michael Ringel
Universität Bielefeld, Germany
Michael Roeckner
Bielefeld University, Germany
Thimo Rohlf
University Leipzig & Max Planck Institute for Mathematics in the Sciences, Germany
David Rumschitzki
City College of CUNY, USA
Ingo Schiermeyer
TU Bergakademie Freiberg, Germany
Renate Schunck
Hermann Schunck
Bundesministerium für Bildung und Forschung (ret.), Germany
Christian Siebeneicher
Universität Bielefeld, Germany
Andreas Spillner
University of Greifswald, Germany
Peter Stadler
IZBI - Universität Leipzig, Germany
Mike Steel
University of Canterbury, New Zealand
Dragan Stevanović
University of Niš, Serbia
Ryokichi Tanaka
Tohoku University, Japan
Tat Dat Tran
Max Planck Institute for Mathematics in the Sciences, Germany
Armin Uhlmann
Universität Leipzig, Germany
Leo van Iersel
Centrum Wiskunde & Informatica, Netherlands
Martin Vingron
Max Planck Institute for Molecular Genetics, Germany
