Parity of ranks for elliptic curves with a cyclic isogeny

Let E be an elliptic curve over a number field K which admits a cyclic p-isogeny with p odd and semistable at primes above p. We determine the root number and the parity of the p-Selmer rank for E/K, in particular confirming the parity conjecture for such curves. We prove the analogous results for p=2 under the additional assumption that E is not supersingular at primes above 2.Comment: Minor corrections; 17 pages, to appear in J. Number Theor

Multi-criteria analysis of multi-material lightweight components on a conceptual level of detail

Multi-material design offers higher degrees of freedom in designing a component due to different design options and material combinations. However, both cause a more complex component design. In addition many development goals - such as weight, costs and environmental impact - and outer conditions - such as restricted installation spaces - have already to be considered in the early stage of development. Otherwise the most suitable design option might not be considered and concepts are no longer pursued after design in detail since they did not fit the requirements from the beginning. As a result, the designer needs assistance in analysing different design options to find those that are able to fulfil the development goals best possible within an appropriate effort. A suitable approach to solve this issue is to represent the considered component by an abstract definition and calculate the component's properties analytically inside an automated tool. Thus the general behaviour of a design option and specific variations can be evaluated by the designer. Consequently components can be designed more purposeful considering a big solution space and a variety of development goals

Increasing the sensitivity of reverse phase protein arrays by antibody-mediated signal amplification

<p>Abstract</p> <p>Background</p> <p>Reverse phase protein arrays (RPPA) emerged as a useful experimental platform to analyze biological samples in a high-throughput format. Different signal detection methods have been described to generate a quantitative readout on RPPA including the use of fluorescently labeled antibodies. Increasing the sensitivity of RPPA approaches is important since many signaling proteins or posttranslational modifications are present at a low level.</p> <p>Results</p> <p>A new antibody-mediated signal amplification (AMSA) strategy relying on sequential incubation steps with fluorescently-labeled secondary antibodies reactive against each other is introduced here. The signal quantification is performed in the near-infrared range. The RPPA-based analysis of 14 endogenous proteins in seven different cell lines demonstrated a strong correlation (r = 0.89) between AMSA and standard NIR detection. Probing serial dilutions of human cancer cell lines with different primary antibodies demonstrated that the new amplification approach improved the limit of detection especially for low abundant target proteins.</p> <p>Conclusions</p> <p>Antibody-mediated signal amplification is a convenient and cost-effective approach for the robust and specific quantification of low abundant proteins on RPPAs. Contrasting other amplification approaches it allows target protein detection over a large linear range.</p

Galois theory and commutators

We prove that the relative commutator with respect to a subvariety of a variety of Omega-groups introduced by the first author can be described in terms of categorical Galois theory. This extends the known correspondence between the Froehlich-Lue and the Janelidze-Kelly notions of central extension. As an example outside the context of Omega-groups we study the reflection of the category of loops to the category of groups where we obtain an interpretation of the associator as a relative commutator.Comment: 14 page

GOSim – an R-package for computation of information theoretic GO similarities between terms and gene products

<p>Abstract</p> <p>Background</p> <p>With the increased availability of high throughput data, such as DNA microarray data, researchers are capable of producing large amounts of biological data. During the analysis of such data often there is the need to further explore the similarity of genes not only with respect to their expression, but also with respect to their functional annotation which can be obtained from Gene Ontology (GO).</p> <p>Results</p> <p>We present the freely available software package <it>GOSim</it>, which allows to calculate the functional similarity of genes based on various information theoretic similarity concepts for GO terms. <it>GOSim </it>extends existing tools by providing additional lately developed functional similarity measures for genes. These can e.g. be used to cluster genes according to their biological function. Vice versa, they can also be used to evaluate the homogeneity of a given grouping of genes with respect to their GO annotation. <it>GOSim </it>hence provides the researcher with a flexible and powerful tool to combine knowledge stored in GO with experimental data. It can be seen as complementary to other tools that, for instance, search for significantly overrepresented GO terms within a given group of genes.</p> <p>Conclusion</p> <p><it>GOSim </it>is implemented as a package for the statistical computing environment <it>R </it>and is distributed under GPL within the CRAN project.</p

Inferring signalling networks from longitudinal data using sampling based approaches in the R-package 'ddepn'

<p>Abstract</p> <p>Background</p> <p>Network inference from high-throughput data has become an important means of current analysis of biological systems. For instance, in cancer research, the functional relationships of cancer related proteins, summarised into signalling networks are of central interest for the identification of pathways that influence tumour development. Cancer cell lines can be used as model systems to study the cellular response to drug treatments in a time-resolved way. Based on these kind of data, modelling approaches for the signalling relationships are needed, that allow to generate hypotheses on potential interference points in the networks.</p> <p>Results</p> <p>We present the R-package 'ddepn' that implements our recent approach on network reconstruction from longitudinal data generated after external perturbation of network components. We extend our approach by two novel methods: a Markov Chain Monte Carlo method for sampling network structures with two edge types (activation and inhibition) and an extension of a prior model that penalises deviances from a given reference network while incorporating these two types of edges. Further, as alternative prior we include a model that learns signalling networks with the scale-free property.</p> <p>Conclusions</p> <p>The package 'ddepn' is freely available on R-Forge and CRAN <url>http://ddepn.r-forge.r-project.org</url>, <url>http://cran.r-project.org</url>. It allows to conveniently perform network inference from longitudinal high-throughput data using two different sampling based network structure search algorithms.</p

Regulator constants and the parity conjecture

The p-parity conjecture for twists of elliptic curves relates multiplicities of Artin representations in p-infinity Selmer groups to root numbers. In this paper we prove this conjecture for a class of such twists. For example, if E/Q is semistable at 2 and 3, K/Q is abelian and K^\infty is its maximal pro-p extension, then the p-parity conjecture holds for twists of E by all orthogonal Artin representations of Gal(K^\infty/Q). We also give analogous results when K/Q is non-abelian, the base field is not Q and E is replaced by an abelian variety. The heart of the paper is a study of relations between permutation representations of finite groups, their "regulator constants", and compatibility between local root numbers and local Tamagawa numbers of abelian varieties in such relations.Comment: 50 pages; minor corrections; final version, to appear in Invent. Mat

Predicting pathway membership via domain signatures

Motivation: Functional characterization of genes is of great importance for the understanding of complex cellular processes. Valuable information for this purpose can be obtained from pathway databases, like KEGG. However, only a small fraction of genes is annotated with pathway information up to now. In contrast, information on contained protein domains can be obtained for a significantly higher number of genes, e.g. from the InterPro database

Deterministic Effects Propagation Networks for reconstructing protein signaling networks from multiple interventions

<p>Abstract</p> <p>Background</p> <p>Modern gene perturbation techniques, like RNA interference (RNAi), enable us to study effects of targeted interventions in cells efficiently. In combination with mRNA or protein expression data this allows to gain insights into the behavior of complex biological systems.</p> <p>Results</p> <p>In this paper, we propose Deterministic Effects Propagation Networks (DEPNs) as a special Bayesian Network approach to reverse engineer signaling networks from a combination of protein expression and perturbation data. DEPNs allow to reconstruct protein networks based on combinatorial intervention effects, which are monitored via changes of the protein expression or activation over one or a few time points. Our implementation of DEPNs allows for latent network nodes (i.e. proteins without measurements) and has a built in mechanism to impute missing data. The robustness of our approach was tested on simulated data. We applied DEPNs to reconstruct the <it>ERBB </it>signaling network in <it>de novo </it>trastuzumab resistant human breast cancer cells, where protein expression was monitored on Reverse Phase Protein Arrays (RPPAs) after knockdown of network proteins using RNAi.</p> <p>Conclusion</p> <p>DEPNs offer a robust, efficient and simple approach to infer protein signaling networks from multiple interventions. The method as well as the data have been made part of the latest version of the R package "nem" available as a supplement to this paper and via the Bioconductor repository.</p