Commutators and Anti-Commutators of Idempotents in Rings

We show that a ring $\,R\,$ has two idempotents $\,e,e'\,$ with an invertible commutator $\,ee'-e'e\,$ if and only if $\,R \cong {\mathbb M}_2(S)\,$ for a ring $\,S\,$ in which $\,1\,$ is a sum of two units. In this case, the "anti-commutator" $\,ee'+e'e\,$ is automatically invertible, so we study also the broader class of rings having such an invertible anti-commutator. Simple artinian rings $\,R\,$ (along with other related classes of matrix rings) with one of the above properties are completely determined. In this study, we also arrive at various new criteria for {\it general\} $\,2\times 2\,$ matrix rings. For instance, $R\,$ is such a matrix ring if and only if it has an invertible commutator $\,er-re\,$ where $\,e^2=e$.Comment: 21 page

Kant, Heidegger und das Verhaeltnis von Repraesentation und Abstraktion

The way in which a schema represents something is precisely by abstracting from some of its features; in a schema, representation and abstraction are thus not opposed to each other but rather internally related. The first part of this paper investigates this internal relation by delineating Kant?s concept of schema as the term mediating concept and intuition. Due to its pivotal position, however, the schema tends to collapse either into the conceptual or into the intuitive. The second part of the paper turns to Heidegger who tries to overcome this difficulty: he does not conceive the schema as a supplementary representation that connects already determinate concepts and intuitions, but rather locates schematization immanently in the very articulation of concept and intuition themselves. The third part of the paper proposes that the schematicity of our representations can be reflected in three pictorial strategies that are important for contemporary art: reduction, serialization, and reconstruction. These strategies are exemplified in certain images which put us in a position to see through our own representational form, as it were, and observe the procedures of figuration involved in that very form

Paradoxes of Autonomy: On the Dialectics of Freedom and Normativity

This paper revisits the concept of autonomy and tries to elucidate the fundamental insight that freedom and law cannot be understood through their opposition, but rather have to be conceived of as conditions of one another. The paper investigates the paradigmatic Kantian formulation of this insight and discusses the diagnosis that the Kantian idea might give rise to a paradox in which autonomy reverts to arbitrariness or heteronomy. The paper argues that the fatal version of the paradox can be defused if we avoid the legalistic model of autonomy and rather turn to the model of participation in a practice. This leads to a dialectical understanding of the idea of autonomy that preserves the insight that freedom and law are mutually conditioning and simultaneously reveals that they remain in irresolvable tension with one anothe

Improved search for galactic white dwarf binaries in Mock LISA Data Challenge 1B using an F-statistic template bank

We report on our F-statistic search for white-dwarf binary signals in the Mock LISA Data Challenge 1B (MLDC1B). We focus in particular on the improvements in our search pipeline since MLDC1, namely refinements in the search pipeline and the use of a more accurate detector response (rigid adiabatic approximation). The search method employs a hierarchical template-grid based exploration of the parameter space, using a coincidence step to distinguish between primary (``true'') and secondary maxima, followed by a final (multi-TDI) ``zoom'' stage to provide an accurate parameter estimation of the final candidates.Comment: 11 pages, 4 included figures, submitted to Classical and Quantum Gravity for GWDAW12 proceeding

Model-based prediction of optogenetic sound encoding in the human cochlea by future optical cochlear implants

When hearing fails, electrical cochlear implants (eCIs) partially restore hearing by direct stimulation of spiral ganglion neurons (SGNs). As light can be better confined in space than electrical current, optical CIs (oCIs) provide more spectral information promising a fundamental improvement of hearing restoration by cochlear implants. Here, we turned to computer modelling for predicting the outcome of optogenetic hearing restoration by future oCIs in humans. We combined three-dimensional reconstruction of the human cochlea with ray-tracing simulation of emission from LED or laser-coupled waveguide emitters of the oCI. Irradiance was read out at the somata of SGNs. The irradiance values reached with waveguides were about 14 times higher than with LEDs, at the same radiant flux of the emitter. Moreover, waveguides outperformed LEDs regarding spectral selectivity. oCIs with either emitter type showed greater spectral selectivity when compared to eCI. In addition, modeling the effects of the source-to-SGN distance, orientation of the sources and impact of scar tissue further informs the development of optogenetic hearing restoration