Abstract:
A by-product of new social media platforms is an abundant textual record of engagements – billions of words across the world-wide-web in, for example, discussion forums, blogs and wiki discussion tabs. Many of these engagements consist of commentary on a particular text and can thus be regarded as supplements to these texts. The larger purpose of this article is to flag the utility value of this electronic supplementarity for critical reading by highlighting how it can reveal particular meanings that the text being responded to can reasonably be said to marginalise and / or repress. Given the potentially very large size of social media textual product, knowing how to explore these supplements with electronic text analysis software is essential. To illustrate the above, I focus on how the content of online discussion forums, explored through electronic text analysis software, can be used to assist critical reading of the texts which initiate them. The paper takes its theoretical orientations from the textual intervention work of Rob Pope together with themes in the work of the philosopher, Jacques Derrida.

Abstract:
With the service economy on the ascension, companies are yearning for mechanisms to connect their service solutions to their customer's problems, and have the customer acknowledge that their solution is the best. In order to meet these requirements, the foundations of the model used to deploy such solutions need to be concrete. The solution must capture the fundamental nature of the target markets and embody all of the customers' expectations. This article reviews literature that will inform the development of these models and identifies relevant strategies to enable growth options around service-based solutions.

Abstract:
The large collecting area of 4+ metre class telescopes allows atronomers to observe bright objects on faster timescales than previously possible. In order to exploit this capability, we designed a novel read-out mode for use on the 10-m Keck-II telescope on Mauna Kea, Hawaii. This took the form of a continuous read-out mode, enabling us to obtain a target spectrum between 3500 and 8500 \AA, with a dispersion of ~2.5 \AA/pix, every *70 milliseconds*. I present results from 5 nights of observations of Interacting Binaries, using this novel data acquisition system in July 1998. During the run we obtained more than 1.2 million optical spectra, many of which were simultaneous with pointed RXTE observations. This fast spectroscopic capability has allowed us to explore regimes previously only accessible with broadband instruments. I will concentrate on results from the coordinated Keck/RXTE observations, which have revealed interesting correlated variability on timescales from seconds to days. I will also show the results of a spectroscopic-timing analysis of QPOs in Hercules X-1, which shows evidence for the decay of individual blobs of material orbiting the neutron star.

Abstract:
A locally complete family of projective symplectic 4-folds is provided by natural double covers of Eisenbud-Popescu-Walter (EPW) sextic hypersurfaces in projective 5-space. The dual of an EPW sextic is another EPW sextic, thus to a double EPW sextic X we may associate a "dual" double EPW sextic X^{\vee}. We show how to obtain the Hodge structure on H^2(X^{\vee}) from that on H^2(X); it turns out that they are isomorphic over the rationals but not over the integers (in general).

Abstract:
An EPW-sextic is a special 4-dimensional hypersurfaces of degree 6 which comes equipped with a double cover which generically is a Hyperkaehler 4-fold deformation equivalent to the Hilbert square of a K3 surface. The family of EPW-sextics is analogous to the family of cubic 4-fold hypersurfaces, more precisely double EPW-sextics are analogous to varieties of lines on cubic 4-folds. This first paper in a series on moduli and periods of double EPW-sextics is mainly concerned with the classification of EPW-sextics which are analogous to cubic 4-folds whose singular locus has strictly positive dimension.

Abstract:
EPW-sextics are special 4-dimensional sextic hypersurfaces (with 20 moduli) which come equipped with a double cover. We analyze the double cover of EPW-sextics parametrized by a certain prime divisor in the moduli space. We associate to the generic sextic parametrized by that divisor a K3 surface of genus 6 and we show that the double epw sextic is a contraction of the Hilbert square of the K3. This result has two consequences. First it gives a new proof of the following result of ours: smooth double EPW-sextics form a locally complete family of hyperkaehler projective deformations of the Hilbert square of a K3. Secondly it shows that away from another prime divisor in the moduli space the period map for double EPW-sextics is as well-behaved as it possibly could be.

Abstract:
Beauville and Voisin proved that the third modified diagonal of a complex K3 surface X represents a torsion class in the Chow group of X^3. Motivated by this result and by conjectures of Beauville and Voisin on the Chow ring of hyperkaehler varieties we prove some results on modified diagonals of projective varieties and we formulate a conjecture.

Abstract:
We prove that moduli spaces of torsion-free sheaves on a projective smooth complex surface are irreducible, reduced and of the expected dimension, provided the expected dimension is large enough. Actually we prove more: given a line bundle on the surface, we show that the number of moduli of sheaves which have a non-zero twisted (by the chosen line-bundle) endomorphism grows slower than the expected dimension of the moduli space (for fixed rank and increasing discriminant). The bounds we get are effective: we concentrate on the case of rank two and we give a lower bound on the discriminant guaranteeing that the moduli space is reduced of the expected dimension. We also give an effective irreducibility result for complete intersections. All of the above follows from a theorem bounding the dimension of complete subsets of the moduli space which do not intersect the boundary.

Abstract:
Let X be a projective complex K3 surface. Beauville and Voisin singled out a 0-cycle c_X on X of degree 1: it is represented by any point lying on a rational curve in X. Huybrechts proved that the second Chern class of a rigid simple vector-bundle on X is a multiple of the Beauville-Voisin class c_X if certain hypotheses hold and he conjectured that the additional hypotheses are unnecessary. We believe that the following generalization of Huybrechts' conjecture holds. Let M and N be moduli spaces of stable pure sheaves on X (with fixed cohomological Chern characters) and suppose that they have the same dimension: then the set whose elements are second Chern classes of sheaves parametrized by the closure of M (in the corresponding moduli spaces of semistable sheaves) is equal to the set whose elements are second Chern classes of sheaves parametrized by the closure of N after a translation by a suitable multiple of c_X (so that degrees match). We will prove that the above statement holds under some additional assumptions.